Finite Group Databasebeta

← C2×#23777769 #35195910

Subgroups — C2×#23777769 #35195910

Order 20224.

8046 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777769C2132yesmaximal, direct product factor
2C2×#19099304C212yesmaximal, complemented
3C2×#19099303C212yesmaximal, complemented
4C2×#19099285C211yesmaximal, characteristic, complemented
5C2×#19099264C212yesmaximal, complemented
6C2×#19099235C211yesmaximal, characteristic, complemented
7C2×#19099234C211yesmaximal, characteristic, complemented
8C2×#19099231C211yesmaximal, characteristic, complemented
9C2×#19099215C211yesmaximal, characteristic, complemented
10C2×#19099208C211yesmaximal, characteristic, complemented
11C2×#19099205C212yesmaximal, complemented
12C2×#19099204C211yesmaximal, characteristic, complemented
13C2×#19099197C211yesmaximal, characteristic, complemented
14C2×#19099187C211yesmaximal, characteristic, complemented
15C2×#19099153C212yesmaximal, complemented
16C2×#19099147C212yesmaximal, complemented
17C2×#19099143C212yesmaximal, complemented
18C2×#19099132C211yesmaximal, characteristic, complemented
19C2×#19099131C212yesmaximal, complemented
20C2×#19099131C211yesmaximal, characteristic, complemented
21C2×#19099114C211yesmaximal, characteristic, complemented
22C2×#19099112C211yesmaximal, characteristic, complemented
23C2×#19099091C211yesmaximal, characteristic, complemented
24C2×#542×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929625C2211yescharacteristic, complemented
27C22×#11929625C2212yescomplemented
28C22×#11929624C2212yescomplemented
29C22×#11929624C2211yescharacteristic, complemented
30C22×#11929623C2211yescharacteristic, complemented
31C23×D316C2211yescharacteristic
32C22×D4×D79C2212yes—
33C22×D4×D79C2211yescharacteristic
34#19099304C22132yescomplemented
35#19099303C22132yescomplemented
36#19099285C22116yescomplemented
37#19099264C22132yescomplemented
38#19099235C22116yescomplemented
39#19099234C22116yescomplemented
40#19099231C22116yescomplemented
41#19099215C22116yescomplemented
42#19099208C22116yescomplemented
43#19099205C22132yescomplemented
44#19099204C22116yescomplemented
45#19099197C22116yescomplemented
46#19099187C22116yescomplemented
47#19099153C22132yescomplemented
48#19099147C22132yescomplemented
49#19099143C22132yescomplemented
50#19099132C22116yescomplemented
51#19099131C22132yescomplemented
52#19099131C22116yescomplemented
53#19099114C22116yescomplemented
54#19099112C22116yescomplemented
55C2×#14579159C2211yescharacteristic, complemented
56C2×#14579158C2211yescharacteristic
57C2×#14579158C2211yescharacteristic, complemented
58C2×#14579158C2212yescomplemented
59C2×#14579157C2211yescharacteristic
60C2×#14579157C2211yescharacteristic, complemented
61C2×#14579157C2212yescomplemented
62#19099091C22116yescomplemented
63C2×#14579156C2212yescomplemented
64C2×#14579156C2211yescharacteristic, complemented
65C2×#14579156C2212yescomplemented
66C2×#14579155C2212yescomplemented
67C2×#14579154C2211yescharacteristic, complemented
68C2×#14579151C2211yescharacteristic, complemented
69C2×#14579150C2211yescharacteristic
70C2×#14579150C2212yescomplemented
71C2×#14579150C2212yescomplemented
72C2×#14579149C2211yescharacteristic
73C2×#14579149C2211yescharacteristic, complemented
74C2×#14579147C2211yescharacteristic
75C2×#14579146C2212yescomplemented
76C2×#14579146C2212yescomplemented
77C2×#14579146C2212yescomplemented
78C2×#14579146C2211yescharacteristic, complemented
79C2×#14579145C2212yescomplemented
80C2×#14579143C2212yescomplemented
81C2×#14579143C2211yescharacteristic, complemented
82C2×#14579141C2211yescharacteristic, complemented
83C2×#14579139C2212yescomplemented
84C2×#14579139C2211yescharacteristic, complemented
85C2×#14579137C2212yescomplemented
86C2×#14579136C2211yescharacteristic
87C2×#14579136C2211yescharacteristic
88C2×#14579136C2212yescomplemented
89C2×#14579136C2212yescomplemented
90C2×#14579136C2211yescharacteristic, complemented
91C2×#14579136C2212yescomplemented
92C2×#14579136C2212yescomplemented
93C2×#14579136C2212yescomplemented
94C2×#14579136C2212yescomplemented
95C2×#14579135C2212yescomplemented
96C2×#14579135C2212yescomplemented
97C2×#14579134C2212yes—
98C2×#14579134C2212yes—
99C2×#14579134C2211yescharacteristic
100C2×#14579134C2212yescomplemented
101C2×#14579134C2212yescomplemented
102C2×#14579134C2212yescomplemented
103C2×#14579134C2212yescomplemented
104C2×#14579134C2212yescomplemented
105C2×#14579134C2212yescomplemented
106C2×#14579134C2212yescomplemented
107C2×#14579133C2212yescomplemented
108C2×#14579131C2212yes—
109C2×#14579131C2212yescomplemented
110C2×#14579131C2212yescomplemented
111C2×#14579131C2212yescomplemented
112C2×#14579131C2212yescomplemented
113C2×#14579131C2212yescomplemented
114C2×#14579131C2212yescomplemented
115C2×#14579129C2212yes—
116C2×C4×Dic158C2211yescharacteristic, complemented
117C2×#14579126C2211yescharacteristic, complemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×C4×D316C2212yescomplemented
120C2×#14579123C2211yescharacteristic
121C2×#14579123C2211yescharacteristic, complemented
122C2×#14579123C2212yescomplemented
123C2×#14579123C2211yescharacteristic, complemented
124C2×C4×C22⋊D79C2211yescharacteristic
125C2×C4×C22⋊D79C2211yescharacteristic, complemented
126C2×(C22⋊D79)⋊C4C2212yescomplemented
127C2×(C22⋊D79)⋊C4C2212yescomplemented
128C2×(C22⋊D79)⋊C4C2212yescomplemented
129C2×#14579118C2211yescharacteristic, complemented
130C2×#14579118C2212yescomplemented
131C2×C4⋊C4×D79C2212yescomplemented
132C22×(C2×D79)⋊C4C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135#542×C79C22116yescomplemented
136C2×C4⋊Q8×C79C2211yescharacteristic, complemented
137C2×#126×C79C2212yescomplemented
138C2×#124×C79C2211yescharacteristic, complemented
139C2×#124×C79C2212yescomplemented
140C2×#123×C79C2212yescomplemented
141C2×C22⋊Q8×C79C2211yescharacteristic, complemented
142C2×C22⋊Q8×C79C2212yescomplemented
143C2×#121×C79C2211yescharacteristic
144C2×C4×Q8×C79C2211yescharacteristic, complemented
145C2×C4×D4×C79C2211yescharacteristic, complemented
146C2×#117×C79C2211yescharacteristic, complemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C2×#11929625—48no—
150C2×#11929625—44no—
151C2×#11929625—44no—
152C2×#11929625C23116yescomplemented
153C2×#11929625C2318yescomplemented
154C2×#11929625C2318yescomplemented
155C2×#11929624—48no—
156C2×#11929624—44no—
157C2×#11929624C23116yescomplemented
158C2×#11929624C2318yescomplemented
159C2×#11929623—44no—
160C2×#11929623C2318yescomplemented
161C22×Dic158C2311yescharacteristic
162C22×Dic158C2311yescharacteristic
163C22×D316—44no—
164C22×D316C2311yescharacteristic
165C22×D316C2311yescharacteristic
166C22×D316C2311yescharacteristic
167C22×D316C2318yes—
168C22×D316C2312yes—
169C22×D316C2311yescharacteristic
170C22×D316C2312yes—
171C22×D316C2312yes—
172C22×D316C2312yes—
173C22×D316C2312yes—
174C22×D316C2312yes—
175C22×D316C2312yes—
176C22×D316C2312yes—
177C22×D316C2312yes—
178C22×D316C2312yes—
179C22×C22⋊D79C2312yes—
180C22×C22⋊D79C2311yescharacteristic
181C22×C22⋊D79C2312yes—
182C22×C22⋊D79C2312yes—
183C22×C22⋊D79C2311yescharacteristic
184C22×C22⋊D79C2312yes—
185C22×C22⋊D79C2312yes—
186C22×C22⋊D79C2312yes—
187C22×C22⋊D79C2312yes—
188C2×D4×D79—48no—
189C2×D4×D79—44no—
190C2×D4×D79C23116yes—
191C2×D4×D79C2318yes—
192C23×Dic79C2312yes—
193C22×C4×D79C2311yescharacteristic
194C22×C4×D79C2311yescharacteristic
195C22×C4×D79C2312yes—
196C22×C4×D79C2311yescharacteristic
197C22×C4×D79C2312yes—
198C22×C4×D79C2311yescharacteristic
199C22×C4×D79C2312yes—
200C22×C4×D79C2312yes—
201C22×C4×D79C2312yes—
202C22×C4×D79C2312yes—
203#14579159C2318yescomplemented
204#14579158C2318yes—
205#14579158C2318yescomplemented
206#14579158C23116yescomplemented
207#14579157C2318yes—
208#14579157C2318yescomplemented
209#14579157C23116yescomplemented
210#14579156C2318yescomplemented
211#14579156C23116yescomplemented
212#14579156C23116yescomplemented
213#14579155C23116yescomplemented
214#14579154C2318yescomplemented
215#14579151C2318yescomplemented
216#14579150C2318yes—
217#14579150C23116yescomplemented
218#14579150C23116yescomplemented
219#14579149C2318yes—
220#14579149C2318yescomplemented
221#14579147C2318yes—
222#14579146C23116yescomplemented
223#14579146C23116yescomplemented
224#14579146C23116yescomplemented
225#14579146C2318yescomplemented
226#14579145C23116yescomplemented
227#14579143C23116yescomplemented
228#14579143C2318yescomplemented
229#14579141C2318yescomplemented
230#14579139C2318yescomplemented
231#14579139C23116yescomplemented
232#14579137C23116yescomplemented
233#14579136C2318yes—
234#14579136C2318yes—
235#14579136C23116yescomplemented
236#14579136C23116yescomplemented
237#14579136C23116yescomplemented
238#14579136C23116yescomplemented
239#14579136C2318yescomplemented
240#14579136C23116yescomplemented
241#14579136C23116yescomplemented
242#14579135C23116yescomplemented
243#14579135C23116yescomplemented
244#14579134C23116yes—
245#14579134C23116yes—
246#14579134C2318yes—
247#14579134C23116yescomplemented
248#14579134C23116yescomplemented
249#14579134C23116yescomplemented
250#14579134C23116yescomplemented
251#14579134C23116yescomplemented
252#14579134C23116yescomplemented
253#14579134C23116yescomplemented
254#14579133C23116yescomplemented
255#14579131C23116yes—
256#14579131C23116yescomplemented
257#14579131C23116yescomplemented
258#14579131C23116yescomplemented
259#14579131C23116yescomplemented
260#14579131C23116yescomplemented
261#14579131C23116yescomplemented
262#14579129C23116yes—
263C4×Dic158C2318yescomplemented
264#14579126C2318yescomplemented
265C4×D316C23116yescomplemented
266C4×D316C2318yescomplemented
267#14579123C2318yes—
268#14579123C2318yescomplemented
269#14579123C23116yescomplemented
270#14579123C2318yescomplemented
271C4×C22⋊D79C2318yes—
272C4×C22⋊D79C2318yescomplemented
273(C22⋊D79)⋊C4C23116yescomplemented
274(C22⋊D79)⋊C4C23116yescomplemented
275(C22⋊D79)⋊C4C23116yescomplemented
276#14579118C2318yescomplemented
277#14579118C23116yescomplemented
278C2×C4⋊Dic79C2312yes—
279C2×C4⋊Dic79C2311yescharacteristic
280C2×C4⋊Dic79C2311yescharacteristic
281C2×Dic79⋊C4C2311yescharacteristic
282C2×Dic79⋊C4C2312yes—
283C2×Dic79⋊C4C2311yescharacteristic
284C2×Dic79⋊C4C2311yescharacteristic
285C2×Dic79⋊C4C2311yescharacteristic
286C2×Dic79⋊C4C2311yescharacteristic
287C2×Dic79⋊C4C2312yes—
288C2×Dic79⋊C4C2312yes—
289C2×Dic79⋊C4C2311yescharacteristic
290C4⋊C4×D79C23116yescomplemented
291C2×C22⋊Dic79C2311yescharacteristic
292C2×C22⋊Dic79C2311yescharacteristic
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2311yescharacteristic
296C2×(C2×D79)⋊C4C2312yes—
297C2×(C2×D79)⋊C4C2312yes—
298C2×(C2×D79)⋊C4C2311yescharacteristic
299C2×(C2×D79)⋊C4C2312yes—
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2311yescharacteristic
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2312yes—
304C2×(C2×D79)⋊C4C2312yes—
305C2×(C2×D79)⋊C4C2311yescharacteristic
306C2×(C2×D79)⋊C4C2311yescharacteristic
307C2×(C2×D79)⋊C4C2312yes—
308C2×(C2×D79)⋊C4C2312yes—
309C2×(C2×D79)⋊C4C2312yes—
310C2×(C2×D79)⋊C4C2312yes—
311C2×(C2×D79)⋊C4C2311yescharacteristic
312C2×(C2×D79)⋊C4C23116yescomplemented
313C22⋊C4×D79C23116yescomplemented
314C2×C4×Dic79C2311yescharacteristic
315C2×C4×Dic79C2311yescharacteristic
316C2×C4×Dic79C2311yescharacteristic
317C2×C4×Dic79C2312yes—
318C2×C4×Dic79C2311yescharacteristic
319C42×D79C2318yescomplemented
320C22×Q8×C79C2311yescharacteristic
321C22×Q8×C79C2312yes—
322C22×D4×C79C2311yescharacteristic
323C22×D4×C79C2312yes—
324C23×C4×C79C2311yescharacteristic
325C23×C4×C79C2312yes—
326C4⋊Q8×C79C2318yescomplemented
327#126×C79C23116yescomplemented
328#124×C79C23116yescomplemented
329#124×C79C2318yescomplemented
330#123×C79C23116yescomplemented
331C22⋊Q8×C79C23116yescomplemented
332C22⋊Q8×C79C2318yescomplemented
333#121×C79C2318yes—
334C4×Q8×C79C2318yescomplemented
335C4×D4×C79C2318yescomplemented
336#117×C79C2318yescomplemented
337C2×C4⋊C4×C79C2311yescharacteristic
338C2×C4⋊C4×C79C2311yescharacteristic
339C2×C4⋊C4×C79C2311yescharacteristic
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C4⋊C4×C79C2312yes—
342C2×C4⋊C4×C79C2312yes—
343C2×C4⋊C4×C79C2312yes—
344C2×C22⋊C4×C79C2311yescharacteristic
345C2×C22⋊C4×C79C2311yescharacteristic
346C2×C22⋊C4×C79C2312yes—
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C22⋊C4×C79C2312yes—
350C2×C22⋊C4×C79C2312yes—
351C2×C42×C79C2311yescharacteristic
352C2×C42×C79C2311yescharacteristic
353C2×C42×C79C2312yes—
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79—44no—
358C23×D79—44no—
359C23×D79—44no—
360C23×D79C2411yescharacteristic
361C23×D79C2412yes—
362C23×D79C2412yes—
363C23×D79C2411yescharacteristic
364C23×D79C2412yes—
365C23×D79C2418yes—
366C23×D79C2418yes—
367#11929625—416no—
368#11929625—416no—
369#11929625—432no—
370#11929624—432no—
371#11929624—416no—
372#11929623—416no—
373C2×Dic158—24no—
374C2×Dic158—24no—
375C2×Dic158C2414yes—
376C2×Dic158C2414yes—
377C2×D316—24no—
378C2×D316—24no—
379C2×D316—24no—
380C2×D316—44no—
381C2×D316—44no—
382C2×D316—44no—
383C2×D316—44no—
384C2×D316—44no—
385C2×D316—44no—
386C2×D316—44no—
387C2×D316—44no—
388C2×D316—44no—
389C2×D316—42no—
390C2×D316—44no—
391C2×D316—416no—
392C2×D316C2414yes—
393C2×D316C2414yes—
394C2×D316C2414yes—
395C2×D316C2418yes—
396C2×D316C2418yes—
397C2×D316C2418yes—
398C2×D316C2418yes—
399C2×D316C2418yes—
400C2×D316C2418yes—
401C2×D316C2418yes—
402C2×D316C2414yes—
403C2×D316C2418yes—
404C2×D316C2418yes—
405C2×D316C2418yes—
406C2×C22⋊D79—28no—
407C2×C22⋊D79—24no—
408C2×C22⋊D79—44no—
409C2×C22⋊D79—44no—
410C2×C22⋊D79—44no—
411C2×C22⋊D79—44no—
412C2×C22⋊D79—42no—
413C2×C22⋊D79—44no—
414C2×C22⋊D79—44no—
415C2×C22⋊D79C2418yes—
416C2×C22⋊D79C2414yes—
417C2×C22⋊D79C2418yes—
418C2×C22⋊D79C2418yes—
419C2×C22⋊D79C2418yes—
420C2×C22⋊D79C2418yes—
421C2×C22⋊D79C2418yes—
422C2×C22⋊D79C2414yes—
423C2×C22⋊D79C2418yes—
424D4×D79—432no—
425D4×D79—416no—
426C22×Dic79—44no—
427C22×Dic79C2412yes—
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2411yescharacteristic
430C22×Dic79C2411yescharacteristic
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2411yescharacteristic
433C22×Dic79C2418yes—
434C22×Dic79C2411yescharacteristic
435C2×C4×D79—28no—
436C2×C4×D79—24no—
437C2×C4×D79—28no—
438C2×C4×D79—24no—
439C2×C4×D79—24no—
440C2×C4×D79—44no—
441C2×C4×D79—44no—
442C2×C4×D79—44no—
443C2×C4×D79—44no—
444C2×C4×D79—42no—
445C2×C4×D79C2414yes—
446C2×C4×D79C2418yes—
447C2×C4×D79C2414yes—
448C2×C4×D79C2414yes—
449C2×C4×D79C2418yes—
450C2×C4×D79C2418yes—
451C2×C4×D79C2418yes—
452C2×C4×D79C2418yes—
453C2×C4×D79C2418yes—
454C2×C4×D79C2414yes—
455C4⋊Dic79C2418yes—
456C4⋊Dic79C2414yes—
457C4⋊Dic79C2414yes—
458Dic79⋊C4C2414yes—
459Dic79⋊C4C2418yes—
460Dic79⋊C4C2414yes—
461Dic79⋊C4C2414yes—
462Dic79⋊C4C2414yes—
463Dic79⋊C4C2414yes—
464Dic79⋊C4C2418yes—
465Dic79⋊C4C2418yes—
466Dic79⋊C4C2414yes—
467C22⋊Dic79C2414yes—
468C22⋊Dic79C2414yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2418yes—
473(C2×D79)⋊C4C2418yes—
474(C2×D79)⋊C4C2414yes—
475(C2×D79)⋊C4C2418yes—
476(C2×D79)⋊C4C2418yes—
477(C2×D79)⋊C4C2414yes—
478(C2×D79)⋊C4C2418yes—
479(C2×D79)⋊C4C2418yes—
480(C2×D79)⋊C4C2418yes—
481(C2×D79)⋊C4C2414yes—
482(C2×D79)⋊C4C2414yes—
483(C2×D79)⋊C4C2418yes—
484(C2×D79)⋊C4C2418yes—
485(C2×D79)⋊C4C2418yes—
486(C2×D79)⋊C4C2418yes—
487(C2×D79)⋊C4C2414yes—
488C4×Dic79C2414yes—
489C4×Dic79C2414yes—
490C4×Dic79C2414yes—
491C4×Dic79C2418yes—
492C4×Dic79C2414yes—
493C24×C79C2411yescharacteristic
494C24×C79C2412yes—
495C2×Q8×C79—24no—
496C2×Q8×C79—44no—
497C2×Q8×C79C2414yes—
498C2×Q8×C79C2418yes—
499C2×D4×C79—24no—
500C2×D4×C79—44no—
501C2×D4×C79C2414yes—
502C2×D4×C79C2418yes—
503C22×C4×C79—24no—
504C22×C4×C79—44no—
505C22×C4×C79C2411yescharacteristic
506C22×C4×C79C2414yes—
507C22×C4×C79C2411yescharacteristic
508C22×C4×C79C2411yescharacteristic
509C22×C4×C79C2412yes—
510C22×C4×C79C2411yescharacteristic
511C22×C4×C79C2412yes—
512C22×C4×C79C2411yescharacteristic
513C22×C4×C79C2412yes—
514C22×C4×C79C2418yes—
515C22×C4×C79C2411yescharacteristic
516C4⋊C4×C79C2414yes—
517C4⋊C4×C79C2414yes—
518C4⋊C4×C79C2414yes—
519C4⋊C4×C79C2414yes—
520C4⋊C4×C79C2418yes—
521C4⋊C4×C79C2418yes—
522C4⋊C4×C79C2418yes—
523C22⋊C4×C79C2414yes—
524C22⋊C4×C79C2414yes—
525C22⋊C4×C79C2418yes—
526C22⋊C4×C79C2418yes—
527C22⋊C4×C79C2418yes—
528C22⋊C4×C79C2418yes—
529C22⋊C4×C79C2418yes—
530C42×C79C2414yes—
531C42×C79C2414yes—
532C42×C79C2418yes—
533C23×C79—24no—
534C23×C79—24no—
535C23×C79—22no—
536C23×C79—22no—
537C23×C79—24no—
538C23×C79—22no—
539C23×C79C2512yes—
540C23×C79C2514yes—
541C23×C79C2511yescharacteristic
542C22×D79—22no—
543C22×D79—24no—
544C22×D79—22no—
545C22×D79—24no—
546C22×D79—22no—
547C22×D79—24no—
548C22×D79—24no—
549C22×D79—24no—
550C22×D79—22no—
551C22×D79—24no—
552C22×D79—22no—
553C22×D79—24no—
554C22×D79—24no—
555C22×D79—22no—
556C22×D79—24no—
557C22×D79—48no—
558C22×D79—48no—
559C22×D79—48no—
560C22×D79—48no—
561C22×D79—48no—
562C22×D79—48no—
563C22×D79—816no—
564C22×D79—816no—
565C22×D79C2512yes—
566C22×D79C2514yes—
567C22×D79C2514yes—
568C22×D79C2512yes—
569C22×D79C2514yes—
570Q8×C79—28no—
571Q8×C79—48no—
572D4×C79—28no—
573D4×C79—48no—
574C2×C4×C79—24no—
575C2×C4×C79—24no—
576C2×C4×C79—22no—
577C2×C4×C79—22no—
578C2×C4×C79—24no—
579C2×C4×C79—22no—
580C2×C4×C79—22no—
581C2×C4×C79—22no—
582C2×C4×C79—28no—
583C2×C4×C79—48no—
584C2×C4×C79H(5,𝔽2)14yes—
585C2×C4×C79C2512yes—
586C2×C4×C79C2512yes—
587C2×C4×C79C2514yes—
588C2×C4×C79C2514yes—
589C2×C4×C79C2512yes—
590C2×C4×C79C2512yes—
591C2×C4×C79C2514yes—
592C2×C4×C79C2512yes—
593C2×C4×C79C2512yes—
594C22⋊D79—28no—
595C22⋊D79—216no—
596C22⋊D79—48no—
597C22⋊D79—44no—
598C22⋊D79—48no—
599C22⋊D79—48no—
600C22⋊D79—48no—
601C22⋊D79—48no—
602C22⋊D79—48no—
603C2×Dic79—22no—
604C2×Dic79—22no—
605C2×Dic79—22no—
606C2×Dic79—24no—
607C2×Dic79—22no—
608C2×Dic79—22no—
609C2×Dic79—48no—
610C2×Dic79H(5,𝔽2)14yes—
611C2×Dic79C2512yes—
612C2×Dic79C2512yes—
613C2×Dic79C2512yes—
614C2×Dic79C2514yes—
615C2×Dic79C2512yes—
616C2×Dic79C2512yes—
617C2×Dic79C2512yes—
618D316—28no—
619D316—28no—
620D316—28no—
621D316—48no—
622D316—48no—
623D316—48no—
624D316—48no—
625D316—44no—
626D316—48no—
627D316—48no—
628D316—48no—
629D316—48no—
630D316—48no—
631D316—48no—
632C4×D79—28no—
633C4×D79—28no—
634C4×D79—216no—
635C4×D79—216no—
636C4×D79—28no—
637C4×D79—44no—
638C4×D79—48no—
639C4×D79—48no—
640C4×D79—48no—
641C4×D79—48no—
642Dic158—28no—
643Dic158—28no—
644C22×C79—24no—
645C22×C79—22no—
646C22×C79—22no—
647C22×C79—24no—
648C22×C79—24no—
649C22×C79—22no—
650C22×C79—44no—
651C22×C79—48no—
652C22×C79C2×H(5,𝔽2)12yes—
653C22×C79C2×H(5,𝔽2)12yes—
654C22×C79#58512yes—
655C22×C79C2611yescharacteristic
656C2×D79—22no—
657C2×D79—24no—
658C2×D79—22no—
659C2×D79—24no—
660C2×D79—24no—
661C2×D79—24no—
662C2×D79—24no—
663C2×D79—22no—
664C2×D79—24no—
665C2×D79—22no—
666C2×D79—24no—
667C2×D79—22no—
668C2×D79—24no—
669C2×D79—22no—
670C2×D79—24no—
671C2×D79—44no—
672C2×D79—48no—
673C2×D79—48no—
674C2×D79—44no—
675C2×D79—48no—
676C2×D79—816no—
677C2×D79—816no—
678C4×C79—22no—
679C4×C79—22no—
680C4×C79—24no—
681C4×C79—24no—
682C4×C79—24no—
683C4×C79—22no—
684C4×C79—22no—
685C4×C79—22no—
686C4×C79C2×H(5,𝔽2)14yes—
687Dic79—22no—
688Dic79—24no—
689Dic79—22no—
690Dic79—22no—
691Dic79—22no—
692Dic79—22no—
693Dic79C2×H(5,𝔽2)14yes—
694C2×#3546—791nomaximal, Sylow
695C2×C79—42no—
696C2×C79—44no—
697C2×C79#354614yescomplemented
698C2×C79C22×H(5,𝔽2)11yescharacteristic
699C2×C79C22×H(5,𝔽2)11yescharacteristic
700C2×C79C2×#58511yescharacteristic
701D79—42no—
702D79—44no—
703D79—44no—
704D79—42no—
705D79—44no—
706#3546—7932no—
707C2×#560—792no—
708C2×#560—792no—
709C2×#556—791no—
710C2×#553—792no—
711C2×#550—791no—
712C2×#550—791no—
713C2×#550—791no—
714C2×#547—791no—
715C2×#546—792no—
716C2×#546—791no—
717C2×#546—791no—
718C2×D42—791no—
719C2×#542—791no—
720C2×#542D7911yescharacteristic, complemented
721C2×#538—792no—
722C2×#538—792no—
723C2×#537—792no—
724C2×#535—791no—
725C2×#535—792no—
726C2×#535—791no—
727C2×#532—791no—
728C2×#532—791no—
729C2×#529—791no—
730C79C2×#354611yescharacteristic, complemented, Sylow
731C22×#41—792no—
732C22×#41—791no—
733C22×#41—791no—
734C22×#41—791no—
735C22×#41—791no—
736C22×#41—792no—
737C23×D4—791no—
738C23×D4—792no—
739C23×D4—791no—
740#560—7932no—
741#560—7932no—
742#556—7916no—
743#553—7932no—
744#550—7916no—
745#550—7916no—
746#550—7916no—
747#547—7916no—
748#546—7932no—
749#546—7916no—
750#546—7916no—
751D42—7916no—
752#542—7916no—
753#542C2×D79116yescomplemented
754#538—7932no—
755#538—7932no—
756#537—7932no—
757#535—7916no—
758#535—7932no—
759#535—7916no—
760#532—7916no—
761#532—7916no—
762C2×C4⋊Q8—791no—
763C2×C4⋊Q8C2×D7911yescharacteristic, complemented
764C2×#127—791no—
765C2×#127—791no—
766C2×#127—792no—
767C2×#127—791no—
768C2×#127—791no—
769C2×#127—792no—
770#529—7916no—
771C2×#126—791no—
772C2×#126—792no—
773C2×#126—792no—
774C2×#126—791no—
775C2×#126—792no—
776C2×#126C2×D7912yescomplemented
777C2×#125—791no—
778C2×#124—792no—
779C2×#124—792no—
780C2×#124—791no—
781C2×#124—791no—
782C2×#124—791no—
783C2×#124—791no—
784C2×#124C2×D7911yescharacteristic, complemented
785C2×#124C2×D7912yescomplemented
786C2×#123—791no—
787C2×#123—792no—
788C2×#123—792no—
789C2×#123—792no—
790C2×#123—791no—
791C2×#123—792no—
792C2×#123—792no—
793C2×#123C2×D7912yescomplemented
794C2×C22⋊Q8—792no—
795C2×C22⋊Q8—791no—
796C2×C22⋊Q8—792no—
797C2×C22⋊Q8—791no—
798C2×C22⋊Q8C2×D7912yescomplemented
799C2×C22⋊Q8C2×D7911yescharacteristic, complemented
800C2×#121—792no—
801C2×#121—792no—
802C2×#121—792no—
803C2×#121—791no—
804C2×#121—791no—
805C2×#121—792no—
806C2×#121—792no—
807C2×#121—792no—
808C2×#121—792no—
809C2×#121—792no—
810C2×#121—792no—
811C2×#121—791no—
812C2×#121—791no—
813C2×#121—792no—
814C2×#121—792no—
815C2×#121—792no—
816C2×#121—792no—
817C2×#121—792no—
818C2×#121—792no—
819C2×#121—792no—
820C2×#121—792no—
821C2×#121—792no—
822C2×#121C2×D7911yescharacteristic
823C2×#120—792no—
824C2×#120—792no—
825C2×#120—792no—
826C2×#120—792no—
827C2×#120—792no—
828C2×#120—792no—
829C2×#120—792no—
830C2×#120—792no—
831C2×C4×Q8—791no—
832C2×C4×Q8—791no—
833C2×C4×Q8C2×D7911yescharacteristic, complemented
834C2×C4×D4—791no—
835C2×C4×D4—791no—
836C2×C4×D4—791no—
837C2×C4×D4—792no—
838C2×C4×D4—791no—
839C2×C4×D4—791no—
840C2×C4×D4—792no—
841C2×C4×D4—792no—
842C2×C4×D4—792no—
843C2×C4×D4—791no—
844C2×C4×D4—792no—
845C2×C4×D4C2×D7911yescharacteristic, complemented
846C2×#117—791no—
847C2×#117—792no—
848C2×#117C2×D7911yescharacteristic, complemented
849C22×C4⋊C4—792no—
850C22×C22⋊C4—792no—
851C22×C22⋊C4—792no—
852C22×C42—791no—
853C25—792no—
854C25—792no—
855C2×#41—3164no—
856C2×#41—3168no—
857C2×#41—3164no—
858C2×#41—3164no—
859C2×#41—3164no—
860C2×#41—3168no—
861C2×#41—7916no—
862C2×#41—798no—
863C2×#41—798no—
864C2×#41—798no—
865C2×#41—798no—
866C2×#41—7916no—
867C22×Q8—791no—
868C22×Q8—791no—
869C22×Q8C22×D7911yescharacteristic
870C22×Q8C22×D7912yes—
871C22×D4—3164no—
872C22×D4—3164no—
873C22×D4—3168no—
874C22×D4—792no—
875C22×D4—791no—
876C22×D4—792no—
877C22×D4—792no—
878C22×D4—792no—
879C22×D4—792no—
880C22×D4—792no—
881C22×D4—798no—
882C22×D4—7916no—
883C22×D4—791no—
884C22×D4—792no—
885C22×D4—792no—
886C22×D4—791no—
887C22×D4—792no—
888C22×D4—792no—
889C22×D4—792no—
890C22×D4—792no—
891C22×D4—792no—
892C22×D4—792no—
893C22×D4—792no—
894C22×D4—792no—
895C22×D4—792no—
896C22×D4—798no—
897C22×D4—791no—
898C22×D4—791no—
899C22×D4—791no—
900C22×D4C22×D7911yescharacteristic
901C22×D4C22×D7912yes—
902C23×C4—792no—
903C23×C4—792no—
904C23×C4—792no—
905C23×C4—792no—
906C23×C4—792no—
907C23×C4—791no—
908C23×C4—792no—
909C23×C4—792no—
910C23×C4—791no—
911C23×C4—791no—
912C23×C4—791no—
913C23×C4C22×D7911yescharacteristic
914C23×C4C22×D7912yes—
915C4⋊Q8—798no—
916C4⋊Q8C22×D7918yescomplemented
917#127—798no—
918#127—798no—
919#127—7916no—
920#127—798no—
921#127—798no—
922#127—7916no—
923#126—798no—
924#126—7916no—
925#126—7916no—
926#126—798no—
927#126—7916no—
928#126C22×D79116yescomplemented
929#125—798no—
930#124—7916no—
931#124—7916no—
932#124—798no—
933#124—798no—
934#124—798no—
935#124—798no—
936#124C22×D7918yescomplemented
937#124C22×D79116yescomplemented
938#123—798no—
939#123—7916no—
940#123—7916no—
941#123—7916no—
942#123—798no—
943#123—7916no—
944#123—7916no—
945#123C22×D79116yescomplemented
946C22⋊Q8—7916no—
947C22⋊Q8—798no—
948C22⋊Q8—7916no—
949C22⋊Q8—798no—
950C22⋊Q8C22×D79116yescomplemented
951C22⋊Q8C22×D7918yescomplemented
952#121—7916no—
953#121—7916no—
954#121—7916no—
955#121—798no—
956#121—798no—
957#121—7916no—
958#121—7916no—
959#121—7916no—
960#121—7916no—
961#121—7916no—
962#121—7916no—
963#121—798no—
964#121—798no—
965#121—7916no—
966#121—7916no—
967#121—7916no—
968#121—7916no—
969#121—7916no—
970#121—7916no—
971#121—7916no—
972#121—7916no—
973#121—7916no—
974#121C22×D7918yes—
975#120—7916no—
976#120—7916no—
977#120—7916no—
978#120—7916no—
979#120—7916no—
980#120—7916no—
981#120—7916no—
982#120—7916no—
983C4×Q8—798no—
984C4×Q8—798no—
985C4×Q8C22×D7918yescomplemented
986C4×D4—798no—
987C4×D4—798no—
988C4×D4—798no—
989C4×D4—7916no—
990C4×D4—798no—
991C4×D4—798no—
992C4×D4—7916no—
993C4×D4—7916no—
994C4×D4—7916no—
995C4×D4—798no—
996C4×D4—7916no—
997C4×D4C22×D7918yescomplemented
998#117—798no—
999#117—7916no—
1000#117C22×D7918yescomplemented
1001C2×C4⋊C4—791no—
1002C2×C4⋊C4—792no—
1003C2×C4⋊C4—792no—
1004C2×C4⋊C4—791no—
1005C2×C4⋊C4—791no—
1006C2×C4⋊C4—791no—
1007C2×C4⋊C4—791no—
1008C2×C4⋊C4—791no—
1009C2×C4⋊C4—792no—
1010C2×C4⋊C4—792no—
1011C2×C4⋊C4—791no—
1012C2×C4⋊C4—791no—
1013C2×C4⋊C4—7916no—
1014C2×C4⋊C4C22×D7912yes—
1015C2×C4⋊C4C22×D7911yescharacteristic
1016C2×C4⋊C4C22×D7911yescharacteristic
1017C2×C4⋊C4C22×D7911yescharacteristic
1018C2×C4⋊C4C22×D7911yescharacteristic
1019C2×C4⋊C4C22×D7912yes—
1020C2×C4⋊C4C22×D7912yes—
1021C2×C22⋊C4—791no—
1022C2×C22⋊C4—791no—
1023C2×C22⋊C4—791no—
1024C2×C22⋊C4—792no—
1025C2×C22⋊C4—792no—
1026C2×C22⋊C4—792no—
1027C2×C22⋊C4—792no—
1028C2×C22⋊C4—7916no—
1029C2×C22⋊C4—792no—
1030C2×C22⋊C4—792no—
1031C2×C22⋊C4—791no—
1032C2×C22⋊C4—791no—
1033C2×C22⋊C4—792no—
1034C2×C22⋊C4—792no—
1035C2×C22⋊C4—791no—
1036C2×C22⋊C4—792no—
1037C2×C22⋊C4—792no—
1038C2×C22⋊C4—792no—
1039C2×C22⋊C4—792no—
1040C2×C22⋊C4—791no—
1041C2×C22⋊C4—791no—
1042C2×C22⋊C4—792no—
1043C2×C22⋊C4—7916no—
1044C2×C22⋊C4C22×D7912yes—
1045C2×C22⋊C4C22×D7911yescharacteristic
1046C2×C22⋊C4C22×D7911yescharacteristic
1047C2×C22⋊C4C22×D7912yes—
1048C2×C22⋊C4C22×D7912yes—
1049C2×C22⋊C4C22×D7912yes—
1050C2×C22⋊C4C22×D7912yes—
1051C2×C42—791no—
1052C2×C42—792no—
1053C2×C42—791no—
1054C2×C42—791no—
1055C2×C42—791no—
1056C2×C42—798no—
1057C2×C42C22×D7911yescharacteristic
1058C2×C42C22×D7912yes—
1059C2×C42C22×D7911yescharacteristic
1060C24—3164no—
1061C24—3164no—
1062C24—3164no—
1063C24—3164no—
1064C24—3164no—
1065C24—3164no—
1066C24—798no—
1067C24—798no—
1068C24—792no—
1069C24—791no—
1070C24—792no—
1071C24—792no—
1072C24—791no—
1073C24C23×D7911yescharacteristic
1074C24C23×D7912yes—
1075#41—31616no—
1076#41—31632no—
1077#41—31616no—
1078#41—31616no—
1079#41—31616no—
1080#41—31632no—
1081C2×Q8—24no—
1082C2×Q8—44no—
1083C2×Q8—794no—
1084C2×Q8—794no—
1085C2×Q8—1584no—
1086C2×Q8—1584no—
1087C2×Q8C23×D7914yes—
1088C2×Q8C23×D7918yes—
1089C2×D4—24no—
1090C2×D4—44no—
1091C2×D4—3164no—
1092C2×D4—3164no—
1093C2×D4—3164no—
1094C2×D4—3162no—
1095C2×D4—3164no—
1096C2×D4—3164no—
1097C2×D4—3164no—
1098C2×D4—3164no—
1099C2×D4—3164no—
1100C2×D4—3164no—
1101C2×D4—3164no—
1102C2×D4—31616no—
1103C2×D4—31616no—
1104C2×D4—31632no—
1105C2×D4—3164no—
1106C2×D4—3164no—
1107C2×D4—3164no—
1108C2×D4—3162no—
1109C2×D4—3164no—
1110C2×D4—3164no—
1111C2×D4—3164no—
1112C2×D4—798no—
1113C2×D4—794no—
1114C2×D4—798no—
1115C2×D4—798no—
1116C2×D4—798no—
1117C2×D4—798no—
1118C2×D4—798no—
1119C2×D4—794no—
1120C2×D4—798no—
1121C2×D4—798no—
1122C2×D4—794no—
1123C2×D4—798no—
1124C2×D4—798no—
1125C2×D4—798no—
1126C2×D4—798no—
1127C2×D4—798no—
1128C2×D4—798no—
1129C2×D4—798no—
1130C2×D4—798no—
1131C2×D4—798no—
1132C2×D4—794no—
1133C2×D4—794no—
1134C2×D4—794no—
1135C2×D4—1584no—
1136C2×D4—1588no—
1137C2×D4—1584no—
1138C2×D4—1584no—
1139C2×D4—1584no—
1140C2×D4C23×D7914yes—
1141C2×D4C23×D7918yes—
1142C22×C4—24no—
1143C22×C4—44no—
1144C22×C4—3162no—
1145C22×C4—3164no—
1146C22×C4—3164no—
1147C22×C4—3164no—
1148C22×C4—3164no—
1149C22×C4—3164no—
1150C22×C4—798no—
1151C22×C4—794no—
1152C22×C4—798no—
1153C22×C4—798no—
1154C22×C4—798no—
1155C22×C4—798no—
1156C22×C4—791no—
1157C22×C4—791no—
1158C22×C4—791no—
1159C22×C4—791no—
1160C22×C4—791no—
1161C22×C4—792no—
1162C22×C4—791no—
1163C22×C4—794no—
1164C22×C4—794no—
1165C22×C4—798no—
1166C22×C4—798no—
1167C22×C4—794no—
1168C22×C4—1588no—
1169C22×C4—1588no—
1170C22×C4—1584no—
1171C22×C4—1584no—
1172C22×C4—1584no—
1173C22×C4C23×D7914yes—
1174C22×C4C23×D7911yescharacteristic
1175C22×C4C23×D7911yescharacteristic
1176C22×C4C23×D7912yes—
1177C22×C4C23×D7911yescharacteristic
1178C22×C4C23×D7911yescharacteristic
1179C22×C4C23×D7912yes—
1180C22×C4C23×D7912yes—
1181C22×C4C23×D7911yescharacteristic
1182C22×C4C23×D7918yes—
1183C22×C4C23×D7911yescharacteristic
1184C4⋊C4—794no—
1185C4⋊C4—798no—
1186C4⋊C4—794no—
1187C4⋊C4—794no—
1188C4⋊C4—794no—
1189C4⋊C4—794no—
1190C4⋊C4—798no—
1191C4⋊C4—798no—
1192C4⋊C4—794no—
1193C4⋊C4—798no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4C23×D7918yes—
1197C4⋊C4C23×D7914yes—
1198C4⋊C4C23×D7914yes—
1199C4⋊C4C23×D7914yes—
1200C4⋊C4C23×D7914yes—
1201C4⋊C4C23×D7918yes—
1202C4⋊C4C23×D7918yes—
1203C22⋊C4—794no—
1204C22⋊C4—794no—
1205C22⋊C4—794no—
1206C22⋊C4—798no—
1207C22⋊C4—798no—
1208C22⋊C4—798no—
1209C22⋊C4—798no—
1210C22⋊C4—798no—
1211C22⋊C4—798no—
1212C22⋊C4—794no—
1213C22⋊C4—794no—
1214C22⋊C4—798no—
1215C22⋊C4—798no—
1216C22⋊C4—794no—
1217C22⋊C4—798no—
1218C22⋊C4—798no—
1219C22⋊C4—798no—
1220C22⋊C4—798no—
1221C22⋊C4—794no—
1222C22⋊C4—794no—
1223C22⋊C4—798no—
1224C22⋊C4C23×D7918yes—
1225C22⋊C4C23×D7914yes—
1226C22⋊C4C23×D7914yes—
1227C22⋊C4C23×D7918yes—
1228C22⋊C4C23×D7918yes—
1229C22⋊C4C23×D7918yes—
1230C22⋊C4C23×D7918yes—
1231C42—794no—
1232C42—794no—
1233C42—794no—
1234C42—794no—
1235C42—798no—
1236C42C23×D7914yes—
1237C42C23×D7918yes—
1238C42C23×D7914yes—
1239C23—24no—
1240C23—22no—
1241C23—22no—
1242C23—24no—
1243C23—24no—
1244C23—22no—
1245C23—3168no—
1246C23—3168no—
1247C23—3168no—
1248C23—3168no—
1249C23—3168no—
1250C23—3168no—
1251C23—794no—
1252C23—792no—
1253C23—794no—
1254C23—794no—
1255C23—792no—
1256C23—63216no—
1257C23—63216no—
1258C23—1584no—
1259C23—1584no—
1260C23—1582no—
1261C23—1584no—
1262C23—1582no—
1263C23—1584no—
1264C23—1584no—
1265C23—1582no—
1266C23—1582no—
1267C23—1584no—
1268C23—1582no—
1269C23—1584no—
1270C23—1584no—
1271C23—1584no—
1272C23—1582no—
1273C23C24×D7912yes—
1274C23C24×D7914yes—
1275C23C24×D7911yescharacteristic
1276Q8—28no—
1277Q8—48no—
1278Q8—1588no—
1279Q8—1588no—
1280D4—28no—
1281D4—48no—
1282D4—3168no—
1283D4—3168no—
1284D4—3168no—
1285D4—3168no—
1286D4—3168no—
1287D4—3168no—
1288D4—3168no—
1289D4—3168no—
1290D4—3168no—
1291D4—3164no—
1292D4—3168no—
1293D4—3168no—
1294D4—3168no—
1295D4—3168no—
1296D4—3164no—
1297D4—3168no—
1298D4—3168no—
1299D4—3168no—
1300D4—1588no—
1301D4—15816no—
1302D4—1588no—
1303D4—1588no—
1304D4—1588no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—28no—
1314C2×C4—48no—
1315C2×C4—3168no—
1316C2×C4—3168no—
1317C2×C4—3168no—
1318C2×C4—3168no—
1319C2×C4—3164no—
1320C2×C4—3168no—
1321C2×C4—794no—
1322C2×C4—792no—
1323C2×C4—792no—
1324C2×C4—792no—
1325C2×C4—792no—
1326C2×C4—792no—
1327C2×C4—794no—
1328C2×C4—792no—
1329C2×C4—15816no—
1330C2×C4—15816no—
1331C2×C4—1588no—
1332C2×C4—1582no—
1333C2×C4—1582no—
1334C2×C4—1582no—
1335C2×C4—1584no—
1336C2×C4—1582no—
1337C2×C4—1582no—
1338C2×C4—1588no—
1339C2×C4—1588no—
1340C2×C4#1457920714yes—
1341C2×C4C24×D7912yes—
1342C2×C4C24×D7912yes—
1343C2×C4C24×D7914yes—
1344C2×C4C24×D7912yes—
1345C2×C4C24×D7912yes—
1346C2×C4C24×D7914yes—
1347C2×C4C24×D7914yes—
1348C2×C4C24×D7912yes—
1349C2×C4C24×D7912yes—
1350C22—24no—
1351C22—22no—
1352C22—22no—
1353C22—24no—
1354C22—24no—
1355C22—22no—
1356C22—44no—
1357C22—48no—
1358C22—3168no—
1359C22—3164no—
1360C22—3168no—
1361C22—3168no—
1362C22—3164no—
1363C22—63216no—
1364C22—63216no—
1365C22—1584no—
1366C22—1582no—
1367C22—1584no—
1368C22—1584no—
1369C22—1582no—
1370C22—1584no—
1371C22—1584no—
1372C22—1582no—
1373C22—1582no—
1374C22—1584no—
1375C22—1582no—
1376C22—1584no—
1377C22—1584no—
1378C22—1584no—
1379C22—1582no—
1380C22H(5,𝔽2)×D7912yes—
1381C22C2×#1457920712yes—
1382C22#1909940012yes—
1383C22C25×D7911yescharacteristic
1384C4—22no—
1385C4—24no—
1386C4—24no—
1387C4—22no—
1388C4—22no—
1389C4—24no—
1390C4—22no—
1391C4—22no—
1392C4—794no—
1393C4—1582no—
1394C4—1582no—
1395C4—1582no—
1396C4—1584no—
1397C4—1582no—
1398C4—1582no—
1399C4C2×#1457920714yes—
1400C2—42no—
1401C2—44no—
1402C2—3164no—
1403C2—3162no—
1404C2—3164no—
1405C2—3164no—
1406C2—3162no—
1407C2#2377776914yesdirect product factor
1408C2C2×H(5,𝔽2)×D7911yescharacteristic
1409C2C22×#1457920711yescharacteristic
1410C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#542×C79C2
socleC23×C79C25
hypercenterC2×#542D79
hypocenterC79C2×#3546
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #23777769C2direct (N × H)
2. C2×#19099304C2semidirect
3. C2×#19099303C2semidirect
4. C2×#19099285C2semidirect
5. C2×#19099264C2semidirect
6. C2×#19099235C2semidirect
7. C2×#19099234C2semidirect
8. C2×#19099231C2semidirect
9. C2×#19099215C2semidirect
10. C2×#19099208C2semidirect
11. C2×#19099205C2semidirect
12. C2×#19099204C2semidirect
13. C2×#19099197C2semidirect
14. C2×#19099187C2semidirect
15. C2×#19099153C2semidirect
16. C2×#19099147C2semidirect
17. C2×#19099143C2semidirect
18. C2×#19099132C2semidirect
19. C2×#19099131C2semidirect
20. C2×#19099131C2semidirect
21. C2×#19099114C2semidirect
22. C2×#19099112C2semidirect
23. C2×#19099091C2semidirect
24. C2×#542×C79C2semidirect
25. C22×#11929625C22semidirect
26. C22×#11929625C22semidirect
27. C22×#11929625C22semidirect
28. C22×#11929624C22semidirect
29. C22×#11929624C22semidirect
30. C22×#11929623C22semidirect
34. #19099304C22semidirect
35. #19099303C22semidirect
36. #19099285C22semidirect
37. #19099264C22semidirect
38. #19099235C22semidirect
39. #19099234C22semidirect
40. #19099231C22semidirect
41. #19099215C22semidirect
42. #19099208C22semidirect
43. #19099205C22semidirect
44. #19099204C22semidirect
45. #19099197C22semidirect
46. #19099187C22semidirect
47. #19099153C22semidirect
48. #19099147C22semidirect
49. #19099143C22semidirect
50. #19099132C22semidirect
51. #19099131C22semidirect
52. #19099131C22semidirect
53. #19099114C22semidirect
54. #19099112C22semidirect
55. C2×#14579159C22semidirect
57. C2×#14579158C22semidirect
58. C2×#14579158C22semidirect
60. C2×#14579157C22semidirect
61. C2×#14579157C22semidirect
62. #19099091C22semidirect
63. C2×#14579156C22semidirect
64. C2×#14579156C22semidirect
65. C2×#14579156C22semidirect
66. C2×#14579155C22semidirect
67. C2×#14579154C22semidirect
68. C2×#14579151C22semidirect
70. C2×#14579150C22semidirect
71. C2×#14579150C22semidirect
73. C2×#14579149C22semidirect
75. C2×#14579146C22semidirect
76. C2×#14579146C22semidirect
77. C2×#14579146C22semidirect
78. C2×#14579146C22semidirect
79. C2×#14579145C22semidirect
80. C2×#14579143C22semidirect
81. C2×#14579143C22semidirect
82. C2×#14579141C22semidirect
83. C2×#14579139C22semidirect
84. C2×#14579139C22semidirect
85. C2×#14579137C22semidirect
88. C2×#14579136C22semidirect
89. C2×#14579136C22semidirect
90. C2×#14579136C22semidirect
91. C2×#14579136C22semidirect
92. C2×#14579136C22semidirect
93. C2×#14579136C22semidirect
94. C2×#14579136C22semidirect
95. C2×#14579135C22semidirect
96. C2×#14579135C22semidirect
100. C2×#14579134C22semidirect
101. C2×#14579134C22semidirect
102. C2×#14579134C22semidirect
103. C2×#14579134C22semidirect
104. C2×#14579134C22semidirect
105. C2×#14579134C22semidirect
106. C2×#14579134C22semidirect
107. C2×#14579133C22semidirect
109. C2×#14579131C22semidirect
110. C2×#14579131C22semidirect
111. C2×#14579131C22semidirect
112. C2×#14579131C22semidirect
113. C2×#14579131C22semidirect
114. C2×#14579131C22semidirect
116. C2×C4×Dic158C22semidirect
117. C2×#14579126C22semidirect
118. C2×C4×D316C22semidirect
119. C2×C4×D316C22semidirect
121. C2×#14579123C22semidirect
122. C2×#14579123C22semidirect
123. C2×#14579123C22semidirect
125. C2×C4×C22⋊D79C22semidirect
126. C2×(C22⋊D79)⋊C4C22semidirect
127. C2×(C22⋊D79)⋊C4C22semidirect
128. C2×(C22⋊D79)⋊C4C22semidirect
129. C2×#14579118C22semidirect
130. C2×#14579118C22semidirect
131. C2×C4⋊C4×D79C22semidirect
132. C22×(C2×D79)⋊C4C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. #542×C79C22semidirect
136. C2×C4⋊Q8×C79C22semidirect
137. C2×#126×C79C22semidirect
138. C2×#124×C79C22semidirect
139. C2×#124×C79C22semidirect
140. C2×#123×C79C22semidirect
141. C2×C22⋊Q8×C79C22semidirect
142. C2×C22⋊Q8×C79C22semidirect
144. C2×C4×Q8×C79C22semidirect
145. C2×C4×D4×C79C22semidirect
146. C2×#117×C79C22semidirect
152. C2×#11929625C23semidirect
153. C2×#11929625C23semidirect
154. C2×#11929625C23semidirect
157. C2×#11929624C23semidirect
158. C2×#11929624C23semidirect
160. C2×#11929623C23semidirect
203. #14579159C23semidirect
205. #14579158C23semidirect
206. #14579158C23semidirect
208. #14579157C23semidirect
209. #14579157C23semidirect
210. #14579156C23semidirect
211. #14579156C23semidirect
212. #14579156C23semidirect
213. #14579155C23semidirect
214. #14579154C23semidirect
215. #14579151C23semidirect
217. #14579150C23semidirect
218. #14579150C23semidirect
220. #14579149C23semidirect
222. #14579146C23semidirect
223. #14579146C23semidirect
224. #14579146C23semidirect
225. #14579146C23semidirect
226. #14579145C23semidirect
227. #14579143C23semidirect
228. #14579143C23semidirect
229. #14579141C23semidirect
230. #14579139C23semidirect
231. #14579139C23semidirect
232. #14579137C23semidirect
235. #14579136C23semidirect
236. #14579136C23semidirect
237. #14579136C23semidirect
238. #14579136C23semidirect
239. #14579136C23semidirect
240. #14579136C23semidirect
241. #14579136C23semidirect
242. #14579135C23semidirect
243. #14579135C23semidirect
247. #14579134C23semidirect
248. #14579134C23semidirect
249. #14579134C23semidirect
250. #14579134C23semidirect
251. #14579134C23semidirect
252. #14579134C23semidirect
253. #14579134C23semidirect
254. #14579133C23semidirect
256. #14579131C23semidirect
257. #14579131C23semidirect
258. #14579131C23semidirect
259. #14579131C23semidirect
260. #14579131C23semidirect
261. #14579131C23semidirect
263. C4×Dic158C23semidirect
264. #14579126C23semidirect
265. C4×D316C23semidirect
266. C4×D316C23semidirect
268. #14579123C23semidirect
269. #14579123C23semidirect
270. #14579123C23semidirect
272. C4×C22⋊D79C23semidirect
273. (C22⋊D79)⋊C4C23semidirect
274. (C22⋊D79)⋊C4C23semidirect
275. (C22⋊D79)⋊C4C23semidirect
276. #14579118C23semidirect
277. #14579118C23semidirect
290. C4⋊C4×D79C23semidirect
312. C2×(C2×D79)⋊C4C23semidirect
313. C22⋊C4×D79C23semidirect
319. C42×D79C23semidirect
326. C4⋊Q8×C79C23semidirect
327. #126×C79C23semidirect
328. #124×C79C23semidirect
329. #124×C79C23semidirect
330. #123×C79C23semidirect
331. C22⋊Q8×C79C23semidirect
332. C22⋊Q8×C79C23semidirect
334. C4×Q8×C79C23semidirect
335. C4×D4×C79C23semidirect
336. #117×C79C23semidirect
697. C2×C79#3546semidirect
720. C2×#542D79semidirect
730. C79C2×#3546semidirect
753. #542C2×D79semidirect
763. C2×C4⋊Q8C2×D79semidirect
776. C2×#126C2×D79semidirect
784. C2×#124C2×D79semidirect
785. C2×#124C2×D79semidirect
793. C2×#123C2×D79semidirect
798. C2×C22⋊Q8C2×D79semidirect
799. C2×C22⋊Q8C2×D79semidirect
833. C2×C4×Q8C2×D79semidirect
845. C2×C4×D4C2×D79semidirect
848. C2×#117C2×D79semidirect
916. C4⋊Q8C22×D79semidirect
928. #126C22×D79semidirect
936. #124C22×D79semidirect
937. #124C22×D79semidirect
945. #123C22×D79semidirect
950. C22⋊Q8C22×D79semidirect
951. C22⋊Q8C22×D79semidirect
985. C4×Q8C22×D79semidirect
997. C4×D4C22×D79semidirect
1000. #117C22×D79semidirect
1407. C2#23777769direct (N × H)

Maximal subgroups

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

subgroupindex
#237777692
C2×#190993042
C2×#190993032
C2×#190992852
C2×#190992642
C2×#190992352
C2×#190992342
C2×#190992312
C2×#190992152
C2×#190992082
C2×#190992052
C2×#190992042
C2×#190991972
C2×#190991872
C2×#190991532
C2×#190991472
C2×#190991432
C2×#190991322
C2×#190991312
C2×#190991142
C2×#190991122
C2×#190990912
C2×#542×C792
C2×#354679