Finite Group Databasebeta

← #14764097

Subgroups — #14764097

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077060C211yesmaximal, characteristic
2#13077059C211yesmaximal, characteristic
3C2×#10622340C211yesmaximal, characteristic
4#13068823C211yesmaximal, characteristic, complemented
5#13068822C211yesmaximal, characteristic, complemented
6#13068822C211yesmaximal, characteristic, complemented
7#13068821C211yesmaximal, characteristic, complemented
8#13068820C211yesmaximal, characteristic, complemented
9#13068819C211yesmaximal, characteristic, complemented
10#13068819C211yesmaximal, characteristic, complemented
11#13068657C211yesmaximal, characteristic, complemented
12#13068655C211yesmaximal, characteristic, complemented
13#13068653C211yesmaximal, characteristic, complemented
14#13068651C211yesmaximal, characteristic, complemented
15C11×#1855C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×M16×D11C2211yescharacteristic
20C2×M16×D11C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C11×#108C2211yescharacteristic
24C2×C11×#108C2211yescharacteristic
25C11×#407C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622820C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622742—21no—
30#10622742—21no—
31#10622739C2211yescharacteristic
32#10622739C2211yescharacteristic
33#10622739C2211yescharacteristic
34#10622739C2211yescharacteristic
35#10622739C2211yescharacteristic
36#10622739C2211yescharacteristic
37C2×#66886C2211yescharacteristic
38C2×#66886C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41#10622723—21no—
42#10622723—21no—
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66883C2211yescharacteristic
46C2×#66883C2211yescharacteristic
47#10622340—21no—
48#10622340—21no—
49#10622340—21no—
50#10622340—21no—
51#10622340C412yes—
52#10622340C412yes—
53#10622340C412yes—
54#10622340C412yes—
55C11×#341C2211yescharacteristic
56C11×#341C2211yescharacteristic
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622190C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11Q811yescharacteristic
65C22×C22⋊D11Q811yescharacteristic
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339—41no—
69C2×#4339—41no—
70C2×#4339C2×C411yescharacteristic
71C2×#4339C2×C411yescharacteristic
72C2×#4339C2×C411yescharacteristic
73C2×#4339C2×C411yescharacteristic
74C2×#4339D411yescharacteristic
75C2×#4339D411yescharacteristic
76C2×#4339D411yescharacteristic
77C2×#4339D411yescharacteristic
78C22×D44Q811yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×Dic22Q811yescharacteristic
82C2×C11×M16—21no—
83C2×C11×M16—41no—
84C2×C11×M16—41no—
85C2×C11×M16C2311yescharacteristic
86C2×C11×M16C2311yescharacteristic
87C2×C11×M16C2311yescharacteristic
88C2×C11×M16C2311yescharacteristic
89C22×C8×C11—21no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318—41no—
94C2×#4318—41no—
95C2×#4318C2311yescharacteristic
96C2×#4318C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C22×C11⋊C8—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102M16×D11—41no—
103M16×D11—41no—
104M16×D11—41no—
105M16×D11—41no—
106C2×#4313—21no—
107C2×#4313—21no—
108C2×#4313—41no—
109C2×#4313—41no—
110C2×#4313C2×C412yes—
111C2×#4313C2×C412yes—
112C2×C8×D11—21no—
113C2×C8×D11—21no—
114C2×C8×D11—41no—
115C2×C8×D11—41no—
116C2×C8×D11C2×C412yes—
117C2×C8×D11C2×C412yes—
118C11×#108—41no—
119C11×#108—41no—
120C11×C22⋊C8—21no—
121C11×C22⋊C8—21no—
122C11×C22⋊C8C2×C412yes—
123C11×C22⋊C8C2×C412yes—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)C2×C412yes—
127C22⋊(C11⋊C8)C2×C412yes—
128#66886—41no—
129#66886—41no—
130#66886—41no—
131#66886—41no—
132(C2×D11)⋊C8—21no—
133(C2×D11)⋊C8—21no—
134(C2×D11)⋊C8—21no—
135(C2×D11)⋊C8—21no—
136(C2×D11)⋊C8—21no—
137(C2×D11)⋊C8—21no—
138(C2×D11)⋊C8—21no—
139(C2×D11)⋊C8—21no—
140(C2×D11)⋊C8—21no—
141(C2×D11)⋊C8—21no—
142(C2×D11)⋊C8—21no—
143(C2×D11)⋊C8—21no—
144(C2×D11)⋊C8C2×C412yes—
145(C2×D11)⋊C8C2×C412yes—
146(C2×D11)⋊C8C2×C412yes—
147(C2×D11)⋊C8C2×C412yes—
148#66883—41no—
149#66883—41no—
150#21950—111nomaximal, Sylow
151C24×C11C2×Q811yescharacteristic
152C23×D11C2×Q811yescharacteristic
153C23×D11C2×Q811yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×Q811yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—41no—
167C2×C22⋊D11—41no—
168C2×C22⋊D11C4⋊C411yescharacteristic
169C2×C22⋊D11C4⋊C411yescharacteristic
170C2×C22⋊D11C4⋊C411yescharacteristic
171C2×C22⋊D11C4⋊C411yescharacteristic
172C2×C22⋊D11C4⋊C411yescharacteristic
173C2×C22⋊D11C4⋊C411yescharacteristic
174C2×C22⋊D11C4⋊C411yescharacteristic
175C2×C22⋊D11C4⋊C411yescharacteristic
176C22×Dic11C2×Q811yescharacteristic
177C22×Dic11C2×Q811yescharacteristic
178#4339—41no—
179#4339—41no—
180#4339—41no—
181#4339—41no—
182#4339—41no—
183#4339—41no—
184#4339—41no—
185#4339—41no—
186#4339—41no—
187#4339—41no—
188#4339—41no—
189#4339—41no—
190#4339—41no—
191#4339—41no—
192#4339—41no—
193#4339—41no—
194C2×D44—41no—
195C2×D44—41no—
196C2×D44C4⋊C411yescharacteristic
197C2×D44C4⋊C411yescharacteristic
198C2×D44C4⋊C411yescharacteristic
199C2×D44C4⋊C411yescharacteristic
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C2×C4×D11—21no—
207C2×C4×D11—21no—
208C2×C4×D11C22×C411yescharacteristic
209C2×C4×D11C22×C411yescharacteristic
210C2×C4×D11C22×C411yescharacteristic
211C2×C4×D11C22×C411yescharacteristic
212C2×C4×D11C2×D411yescharacteristic
213C2×C4×D11C2×D411yescharacteristic
214C2×C4×D11C2×D411yescharacteristic
215C2×C4×D11C2×D411yescharacteristic
216C2×Dic22—41no—
217C2×Dic22—41no—
218C2×Dic22C4⋊C411yescharacteristic
219C2×Dic22C4⋊C411yescharacteristic
220C2×Dic22C4⋊C411yescharacteristic
221C2×Dic22C4⋊C411yescharacteristic
222C11×M16—21no—
223C11×M16—21no—
224C11×M16—21no—
225C11×M16—21no—
226C11×M16—21no—
227C11×M16—21no—
228C11×M16—21no—
229C11×M16—21no—
230C11×M16—42no—
231C2×C8×C11—21no—
232C2×C8×C11—21no—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—42no—
240C2×C8×C11C22×C412yes—
241C2×C8×C11C22×C412yes—
242#4318—21no—
243#4318—21no—
244#4318—21no—
245#4318—21no—
246#4318—21no—
247#4318—21no—
248#4318—21no—
249#4318—21no—
250#4318—42no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—42no—
260C2×C11⋊C8C22×C412yes—
261C2×C11⋊C8C22×C412yes—
262#4313—42no—
263#4313—42no—
264#4313—42no—
265#4313—42no—
266C8×D11—42no—
267C8×D11—42no—
268C8×D11—42no—
269C8×D11—42no—
270#2879—111no—
271#2879—111no—
272C2×#408—111no—
273#1855—111no—
274#1855—111no—
275#1855—111no—
276#1855—111no—
277#1855—111no—
278#1855—111no—
279#1855—111no—
280#1855D1111yescharacteristic, complemented
281#1811—111no—
282#1811—111no—
283#1810—111no—
284#1810—111no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11C2×C4⋊C411yescharacteristic
290C23×C11C2×C4⋊C411yescharacteristic
291C23×C11C22×Q811yescharacteristic
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—41no—
299C22×D11—41no—
300C22×D11C2×C4⋊C411yescharacteristic
301C22×D11C2×C4⋊C411yescharacteristic
302C22×D11C2×C4⋊C411yescharacteristic
303C22×D11C2×C4⋊C411yescharacteristic
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11C2×C4⋊C411yescharacteristic
315C2×C4×C11C2×C4⋊C411yescharacteristic
316C2×C4×C11C23×C411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C22⋊D11—41no—
323C22⋊D11—41no—
324C22⋊D11—41no—
325C22⋊D11—41no—
326C22⋊D11—41no—
327C22⋊D11—41no—
328C22⋊D11—41no—
329C22⋊D11—41no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11C2×C4⋊C411yescharacteristic
335C2×Dic11C2×C4⋊C411yescharacteristic
336C2×Dic11C2×C4⋊C411yescharacteristic
337C2×Dic11C2×C4⋊C411yescharacteristic
338D44—41no—
339D44—41no—
340D44—41no—
341D44—41no—
342C4×D11—21no—
343C4×D11—21no—
344C4×D11—21no—
345C4×D11—21no—
346C4×D11—21no—
347C4×D11—21no—
348C4×D11—21no—
349C4×D11—21no—
350C4×D11—21no—
351C4×D11—21no—
352C4×D11—21no—
353C4×D11—21no—
354C4×D11—21no—
355C4×D11—21no—
356C4×D11—21no—
357C4×D11—21no—
358Dic22—41no—
359Dic22—41no—
360Dic22—41no—
361Dic22—41no—
362C8×C11—22no—
363C8×C11—22no—
364C8×C11—41no—
365C8×C11—41no—
366C8×C11—41no—
367C8×C11—41no—
368C11⋊C8—22no—
369C11⋊C8—22no—
370C11⋊C8—41no—
371C11⋊C8—41no—
372C11⋊C8—41no—
373C11⋊C8—41no—
374C22×#41—111no—
375C22×M16—111no—
376C22×M16—111no—
377C22×M16—111no—
378C22×M16—111no—
379C22×M16C2×D1111yescharacteristic
380C23×C8—111no—
381C2×#108—111no—
382C2×#108—111no—
383C2×#108—111no—
384C2×#108—111no—
385C2×#108—111no—
386C2×#108—111no—
387C2×#108C2×D1111yescharacteristic
388C2×#108C2×D1111yescharacteristic
389#408—112no—
390#408—112no—
391#408—112no—
392#408—112no—
393#408—221no—
394#408—221no—
395#408—221no—
396#408—221no—
397#408—221no—
398#408—221no—
399#408—221no—
400#408—221no—
401#407—111no—
402#407—111no—
403#407—111no—
404#407—111no—
405#407—111no—
406#407—111no—
407#407—111no—
408#407C2×D1111yescharacteristic
409C2×C22⋊C8—111no—
410C2×C22⋊C8—111no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8C2×D1111yescharacteristic
413#341—111no—
414#341—111no—
415#341—111no—
416#341—111no—
417#341—111no—
418#341—111no—
419#341C2×D1111yescharacteristic
420#341C2×D1111yescharacteristic
421C22×C11—21no—
422C22×C11—21no—
423C22×C11—21no—
424C22×C11—21no—
425C22×C11—21no—
426C22×C11—21no—
427C22×C11—21no—
428C22×C11—21no—
429C22×C11—81no—
430C22×C11—81no—
431C22×C11C22×C4⋊C411yescharacteristic
432C22×C11#54311yescharacteristic
433C22×C11#54311yescharacteristic
434C2×D11—21no—
435C2×D11—21no—
436C2×D11—21no—
437C2×D11—21no—
438C2×D11—21no—
439C2×D11—21no—
440C2×D11—21no—
441C2×D11—21no—
442C2×D11—21no—
443C2×D11—21no—
444C2×D11—21no—
445C2×D11—21no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—81no—
449C2×D11—81no—
450C4×C11—21no—
451C4×C11—21no—
452C4×C11#51811yescharacteristic
453C4×C11#51811yescharacteristic
454C4×C11#53411yescharacteristic
455C4×C11#53411yescharacteristic
456Dic11—21no—
457Dic11—21no—
458Dic11—21no—
459Dic11—21no—
460C2×#41—111no—
461C2×#41—111no—
462C2×#41—111no—
463C2×#41—111no—
464C2×#41—111no—
465C2×#41—111no—
466C2×#41—111no—
467C2×#41—111no—
468C2×#41—441no—
469C2×#41—441no—
470C2×#41—441no—
471C2×#41—441no—
472C22×Q8—111no—
473C22×D4—111no—
474C22×D4—111no—
475C22×D4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4C22×D1111yescharacteristic
479C2×M16—21no—
480C2×M16—41no—
481C2×M16—41no—
482C2×M16—112no—
483C2×M16—112no—
484C2×M16—111no—
485C2×M16—111no—
486C2×M16—111no—
487C2×M16—111no—
488C2×M16—221no—
489C2×M16—221no—
490C2×M16—221no—
491C2×M16—441no—
492C2×M16—441no—
493C2×M16—441no—
494C2×M16—441no—
495C2×M16—441no—
496C2×M16—441no—
497C2×M16—441no—
498C2×M16—441no—
499C2×M16C22×D1111yescharacteristic
500C2×M16C22×D1111yescharacteristic
501C2×M16C22×D1111yescharacteristic
502C2×M16C22×D1111yescharacteristic
503C22×C8—21no—
504C22×C8—111no—
505C22×C8—111no—
506C22×C8—112no—
507C22×C8—112no—
508C22×C8—221no—
509C22×C8—221no—
510C22×C8—221no—
511C22×C8—441no—
512C22×C8—441no—
513C22×C8C22×D1111yescharacteristic
514C22×C8C22×D1111yescharacteristic
515#108—41no—
516#108—41no—
517#108—441no—
518#108—441no—
519#108—441no—
520#108—441no—
521#108—441no—
522#108—441no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525C22⋊C8—112no—
526C22⋊C8—112no—
527C22⋊C8—112no—
528C22⋊C8—112no—
529C22⋊C8—112no—
530C22⋊C8—112no—
531C22⋊C8—221no—
532C22⋊C8—221no—
533C22⋊C8—221no—
534C22⋊C8—221no—
535C22⋊C8—221no—
536C22⋊C8—221no—
537C22⋊C8—221no—
538C22⋊C8—221no—
539C22⋊C8—221no—
540C22⋊C8—221no—
541C22⋊C8—221no—
542C22⋊C8—221no—
543C22⋊C8—221no—
544C22⋊C8—221no—
545C22⋊C8C4×D1112yes—
546C22⋊C8C4×D1112yes—
547C2×C11—21no—
548C2×C11—21no—
549C2×C11—41no—
550C2×C11—41no—
551C2×C11#231511yescharacteristic
552C2×C11#291611yescharacteristic
553C2×C11#291611yescharacteristic
554D11—41no—
555D11—41no—
556D11—41no—
557D11—41no—
558C24—111no—
559C24—111no—
560C24Q8×D1111yescharacteristic
561#41—441no—
562#41—441no—
563#41—441no—
564#41—441no—
565#41—441no—
566#41—441no—
567#41—441no—
568#41—441no—
569#41—441no—
570#41—441no—
571#41—441no—
572#41—441no—
573#41—441no—
574#41—441no—
575#41—441no—
576#41—441no—
577C2×Q8—111no—
578C2×Q8—111no—
579C2×Q8—111no—
580C2×Q8—111no—
581C2×Q8—441no—
582C2×Q8—441no—
583C2×D4—111no—
584C2×D4—111no—
585C2×D4—111no—
586C2×D4—111no—
587C2×D4—111no—
588C2×D4—111no—
589C2×D4—111no—
590C2×D4—111no—
591C2×D4—111no—
592C2×D4—111no—
593C2×D4—111no—
594C2×D4—111no—
595C2×D4—441no—
596C2×D4—441no—
597C2×D4—441no—
598C2×D4—441no—
599C2×D4—441no—
600C2×D4—441no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—221no—
623C22×C4C2×C4×D1111yescharacteristic
624C22×C4C2×C4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4D4×D1111yescharacteristic
627C22×C4Q8×D1111yescharacteristic
628C22×C4C23×D1111yescharacteristic
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—42no—
638M16—221no—
639M16—221no—
640M16—221no—
641M16—221no—
642M16—221no—
643M16—221no—
644M16—221no—
645M16—221no—
646M16—442no—
647M16—442no—
648M16—442no—
649M16—442no—
650M16—442no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—42no—
660C2×C8—112no—
661C2×C8—112no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C2×C8—221no—
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—221no—
670C2×C8—442no—
671C2×C8—442no—
672C2×C8—442no—
673C2×C8—442no—
674C2×C8—442no—
675C2×C8C2×C4×D1112yes—
676C2×C8C2×C4×D1112yes—
677C11#2195011yescharacteristic, complemented, Sylow
678C23—21no—
679C23—21no—
680C23—41no—
681C23—41no—
682C23—111no—
683C23—111no—
684C23—111no—
685C23—111no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—221no—
690C23—441no—
691C23—441no—
692C23—441no—
693C23—441no—
694C23C4⋊C4×D1111yescharacteristic
695C23C4⋊C4×D1111yescharacteristic
696C23C2×Q8×D1111yescharacteristic
697Q8—441no—
698Q8—441no—
699Q8—441no—
700Q8—441no—
701D4—441no—
702D4—441no—
703D4—441no—
704D4—441no—
705D4—441no—
706D4—441no—
707D4—441no—
708D4—441no—
709D4—441no—
710D4—441no—
711D4—441no—
712D4—441no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—111no—
724C2×C4—111no—
725C2×C4—111no—
726C2×C4—111no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—221no—
740C2×C4—221no—
741C2×C4—221no—
742C2×C4—221no—
743C2×C4—221no—
744C2×C4—221no—
745C2×C4—221no—
746C2×C4—221no—
747C2×C4C4⋊C4×D1111yescharacteristic
748C2×C4C4⋊C4×D1111yescharacteristic
749C2×C4C22×C4×D1111yescharacteristic
750C2×C4C2×D4×D1111yescharacteristic
751C2×C4#6703711yescharacteristic
752C2×C4#6703711yescharacteristic
753C2×C4#6704211yescharacteristic
754C2×C4#6704211yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—222no—
762C8—222no—
763C8—441no—
764C8—441no—
765C8—441no—
766C8—441no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—81no—
776C22—81no—
777C22—221no—
778C22—221no—
779C22—221no—
780C22—221no—
781C22—221no—
782C22—221no—
783C22—221no—
784C22—221no—
785C22—221no—
786C22—221no—
787C22—221no—
788C22—221no—
789C22—442no—
790C22—442no—
791C22—881no—
792C22—881no—
793C22C2×C4⋊C4×D1111yescharacteristic
794C22#1062316511yescharacteristic
795C22#1062316511yescharacteristic
796C4—21no—
797C4—21no—
798C4—221no—
799C4—221no—
800C4—221no—
801C4—221no—
802C4#1062307611yescharacteristic
803C4#1062307611yescharacteristic
804C4#1062312011yescharacteristic
805C4#1062318411yescharacteristic
806C2—21no—
807C2—21no—
808C2—41no—
809C2—41no—
810C2—441no—
811C2—441no—
812C2—441no—
813C2—441no—
814C2#1307122711yescharacteristic
815C2#1307722411yescharacteristic
816C2#1307722611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1855C2
socleC22×C11C22×C4⋊C4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1855D11
hypocenterC11#21950
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
4. #13068823C2semidirect
5. #13068822C2semidirect
6. #13068822C2semidirect
7. #13068821C2semidirect
8. #13068820C2semidirect
9. #13068819C2semidirect
10. #13068819C2semidirect
11. #13068657C2semidirect
12. #13068655C2semidirect
13. #13068653C2semidirect
14. #13068651C2semidirect
15. C11×#1855C2semidirect
280. #1855D11semidirect
677. C11#21950semidirect

Maximal subgroups

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

subgroupindex
#130770602
#130770592
C2×#106223402
#130688232
#130688222
#130688212
#130688202
#130688192
#130686572
#130686552
#130686532
#130686512
C11×#18552
#2195011