Finite Group Databasebeta

← #32158267

Subgroups — #32158267

Order 18176.

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×#14556115C211yesmaximal, characteristic
2#22591449C214yesmaximal, complemented
3#22591413C212yesmaximal, complemented
4#22591410C212yesmaximal, complemented
5#22591191C212yesmaximal, complemented
6#22591185C212yesmaximal, complemented
7C22⋊C4×Dic142C211yesmaximal, characteristic, complemented
8#22591172C211yesmaximal, characteristic, complemented
9D4×C22⋊Dic71C211yesmaximal, characteristic
10#22591149C214yesmaximal, complemented
11#22590936C212yesmaximal, complemented
12#22590887C212yesmaximal, complemented
13C4×#14556115C212yesmaximal, complemented
14#22590735C211yesmaximal, characteristic, complemented
15#22590693C212yesmaximal, complemented
16C4×#14556084C211yesmaximal, characteristic, complemented
17D4×C22⋊C4×C71C211yesmaximal, characteristic
18C23×Dic142C2211yescharacteristic
19C2×#14556115C4116yescomplemented
20C2×#14556115C2211yescharacteristic
21C2×#14556115C2211yescharacteristic
22C2×#14556115C2212yes—
23C2×#14556115C2211yescharacteristic
24C2×#14556115C2211yescharacteristic
25C2×#14556115C2212yes—
26C2×C4×Dic142C2212yescomplemented
27C2×#14556093C2212yescomplemented
28C2×D4×Dic71C2212yes—
29C2×#14556084C2211yescharacteristic
30C2×#14556084C2211yescharacteristic
31C22×C22⋊Dic71C2212yes—
32C22×C22⋊Dic71C2212yes—
33C22×C22⋊Dic71C2212yes—
34C22×C4×Dic71C2211yescharacteristic
35#17985905C2212yescomplemented
36#17985904C2212yescomplemented
37#17985903C2214yescomplemented
38#17985903C2214yescomplemented
39#17985902C2212yes—
40#17985893C2214yescomplemented
41#17985893C2214yescomplemented
42#17985893C2214yescomplemented
43#17985893C2214yescomplemented
44#17985887C2214yescomplemented
45#17985887C2214yescomplemented
46#17985887C2214yescomplemented
47#17985887C2214yescomplemented
48#17985879C2214yes—
49#17985872C2214yescomplemented
50#17985871C2214yescomplemented
51#17985866C2212yescomplemented
52#17985864C2212yescomplemented
53#17985860C2212yes—
54#17985859C2211yescharacteristic
55#17985857C2212yes—
56#17985857C2212yes—
57#17985855C2212yes—
58C4⋊C4×Dic71C2212yescomplemented
59C4×Dic71⋊C4C2212yescomplemented
60#17985850C2212yescomplemented
61C22⋊C4×Dic71C2212yes—
62C22⋊C4×Dic71C2212yes—
63C22⋊C4×Dic71C2212yes—
64C22⋊C4×Dic71C2211yescharacteristic
65C22⋊C4×Dic71C2211yescharacteristic
66C22⋊C4×Dic71C2214yescomplemented
67C22⋊C4×Dic71C2214yescomplemented
68C22⋊C4×Dic71C2214yescomplemented
69C4×C22⋊Dic71C2211yescharacteristic
70C4×C22⋊Dic71C2214yescomplemented
71C4×C22⋊Dic71C2214yescomplemented
72C4×C22⋊Dic71C2214yescomplemented
73#17985844C2212yescomplemented
74#17985844C2212yescomplemented
75C42×Dic71C2212yescomplemented
76C23×D4×C71C2211yescharacteristic
77C2×C4×D4×C71C2212yes—
78C22×C22⋊C4×C71C2212yes—
79#390×C71C2212yes—
80#386×C71C2214yes—
81#380×C71C2211yescharacteristic
82#379×C71C2212yes—
83C4×C22⋊C4×C71C2211yescharacteristic
84C22×Dic142—44no—
85C22×Dic142C2×C418yescomplemented
86C22×Dic142C2311yescharacteristic
87C22×Dic142C2311yescharacteristic
88C22×Dic142C2312yes—
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2314yes—
91C23×Dic71C2312yes—
92C23×Dic71C2311yescharacteristic
93#14556115C2×C418yescomplemented
94#14556115C2×C418yescomplemented
95#14556115C2×C418yescomplemented
96#14556115C2×C418yescomplemented
97#14556115C2×C4116yescomplemented
98#14556115C2×C4116yescomplemented
99C4×Dic142—44no—
100#14556093—44no—
101D4×Dic71—44no—
102#14556084—24no—
103#14556084—24no—
104C2×C4⋊Dic71C2312yes—
105C2×Dic71⋊C4C2312yes—
106C2×Dic71⋊C4C2312yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×C22⋊Dic71—28no—
110C2×C22⋊Dic71C2×C4116yescomplemented
111C2×C22⋊Dic71C2×C4116yescomplemented
112C2×C22⋊Dic71C2311yescharacteristic
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2312yes—
115C2×C22⋊Dic71C2314yes—
116C2×C22⋊Dic71C2314yes—
117C2×C22⋊Dic71C2312yes—
118C2×C22⋊Dic71C2312yes—
119C2×C22⋊Dic71C2312yes—
120C2×C22⋊Dic71C2312yes—
121C2×C22⋊Dic71C2312yes—
122C2×C22⋊Dic71C2312yes—
123C2×C22⋊Dic71C2312yes—
124C2×C22⋊Dic71C2312yes—
125C2×C22⋊Dic71C2311yescharacteristic
126C2×C4×Dic71C2×C418yescomplemented
127C2×C4×Dic71C2312yes—
128C2×C4×Dic71C2312yes—
129C2×C4×Dic71C2312yes—
130C2×C4×Dic71C2312yes—
131C2×C4×Dic71C2312yes—
132C2×C4×Dic71C2314yes—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2314yes—
135C2×C4×Dic71C2311yescharacteristic
136C2×C4×Dic71C2311yescharacteristic
137C2×C4×Dic71C2311yescharacteristic
138C2×C4×Dic71C2311yescharacteristic
139C71⋊#95C2312yes—
140C71⋊#95C2312yes—
141C71⋊#95C2314yes—
142C71⋊#95C2312yes—
143C71⋊#95C2312yes—
144C71⋊#95C2314yes—
145C71⋊#95C2314yes—
146C71⋊#95C2314yes—
147C71⋊#95C2314yes—
148C71⋊#95C2314yes—
149C71⋊#95C2314yes—
150C25×C71C2312yes—
151C22×D4×C71—44no—
152C22×D4×C71C2×C418yes—
153C22×D4×C71C2311yescharacteristic
154C22×D4×C71C2311yescharacteristic
155C22×D4×C71C2312yes—
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2314yes—
158C4×D4×C71—44no—
159C2×C4⋊C4×C71C2312yes—
160C2×C22⋊C4×C71—28no—
161C2×C22⋊C4×C71C2312yes—
162C2×C22⋊C4×C71C2311yescharacteristic
163C2×C22⋊C4×C71C2314yes—
164C2×C22⋊C4×C71C2314yes—
165C2×C22⋊C4×C71C2314yes—
166C2×C22⋊C4×C71C2311yescharacteristic
167C2×C42×C71C2312yes—
168#95×C71C2312yes—
169#95×C71C2312yes—
170C2×Dic142—24no—
171C2×Dic142—24no—
172C2×Dic142—416no—
173C2×Dic142—44no—
174C2×Dic142C22×C414yes—
175C2×Dic142C22×C414yes—
176C2×Dic142C22×C418yes—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—28no—
180C22×Dic71—42no—
181C22×Dic71—44no—
182C22×Dic71—44no—
183C22×Dic71—44no—
184C22×Dic71C22×C414yes—
185C22×Dic71C22×C418yes—
186C22×Dic71C22×C414yes—
187C22×Dic71C2414yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2411yescharacteristic
192C22×Dic71C2411yescharacteristic
193C22×Dic71C2411yescharacteristic
194C22×Dic71C2411yescharacteristic
195C22×Dic71C2412yes—
196C4⋊Dic71—24no—
197Dic71⋊C4—24no—
198Dic71⋊C4—24no—
199Dic71⋊C4—44no—
200Dic71⋊C4—44no—
201C22⋊Dic71—24no—
202C22⋊Dic71—22no—
203C22⋊Dic71—28no—
204C22⋊Dic71—44no—
205C22⋊Dic71—44no—
206C22⋊Dic71C22×C418yes—
207C22⋊Dic71C22×C418yes—
208C22⋊Dic71C22×C418yes—
209C22⋊Dic71C22×C418yes—
210C22⋊Dic71C22×C418yes—
211C22⋊Dic71C22×C418yes—
212C22⋊Dic71C22×C418yes—
213C22⋊Dic71C22×C418yes—
214C22⋊Dic71#4114yes—
215C4×Dic71—24no—
216C4×Dic71—24no—
217C4×Dic71—24no—
218C4×Dic71—42no—
219C4×Dic71—42no—
220C4×Dic71—44no—
221C4×Dic71—44no—
222C4×Dic71—44no—
223C4×Dic71C22×C414yes—
224C4×Dic71C22×C414yes—
225C4×Dic71C22×C414yes—
226C4×Dic71C22×C414yes—
227C24×C71—24no—
228C24×C71—24no—
229C24×C71—44no—
230C24×C71—44no—
231C24×C71C22×C418yes—
232C24×C71C2412yes—
233C24×C71C2412yes—
234C24×C71C2411yescharacteristic
235C2×D4×C71—24no—
236C2×D4×C71—24no—
237C2×D4×C71—416no—
238C2×D4×C71—44no—
239C2×D4×C71C22×C414yes—
240C2×D4×C71C22×C414yes—
241C2×D4×C71C22×C418yes—
242C22×C4×C71—24no—
243C22×C4×C71—28no—
244C22×C4×C71—44no—
245C22×C4×C71—44no—
246C22×C4×C71C22×C414yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2414yes—
249C22×C4×C71C2411yescharacteristic
250C22×C4×C71C2412yes—
251C22×C4×C71C2411yescharacteristic
252C4⋊C4×C71—24no—
253C22⋊C4×C71—24no—
254C22⋊C4×C71—22no—
255C22⋊C4×C71—28no—
256C22⋊C4×C71—44no—
257C22⋊C4×C71—44no—
258C22⋊C4×C71#4114yes—
259C42×C71—24no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—22no—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71—24no—
267C23×C71—24no—
268C23×C71—24no—
269C23×C71—24no—
270C23×C71—216no—
271C23×C71—48no—
272C23×C71—48no—
273C23×C71—88no—
274C23×C71—88no—
275C23×C71C23×C414yes—
276C23×C71C23×C414yes—
277C23×C71C23×C412yes—
278C23×C71C2×#4112yes—
279C23×C71C2×#4112yes—
280C23×C71C2511yescharacteristic
281D4×C71—28no—
282D4×C71—28no—
283D4×C71—48no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—28no—
288C2×C4×C71—24no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—24no—
292C2×C4×C71—22no—
293C2×C4×C71—24no—
294C2×C4×C71—88no—
295C2×C4×C71C23×C412yes—
296C2×C4×C71C23×C412yes—
297C2×C4×C71C2×#4114yes—
298C2×C4×C71H(5,𝔽2)14yes—
299C2×Dic71—28no—
300C2×Dic71—21no—
301C2×Dic71—21no—
302C2×Dic71—21no—
303C2×Dic71—21no—
304C2×Dic71—22no—
305C2×Dic71—24no—
306C2×Dic71—24no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—24no—
312C2×Dic71—22no—
313C2×Dic71—24no—
314C2×Dic71—22no—
315C2×Dic71—24no—
316C2×Dic71—44no—
317C2×Dic71—48no—
318C2×Dic71—88no—
319C2×Dic71C23×C412yes—
320C2×Dic71C23×C412yes—
321C2×Dic71C23×C412yes—
322C2×Dic71C23×C412yes—
323C2×Dic71C23×C414yes—
324C2×Dic71C23×C414yes—
325C2×Dic71C2×#4114yes—
326Dic142—28no—
327Dic142—28no—
328Dic142—48no—
329C22×C71—22no—
330C22×C71—22no—
331C22×C71—24no—
332C22×C71—24no—
333C22×C71—24no—
334C22×C71—24no—
335C22×C71—24no—
336C22×C71—24no—
337C22×C71—24no—
338C22×C71—24no—
339C22×C71—44no—
340C22×C71—44no—
341C22×C71—44no—
342C22×C71—44no—
343C22×C71—816no—
344C22×C71C4×#4114yes—
345C22×C71C24×C411yescharacteristic
346C22×C71C22×#4111yescharacteristic
347C22×C71C22×#4111yescharacteristic
348C22×C71C2×H(5,𝔽2)12yes—
349C22×C71#58512yes—
350C4×C71—22no—
351C4×C71—24no—
352C4×C71—42no—
353C4×C71—44no—
354C4×C71#51814yes—
355Dic71—22no—
356Dic71—22no—
357Dic71—24no—
358Dic71—24no—
359Dic71—22no—
360Dic71—22no—
361Dic71—24no—
362Dic71—42no—
363Dic71—44no—
364#34240—711nomaximal, Sylow
365C2×C71—24no—
366C2×C71—44no—
367C2×C71—44no—
368C2×C71C2×C4×#4111yescharacteristic
369C2×C71C2×#51811yescharacteristic
370C2×C71#342811yescharacteristic
371C2×C71#351412yes—
372C2×C71#351412yes—
373C22×#124—711no—
374#2372—714no—
375#2367—712no—
376#2367—712no—
377#2342—712no—
378#2342—712no—
379Q8×C22⋊C4—711no—
380Q8×C22⋊C4—711no—
381D4×C22⋊C4—711no—
382D4×C22⋊C4D7111yescharacteristic
383#2337—714no—
384#2312—712no—
385C4×#124—712no—
386C4×#124—712no—
387#2283—711no—
388#2273—712no—
389C4×#117—711no—
390C71#3424011yescharacteristic, complemented, Sylow
391C23×Q8—711no—
392C23×D4C2×D7111yescharacteristic
393C2×#124—7116no—
394C2×#124—712no—
395C2×#124—711no—
396C2×#124—711no—
397C2×#124—712no—
398C2×#124—711no—
399C2×#124—711no—
400C2×C4×Q8—712no—
401C2×C4×Q8—712no—
402C2×C4×D4—712no—
403C2×C4×D4C2×D7112yes—
404C2×#117—711no—
405C2×#117—711no—
406C22×C22⋊C4—712no—
407C22×C22⋊C4—712no—
408C22×C22⋊C4—712no—
409C22×C22⋊C4C2×D7112yes—
410C22×C42—711no—
411#391—712no—
412#391—712no—
413#391—714no—
414#391—714no—
415#390—712no—
416#390C2×D7112yes—
417#388—714no—
418#388—714no—
419#388—714no—
420#388—714no—
421#388—714no—
422#388—714no—
423#388—714no—
424#388—714no—
425#386—714no—
426#386C2×D7114yes—
427#385—714no—
428#385—714no—
429#383—712no—
430#382—712no—
431#381—712no—
432#380—711no—
433#380—712no—
434#380—712no—
435#380C2×D7111yescharacteristic
436#379—712no—
437#379C2×D7112yes—
438C4×C4⋊C4—712no—
439C4×C4⋊C4—712no—
440C4×C4⋊C4—712no—
441C4×C22⋊C4—714no—
442C4×C22⋊C4—711no—
443C4×C22⋊C4—714no—
444C4×C22⋊C4—714no—
445C4×C22⋊C4—711no—
446C4×C22⋊C4—712no—
447C4×C22⋊C4—714no—
448C4×C22⋊C4—712no—
449C4×C22⋊C4—712no—
450C4×C22⋊C4—714no—
451C4×C22⋊C4—711no—
452C4×C22⋊C4—714no—
453C4×C22⋊C4C2×D7111yescharacteristic
454#376—712no—
455#376—712no—
456C43—712no—
457C25C22×D7112yes—
458C22×Q8—2844no—
459C22×Q8—718no—
460C22×Q8—712no—
461C22×Q8—711no—
462C22×Q8—711no—
463C22×D4—44no—
464C22×D4C4×D7118yes—
465C22×D4C22×D7111yescharacteristic
466C22×D4C22×D7111yescharacteristic
467C22×D4C22×D7112yes—
468C23×C4—712no—
469C23×C4—711no—
470C23×C4—714no—
471C23×C4—711no—
472C23×C4C22×D7111yescharacteristic
473C23×C4C22×D7114yes—
474#124—718no—
475#124—718no—
476#124—718no—
477#124—718no—
478#124—7116no—
479#124—7116no—
480C4×Q8—2844no—
481C4×Q8—2844no—
482C4×D4—44no—
483C4×D4—2844no—
484#117—1424no—
485#117—1424no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—714no—
488C2×C4⋊C4—712no—
489C2×C4⋊C4—712no—
490C2×C4⋊C4—712no—
491C2×C4⋊C4C22×D7112yes—
492C2×C22⋊C4—28no—
493C2×C22⋊C4—714no—
494C2×C22⋊C4—714no—
495C2×C22⋊C4—7116no—
496C2×C22⋊C4—7116no—
497C2×C22⋊C4—711no—
498C2×C22⋊C4—712no—
499C2×C22⋊C4—712no—
500C2×C22⋊C4—712no—
501C2×C22⋊C4—712no—
502C2×C22⋊C4—712no—
503C2×C22⋊C4—712no—
504C2×C22⋊C4—712no—
505C2×C22⋊C4—712no—
506C2×C22⋊C4—712no—
507C2×C22⋊C4—714no—
508C2×C22⋊C4—711no—
509C2×C22⋊C4—1428no—
510C2×C22⋊C4C22×D7112yes—
511C2×C22⋊C4C22×D7114yes—
512C2×C22⋊C4C22×D7111yescharacteristic
513C2×C22⋊C4C22×D7114yes—
514C2×C22⋊C4C22×D7114yes—
515C2×C22⋊C4C22×D7111yescharacteristic
516C2×C42—714no—
517C2×C42—714no—
518C2×C42—712no—
519C2×C42—712no—
520C2×C42—714no—
521C2×C42—718no—
522C2×C42—711no—
523C2×C42—711no—
524C2×C42—711no—
525C2×C42—711no—
526C2×C42—712no—
527C2×C42—712no—
528C2×C42—712no—
529C2×C42C22×D7112yes—
530#95—712no—
531#95—714no—
532#95—712no—
533#95—712no—
534#95—712no—
535#95—714no—
536#95—714no—
537#95—714no—
538#95—714no—
539#95—714no—
540#95—714no—
541#95C22×D7112yes—
542#95C22×D7112yes—
543C24—24no—
544C24—24no—
545C24—44no—
546C24—44no—
547C24C2×C4×D7118yes—
548C24C23×D7112yes—
549C24C23×D7112yes—
550C24C23×D7111yescharacteristic
551C2×Q8—28416no—
552C2×Q8—2844no—
553C2×Q8—718no—
554C2×Q8—714no—
555C2×Q8—714no—
556C2×Q8—1424no—
557C2×Q8—1424no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—416no—
561C2×D4—44no—
562C2×D4C2×C4×D7114yes—
563C2×D4C2×C4×D7114yes—
564C2×D4C2×C4×D7118yes—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—2842no—
570C22×C4—2844no—
571C22×C4—2844no—
572C22×C4—2844no—
573C22×C4—714no—
574C22×C4—718no—
575C22×C4—714no—
576C22×C4—711no—
577C22×C4—711no—
578C22×C4—711no—
579C22×C4—712no—
580C22×C4—711no—
581C22×C4—712no—
582C22×C4—712no—
583C22×C4—714no—
584C22×C4—712no—
585C22×C4—1428no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4C2×C4×D7114yes—
589C22×C4C23×D7114yes—
590C22×C4C23×D7112yes—
591C22×C4C23×D7111yescharacteristic
592C22×C4C23×D7112yes—
593C22×C4C23×D7111yescharacteristic
594C4⋊C4—24no—
595C4⋊C4—2844no—
596C4⋊C4—2844no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C22⋊C4—22no—
601C22⋊C4—24no—
602C22⋊C4—28no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—2844no—
606C22⋊C4—2844no—
607C22⋊C4—718no—
608C22⋊C4—718no—
609C22⋊C4—718no—
610C22⋊C4—718no—
611C22⋊C4—718no—
612C22⋊C4—718no—
613C22⋊C4—718no—
614C22⋊C4—718no—
615C22⋊C4—714no—
616C22⋊C4—1428no—
617C22⋊C4—1424no—
618C22⋊C4—1422no—
619C22⋊C4#1176586414yes—
620C42—24no—
621C42—2842no—
622C42—2842no—
623C42—2844no—
624C42—2844no—
625C42—2844no—
626C42—714no—
627C42—714no—
628C42—714no—
629C42—714no—
630C42—1424no—
631C42—1424no—
632C42—1424no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—216no—
644C23—48no—
645C23—48no—
646C23—88no—
647C23—88no—
648C23C22×C4×D7114yes—
649C23C22×C4×D7114yes—
650C23C22×C4×D7112yes—
651C23#41×D7112yes—
652C23C2×#1176586412yes—
653C23C24×D7111yescharacteristic
654Q8—2848no—
655Q8—1428no—
656Q8—1428no—
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—2848no—
672C2×C4—2844no—
673C2×C4—5688no—
674C2×C4—712no—
675C2×C4—712no—
676C2×C4—712no—
677C2×C4—712no—
678C2×C4—714no—
679C2×C4—714no—
680C2×C4—714no—
681C2×C4—1424no—
682C2×C4—1422no—
683C2×C4—1424no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1424no—
687C2×C4—1421no—
688C2×C4—1421no—
689C2×C4—1421no—
690C2×C4—1421no—
691C2×C4—1422no—
692C2×C4—1424no—
693C2×C4—1424no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1428no—
698C2×C4C22×C4×D7112yes—
699C2×C4C22×C4×D7112yes—
700C2×C4C2×#1176586414yes—
701C2×C4#1455617314yes—
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×#1176586414yes—
718C22C23×C4×D7111yescharacteristic
719C22C2×#41×D7111yescharacteristic
720C22C22×#1176586411yescharacteristic
721C22C2×#1455617312yes—
722C22#1798683412yes—
723C4—24no—
724C4—22no—
725C4—44no—
726C4—42no—
727C4—2842no—
728C4—2844no—
729C4—1422no—
730C4—1422no—
731C4—1424no—
732C4—1424no—
733C4—1424no—
734C4—1422no—
735C4—1422no—
736C4#1798647214yes—
737C2—24no—
738C2—44no—
739C2—44no—
740C2C2×C4×#1176586411yescharacteristic
741C2C2×#1798647211yescharacteristic
742C2#2260153811yescharacteristic
743C2#2260229212yes—
744C2#2260229812yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingD4×C22⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC23×D4×C71C22
hypercenterD4×C22⋊C4D71
hypocenterC71#34240
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22591449C2semidirect
3. #22591413C2semidirect
4. #22591410C2semidirect
5. #22591191C2semidirect
6. #22591185C2semidirect
7. C22⋊C4×Dic142C2semidirect
8. #22591172C2semidirect
10. #22591149C2semidirect
11. #22590936C2semidirect
12. #22590887C2semidirect
13. C4×#14556115C2semidirect
14. #22590735C2semidirect
15. #22590693C2semidirect
16. C4×#14556084C2semidirect
19. C2×#14556115C4semidirect
26. C2×C4×Dic142C22semidirect
27. C2×#14556093C22semidirect
35. #17985905C22semidirect
36. #17985904C22semidirect
37. #17985903C22semidirect
38. #17985903C22semidirect
40. #17985893C22semidirect
41. #17985893C22semidirect
42. #17985893C22semidirect
43. #17985893C22semidirect
44. #17985887C22semidirect
45. #17985887C22semidirect
46. #17985887C22semidirect
47. #17985887C22semidirect
49. #17985872C22semidirect
50. #17985871C22semidirect
51. #17985866C22semidirect
52. #17985864C22semidirect
58. C4⋊C4×Dic71C22semidirect
59. C4×Dic71⋊C4C22semidirect
60. #17985850C22semidirect
66. C22⋊C4×Dic71C22semidirect
67. C22⋊C4×Dic71C22semidirect
68. C22⋊C4×Dic71C22semidirect
70. C4×C22⋊Dic71C22semidirect
71. C4×C22⋊Dic71C22semidirect
72. C4×C22⋊Dic71C22semidirect
73. #17985844C22semidirect
74. #17985844C22semidirect
75. C42×Dic71C22semidirect
85. C22×Dic142C2×C4semidirect
93. #14556115C2×C4semidirect
94. #14556115C2×C4semidirect
95. #14556115C2×C4semidirect
96. #14556115C2×C4semidirect
97. #14556115C2×C4semidirect
98. #14556115C2×C4semidirect
110. C2×C22⋊Dic71C2×C4semidirect
111. C2×C22⋊Dic71C2×C4semidirect
126. C2×C4×Dic71C2×C4semidirect
390. C71#34240semidirect

Maximal subgroups

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

subgroupindex
C22×#145561152
#225914492
#225914132
#225914102
#225911912
#225911852
C22⋊C4×Dic1422
#225911722
D4×C22⋊Dic712
#225911492
#225909362
#225908872
C4×#145561152
#225907352
#225906932
C4×#145560842
D4×C22⋊C4×C712
#3424071