Finite Group Databasebeta

← C2×#23777343 #35196247

Subgroups — C2×#23777343 #35196247

Order 20224.

8082 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777343C2132yesmaximal, direct product factor
2C2×#19099298C211yesmaximal, characteristic, complemented
3C2×#19099266C211yesmaximal, characteristic, complemented
4C2×#19099261C212yesmaximal, complemented
5C2×#19099251C211yesmaximal, characteristic, complemented
6C2×#19099240C212yesmaximal, complemented
7C2×#19099240C212yesmaximal, complemented
8C2×#19099216C211yesmaximal, characteristic, complemented
9C2×#19099208C211yesmaximal, characteristic, complemented
10C2×#19099208C211yesmaximal, characteristic, complemented
11C2×#19099204C212yesmaximal, complemented
12C2×D4×D316C211yesmaximal, characteristic, complemented
13C2×#19099187C211yesmaximal, characteristic, complemented
14C2×#19099169C211yesmaximal, characteristic, complemented
15C2×#19099162C212yesmaximal, complemented
16C2×#19099153C212yesmaximal, complemented
17C2×#19099100C211yesmaximal, characteristic, complemented
18C2×#19099098C211yesmaximal, characteristic, complemented
19C2×#19099076C212yesmaximal, complemented
20C22×#14579146C212yesmaximal, complemented
21C2×#19099042C211yesmaximal, characteristic, complemented
22C2×#19099035C211yesmaximal, characteristic, complemented
23C2×C4×D4×D79C211yesmaximal, characteristic, complemented
24C2×#554×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2212yescomplemented
26C22×#11929623C2211yescharacteristic
27C23×D316C2212yes—
28C22×D4×D79C2211yescharacteristic
29C22×D4×D79C2211yescharacteristic
30C23×C4×D79C2212yescomplemented
31#19099298C22116yescomplemented
32#19099266C22116yescomplemented
33#19099261C22132yescomplemented
34#19099251C22116yescomplemented
35#19099240C22132yescomplemented
36#19099240C22132yescomplemented
37#19099216C22116yescomplemented
38#19099208C22116yescomplemented
39#19099208C22116yescomplemented
40#19099204C22132yescomplemented
41D4×D316C22116yescomplemented
42#19099187C22116yescomplemented
43#19099169C22116yescomplemented
44#19099162C22132yescomplemented
45#19099153C22132yescomplemented
46C2×#14579158C2211yescharacteristic
47#19099100C22116yescomplemented
48#19099098C22116yescomplemented
49C2×#14579156C2212yescomplemented
50C2×#14579156C2211yescharacteristic, complemented
51C2×#14579156C2212yescomplemented
52C2×#14579156C2212yescomplemented
53C2×#14579156C2211yescharacteristic, complemented
54C2×#14579156C2212yescomplemented
55C2×#14579152C2212yescomplemented
56C2×#14579152C2211yescharacteristic, complemented
57C2×#14579150C2212yescomplemented
58C2×#14579150C2212yescomplemented
59C2×#14579150C2211yescharacteristic, complemented
60C2×#14579149C2211yescharacteristic, complemented
61C2×#14579149C2211yescharacteristic, complemented
62#19099076C22132yescomplemented
63C2×#14579146C2212yes—
64C2×#14579146C2211yescharacteristic
65C2×#14579146C2212yescomplemented
66C2×#14579146C2212yescomplemented
67C2×#14579146C2212yescomplemented
68C2×#14579146C2212yescomplemented
69C2×#14579146C2212yescomplemented
70C2×#14579146C2212yescomplemented
71C2×#14579146C2212yescomplemented
72C2×#14579146C2212yescomplemented
73C2×#14579146C2212yescomplemented
74C2×#14579146C2211yescharacteristic, complemented
75C2×#14579146C22132yescomplemented
76C2×#14579145C2212yescomplemented
77C2×#14579145C2212yescomplemented
78C2×#14579141C2211yescharacteristic, complemented
79C2×#14579141C2211yescharacteristic, complemented
80C2×#14579137C2212yescomplemented
81C2×#14579137C2212yescomplemented
82C2×#14579137C2211yescharacteristic, complemented
83C2×#14579136C2211yescharacteristic
84C2×#14579136C2211yescharacteristic
85C2×#14579136C2211yescharacteristic
86C2×#14579136C2212yescomplemented
87C2×#14579136C2212yescomplemented
88C2×#14579136C2211yescharacteristic, complemented
89C2×#14579136C2211yescharacteristic, complemented
90C2×#14579136C2212yescomplemented
91C2×#14579135C2212yes—
92C2×#14579135C2212yescomplemented
93C2×#14579135C2212yescomplemented
94C2×#14579131C2212yes—
95C2×#14579131C2212yes—
96C2×#14579131C2212yescomplemented
97C2×#14579131C2212yescomplemented
98#19099042C22116yescomplemented
99#19099035C22116yescomplemented
100C2×C4×Dic158C2211yescharacteristic, complemented
101C2×#14579126C2211yescharacteristic, complemented
102C2×C4×D316C2211yescharacteristic
103C2×C4×D316C2211yescharacteristic, complemented
104C2×C4×D316C2211yescharacteristic, complemented
105C2×C4×D316C2211yescharacteristic, complemented
106C2×C4×D316C2211yescharacteristic, complemented
107C2×D4×Dic79C2211yescharacteristic
108C2×#14579123C2211yescharacteristic, complemented
109C2×#14579123C2211yescharacteristic, complemented
110C2×#14579123C2212yescomplemented
111C2×#14579123C2212yescomplemented
112C2×#14579123C2212yescomplemented
113C2×C4×C22⋊D79C2212yescomplemented
114C2×C4×C22⋊D79C2212yescomplemented
115C2×C4×C22⋊D79C2212yescomplemented
116C2×(C22⋊D79)⋊C4C2212yescomplemented
117C2×(C22⋊D79)⋊C4C2212yescomplemented
118C2×(C22⋊D79)⋊C4C2212yescomplemented
119C4×D4×D79C22116yescomplemented
120C2×#14579119C2211yescharacteristic, complemented
121C2×#14579119C2212yescomplemented
122C2×#14579119C2212yescomplemented
123C2×#14579118C2211yescharacteristic, complemented
124C2×#14579118C2211yescharacteristic, complemented
125C2×#14579117C2212yescomplemented
126C22×Dic79⋊C4C2212yescomplemented
127C2×C4⋊C4×D79C2211yescharacteristic, complemented
128C2×C4⋊C4×D79C2211yescharacteristic, complemented
129C22×(C2×D79)⋊C4C2212yescomplemented
130C22×(C2×D79)⋊C4C2212yescomplemented
131C22×(C2×D79)⋊C4C2212yescomplemented
132C2×C22⋊C4×D79C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C42×D79C2211yescharacteristic, complemented
135#554×C79C22116yescomplemented
136C2×C4⋊Q8×C79C2211yescharacteristic, complemented
137C2×#125×C79C2211yescharacteristic, complemented
138C2×#125×C79C2211yescharacteristic, complemented
139C2×C22⋊Q8×C79C2212yescomplemented
140C2×C22⋊Q8×C79C2212yescomplemented
141C2×C22⋊Q8×C79C2212yescomplemented
142C2×C4×Q8×C79C2211yescharacteristic, complemented
143C2×C4×D4×C79C2211yescharacteristic
144C2×C4×D4×C79C2211yescharacteristic
145C2×C4×D4×C79C2211yescharacteristic
146C22×C4⋊C4×C79C2212yescomplemented
147C24×D79C2312yes—
148C24×D79C2312yes—
149C2×#11929625—48no—
150C2×#11929625C23116yescomplemented
151C2×#11929623—28no—
152C2×#11929623C2318yes—
153C22×Dic158C2311yescharacteristic
154C22×D316—48no—
155C22×D316C2311yescharacteristic
156C22×D316C2311yescharacteristic
157C22×D316C2312yes—
158C22×D316C2311yescharacteristic
159C22×D316C2311yescharacteristic
160C22×D316C23116yes—
161C22×D316C2312yes—
162C22×D316C2312yes—
163C22×D316C2311yescharacteristic
164C22×D316C2312yes—
165C22×D316C2312yes—
166C22×D316C2312yes—
167C22×C22⋊D79C2312yes—
168C22×C22⋊D79C2312yes—
169C22×C22⋊D79C2312yes—
170C2×D4×D79—28no—
171C2×D4×D79—28no—
172C2×D4×D79C2318yes—
173C2×D4×D79C2318yes—
174C23×Dic79C2312yes—
175C23×Dic79C2312yes—
176C22×C4×D79—48no—
177C22×C4×D79C2311yescharacteristic
178C22×C4×D79C2311yescharacteristic
179C22×C4×D79C2312yes—
180C22×C4×D79C2311yescharacteristic
181C22×C4×D79C2311yescharacteristic
182C22×C4×D79C2311yescharacteristic
183C22×C4×D79C2312yes—
184C22×C4×D79C2312yes—
185C22×C4×D79C2312yes—
186C22×C4×D79C2312yes—
187C22×C4×D79C2312yes—
188C22×C4×D79C23116yescomplemented
189#14579158C2318yes—
190#14579156C23116yescomplemented
191#14579156C23116yescomplemented
192#14579156C23116yescomplemented
193#14579156C23116yescomplemented
194#14579156C2318yescomplemented
195#14579156C2318yescomplemented
196#14579152C2318yescomplemented
197#14579152C23116yescomplemented
198#14579150C2318yescomplemented
199#14579150C23116yescomplemented
200#14579150C23116yescomplemented
201#14579149C2318yescomplemented
202#14579149C2318yescomplemented
203#14579146C23116yes—
204#14579146C2318yes—
205#14579146C23116yescomplemented
206#14579146C23116yescomplemented
207#14579146C23116yescomplemented
208#14579146C23116yescomplemented
209#14579146C23116yescomplemented
210#14579146C23116yescomplemented
211#14579146C23116yescomplemented
212#14579146C23116yescomplemented
213#14579146C23116yescomplemented
214#14579146C2318yescomplemented
215#14579145C23116yescomplemented
216#14579145C23116yescomplemented
217#14579141C2318yescomplemented
218#14579141C2318yescomplemented
219#14579137C23116yescomplemented
220#14579137C23116yescomplemented
221#14579137C2318yescomplemented
222#14579136C2318yes—
223#14579136C2318yes—
224#14579136C2318yes—
225#14579136C23116yescomplemented
226#14579136C23116yescomplemented
227#14579136C23116yescomplemented
228#14579136C2318yescomplemented
229#14579136C2318yescomplemented
230#14579135C23116yes—
231#14579135C23116yescomplemented
232#14579135C23116yescomplemented
233#14579131C23116yes—
234#14579131C23116yes—
235#14579131C23116yescomplemented
236#14579131C23116yescomplemented
237C4×Dic158C2318yescomplemented
238#14579126C2318yescomplemented
239C4×D316C2318yes—
240C4×D316C2318yescomplemented
241C4×D316C2318yescomplemented
242C4×D316C2318yescomplemented
243C4×D316C2318yescomplemented
244D4×Dic79C2318yes—
245#14579123C2318yescomplemented
246#14579123C2318yescomplemented
247#14579123C23116yescomplemented
248#14579123C23116yescomplemented
249#14579123C23116yescomplemented
250C4×C22⋊D79C23116yescomplemented
251C4×C22⋊D79C23116yescomplemented
252C4×C22⋊D79C23116yescomplemented
253(C22⋊D79)⋊C4C23116yescomplemented
254(C22⋊D79)⋊C4C23116yescomplemented
255(C22⋊D79)⋊C4C23116yescomplemented
256#14579119C23116yescomplemented
257#14579119C23116yescomplemented
258#14579119C2318yescomplemented
259#14579118C2318yescomplemented
260#14579118C2318yescomplemented
261#14579117C23116yescomplemented
262C2×C4⋊Dic79C2311yescharacteristic
263C2×C4⋊Dic79C2312yes—
264C2×C4⋊Dic79C2312yes—
265C2×C4⋊Dic79C2311yescharacteristic
266C2×C4⋊Dic79C2311yescharacteristic
267C2×C4⋊Dic79C2311yescharacteristic
268C2×Dic79⋊C4C2312yes—
269C2×Dic79⋊C4C2312yes—
270C2×Dic79⋊C4C2311yescharacteristic
271C2×Dic79⋊C4C2312yes—
272C2×Dic79⋊C4C2312yes—
273C2×Dic79⋊C4C2311yescharacteristic
274C2×Dic79⋊C4C2311yescharacteristic
275C2×Dic79⋊C4C2311yescharacteristic
276C2×Dic79⋊C4C23116yescomplemented
277C4⋊C4×D79C2318yescomplemented
278C4⋊C4×D79C2318yescomplemented
279C2×C22⋊Dic79C2312yes—
280C2×(C2×D79)⋊C4C2311yescharacteristic
281C2×(C2×D79)⋊C4C2312yes—
282C2×(C2×D79)⋊C4C2312yes—
283C2×(C2×D79)⋊C4C2312yes—
284C2×(C2×D79)⋊C4C2311yescharacteristic
285C2×(C2×D79)⋊C4C2311yescharacteristic
286C2×(C2×D79)⋊C4C2311yescharacteristic
287C2×(C2×D79)⋊C4C2312yes—
288C2×(C2×D79)⋊C4C2312yes—
289C2×(C2×D79)⋊C4C2312yes—
290C2×(C2×D79)⋊C4C2312yes—
291C2×(C2×D79)⋊C4C2312yes—
292C2×(C2×D79)⋊C4C2312yes—
293C2×(C2×D79)⋊C4C2312yes—
294C2×(C2×D79)⋊C4C2312yes—
295C2×(C2×D79)⋊C4C2311yescharacteristic
296C2×(C2×D79)⋊C4C2311yescharacteristic
297C2×(C2×D79)⋊C4C2311yescharacteristic
298C2×(C2×D79)⋊C4C2312yes—
299C2×(C2×D79)⋊C4C2311yescharacteristic
300C2×(C2×D79)⋊C4C2312yes—
301C2×(C2×D79)⋊C4C2312yes—
302C2×(C2×D79)⋊C4C2312yes—
303C2×(C2×D79)⋊C4C2311yescharacteristic
304C2×(C2×D79)⋊C4C2311yescharacteristic
305C2×(C2×D79)⋊C4C23116yescomplemented
306C2×(C2×D79)⋊C4C23116yescomplemented
307C2×(C2×D79)⋊C4C23116yescomplemented
308C22⋊C4×D79C23116yescomplemented
309C22⋊C4×D79C23116yescomplemented
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2312yes—
314C2×C4×Dic79C2312yes—
315C2×C4×Dic79C2312yes—
316C42×D79C2318yescomplemented
317C22×Q8×C79C2311yescharacteristic
318C22×Q8×C79C2312yes—
319C22×D4×C79C2311yescharacteristic
320C23×C4×C79C2312yes—
321C23×C4×C79C2312yes—
322C23×C4×C79C2312yes—
323C4⋊Q8×C79C2318yescomplemented
324#125×C79C2318yescomplemented
325#125×C79C2318yescomplemented
326C22⋊Q8×C79C23116yescomplemented
327C22⋊Q8×C79C23116yescomplemented
328C22⋊Q8×C79C23116yescomplemented
329C4×Q8×C79C2318yescomplemented
330C4×D4×C79C2318yes—
331C4×D4×C79C2318yes—
332C4×D4×C79C2318yes—
333C2×C4⋊C4×C79C2311yescharacteristic
334C2×C4⋊C4×C79C2312yes—
335C2×C4⋊C4×C79C2312yes—
336C2×C4⋊C4×C79C2312yes—
337C2×C4⋊C4×C79C2311yescharacteristic
338C2×C4⋊C4×C79C2311yescharacteristic
339C2×C4⋊C4×C79C2311yescharacteristic
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C4⋊C4×C79C2311yescharacteristic
342C2×C4⋊C4×C79C2312yes—
343C2×C4⋊C4×C79C2312yes—
344C2×C4⋊C4×C79C23116yescomplemented
345C2×C22⋊C4×C79C2312yes—
346C2×C22⋊C4×C79C2312yes—
347C2×C22⋊C4×C79C2312yes—
348C2×C42×C79C2311yescharacteristic
349C2×C42×C79C2311yescharacteristic
350C2×C42×C79C2311yescharacteristic
351C23×D79—28no—
352C23×D79—28no—
353C23×D79—28no—
354C23×D79—44no—
355C23×D79—44no—
356C23×D79—44no—
357C23×D79C2411yescharacteristic
358C23×D79C2412yes—
359C23×D79C2412yes—
360C23×D79C2411yescharacteristic
361C23×D79C2418yes—
362C23×D79C2411yescharacteristic
363C23×D79C2418yes—
364#11929625—432no—
365#11929623—232no—
366C2×Dic158—24no—
367C2×Dic158C2414yes—
368C2×D316—24no—
369C2×D316—28no—
370C2×D316—24no—
371C2×D316—24no—
372C2×D316—24no—
373C2×D316—44no—
374C2×D316—44no—
375C2×D316—44no—
376C2×D316—44no—
377C2×D316—42no—
378C2×D316—44no—
379C2×D316—432no—
380C2×D316C2414yes—
381C2×D316C2418yes—
382C2×D316C2414yes—
383C2×D316C2414yes—
384C2×D316C2414yes—
385C2×D316C2418yes—
386C2×D316C2418yes—
387C2×D316C2418yes—
388C2×D316C2414yes—
389C2×D316C2418yes—
390C2×D316C2418yes—
391C2×C22⋊D79—28no—
392C2×C22⋊D79—28no—
393C2×C22⋊D79—28no—
394C2×C22⋊D79C2418yes—
395C2×C22⋊D79C2418yes—
396C2×C22⋊D79C2418yes—
397D4×D79—232no—
398D4×D79—232no—
399C22×Dic79—28no—
400C22×Dic79—44no—
401C22×Dic79C2412yes—
402C22×Dic79C2418yes—
403C22×Dic79C2411yescharacteristic
404C22×Dic79C2411yescharacteristic
405C22×Dic79C2411yescharacteristic
406C22×Dic79C2411yescharacteristic
407C22×Dic79C2412yes—
408C22×Dic79C2411yescharacteristic
409C22×Dic79C2418yes—
410C2×C4×D79—28no—
411C2×C4×D79—24no—
412C2×C4×D79—24no—
413C2×C4×D79—24no—
414C2×C4×D79—24no—
415C2×C4×D79—44no—
416C2×C4×D79—44no—
417C2×C4×D79—44no—
418C2×C4×D79—44no—
419C2×C4×D79—44no—
420C2×C4×D79—42no—
421C2×C4×D79—432no—
422C2×C4×D79C2414yes—
423C2×C4×D79C2418yes—
424C2×C4×D79C2414yes—
425C2×C4×D79C2414yes—
426C2×C4×D79C2414yes—
427C2×C4×D79C2418yes—
428C2×C4×D79C2418yes—
429C2×C4×D79C2414yes—
430C2×C4×D79C2418yes—
431C2×C4×D79C2418yes—
432C2×C4×D79C2418yes—
433C4⋊Dic79C2414yes—
434C4⋊Dic79C2418yes—
435C4⋊Dic79C2418yes—
436C4⋊Dic79C2414yes—
437C4⋊Dic79C2414yes—
438C4⋊Dic79C2414yes—
439Dic79⋊C4C2418yes—
440Dic79⋊C4C2418yes—
441Dic79⋊C4C2414yes—
442Dic79⋊C4C2418yes—
443Dic79⋊C4C2418yes—
444Dic79⋊C4C2414yes—
445Dic79⋊C4C2414yes—
446Dic79⋊C4C2414yes—
447C22⋊Dic79C2418yes—
448(C2×D79)⋊C4C2414yes—
449(C2×D79)⋊C4C2418yes—
450(C2×D79)⋊C4C2418yes—
451(C2×D79)⋊C4C2418yes—
452(C2×D79)⋊C4C2414yes—
453(C2×D79)⋊C4C2414yes—
454(C2×D79)⋊C4C2414yes—
455(C2×D79)⋊C4C2418yes—
456(C2×D79)⋊C4C2418yes—
457(C2×D79)⋊C4C2418yes—
458(C2×D79)⋊C4C2418yes—
459(C2×D79)⋊C4C2418yes—
460(C2×D79)⋊C4C2418yes—
461(C2×D79)⋊C4C2418yes—
462(C2×D79)⋊C4C2418yes—
463(C2×D79)⋊C4C2414yes—
464(C2×D79)⋊C4C2414yes—
465(C2×D79)⋊C4C2414yes—
466(C2×D79)⋊C4C2418yes—
467(C2×D79)⋊C4C2414yes—
468(C2×D79)⋊C4C2418yes—
469(C2×D79)⋊C4C2418yes—
470(C2×D79)⋊C4C2418yes—
471(C2×D79)⋊C4C2414yes—
472(C2×D79)⋊C4C2414yes—
473C4×Dic79C2414yes—
474C4×Dic79C2414yes—
475C4×Dic79C2414yes—
476C4×Dic79C2418yes—
477C4×Dic79C2418yes—
478C4×Dic79C2418yes—
479C24×C79C2412yes—
480C2×Q8×C79—44no—
481C2×Q8×C79—42no—
482C2×Q8×C79C2418yes—
483C2×Q8×C79C2414yes—
484C2×D4×C79#4118yescomplemented
485C2×D4×C79C2414yes—
486C22×C4×C79—44no—
487C22×C4×C79—44no—
488C22×C4×C79—44no—
489C22×C4×C79C2411yescharacteristic
490C22×C4×C79C2411yescharacteristic
491C22×C4×C79C2411yescharacteristic
492C22×C4×C79C2411yescharacteristic
493C22×C4×C79C2411yescharacteristic
494C22×C4×C79C2411yescharacteristic
495C22×C4×C79C2412yes—
496C22×C4×C79C2412yes—
497C22×C4×C79C2412yes—
498C22×C4×C79C2418yes—
499C22×C4×C79C2418yes—
500C22×C4×C79C2418yes—
501C22×C4×C79C2411yescharacteristic
502C4⋊C4×C79C2414yes—
503C4⋊C4×C79C2418yes—
504C4⋊C4×C79C2418yes—
505C4⋊C4×C79C2418yes—
506C4⋊C4×C79C2414yes—
507C4⋊C4×C79C2414yes—
508C4⋊C4×C79C2414yes—
509C4⋊C4×C79C2414yes—
510C4⋊C4×C79C2414yes—
511C4⋊C4×C79C2418yes—
512C4⋊C4×C79C2418yes—
513C22⋊C4×C79C2418yes—
514C22⋊C4×C79C2418yes—
515C22⋊C4×C79C2418yes—
516C42×C79C2414yes—
517C42×C79C2414yes—
518C42×C79C2414yes—
519C23×C79—24no—
520C23×C79—24no—
521C23×C79C2×#4118yes—
522C23×C79C2514yes—
523C23×C79C2511yescharacteristic
524C22×D79—22no—
525C22×D79—22no—
526C22×D79—22no—
527C22×D79—22no—
528C22×D79—216no—
529C22×D79—24no—
530C22×D79—24no—
531C22×D79—22no—
532C22×D79—24no—
533C22×D79—24no—
534C22×D79—22no—
535C22×D79—24no—
536C22×D79—22no—
537C22×D79—24no—
538C22×D79—22no—
539C22×D79—216no—
540C22×D79—216no—
541C22×D79—48no—
542C22×D79—48no—
543C22×D79—48no—
544C22×D79—432no—
545C22×D79—816no—
546C22×D79H(5,𝔽2)14yes—
547C22×D79C2512yes—
548C22×D79C2514yes—
549C22×D79C2514yes—
550C22×D79C2512yes—
551C22×D79C2512yes—
552Q8×C79—48no—
553Q8×C79—44no—
554D4×C79C2×#41116yescomplemented
555C2×C4×C79—22no—
556C2×C4×C79—24no—
557C2×C4×C79—22no—
558C2×C4×C79—24no—
559C2×C4×C79—22no—
560C2×C4×C79—24no—
561C2×C4×C79—22no—
562C2×C4×C79—22no—
563C2×C4×C79—22no—
564C2×C4×C79—48no—
565C2×C4×C79—48no—
566C2×C4×C79—48no—
567C2×C4×C79C2×#4114yes—
568C2×C4×C79C2512yes—
569C2×C4×C79C2512yes—
570C2×C4×C79C2514yes—
571C2×C4×C79C2512yes—
572C2×C4×C79C2514yes—
573C2×C4×C79C2512yes—
574C2×C4×C79C2512yes—
575C2×C4×C79C2514yes—
576C2×C4×C79C2512yes—
577C2×C4×C79C2512yes—
578C22⋊D79—216no—
579C22⋊D79—216no—
580C22⋊D79—216no—
581C2×Dic79—22no—
582C2×Dic79—22no—
583C2×Dic79—22no—
584C2×Dic79—24no—
585C2×Dic79—216no—
586C2×Dic79—24no—
587C2×Dic79—22no—
588C2×Dic79—22no—
589C2×Dic79—48no—
590C2×Dic79C2512yes—
591C2×Dic79C2514yes—
592C2×Dic79C2512yes—
593C2×Dic79C2512yes—
594C2×Dic79C2512yes—
595C2×Dic79C2514yes—
596C2×Dic79C2512yes—
597D316—28no—
598D316—216no—
599D316—28no—
600D316—28no—
601D316—28no—
602D316—48no—
603D316—48no—
604D316—48no—
605D316—44no—
606D316—48no—
607D316—48no—
608C4×D79—28no—
609C4×D79—216no—
610C4×D79—28no—
611C4×D79—28no—
612C4×D79—28no—
613C4×D79—48no—
614C4×D79—48no—
615C4×D79—48no—
616C4×D79—44no—
617C4×D79—48no—
618C4×D79—48no—
619Dic158—28no—
620C22×C79—24no—
621C22×C79—24no—
622C22×C79—216no—
623C22×C79C22×#4118yes—
624C22×C79C22×#4112yes—
625C22×C79C2×H(5,𝔽2)12yes—
626C22×C79#58512yes—
627C22×C79C2611yescharacteristic
628C2×D79—22no—
629C2×D79—22no—
630C2×D79—28no—
631C2×D79—22no—
632C2×D79—24no—
633C2×D79—24no—
634C2×D79—22no—
635C2×D79—24no—
636C2×D79—22no—
637C2×D79—24no—
638C2×D79—22no—
639C2×D79—22no—
640C2×D79—24no—
641C2×D79—24no—
642C2×D79—22no—
643C2×D79—432no—
644C2×D79—44no—
645C2×D79—48no—
646C2×D79—48no—
647C2×D79—44no—
648C2×D79—816no—
649C2×D79C2×H(5,𝔽2)14yes—
650C4×C79—22no—
651C4×C79—22no—
652C4×C79—24no—
653C4×C79—24no—
654C4×C79—22no—
655C4×C79—22no—
656C4×C79—24no—
657C4×C79—22no—
658C4×C79—22no—
659C4×C79C22×#4114yes—
660Dic79—22no—
661Dic79—22no—
662Dic79—24no—
663Dic79—22no—
664Dic79—24no—
665Dic79—22no—
666Dic79—22no—
667C2×#3513—791nomaximal, Sylow
668C2×C79—28no—
669C2×C79#351314yescomplemented
670C2×C79C23×#4111yescharacteristic
671C2×C79C22×H(5,𝔽2)11yescharacteristic
672C2×C79C2×#58511yescharacteristic
673D79—24no—
674D79—42no—
675D79—44no—
676D79—44no—
677D79—42no—
678#3513—7932no—
679C2×#559—791no—
680C2×#554D7911yescharacteristic, complemented
681C2×#553—791no—
682C2×#553—792no—
683C2×#552—791no—
684C2×#551—792no—
685C2×#551—792no—
686C2×#547—791no—
687C2×#546—792no—
688C2×#546—791no—
689C2×#546—791no—
690C2×D42—791no—
691C2×#542—791no—
692C2×#540—791no—
693C2×#539—792no—
694C2×#538—792no—
695C2×#529—791no—
696C2×#529—791no—
697C2×#525—792no—
698C22×#123—792no—
699C2×#520—791no—
700C2×#518—791no—
701C22×C4×D4—791no—
702C79C2×#351311yescharacteristic, complemented, Sylow
703C22×#41—792no—
704C22×#41—791no—
705C23×D4—791no—
706C23×D4—791no—
707C23×D4—792no—
708C24×C4—792no—
709#559—7916no—
710#554C2×D79116yescomplemented
711#553—7916no—
712#553—7932no—
713#552—7916no—
714#551—7932no—
715#551—7932no—
716#547—7916no—
717#546—7932no—
718#546—7916no—
719#546—7916no—
720D42—7916no—
721#542—7916no—
722#540—7916no—
723#539—7932no—
724#538—7932no—
725C2×C4⋊Q8C2×D7911yescharacteristic, complemented
726C2×#127—791no—
727#529—7916no—
728#529—7916no—
729C2×#126—792no—
730C2×#126—791no—
731C2×#126—791no—
732C2×#126—792no—
733C2×#126—792no—
734C2×#126—792no—
735C2×#125—791no—
736C2×#125—792no—
737C2×#125C2×D7911yescharacteristic, complemented
738C2×#125C2×D7911yescharacteristic, complemented
739C2×#124—791no—
740C2×#124—792no—
741C2×#124—792no—
742C2×#124—791no—
743C2×#124—791no—
744#525—7932no—
745C2×#123—791no—
746C2×#123—792no—
747C2×#123—792no—
748C2×#123—792no—
749C2×#123—792no—
750C2×#123—792no—
751C2×#123—792no—
752C2×#123—792no—
753C2×#123—791no—
754C2×#123—792no—
755C2×#123—792no—
756C2×#123—792no—
757C2×#123—7932no—
758C2×#123—792no—
759C2×#123—792no—
760C2×C22⋊Q8—792no—
761C2×C22⋊Q8—791no—
762C2×C22⋊Q8—792no—
763C2×C22⋊Q8—791no—
764C2×C22⋊Q8—791no—
765C2×C22⋊Q8C2×D7912yescomplemented
766C2×C22⋊Q8C2×D7912yescomplemented
767C2×C22⋊Q8C2×D7912yescomplemented
768C2×#121—792no—
769C2×#121—792no—
770C2×#121—792no—
771C2×#121—792no—
772C2×#121—791no—
773C2×#121—791no—
774C2×#121—792no—
775C2×#121—791no—
776C2×#121—792no—
777C2×#121—791no—
778C2×#121—791no—
779C2×#120—792no—
780C2×#120—792no—
781C2×#120—792no—
782C2×#120—792no—
783#520—7916no—
784#518—7916no—
785C2×C4×Q8—791no—
786C2×C4×Q8—791no—
787C2×C4×Q8C2×D7911yescharacteristic, complemented
788C2×C4×D4—791no—
789C2×C4×D4—792no—
790C2×C4×D4—792no—
791C2×C4×D4—792no—
792C2×C4×D4—7916no—
793C2×C4×D4—791no—
794C2×C4×D4—791no—
795C2×C4×D4—792no—
796C2×C4×D4—792no—
797C2×C4×D4—792no—
798C2×C4×D4—792no—
799C2×C4×D4—792no—
800C2×C4×D4—792no—
801C2×C4×D4—791no—
802C2×C4×D4—791no—
803C2×C4×D4—791no—
804C2×C4×D4—791no—
805C2×C4×D4—791no—
806C2×C4×D4C2×D7911yescharacteristic
807C2×C4×D4C2×D7911yescharacteristic
808C2×C4×D4C2×D7911yescharacteristic
809C2×#117—791no—
810C2×#117—792no—
811C2×#117—792no—
812C2×#117—792no—
813C2×#117—791no—
814C2×#117—791no—
815C22×C4⋊C4—792no—
816C22×C4⋊C4—791no—
817C22×C4⋊C4—791no—
818C22×C4⋊C4C2×D7912yescomplemented
819C22×C22⋊C4—792no—
820C22×C22⋊C4—792no—
821C22×C22⋊C4—792no—
822C22×C22⋊C4—792no—
823C22×C22⋊C4—792no—
824C22×C42—791no—
825C25—792no—
826C25—792no—
827C2×#41—3168no—
828C2×#41—7916no—
829C2×#41—798no—
830C2×#41—1588no—
831C22×Q8—791no—
832C22×Q8C22×D7911yescharacteristic
833C22×Q8C22×D7912yes—
834C22×D4—3168no—
835C22×D4—792no—
836C22×D4—792no—
837C22×D4—792no—
838C22×D4—798no—
839C22×D4—798no—
840C22×D4—791no—
841C22×D4—792no—
842C22×D4—792no—
843C22×D4—792no—
844C22×D4—792no—
845C22×D4—792no—
846C22×D4—7916no—
847C22×D4—791no—
848C22×D4—791no—
849C22×D4—791no—
850C22×D4—792no—
851C22×D4—791no—
852C22×D4—1588no—
853C22×D4—1588no—
854C22×D4C22×D7911yescharacteristic
855C23×C4—3168no—
856C23×C4—792no—
857C23×C4—791no—
858C23×C4—792no—
859C23×C4—792no—
860C23×C4—792no—
861C23×C4—792no—
862C23×C4—792no—
863C23×C4—7916no—
864C23×C4—792no—
865C23×C4—792no—
866C23×C4—791no—
867C23×C4—791no—
868C23×C4—791no—
869C23×C4—791no—
870C23×C4C22×D7912yes—
871C23×C4C22×D7912yes—
872C23×C4C22×D7912yes—
873C4⋊Q8C22×D7918yescomplemented
874#127—798no—
875#126—7916no—
876#126—798no—
877#126—798no—
878#126—7916no—
879#126—7916no—
880#126—7916no—
881#125—798no—
882#125—7916no—
883#125C22×D7918yescomplemented
884#125C22×D7918yescomplemented
885#124—798no—
886#124—7916no—
887#124—7916no—
888#124—798no—
889#124—798no—
890#123—798no—
891#123—7916no—
892#123—7916no—
893#123—7916no—
894#123—7916no—
895#123—7916no—
896#123—7916no—
897#123—7916no—
898#123—798no—
899#123—7916no—
900#123—7916no—
901#123—7916no—
902#123—7916no—
903#123—7916no—
904C22⋊Q8—7916no—
905C22⋊Q8—798no—
906C22⋊Q8—7916no—
907C22⋊Q8—798no—
908C22⋊Q8—798no—
909C22⋊Q8C22×D79116yescomplemented
910C22⋊Q8C22×D79116yescomplemented
911C22⋊Q8C22×D79116yescomplemented
912#121—7916no—
913#121—7916no—
914#121—7916no—
915#121—7916no—
916#121—798no—
917#121—798no—
918#121—7916no—
919#121—798no—
920#121—7916no—
921#121—798no—
922#121—798no—
923#120—7916no—
924#120—7916no—
925#120—7916no—
926#120—7916no—
927C4×Q8—798no—
928C4×Q8—798no—
929C4×Q8C22×D7918yescomplemented
930C4×D4—798no—
931C4×D4—7916no—
932C4×D4—7916no—
933C4×D4—7916no—
934C4×D4—798no—
935C4×D4—798no—
936C4×D4—7916no—
937C4×D4—7916no—
938C4×D4—7916no—
939C4×D4—7916no—
940C4×D4—7916no—
941C4×D4—7916no—
942C4×D4—798no—
943C4×D4—798no—
944C4×D4—798no—
945C4×D4—798no—
946C4×D4—798no—
947C4×D4C22×D7918yes—
948C4×D4C22×D7918yes—
949C4×D4C22×D7918yes—
950#117—798no—
951#117—7916no—
952#117—7916no—
953#117—7916no—
954#117—798no—
955#117—798no—
956C2×C4⋊C4—791no—
957C2×C4⋊C4—792no—
958C2×C4⋊C4—791no—
959C2×C4⋊C4—792no—
960C2×C4⋊C4—792no—
961C2×C4⋊C4—792no—
962C2×C4⋊C4—7916no—
963C2×C4⋊C4—791no—
964C2×C4⋊C4—791no—
965C2×C4⋊C4—791no—
966C2×C4⋊C4—792no—
967C2×C4⋊C4—792no—
968C2×C4⋊C4—791no—
969C2×C4⋊C4—791no—
970C2×C4⋊C4—791no—
971C2×C4⋊C4—798no—
972C2×C4⋊C4—798no—
973C2×C4⋊C4C22×D7911yescharacteristic
974C2×C4⋊C4C22×D7911yescharacteristic
975C2×C4⋊C4C22×D7911yescharacteristic
976C2×C4⋊C4C22×D7912yes—
977C2×C4⋊C4C22×D7912yes—
978C2×C4⋊C4C22×D7912yes—
979C2×C4⋊C4C22×D7911yescharacteristic
980C2×C4⋊C4C22×D7912yes—
981C2×C4⋊C4C22×D7911yescharacteristic
982C2×C4⋊C4C22×D7912yes—
983C2×C4⋊C4C22×D7911yescharacteristic
984C2×C4⋊C4C22×D79116yescomplemented
985C2×C22⋊C4—792no—
986C2×C22⋊C4—792no—
987C2×C22⋊C4—791no—
988C2×C22⋊C4—791no—
989C2×C22⋊C4—791no—
990C2×C22⋊C4—791no—
991C2×C22⋊C4—792no—
992C2×C22⋊C4—792no—
993C2×C22⋊C4—792no—
994C2×C22⋊C4—792no—
995C2×C22⋊C4—792no—
996C2×C22⋊C4—792no—
997C2×C22⋊C4—7916no—
998C2×C22⋊C4—792no—
999C2×C22⋊C4—792no—
1000C2×C22⋊C4—792no—
1001C2×C22⋊C4—792no—
1002C2×C22⋊C4—7916no—
1003C2×C22⋊C4—7916no—
1004C2×C22⋊C4—791no—
1005C2×C22⋊C4—791no—
1006C2×C22⋊C4—791no—
1007C2×C22⋊C4—792no—
1008C2×C22⋊C4—791no—
1009C2×C22⋊C4—791no—
1010C2×C22⋊C4—792no—
1011C2×C22⋊C4—792no—
1012C2×C22⋊C4—792no—
1013C2×C22⋊C4—791no—
1014C2×C22⋊C4—7916no—
1015C2×C22⋊C4—7916no—
1016C2×C22⋊C4C22×D7912yes—
1017C2×C22⋊C4C22×D7912yes—
1018C2×C22⋊C4C22×D7912yes—
1019C2×C42—791no—
1020C2×C42—792no—
1021C2×C42—792no—
1022C2×C42—792no—
1023C2×C42—791no—
1024C2×C42—791no—
1025C2×C42—798no—
1026C2×C42C22×D7911yescharacteristic
1027C2×C42C22×D7911yescharacteristic
1028C2×C42C22×D7911yescharacteristic
1029C24—3164no—
1030C24—3164no—
1031C24—3164no—
1032C24—798no—
1033C24—798no—
1034C24—791no—
1035C24—791no—
1036C24—792no—
1037C24—792no—
1038C24—791no—
1039C24—1588no—
1040C24—1588no—
1041C24—1588no—
1042C24C23×D7912yes—
1043#41—31632no—
1044#41—15832no—
1045C2×Q8—44no—
1046C2×Q8—42no—
1047C2×Q8—794no—
1048C2×Q8—1584no—
1049C2×Q8C23×D7914yes—
1050C2×Q8C23×D7918yes—
1051C2×D4—3164no—
1052C2×D4—3164no—
1053C2×D4—3164no—
1054C2×D4—3162no—
1055C2×D4—3164no—
1056C2×D4—3164no—
1057C2×D4—31632no—
1058C2×D4—798no—
1059C2×D4—798no—
1060C2×D4—798no—
1061C2×D4—794no—
1062C2×D4—798no—
1063C2×D4—798no—
1064C2×D4—798no—
1065C2×D4—798no—
1066C2×D4—798no—
1067C2×D4—794no—
1068C2×D4—794no—
1069C2×D4—794no—
1070C2×D4—798no—
1071C2×D4—794no—
1072C2×D4—1584no—
1073C2×D4—1588no—
1074C2×D4—1584no—
1075C2×D4—1588no—
1076C2×D4—1588no—
1077C2×D4—1588no—
1078C2×D4—15832no—
1079C2×D4—15832no—
1080C2×D4—1584no—
1081C2×D4—1584no—
1082C2×D4#1192962518yescomplemented
1083C2×D4C23×D7914yes—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—3164no—
1088C22×C4—3164no—
1089C22×C4—3164no—
1090C22×C4—3162no—
1091C22×C4—3164no—
1092C22×C4—3164no—
1093C22×C4—31632no—
1094C22×C4—3164no—
1095C22×C4—798no—
1096C22×C4—794no—
1097C22×C4—798no—
1098C22×C4—798no—
1099C22×C4—798no—
1100C22×C4—798no—
1101C22×C4—798no—
1102C22×C4—798no—
1103C22×C4—791no—
1104C22×C4—792no—
1105C22×C4—791no—
1106C22×C4—791no—
1107C22×C4—791no—
1108C22×C4—792no—
1109C22×C4—791no—
1110C22×C4—794no—
1111C22×C4—794no—
1112C22×C4—798no—
1113C22×C4—794no—
1114C22×C4—794no—
1115C22×C4—1584no—
1116C22×C4—1588no—
1117C22×C4—1588no—
1118C22×C4—1584no—
1119C22×C4—1584no—
1120C22×C4—1584no—
1121C22×C4C23×D7911yescharacteristic
1122C22×C4C23×D7911yescharacteristic
1123C22×C4C23×D7911yescharacteristic
1124C22×C4C23×D7912yes—
1125C22×C4C23×D7912yes—
1126C22×C4C23×D7911yescharacteristic
1127C22×C4C23×D7911yescharacteristic
1128C22×C4C23×D7911yescharacteristic
1129C22×C4C23×D7912yes—
1130C22×C4C23×D7918yes—
1131C22×C4C23×D7918yes—
1132C22×C4C23×D7918yes—
1133C22×C4C23×D7911yescharacteristic
1134C4⋊C4—798no—
1135C4⋊C4—794no—
1136C4⋊C4—798no—
1137C4⋊C4—798no—
1138C4⋊C4—798no—
1139C4⋊C4—794no—
1140C4⋊C4—794no—
1141C4⋊C4—794no—
1142C4⋊C4—794no—
1143C4⋊C4—798no—
1144C4⋊C4—798no—
1145C4⋊C4—794no—
1146C4⋊C4—794no—
1147C4⋊C4—794no—
1148C4⋊C4C23×D7914yes—
1149C4⋊C4C23×D7914yes—
1150C4⋊C4C23×D7914yes—
1151C4⋊C4C23×D7918yes—
1152C4⋊C4C23×D7918yes—
1153C4⋊C4C23×D7918yes—
1154C4⋊C4C23×D7914yes—
1155C4⋊C4C23×D7918yes—
1156C4⋊C4C23×D7914yes—
1157C4⋊C4C23×D7918yes—
1158C4⋊C4C23×D7914yes—
1159C22⋊C4—798no—
1160C22⋊C4—798no—
1161C22⋊C4—794no—
1162C22⋊C4—794no—
1163C22⋊C4—794no—
1164C22⋊C4—794no—
1165C22⋊C4—798no—
1166C22⋊C4—798no—
1167C22⋊C4—798no—
1168C22⋊C4—798no—
1169C22⋊C4—798no—
1170C22⋊C4—798no—
1171C22⋊C4—798no—
1172C22⋊C4—798no—
1173C22⋊C4—798no—
1174C22⋊C4—798no—
1175C22⋊C4—794no—
1176C22⋊C4—794no—
1177C22⋊C4—794no—
1178C22⋊C4—798no—
1179C22⋊C4—794no—
1180C22⋊C4—794no—
1181C22⋊C4—798no—
1182C22⋊C4—798no—
1183C22⋊C4—798no—
1184C22⋊C4—794no—
1185C22⋊C4C23×D7918yes—
1186C22⋊C4C23×D7918yes—
1187C22⋊C4C23×D7918yes—
1188C42—794no—
1189C42—794no—
1190C42—794no—
1191C42—798no—
1192C42—798no—
1193C42—798no—
1194C42C23×D7914yes—
1195C42C23×D7914yes—
1196C42C23×D7914yes—
1197C23—24no—
1198C23—24no—
1199C23—31632no—
1200C23—3168no—
1201C23—3168no—
1202C23—3168no—
1203C23—794no—
1204C23—792no—
1205C23—792no—
1206C23—794no—
1207C23—794no—
1208C23—792no—
1209C23—63216no—
1210C23—15816no—
1211C23—1582no—
1212C23—1584no—
1213C23—1584no—
1214C23—1582no—
1215C23—1584no—
1216C23—1582no—
1217C23—1584no—
1218C23—1582no—
1219C23—1582no—
1220C23—1582no—
1221C23—15816no—
1222C23—1584no—
1223C23—1584no—
1224C23—15816no—
1225C23—1582no—
1226C23—1582no—
1227C23C2×#1192962518yes—
1228C23C24×D7914yes—
1229C23C24×D7911yescharacteristic
1230Q8—44no—
1231Q8—48no—
1232Q8—1588no—
1233D4—3168no—
1234D4—3168no—
1235D4—3168no—
1236D4—3168no—
1237D4—3164no—
1238D4—3168no—
1239D4—1588no—
1240D4—15816no—
1241D4—1588no—
1242D4—15816no—
1243D4—15816no—
1244D4—15816no—
1245D4—1588no—
1246D4—1588no—
1247D4C2×#11929625116yescomplemented
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—48no—
1258C2×C4—48no—
1259C2×C4—48no—
1260C2×C4—3168no—
1261C2×C4—3168no—
1262C2×C4—3168no—
1263C2×C4—3168no—
1264C2×C4—3168no—
1265C2×C4—3164no—
1266C2×C4—3168no—
1267C2×C4—792no—
1268C2×C4—794no—
1269C2×C4—792no—
1270C2×C4—792no—
1271C2×C4—792no—
1272C2×C4—794no—
1273C2×C4—792no—
1274C2×C4—1588no—
1275C2×C4—15816no—
1276C2×C4—1582no—
1277C2×C4—1584no—
1278C2×C4—1582no—
1279C2×C4—1582no—
1280C2×C4—1582no—
1281C2×C4—1582no—
1282C2×C4—1584no—
1283C2×C4—15816no—
1284C2×C4—1588no—
1285C2×C4—1588no—
1286C2×C4—1588no—
1287C2×C4C2×#1192962514yes—
1288C2×C4C24×D7912yes—
1289C2×C4C24×D7912yes—
1290C2×C4C24×D7912yes—
1291C2×C4C24×D7914yes—
1292C2×C4C24×D7914yes—
1293C2×C4C24×D7912yes—
1294C2×C4C24×D7912yes—
1295C2×C4C24×D7912yes—
1296C2×C4C24×D7914yes—
1297C2×C4C24×D7912yes—
1298C22—216no—
1299C22—24no—
1300C22—24no—
1301C22—31632no—
1302C22—3168no—
1303C22—3164no—
1304C22—3168no—
1305C22—3164no—
1306C22—794no—
1307C22—63216no—
1308C22—1582no—
1309C22—1582no—
1310C22—1584no—
1311C22—1584no—
1312C22—1582no—
1313C22—1584no—
1314C22—1584no—
1315C22—1582no—
1316C22—1584no—
1317C22—1582no—
1318C22—1584no—
1319C22—1582no—
1320C22—1588no—
1321C22—1582no—
1322C22—1582no—
1323C22C22×#1192962518yes—
1324C22C22×#1192962512yes—
1325C22H(5,𝔽2)×D7912yes—
1326C22#1909939912yes—
1327C22C25×D7911yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—24no—
1331C4—24no—
1332C4—22no—
1333C4—22no—
1334C4—24no—
1335C4—22no—
1336C4—22no—
1337C4—1582no—
1338C4—1582no—
1339C4—1582no—
1340C4—1584no—
1341C4—1582no—
1342C4—1584no—
1343C4—1582no—
1344C4C22×#1192962514yes—
1345C2—28no—
1346C2—3164no—
1347C2—3162no—
1348C2—3164no—
1349C2—3162no—
1350C2—1584no—
1351C2#2377734314yesdirect product factor
1352C2C23×#1192962511yescharacteristic
1353C2C2×H(5,𝔽2)×D7911yescharacteristic
1354C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#554×C79C2
socleC23×C79C25
hypercenterC2×#554D79
hypocenterC79C2×#3513
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #23777343C2direct (N × H)
2. C2×#19099298C2semidirect
3. C2×#19099266C2semidirect
4. C2×#19099261C2semidirect
5. C2×#19099251C2semidirect
6. C2×#19099240C2semidirect
7. C2×#19099240C2semidirect
8. C2×#19099216C2semidirect
9. C2×#19099208C2semidirect
10. C2×#19099208C2semidirect
11. C2×#19099204C2semidirect
12. C2×D4×D316C2semidirect
13. C2×#19099187C2semidirect
14. C2×#19099169C2semidirect
15. C2×#19099162C2semidirect
16. C2×#19099153C2semidirect
17. C2×#19099100C2semidirect
18. C2×#19099098C2semidirect
19. C2×#19099076C2semidirect
20. C22×#14579146C2semidirect
21. C2×#19099042C2semidirect
22. C2×#19099035C2semidirect
23. C2×C4×D4×D79C2semidirect
24. C2×#554×C79C2semidirect
25. C22×#11929625C22semidirect
30. C23×C4×D79C22semidirect
31. #19099298C22semidirect
32. #19099266C22semidirect
33. #19099261C22semidirect
34. #19099251C22semidirect
35. #19099240C22semidirect
36. #19099240C22semidirect
37. #19099216C22semidirect
38. #19099208C22semidirect
39. #19099208C22semidirect
40. #19099204C22semidirect
41. D4×D316C22semidirect
42. #19099187C22semidirect
43. #19099169C22semidirect
44. #19099162C22semidirect
45. #19099153C22semidirect
47. #19099100C22semidirect
48. #19099098C22semidirect
49. C2×#14579156C22semidirect
50. C2×#14579156C22semidirect
51. C2×#14579156C22semidirect
52. C2×#14579156C22semidirect
53. C2×#14579156C22semidirect
54. C2×#14579156C22semidirect
55. C2×#14579152C22semidirect
56. C2×#14579152C22semidirect
57. C2×#14579150C22semidirect
58. C2×#14579150C22semidirect
59. C2×#14579150C22semidirect
60. C2×#14579149C22semidirect
61. C2×#14579149C22semidirect
62. #19099076C22semidirect
65. C2×#14579146C22semidirect
66. C2×#14579146C22semidirect
67. C2×#14579146C22semidirect
68. C2×#14579146C22semidirect
69. C2×#14579146C22semidirect
70. C2×#14579146C22semidirect
71. C2×#14579146C22semidirect
72. C2×#14579146C22semidirect
73. C2×#14579146C22semidirect
74. C2×#14579146C22semidirect
75. C2×#14579146C22semidirect
76. C2×#14579145C22semidirect
77. C2×#14579145C22semidirect
78. C2×#14579141C22semidirect
79. C2×#14579141C22semidirect
80. C2×#14579137C22semidirect
81. C2×#14579137C22semidirect
82. C2×#14579137C22semidirect
86. C2×#14579136C22semidirect
87. C2×#14579136C22semidirect
88. C2×#14579136C22semidirect
89. C2×#14579136C22semidirect
90. C2×#14579136C22semidirect
92. C2×#14579135C22semidirect
93. C2×#14579135C22semidirect
96. C2×#14579131C22semidirect
97. C2×#14579131C22semidirect
98. #19099042C22semidirect
99. #19099035C22semidirect
100. C2×C4×Dic158C22semidirect
101. C2×#14579126C22semidirect
103. C2×C4×D316C22semidirect
104. C2×C4×D316C22semidirect
105. C2×C4×D316C22semidirect
106. C2×C4×D316C22semidirect
108. C2×#14579123C22semidirect
109. C2×#14579123C22semidirect
110. C2×#14579123C22semidirect
111. C2×#14579123C22semidirect
112. C2×#14579123C22semidirect
113. C2×C4×C22⋊D79C22semidirect
114. C2×C4×C22⋊D79C22semidirect
115. 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×#14579119C22semidirect
121. C2×#14579119C22semidirect
122. C2×#14579119C22semidirect
123. C2×#14579118C22semidirect
124. C2×#14579118C22semidirect
125. C2×#14579117C22semidirect
126. C22×Dic79⋊C4C22semidirect
127. C2×C4⋊C4×D79C22semidirect
128. C2×C4⋊C4×D79C22semidirect
129. C22×(C2×D79)⋊C4C22semidirect
130. C22×(C2×D79)⋊C4C22semidirect
131. C22×(C2×D79)⋊C4C22semidirect
132. C2×C22⋊C4×D79C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C42×D79C22semidirect
135. #554×C79C22semidirect
136. C2×C4⋊Q8×C79C22semidirect
137. C2×#125×C79C22semidirect
138. C2×#125×C79C22semidirect
139. C2×C22⋊Q8×C79C22semidirect
140. C2×C22⋊Q8×C79C22semidirect
141. C2×C22⋊Q8×C79C22semidirect
142. C2×C4×Q8×C79C22semidirect
146. C22×C4⋊C4×C79C22semidirect
150. C2×#11929625C23semidirect
188. C22×C4×D79C23semidirect
190. #14579156C23semidirect
191. #14579156C23semidirect
192. #14579156C23semidirect
193. #14579156C23semidirect
194. #14579156C23semidirect
195. #14579156C23semidirect
196. #14579152C23semidirect
197. #14579152C23semidirect
198. #14579150C23semidirect
199. #14579150C23semidirect
200. #14579150C23semidirect
201. #14579149C23semidirect
202. #14579149C23semidirect
205. #14579146C23semidirect
206. #14579146C23semidirect
207. #14579146C23semidirect
208. #14579146C23semidirect
209. #14579146C23semidirect
210. #14579146C23semidirect
211. #14579146C23semidirect
212. #14579146C23semidirect
213. #14579146C23semidirect
214. #14579146C23semidirect
215. #14579145C23semidirect
216. #14579145C23semidirect
217. #14579141C23semidirect
218. #14579141C23semidirect
219. #14579137C23semidirect
220. #14579137C23semidirect
221. #14579137C23semidirect
225. #14579136C23semidirect
226. #14579136C23semidirect
227. #14579136C23semidirect
228. #14579136C23semidirect
229. #14579136C23semidirect
231. #14579135C23semidirect
232. #14579135C23semidirect
235. #14579131C23semidirect
236. #14579131C23semidirect
237. C4×Dic158C23semidirect
238. #14579126C23semidirect
240. C4×D316C23semidirect
241. C4×D316C23semidirect
242. C4×D316C23semidirect
243. C4×D316C23semidirect
245. #14579123C23semidirect
246. #14579123C23semidirect
247. #14579123C23semidirect
248. #14579123C23semidirect
249. #14579123C23semidirect
250. C4×C22⋊D79C23semidirect
251. C4×C22⋊D79C23semidirect
252. C4×C22⋊D79C23semidirect
253. (C22⋊D79)⋊C4C23semidirect
254. (C22⋊D79)⋊C4C23semidirect
255. (C22⋊D79)⋊C4C23semidirect
256. #14579119C23semidirect
257. #14579119C23semidirect
258. #14579119C23semidirect
259. #14579118C23semidirect
260. #14579118C23semidirect
261. #14579117C23semidirect
276. C2×Dic79⋊C4C23semidirect
277. C4⋊C4×D79C23semidirect
278. C4⋊C4×D79C23semidirect
305. C2×(C2×D79)⋊C4C23semidirect
306. C2×(C2×D79)⋊C4C23semidirect
307. C2×(C2×D79)⋊C4C23semidirect
308. C22⋊C4×D79C23semidirect
309. C22⋊C4×D79C23semidirect
316. C42×D79C23semidirect
323. C4⋊Q8×C79C23semidirect
324. #125×C79C23semidirect
325. #125×C79C23semidirect
326. C22⋊Q8×C79C23semidirect
327. C22⋊Q8×C79C23semidirect
328. C22⋊Q8×C79C23semidirect
329. C4×Q8×C79C23semidirect
344. C2×C4⋊C4×C79C23semidirect
484. C2×D4×C79#41semidirect
554. D4×C79C2×#41semidirect
669. C2×C79#3513semidirect
680. C2×#554D79semidirect
702. C79C2×#3513semidirect
710. #554C2×D79semidirect
725. C2×C4⋊Q8C2×D79semidirect
737. C2×#125C2×D79semidirect
738. C2×#125C2×D79semidirect
765. C2×C22⋊Q8C2×D79semidirect
766. C2×C22⋊Q8C2×D79semidirect
767. C2×C22⋊Q8C2×D79semidirect
787. C2×C4×Q8C2×D79semidirect
818. C22×C4⋊C4C2×D79semidirect
873. C4⋊Q8C22×D79semidirect
883. #125C22×D79semidirect
884. #125C22×D79semidirect
909. C22⋊Q8C22×D79semidirect
910. C22⋊Q8C22×D79semidirect
911. C22⋊Q8C22×D79semidirect
929. C4×Q8C22×D79semidirect
984. C2×C4⋊C4C22×D79semidirect
1082. C2×D4#11929625semidirect
1247. D4C2×#11929625semidirect
1351. C2#23777343direct (N × H)

Maximal subgroups

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

subgroupindex
#237773432
C2×#190992982
C2×#190992662
C2×#190992612
C2×#190992512
C2×#190992402
C2×#190992162
C2×#190992082
C2×#190992042
C2×D4×D3162
C2×#190991872
C2×#190991692
C2×#190991622
C2×#190991532
C2×#190991002
C2×#190990982
C2×#190990762
C22×#145791462
C2×#190990422
C2×#190990352
C2×C4×D4×D792
C2×#554×C792
C2×#351379