Finite Group Databasebeta

← #32008879

Subgroups — #32008879

Order 18176.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22597044C211yesmaximal, characteristic, complemented
2#22596785C211yesmaximal, characteristic, complemented
3#22589234C211yesmaximal, characteristic, complemented
4#22589229C211yesmaximal, characteristic, complemented
5#22589053C211yesmaximal, characteristic, complemented
6#22589046C211yesmaximal, characteristic, complemented
7#22588990C211yesmaximal, characteristic, complemented
8#22588990C211yesmaximal, characteristic, complemented
9#22588669C211yesmaximal, characteristic, complemented
10#22588669C211yesmaximal, characteristic, complemented
11#22588643C211yesmaximal, characteristic, complemented
12#22588547C211yesmaximal, characteristic, complemented
13#22588284C211yesmaximal, characteristic, complemented
14#22588126C211yesmaximal, characteristic, complemented
15C71×#3002C211yesmaximal, characteristic
16C2×#14556135C2211yescharacteristic, complemented
17C22×#11765849C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19#17986077—21no—
20#17986077—21no—
21#17986071—21no—
22#17986071—21no—
23C2×#14556064C2211yescharacteristic, complemented
24C2×#14556064C2211yescharacteristic, complemented
25#17986026C2211yescharacteristic, complemented
26C2×#14556055C2211yescharacteristic
27C2×#14556055C2211yescharacteristic
28C2×#14556055C2211yescharacteristic
29C2×#14556055C2211yescharacteristic
30C2×#14556055C2211yescharacteristic, complemented
31C2×#14556055C2211yescharacteristic, complemented
32#17985966—21no—
33#17985966—21no—
34#17985966C2211yescharacteristic
35#17985966C2211yescharacteristic
36#17985966C2211yescharacteristic
37#17985966C2211yescharacteristic
38#17985966C2211yescharacteristic, complemented
39#17985963—21no—
40#17985963—21no—
41#17985963C2211yescharacteristic
42#17985955C2211yescharacteristic, complemented
43C2×#14556038C2211yescharacteristic, complemented
44C2×C8×Dic71C2211yescharacteristic, complemented
45C4×C22⋊Dic71C2211yescharacteristic
46#17985764C2211yescharacteristic, complemented
47#17985764C2211yescharacteristic, complemented
48#17985758C2211yescharacteristic, complemented
49#17985758C2211yescharacteristic, complemented
50#17985753C2211yescharacteristic, complemented
51#17985753C2211yescharacteristic, complemented
52C22×#41×C71C2211yescharacteristic
53C2×#135×C71C2211yescharacteristic
54C2×#135×C71C2211yescharacteristic
55#525×C71C2211yescharacteristic
56#452×C71C411yescharacteristic, complemented
57#452×C71C411yescharacteristic, complemented
58#451×C71C411yescharacteristic, complemented
59#450×C71C411yescharacteristic, complemented
60#449×C71C411yescharacteristic, complemented
61#449×C71C411yescharacteristic, complemented
62#448×C71C411yescharacteristic, complemented
63#447×C71C411yescharacteristic, complemented
64#416×C71C2211yescharacteristic
65#416×C71C2211yescharacteristic
66C2×C22⋊C8×C71C2211yescharacteristic
67#14556135—41no—
68#14556135—41no—
69C2×#11765849—21no—
70C2×#11765849—21no—
71C2×#11765849—41no—
72C2×#11765849—41no—
73C2×#11765849—41no—
74C2×#11765849—41no—
75C2×#11765849D411yescharacteristic
76C2×#11765849D411yescharacteristic
77C2×#11765849D411yescharacteristic
78C2×#11765849D411yescharacteristic
79C2×#11765849C2311yescharacteristic
80C2×#11765849C2311yescharacteristic
81C2×#11765849C2311yescharacteristic
82C2×#11765849C2311yescharacteristic
83C22×C71⋊C8—21no—
84C22×C71⋊C8—21no—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C2×C22⋊Dic71—21no—
88C2×C4×Dic71C2311yescharacteristic
89C2×C4×Dic71C2311yescharacteristic
90#14556064—41no—
91#14556064—41no—
92C4⋊(C71⋊C8)—21no—
93C4⋊(C71⋊C8)—21no—
94#14556055—41no—
95#14556055—41no—
96#14556055—41no—
97#14556055—41no—
98#14556055—41no—
99#14556055—41no—
100C22⋊(C71⋊C8)—21no—
101C22⋊(C71⋊C8)—21no—
102C22⋊(C71⋊C8)—21no—
103C22⋊(C71⋊C8)—21no—
104C22⋊(C71⋊C8)—21no—
105C22⋊(C71⋊C8)—21no—
106C22⋊(C71⋊C8)—21no—
107C22⋊(C71⋊C8)—21no—
108C22⋊(C71⋊C8)—21no—
109C22⋊(C71⋊C8)—21no—
110C22⋊(C71⋊C8)—21no—
111C22⋊(C71⋊C8)—21no—
112#14556039—21no—
113#14556038—41no—
114C4×C71⋊C8—21no—
115C8×Dic71—41no—
116C71⋊#95—21no—
117C2×#41×C71—21no—
118C2×#41×C71—21no—
119C2×#41×C71—41no—
120C2×#41×C71—41no—
121C2×#41×C71—41no—
122C2×#41×C71—41no—
123C2×#41×C71C2×C411yescharacteristic
124C2×#41×C71C2×C411yescharacteristic
125C2×#41×C71C2311yescharacteristic
126C2×#41×C71C2311yescharacteristic
127C2×#41×C71C2311yescharacteristic
128C22×Q8×C71C2×C411yescharacteristic
129C22×D4×C71—21no—
130C22×D4×C71C2×C411yescharacteristic
131C23×C4×C71—21no—
132C23×C4×C71C2311yescharacteristic
133#135×C71—41no—
134#135×C71—41no—
135#135×C71—41no—
136#135×C71—41no—
137C2×Q16×C71C2×C411yescharacteristic
138C2×Q16×C71C2×C411yescharacteristic
139C2×SD16×C71C2×C411yescharacteristic
140C2×SD16×C71C2×C411yescharacteristic
141C2×SD16×C71C2×C411yescharacteristic
142C2×SD16×C71C2×C411yescharacteristic
143C2×D8×C71C2×C411yescharacteristic
144C2×D8×C71C2×C411yescharacteristic
145C22×C8×C71C2311yescharacteristic
146C22×C8×C71C2311yescharacteristic
147#123×C71—21no—
148C22⋊Q8×C71C2×C411yescharacteristic
149C22⋊Q8×C71C2×C411yescharacteristic
150#121×C71C2×C411yescharacteristic
151#121×C71C2×C411yescharacteristic
152#120×C71—21no—
153C4×D4×C71—21no—
154C4×D4×C71—21no—
155#117×C71C2311yescharacteristic
156#103×C71C2×C411yescharacteristic
157#103×C71C2×C411yescharacteristic
158#103×C71C2×C411yescharacteristic
159#103×C71C2×C411yescharacteristic
160#102×C71C2×C411yescharacteristic
161#102×C71C2×C411yescharacteristic
162#102×C71C2×C411yescharacteristic
163#102×C71C2×C411yescharacteristic
164C22⋊C8×C71C2×C411yescharacteristic
165C22⋊C8×C71C2×C411yescharacteristic
166C22⋊C8×C71C2×C411yescharacteristic
167C22⋊C8×C71C2×C411yescharacteristic
168C22×Dic71—21no—
169C22×Dic71—21no—
170#11765849—21no—
171#11765849—21no—
172#11765849—21no—
173#11765849—21no—
174#11765849—21no—
175#11765849—21no—
176#11765849—21no—
177#11765849—21no—
178#11765849—41no—
179#11765849—41no—
180#11765849—41no—
181#11765849—41no—
182#11765849—42no—
183#11765849—42no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8—21no—
186C2×C71⋊C8—21no—
187C2×C71⋊C8—21no—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8—21no—
191C2×C71⋊C8—21no—
192C2×C71⋊C8—42no—
193C2×C71⋊C8—42no—
194C2×C71⋊C8C2×D411yescharacteristic
195C2×C71⋊C8C2×D411yescharacteristic
196C2×C71⋊C8C2×D411yescharacteristic
197C2×C71⋊C8C2×D411yescharacteristic
198C22⋊Dic71—42no—
199C4×Dic71—21no—
200C4×Dic71—21no—
201C4×Dic71—21no—
202C4×Dic71—21no—
203C24×C71—21no—
204C24×C71#4111yescharacteristic
205#41×C71—21no—
206#41×C71—21no—
207#41×C71—21no—
208#41×C71—21no—
209#41×C71—21no—
210#41×C71—21no—
211#41×C71—21no—
212#41×C71—21no—
213#41×C71—21no—
214#41×C71—21no—
215#41×C71—21no—
216#41×C71—21no—
217#41×C71—41no—
218#41×C71—41no—
219#41×C71—41no—
220#41×C71—41no—
221#41×C71—42no—
222#41×C71—42no—
223#41×C71—42no—
224#41×C71—42no—
225C2×Q8×C71—21no—
226C2×Q8×C71—41no—
227C2×Q8×C71—41no—
228C2×Q8×C71C22×C411yescharacteristic
229C2×Q8×C71C22×C411yescharacteristic
230C2×Q8×C71C22×C411yescharacteristic
231C2×D4×C71—21no—
232C2×D4×C71—21no—
233C2×D4×C71—21no—
234C2×D4×C71—21no—
235C2×D4×C71—21no—
236C2×D4×C71—21no—
237C2×D4×C71—21no—
238C2×D4×C71—21no—
239C2×D4×C71—41no—
240C2×D4×C71—41no—
241C2×D4×C71—42no—
242C2×D4×C71—42no—
243C2×D4×C71C22×C411yescharacteristic
244C2×D4×C71C22×C411yescharacteristic
245C2×D4×C71C22×C411yescharacteristic
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—42no—
257C22×C4×C71—42no—
258C22×C4×C71C22×C411yescharacteristic
259C22×C4×C71C22×C411yescharacteristic
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71#4111yescharacteristic
263C22×C4×C71C2411yescharacteristic
264Q16×C71—41no—
265Q16×C71—41no—
266SD16×C71—41no—
267SD16×C71—41no—
268SD16×C71—41no—
269SD16×C71—41no—
270D8×C71—41no—
271D8×C71—41no—
272C2×C8×C71—21no—
273C2×C8×C71—21no—
274C2×C8×C71—21no—
275C2×C8×C71—21no—
276C2×C8×C71C22×C411yescharacteristic
277C2×C8×C71C22×C411yescharacteristic
278C2×C8×C71C22×C411yescharacteristic
279C2×C8×C71C22×C411yescharacteristic
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71C22×C411yescharacteristic
283C4⋊C4×C71C22×C411yescharacteristic
284C22⋊C4×C71—21no—
285C22⋊C4×C71—21no—
286C22⋊C4×C71—21no—
287C22⋊C4×C71—21no—
288C22⋊C4×C71—21no—
289C42×C71—21no—
290C23×C71—21no—
291C23×C71—21no—
292C23×C71—21no—
293C23×C71—21no—
294C23×C71—21no—
295C23×C71—41no—
296C23×C71—41no—
297C23×C71—42no—
298C23×C71—81no—
299C23×C71—81no—
300C23×C71C4×D411yescharacteristic
301C23×C71C4×D411yescharacteristic
302C23×C71C2×#4111yescharacteristic
303Q8×C71—21no—
304Q8×C71—21no—
305Q8×C71—21no—
306Q8×C71—21no—
307Q8×C71—21no—
308Q8×C71—21no—
309Q8×C71—42no—
310D4×C71—21no—
311D4×C71—21no—
312D4×C71—21no—
313D4×C71—21no—
314D4×C71—21no—
315D4×C71—21no—
316D4×C71—42no—
317D4×C71—42no—
318D4×C71—42no—
319D4×C71—41no—
320D4×C71—41no—
321D4×C71—41no—
322D4×C71—41no—
323D4×C71—41no—
324D4×C71—41no—
325D4×C71—81no—
326D4×C71—81no—
327C2×C4×C71—21no—
328C2×C4×C71—21no—
329C2×C4×C71—21no—
330C2×C4×C71—21no—
331C2×C4×C71—21no—
332C2×C4×C71—21no—
333C2×C4×C71—21no—
334C2×C4×C71—21no—
335C2×C4×C71—21no—
336C2×C4×C71—21no—
337C2×C4×C71—21no—
338C2×C4×C71—21no—
339C2×C4×C71—21no—
340C2×C4×C71—21no—
341C2×C4×C71—21no—
342C2×C4×C71—42no—
343C2×C4×C71—42no—
344C2×C4×C71—42no—
345C2×C4×C71—41no—
346C2×C4×C71—41no—
347C2×C4×C71—41no—
348C2×C4×C71—41no—
349C2×C4×C71—41no—
350C2×C4×C71—41no—
351C2×C4×C71C4×D411yescharacteristic
352C2×C4×C71C4×D411yescharacteristic
353C2×C4×C71C23×C411yescharacteristic
354C2×C4×C71C22×D411yescharacteristic
355C2×C4×C71H(5,𝔽2)11yescharacteristic
356C2×C4×C71H(5,𝔽2)11yescharacteristic
357C2×C4×C71H(5,𝔽2)11yescharacteristic
358C2×C4×C71H(5,𝔽2)11yescharacteristic
359C2×Dic71—22no—
360C2×Dic71—41no—
361C2×Dic71—41no—
362C2×Dic71—41no—
363C2×Dic71—41no—
364C2×Dic71—41no—
365C8×C71—21no—
366C8×C71—21no—
367C8×C71—21no—
368C8×C71—21no—
369C71⋊C8—21no—
370C71⋊C8—21no—
371C71⋊C8—21no—
372C71⋊C8—21no—
373C71⋊C8—41no—
374C71⋊C8—41no—
375C71⋊C8—41no—
376C71⋊C8—41no—
377C22×C71—21no—
378C22×C71—21no—
379C22×C71—21no—
380C22×C71—21no—
381C22×C71—21no—
382C22×C71—21no—
383C22×C71—21no—
384C22×C71—21no—
385C22×C71—41no—
386C22×C71—41no—
387C22×C71—41no—
388C22×C71—41no—
389C22×C71—41no—
390C22×C71—41no—
391C22×C71—41no—
392C22×C71—41no—
393C22×C71—41no—
394C22×C71—81no—
395C22×C71—81no—
396C22×C71—84no—
397C22×C71C2×C4×D411yescharacteristic
398C22×C71#53811yescharacteristic
399C22×C71#53811yescharacteristic
400C4×C71—21no—
401C4×C71—21no—
402C4×C71—41no—
403C4×C71—41no—
404C4×C71—41no—
405C4×C71—41no—
406C4×C71—41no—
407C4×C71#51811yescharacteristic
408C4×C71#51811yescharacteristic
409C4×C71#53411yescharacteristic
410C4×C71#53511yescharacteristic
411Dic71—42no—
412Dic71—81no—
413#22062—711nomaximal, Sylow
414C2×C71—21no—
415C2×C71—21no—
416C2×C71—41no—
417C2×C71—41no—
418C2×C71—81no—
419C2×C71—81no—
420C2×C71—81no—
421C2×C71#232111yescharacteristic
422C2×C71#295611yescharacteristic
423C2×C71#295711yescharacteristic
424#3002D7111yescharacteristic
425#2930—711no—
426#2879—711no—
427#1975—711no—
428#1974—711no—
429#1938—711no—
430#1937—711no—
431#1929—711no—
432#1929—711no—
433#1876—711no—
434#1876—711no—
435#1871—711no—
436#1855—711no—
437#1789—711no—
438#1753—711no—
439C71#2206211yescharacteristic, complemented, Sylow
440C22×#41C2×D7111yescharacteristic
441C2×#135C2×D7111yescharacteristic
442C2×#135C2×D7111yescharacteristic
443C2×#131—711no—
444C22×M16—711no—
445C22×M16—711no—
446#525C2×D7111yescharacteristic
447#452Dic7111yescharacteristic, complemented
448#452Dic7111yescharacteristic, complemented
449#451Dic7111yescharacteristic, complemented
450#450Dic7111yescharacteristic, complemented
451#449Dic7111yescharacteristic, complemented
452#449Dic7111yescharacteristic, complemented
453#448Dic7111yescharacteristic, complemented
454#447Dic7111yescharacteristic, complemented
455#436—1421no—
456#436—1421no—
457#435—1421no—
458#435—1421no—
459C2×#108—711no—
460C2×#108—711no—
461#424—711no—
462C2×#104—711no—
463C2×#104—711no—
464C2×#104—711no—
465C2×#104—711no—
466C2×#104—711no—
467C2×#104—711no—
468#416C2×D7111yescharacteristic
469#416C2×D7111yescharacteristic
470#408—711no—
471#408—711no—
472#408—711no—
473#408—711no—
474#408—711no—
475#408—1421no—
476#408—1421no—
477#407—711no—
478#407—1421no—
479#407—1421no—
480C2×C22⋊C8C2×D7111yescharacteristic
481#405—711no—
482C2×#97—711no—
483C2×C4×C8—711no—
484C4×C22⋊C4—711no—
485#341—711no—
486#341—711no—
487#339—711no—
488#339—711no—
489#336—711no—
490#336—711no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×Dic7111yescharacteristic
498C2×#41C2×Dic7111yescharacteristic
499C2×#41C22×D7111yescharacteristic
500C2×#41C22×D7111yescharacteristic
501C2×#41C22×D7111yescharacteristic
502C22×Q8C2×Dic7111yescharacteristic
503C22×D4—21no—
504C22×D4C2×Dic7111yescharacteristic
505C23×C4—21no—
506C23×C4C22×D7111yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×Dic7111yescharacteristic
512C2×Q16C2×Dic7111yescharacteristic
513C2×SD16C2×Dic7111yescharacteristic
514C2×SD16C2×Dic7111yescharacteristic
515C2×SD16C2×Dic7111yescharacteristic
516C2×SD16C2×Dic7111yescharacteristic
517C2×D8C2×Dic7111yescharacteristic
518C2×D8C2×Dic7111yescharacteristic
519#131—2841no—
520#131—2841no—
521C2×M16—2841no—
522C2×M16—2841no—
523C2×M16—2841no—
524C2×M16—2841no—
525C2×M16—711no—
526C2×M16—711no—
527C2×M16—711no—
528C2×M16—711no—
529C2×M16—711no—
530C2×M16—711no—
531C2×M16—711no—
532C2×M16—711no—
533C2×M16—1421no—
534C2×M16—1421no—
535C22×C8—711no—
536C22×C8—711no—
537C22×C8—1421no—
538C22×C8—1421no—
539C22×C8C22×D7111yescharacteristic
540C22×C8C22×D7111yescharacteristic
541#123—21no—
542C22⋊Q8C2×Dic7111yescharacteristic
543C22⋊Q8C2×Dic7111yescharacteristic
544#121C2×Dic7111yescharacteristic
545#121C2×Dic7111yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C22×D7111yescharacteristic
550C2×C22⋊C4—1421no—
551C2×C42—711no—
552C2×C42—711no—
553#108—2841no—
554#108—2841no—
555C4⋊C8—1421no—
556C4⋊C8—1421no—
557#104—2841no—
558#104—2841no—
559#104—2841no—
560#104—2841no—
561#104—2841no—
562#104—2841no—
563#103C2×Dic7111yescharacteristic
564#103C2×Dic7111yescharacteristic
565#103C2×Dic7111yescharacteristic
566#103C2×Dic7111yescharacteristic
567#102C2×Dic7111yescharacteristic
568#102C2×Dic7111yescharacteristic
569#102C2×Dic7111yescharacteristic
570#102C2×Dic7111yescharacteristic
571C22⋊C8—1421no—
572C22⋊C8—1421no—
573C22⋊C8—1421no—
574C22⋊C8—1421no—
575C22⋊C8—1421no—
576C22⋊C8—1421no—
577C22⋊C8—1421no—
578C22⋊C8—1421no—
579C22⋊C8—1421no—
580C22⋊C8—1421no—
581C22⋊C8—1421no—
582C22⋊C8—1421no—
583C22⋊C8C2×Dic7111yescharacteristic
584C22⋊C8C2×Dic7111yescharacteristic
585C22⋊C8C2×Dic7111yescharacteristic
586C22⋊C8C2×Dic7111yescharacteristic
587#97—2841no—
588#97—1421no—
589C4×C8—2841no—
590C4×C8—1421no—
591#95—1421no—
592C24—21no—
593C24#1176586411yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×Dic7111yescharacteristic
618C2×Q8C22×Dic7111yescharacteristic
619C2×Q8C22×Dic7111yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×Dic7111yescharacteristic
633C2×D4C22×Dic7111yescharacteristic
634C2×D4C22×Dic7111yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4—1421no—
648C22×C4—1421no—
649C22×C4C22×Dic7111yescharacteristic
650C22×C4C22×Dic7111yescharacteristic
651C22×C4D4×D7111yescharacteristic
652C22×C4D4×D7111yescharacteristic
653C22×C4#1176586411yescharacteristic
654C22×C4C23×D7111yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—2842no—
664M16—2842no—
665M16—2841no—
666M16—2841no—
667M16—2841no—
668M16—2841no—
669M16—1421no—
670M16—1421no—
671M16—1421no—
672M16—1421no—
673M16—1421no—
674M16—1421no—
675M16—1421no—
676M16—1421no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—2842no—
682C2×C8—2842no—
683C2×C8—711no—
684C2×C8—711no—
685C2×C8—711no—
686C2×C8—711no—
687C2×C8—1421no—
688C2×C8—1421no—
689C2×C8—1421no—
690C2×C8—1421no—
691C2×C8—1421no—
692C2×C8—1421no—
693C2×C8—1421no—
694C2×C8—1421no—
695C2×C8C22×Dic7111yescharacteristic
696C2×C8C22×Dic7111yescharacteristic
697C2×C8C22×Dic7111yescharacteristic
698C2×C8C22×Dic7111yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×Dic7111yescharacteristic
702C4⋊C4C22×Dic7111yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—2842no—
709C42—21no—
710C42—1421no—
711C42—1421no—
712C42—1421no—
713C42—1421no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23D4×Dic7111yescharacteristic
725C23D4×Dic7111yescharacteristic
726C23C2×#1176586411yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—2841no—
776C2×C4—2841no—
777C2×C4—2841no—
778C2×C4—2841no—
779C2×C4—2841no—
780C2×C4—1422no—
781C2×C4D4×Dic7111yescharacteristic
782C2×C4D4×Dic7111yescharacteristic
783C2×C4C23×Dic7111yescharacteristic
784C2×C4C2×D4×D7111yescharacteristic
785C2×C4#1455617311yescharacteristic
786C2×C4#1455617311yescharacteristic
787C2×C4#1455617311yescharacteristic
788C2×C4#1455617311yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—2841no—
794C8—2841no—
795C8—2841no—
796C8—2841no—
797C8—1421no—
798C8—1421no—
799C8—1421no—
800C8—1421no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×D4×Dic7111yescharacteristic
822C22#1798658411yescharacteristic
823C22#1798658411yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—2842no—
832C4—5681no—
833C4#1798647411yescharacteristic
834C4#1798647411yescharacteristic
835C4#1798655911yescharacteristic
836C4#1798656411yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#2259100111yescharacteristic
845C2#2259725011yescharacteristic
846C2#2259725711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC71×#3002C2
socleC22×C71C2×C4×D4
cosocleC22×C4×C71C24
hypercenter#3002D71
hypocenterC71#22062
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #22597044C2semidirect
2. #22596785C2semidirect
3. #22589234C2semidirect
4. #22589229C2semidirect
5. #22589053C2semidirect
6. #22589046C2semidirect
7. #22588990C2semidirect
8. #22588990C2semidirect
9. #22588669C2semidirect
10. #22588669C2semidirect
11. #22588643C2semidirect
12. #22588547C2semidirect
13. #22588284C2semidirect
14. #22588126C2semidirect
16. C2×#14556135C22semidirect
23. C2×#14556064C22semidirect
24. C2×#14556064C22semidirect
25. #17986026C22semidirect
30. C2×#14556055C22semidirect
31. C2×#14556055C22semidirect
38. #17985966C22semidirect
42. #17985955C22semidirect
43. C2×#14556038C22semidirect
44. C2×C8×Dic71C22semidirect
46. #17985764C22semidirect
47. #17985764C22semidirect
48. #17985758C22semidirect
49. #17985758C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
56. #452×C71C4semidirect
57. #452×C71C4semidirect
58. #451×C71C4semidirect
59. #450×C71C4semidirect
60. #449×C71C4semidirect
61. #449×C71C4semidirect
62. #448×C71C4semidirect
63. #447×C71C4semidirect
439. C71#22062semidirect
447. #452Dic71semidirect
448. #452Dic71semidirect
449. #451Dic71semidirect
450. #450Dic71semidirect
451. #449Dic71semidirect
452. #449Dic71semidirect
453. #448Dic71semidirect
454. #447Dic71semidirect

Maximal subgroups

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

subgroupindex
#225970442
#225967852
#225892342
#225892292
#225890532
#225890462
#225889902
#225886692
#225886432
#225885472
#225882842
#225881262
C71×#30022
#2206271