Finite Group Databasebeta

← C2×#23775806 #35166746

Subgroups — C2×#23775806 #35166746

Order 20224.

1918 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099284C211yesmaximal, characteristic, complemented
2C2×#19099276C211yesmaximal, characteristic
3#23775806C2116yesmaximal, direct product factor
4C2×#19098960C211yesmaximal, characteristic, complemented
5C2×#19098902C211yesmaximal, characteristic, complemented
6C2×#19098889C211yesmaximal, characteristic, complemented
7C2×#19098888C211yesmaximal, characteristic, complemented
8C2×#19098856C211yesmaximal, characteristic, complemented
9C2×#19098842C211yesmaximal, characteristic, complemented
10C2×#19098795C211yesmaximal, characteristic, complemented
11C2×#19098794C211yesmaximal, characteristic, complemented
12C2×#19098648C211yesmaximal, characteristic, complemented
13C2×(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
14C2×#19098600C211yesmaximal, characteristic, complemented
15C2×#19098599C211yesmaximal, characteristic, complemented
16C2×#485×C79C211yesmaximal, characteristic, complemented
17C22×#11929611C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099284—24no—
21#19099284C2218yescomplemented
22#19099276—24no—
23#19099276C2218yes—
24C2×#14579160C2211yescharacteristic
25C2×#14579160C2211yescharacteristic
26C2×#14579156—21no—
27C2×#14579154—21no—
28C2×#14579149—21no—
29C2×#14579147—21no—
30C2×#14579147—21no—
31C2×#14579137C2211yescharacteristic
32C2×#14579136C2211yescharacteristic
33C2×#14579135C2211yescharacteristic
34C2×#14579134—21no—
35C2×Q8×Dic79C2211yescharacteristic
36C2×#14579126—21no—
37C2×#14579123C2211yescharacteristic
38C2×C4×C22⋊D79C2211yescharacteristic
39C2×#14579120C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×#14579119C2211yescharacteristic
42C2×#14579118—21no—
43#19098960C2218yescomplemented
44#19098902C2218yescomplemented
45#19098889C2218yescomplemented
46#19098888C2218yescomplemented
47#19098856C2218yescomplemented
48#19098842C2218yescomplemented
49#19098795C2218yescomplemented
50#19098794C2218yescomplemented
51#19098648C2218yescomplemented
52(C22⋊D79)⋊C8C2218yescomplemented
53#19098600C2218yescomplemented
54#19098599C2218yescomplemented
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×#14579092C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C2×C22⋊Q8×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71#485×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#103×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158—21no—
79C22×D316—21no—
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C22×C22⋊D79D411yescharacteristic
83C22×C4×D79—21no—
84C22×C4×D79C2311yescharacteristic
85C2×#11929611—24no—
86C2×#11929611C2314yes—
87C22×C79⋊C8—24no—
88C22×C79⋊C8C2314yes—
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91C2×C8×D79—24no—
92C2×C8×D79C2314yes—
93#14579160—22no—
94#14579160—22no—
95#14579160C2314yes—
96#14579160C2314yes—
97#14579156—28no—
98#14579154—28no—
99#14579149—28no—
100#14579147—28no—
101#14579147—28no—
102#14579137—22no—
103#14579137C2314yes—
104#14579136—22no—
105#14579136C2314yes—
106#14579135—22no—
107#14579135C2314yes—
108#14579134—28no—
109Q8×Dic79—22no—
110Q8×Dic79C2314yes—
111#14579126—28no—
112#14579123—22no—
113#14579123C2314yes—
114C4×C22⋊D79D414yes—
115C4×C22⋊D79C2314yes—
116#14579120—22no—
117#14579120C2314yes—
118#14579119—22no—
119#14579119—22no—
120#14579119C2314yes—
121#14579119C2314yes—
122#14579118—28no—
123C2×C4⋊Dic79—21no—
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×Dic79⋊C4—21no—
128C2×Dic79⋊C4—21no—
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4D411yescharacteristic
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79D411yescharacteristic
133C2×(C2×D79)⋊C4—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4D411yescharacteristic
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579095C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151#14579092C2314yes—
152Dic79⋊C8C2314yes—
153#14579085C2314yes—
154#14579083C2314yes—
155#14579083C2314yes—
156#14579081C2314yes—
157(C2×D79)⋊C8C2314yes—
158C8×Dic79C2314yes—
159C22×Q8×C79C2311yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C22×C8×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163C22⋊Q8×C79—22no—
164C22⋊Q8×C79C2314yes—
165#117×C79—22no—
166#117×C79C2314yes—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C22⋊C4×C79—21no—
173C2×C42×C79—21no—
174#107×C79C2314yes—
175#106×C79C2314yes—
176#103×C79C2314yes—
177#103×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C23×D79—21no—
180C23×D79C2×D411yescharacteristic
181C2×Dic158—24no—
182C2×Dic158—24no—
183C2×Dic158—44no—
184C2×Dic158—82no—
185C2×D316—24no—
186C2×D316—21no—
187C2×D316—22no—
188C2×D316—22no—
189C2×D316—82no—
190C2×D316C2412yes—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—24no—
193C2×C22⋊D79—82no—
194C2×C22⋊D79C2×D414yes—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C2×C4×D79—24no—
202C2×C4×D79—22no—
203C2×C4×D79—22no—
204C2×C4×D79—44no—
205C2×C4×D79C2×D412yes—
206C2×C4×D79C2412yes—
207#11929611—28no—
208C2×C79⋊C8—28no—
209C2×C79⋊C8—22no—
210C2×C79⋊C8#4114yes—
211C2×C79⋊C8C2412yes—
212C2×C79⋊C8C2412yes—
213C8×D79—28no—
214C4⋊Dic79—24no—
215C4⋊Dic79—21no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225C22⋊Dic79—24no—
226C22⋊Dic79C2×D414yes—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4C2×D414yes—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79—24no—
238C4×Dic79C2×D412yes—
239C4×Dic79C2412yes—
240C24×C79C2×D411yescharacteristic
241C2×Q8×C79—21no—
242C2×Q8×C79—22no—
243C2×Q8×C79—22no—
244C2×Q8×C79C2412yes—
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D412yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2411yescharacteristic
255C2×C8×C79—22no—
256C2×C8×C79—22no—
257C2×C8×C79C2412yes—
258C2×C8×C79C2412yes—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C4⋊C4×C79C2412yes—
266C22⋊C4×C79—24no—
267C22⋊C4×C79—24no—
268C42×C79—24no—
269C23×C79—22no—
270C23×C79—22no—
271C23×C79—22no—
272C23×C79C22×D412yes—
273C23×C79C22×D411yescharacteristic
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—42no—
279C22×D79—42no—
280C22×D79—42no—
281C22×D79C22×D412yes—
282Q8×C79—22no—
283Q8×C79—22no—
284Q8×C79—42no—
285C2×C4×C79—22no—
286C2×C4×C79—24no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—42no—
294C2×C4×C79—42no—
295C2×C4×C79—42no—
296C2×C4×C79—42no—
297C2×C4×C79C22×D412yes—
298C2×C4×C79C22×D411yescharacteristic
299C2×C4×C79C2×#4112yes—
300C2×C4×C792−1+412yes—
301C2×C4×C79C2511yescharacteristic
302C22⋊D79—28no—
303C22⋊D79—84no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—42no—
310C2×Dic79—42no—
311C2×Dic79—42no—
312C2×Dic79#13514yes—
313C2×Dic79C22×D412yes—
314C2×Dic79C22×D412yes—
315C2×Dic79C22×D412yes—
316D316—22no—
317D316—22no—
318D316—42no—
319D316—84no—
320C4×D79—24no—
321C4×D79—22no—
322C4×D79—22no—
323C4×D79—48no—
324Dic158—48no—
325Dic158—84no—
326C8×C79—22no—
327C8×C79—22no—
328C79⋊C8—22no—
329C79⋊C8C2×#4114yes—
330C22×C79—22no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—44no—
334C22×C79#54712yes—
335C22×C79C2×#13512yes—
336C22×C79#57712yes—
337C22×C79C23×D411yescharacteristic
338C2×D79—22no—
339C2×D79—22no—
340C2×D79—22no—
341C2×D79—44no—
342C2×D79—42no—
343C2×D79—42no—
344C2×D79—42no—
345C2×D79—84no—
346C4×C79—22no—
347C4×C79—42no—
348C4×C79—42no—
349C4×C79—42no—
350C4×C79—42no—
351C4×C79#54712yes—
352C4×C79C22×#4111yescharacteristic
353C4×C79C2×2−1+411yescharacteristic
354Dic79—22no—
355Dic79—22no—
356Dic79—42no—
357Dic79—42no—
358Dic79—42no—
359Dic79C2×#13514yes—
360C2×#3340—791nomaximal, Sylow
361C2×C79—42no—
362C2×C79#334014yescomplemented
363C2×C79C2×#54711yescharacteristic
364C2×C79C22×#13511yescharacteristic
365C2×C79C2×#57711yescharacteristic
366D79—42no—
367D79—82no—
368C2×#556—791no—
369C2×#555—791no—
370#3340—7916no—
371C2×#498—791no—
372C2×#485—791no—
373C2×#485D7911yescharacteristic, complemented
374C2×#482—791no—
375C2×#482—791no—
376C2×#477—791no—
377C2×#474—791no—
378C2×#465—791no—
379C2×#465—791no—
380C2×C4×SD16—791no—
381C2×C8×D4—791no—
382C2×#427—791no—
383C2×#427—791no—
384C79C2×#334011yescharacteristic, complemented, Sylow
385C22×SD16—791no—
386C23×C8—791no—
387C23×C8—791no—
388#556—798no—
389#556—1584no—
390#555—798no—
391#555—1584no—
392C2×C4⋊Q8—791no—
393C2×C4⋊Q8—791no—
394C2×#126—1581no—
395C2×#126—1581no—
396C2×#124—1581no—
397C2×#124—1581no—
398C2×#124—1581no—
399C2×C22⋊Q8—791no—
400C2×C22⋊Q8C2×D7911yescharacteristic
401C2×#121—791no—
402C2×#121—791no—
403C2×#121—1581no—
404C2×C4×Q8—791no—
405C2×C4×Q8—1581no—
406C2×C4×D4—791no—
407C2×C4×D4—791no—
408C2×#117—791no—
409C2×#117—791no—
410C2×#117—791no—
411C2×#117—1581no—
412C2×#117C2×D7911yescharacteristic
413#498—798no—
414#485—798no—
415#485C2×D7918yescomplemented
416#482—798no—
417#482—798no—
418#477—798no—
419#474—798no—
420#465—798no—
421#465—798no—
422C4×SD16—798no—
423C8×D4—798no—
424#427—798no—
425#427—798no—
426C2×#107—791no—
427C2×#107—791no—
428C2×#107—791no—
429C2×#107C2×D7911yescharacteristic
430C2×#106—791no—
431C2×#106—791no—
432C2×#106—791no—
433C2×#106—791no—
434C2×#106C2×D7911yescharacteristic
435C2×C4⋊C8—791no—
436C2×#103—791no—
437C2×#103C2×D7911yescharacteristic
438C2×#103C2×D7911yescharacteristic
439C2×#102—791no—
440C2×#102—791no—
441C2×#102—791no—
442C2×C22⋊C8—791no—
443C2×C22⋊C8C2×D7911yescharacteristic
444C2×C4×C8—791no—
445C22×Q8—1581no—
446C22×Q8—1581no—
447C22×Q8C22×D7911yescharacteristic
448C22×D4—791no—
449C22×D4—791no—
450C22×D4—1581no—
451C22×D4—1581no—
452C23×C4—791no—
453C23×C4—1581no—
454C23×C4C22×D7911yescharacteristic
455C2×SD16—794no—
456C2×SD16—1584no—
457C22×C8—791no—
458C22×C8—791no—
459C22×C8—794no—
460C22×C8—794no—
461C22×C8—1584no—
462C22×C8—1584no—
463C22×C8C22×D7911yescharacteristic
464C22×C8C22×D7911yescharacteristic
465C4⋊Q8—794no—
466C4⋊Q8—794no—
467C4⋊Q8—1582no—
468C4⋊Q8—1582no—
469#126—1588no—
470#126—1588no—
471#124—1588no—
472#124—1588no—
473#124—1588no—
474C22⋊Q8—22no—
475C22⋊Q8—794no—
476C22⋊Q8—1582no—
477C22⋊Q8C22×D7914yes—
478#121—794no—
479#121—794no—
480#121—1588no—
481#121—1582no—
482#121—1582no—
483C4×Q8—794no—
484C4×Q8—1582no—
485C4×Q8—1588no—
486C4×D4—794no—
487C4×D4—794no—
488C4×D4—794no—
489C4×D4—1582no—
490#117—22no—
491#117—794no—
492#117—794no—
493#117—794no—
494#117—1588no—
495#117—1582no—
496#117—1582no—
497#117—1582no—
498#117C22×D7914yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—791no—
501C2×C4⋊C4—791no—
502C2×C4⋊C4—791no—
503C2×C4⋊C4—791no—
504C2×C4⋊C4—1581no—
505C2×C4⋊C4—1581no—
506C2×C4⋊C4—1581no—
507C2×C4⋊C4—1581no—
508C2×C4⋊C4C22×D7911yescharacteristic
509C2×C4⋊C4C22×D7911yescharacteristic
510C2×C4⋊C4C22×D7911yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—791no—
514C2×C22⋊C4—791no—
515C2×C22⋊C4—1581no—
516C2×C22⋊C4—1581no—
517C2×C22⋊C4—1581no—
518C2×C22⋊C4—1581no—
519C2×C22⋊C4—1581no—
520C2×C22⋊C4—1581no—
521C2×C22⋊C4—1581no—
522C2×C42—21no—
523C2×C42—791no—
524C2×C42—1581no—
525C2×C42—1581no—
526C2×C42—1581no—
527C2×C42—1581no—
528#107—794no—
529#107—794no—
530#107—794no—
531#107C22×D7914yes—
532#106—794no—
533#106—794no—
534#106—794no—
535#106—794no—
536#106C22×D7914yes—
537C4⋊C8—794no—
538#103—794no—
539#103C22×D7914yes—
540#103C22×D7914yes—
541#102—794no—
542#102—794no—
543#102—794no—
544C22⋊C8—794no—
545C22⋊C8C22×D7914yes—
546C4×C8—794no—
547C24—791no—
548C24—1581no—
549C24D4×D7911yescharacteristic
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—3164no—
554C2×Q8—6322no—
555C2×Q8—1584no—
556C2×Q8—1584no—
557C2×Q8C23×D7912yes—
558C2×D4—794no—
559C2×D4—792no—
560C2×D4—6322no—
561C2×D4—6322no—
562C2×D4—1584no—
563C2×D4—1584no—
564C2×D4—1584no—
565C2×D4—1582no—
566C2×D4—1582no—
567C2×D4—1581no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—3164no—
575C22×C4—791no—
576C22×C4—791no—
577C22×C4—791no—
578C22×C4—792no—
579C22×C4—792no—
580C22×C4—1584no—
581C22×C4—1581no—
582C22×C4—1581no—
583C22×C4—1581no—
584C22×C4—1582no—
585C22×C4—1582no—
586C22×C4D4×D7912yes—
587C22×C4D4×D7911yescharacteristic
588C22×C4C23×D7912yes—
589C22×C4C23×D7911yescharacteristic
590SD16—1588no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—794no—
594C2×C8—792no—
595C2×C8—792no—
596C2×C8—1588no—
597C2×C8—1588no—
598C2×C8—1582no—
599C2×C8C23×D7912yes—
600C2×C8C23×D7912yes—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—794no—
606C4⋊C4—792no—
607C4⋊C4—792no—
608C4⋊C4—792no—
609C4⋊C4—1584no—
610C4⋊C4—1584no—
611C4⋊C4—1584no—
612C4⋊C4—1584no—
613C4⋊C4—1581no—
614C4⋊C4—1581no—
615C4⋊C4—1581no—
616C4⋊C4C23×D7912yes—
617C4⋊C4C23×D7912yes—
618C4⋊C4C23×D7912yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—794no—
622C22⋊C4—794no—
623C22⋊C4—1584no—
624C22⋊C4—1584no—
625C22⋊C4—1584no—
626C22⋊C4—1584no—
627C22⋊C4—1584no—
628C22⋊C4—1584no—
629C22⋊C4—1584no—
630C42—24no—
631C42—792no—
632C42—792no—
633C42—1584no—
634C42—1584no—
635C42—1584no—
636C42—1584no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—3162no—
641C23—3162no—
642C23—3162no—
643C23—792no—
644C23—1582no—
645C23—1582no—
646C23—1582no—
647C23—1582no—
648C23C2×D4×D7912yes—
649C23C2×D4×D7911yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—42no—
653Q8—3168no—
654Q8—6324no—
655D4—3162no—
656D4—6324no—
657D4—6324no—
658D4—1588no—
659D4—1582no—
660D4—1582no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—3168no—
674C2×C4—3162no—
675C2×C4—3162no—
676C2×C4—3162no—
677C2×C4—794no—
678C2×C4—792no—
679C2×C4—792no—
680C2×C4—792no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1582no—
685C2×C4—1582no—
686C2×C4—1582no—
687C2×C4—1584no—
688C2×C4—1582no—
689C2×C4C2×D4×D7912yes—
690C2×C4C2×D4×D7911yescharacteristic
691C2×C4#41×D7912yes—
692C2×C4#1457920812yes—
693C2×C4C24×D7911yescharacteristic
694C8—22no—
695C8—22no—
696C8—794no—
697C8—1582no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—3164no—
703C22—3162no—
704C22—3162no—
705C22—3162no—
706C22—6324no—
707C22—1582no—
708C22—1582no—
709C22—1582no—
710C22#1909921112yes—
711C22#135×D7912yes—
712C22#1909937212yes—
713C22C22×D4×D7911yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—3162no—
720C4—3162no—
721C4—3162no—
722C4—794no—
723C4—1582no—
724C4—1582no—
725C4#1909921112yes—
726C4C2×#41×D7911yescharacteristic
727C4C2×#1457920811yescharacteristic
728C2—42no—
729C2—3162no—
730C2—6322no—
731C2#2377580614yesdirect product factor
732C2C2×#1909921111yescharacteristic
733C2C2×#135×D7911yescharacteristic
734C2C2×#1909937211yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#485×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099276C2
hypercenterC2×#485D79
hypocenterC79C2×#3340
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#19099284C2semidirect
3. #23775806C2direct (N × H)
4. C2×#19098960C2semidirect
5. C2×#19098902C2semidirect
6. C2×#19098889C2semidirect
7. C2×#19098888C2semidirect
8. C2×#19098856C2semidirect
9. C2×#19098842C2semidirect
10. C2×#19098795C2semidirect
11. C2×#19098794C2semidirect
12. C2×#19098648C2semidirect
13. C2×(C22⋊D79)⋊C8C2semidirect
14. C2×#19098600C2semidirect
15. C2×#19098599C2semidirect
16. C2×#485×C79C2semidirect
21. #19099284C22semidirect
43. #19098960C22semidirect
44. #19098902C22semidirect
45. #19098889C22semidirect
46. #19098888C22semidirect
47. #19098856C22semidirect
48. #19098842C22semidirect
49. #19098795C22semidirect
50. #19098794C22semidirect
51. #19098648C22semidirect
52. (C22⋊D79)⋊C8C22semidirect
53. #19098600C22semidirect
54. #19098599C22semidirect
71. #485×C79C22semidirect
362. C2×C79#3340semidirect
373. C2×#485D79semidirect
384. C79C2×#3340semidirect
415. #485C2×D79semidirect
731. C2#23775806direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992842
C2×#190992762
#237758062
C2×#190989602
C2×#190989022
C2×#190988892
C2×#190988882
C2×#190988562
C2×#190988422
C2×#190987952
C2×#190987942
C2×#190986482
C2×(C22⋊D79)⋊C82
C2×#190986002
C2×#190985992
C2×#485×C792
C2×#334079