Finite Group Databasebeta

← C2×#23773511 #35156451

Subgroups — C2×#23773511 #35156451

Order 20224.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099097C211yesmaximal, characteristic, complemented
2C2×C4×#11929624C211yesmaximal, characteristic, complemented
3#23773511C2116yesmaximal, direct product factor
4C2×#19098905C211yesmaximal, characteristic, complemented
5C2×#19098888C211yesmaximal, characteristic, complemented
6C2×#19098871C211yesmaximal, characteristic, complemented
7C2×#19098864C211yesmaximal, characteristic, complemented
8C2×#19098786C211yesmaximal, characteristic, complemented
9C2×#19098779C211yesmaximal, characteristic, complemented
10C2×#19098727C211yesmaximal, characteristic, complemented
11C2×#19098710C211yesmaximal, characteristic
12C2×#19098676C211yesmaximal, characteristic, complemented
13C2×#19098671C211yesmaximal, characteristic, complemented
14C2×#19098665C211yesmaximal, characteristic, complemented
15C2×#19098665C211yesmaximal, characteristic, complemented
16C2×#432×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×Dic316C2211yescharacteristic
19C22×#11929613C2211yescharacteristic
20C22×#11929613C2211yescharacteristic
21C22×D632C2211yescharacteristic
22#19099097—24no—
23#19099097C2218yescomplemented
24C2×#14579155—21no—
25C2×#14579153C2211yescharacteristic
26C2×#14579149C2211yescharacteristic
27C2×#14579144—21no—
28C2×#14579140C2211yescharacteristic
29C2×#14579135C2211yescharacteristic
30C4×#11929624—24no—
31C4×#11929624C2218yescomplemented
32C2×C4×Dic158C2211yescharacteristic
33C2×C4×Dic158C2211yescharacteristic
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×C4×D316C2211yescharacteristic
38C2×C4×C22⋊D79—21no—
39C2×C4×C22⋊D79—21no—
40C2×C4×C22⋊D79—21no—
41C2×#14579120C2211yescharacteristic
42C2×#14579118—21no—
43C2×#14579118—21no—
44C2×C42×D79—21no—
45#19098905C2218yescomplemented
46#19098888C2218yescomplemented
47#19098871C2218yescomplemented
48#19098864C2218yescomplemented
49#19098786C2218yescomplemented
50#19098779C2218yescomplemented
51#19098727C2218yescomplemented
52#19098710C2218yes—
53#19098676C2218yescomplemented
54#19098671C2218yescomplemented
55#19098665C2218yescomplemented
56#19098665C2218yescomplemented
57C2×#14579095C2211yescharacteristic
58C2×#14579095C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579093C2211yescharacteristic
61C2×#14579086C2211yescharacteristic
62C2×#14579086C2211yescharacteristic
63C2×#14579086C2211yescharacteristic
64C2×#14579086C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C22×C42×C79C2211yescharacteristic
70#432×C79C2218yescomplemented
71C2×C4⋊C8×C79C2211yescharacteristic
72C2×C4⋊C8×C79C2211yescharacteristic
73C2×C22⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×#97×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—24no—
79C2×#11929624—24no—
80C2×#11929624C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×Dic158C2311yescharacteristic
83C22×D316C2311yescharacteristic
84C22×D316C2311yescharacteristic
85C22×C22⋊D79—21no—
86C22×C22⋊D79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79—21no—
90C22×C4×D79—21no—
91C2×Dic316—24no—
92C2×Dic316C2314yes—
93C2×#11929613—24no—
94C2×#11929613—24no—
95C2×#11929613C2314yes—
96C2×#11929613C2314yes—
97C2×D632—24no—
98C2×D632C2314yes—
99#14579155—28no—
100#14579153—22no—
101#14579153C2314yes—
102#14579149—22no—
103#14579149C2314yes—
104#14579144—28no—
105#14579140—22no—
106#14579140C2314yes—
107#14579135—22no—
108#14579135C2314yes—
109C4×Dic158—22no—
110C4×Dic158—22no—
111C4×Dic158—22no—
112C4×Dic158C2314yes—
113C4×Dic158C2314yes—
114C4×Dic158C2314yes—
115C4×D316—22no—
116C4×D316—22no—
117C4×D316—22no—
118C4×D316C2314yes—
119C4×D316C2314yes—
120C4×D316C2314yes—
121C4×C22⋊D79—28no—
122C4×C22⋊D79—28no—
123C4×C22⋊D79—28no—
124#14579120—22no—
125#14579120C2314yes—
126#14579118—28no—
127#14579118—28no—
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×C4⋊Dic79C2311yescharacteristic
131C2×C4⋊Dic79C2311yescharacteristic
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4—21no—
134C2×Dic79⋊C4—21no—
135C2×Dic79⋊C4—21no—
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×C22⋊Dic79—21no—
139C2×C22⋊Dic79—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4—21no—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×C4×Dic79—21no—
147C2×C4×Dic79—21no—
148C2×C4×Dic79—21no—
149C2×C4×Dic79—21no—
150C42×D79—28no—
151#14579095C2314yes—
152#14579095C2314yes—
153#14579093C2314yes—
154#14579093C2314yes—
155#14579086C2314yes—
156#14579086C2314yes—
157#14579086C2314yes—
158#14579086C2314yes—
159#14579083C2314yes—
160#14579083C2314yes—
161#14579083C2314yes—
162#14579083C2314yes—
163C23×C4×C79D411yescharacteristic
164C23×C4×C79D411yescharacteristic
165C23×C4×C79C2311yescharacteristic
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C22×C8×C79C2311yescharacteristic
170C2×C42×C79D411yescharacteristic
171C2×C42×C79D411yescharacteristic
172C2×C42×C79D414yes—
173C2×C42×C79C2311yescharacteristic
174C2×C42×C79C2314yes—
175C2×C42×C79C2311yescharacteristic
176C4⋊C8×C79C2314yes—
177C4⋊C8×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C22⋊C8×C79C2314yes—
180#97×C79C2314yes—
181#97×C79C2314yes—
182C23×D79—21no—
183C23×D79—21no—
184#11929624—216no—
185#11929624—28no—
186#11929624—28no—
187C2×Dic158—21no—
188C2×Dic158—21no—
189C2×Dic158—22no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158#4114yes—
193C2×Dic158C2412yes—
194C2×Dic158C2412yes—
195C2×D316—21no—
196C2×D316—21no—
197C2×D316—22no—
198C2×D316—22no—
199C2×D316—22no—
200C2×D316#4114yes—
201C2×D316C2412yes—
202C2×D316C2412yes—
203C2×C22⋊D79—28no—
204C2×C22⋊D79—24no—
205C2×C22⋊D79—24no—
206C2×C22⋊D79—44no—
207C22×Dic79—21no—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79—21no—
212C22×Dic79—21no—
213C2×C4×D79—28no—
214C2×C4×D79—24no—
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—24no—
218C2×C4×D79—44no—
219C2×C4×D79—44no—
220C2×C4×D79—44no—
221Dic316—28no—
222#11929613—28no—
223#11929613—28no—
224D632—28no—
225C4⋊Dic79—21no—
226C4⋊Dic79—21no—
227C4⋊Dic79—21no—
228C4⋊Dic79—21no—
229C4⋊Dic79C2412yes—
230C4⋊Dic79C2412yes—
231C4⋊Dic79C2412yes—
232C4⋊Dic79C2412yes—
233Dic79⋊C4—24no—
234Dic79⋊C4—24no—
235Dic79⋊C4—24no—
236Dic79⋊C4—24no—
237Dic79⋊C4—24no—
238Dic79⋊C4—24no—
239C22⋊Dic79—24no—
240C22⋊Dic79—24no—
241(C2×D79)⋊C4—24no—
242(C2×D79)⋊C4—24no—
243(C2×D79)⋊C4—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4—24no—
246(C2×D79)⋊C4—24no—
247C4×Dic79—24no—
248C4×Dic79—24no—
249C4×Dic79—24no—
250C4×Dic79—24no—
251C24×C79C2×D411yescharacteristic
252C22×C4×C79—22no—
253C22×C4×C79—22no—
254C22×C4×C79—42no—
255C22×C4×C79—42no—
256C22×C4×C79C2×D412yes—
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2×D414yes—
263C22×C4×C79C2×D414yes—
264C22×C4×C79C2412yes—
265C22×C4×C79C2411yescharacteristic
266C2×C8×C79—22no—
267C2×C8×C79—22no—
268C2×C8×C79—22no—
269C2×C8×C79—22no—
270C2×C8×C79C2412yes—
271C2×C8×C79C2412yes—
272C2×C8×C79C2412yes—
273C2×C8×C79C2412yes—
274C42×C79C2×D414yes—
275C42×C79C2×D414yes—
276C42×C79C2×D412yes—
277C42×C79C2×D412yes—
278C42×C79C2412yes—
279C42×C79C2412yes—
280C23×C79—22no—
281C23×C79—22no—
282C23×C79—22no—
283C23×C79C22×D412yes—
284C23×C79C22×D411yescharacteristic
285C22×D79—24no—
286C22×D79—22no—
287C22×D79—22no—
288C22×D79—42no—
289C22×D79—42no—
290C22×D79—42no—
291C22×D79—42no—
292C22×D79—42no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—24no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—44no—
302C2×C4×C79—44no—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D412yes—
305C2×C4×C79C22×D412yes—
306C2×C4×C79C22×D412yes—
307C2×C4×C79C22×D412yes—
308C2×C4×C79C22×D411yescharacteristic
309C2×C4×C79C2×#4112yes—
310C2×C4×C79C2×#4112yes—
311C2×C4×C79C2511yescharacteristic
312C22⋊D79—216no—
313C22⋊D79—48no—
314C2×Dic79—24no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—42no—
322C2×Dic79—42no—
323C2×Dic79—42no—
324C2×Dic79—42no—
325C2×Dic79—42no—
326D316—24no—
327D316—22no—
328D316—22no—
329D316—22no—
330D316—42no—
331D316C2×#4114yes—
332C4×D79—216no—
333C4×D79—48no—
334C4×D79—48no—
335C4×D79—48no—
336Dic158—24no—
337Dic158—22no—
338Dic158—22no—
339Dic158—22no—
340Dic158—42no—
341Dic158C2×#4114yes—
342C8×C79—22no—
343C8×C79—22no—
344C8×C79—22no—
345C8×C79—22no—
346C22×C79—22no—
347C22×C79—22no—
348C22×C79—22no—
349C22×C79—44no—
350C22×C79#52512yes—
351C22×C79#57512yes—
352C22×C79#57512yes—
353C22×C79C23×D411yescharacteristic
354C2×D79—24no—
355C2×D79—48no—
356C2×D79—42no—
357C2×D79—42no—
358C2×D79—42no—
359C2×D79—42no—
360C2×D79—42no—
361C2×D79—84no—
362C4×C79—22no—
363C4×C79—22no—
364C4×C79—22no—
365C4×C79—22no—
366C4×C79—22no—
367C4×C79#52512yes—
368C4×C79C22×#4111yescharacteristic
369C4×C79C22×#4111yescharacteristic
370Dic79—24no—
371Dic79—42no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376C2×#3111—791nomaximal, Sylow
377C2×C79—42no—
378C2×C79#311114yescomplemented
379C2×C79C2×#52511yescharacteristic
380C2×C79C2×#57511yescharacteristic
381C2×C79C2×#57511yescharacteristic
382D79—44no—
383D79—82no—
384C2×#529—791no—
385C2×C4×#41—791no—
386#3111—7916no—
387C2×#485—791no—
388C2×#482—791no—
389C2×#479—791no—
390C2×#478—791no—
391C2×#464—791no—
392C2×#463—791no—
393C2×#452—791no—
394C2×#449—791no—
395C2×#442—791no—
396C2×#441—791no—
397C2×#440—791no—
398C2×#440—791no—
399C2×#432D7911yescharacteristic, complemented
400C79C2×#311111yescharacteristic, complemented, Sylow
401C22×#41—791no—
402C22×Q16—791no—
403C22×SD16—791no—
404C22×SD16—791no—
405C22×D8—791no—
406#529—798no—
407#529—1584no—
408C2×#126—1581no—
409C2×#125—791no—
410C2×#124—791no—
411C2×#123—1581no—
412C2×C22⋊Q8—791no—
413C2×#121—791no—
414C4×#41—798no—
415C4×#41—1584no—
416C2×C4×Q8—791no—
417C2×C4×Q8—791no—
418C2×C4×Q8—791no—
419C2×C4×D4—791no—
420C2×C4×D4—791no—
421C2×C4×D4—791no—
422C2×C4×D4—1581no—
423C2×C4×D4—1581no—
424C2×C4×D4—1581no—
425C2×#117—791no—
426C2×#117—1581no—
427C2×#117—1581no—
428C22×C42—1581no—
429C22×C42C2×D7911yescharacteristic
430#485—798no—
431#482—798no—
432#479—798no—
433#478—798no—
434#464—798no—
435#463—798no—
436#452—798no—
437#449—798no—
438#442—798no—
439#441—798no—
440#440—798no—
441#440—798no—
442#432C2×D7918yescomplemented
443C2×#107—791no—
444C2×#107—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8C2×D7911yescharacteristic
448C2×C4⋊C8C2×D7911yescharacteristic
449C2×#103—791no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#102—791no—
454C2×#102—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×C22⋊C8C2×D7911yescharacteristic
458C2×C22⋊C8C2×D7911yescharacteristic
459C2×#97C2×D7911yescharacteristic
460C2×#97C2×D7911yescharacteristic
461C2×#41—794no—
462C2×#41—1584no—
463C2×#41—1584no—
464C2×#41—1582no—
465C22×Q8—791no—
466C22×Q8—791no—
467C22×D4—791no—
468C22×D4—791no—
469C22×D4—1581no—
470C22×D4—1581no—
471C23×C4—1581no—
472C23×C4—1581no—
473C23×C4—1581no—
474C23×C4—1581no—
475C23×C4D31611yescharacteristic
476C23×C4D31611yescharacteristic
477C23×C4C22×D7911yescharacteristic
478C2×Q16—794no—
479C2×Q16—1584no—
480C2×SD16—794no—
481C2×SD16—794no—
482C2×SD16—1584no—
483C2×SD16—1584no—
484C2×D8—794no—
485C2×D8—1584no—
486C22×C8C22×D7911yescharacteristic
487C22×C8C22×D7911yescharacteristic
488C22×C8C22×D7911yescharacteristic
489C22×C8C22×D7911yescharacteristic
490#126—1588no—
491#125—794no—
492#125—1582no—
493#124—794no—
494#124—1582no—
495#123—1588no—
496C22⋊Q8—794no—
497C22⋊Q8—1582no—
498#121—794no—
499#121—1582no—
500C4×Q8—794no—
501C4×Q8—794no—
502C4×Q8—794no—
503C4×Q8—1582no—
504C4×Q8—1582no—
505C4×Q8—1582no—
506C4×D4—794no—
507C4×D4—794no—
508C4×D4—794no—
509C4×D4—1588no—
510C4×D4—1588no—
511C4×D4—1588no—
512C4×D4—1582no—
513C4×D4—1582no—
514C4×D4—1582no—
515#117—794no—
516#117—1582no—
517#117—1588no—
518#117—1588no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—791no—
523C2×C4⋊C4—1581no—
524C2×C4⋊C4—1581no—
525C2×C4⋊C4—1581no—
526C2×C4⋊C4—1581no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C22⋊C4—1581no—
537C2×C42—1581no—
538C2×C42—1581no—
539C2×C42—1581no—
540C2×C42—1581no—
541C2×C42—1588no—
542C2×C42D31611yescharacteristic
543C2×C42D31614yes—
544C2×C42D31611yescharacteristic
545C2×C42C22×D7911yescharacteristic
546C2×C42C22×D7911yescharacteristic
547C2×C42C22×D7914yes—
548#107—794no—
549#107—794no—
550#106—794no—
551#106—794no—
552C4⋊C8C22×D7914yes—
553C4⋊C8C22×D7914yes—
554#103—794no—
555#103—794no—
556#103—794no—
557#103—794no—
558#102—794no—
559#102—794no—
560#102—794no—
561#102—794no—
562C22⋊C8C22×D7914yes—
563C22⋊C8C22×D7914yes—
564#97C22×D7914yes—
565#97C22×D7914yes—
566C24—1581no—
567C24—1581no—
568C24C2×D31611yescharacteristic
569#41—1588no—
570#41—1588no—
571#41—15816no—
572C2×Q8—794no—
573C2×Q8—792no—
574C2×Q8—792no—
575C2×Q8—1582no—
576C2×Q8—1582no—
577C2×Q8—1582no—
578C2×Q8—1581no—
579C2×Q8—1581no—
580C2×D4—3164no—
581C2×D4—794no—
582C2×D4—792no—
583C2×D4—792no—
584C2×D4—1584no—
585C2×D4—1588no—
586C2×D4—1584no—
587C2×D4—1582no—
588C2×D4—1582no—
589C2×D4—1582no—
590C2×D4—1581no—
591C2×D4—1581no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—3164no—
597C22×C4—3164no—
598C22×C4—3164no—
599C22×C4—1588no—
600C22×C4—1581no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1581no—
604C22×C4—1581no—
605C22×C4—1584no—
606C22×C4—1584no—
607C22×C4—1584no—
608C22×C4—1581no—
609C22×C4—1584no—
610C22×C4C2×D31612yes—
611C22×C4C2×D31611yescharacteristic
612C22×C4C2×D31611yescharacteristic
613C22×C4C2×D31611yescharacteristic
614C22×C4C2×D31611yescharacteristic
615C22×C4C2×D31611yescharacteristic
616C22×C4C2×D31614yes—
617C22×C4C2×D31614yes—
618C22×C4C23×D7912yes—
619C22×C4C23×D7911yescharacteristic
620Q16—1588no—
621SD16—1588no—
622SD16—1588no—
623D8—1588no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8C23×D7912yes—
629C2×C8C23×D7912yes—
630C2×C8C23×D7912yes—
631C2×C8C23×D7912yes—
632C4⋊C4—792no—
633C4⋊C4—792no—
634C4⋊C4—792no—
635C4⋊C4—792no—
636C4⋊C4—1584no—
637C4⋊C4—1584no—
638C4⋊C4—1584no—
639C4⋊C4—1584no—
640C4⋊C4—1584no—
641C4⋊C4—1584no—
642C4⋊C4—1581no—
643C4⋊C4—1581no—
644C4⋊C4—1581no—
645C4⋊C4—1581no—
646C22⋊C4—1584no—
647C22⋊C4—1584no—
648C22⋊C4—1584no—
649C22⋊C4—1584no—
650C22⋊C4—1584no—
651C22⋊C4—1584no—
652C22⋊C4—1584no—
653C22⋊C4—1584no—
654C42—1584no—
655C42—1584no—
656C42—1584no—
657C42—1584no—
658C42C2×D31614yes—
659C42C2×D31614yes—
660C42C2×D31612yes—
661C42C2×D31612yes—
662C42C23×D7912yes—
663C42C23×D7912yes—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—3162no—
668C23—3162no—
669C23—3162no—
670C23—3162no—
671C23—3162no—
672C23—1582no—
673C23—1584no—
674C23—1582no—
675C23C22×D31612yes—
676C23C22×D31611yescharacteristic
677Q8—3162no—
678Q8—794no—
679Q8—1582no—
680Q8—1582no—
681Q8—1584no—
682Q8—1582no—
683D4—3168no—
684D4—3162no—
685D4—794no—
686D4—15816no—
687D4—1584no—
688D4—1582no—
689D4—1582no—
690D4—1582no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—3168no—
702C2×C4—3168no—
703C2×C4—3168no—
704C2×C4—3162no—
705C2×C4—3162no—
706C2×C4—3162no—
707C2×C4—3162no—
708C2×C4—3162no—
709C2×C4—15816no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1582no—
713C2×C4—1582no—
714C2×C4—1582no—
715C2×C4—1584no—
716C2×C4—1582no—
717C2×C4C22×D31612yes—
718C2×C4C22×D31612yes—
719C2×C4C22×D31612yes—
720C2×C4C22×D31612yes—
721C2×C4C22×D31612yes—
722C2×C4C22×D31611yescharacteristic
723C2×C4#41×D7912yes—
724C2×C4#41×D7912yes—
725C2×C4C24×D7911yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—3168no—
735C22—3162no—
736C22—3162no—
737C22—3162no—
738C22—3162no—
739C22—3162no—
740C22—6324no—
741C22—1584no—
742C22#1909907512yes—
743C22#1909936312yes—
744C22#1909936312yes—
745C22C23×D31611yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—3162no—
752C4—3162no—
753C4—3162no—
754C4—3162no—
755C4—3162no—
756C4—1584no—
757C4#1909907512yes—
758C4C2×#41×D7911yescharacteristic
759C4C2×#41×D7911yescharacteristic
760C2—42no—
761C2—3164no—
762C2—6322no—
763C2#2377351114yesdirect product factor
764C2C2×#1909907511yescharacteristic
765C2C2×#1909936311yescharacteristic
766C2C2×#1909936311yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#432×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098710C2
hypercenterC2×#432D79
hypocenterC79C2×#3111
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
1. C2×#19099097C2semidirect
2. C2×C4×#11929624C2semidirect
3. #23773511C2direct (N × H)
4. C2×#19098905C2semidirect
5. C2×#19098888C2semidirect
6. C2×#19098871C2semidirect
7. C2×#19098864C2semidirect
8. C2×#19098786C2semidirect
9. C2×#19098779C2semidirect
10. C2×#19098727C2semidirect
12. C2×#19098676C2semidirect
13. C2×#19098671C2semidirect
14. C2×#19098665C2semidirect
15. C2×#19098665C2semidirect
16. C2×#432×C79C2semidirect
23. #19099097C22semidirect
31. C4×#11929624C22semidirect
45. #19098905C22semidirect
46. #19098888C22semidirect
47. #19098871C22semidirect
48. #19098864C22semidirect
49. #19098786C22semidirect
50. #19098779C22semidirect
51. #19098727C22semidirect
53. #19098676C22semidirect
54. #19098671C22semidirect
55. #19098665C22semidirect
56. #19098665C22semidirect
70. #432×C79C22semidirect
378. C2×C79#3111semidirect
399. C2×#432D79semidirect
400. C79C2×#3111semidirect
442. #432C2×D79semidirect
763. C2#23773511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990972
C2×C4×#119296242
#237735112
C2×#190989052
C2×#190988882
C2×#190988712
C2×#190988642
C2×#190987862
C2×#190987792
C2×#190987272
C2×#190987102
C2×#190986762
C2×#190986712
C2×#190986652
C2×#432×C792
C2×#311179