Finite Group Databasebeta

← #34449084

Subgroups — #34449084

Order 20224.

2682 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579148C211yesmaximal, characteristic
2#23766509C214yesmaximal, complemented
3#23766473C212yesmaximal, complemented
4#23766470C212yesmaximal, complemented
5#23766251C212yesmaximal, complemented
6#23766245C212yesmaximal, complemented
7C22⋊C4×Dic158C211yesmaximal, characteristic, complemented
8#23766232C211yesmaximal, characteristic, complemented
9D4×C22⋊Dic79C211yesmaximal, characteristic
10#23766209C214yesmaximal, complemented
11#23765996C212yesmaximal, complemented
12#23765947C212yesmaximal, complemented
13C4×#14579148C212yesmaximal, complemented
14#23765795C211yesmaximal, characteristic, complemented
15#23765753C212yesmaximal, complemented
16C4×#14579117C211yesmaximal, characteristic, complemented
17D4×C22⋊C4×C79C211yesmaximal, characteristic
18C23×Dic158C2211yescharacteristic
19C2×#14579148C4116yescomplemented
20C2×#14579148C2211yescharacteristic
21C2×#14579148C2211yescharacteristic
22C2×#14579148C2212yes—
23C2×#14579148C2211yescharacteristic
24C2×#14579148C2211yescharacteristic
25C2×#14579148C2212yes—
26C2×C4×Dic158C2212yescomplemented
27C2×#14579126C2212yescomplemented
28C2×D4×Dic79C2212yes—
29C2×#14579117C2211yescharacteristic
30C2×#14579117C2211yescharacteristic
31C22×C22⋊Dic79C2212yes—
32C22×C22⋊Dic79C2212yes—
33C22×C22⋊Dic79C2212yes—
34C22×C4×Dic79C2211yescharacteristic
35#19098469C2212yescomplemented
36#19098468C2212yescomplemented
37#19098467C2214yescomplemented
38#19098467C2214yescomplemented
39#19098466C2212yes—
40#19098457C2214yescomplemented
41#19098457C2214yescomplemented
42#19098457C2214yescomplemented
43#19098457C2214yescomplemented
44#19098451C2214yescomplemented
45#19098451C2214yescomplemented
46#19098451C2214yescomplemented
47#19098451C2214yescomplemented
48#19098443C2214yes—
49#19098436C2214yescomplemented
50#19098435C2214yescomplemented
51#19098430C2212yescomplemented
52#19098428C2212yescomplemented
53#19098424C2212yes—
54#19098423C2211yescharacteristic
55#19098421C2212yes—
56#19098421C2212yes—
57#19098419C2212yes—
58C4⋊C4×Dic79C2212yescomplemented
59C4×Dic79⋊C4C2212yescomplemented
60#19098414C2212yescomplemented
61C22⋊C4×Dic79C2212yes—
62C22⋊C4×Dic79C2212yes—
63C22⋊C4×Dic79C2212yes—
64C22⋊C4×Dic79C2211yescharacteristic
65C22⋊C4×Dic79C2211yescharacteristic
66C22⋊C4×Dic79C2214yescomplemented
67C22⋊C4×Dic79C2214yescomplemented
68C22⋊C4×Dic79C2214yescomplemented
69C4×C22⋊Dic79C2211yescharacteristic
70C4×C22⋊Dic79C2214yescomplemented
71C4×C22⋊Dic79C2214yescomplemented
72C4×C22⋊Dic79C2214yescomplemented
73#19098408C2212yescomplemented
74#19098408C2212yescomplemented
75C42×Dic79C2212yescomplemented
76C23×D4×C79C2211yescharacteristic
77C2×C4×D4×C79C2212yes—
78C22×C22⋊C4×C79C2212yes—
79#390×C79C2212yes—
80#386×C79C2214yes—
81#380×C79C2211yescharacteristic
82#379×C79C2212yes—
83C4×C22⋊C4×C79C2211yescharacteristic
84C22×Dic158—44no—
85C22×Dic158C2×C418yescomplemented
86C22×Dic158C2311yescharacteristic
87C22×Dic158C2311yescharacteristic
88C22×Dic158C2312yes—
89C23×Dic79C2311yescharacteristic
90C23×Dic79C2314yes—
91C23×Dic79C2311yescharacteristic
92C23×Dic79C2312yes—
93#14579148C2×C418yescomplemented
94#14579148C2×C418yescomplemented
95#14579148C2×C418yescomplemented
96#14579148C2×C418yescomplemented
97#14579148C2×C4116yescomplemented
98#14579148C2×C4116yescomplemented
99C4×Dic158—44no—
100#14579126—44no—
101D4×Dic79—44no—
102#14579117—24no—
103#14579117—24no—
104C2×C4⋊Dic79C2312yes—
105C2×Dic79⋊C4C2312yes—
106C2×Dic79⋊C4C2312yes—
107C2×Dic79⋊C4C2314yes—
108C2×Dic79⋊C4C2314yes—
109C2×C22⋊Dic79—28no—
110C2×C22⋊Dic79C2×C4116yescomplemented
111C2×C22⋊Dic79C2×C4116yescomplemented
112C2×C22⋊Dic79C2311yescharacteristic
113C2×C22⋊Dic79C2314yes—
114C2×C22⋊Dic79C2312yes—
115C2×C22⋊Dic79C2314yes—
116C2×C22⋊Dic79C2314yes—
117C2×C22⋊Dic79C2312yes—
118C2×C22⋊Dic79C2312yes—
119C2×C22⋊Dic79C2312yes—
120C2×C22⋊Dic79C2312yes—
121C2×C22⋊Dic79C2312yes—
122C2×C22⋊Dic79C2312yes—
123C2×C22⋊Dic79C2312yes—
124C2×C22⋊Dic79C2312yes—
125C2×C22⋊Dic79C2311yescharacteristic
126C2×C4×Dic79C2×C418yescomplemented
127C2×C4×Dic79C2312yes—
128C2×C4×Dic79C2312yes—
129C2×C4×Dic79C2312yes—
130C2×C4×Dic79C2312yes—
131C2×C4×Dic79C2312yes—
132C2×C4×Dic79C2314yes—
133C2×C4×Dic79C2314yes—
134C2×C4×Dic79C2314yes—
135C2×C4×Dic79C2311yescharacteristic
136C2×C4×Dic79C2311yescharacteristic
137C2×C4×Dic79C2311yescharacteristic
138C2×C4×Dic79C2311yescharacteristic
139C79⋊#95C2312yes—
140C79⋊#95C2312yes—
141C79⋊#95C2314yes—
142C79⋊#95C2312yes—
143C79⋊#95C2312yes—
144C79⋊#95C2314yes—
145C79⋊#95C2314yes—
146C79⋊#95C2314yes—
147C79⋊#95C2314yes—
148C79⋊#95C2314yes—
149C79⋊#95C2314yes—
150C25×C79C2312yes—
151C22×D4×C79—44no—
152C22×D4×C79C2×C418yes—
153C22×D4×C79C2311yescharacteristic
154C22×D4×C79C2311yescharacteristic
155C22×D4×C79C2312yes—
156C23×C4×C79C2311yescharacteristic
157C23×C4×C79C2314yes—
158C4×D4×C79—44no—
159C2×C4⋊C4×C79C2312yes—
160C2×C22⋊C4×C79—28no—
161C2×C22⋊C4×C79C2312yes—
162C2×C22⋊C4×C79C2311yescharacteristic
163C2×C22⋊C4×C79C2314yes—
164C2×C22⋊C4×C79C2314yes—
165C2×C22⋊C4×C79C2314yes—
166C2×C22⋊C4×C79C2311yescharacteristic
167C2×C42×C79C2312yes—
168#95×C79C2312yes—
169#95×C79C2312yes—
170C2×Dic158—24no—
171C2×Dic158—24no—
172C2×Dic158—416no—
173C2×Dic158—44no—
174C2×Dic158C22×C414yes—
175C2×Dic158C22×C414yes—
176C2×Dic158C22×C418yes—
177C22×Dic79—28no—
178C22×Dic79—22no—
179C22×Dic79—22no—
180C22×Dic79—44no—
181C22×Dic79—42no—
182C22×Dic79—44no—
183C22×Dic79—44no—
184C22×Dic79C22×C414yes—
185C22×Dic79C22×C418yes—
186C22×Dic79C22×C414yes—
187C22×Dic79C2414yes—
188C22×Dic79C2412yes—
189C22×Dic79C2412yes—
190C22×Dic79C2412yes—
191C22×Dic79C2411yescharacteristic
192C22×Dic79C2411yescharacteristic
193C22×Dic79C2411yescharacteristic
194C22×Dic79C2411yescharacteristic
195C22×Dic79C2412yes—
196C4⋊Dic79—24no—
197Dic79⋊C4—24no—
198Dic79⋊C4—24no—
199Dic79⋊C4—44no—
200Dic79⋊C4—44no—
201C22⋊Dic79—28no—
202C22⋊Dic79—24no—
203C22⋊Dic79—22no—
204C22⋊Dic79—44no—
205C22⋊Dic79—44no—
206C22⋊Dic79C22×C418yes—
207C22⋊Dic79C22×C418yes—
208C22⋊Dic79C22×C418yes—
209C22⋊Dic79C22×C418yes—
210C22⋊Dic79C22×C418yes—
211C22⋊Dic79C22×C418yes—
212C22⋊Dic79C22×C418yes—
213C22⋊Dic79C22×C418yes—
214C22⋊Dic79#4114yes—
215C4×Dic79—24no—
216C4×Dic79—24no—
217C4×Dic79—24no—
218C4×Dic79—42no—
219C4×Dic79—42no—
220C4×Dic79—44no—
221C4×Dic79—44no—
222C4×Dic79—44no—
223C4×Dic79C22×C414yes—
224C4×Dic79C22×C414yes—
225C4×Dic79C22×C414yes—
226C4×Dic79C22×C414yes—
227C24×C79—24no—
228C24×C79—24no—
229C24×C79—44no—
230C24×C79—44no—
231C24×C79C22×C418yes—
232C24×C79C2412yes—
233C24×C79C2412yes—
234C24×C79C2411yescharacteristic
235C2×D4×C79—24no—
236C2×D4×C79—24no—
237C2×D4×C79—416no—
238C2×D4×C79—44no—
239C2×D4×C79C22×C414yes—
240C2×D4×C79C22×C414yes—
241C2×D4×C79C22×C418yes—
242C22×C4×C79—24no—
243C22×C4×C79—28no—
244C22×C4×C79—44no—
245C22×C4×C79—44no—
246C22×C4×C79C22×C414yes—
247C22×C4×C79C2412yes—
248C22×C4×C79C2414yes—
249C22×C4×C79C2411yescharacteristic
250C22×C4×C79C2412yes—
251C22×C4×C79C2411yescharacteristic
252C4⋊C4×C79—24no—
253C22⋊C4×C79—24no—
254C22⋊C4×C79—22no—
255C22⋊C4×C79—28no—
256C22⋊C4×C79—44no—
257C22⋊C4×C79—44no—
258C22⋊C4×C79#4114yes—
259C42×C79—24no—
260C23×C79—22no—
261C23×C79—22no—
262C23×C79—22no—
263C23×C79—22no—
264C23×C79—22no—
265C23×C79—22no—
266C23×C79—24no—
267C23×C79—24no—
268C23×C79—24no—
269C23×C79—24no—
270C23×C79—216no—
271C23×C79—48no—
272C23×C79—48no—
273C23×C79—88no—
274C23×C79—88no—
275C23×C79C23×C414yes—
276C23×C79C23×C414yes—
277C23×C79C23×C412yes—
278C23×C79C2×#4112yes—
279C23×C79C2×#4112yes—
280C23×C79C2511yescharacteristic
281D4×C79—28no—
282D4×C79—28no—
283D4×C79—48no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—28no—
288C2×C4×C79—22no—
289C2×C4×C79—24no—
290C2×C4×C79—24no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—24no—
294C2×C4×C79—88no—
295C2×C4×C79C23×C412yes—
296C2×C4×C79C23×C412yes—
297C2×C4×C79C2×#4114yes—
298C2×C4×C79H(5,𝔽2)14yes—
299C2×Dic79—28no—
300C2×Dic79—21no—
301C2×Dic79—21no—
302C2×Dic79—21no—
303C2×Dic79—21no—
304C2×Dic79—22no—
305C2×Dic79—24no—
306C2×Dic79—24no—
307C2×Dic79—22no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—24no—
312C2×Dic79—22no—
313C2×Dic79—24no—
314C2×Dic79—22no—
315C2×Dic79—24no—
316C2×Dic79—44no—
317C2×Dic79—48no—
318C2×Dic79—88no—
319C2×Dic79C23×C412yes—
320C2×Dic79C23×C412yes—
321C2×Dic79C23×C412yes—
322C2×Dic79C23×C412yes—
323C2×Dic79C23×C414yes—
324C2×Dic79C23×C414yes—
325C2×Dic79C2×#4114yes—
326Dic158—28no—
327Dic158—28no—
328Dic158—48no—
329C22×C79—22no—
330C22×C79—22no—
331C22×C79—24no—
332C22×C79—24no—
333C22×C79—24no—
334C22×C79—24no—
335C22×C79—24no—
336C22×C79—24no—
337C22×C79—24no—
338C22×C79—24no—
339C22×C79—44no—
340C22×C79—44no—
341C22×C79—44no—
342C22×C79—44no—
343C22×C79—816no—
344C22×C79C4×#4114yes—
345C22×C79C24×C411yescharacteristic
346C22×C79C22×#4111yescharacteristic
347C22×C79C22×#4111yescharacteristic
348C22×C79C2×H(5,𝔽2)12yes—
349C22×C79#58512yes—
350C4×C79—22no—
351C4×C79—24no—
352C4×C79—42no—
353C4×C79—44no—
354C4×C79#51814yes—
355Dic79—22no—
356Dic79—22no—
357Dic79—24no—
358Dic79—24no—
359Dic79—22no—
360Dic79—22no—
361Dic79—24no—
362Dic79—42no—
363Dic79—44no—
364#34240—791nomaximal, Sylow
365C2×C79—24no—
366C2×C79—44no—
367C2×C79—44no—
368C2×C79C2×C4×#4111yescharacteristic
369C2×C79C2×#51811yescharacteristic
370C2×C79#342811yescharacteristic
371C2×C79#351412yes—
372C2×C79#351412yes—
373C22×#124—791no—
374#2372—794no—
375#2367—792no—
376#2367—792no—
377#2342—792no—
378#2342—792no—
379Q8×C22⋊C4—791no—
380Q8×C22⋊C4—791no—
381D4×C22⋊C4—791no—
382D4×C22⋊C4D7911yescharacteristic
383#2337—794no—
384#2312—792no—
385C4×#124—792no—
386C4×#124—792no—
387#2283—791no—
388#2273—792no—
389C4×#117—791no—
390C79#3424011yescharacteristic, complemented, Sylow
391C23×Q8—791no—
392C23×D4C2×D7911yescharacteristic
393C2×#124—792no—
394C2×#124—791no—
395C2×#124—791no—
396C2×#124—792no—
397C2×#124—791no—
398C2×#124—791no—
399C2×#124—7916no—
400C2×C4×Q8—792no—
401C2×C4×Q8—792no—
402C2×C4×D4—792no—
403C2×C4×D4C2×D7912yes—
404C2×#117—791no—
405C2×#117—791no—
406C22×C22⋊C4—792no—
407C22×C22⋊C4—792no—
408C22×C22⋊C4—792no—
409C22×C22⋊C4C2×D7912yes—
410C22×C42—791no—
411#391—792no—
412#391—792no—
413#391—794no—
414#391—794no—
415#390—792no—
416#390C2×D7912yes—
417#388—794no—
418#388—794no—
419#388—794no—
420#388—794no—
421#388—794no—
422#388—794no—
423#388—794no—
424#388—794no—
425#386—794no—
426#386C2×D7914yes—
427#385—794no—
428#385—794no—
429#383—792no—
430#382—792no—
431#381—792no—
432#380—791no—
433#380—792no—
434#380—792no—
435#380C2×D7911yescharacteristic
436#379—792no—
437#379C2×D7912yes—
438C4×C4⋊C4—792no—
439C4×C4⋊C4—792no—
440C4×C4⋊C4—792no—
441C4×C22⋊C4—794no—
442C4×C22⋊C4—791no—
443C4×C22⋊C4—794no—
444C4×C22⋊C4—794no—
445C4×C22⋊C4—791no—
446C4×C22⋊C4—792no—
447C4×C22⋊C4—794no—
448C4×C22⋊C4—792no—
449C4×C22⋊C4—792no—
450C4×C22⋊C4—794no—
451C4×C22⋊C4—791no—
452C4×C22⋊C4—794no—
453C4×C22⋊C4C2×D7911yescharacteristic
454#376—792no—
455#376—792no—
456C43—792no—
457C25C22×D7912yes—
458C22×Q8—3164no—
459C22×Q8—798no—
460C22×Q8—792no—
461C22×Q8—791no—
462C22×Q8—791no—
463C22×D4—44no—
464C22×D4C4×D7918yes—
465C22×D4C22×D7911yescharacteristic
466C22×D4C22×D7911yescharacteristic
467C22×D4C22×D7912yes—
468C23×C4—792no—
469C23×C4—791no—
470C23×C4—794no—
471C23×C4—791no—
472C23×C4C22×D7911yescharacteristic
473C23×C4C22×D7914yes—
474#124—798no—
475#124—798no—
476#124—798no—
477#124—798no—
478#124—7916no—
479#124—7916no—
480C4×Q8—3164no—
481C4×Q8—3164no—
482C4×D4—44no—
483C4×D4—3164no—
484#117—1584no—
485#117—1584no—
486C2×C4⋊C4—794no—
487C2×C4⋊C4—794no—
488C2×C4⋊C4—792no—
489C2×C4⋊C4—792no—
490C2×C4⋊C4—792no—
491C2×C4⋊C4C22×D7912yes—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—794no—
494C2×C22⋊C4—794no—
495C2×C22⋊C4—7916no—
496C2×C22⋊C4—7916no—
497C2×C22⋊C4—791no—
498C2×C22⋊C4—792no—
499C2×C22⋊C4—792no—
500C2×C22⋊C4—792no—
501C2×C22⋊C4—792no—
502C2×C22⋊C4—792no—
503C2×C22⋊C4—792no—
504C2×C22⋊C4—792no—
505C2×C22⋊C4—792no—
506C2×C22⋊C4—792no—
507C2×C22⋊C4—794no—
508C2×C22⋊C4—791no—
509C2×C22⋊C4—1588no—
510C2×C22⋊C4C22×D7912yes—
511C2×C22⋊C4C22×D7914yes—
512C2×C22⋊C4C22×D7911yescharacteristic
513C2×C22⋊C4C22×D7914yes—
514C2×C22⋊C4C22×D7914yes—
515C2×C22⋊C4C22×D7911yescharacteristic
516C2×C42—794no—
517C2×C42—794no—
518C2×C42—792no—
519C2×C42—792no—
520C2×C42—794no—
521C2×C42—798no—
522C2×C42—791no—
523C2×C42—791no—
524C2×C42—791no—
525C2×C42—791no—
526C2×C42—792no—
527C2×C42—792no—
528C2×C42—792no—
529C2×C42C22×D7912yes—
530#95—792no—
531#95—794no—
532#95—792no—
533#95—792no—
534#95—792no—
535#95—794no—
536#95—794no—
537#95—794no—
538#95—794no—
539#95—794no—
540#95—794no—
541#95C22×D7912yes—
542#95C22×D7912yes—
543C24—24no—
544C24—24no—
545C24—44no—
546C24—44no—
547C24C2×C4×D7918yes—
548C24C23×D7912yes—
549C24C23×D7912yes—
550C24C23×D7911yescharacteristic
551C2×Q8—31616no—
552C2×Q8—3164no—
553C2×Q8—798no—
554C2×Q8—794no—
555C2×Q8—794no—
556C2×Q8—1584no—
557C2×Q8—1584no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—416no—
561C2×D4—44no—
562C2×D4C2×C4×D7914yes—
563C2×D4C2×C4×D7914yes—
564C2×D4C2×C4×D7918yes—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—3162no—
570C22×C4—3164no—
571C22×C4—3164no—
572C22×C4—3164no—
573C22×C4—794no—
574C22×C4—798no—
575C22×C4—791no—
576C22×C4—791no—
577C22×C4—791no—
578C22×C4—792no—
579C22×C4—791no—
580C22×C4—792no—
581C22×C4—792no—
582C22×C4—794no—
583C22×C4—794no—
584C22×C4—792no—
585C22×C4—1588no—
586C22×C4—1582no—
587C22×C4—1582no—
588C22×C4C2×C4×D7914yes—
589C22×C4C23×D7914yes—
590C22×C4C23×D7912yes—
591C22×C4C23×D7912yes—
592C22×C4C23×D7911yescharacteristic
593C22×C4C23×D7911yescharacteristic
594C4⋊C4—24no—
595C4⋊C4—3164no—
596C4⋊C4—3164no—
597C4⋊C4—1584no—
598C4⋊C4—1584no—
599C4⋊C4—1584no—
600C22⋊C4—22no—
601C22⋊C4—24no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—3164no—
606C22⋊C4—3164no—
607C22⋊C4—794no—
608C22⋊C4—798no—
609C22⋊C4—798no—
610C22⋊C4—798no—
611C22⋊C4—798no—
612C22⋊C4—798no—
613C22⋊C4—798no—
614C22⋊C4—798no—
615C22⋊C4—798no—
616C22⋊C4—1588no—
617C22⋊C4—1584no—
618C22⋊C4—1582no—
619C22⋊C4#1192962314yes—
620C42—24no—
621C42—3162no—
622C42—3162no—
623C42—3164no—
624C42—3164no—
625C42—3164no—
626C42—794no—
627C42—794no—
628C42—794no—
629C42—794no—
630C42—1584no—
631C42—1584no—
632C42—1584no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—216no—
644C23—48no—
645C23—48no—
646C23—88no—
647C23—88no—
648C23C22×C4×D7914yes—
649C23C22×C4×D7914yes—
650C23C22×C4×D7912yes—
651C23#41×D7912yes—
652C23C2×#1192962312yes—
653C23C24×D7911yescharacteristic
654Q8—3168no—
655Q8—1588no—
656Q8—1588no—
657D4—28no—
658D4—28no—
659D4—48no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—28no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—88no—
671C2×C4—3168no—
672C2×C4—3164no—
673C2×C4—792no—
674C2×C4—792no—
675C2×C4—792no—
676C2×C4—792no—
677C2×C4—794no—
678C2×C4—794no—
679C2×C4—794no—
680C2×C4—6328no—
681C2×C4—1584no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4—1584no—
685C2×C4—1584no—
686C2×C4—1582no—
687C2×C4—1582no—
688C2×C4—1584no—
689C2×C4—1584no—
690C2×C4—1582no—
691C2×C4—1582no—
692C2×C4—1582no—
693C2×C4—1588no—
694C2×C4—1581no—
695C2×C4—1581no—
696C2×C4—1581no—
697C2×C4—1581no—
698C2×C4C22×C4×D7912yes—
699C2×C4C22×C4×D7912yes—
700C2×C4C2×#1192962314yes—
701C2×C4#1457920614yes—
702C22—24no—
703C22—22no—
704C22—24no—
705C22—22no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—816no—
717C22C4×#1192962314yes—
718C22C23×C4×D7911yescharacteristic
719C22C2×#41×D7911yescharacteristic
720C22C22×#1192962311yescharacteristic
721C22C2×#1457920612yes—
722C22#1909939812yes—
723C4—24no—
724C4—22no—
725C4—44no—
726C4—42no—
727C4—3162no—
728C4—3164no—
729C4—1582no—
730C4—1582no—
731C4—1584no—
732C4—1584no—
733C4—1584no—
734C4—1582no—
735C4—1582no—
736C4#1909903614yes—
737C2—24no—
738C2—44no—
739C2—44no—
740C2C2×C4×#1192962311yescharacteristic
741C2C2×#1909903611yescharacteristic
742C2#2377659811yescharacteristic
743C2#2377735212yes—
744C2#2377735812yes—
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingD4×C22⋊C4×C79C2
socle, cosocleC23×C79C25
prime radicalC23×D4×C79C22
hypercenterD4×C22⋊C4D79
hypocenterC79#34240
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #23766509C2semidirect
3. #23766473C2semidirect
4. #23766470C2semidirect
5. #23766251C2semidirect
6. #23766245C2semidirect
7. C22⋊C4×Dic158C2semidirect
8. #23766232C2semidirect
10. #23766209C2semidirect
11. #23765996C2semidirect
12. #23765947C2semidirect
13. C4×#14579148C2semidirect
14. #23765795C2semidirect
15. #23765753C2semidirect
16. C4×#14579117C2semidirect
19. C2×#14579148C4semidirect
26. C2×C4×Dic158C22semidirect
27. C2×#14579126C22semidirect
35. #19098469C22semidirect
36. #19098468C22semidirect
37. #19098467C22semidirect
38. #19098467C22semidirect
40. #19098457C22semidirect
41. #19098457C22semidirect
42. #19098457C22semidirect
43. #19098457C22semidirect
44. #19098451C22semidirect
45. #19098451C22semidirect
46. #19098451C22semidirect
47. #19098451C22semidirect
49. #19098436C22semidirect
50. #19098435C22semidirect
51. #19098430C22semidirect
52. #19098428C22semidirect
58. C4⋊C4×Dic79C22semidirect
59. C4×Dic79⋊C4C22semidirect
60. #19098414C22semidirect
66. C22⋊C4×Dic79C22semidirect
67. C22⋊C4×Dic79C22semidirect
68. C22⋊C4×Dic79C22semidirect
70. C4×C22⋊Dic79C22semidirect
71. C4×C22⋊Dic79C22semidirect
72. C4×C22⋊Dic79C22semidirect
73. #19098408C22semidirect
74. #19098408C22semidirect
75. C42×Dic79C22semidirect
85. C22×Dic158C2×C4semidirect
93. #14579148C2×C4semidirect
94. #14579148C2×C4semidirect
95. #14579148C2×C4semidirect
96. #14579148C2×C4semidirect
97. #14579148C2×C4semidirect
98. #14579148C2×C4semidirect
110. C2×C22⋊Dic79C2×C4semidirect
111. C2×C22⋊Dic79C2×C4semidirect
126. C2×C4×Dic79C2×C4semidirect
390. C79#34240semidirect

Maximal subgroups

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

subgroupindex
C22×#145791482
#237665092
#237664732
#237664702
#237662512
#237662452
C22⋊C4×Dic1582
#237662322
D4×C22⋊Dic792
#237662092
#237659962
#237659472
C4×#145791482
#237657952
#237657532
C4×#145791172
D4×C22⋊C4×C792
#3424079