Finite Group Databasebeta

← C2×#23773373 #35156113

Subgroups — C2×#23773373 #35156113

Order 20224.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099142C211yesmaximal, characteristic
2C2×#19099044C211yesmaximal, characteristic, complemented
3#23773373C2116yesmaximal, direct product factor
4C2×#19098900C211yesmaximal, characteristic, complemented
5C2×#19098898C211yesmaximal, characteristic, complemented
6C2×#19098906C211yesmaximal, characteristic, complemented
7C2×#19098905C211yesmaximal, characteristic, complemented
8C2×#19098886C211yesmaximal, characteristic, complemented
9C2×#19098884C211yesmaximal, characteristic, complemented
10C2×#19098875C211yesmaximal, characteristic, complemented
11C2×#19098604C211yesmaximal, characteristic, complemented
12C2×#107×D79C211yesmaximal, characteristic, complemented
13C2×#19098561C211yesmaximal, characteristic, complemented
14C2×#19098556C211yesmaximal, characteristic, complemented
15C2×#19098528C211yesmaximal, characteristic, complemented
16C2×#480×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929623C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C22×C8×D79C2211yescharacteristic
21#19099142—24no—
22#19099142C2218yes—
23C2×#14579141C2211yescharacteristic
24C2×#14579140C2211yescharacteristic
25C2×#14579138—21no—
26C2×#14579134—21no—
27C2×#14579133—21no—
28C2×#14579132—21no—
29C2×#14579132C2211yescharacteristic
30#19099044—24no—
31#19099044C2218yescomplemented
32C2×#14579126—21no—
33C2×#14579123—21no—
34C2×C4×C22⋊D79—21no—
35C2×C4×C22⋊D79—21no—
36C2×#14579120C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C2×C4⋊C4×D79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41C2×C4⋊C4×D79C2211yescharacteristic
42#19098906C2218yescomplemented
43#19098905C2218yescomplemented
44#19098900C2218yescomplemented
45#19098898C2218yescomplemented
46#19098886C2218yescomplemented
47#19098884C2218yescomplemented
48#19098875C2218yescomplemented
49#19098604C2218yescomplemented
50C2×#14579095C2211yescharacteristic
51C2×#14579094C2211yescharacteristic
52C2×#14579094C2211yescharacteristic
53C2×#14579094C2211yescharacteristic
54#107×D79C2218yescomplemented
55C2×#14579093C2211yescharacteristic
56C2×#14579092C2211yescharacteristic
57#19098561C2218yescomplemented
58#19098556C2218yescomplemented
59C2×#14579086C2211yescharacteristic
60C2×#14579086C2211yescharacteristic
61C2×#14579084C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65#19098528C2218yescomplemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic
69C2×#121×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71#480×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#107×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C2×#11929624—24no—
78C2×#11929624—24no—
79C2×#11929624D414yes—
80C2×#11929624C2314yes—
81C2×#11929623—22no—
82C2×#11929623—24no—
83C2×#11929623—24no—
84C2×#11929623C2314yes—
85C22×Dic158D411yescharacteristic
86C22×Dic158C2311yescharacteristic
87C22×D316D411yescharacteristic
88C22×C22⋊D79—21no—
89C22×C22⋊D79—21no—
90C22×C22⋊D79D411yescharacteristic
91C22×C22⋊D79D411yescharacteristic
92C23×Dic79—21no—
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79—21no—
96C22×C4×D79C2311yescharacteristic
97C22×C4×D79C2311yescharacteristic
98C2×#11929607—24no—
99C2×#11929607C2314yes—
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2311yescharacteristic
102C2×C8×D79—24no—
103C2×C8×D79C2314yes—
104#14579141—22no—
105#14579141C2314yes—
106#14579140—22no—
107#14579140C2314yes—
108#14579138—28no—
109#14579134—28no—
110#14579133—28no—
111#14579132—28no—
112#14579132—22no—
113#14579132C2314yes—
114#14579126—28no—
115#14579123—28no—
116C4×C22⋊D79—28no—
117C4×C22⋊D79—28no—
118#14579120—22no—
119#14579120C2314yes—
120#14579119—22no—
121#14579119—22no—
122#14579119C2314yes—
123#14579119C2314yes—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C4⋊C4×D79—22no—
133C4⋊C4×D79—22no—
134C4⋊C4×D79—22no—
135C4⋊C4×D79C2314yes—
136C4⋊C4×D79C2314yes—
137C4⋊C4×D79C2314yes—
138C2×C22⋊Dic79—21no—
139C2×C22⋊Dic79—21no—
140C2×C22⋊Dic79—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×C4×Dic79—21no—
145C2×C4×Dic79—21no—
146C2×C4×Dic79—21no—
147#14579095C2314yes—
148#14579094C2314yes—
149#14579094C2314yes—
150#14579094C2314yes—
151#14579093C2314yes—
152#14579092C2314yes—
153#14579086C2314yes—
154#14579086C2314yes—
155#14579084C2314yes—
156#14579084C2314yes—
157#14579082C2314yes—
158#14579082C2314yes—
159C22⋊(C79⋊C8)C2314yes—
160(C2×D79)⋊C8C2314yes—
161(C2×D79)⋊C8C2314yes—
162C22×D4×C79—21no—
163C22×D4×C79C2311yescharacteristic
164C23×C4×C79—21no—
165C23×C4×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168#121×C79—22no—
169#121×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79—22no—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C4⋊C4×C79C2314yes—
176C2×C22⋊C4×C79—21no—
177#107×C79C2314yes—
178#107×C79C2314yes—
179#102×C79C2314yes—
180#102×C79C2314yes—
181C22⋊C8×C79C2314yes—
182C23×D79C2×D411yescharacteristic
183C23×D79C2×D411yescharacteristic
184#11929624—216no—
185#11929624—28no—
186#11929624—28no—
187#11929623—28no—
188#11929623—28no—
189#11929623—48no—
190C2×Dic158—24no—
191C2×Dic158—21no—
192C2×Dic158—22no—
193C2×Dic158—22no—
194C2×Dic158C2×D414yes—
195C2×Dic158C2412yes—
196C2×D316—24no—
197C2×D316C2×D414yes—
198C2×C22⋊D79—24no—
199C2×C22⋊D79—24no—
200C2×C22⋊D79—24no—
201C2×C22⋊D79—24no—
202C2×C22⋊D79—44no—
203C2×C22⋊D79—82no—
204C2×C22⋊D79C2×D414yes—
205C2×C22⋊D79C2×D414yes—
206C22×Dic79—24no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79—44no—
212C22×Dic79C2×D411yescharacteristic
213C22×Dic79C2×D411yescharacteristic
214C2×C4×D79—24no—
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—22no—
218C2×C4×D79—22no—
219C2×C4×D79—82no—
220C2×C4×D79—82no—
221C2×C4×D79—82no—
222C2×C4×D79C2×D412yes—
223C2×C4×D79C2×D412yes—
224C2×C4×D79#4114yes—
225C2×C4×D79#4114yes—
226C2×C4×D79C2412yes—
227C2×C4×D79C2412yes—
228#11929607—28no—
229C2×C79⋊C8—22no—
230C2×C79⋊C8—22no—
231C2×C79⋊C8C2412yes—
232C2×C79⋊C8C2412yes—
233C8×D79—28no—
234C4⋊Dic79—24no—
235C4⋊Dic79—21no—
236C4⋊Dic79—21no—
237C4⋊Dic79—21no—
238C4⋊Dic79C2412yes—
239C4⋊Dic79C2412yes—
240C4⋊Dic79C2412yes—
241Dic79⋊C4—24no—
242Dic79⋊C4—24no—
243Dic79⋊C4—24no—
244Dic79⋊C4—24no—
245C22⋊Dic79—24no—
246C22⋊Dic79—24no—
247C22⋊Dic79—24no—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250(C2×D79)⋊C4—24no—
251C4×Dic79—24no—
252C4×Dic79—24no—
253C4×Dic79—24no—
254C24×C79—21no—
255C24×C79C2×D411yescharacteristic
256C2×D4×C79—24no—
257C2×D4×C79—21no—
258C2×D4×C79—22no—
259C2×D4×C79—22no—
260C2×D4×C79—82no—
261C2×D4×C79C2412yes—
262C22×C4×C79—22no—
263C22×C4×C79—22no—
264C22×C4×C79—21no—
265C22×C4×C79—21no—
266C22×C4×C79—21no—
267C22×C4×C79—24no—
268C22×C4×C79—82no—
269C22×C4×C79C2×D411yescharacteristic
270C22×C4×C79C2×D412yes—
271C22×C4×C79C2412yes—
272C22×C4×C79C2411yescharacteristic
273C2×C8×C79—22no—
274C2×C8×C79—22no—
275C2×C8×C79C2412yes—
276C2×C8×C79C2412yes—
277C4⋊C4×C79—21no—
278C4⋊C4×C79—21no—
279C4⋊C4×C79—24no—
280C4⋊C4×C79—21no—
281C4⋊C4×C79C2412yes—
282C4⋊C4×C79C2412yes—
283C4⋊C4×C79C2412yes—
284C22⋊C4×C79—24no—
285C23×C79—22no—
286C23×C79—22no—
287C23×C79—22no—
288C23×C79—22no—
289C23×C79—42no—
290C23×C79—42no—
291C23×C79—42no—
292C23×C79C22×D412yes—
293C23×C79C22×D411yescharacteristic
294C22×D79—22no—
295C22×D79—22no—
296C22×D79—22no—
297C22×D79—22no—
298C22×D79—22no—
299C22×D79#12314yes—
300C22×D79C22×D412yes—
301C22×D79C22×D412yes—
302D4×C79—22no—
303D4×C79—22no—
304D4×C79—42no—
305D4×C79—84no—
306C2×C4×C79—22no—
307C2×C4×C79—24no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—42no—
314C2×C4×C79—42no—
315C2×C4×C79—42no—
316C2×C4×C79—84no—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D411yescharacteristic
319C2×C4×C79C2×#4112yes—
320C2×C4×C79C2×#4112yes—
321C2×C4×C79C2511yescharacteristic
322C22⋊D79—28no—
323C22⋊D79—28no—
324C22⋊D79—48no—
325C22⋊D79—84no—
326C2×Dic79—22no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79—42no—
334C2×Dic79—42no—
335C2×Dic79—48no—
336C2×Dic79#12314yes—
337C2×Dic79C22×D412yes—
338C2×Dic79C22×D412yes—
339D316—28no—
340C4×D79—24no—
341C4×D79—22no—
342C4×D79—22no—
343C4×D79—84no—
344C4×D79—84no—
345C4×D79—84no—
346C4×D79#12318yes—
347C4×D79C2×#4114yes—
348C4×D79C2×#4114yes—
349Dic158—28no—
350Dic158—22no—
351Dic158—22no—
352Dic158—42no—
353C8×C79—22no—
354C8×C79—22no—
355C79⋊C8—22no—
356C79⋊C8—22no—
357C22×C79—22no—
358C22×C79—22no—
359C22×C79—22no—
360C22×C79—44no—
361C22×C79—42no—
362C22×C79—42no—
363C22×C79—42no—
364C22×C79—84no—
365C22×C79C2×#12312yes—
366C22×C79#57612yes—
367C22×C79#57812yes—
368C22×C79C23×D411yescharacteristic
369C2×D79—28no—
370C2×D79—22no—
371C2×D79—22no—
372C2×D79—22no—
373C2×D79—22no—
374C2×D79—22no—
375C2×D79—44no—
376C2×D79C2×#12314yes—
377C4×C79—22no—
378C4×C79—42no—
379C4×C79—42no—
380C4×C79—42no—
381C4×C79C2×#12312yes—
382C4×C79C22×#4111yescharacteristic
383C4×C79C22×#4111yescharacteristic
384Dic79—22no—
385Dic79—42no—
386Dic79—42no—
387Dic79—42no—
388Dic79—42no—
389Dic79C2×#12314yes—
390C2×#3098—791nomaximal, Sylow
391C2×C79—42no—
392C2×C79—82no—
393C2×C79#309814yescomplemented
394C2×C79C22×#12311yescharacteristic
395C2×C79C2×#57611yescharacteristic
396C2×C79C2×#57811yescharacteristic
397D79—24no—
398D79—42no—
399C2×#537—791no—
400C2×#520—791no—
401#3098—7916no—
402C2×#484—791no—
403C2×#484—791no—
404C2×#485—791no—
405C2×#485—791no—
406C2×#482—791no—
407C2×#482—791no—
408C2×#480—791no—
409C2×#480D7911yescharacteristic, complemented
410C2×#428—791no—
411C22×#107—791no—
412C2×#417—791no—
413C2×#416—791no—
414C2×#408—791no—
415C79C2×#309811yescharacteristic, complemented, Sylow
416C22×#41—791no—
417C22×#41—791no—
418C22×M16—791no—
419C23×C8—791no—
420#537—798no—
421#537—1584no—
422C2×C22⋊Q8—791no—
423C2×C22⋊Q8—791no—
424C2×C22⋊Q8—1581no—
425C2×#121—791no—
426C2×#121—1581no—
427C2×#121—1581no—
428C2×#121—1581no—
429C2×#121C2×D7911yescharacteristic
430#520—798no—
431#520—1584no—
432C2×C4×Q8—1581no—
433C2×C4×D4—1581no—
434C2×C4×D4—1581no—
435C2×C4×D4—1581no—
436C2×#117—791no—
437C2×#117—791no—
438C2×#117—791no—
439C22×C4⋊C4—791no—
440C22×C4⋊C4—791no—
441C22×C4⋊C4—791no—
442C22×C4⋊C4C2×D7911yescharacteristic
443#485—798no—
444#485—798no—
445#484—798no—
446#484—798no—
447#482—798no—
448#482—798no—
449#480—798no—
450#480C2×D7918yescomplemented
451#428—798no—
452C2×#107—791no—
453C2×#107—791no—
454C2×#107—791no—
455C2×#107—791no—
456C2×#107—798no—
457C2×#107C2×D7911yescharacteristic
458C2×#107C2×D7911yescharacteristic
459C2×#106—791no—
460C2×#106—791no—
461#417—798no—
462#416—798no—
463C2×#103—791no—
464C2×#103—791no—
465C2×#103—791no—
466C2×#103—791no—
467C2×#102—791no—
468C2×#102—791no—
469C2×#102C2×D7911yescharacteristic
470C2×#102C2×D7911yescharacteristic
471#408—798no—
472C2×C22⋊C8—791no—
473C2×C22⋊C8—791no—
474C2×C22⋊C8—791no—
475C2×C22⋊C8C2×D7911yescharacteristic
476C2×#41—794no—
477C2×#41—794no—
478C2×#41—794no—
479C2×#41—1584no—
480C2×#41—1584no—
481C2×#41—1584no—
482C2×#41—1584no—
483C2×#41—1582no—
484C22×Q8—791no—
485C22×Q8—791no—
486C22×D4—21no—
487C22×D4—791no—
488C22×D4—791no—
489C22×D4—791no—
490C22×D4—1581no—
491C22×D4—1581no—
492C22×D4C22×D7911yescharacteristic
493C23×C4—21no—
494C23×C4—791no—
495C23×C4—791no—
496C23×C4—1581no—
497C23×C4—1581no—
498C23×C4—1581no—
499C23×C4—1581no—
500C23×C4C22×D7911yescharacteristic
501C2×M16—794no—
502C2×M16—1584no—
503C22×C8—791no—
504C22×C8—791no—
505C22×C8—794no—
506C22×C8—1584no—
507C22×C8C22×D7911yescharacteristic
508C22×C8C22×D7911yescharacteristic
509C22⋊Q8—794no—
510C22⋊Q8—794no—
511C22⋊Q8—1588no—
512C22⋊Q8—1582no—
513C22⋊Q8—1582no—
514#121—22no—
515#121—794no—
516#121—1588no—
517#121—1582no—
518#121—1588no—
519#121—1588no—
520#121C22×D7914yes—
521C4×Q8—1588no—
522C4×D4—1588no—
523C4×D4—1588no—
524C4×D4—1588no—
525#117—794no—
526#117—794no—
527#117—794no—
528#117—1582no—
529#117—1582no—
530#117—1582no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—791no—
534C2×C4⋊C4—791no—
535C2×C4⋊C4—791no—
536C2×C4⋊C4—794no—
537C2×C4⋊C4—794no—
538C2×C4⋊C4—794no—
539C2×C4⋊C4—1582no—
540C2×C4⋊C4—1582no—
541C2×C4⋊C4—1582no—
542C2×C4⋊C4—1581no—
543C2×C4⋊C4—1581no—
544C2×C4⋊C4—1581no—
545C2×C4⋊C4—1581no—
546C2×C4⋊C4—1581no—
547C2×C4⋊C4C22×D7911yescharacteristic
548C2×C4⋊C4C22×D7911yescharacteristic
549C2×C4⋊C4C22×D7911yescharacteristic
550C2×C4⋊C4C22×D7914yes—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1581no—
553C2×C22⋊C4—1581no—
554C2×C22⋊C4—1581no—
555C2×C22⋊C4—1581no—
556C2×C22⋊C4—1581no—
557C2×C22⋊C4—1581no—
558C2×C42—1581no—
559C2×C42—1581no—
560C2×C42—1581no—
561#107—794no—
562#107—794no—
563#107—794no—
564#107—794no—
565#107C22×D7914yes—
566#107C22×D7914yes—
567#106—794no—
568#106—794no—
569#103—794no—
570#103—794no—
571#103—794no—
572#103—794no—
573#102—794no—
574#102—794no—
575#102C22×D7914yes—
576#102C22×D7914yes—
577C22⋊C8—794no—
578C22⋊C8—794no—
579C22⋊C8—794no—
580C22⋊C8C22×D7914yes—
581C24—21no—
582C24—791no—
583C24—791no—
584C24D4×D7911yescharacteristic
585#41—3168no—
586#41—15816no—
587#41—1588no—
588#41—1588no—
589#41—1588no—
590#41—1588no—
591C2×Q8—794no—
592C2×Q8—792no—
593C2×Q8—1584no—
594C2×Q8—1582no—
595C2×Q8—1582no—
596C2×Q8—1581no—
597C2×D4—24no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—82no—
602C2×D4—3164no—
603C2×D4—794no—
604C2×D4—794no—
605C2×D4—794no—
606C2×D4—6322no—
607C2×D4—1584no—
608C2×D4—1584no—
609C2×D4—1584no—
610C2×D4—1584no—
611C2×D4—1584no—
612C2×D4C23×D7912yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—3164no—
621C22×C4—791no—
622C22×C4—794no—
623C22×C4—794no—
624C22×C4—792no—
625C22×C4—792no—
626C22×C4—791no—
627C22×C4—792no—
628C22×C4—792no—
629C22×C4—6322no—
630C22×C4—6322no—
631C22×C4—6322no—
632C22×C4—1584no—
633C22×C4—1584no—
634C22×C4—1584no—
635C22×C4—1584no—
636C22×C4—1581no—
637C22×C4—1581no—
638C22×C4—1581no—
639C22×C4—1581no—
640C22×C4—1582no—
641C22×C4—1582no—
642C22×C4D4×D7912yes—
643C22×C4D4×D7911yescharacteristic
644C22×C4C23×D7912yes—
645C22×C4C23×D7911yescharacteristic
646M16—1588no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—792no—
650C2×C8—792no—
651C2×C8—1588no—
652C2×C8—1582no—
653C2×C8—1582no—
654C2×C8C23×D7912yes—
655C2×C8C23×D7912yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—792no—
661C4⋊C4—792no—
662C4⋊C4—792no—
663C4⋊C4—1584no—
664C4⋊C4—1584no—
665C4⋊C4—1584no—
666C4⋊C4—1584no—
667C4⋊C4—1584no—
668C4⋊C4—1581no—
669C4⋊C4—1581no—
670C4⋊C4—1581no—
671C4⋊C4C23×D7912yes—
672C4⋊C4C23×D7912yes—
673C4⋊C4C23×D7912yes—
674C22⋊C4—24no—
675C22⋊C4—1584no—
676C22⋊C4—1584no—
677C22⋊C4—1584no—
678C22⋊C4—1584no—
679C22⋊C4—1584no—
680C22⋊C4—1584no—
681C42—1584no—
682C42—1584no—
683C42—1584no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—794no—
692C23—792no—
693C23—792no—
694C23—1582no—
695C23—1582no—
696C23—1582no—
697C23—1582no—
698C23—1582no—
699C23C2×D4×D7912yes—
700C23C2×D4×D7911yescharacteristic
701Q8—3162no—
702Q8—1588no—
703Q8—1582no—
704Q8—1582no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—84no—
709D4—3168no—
710D4—6324no—
711D4—1588no—
712D4—1588no—
713D4—1588no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—84no—
725C2×C4—3162no—
726C2×C4—3162no—
727C2×C4—3162no—
728C2×C4—3162no—
729C2×C4—3168no—
730C2×C4—794no—
731C2×C4—792no—
732C2×C4—798no—
733C2×C4—794no—
734C2×C4—794no—
735C2×C4—792no—
736C2×C4—6324no—
737C2×C4—6324no—
738C2×C4—6324no—
739C2×C4—1582no—
740C2×C4—1582no—
741C2×C4—1582no—
742C2×C4—1582no—
743C2×C4—1582no—
744C2×C4—1584no—
745C2×C4—1582no—
746C2×C4—1582no—
747C2×C4C2×D4×D7912yes—
748C2×C4C2×D4×D7911yescharacteristic
749C2×C4#41×D7912yes—
750C2×C4#41×D7912yes—
751C2×C4C24×D7911yescharacteristic
752C8—22no—
753C8—22no—
754C8—1582no—
755C8—1582no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—3164no—
765C22—794no—
766C22—1582no—
767C22—1582no—
768C22—1582no—
769C22—1582no—
770C22—1582no—
771C22—1588no—
772C22#123×D7912yes—
773C22#1909936412yes—
774C22#1909937912yes—
775C22C22×D4×D7911yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—3162no—
781C4—3162no—
782C4—3162no—
783C4—3162no—
784C4—794no—
785C4—1582no—
786C4#123×D7912yes—
787C4C2×#41×D7911yescharacteristic
788C4C2×#41×D7911yescharacteristic
789C2—42no—
790C2—82no—
791C2—3162no—
792C2—1584no—
793C2#2377337314yesdirect product factor
794C2C2×#123×D7911yescharacteristic
795C2C2×#1909936411yescharacteristic
796C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#480×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099142C2
hypercenterC2×#480D79
hypocenterC79C2×#3098
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C2×#19099044C2semidirect
3. #23773373C2direct (N × H)
4. C2×#19098900C2semidirect
5. C2×#19098898C2semidirect
6. C2×#19098906C2semidirect
7. C2×#19098905C2semidirect
8. C2×#19098886C2semidirect
9. C2×#19098884C2semidirect
10. C2×#19098875C2semidirect
11. C2×#19098604C2semidirect
12. C2×#107×D79C2semidirect
13. C2×#19098561C2semidirect
14. C2×#19098556C2semidirect
15. C2×#19098528C2semidirect
16. C2×#480×C79C2semidirect
31. #19099044C22semidirect
42. #19098906C22semidirect
43. #19098905C22semidirect
44. #19098900C22semidirect
45. #19098898C22semidirect
46. #19098886C22semidirect
47. #19098884C22semidirect
48. #19098875C22semidirect
49. #19098604C22semidirect
54. #107×D79C22semidirect
57. #19098561C22semidirect
58. #19098556C22semidirect
65. #19098528C22semidirect
71. #480×C79C22semidirect
393. C2×C79#3098semidirect
409. C2×#480D79semidirect
415. C79C2×#3098semidirect
450. #480C2×D79semidirect
793. C2#23773373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991422
C2×#190990442
#237733732
C2×#190989002
C2×#190988982
C2×#190989062
C2×#190989052
C2×#190988862
C2×#190988842
C2×#190988752
C2×#190986042
C2×#107×D792
C2×#190985612
C2×#190985562
C2×#190985282
C2×#480×C792
C2×#309879