Finite Group Databasebeta

← C2×#23777229 #35196187

Subgroups — C2×#23777229 #35196187

Order 20224.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777229C2132yesmaximal, direct product factor
2C2×#19099265C212yesmaximal, complemented
3C2×#19099261C211yesmaximal, characteristic, complemented
4C2×#19099259C212yesmaximal, complemented
5C2×#19099252C211yesmaximal, characteristic, complemented
6C2×#19099251C211yesmaximal, characteristic, complemented
7C2×#19099238C212yesmaximal, complemented
8C2×#19099236C212yesmaximal, complemented
9C2×#19099222C211yesmaximal, characteristic, complemented
10C2×#19099219C211yesmaximal, characteristic, complemented
11C2×#19099210C211yesmaximal, characteristic, complemented
12C2×#19099208C211yesmaximal, characteristic, complemented
13C2×#19099154C212yesmaximal, complemented
14C2×#19099149C212yesmaximal, complemented
15C2×#19099121C212yesmaximal, complemented
16C2×#19099098C211yesmaximal, characteristic, complemented
17C2×#19099095C211yesmaximal, characteristic, complemented
18C2×#19099075C211yesmaximal, characteristic, complemented
19C2×#19099073C211yesmaximal, characteristic, complemented
20C22×#14579141C211yesmaximal, characteristic, complemented
21C2×#121×D79C211yesmaximal, characteristic, complemented
22C2×#19099035C212yesmaximal, complemented
23C2×C4×D4×D79C211yesmaximal, characteristic, complemented
24C2×#553×C79C211yesmaximal, characteristic, complemented
25C22×#11929624C2211yescharacteristic, complemented
26C22×#11929623C2211yescharacteristic, complemented
27C23×Dic158C2211yescharacteristic, complemented
28C22×D4×D79C2211yescharacteristic
29C22×D4×D79C2212yes—
30C22×D4×D79C2211yescharacteristic, complemented
31C23×C4×D79C2211yescharacteristic
32C23×C4×D79C2211yescharacteristic, complemented
33#19099265C22132yescomplemented
34#19099261C22116yescomplemented
35#19099259C22132yescomplemented
36#19099252C22116yescomplemented
37#19099251C22116yescomplemented
38#19099238C22132yescomplemented
39#19099236C22132yescomplemented
40#19099222C22116yescomplemented
41#19099219C22116yescomplemented
42#19099210C22116yescomplemented
43#19099208C22116yescomplemented
44#19099154C22132yescomplemented
45#19099149C22132yescomplemented
46#19099121C22132yescomplemented
47#19099098C22116yescomplemented
48#19099095C22116yescomplemented
49C2×#14579156C2212yescomplemented
50C2×#14579156C2212yescomplemented
51C2×#14579156C2212yescomplemented
52C2×#14579154C2212yescomplemented
53C2×#14579154C2212yescomplemented
54C2×#14579153C2212yescomplemented
55C2×#14579152C2212yescomplemented
56C2×#14579152C2211yescharacteristic, complemented
57C2×#14579149C2211yescharacteristic, complemented
58C2×#14579148C2211yescharacteristic, complemented
59C2×#14579147C2212yescomplemented
60C2×#14579147C2212yescomplemented
61#19099075C22116yescomplemented
62#19099073C22116yescomplemented
63C2×#14579146C2212yes—
64C2×#14579146C2212yescomplemented
65C2×#14579146C2212yescomplemented
66C2×#14579145C2212yescomplemented
67C2×#14579145C2212yescomplemented
68C2×#14579143C2212yes—
69C2×#14579143C2212yescomplemented
70C2×#14579143C2212yescomplemented
71C2×#14579143C2212yescomplemented
72C2×#14579141C2211yescharacteristic, complemented
73C2×#14579141C2211yescharacteristic, complemented
74C2×#14579141C2211yescharacteristic, complemented
75C2×#14579141C2212yescomplemented
76C2×#14579141C2211yescharacteristic, complemented
77C2×#14579141C2211yescharacteristic, complemented
78C2×#14579141C2212yescomplemented
79C2×#14579141C22116yescomplemented
80C2×#14579140C2211yescharacteristic, complemented
81C2×#14579139C2212yescomplemented
82C2×#14579138C2212yescomplemented
83C2×#14579136C2211yescharacteristic
84C2×#14579136C2211yescharacteristic, complemented
85C2×#14579135C2212yescomplemented
86C2×#14579135C2211yescharacteristic, complemented
87C2×#14579135C2212yescomplemented
88C2×#14579134C2212yes—
89C2×#14579133C2212yescomplemented
90C2×#14579133C2212yescomplemented
91C2×#14579133C2212yescomplemented
92C2×#14579132C2211yescharacteristic
93C2×#14579132C2212yescomplemented
94#121×D79C22116yescomplemented
95C2×#14579131C2212yes—
96C2×#14579131C2212yescomplemented
97C2×#14579129C2212yes—
98C2×#14579129C2212yescomplemented
99#19099035C22132yescomplemented
100C2×C4×Dic158C2211yescharacteristic, complemented
101C2×#14579126C2211yescharacteristic, complemented
102C2×C4×D316C2211yescharacteristic
103C2×C4×D316C2212yescomplemented
104C2×C4×D316C2212yescomplemented
105C2×D4×Dic79C2211yescharacteristic, complemented
106C2×D4×Dic79C2212yescomplemented
107C2×D4×Dic79C2212yescomplemented
108C2×#14579123C2211yescharacteristic
109C2×#14579123C2212yescomplemented
110C2×#14579123C2211yescharacteristic, complemented
111C2×C4×C22⋊D79C2211yescharacteristic
112C2×C4×C22⋊D79C2211yescharacteristic, complemented
113C2×C4×C22⋊D79C2212yescomplemented
114C2×C4×C22⋊D79C2212yescomplemented
115C2×(C22⋊D79)⋊C4C2211yescharacteristic
116C2×(C22⋊D79)⋊C4C2211yescharacteristic, complemented
117C2×(C22⋊D79)⋊C4C2212yescomplemented
118C2×(C22⋊D79)⋊C4C2212yescomplemented
119C4×D4×D79C22116yescomplemented
120C2×#14579120C2212yescomplemented
121C2×#14579119C2212yescomplemented
122C2×#14579119C2212yescomplemented
123C2×#14579119C2211yescharacteristic, complemented
124C2×#14579118C2212yescomplemented
125C22×C4⋊Dic79C2212yescomplemented
126C2×C4⋊C4×D79C2211yescharacteristic, complemented
127C2×C4⋊C4×D79C2211yescharacteristic, complemented
128C22×(C2×D79)⋊C4C2212yes—
129C22×(C2×D79)⋊C4C2212yescomplemented
130C2×C22⋊C4×D79C2211yescharacteristic
131C2×C22⋊C4×D79C2211yescharacteristic, complemented
132C2×C22⋊C4×D79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135#553×C79C22116yescomplemented
136C2×#126×C79C2212yescomplemented
137C2×#125×C79C2211yescharacteristic, complemented
138C2×#123×C79C2212yescomplemented
139C2×#121×C79C2211yescharacteristic, complemented
140C2×#121×C79C2211yescharacteristic, complemented
141C2×#121×C79C2212yescomplemented
142C2×C4×D4×C79C2211yescharacteristic, complemented
143C2×C4×D4×C79C2212yescomplemented
144C2×C4×D4×C79C2211yescharacteristic, complemented
145C2×#117×C79C2211yescharacteristic, complemented
146C22×C4⋊C4×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C24×D79C2311yescharacteristic
149C24×D79C2311yescharacteristic
150C2×#11929624—44no—
151C2×#11929624C2318yescomplemented
152C2×#11929623—44no—
153C2×#11929623C2318yescomplemented
154C22×Dic158—44no—
155C22×Dic158C2311yescharacteristic
156C22×Dic158C2311yescharacteristic
157C22×Dic158C2312yes—
158C22×Dic158C2318yescomplemented
159C22×D316C2311yescharacteristic
160C22×D316C2312yes—
161C22×D316C2311yescharacteristic
162C22×D316C2312yes—
163C22×C22⋊D79C2311yescharacteristic
164C22×C22⋊D79C2312yes—
165C22×C22⋊D79C2311yescharacteristic
166C22×C22⋊D79C2312yes—
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C2×D4×D79—28no—
171C2×D4×D79—216no—
172C2×D4×D79—44no—
173C2×D4×D79C2318yes—
174C2×D4×D79C23116yes—
175C2×D4×D79C2318yescomplemented
176C23×Dic79C2312yes—
177C23×Dic79C2312yes—
178C23×Dic79C2311yescharacteristic
179C23×Dic79C2311yescharacteristic
180C22×C4×D79—44no—
181C22×C4×D79—44no—
182C22×C4×D79C2311yescharacteristic
183C22×C4×D79C2311yescharacteristic
184C22×C4×D79C2312yes—
185C22×C4×D79C2311yescharacteristic
186C22×C4×D79C2311yescharacteristic
187C22×C4×D79C2311yescharacteristic
188C22×C4×D79C2311yescharacteristic
189C22×C4×D79C2311yescharacteristic
190C22×C4×D79C2311yescharacteristic
191C22×C4×D79C2312yes—
192C22×C4×D79C2312yes—
193C22×C4×D79C2318yes—
194C22×C4×D79C2311yescharacteristic
195C22×C4×D79C2318yescomplemented
196#14579156C23116yescomplemented
197#14579156C23116yescomplemented
198#14579156C23116yescomplemented
199#14579154C23116yescomplemented
200#14579154C23116yescomplemented
201#14579153C23116yescomplemented
202#14579152C23116yescomplemented
203#14579152C2318yescomplemented
204#14579149C2318yescomplemented
205#14579148C2318yescomplemented
206#14579147C23116yescomplemented
207#14579147C23116yescomplemented
208#14579146C23116yes—
209#14579146C23116yescomplemented
210#14579146C23116yescomplemented
211#14579145C23116yescomplemented
212#14579145C23116yescomplemented
213#14579143C23116yes—
214#14579143C23116yescomplemented
215#14579143C23116yescomplemented
216#14579143C23116yescomplemented
217#14579141C23116yescomplemented
218#14579141C2318yescomplemented
219#14579141C2318yescomplemented
220#14579141C2318yescomplemented
221#14579141C23116yescomplemented
222#14579141C2318yescomplemented
223#14579141C2318yescomplemented
224#14579140C2318yescomplemented
225#14579139C23116yescomplemented
226#14579138C23116yescomplemented
227#14579136C2318yes—
228#14579136C2318yescomplemented
229#14579135C23116yescomplemented
230#14579135C2318yescomplemented
231#14579135C23116yescomplemented
232#14579134C23116yes—
233#14579133C23116yescomplemented
234#14579133C23116yescomplemented
235#14579133C23116yescomplemented
236#14579132C2318yes—
237#14579132C23116yescomplemented
238#14579131C23116yes—
239#14579131C23116yescomplemented
240#14579129C23116yes—
241#14579129C23116yescomplemented
242C4×Dic158C2318yescomplemented
243#14579126C2318yescomplemented
244C4×D316C2318yes—
245C4×D316C23116yescomplemented
246C4×D316C23116yescomplemented
247D4×Dic79C23116yescomplemented
248D4×Dic79C23116yescomplemented
249D4×Dic79C2318yescomplemented
250#14579123C2318yes—
251#14579123C23116yescomplemented
252#14579123C2318yescomplemented
253C4×C22⋊D79C2318yes—
254C4×C22⋊D79C23116yescomplemented
255C4×C22⋊D79C2318yescomplemented
256C4×C22⋊D79C23116yescomplemented
257(C22⋊D79)⋊C4C2318yes—
258(C22⋊D79)⋊C4C23116yescomplemented
259(C22⋊D79)⋊C4C23116yescomplemented
260(C22⋊D79)⋊C4C2318yescomplemented
261#14579120C23116yescomplemented
262#14579119C23116yescomplemented
263#14579119C23116yescomplemented
264#14579119C2318yescomplemented
265#14579118C23116yescomplemented
266C2×C4⋊Dic79C2311yescharacteristic
267C2×C4⋊Dic79C2311yescharacteristic
268C2×C4⋊Dic79C2312yes—
269C2×C4⋊Dic79C2312yes—
270C2×C4⋊Dic79C2312yes—
271C2×C4⋊Dic79C2312yes—
272C2×C4⋊Dic79C2312yes—
273C2×C4⋊Dic79C2312yes—
274C2×C4⋊Dic79C23116yescomplemented
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C2311yescharacteristic
277C2×Dic79⋊C4C2312yes—
278C2×Dic79⋊C4C2312yes—
279C2×Dic79⋊C4C2312yes—
280C2×Dic79⋊C4C2312yes—
281C2×Dic79⋊C4C2312yes—
282C4⋊C4×D79C2318yescomplemented
283C4⋊C4×D79C2318yescomplemented
284C2×C22⋊Dic79C2311yescharacteristic
285C2×C22⋊Dic79C2312yes—
286C2×C22⋊Dic79C2311yescharacteristic
287C2×C22⋊Dic79C2312yes—
288C2×C22⋊Dic79C2312yes—
289C2×C22⋊Dic79C2312yes—
290C2×(C2×D79)⋊C4C2311yescharacteristic
291C2×(C2×D79)⋊C4C2311yescharacteristic
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2311yescharacteristic
295C2×(C2×D79)⋊C4C2311yescharacteristic
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2312yes—
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C23116yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2312yes—
306C2×(C2×D79)⋊C4C2312yes—
307C2×(C2×D79)⋊C4C23116yescomplemented
308C22⋊C4×D79C2318yes—
309C22⋊C4×D79C2318yescomplemented
310C22⋊C4×D79C23116yescomplemented
311C22⋊C4×D79C23116yescomplemented
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C2×C4×Dic79C2311yescharacteristic
315C2×C4×Dic79C2312yes—
316C2×C4×Dic79C2312yes—
317C2×C4×Dic79C2312yes—
318C42×D79C2318yescomplemented
319C22×D4×C79C2311yescharacteristic
320C22×D4×C79C2312yes—
321C22×D4×C79C2311yescharacteristic
322C22×D4×C79C2312yes—
323C23×C4×C79C2311yescharacteristic
324C23×C4×C79C2311yescharacteristic
325C23×C4×C79C2312yes—
326C23×C4×C79C2312yes—
327#126×C79C23116yescomplemented
328#125×C79C2318yescomplemented
329#123×C79C23116yescomplemented
330#121×C79C2318yescomplemented
331#121×C79C2318yescomplemented
332#121×C79C23116yescomplemented
333C4×D4×C79C2318yescomplemented
334C4×D4×C79C2318yescomplemented
335C4×D4×C79C23116yescomplemented
336#117×C79C2318yescomplemented
337C2×C4⋊C4×C79C2311yescharacteristic
338C2×C4⋊C4×C79C2311yescharacteristic
339C2×C4⋊C4×C79C2312yes—
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C4⋊C4×C79C2312yes—
342C2×C4⋊C4×C79C2311yescharacteristic
343C2×C4⋊C4×C79C2312yes—
344C2×C4⋊C4×C79C2318yescomplemented
345C2×C22⋊C4×C79C2312yes—
346C2×C22⋊C4×C79C2311yescharacteristic
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2311yescharacteristic
350C2×C22⋊C4×C79C2312yes—
351C2×C42×C79C2312yes—
352C2×C42×C79C2311yescharacteristic
353C23×D79—24no—
354C23×D79—28no—
355C23×D79—42no—
356C23×D79—42no—
357C23×D79—42no—
358C23×D79—42no—
359C23×D79—44no—
360C23×D79—44no—
361C23×D79#4118yescomplemented
362C23×D79C2411yescharacteristic
363C23×D79C2412yes—
364C23×D79C2411yescharacteristic
365C23×D79C2411yescharacteristic
366C23×D79C2418yes—
367C23×D79C2414yes—
368C23×D79C2414yes—
369#11929624—416no—
370#11929623—416no—
371C2×Dic158—24no—
372C2×Dic158—24no—
373C2×Dic158—416no—
374C2×Dic158—44no—
375C2×Dic158C2414yes—
376C2×Dic158C2414yes—
377C2×Dic158C2418yes—
378C2×D316—24no—
379C2×D316—28no—
380C2×D316—24no—
381C2×D316—44no—
382C2×D316C2414yes—
383C2×D316C2414yes—
384C2×D316C2418yes—
385C2×D316C2418yes—
386C2×C22⋊D79—24no—
387C2×C22⋊D79—28no—
388C2×C22⋊D79—24no—
389C2×C22⋊D79—28no—
390C2×C22⋊D79—44no—
391C2×C22⋊D79—44no—
392C2×C22⋊D79—44no—
393C2×C22⋊D79C2414yes—
394C2×C22⋊D79C2418yes—
395C2×C22⋊D79C2418yes—
396C2×C22⋊D79C2414yes—
397C2×C22⋊D79C2418yes—
398C2×C22⋊D79C2418yes—
399C2×C22⋊D79C2418yes—
400D4×D79—232no—
401D4×D79—264no—
402D4×D79—416no—
403C22×Dic79—44no—
404C22×Dic79—44no—
405C22×Dic79—42no—
406C22×Dic79—42no—
407C22×Dic79C2412yes—
408C22×Dic79C2412yes—
409C22×Dic79C2411yescharacteristic
410C22×Dic79C2411yescharacteristic
411C22×Dic79C2411yescharacteristic
412C22×Dic79C2412yes—
413C22×Dic79C2411yescharacteristic
414C22×Dic79C2411yescharacteristic
415C22×Dic79C2418yes—
416C22×Dic79C2418yes—
417C22×Dic79C2414yes—
418C22×Dic79C2414yes—
419C2×C4×D79—28no—
420C2×C4×D79—24no—
421C2×C4×D79—24no—
422C2×C4×D79—24no—
423C2×C4×D79—24no—
424C2×C4×D79—44no—
425C2×C4×D79—42no—
426C2×C4×D79—42no—
427C2×C4×D79—42no—
428C2×C4×D79—42no—
429C2×C4×D79—42no—
430C2×C4×D79—44no—
431C2×C4×D79—416no—
432C2×C4×D79—416no—
433C2×C4×D79C2414yes—
434C2×C4×D79C2414yes—
435C2×C4×D79C2414yes—
436C2×C4×D79C2418yes—
437C2×C4×D79C2414yes—
438C2×C4×D79C2418yes—
439C2×C4×D79C2414yes—
440C2×C4×D79C2414yes—
441C2×C4×D79C2414yes—
442C2×C4×D79C2414yes—
443C2×C4×D79C2418yes—
444C2×C4×D79C2414yes—
445C4⋊Dic79C2414yes—
446C4⋊Dic79C2414yes—
447C4⋊Dic79C2418yes—
448C4⋊Dic79C2418yes—
449C4⋊Dic79C2418yes—
450C4⋊Dic79C2418yes—
451C4⋊Dic79C2418yes—
452C4⋊Dic79C2418yes—
453Dic79⋊C4C2414yes—
454Dic79⋊C4C2414yes—
455Dic79⋊C4C2418yes—
456Dic79⋊C4C2418yes—
457Dic79⋊C4C2418yes—
458Dic79⋊C4C2418yes—
459Dic79⋊C4C2418yes—
460C22⋊Dic79C2414yes—
461C22⋊Dic79C2418yes—
462C22⋊Dic79C2414yes—
463C22⋊Dic79C2418yes—
464C22⋊Dic79C2418yes—
465C22⋊Dic79C2418yes—
466(C2×D79)⋊C4C2414yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2414yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2418yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2418yes—
477(C2×D79)⋊C4C2418yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480(C2×D79)⋊C4C2418yes—
481(C2×D79)⋊C4C2418yes—
482C4×Dic79C2414yes—
483C4×Dic79C2414yes—
484C4×Dic79C2414yes—
485C4×Dic79C2418yes—
486C4×Dic79C2418yes—
487C4×Dic79C2418yes—
488C24×C79C2411yescharacteristic
489C24×C79C2412yes—
490C24×C79C2411yescharacteristic
491C2×D4×C79—24no—
492C2×D4×C79—28no—
493C2×D4×C79—24no—
494C2×D4×C79—44no—
495C2×D4×C79C2414yes—
496C2×D4×C79C2414yes—
497C2×D4×C79C2418yes—
498C2×D4×C79C2418yes—
499C22×C4×C79—24no—
500C22×C4×C79—24no—
501C22×C4×C79—44no—
502C22×C4×C79—44no—
503C22×C4×C79C2411yescharacteristic
504C22×C4×C79C2414yes—
505C22×C4×C79C2414yes—
506C22×C4×C79C2411yescharacteristic
507C22×C4×C79C2412yes—
508C22×C4×C79C2411yescharacteristic
509C22×C4×C79C2411yescharacteristic
510C22×C4×C79C2412yes—
511C22×C4×C79C2412yes—
512C22×C4×C79C2418yes—
513C22×C4×C79C2418yes—
514C22×C4×C79C2411yescharacteristic
515C4⋊C4×C79C2414yes—
516C4⋊C4×C79C2414yes—
517C4⋊C4×C79C2418yes—
518C4⋊C4×C79C2414yes—
519C4⋊C4×C79C2418yes—
520C4⋊C4×C79C2414yes—
521C4⋊C4×C79C2418yes—
522C22⋊C4×C79C2418yes—
523C22⋊C4×C79C2414yes—
524C22⋊C4×C79C2418yes—
525C22⋊C4×C79C2418yes—
526C22⋊C4×C79C2414yes—
527C22⋊C4×C79C2418yes—
528C42×C79C2418yes—
529C42×C79C2414yes—
530C23×C79—22no—
531C23×C79—22no—
532C23×C79—22no—
533C23×C79—24no—
534C23×C79—22no—
535C23×C79—24no—
536C23×C79—24no—
537C23×C79—22no—
538C23×C79C2×#4114yes—
539C23×C79C2512yes—
540C23×C79C2514yes—
541C23×C79C2512yes—
542C23×C79C2511yescharacteristic
543C22×D79—22no—
544C22×D79—22no—
545C22×D79—22no—
546C22×D79—22no—
547C22×D79—22no—
548C22×D79—24no—
549C22×D79—22no—
550C22×D79—24no—
551C22×D79—24no—
552C22×D79—22no—
553C22×D79—28no—
554C22×D79—216no—
555C22×D79—44no—
556C22×D79—44no—
557C22×D79—416no—
558C22×D79—44no—
559C22×D79—44no—
560C22×D79—48no—
561C22×D79—48no—
562C22×D79—416no—
563C22×D79—816no—
564C22×D79C2×#4114yes—
565C22×D79C2×#4114yes—
566C22×D79C2×#41116yescomplemented
567C22×D79C2512yes—
568C22×D79C2514yes—
569C22×D79C2512yes—
570C22×D79C2512yes—
571D4×C79—28no—
572D4×C79—216no—
573D4×C79—28no—
574D4×C79—48no—
575C2×C4×C79—24no—
576C2×C4×C79—22no—
577C2×C4×C79—22no—
578C2×C4×C79—22no—
579C2×C4×C79—22no—
580C2×C4×C79—24no—
581C2×C4×C79—24no—
582C2×C4×C79—28no—
583C2×C4×C79—28no—
584C2×C4×C79—48no—
585C2×C4×C79—48no—
586C2×C4×C79H(5,𝔽2)14yes—
587C2×C4×C79C2512yes—
588C2×C4×C79C2514yes—
589C2×C4×C79C2512yes—
590C2×C4×C79C2514yes—
591C2×C4×C79C2514yes—
592C2×C4×C79C2512yes—
593C2×C4×C79C2512yes—
594C2×C4×C79C2512yes—
595C22⋊D79—28no—
596C22⋊D79—216no—
597C22⋊D79—216no—
598C22⋊D79—28no—
599C22⋊D79—48no—
600C22⋊D79—48no—
601C22⋊D79—48no—
602C2×Dic79—24no—
603C2×Dic79—22no—
604C2×Dic79—22no—
605C2×Dic79—22no—
606C2×Dic79—22no—
607C2×Dic79—24no—
608C2×Dic79—24no—
609C2×Dic79—22no—
610C2×Dic79—44no—
611C2×Dic79—44no—
612C2×Dic79—48no—
613C2×Dic79—48no—
614C2×Dic79C2512yes—
615C2×Dic79C2512yes—
616C2×Dic79C2512yes—
617C2×Dic79C2514yes—
618C2×Dic79C2512yes—
619C2×Dic79C2514yes—
620C2×Dic79C2514yes—
621C2×Dic79C2512yes—
622D316—216no—
623D316—28no—
624D316—28no—
625D316—48no—
626C4×D79—28no—
627C4×D79—216no—
628C4×D79—28no—
629C4×D79—28no—
630C4×D79—28no—
631C4×D79—44no—
632C4×D79—44no—
633C4×D79—44no—
634C4×D79—44no—
635C4×D79—44no—
636C4×D79—48no—
637C4×D79—48no—
638Dic158—28no—
639Dic158—28no—
640Dic158—48no—
641C22×C79—22no—
642C22×C79—22no—
643C22×C79—28no—
644C22×C79—22no—
645C22×C79—24no—
646C22×C79—22no—
647C22×C79—24no—
648C22×C79—24no—
649C22×C79—22no—
650C22×C79—44no—
651C22×C79—48no—
652C22×C79C22×#4114yes—
653C22×C79C22×#4112yes—
654C22×C79C2×H(5,𝔽2)12yes—
655C22×C79#58512yes—
656C22×C79C2611yescharacteristic
657C2×D79—22no—
658C2×D79—22no—
659C2×D79—22no—
660C2×D79—22no—
661C2×D79—28no—
662C2×D79—28no—
663C2×D79—22no—
664C2×D79—24no—
665C2×D79—22no—
666C2×D79—24no—
667C2×D79—24no—
668C2×D79—22no—
669C2×D79—416no—
670C2×D79—416no—
671C2×D79—44no—
672C2×D79—48no—
673C2×D79—816no—
674C2×D79C22×#4114yes—
675C2×D79C22×#4114yes—
676C4×C79—22no—
677C4×C79—24no—
678C4×C79—22no—
679C4×C79—22no—
680C4×C79—22no—
681C4×C79—24no—
682C4×C79—24no—
683C4×C79C2×H(5,𝔽2)14yes—
684Dic79—24no—
685Dic79—22no—
686Dic79—22no—
687Dic79—24no—
688Dic79—24no—
689Dic79—22no—
690Dic79—22no—
691Dic79—22no—
692C2×#3505—791nomaximal, Sylow
693C2×C79—24no—
694C2×C79—42no—
695C2×C79—44no—
696C2×C79#350514yescomplemented
697C2×C79C23×#4111yescharacteristic
698C2×C79C22×H(5,𝔽2)11yescharacteristic
699C2×C79C2×#58511yescharacteristic
700D79—24no—
701D79—24no—
702D79—42no—
703D79—44no—
704#3505—7932no—
705C2×#553—792no—
706C2×#553—792no—
707C2×#553—791no—
708C2×#553D7911yescharacteristic, complemented
709C2×#552—791no—
710C2×#552—791no—
711C2×#551—792no—
712C2×#551—792no—
713C2×#548—791no—
714C2×#548—791no—
715C2×#546—791no—
716C2×#546—791no—
717C2×#539—792no—
718C2×#538—792no—
719C2×#534—792no—
720C2×#529—791no—
721C2×#529—791no—
722C2×#525—791no—
723C2×#525—791no—
724C22×C22⋊Q8—791no—
725C22×#121—791no—
726C2×#518—792no—
727C22×C4×D4—791no—
728C79C2×#350511yescharacteristic, complemented, Sylow
729C22×#41—791no—
730C22×#41—791no—
731C23×Q8—791no—
732C23×D4—791no—
733C23×D4—791no—
734C23×D4—792no—
735C24×C4—791no—
736C24×C4—791no—
737#553—7932no—
738#553—7932no—
739#553—7916no—
740#553C2×D79116yescomplemented
741#552—7916no—
742#552—7916no—
743#551—7932no—
744#551—7932no—
745#548—7916no—
746#548—7916no—
747#546—7916no—
748#546—7916no—
749#539—7932no—
750#538—7932no—
751#534—7932no—
752#529—7916no—
753#529—7916no—
754C2×#126—792no—
755C2×#126—792no—
756C2×#126—792no—
757C2×#126—792no—
758C2×#126—792no—
759C2×#126C2×D7912yescomplemented
760C2×#125—791no—
761C2×#125—792no—
762C2×#125—792no—
763C2×#125C2×D7911yescharacteristic, complemented
764C2×#124—791no—
765C2×#124—792no—
766C2×#124—792no—
767C2×#124—791no—
768#525—7916no—
769#525—7916no—
770C2×#123—792no—
771C2×#123—792no—
772C2×#123—792no—
773C2×#123—792no—
774C2×#123—792no—
775C2×#123—792no—
776C2×#123—792no—
777C2×#123—792no—
778C2×#123—792no—
779C2×#123C2×D7912yescomplemented
780C2×C22⋊Q8—791no—
781C2×C22⋊Q8—791no—
782C2×C22⋊Q8—791no—
783C2×C22⋊Q8—792no—
784C2×C22⋊Q8—791no—
785C2×C22⋊Q8—791no—
786C2×C22⋊Q8—792no—
787C2×C22⋊Q8—791no—
788C2×C22⋊Q8—792no—
789C2×C22⋊Q8—7916no—
790C2×C22⋊Q8—792no—
791C2×#121—791no—
792C2×#121—792no—
793C2×#121—792no—
794C2×#121—792no—
795C2×#121—792no—
796C2×#121—791no—
797C2×#121—792no—
798C2×#121—792no—
799C2×#121—7916no—
800C2×#121—791no—
801C2×#121—791no—
802C2×#121—792no—
803C2×#121C2×D7911yescharacteristic, complemented
804C2×#121C2×D7911yescharacteristic, complemented
805C2×#121C2×D7912yescomplemented
806C2×#120—792no—
807C2×#120—792no—
808C2×#120—792no—
809C2×#120—792no—
810#518—7932no—
811C2×C4×Q8—791no—
812C2×C4×Q8—791no—
813C2×C4×D4—791no—
814C2×C4×D4—792no—
815C2×C4×D4—792no—
816C2×C4×D4—791no—
817C2×C4×D4—791no—
818C2×C4×D4—792no—
819C2×C4×D4—792no—
820C2×C4×D4—7916no—
821C2×C4×D4—791no—
822C2×C4×D4—792no—
823C2×C4×D4—791no—
824C2×C4×D4—791no—
825C2×C4×D4—791no—
826C2×C4×D4—792no—
827C2×C4×D4—792no—
828C2×C4×D4—791no—
829C2×C4×D4—792no—
830C2×C4×D4—792no—
831C2×C4×D4C2×D7911yescharacteristic, complemented
832C2×C4×D4C2×D7912yescomplemented
833C2×C4×D4C2×D7911yescharacteristic, complemented
834C2×#117—792no—
835C2×#117—792no—
836C2×#117—791no—
837C2×#117—792no—
838C2×#117—792no—
839C2×#117C2×D7911yescharacteristic, complemented
840C22×C4⋊C4—792no—
841C22×C4⋊C4—791no—
842C22×C4⋊C4—791no—
843C22×C4⋊C4C2×D7911yescharacteristic, complemented
844C22×C22⋊C4—792no—
845C22×C22⋊C4—792no—
846C22×C22⋊C4—791no—
847C22×C22⋊C4—791no—
848C22×C22⋊C4—792no—
849C22×C22⋊C4—792no—
850C22×C42—791no—
851C25—791no—
852C25—792no—
853C25—791no—
854C2×#41—3164no—
855C2×#41—3164no—
856C2×#41—798no—
857C2×#41—798no—
858C22×Q8—3164no—
859C22×Q8—792no—
860C22×Q8—798no—
861C22×Q8—791no—
862C22×Q8—791no—
863C22×D4—3164no—
864C22×D4—792no—
865C22×D4—792no—
866C22×D4—792no—
867C22×D4—798no—
868C22×D4—791no—
869C22×D4—792no—
870C22×D4—791no—
871C22×D4—792no—
872C22×D4—798no—
873C22×D4—7916no—
874C22×D4—792no—
875C22×D4—791no—
876C22×D4—792no—
877C22×D4—791no—
878C22×D4—1588no—
879C22×D4—15816no—
880C22×D4C22×D7911yescharacteristic
881C22×D4C22×D7912yes—
882C22×D4C22×D7911yescharacteristic
883C22×D4C22×D7912yes—
884C23×C4—3164no—
885C23×C4—3164no—
886C23×C4—792no—
887C23×C4—792no—
888C23×C4—791no—
889C23×C4—791no—
890C23×C4—791no—
891C23×C4—791no—
892C23×C4—791no—
893C23×C4—791no—
894C23×C4—792no—
895C23×C4—792no—
896C23×C4—791no—
897C23×C4—798no—
898C23×C4—798no—
899C23×C4—792no—
900C23×C4—791no—
901C23×C4—791no—
902C23×C4—791no—
903C23×C4—791no—
904C23×C4C22×D7911yescharacteristic
905C23×C4C22×D7911yescharacteristic
906C23×C4C22×D7912yes—
907C23×C4C22×D7912yes—
908#126—7916no—
909#126—7916no—
910#126—7916no—
911#126—7916no—
912#126—7916no—
913#126C22×D79116yescomplemented
914#125—798no—
915#125—7916no—
916#125—7916no—
917#125C22×D7918yescomplemented
918#124—798no—
919#124—7916no—
920#124—7916no—
921#124—798no—
922#123—7916no—
923#123—7916no—
924#123—7916no—
925#123—7916no—
926#123—7916no—
927#123—7916no—
928#123—7916no—
929#123—7916no—
930#123—7916no—
931#123C22×D79116yescomplemented
932C22⋊Q8—798no—
933C22⋊Q8—798no—
934C22⋊Q8—798no—
935C22⋊Q8—7916no—
936C22⋊Q8—798no—
937C22⋊Q8—798no—
938C22⋊Q8—7916no—
939C22⋊Q8—798no—
940C22⋊Q8—7916no—
941C22⋊Q8—7916no—
942#121—798no—
943#121—7916no—
944#121—7916no—
945#121—7916no—
946#121—7916no—
947#121—798no—
948#121—7916no—
949#121—7916no—
950#121—798no—
951#121—798no—
952#121—7916no—
953#121C22×D7918yescomplemented
954#121C22×D7918yescomplemented
955#121C22×D79116yescomplemented
956#120—7916no—
957#120—7916no—
958#120—7916no—
959#120—7916no—
960C4×Q8—798no—
961C4×Q8—798no—
962C4×D4—798no—
963C4×D4—7916no—
964C4×D4—7916no—
965C4×D4—798no—
966C4×D4—798no—
967C4×D4—7916no—
968C4×D4—7916no—
969C4×D4—798no—
970C4×D4—7916no—
971C4×D4—798no—
972C4×D4—798no—
973C4×D4—798no—
974C4×D4—7916no—
975C4×D4—7916no—
976C4×D4—798no—
977C4×D4—7916no—
978C4×D4—7916no—
979C4×D4C22×D7918yescomplemented
980C4×D4C22×D79116yescomplemented
981C4×D4C22×D7918yescomplemented
982#117—7916no—
983#117—7916no—
984#117—798no—
985#117—7916no—
986#117—7916no—
987#117C22×D7918yescomplemented
988C2×C4⋊C4—792no—
989C2×C4⋊C4—792no—
990C2×C4⋊C4—791no—
991C2×C4⋊C4—791no—
992C2×C4⋊C4—791no—
993C2×C4⋊C4—791no—
994C2×C4⋊C4—792no—
995C2×C4⋊C4—792no—
996C2×C4⋊C4—792no—
997C2×C4⋊C4—7916no—
998C2×C4⋊C4—792no—
999C2×C4⋊C4—792no—
1000C2×C4⋊C4—792no—
1001C2×C4⋊C4—792no—
1002C2×C4⋊C4—792no—
1003C2×C4⋊C4—792no—
1004C2×C4⋊C4—798no—
1005C2×C4⋊C4—798no—
1006C2×C4⋊C4C22×D7911yescharacteristic
1007C2×C4⋊C4C22×D7911yescharacteristic
1008C2×C4⋊C4C22×D7911yescharacteristic
1009C2×C4⋊C4C22×D7911yescharacteristic
1010C2×C4⋊C4C22×D7912yes—
1011C2×C4⋊C4C22×D7912yes—
1012C2×C4⋊C4C22×D7912yes—
1013C2×C4⋊C4C22×D7918yescomplemented
1014C2×C22⋊C4—792no—
1015C2×C22⋊C4—791no—
1016C2×C22⋊C4—791no—
1017C2×C22⋊C4—792no—
1018C2×C22⋊C4—792no—
1019C2×C22⋊C4—792no—
1020C2×C22⋊C4—791no—
1021C2×C22⋊C4—791no—
1022C2×C22⋊C4—792no—
1023C2×C22⋊C4—792no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—792no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—791no—
1028C2×C22⋊C4—792no—
1029C2×C22⋊C4—792no—
1030C2×C22⋊C4—791no—
1031C2×C22⋊C4—7916no—
1032C2×C22⋊C4—7916no—
1033C2×C22⋊C4—792no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—792no—
1036C2×C22⋊C4—792no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—798no—
1039C2×C22⋊C4—798no—
1040C2×C22⋊C4—7916no—
1041C2×C22⋊C4—7916no—
1042C2×C22⋊C4C22×D7911yescharacteristic
1043C2×C22⋊C4C22×D7912yes—
1044C2×C22⋊C4C22×D7911yescharacteristic
1045C2×C22⋊C4C22×D7912yes—
1046C2×C22⋊C4C22×D7912yes—
1047C2×C22⋊C4C22×D7912yes—
1048C2×C42—792no—
1049C2×C42—792no—
1050C2×C42—792no—
1051C2×C42—791no—
1052C2×C42—791no—
1053C2×C42—791no—
1054C2×C42—798no—
1055C2×C42C22×D7912yes—
1056C2×C42C22×D7911yescharacteristic
1057C24—3162no—
1058C24—3162no—
1059C24—3162no—
1060C24—3162no—
1061C24—3164no—
1062C24—3164no—
1063C24—798no—
1064C24—794no—
1065C24—798no—
1066C24—794no—
1067C24—791no—
1068C24—791no—
1069C24—791no—
1070C24—792no—
1071C24—1584no—
1072C24—1588no—
1073C24C23×D7911yescharacteristic
1074C24C23×D7912yes—
1075C24C23×D7911yescharacteristic
1076#41—31616no—
1077#41—31616no—
1078C2×Q8—31616no—
1079C2×Q8—3164no—
1080C2×Q8—798no—
1081C2×Q8—794no—
1082C2×Q8—794no—
1083C2×Q8—1584no—
1084C2×Q8—1584no—
1085C2×D4—24no—
1086C2×D4—28no—
1087C2×D4—24no—
1088C2×D4—44no—
1089C2×D4—3164no—
1090C2×D4—31616no—
1091C2×D4—3164no—
1092C2×D4—3164no—
1093C2×D4—3164no—
1094C2×D4—798no—
1095C2×D4—798no—
1096C2×D4—798no—
1097C2×D4—794no—
1098C2×D4—798no—
1099C2×D4—794no—
1100C2×D4—798no—
1101C2×D4—798no—
1102C2×D4—794no—
1103C2×D4—798no—
1104C2×D4—794no—
1105C2×D4—1584no—
1106C2×D4—1588no—
1107C2×D4—15832no—
1108C2×D4—15864no—
1109C2×D4—1584no—
1110C2×D4—1588no—
1111C2×D4—1584no—
1112C2×D4—1588no—
1113C2×D4—1584no—
1114C2×D4C23×D7914yes—
1115C2×D4C23×D7918yes—
1116C2×D4C23×D7914yes—
1117C2×D4C23×D7918yes—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—3162no—
1123C22×C4—3162no—
1124C22×C4—3162no—
1125C22×C4—3162no—
1126C22×C4—3162no—
1127C22×C4—3164no—
1128C22×C4—3164no—
1129C22×C4—31616no—
1130C22×C4—31616no—
1131C22×C4—3162no—
1132C22×C4—3162no—
1133C22×C4—3164no—
1134C22×C4—3164no—
1135C22×C4—798no—
1136C22×C4—798no—
1137C22×C4—794no—
1138C22×C4—794no—
1139C22×C4—794no—
1140C22×C4—794no—
1141C22×C4—794no—
1142C22×C4—794no—
1143C22×C4—798no—
1144C22×C4—798no—
1145C22×C4—794no—
1146C22×C4—791no—
1147C22×C4—792no—
1148C22×C4—791no—
1149C22×C4—791no—
1150C22×C4—791no—
1151C22×C4—792no—
1152C22×C4—792no—
1153C22×C4—791no—
1154C22×C4—794no—
1155C22×C4—794no—
1156C22×C4—798no—
1157C22×C4—794no—
1158C22×C4—794no—
1159C22×C4—1588no—
1160C22×C4—1584no—
1161C22×C4—1584no—
1162C22×C4—1584no—
1163C22×C4—1584no—
1164C22×C4C23×D7914yes—
1165C22×C4C23×D7914yes—
1166C22×C4C23×D7911yescharacteristic
1167C22×C4C23×D7912yes—
1168C22×C4C23×D7911yescharacteristic
1169C22×C4C23×D7912yes—
1170C22×C4C23×D7911yescharacteristic
1171C22×C4C23×D7912yes—
1172C22×C4C23×D7911yescharacteristic
1173C22×C4C23×D7918yes—
1174C22×C4C23×D7918yes—
1175C22×C4C23×D7911yescharacteristic
1176C4⋊C4—794no—
1177C4⋊C4—794no—
1178C4⋊C4—798no—
1179C4⋊C4—798no—
1180C4⋊C4—798no—
1181C4⋊C4—798no—
1182C4⋊C4—798no—
1183C4⋊C4—798no—
1184C4⋊C4—798no—
1185C4⋊C4—794no—
1186C4⋊C4—794no—
1187C4⋊C4—798no—
1188C4⋊C4—798no—
1189C4⋊C4—798no—
1190C4⋊C4—798no—
1191C4⋊C4C23×D7914yes—
1192C4⋊C4C23×D7914yes—
1193C4⋊C4C23×D7914yes—
1194C4⋊C4C23×D7914yes—
1195C4⋊C4C23×D7918yes—
1196C4⋊C4C23×D7918yes—
1197C4⋊C4C23×D7918yes—
1198C22⋊C4—798no—
1199C22⋊C4—794no—
1200C22⋊C4—794no—
1201C22⋊C4—798no—
1202C22⋊C4—798no—
1203C22⋊C4—798no—
1204C22⋊C4—794no—
1205C22⋊C4—794no—
1206C22⋊C4—798no—
1207C22⋊C4—798no—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—798no—
1211C22⋊C4—794no—
1212C22⋊C4—798no—
1213C22⋊C4—798no—
1214C22⋊C4—794no—
1215C22⋊C4—798no—
1216C22⋊C4—798no—
1217C22⋊C4—798no—
1218C22⋊C4—798no—
1219C22⋊C4—798no—
1220C22⋊C4C23×D7914yes—
1221C22⋊C4C23×D7918yes—
1222C22⋊C4C23×D7914yes—
1223C22⋊C4C23×D7918yes—
1224C22⋊C4C23×D7918yes—
1225C22⋊C4C23×D7918yes—
1226C42—794no—
1227C42—794no—
1228C42—794no—
1229C42—798no—
1230C42—798no—
1231C42—798no—
1232C42C23×D7914yes—
1233C42C23×D7918yes—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—24no—
1238C23—24no—
1239C23—22no—
1240C23—22no—
1241C23—24no—
1242C23—3164no—
1243C23—3164no—
1244C23—3164no—
1245C23—31616no—
1246C23—3164no—
1247C23—3168no—
1248C23—3168no—
1249C23—31616no—
1250C23—7916no—
1251C23—792no—
1252C23—792no—
1253C23—794no—
1254C23—794no—
1255C23—792no—
1256C23—794no—
1257C23—63216no—
1258C23—1588no—
1259C23—15816no—
1260C23—1582no—
1261C23—1584no—
1262C23—1584no—
1263C23—1582no—
1264C23—1582no—
1265C23—1584no—
1266C23—1582no—
1267C23—1582no—
1268C23—1582no—
1269C23—1582no—
1270C23#41×D7914yes—
1271C23C24×D7912yes—
1272C23C24×D7914yes—
1273C23C24×D7912yes—
1274C23C24×D7911yescharacteristic
1275Q8—3168no—
1276Q8—1588no—
1277Q8—1588no—
1278D4—28no—
1279D4—216no—
1280D4—28no—
1281D4—48no—
1282D4—3168no—
1283D4—3168no—
1284D4—3168no—
1285D4—3168no—
1286D4—1588no—
1287D4—15816no—
1288D4—1588no—
1289D4—15816no—
1290D4—1588no—
1291D4—15816no—
1292D4—1588no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—28no—
1301C2×C4—28no—
1302C2×C4—48no—
1303C2×C4—48no—
1304C2×C4—3164no—
1305C2×C4—3164no—
1306C2×C4—3164no—
1307C2×C4—3164no—
1308C2×C4—3168no—
1309C2×C4—3164no—
1310C2×C4—3168no—
1311C2×C4—3164no—
1312C2×C4—3164no—
1313C2×C4—3168no—
1314C2×C4—3168no—
1315C2×C4—792no—
1316C2×C4—792no—
1317C2×C4—794no—
1318C2×C4—792no—
1319C2×C4—792no—
1320C2×C4—794no—
1321C2×C4—794no—
1322C2×C4—792no—
1323C2×C4—15816no—
1324C2×C4—1588no—
1325C2×C4—1582no—
1326C2×C4—1582no—
1327C2×C4—1582no—
1328C2×C4—1584no—
1329C2×C4—1584no—
1330C2×C4—1582no—
1331C2×C4—1584no—
1332C2×C4—1582no—
1333C2×C4—1588no—
1334C2×C4—1588no—
1335C2×C4—1588no—
1336C2×C4#1457920714yes—
1337C2×C4C24×D7912yes—
1338C2×C4C24×D7912yes—
1339C2×C4C24×D7914yes—
1340C2×C4C24×D7914yes—
1341C2×C4C24×D7912yes—
1342C2×C4C24×D7914yes—
1343C2×C4C24×D7912yes—
1344C2×C4C24×D7912yes—
1345C22—22no—
1346C22—22no—
1347C22—28no—
1348C22—22no—
1349C22—24no—
1350C22—22no—
1351C22—24no—
1352C22—24no—
1353C22—22no—
1354C22—44no—
1355C22—48no—
1356C22—31616no—
1357C22—31616no—
1358C22—3164no—
1359C22—3168no—
1360C22—794no—
1361C22—794no—
1362C22—63216no—
1363C22—1582no—
1364C22—1584no—
1365C22—1582no—
1366C22—1584no—
1367C22—1584no—
1368C22—1582no—
1369C22—1582no—
1370C22—1582no—
1371C22—1582no—
1372C22—1582no—
1373C22—1588no—
1374C22—1588no—
1375C22C2×#41×D7914yes—
1376C22C2×#41×D7912yes—
1377C22C2×#1457920712yes—
1378C22#1909939812yes—
1379C22C25×D7911yescharacteristic
1380C4—24no—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—24no—
1386C4—24no—
1387C4—1582no—
1388C4—1584no—
1389C4—1582no—
1390C4—1582no—
1391C4—1582no—
1392C4—1584no—
1393C4—1584no—
1394C4—1582no—
1395C4C2×#1457920714yes—
1396C2—24no—
1397C2—42no—
1398C2—44no—
1399C2—3162no—
1400C2—3164no—
1401C2—1584no—
1402C2—1584no—
1403C2#2377722914yesdirect product factor
1404C2C22×#41×D7911yescharacteristic
1405C2C22×#1457920711yescharacteristic
1406C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#553×C79C2
socleC23×C79C25
hypercenterC2×#553D79
hypocenterC79C2×#3505
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#553

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23777229C2direct (N × H)
2. C2×#19099265C2semidirect
3. C2×#19099261C2semidirect
4. C2×#19099259C2semidirect
5. C2×#19099252C2semidirect
6. C2×#19099251C2semidirect
7. C2×#19099238C2semidirect
8. C2×#19099236C2semidirect
9. C2×#19099222C2semidirect
10. C2×#19099219C2semidirect
11. C2×#19099210C2semidirect
12. C2×#19099208C2semidirect
13. C2×#19099154C2semidirect
14. C2×#19099149C2semidirect
15. C2×#19099121C2semidirect
16. C2×#19099098C2semidirect
17. C2×#19099095C2semidirect
18. C2×#19099075C2semidirect
19. C2×#19099073C2semidirect
20. C22×#14579141C2semidirect
21. C2×#121×D79C2semidirect
22. C2×#19099035C2semidirect
23. C2×C4×D4×D79C2semidirect
24. C2×#553×C79C2semidirect
25. C22×#11929624C22semidirect
26. C22×#11929623C22semidirect
27. C23×Dic158C22semidirect
30. C22×D4×D79C22semidirect
32. C23×C4×D79C22semidirect
33. #19099265C22semidirect
34. #19099261C22semidirect
35. #19099259C22semidirect
36. #19099252C22semidirect
37. #19099251C22semidirect
38. #19099238C22semidirect
39. #19099236C22semidirect
40. #19099222C22semidirect
41. #19099219C22semidirect
42. #19099210C22semidirect
43. #19099208C22semidirect
44. #19099154C22semidirect
45. #19099149C22semidirect
46. #19099121C22semidirect
47. #19099098C22semidirect
48. #19099095C22semidirect
49. C2×#14579156C22semidirect
50. C2×#14579156C22semidirect
51. C2×#14579156C22semidirect
52. C2×#14579154C22semidirect
53. C2×#14579154C22semidirect
54. C2×#14579153C22semidirect
55. C2×#14579152C22semidirect
56. C2×#14579152C22semidirect
57. C2×#14579149C22semidirect
58. C2×#14579148C22semidirect
59. C2×#14579147C22semidirect
60. C2×#14579147C22semidirect
61. #19099075C22semidirect
62. #19099073C22semidirect
64. C2×#14579146C22semidirect
65. C2×#14579146C22semidirect
66. C2×#14579145C22semidirect
67. C2×#14579145C22semidirect
69. C2×#14579143C22semidirect
70. C2×#14579143C22semidirect
71. C2×#14579143C22semidirect
72. C2×#14579141C22semidirect
73. C2×#14579141C22semidirect
74. C2×#14579141C22semidirect
75. C2×#14579141C22semidirect
76. C2×#14579141C22semidirect
77. C2×#14579141C22semidirect
78. C2×#14579141C22semidirect
79. C2×#14579141C22semidirect
80. C2×#14579140C22semidirect
81. C2×#14579139C22semidirect
82. C2×#14579138C22semidirect
84. C2×#14579136C22semidirect
85. C2×#14579135C22semidirect
86. C2×#14579135C22semidirect
87. C2×#14579135C22semidirect
89. C2×#14579133C22semidirect
90. C2×#14579133C22semidirect
91. C2×#14579133C22semidirect
93. C2×#14579132C22semidirect
94. #121×D79C22semidirect
96. C2×#14579131C22semidirect
98. C2×#14579129C22semidirect
99. #19099035C22semidirect
100. C2×C4×Dic158C22semidirect
101. C2×#14579126C22semidirect
103. C2×C4×D316C22semidirect
104. C2×C4×D316C22semidirect
105. C2×D4×Dic79C22semidirect
106. C2×D4×Dic79C22semidirect
107. C2×D4×Dic79C22semidirect
109. C2×#14579123C22semidirect
110. C2×#14579123C22semidirect
112. C2×C4×C22⋊D79C22semidirect
113. C2×C4×C22⋊D79C22semidirect
114. C2×C4×C22⋊D79C22semidirect
116. C2×(C22⋊D79)⋊C4C22semidirect
117. C2×(C22⋊D79)⋊C4C22semidirect
118. C2×(C22⋊D79)⋊C4C22semidirect
119. C4×D4×D79C22semidirect
120. C2×#14579120C22semidirect
121. C2×#14579119C22semidirect
122. C2×#14579119C22semidirect
123. C2×#14579119C22semidirect
124. C2×#14579118C22semidirect
125. C22×C4⋊Dic79C22semidirect
126. C2×C4⋊C4×D79C22semidirect
127. C2×C4⋊C4×D79C22semidirect
129. C22×(C2×D79)⋊C4C22semidirect
131. C2×C22⋊C4×D79C22semidirect
132. C2×C22⋊C4×D79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. #553×C79C22semidirect
136. C2×#126×C79C22semidirect
137. C2×#125×C79C22semidirect
138. C2×#123×C79C22semidirect
139. C2×#121×C79C22semidirect
140. C2×#121×C79C22semidirect
141. C2×#121×C79C22semidirect
142. C2×C4×D4×C79C22semidirect
143. C2×C4×D4×C79C22semidirect
144. C2×C4×D4×C79C22semidirect
145. C2×#117×C79C22semidirect
146. C22×C4⋊C4×C79C22semidirect
151. C2×#11929624C23semidirect
153. C2×#11929623C23semidirect
158. C22×Dic158C23semidirect
175. C2×D4×D79C23semidirect
195. C22×C4×D79C23semidirect
196. #14579156C23semidirect
197. #14579156C23semidirect
198. #14579156C23semidirect
199. #14579154C23semidirect
200. #14579154C23semidirect
201. #14579153C23semidirect
202. #14579152C23semidirect
203. #14579152C23semidirect
204. #14579149C23semidirect
205. #14579148C23semidirect
206. #14579147C23semidirect
207. #14579147C23semidirect
209. #14579146C23semidirect
210. #14579146C23semidirect
211. #14579145C23semidirect
212. #14579145C23semidirect
214. #14579143C23semidirect
215. #14579143C23semidirect
216. #14579143C23semidirect
217. #14579141C23semidirect
218. #14579141C23semidirect
219. #14579141C23semidirect
220. #14579141C23semidirect
221. #14579141C23semidirect
222. #14579141C23semidirect
223. #14579141C23semidirect
224. #14579140C23semidirect
225. #14579139C23semidirect
226. #14579138C23semidirect
228. #14579136C23semidirect
229. #14579135C23semidirect
230. #14579135C23semidirect
231. #14579135C23semidirect
233. #14579133C23semidirect
234. #14579133C23semidirect
235. #14579133C23semidirect
237. #14579132C23semidirect
239. #14579131C23semidirect
241. #14579129C23semidirect
242. C4×Dic158C23semidirect
243. #14579126C23semidirect
245. C4×D316C23semidirect
246. C4×D316C23semidirect
247. D4×Dic79C23semidirect
248. D4×Dic79C23semidirect
249. D4×Dic79C23semidirect
251. #14579123C23semidirect
252. #14579123C23semidirect
254. C4×C22⋊D79C23semidirect
255. C4×C22⋊D79C23semidirect
256. C4×C22⋊D79C23semidirect
258. (C22⋊D79)⋊C4C23semidirect
259. (C22⋊D79)⋊C4C23semidirect
260. (C22⋊D79)⋊C4C23semidirect
261. #14579120C23semidirect
262. #14579119C23semidirect
263. #14579119C23semidirect
264. #14579119C23semidirect
265. #14579118C23semidirect
274. C2×C4⋊Dic79C23semidirect
282. C4⋊C4×D79C23semidirect
283. C4⋊C4×D79C23semidirect
307. C2×(C2×D79)⋊C4C23semidirect
309. C22⋊C4×D79C23semidirect
310. C22⋊C4×D79C23semidirect
311. C22⋊C4×D79C23semidirect
318. C42×D79C23semidirect
327. #126×C79C23semidirect
328. #125×C79C23semidirect
329. #123×C79C23semidirect
330. #121×C79C23semidirect
331. #121×C79C23semidirect
332. #121×C79C23semidirect
333. C4×D4×C79C23semidirect
334. C4×D4×C79C23semidirect
335. C4×D4×C79C23semidirect
336. #117×C79C23semidirect
344. C2×C4⋊C4×C79C23semidirect
361. C23×D79#41semidirect
566. C22×D79C2×#41semidirect
696. C2×C79#3505semidirect
708. C2×#553D79semidirect
728. C79C2×#3505semidirect
740. #553C2×D79semidirect
759. C2×#126C2×D79semidirect
763. C2×#125C2×D79semidirect
779. C2×#123C2×D79semidirect
803. C2×#121C2×D79semidirect
804. C2×#121C2×D79semidirect
805. C2×#121C2×D79semidirect
831. C2×C4×D4C2×D79semidirect
832. C2×C4×D4C2×D79semidirect
833. C2×C4×D4C2×D79semidirect
839. C2×#117C2×D79semidirect
843. C22×C4⋊C4C2×D79semidirect
913. #126C22×D79semidirect
917. #125C22×D79semidirect
931. #123C22×D79semidirect
953. #121C22×D79semidirect
954. #121C22×D79semidirect
955. #121C22×D79semidirect
979. C4×D4C22×D79semidirect
980. C4×D4C22×D79semidirect
981. C4×D4C22×D79semidirect
987. #117C22×D79semidirect
1013. C2×C4⋊C4C22×D79semidirect
1403. C2#23777229direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237772292
C2×#190992652
C2×#190992612
C2×#190992592
C2×#190992522
C2×#190992512
C2×#190992382
C2×#190992362
C2×#190992222
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