Finite Group Databasebeta

← #32160772

Subgroups — #32160772

Order 18176.

2586 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986510C211yesmaximal, characteristic
2#22591484C214yesmaximal, complemented
3#22591354C212yesmaximal, complemented
4#22591343C212yesmaximal, complemented
5#22591282C212yesmaximal, complemented
6#22591244C212yesmaximal, complemented
7#22591231C211yesmaximal, characteristic, complemented
8#22591223C211yesmaximal, characteristic, complemented
9#22591180C211yesmaximal, characteristic, complemented
10#22591171C211yesmaximal, characteristic, complemented
11#22591033C212yesmaximal, complemented
12#22591022C212yesmaximal, complemented
13#22590995C214yesmaximal, complemented
14#22590980C212yesmaximal, complemented
15#22590969C212yesmaximal, complemented
16C2×#17985859C211yesmaximal, characteristic, complemented
17C71×#2280C211yesmaximal, characteristic, complemented
18C22×#11765865C2211yescharacteristic
19#17986510C4116yescomplemented
20C2×#14556111C2212yes—
21C2×#14556107C2211yescharacteristic
22C2×#14556107C2211yescharacteristic
23C2×#14556102C2211yescharacteristic
24C2×#14556102C2211yescharacteristic
25C2×#14556097C2212yes—
26C2×C4×Dic142C2212yescomplemented
27C2×C4×D284C2212yescomplemented
28C2×C4×C22⋊D71C2212yes—
29C2×C4×C22⋊D71C2212yes—
30C2×(C22⋊D71)⋊C4C2214yes—
31C2×#14556087C2211yescharacteristic
32C22×C4⋊Dic71C2212yes—
33C22×C22⋊Dic71C2212yes—
34#17985905C2212yescomplemented
35#17985901C2212yescomplemented
36#17985899C2214yes—
37#17985899C2214yes—
38#17985897C2212yescomplemented
39#17985897C2212yescomplemented
40#17985896C2214yescomplemented
41#17985894C2214yescomplemented
42#17985893C2214yes—
43#17985893C2214yes—
44#17985891C2214yescomplemented
45#17985889C2214yescomplemented
46#17985887C2214yes—
47#17985887C2214yes—
48#17985886C2214yescomplemented
49#17985880C2214yescomplemented
50#17985876C2214yes—
51#17985875C2214yes—
52#17985875C2214yes—
53#17985873C2214yescomplemented
54#17985871C2214yes—
55#17985870C2214yescomplemented
56#17985866C2212yescomplemented
57#17985863C2212yescomplemented
58#17985861C2212yescomplemented
59#17985859C2212yes—
60#17985859C2212yes—
61#17985859C2211yescharacteristic
62#17985859C2211yescharacteristic
63#17985859C2212yes—
64#17985858C2212yescomplemented
65C4×C4⋊Dic71C2212yescomplemented
66C4×C4⋊Dic71C2212yescomplemented
67#17985850C2212yescomplemented
68C22⋊C4×Dic71C2214yes—
69#17985846C2212yescomplemented
70#17985844C2212yescomplemented
71C2×C71⋊#95C2212yes—
72#95×D71C2212yescomplemented
73C24×C4×C71C2211yescharacteristic
74C2×#117×C71C2212yes—
75#381×C71C2211yescharacteristic
76#381×C71C2211yescharacteristic
77#380×C71C2211yescharacteristic
78#380×C71C2211yescharacteristic
79#380×C71C2212yes—
80#379×C71C2212yes—
81C4×C22⋊C4×C71C2212yes—
82C4×C22⋊C4×C71C2211yescharacteristic
83C4×C22⋊C4×C71C2211yescharacteristic
84C2×#11765865—44no—
85C2×#11765865C2×C418yescomplemented
86C22×Dic142C2311yescharacteristic
87C22×D284C2311yescharacteristic
88C22×C22⋊D71C2312yes—
89C22×C22⋊D71C2312yes—
90C22×C22⋊D71C2312yes—
91C23×Dic71C2314yes—
92C22×C4×D71C2314yes—
93C22×C4×D71C2312yes—
94#14556111C2×C4116yescomplemented
95#14556107C2×C418yescomplemented
96#14556107C2×C418yescomplemented
97#14556102C2×C418yes—
98#14556102C2×C418yescomplemented
99#14556097C2×C4116yescomplemented
100C4×Dic142—44no—
101C4×D284—44no—
102C4×C22⋊D71C2×C4116yescomplemented
103C4×C22⋊D71C2×C4116yescomplemented
104(C22⋊D71)⋊C4—48no—
105#14556087C2×C418yescomplemented
106C2×C4⋊Dic71—44no—
107C2×C4⋊Dic71C2312yes—
108C2×C4⋊Dic71C2312yes—
109C2×C4⋊Dic71C2314yes—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×Dic71⋊C4C2314yes—
113C2×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C2×Dic71⋊C4C2312yes—
116C2×Dic71⋊C4C2312yes—
117C2×C22⋊Dic71—44no—
118C2×C22⋊Dic71C2312yes—
119C2×C22⋊Dic71C2314yes—
120C2×C22⋊Dic71C2312yes—
121C2×C22⋊Dic71C2312yes—
122C2×C22⋊Dic71C2312yes—
123C2×C22⋊Dic71C2312yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2312yes—
128C2×(C2×D71)⋊C4C2312yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2312yes—
133C71⋊#95C2312yes—
134C71⋊#95C2314yes—
135C71⋊#95C2312yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C71⋊#95C2314yes—
141C71⋊#95C2314yes—
142C25×C71C2311yescharacteristic
143C23×C4×C71—44no—
144C23×C4×C71C2×C418yescomplemented
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151#117×C71—44no—
152C2×C4⋊C4×C71C2312yes—
153C2×C4⋊C4×C71C2312yes—
154C2×C22⋊C4×C71C2312yes—
155C2×C22⋊C4×C71C2312yes—
156C2×C22⋊C4×C71C2312yes—
157C2×C22⋊C4×C71C2312yes—
158C2×C22⋊C4×C71C2312yes—
159C2×C22⋊C4×C71C2312yes—
160C2×C42×C71C2312yes—
161C2×C42×C71C2312yes—
162#95×C71C2311yescharacteristic
163#95×C71C2311yescharacteristic
164#95×C71C2311yescharacteristic
165#95×C71C2311yescharacteristic
166#95×C71C2312yes—
167#95×C71C2312yes—
168C23×D71C2412yes—
169#11765865—416no—
170C2×Dic142—24no—
171C2×Dic142C22×C414yes—
172C2×D284—24no—
173C2×D284C22×C414yes—
174C2×C22⋊D71—24no—
175C2×C22⋊D71—24no—
176C2×C22⋊D71—44no—
177C2×C22⋊D71—44no—
178C2×C22⋊D71C22×C418yes—
179C2×C22⋊D71C22×C418yes—
180C2×C22⋊D71C22×C418yes—
181C22×Dic71—28no—
182C22×Dic71—44no—
183C22×Dic71—44no—
184C22×Dic71C2414yes—
185C22×Dic71C2414yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C2×C4×D71—44no—
190C2×C4×D71—44no—
191C2×C4×D71—44no—
192C2×C4×D71—44no—
193C2×C4×D71C22×C418yes—
194C4⋊Dic71—24no—
195C4⋊Dic71—24no—
196C4⋊Dic71—44no—
197C4⋊Dic71C22×C414yes—
198C4⋊Dic71C22×C414yes—
199Dic71⋊C4—44no—
200Dic71⋊C4—44no—
201Dic71⋊C4—44no—
202Dic71⋊C4C22×C418yes—
203Dic71⋊C4C22×C418yes—
204C22⋊Dic71—42no—
205C22⋊Dic71—44no—
206C22⋊Dic71—42no—
207C22⋊Dic71C22×C418yes—
208C22⋊Dic71C22×C418yes—
209C22⋊Dic71C22×C418yes—
210(C2×D71)⋊C4—44no—
211(C2×D71)⋊C4—44no—
212(C2×D71)⋊C4—44no—
213(C2×D71)⋊C4C22×C418yes—
214(C2×D71)⋊C4C22×C418yes—
215C4×Dic71—44no—
216C4×Dic71—44no—
217C4×Dic71—44no—
218C4×Dic71C22×C418yes—
219C24×C71—22no—
220C24×C71—22no—
221C24×C71—42no—
222C24×C71—42no—
223C24×C71C22×C414yes—
224C24×C71C2411yescharacteristic
225C24×C71C2411yescharacteristic
226C24×C71C2411yescharacteristic
227C22×C4×C71—24no—
228C22×C4×C71—24no—
229C22×C4×C71—24no—
230C22×C4×C71—416no—
231C22×C4×C71—42no—
232C22×C4×C71—42no—
233C22×C4×C71—42no—
234C22×C4×C71C22×C414yes—
235C22×C4×C71C22×C414yes—
236C22×C4×C71C22×C414yes—
237C22×C4×C71C22×C414yes—
238C22×C4×C71C22×C414yes—
239C22×C4×C71C22×C414yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2411yescharacteristic
245C22×C4×C71C2411yescharacteristic
246C22×C4×C71C2411yescharacteristic
247C22×C4×C71C2411yescharacteristic
248C4⋊C4×C71—42no—
249C4⋊C4×C71—42no—
250C22⋊C4×C71—24no—
251C22⋊C4×C71—24no—
252C22⋊C4×C71—42no—
253C22⋊C4×C71—42no—
254C22⋊C4×C71—42no—
255C22⋊C4×C71—42no—
256C42×C71—24no—
257C42×C71—24no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—28no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—21no—
264C23×C71—21no—
265C23×C71—21no—
266C23×C71—21no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71—44no—
270C23×C71—44no—
271C23×C71—48no—
272C23×C71—48no—
273C23×C71C23×C412yes—
274C23×C71C23×C412yes—
275C23×C71C23×C412yes—
276C23×C71H(5,𝔽2)12yes—
277C23×C712−1+412yes—
278C23×C71C2511yescharacteristic
279C22×D71—22no—
280C22×D71—24no—
281C22×D71—22no—
282C22×D71—24no—
283C22×D71C23×C414yes—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—28no—
288C2×C4×C71—28no—
289C2×C4×C71—28no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—44no—
303C2×C4×C71—44no—
304C2×C4×C71—44no—
305C2×C4×C71C23×C412yes—
306C2×C4×C71C23×C412yes—
307C2×C4×C71C23×C412yes—
308C2×C4×C71C23×C412yes—
309C2×C4×C71H(5,𝔽2)14yes—
310C22⋊D71—216no—
311C22⋊D71—48no—
312C22⋊D71—48no—
313C2×Dic71—22no—
314C2×Dic71—24no—
315C2×Dic71—22no—
316C2×Dic71—24no—
317C2×Dic71—24no—
318C2×Dic71—24no—
319C2×Dic71—24no—
320C2×Dic71—24no—
321C2×Dic71—24no—
322C2×Dic71—24no—
323C2×Dic71—88no—
324C2×Dic71C23×C414yes—
325C2×Dic71C23×C414yes—
326C2×Dic71C23×C414yes—
327D284—28no—
328C4×D71—48no—
329C4×D71—88no—
330Dic142—28no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71—24no—
334C22×C71—24no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—416no—
342C22×C71—42no—
343C22×C71—42no—
344C22×C71—42no—
345C22×C71—42no—
346C22×C71#52014yes—
347C22×C71C24×C411yescharacteristic
348C22×C71C2×H(5,𝔽2)12yes—
349C22×C71C2×H(5,𝔽2)11yescharacteristic
350C22×C71C2×2−1+411yescharacteristic
351C22×C71#58512yes—
352C2×D71—24no—
353C2×D71—24no—
354C2×D71—24no—
355C2×D71—44no—
356C2×D71—44no—
357C4×C71—22no—
358C4×C71—22no—
359C4×C71—22no—
360C4×C71—42no—
361C4×C71—42no—
362C4×C71—42no—
363C4×C71—42no—
364C4×C71#51814yes—
365Dic71—24no—
366Dic71—24no—
367Dic71—24no—
368Dic71—44no—
369Dic71—44no—
370#34404—711nomaximal, Sylow
371C2×C71—24no—
372C2×C71—42no—
373C2×C71—42no—
374C2×C71C2×#51811yescharacteristic
375C2×C71C2×#52011yescharacteristic
376C2×C71#342811yescharacteristic
377C2×C71#354112yes—
378C2×C71#354212yes—
379D71—44no—
380C2×#525—711no—
381#2376—714no—
382#2361—712no—
383#2360—712no—
384#2353—712no—
385#2349—712no—
386#2347—711no—
387#2346—711no—
388#2341—711no—
389#2339—711no—
390#2324—712no—
391#2323—712no—
392#2321—714no—
393#2319—712no—
394#2318—712no—
395#2280D7111yescharacteristic, complemented
396C2×#380—711no—
397C71#3440411yescharacteristic, complemented, Sylow
398C22×#41—711no—
399C24×C4C2×D7111yescharacteristic
400#525—7116no—
401C2×#123—712no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—711no—
404C2×#121—711no—
405C2×#121—711no—
406C2×#120—712no—
407C2×C4×Q8—712no—
408C2×C4×D4—712no—
409C2×C4×D4—712no—
410C2×C4×D4—714no—
411C2×C4×D4—712no—
412C2×#117—711no—
413C2×#117C2×D7112yes—
414C22×C4⋊C4—712no—
415C22×C22⋊C4—712no—
416#391—712no—
417#390—714no—
418#390—714no—
419#390—712no—
420#389—714no—
421#389—712no—
422#389—712no—
423#389—714no—
424#388—714no—
425#388—714no—
426#388—714no—
427#388—714no—
428#388—714no—
429#388—714no—
430#387—714no—
431#387—714no—
432#386—714no—
433#386—714no—
434#386—714no—
435#385—714no—
436#385—714no—
437#385—714no—
438#383—712no—
439#382—712no—
440#381—712no—
441#381C2×D7111yescharacteristic
442#381C2×D7111yescharacteristic
443#380—712no—
444#380—712no—
445#380—711no—
446#380—711no—
447#380—712no—
448#380—712no—
449#380C2×D7111yescharacteristic
450#380C2×D7111yescharacteristic
451#380C2×D7112yes—
452#379C2×D7112yes—
453C4×C4⋊C4—712no—
454C4×C4⋊C4—712no—
455C4×C4⋊C4—712no—
456C4×C22⋊C4—714no—
457C4×C22⋊C4—712no—
458C4×C22⋊C4C2×D7111yescharacteristic
459C4×C22⋊C4C2×D7111yescharacteristic
460C4×C22⋊C4C2×D7112yes—
461#376—712no—
462C2×#95—712no—
463C2×#95—712no—
464C25C22×D7111yescharacteristic
465C2×#41—2844no—
466C2×#41—718no—
467C22×Q8—711no—
468C22×D4—712no—
469C22×D4—712no—
470C22×D4—712no—
471C22×D4—711no—
472C23×C4—44no—
473C23×C4—714no—
474C23×C4—712no—
475C23×C4—714no—
476C23×C4C4×D7118yescomplemented
477C23×C4C22×D7111yescharacteristic
478C23×C4C22×D7111yescharacteristic
479C23×C4C22×D7111yescharacteristic
480C23×C4C22×D7111yescharacteristic
481C23×C4C22×D7111yescharacteristic
482C23×C4C22×D7111yescharacteristic
483#123—7116no—
484C22⋊Q8—718no—
485C22⋊Q8—718no—
486#121—718no—
487#121—718no—
488#120—7116no—
489C4×Q8—2844no—
490C4×D4—2844no—
491C4×D4—2848no—
492C4×D4—7116no—
493C4×D4—7116no—
494#117—44no—
495#117—718no—
496C2×C4⋊C4—2844no—
497C2×C4⋊C4—714no—
498C2×C4⋊C4—714no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—712no—
504C2×C4⋊C4—712no—
505C2×C4⋊C4—712no—
506C2×C4⋊C4—712no—
507C2×C4⋊C4C22×D7112yes—
508C2×C4⋊C4C22×D7112yes—
509C2×C22⋊C4—2844no—
510C2×C22⋊C4—712no—
511C2×C22⋊C4—714no—
512C2×C22⋊C4—712no—
513C2×C22⋊C4—714no—
514C2×C22⋊C4—714no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—712no—
517C2×C22⋊C4—712no—
518C2×C22⋊C4—712no—
519C2×C22⋊C4—712no—
520C2×C22⋊C4—712no—
521C2×C22⋊C4C22×D7112yes—
522C2×C22⋊C4C22×D7112yes—
523C2×C22⋊C4C22×D7112yes—
524C2×C22⋊C4C22×D7112yes—
525C2×C22⋊C4C22×D7112yes—
526C2×C22⋊C4C22×D7112yes—
527C2×C42—714no—
528C2×C42—714no—
529C2×C42—714no—
530C2×C42—712no—
531C2×C42C22×D7112yes—
532C2×C42C22×D7112yes—
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#95—714no—
542#95C22×D7111yescharacteristic
543#95C22×D7111yescharacteristic
544#95C22×D7111yescharacteristic
545#95C22×D7111yescharacteristic
546#95C22×D7112yes—
547#95C22×D7112yes—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—712no—
553C24C2×C4×D7114yes—
554C24C23×D7111yescharacteristic
555C24C23×D7111yescharacteristic
556C24C23×D7111yescharacteristic
557#41—28416no—
558C2×Q8—714no—
559C2×Q8—1424no—
560C2×D4—2844no—
561C2×D4—2844no—
562C2×D4—718no—
563C2×D4—718no—
564C2×D4—718no—
565C2×D4—714no—
566C2×D4—1424no—
567C2×D4—1424no—
568C2×D4—1424no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—416no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—2844no—
577C22×C4—2844no—
578C22×C4—2844no—
579C22×C4—2844no—
580C22×C4—2844no—
581C22×C4—2844no—
582C22×C4—718no—
583C22×C4—712no—
584C22×C4—712no—
585C22×C4—712no—
586C22×C4—714no—
587C22×C4—714no—
588C22×C4—1428no—
589C22×C4C2×C4×D7114yes—
590C22×C4C2×C4×D7114yes—
591C22×C4C2×C4×D7114yes—
592C22×C4C2×C4×D7114yes—
593C22×C4C2×C4×D7114yes—
594C22×C4C2×C4×D7114yes—
595C22×C4C23×D7112yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7112yes—
598C22×C4C23×D7112yes—
599C22×C4C23×D7111yescharacteristic
600C22×C4C23×D7111yescharacteristic
601C22×C4C23×D7111yescharacteristic
602C22×C4C23×D7111yescharacteristic
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—2844no—
606C4⋊C4—2844no—
607C4⋊C4—2844no—
608C4⋊C4—2844no—
609C4⋊C4—718no—
610C4⋊C4—718no—
611C4⋊C4—714no—
612C4⋊C4—714no—
613C4⋊C4—1424no—
614C4⋊C4—1424no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—2844no—
622C22⋊C4—2844no—
623C22⋊C4—2844no—
624C22⋊C4—2842no—
625C22⋊C4—2844no—
626C22⋊C4—2842no—
627C22⋊C4—718no—
628C22⋊C4—718no—
629C22⋊C4—718no—
630C22⋊C4—718no—
631C22⋊C4—718no—
632C42—24no—
633C42—24no—
634C42—2844no—
635C42—2844no—
636C42—2844no—
637C42—718no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—714no—
654C23—1424no—
655C23—1422no—
656C23—1422no—
657C23—1424no—
658C23C22×C4×D7112yes—
659C23C22×C4×D7112yes—
660C23C22×C4×D7112yes—
661C23#1455617412yes—
662C23#1455617512yes—
663C23C24×D7111yescharacteristic
664Q8—1428no—
665D4—2848no—
666D4—2848no—
667D4—14216no—
668D4—1428no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—2848no—
691C2×C4—5688no—
692C2×C4—5688no—
693C2×C4—714no—
694C2×C4—714no—
695C2×C4—714no—
696C2×C4—1424no—
697C2×C4—1424no—
698C2×C4—1424no—
699C2×C4—1424no—
700C2×C4—1424no—
701C2×C4—1424no—
702C2×C4—1424no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1424no—
706C2×C4C22×C4×D7112yes—
707C2×C4C22×C4×D7112yes—
708C2×C4C22×C4×D7112yes—
709C2×C4C22×C4×D7112yes—
710C2×C4#1455617314yes—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—2844no—
727C22—2844no—
728C22—1424no—
729C22—1424no—
730C22—1424no—
731C22#1798647914yes—
732C22C23×C4×D7111yescharacteristic
733C22C2×#1455617312yes—
734C22C2×#1455617411yescharacteristic
735C22C2×#1455617511yescharacteristic
736C22#1798683512yes—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2844no—
745C4—2844no—
746C4—1424no—
747C4—1424no—
748C4—1424no—
749C4#1798647214yes—
750C2—24no—
751C2—42no—
752C2—42no—
753C2—2844no—
754C2C2×#1798647211yescharacteristic
755C2C2×#1798647911yescharacteristic
756C2#2260154111yescharacteristic
757C2#2260263312yes—
758C2#2260265612yes—
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingC71×#2280C2
socle, cosocleC23×C71C25
prime radicalC2×#17986510C2
hypercenter#2280D71
hypocenterC71#34404
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #22591484C2semidirect
3. #22591354C2semidirect
4. #22591343C2semidirect
5. #22591282C2semidirect
6. #22591244C2semidirect
7. #22591231C2semidirect
8. #22591223C2semidirect
9. #22591180C2semidirect
10. #22591171C2semidirect
11. #22591033C2semidirect
12. #22591022C2semidirect
13. #22590995C2semidirect
14. #22590980C2semidirect
15. #22590969C2semidirect
16. C2×#17985859C2semidirect
17. C71×#2280C2semidirect
19. #17986510C4semidirect
26. C2×C4×Dic142C22semidirect
27. C2×C4×D284C22semidirect
34. #17985905C22semidirect
35. #17985901C22semidirect
38. #17985897C22semidirect
39. #17985897C22semidirect
40. #17985896C22semidirect
41. #17985894C22semidirect
44. #17985891C22semidirect
45. #17985889C22semidirect
48. #17985886C22semidirect
49. #17985880C22semidirect
53. #17985873C22semidirect
55. #17985870C22semidirect
56. #17985866C22semidirect
57. #17985863C22semidirect
58. #17985861C22semidirect
64. #17985858C22semidirect
65. C4×C4⋊Dic71C22semidirect
66. C4×C4⋊Dic71C22semidirect
67. #17985850C22semidirect
69. #17985846C22semidirect
70. #17985844C22semidirect
72. #95×D71C22semidirect
85. C2×#11765865C2×C4semidirect
94. #14556111C2×C4semidirect
95. #14556107C2×C4semidirect
96. #14556107C2×C4semidirect
98. #14556102C2×C4semidirect
99. #14556097C2×C4semidirect
102. C4×C22⋊D71C2×C4semidirect
103. C4×C22⋊D71C2×C4semidirect
105. #14556087C2×C4semidirect
144. C23×C4×C71C2×C4semidirect
395. #2280D71semidirect
397. C71#34404semidirect
476. C23×C4C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865102
#225914842
#225913542
#225913432
#225912822
#225912442
#225912312
#225912232
#225911802
#225911712
#225910332
#225910222
#225909952
#225909802
#225909692
C2×#179858592
C71×#22802
#3440471