Finite Group Databasebeta

← #14765198

Subgroups — #14765198

Order 2816.

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#13077838C211yesmaximal, characteristic
2#13077319C211yesmaximal, characteristic, complemented
3#13077060C211yesmaximal, characteristic, complemented
4#13069509C211yesmaximal, characteristic, complemented
5#13069504C211yesmaximal, characteristic, complemented
6#13069327C211yesmaximal, characteristic, complemented
7#13069320C211yesmaximal, characteristic, complemented
8#13069265C211yesmaximal, characteristic, complemented
9#13069265C211yesmaximal, characteristic, complemented
10#13068942C211yesmaximal, characteristic, complemented
11#13068942C211yesmaximal, characteristic, complemented
12#13068916C211yesmaximal, characteristic, complemented
13#13068823C211yesmaximal, characteristic, complemented
14#13068561C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18#10623322C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66957C2211yescharacteristic
21C2×#66957C2211yescharacteristic
22C2×#66954C2211yescharacteristic, complemented
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic, complemented
25C2×C4×C8×C11C2211yescharacteristic, complemented
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622820C2211yescharacteristic
28#10622742—21no—
29#10622742—21no—
30#10622741—21no—
31#10622741—21no—
32#10622740—21no—
33#10622740—21no—
34#10622739—21no—
35#10622739—21no—
36#10622726C2211yescharacteristic
37#10622726C2211yescharacteristic
38#10622723C2211yescharacteristic
39#10622723C2211yescharacteristic
40#10622723C2211yescharacteristic
41#10622723C2211yescharacteristic
42#10622723C2211yescharacteristic, complemented
43C2×#66883C2211yescharacteristic, complemented
44C2×#66883C2211yescharacteristic, complemented
45#10622715C2211yescharacteristic, complemented
46#10622714C2211yescharacteristic, complemented
47C2×#66869C2211yescharacteristic
48C2×#66869C2211yescharacteristic
49C2×#66869C2211yescharacteristic
50C2×#66869C2211yescharacteristic
51C2×#66869C2211yescharacteristic, complemented
52C2×#66869C2211yescharacteristic, complemented
53#10622352C411yescharacteristic, complemented
54#10622351C411yescharacteristic, complemented
55#10622347C411yescharacteristic, complemented
56#10622347C411yescharacteristic, complemented
57#10622346C411yescharacteristic, complemented
58#10622346C411yescharacteristic, complemented
59#10622345C411yescharacteristic, complemented
60#10622344C411yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62C11×#336C2211yescharacteristic, complemented
63#10622190C2211yescharacteristic, complemented
64#10622190C2211yescharacteristic, complemented
65#10622161C2211yescharacteristic, complemented
66#10622161C2211yescharacteristic, complemented
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—41no—
72C2×#4339—41no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339C2×C411yescharacteristic
76C2×#4339C2×C411yescharacteristic
77C2×#4339C2311yescharacteristic
78C2×#4339C2311yescharacteristic
79C2×#4339C2311yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—21no—
82C22×Dic22C2×C411yescharacteristic
83C2×C11×M16—41no—
84C2×C11×M16—41no—
85C2×C11×M16D411yescharacteristic
86C2×C11×M16D411yescharacteristic
87C2×C11×M16D411yescharacteristic
88C2×C11×M16D411yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96#67006—21no—
97#66983C2×C411yescharacteristic
98#66983C2×C411yescharacteristic
99#66982—21no—
100C4×C22⋊D11—21no—
101C4×C22⋊D11—21no—
102#66979C2311yescharacteristic
103#66977C2×C411yescharacteristic
104#66977C2×C411yescharacteristic
105C2×#4318—21no—
106C2×#4318—41no—
107C2×#4318—41no—
108C2×#4318C2311yescharacteristic
109C2×#4318C2311yescharacteristic
110C2×#4318C2311yescharacteristic
111C2×#4318C2311yescharacteristic
112C22×C11⋊C8—21no—
113C2×Dic44C2×C411yescharacteristic
114C2×Dic44C2×C411yescharacteristic
115#66957—41no—
116#66957—41no—
117#66957—41no—
118#66957—41no—
119C2×D88C2×C411yescharacteristic
120C2×D88C2×C411yescharacteristic
121C2×#4314C2×C411yescharacteristic
122C2×#4314C2×C411yescharacteristic
123C2×#4314C2×C411yescharacteristic
124C2×#4314C2×C411yescharacteristic
125#66954—41no—
126#66954—41no—
127C2×#4313—21no—
128C2×C8×D11—21no—
129C11×C22⋊C8C2×C411yescharacteristic
130C11×C22⋊C8C2×C411yescharacteristic
131C11×C22⋊C8C2×C411yescharacteristic
132C11×C22⋊C8C2×C411yescharacteristic
133C11×#97—41no—
134C4×C8×C11—41no—
135C11×#95—21no—
136C22⋊(C11⋊C8)—21no—
137C22⋊(C11⋊C8)—21no—
138#66885C2×C411yescharacteristic
139#66885C2×C411yescharacteristic
140#66885C2×C411yescharacteristic
141#66885C2×C411yescharacteristic
142(C2×D11)⋊C8—21no—
143(C2×D11)⋊C8—21no—
144(C2×D11)⋊C8—21no—
145(C2×D11)⋊C8—21no—
146(C2×D11)⋊C8—21no—
147(C2×D11)⋊C8—21no—
148(C2×D11)⋊C8—21no—
149(C2×D11)⋊C8—21no—
150(C2×D11)⋊C8—21no—
151(C2×D11)⋊C8—21no—
152#66883—41no—
153#66883—41no—
154#66880C2×C411yescharacteristic
155#66880C2×C411yescharacteristic
156#66880C2×C411yescharacteristic
157#66880C2×C411yescharacteristic
158#66879—21no—
159Dic11⋊C8—21no—
160Dic11⋊C8—21no—
161C8×Dic11—21no—
162#66869—41no—
163#66869—41no—
164#66869—41no—
165#66869—41no—
166#66869—41no—
167#66869—41no—
168#22062—111nomaximal, Sylow
169C24×C11#4111yescharacteristic
170C23×D11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11#4111yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—21no—
184C2×C22⋊D11—21no—
185C2×C22⋊D11—21no—
186C2×C22⋊D11—21no—
187C2×C22⋊D11—21no—
188C2×C22⋊D11—21no—
189C2×C22⋊D11—21no—
190C2×C22⋊D11—42no—
191C2×C22⋊D11—42no—
192C22×Dic11—21no—
193#4339—21no—
194#4339—21no—
195#4339—21no—
196#4339—21no—
197#4339—21no—
198#4339—21no—
199#4339—21no—
200#4339—21no—
201#4339—21no—
202#4339—21no—
203#4339—21no—
204#4339—21no—
205#4339—41no—
206#4339—41no—
207#4339—41no—
208#4339—41no—
209#4339—42no—
210#4339—42no—
211#4339—42no—
212#4339—42no—
213C2×D44—21no—
214C2×D44—41no—
215C2×D44—41no—
216C2×D44C22×C411yescharacteristic
217C2×D44C22×C411yescharacteristic
218C2×D44C22×C411yescharacteristic
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×Dic22—21no—
227C2×Dic22—41no—
228C2×Dic22—41no—
229C2×Dic22C22×C411yescharacteristic
230C2×Dic22C22×C411yescharacteristic
231C2×Dic22C22×C411yescharacteristic
232C11×M16—41no—
233C11×M16—41no—
234C11×M16—41no—
235C11×M16—41no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11C22×C411yescharacteristic
245C2×C8×C11C22×C411yescharacteristic
246C2×C8×C11C22×C411yescharacteristic
247C2×C8×C11C22×C411yescharacteristic
248C2×C8×C11C2×D411yescharacteristic
249C2×C8×C11C2×D411yescharacteristic
250C2×C8×C11C2×D411yescharacteristic
251C2×C8×C11C2×D411yescharacteristic
252C11×C22⋊C4—42no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11—21no—
256C42×C11—21no—
257C22⋊Dic11—21no—
258C22⋊Dic11—21no—
259C22⋊Dic11—21no—
260(C2×D11)⋊C4—21no—
261(C2×D11)⋊C4—21no—
262C4⋊Dic11C22×C411yescharacteristic
263C4⋊Dic11C22×C411yescharacteristic
264Dic11⋊C4—21no—
265Dic11⋊C4—21no—
266C4×Dic11—21no—
267#4318—21no—
268#4318—21no—
269#4318—21no—
270#4318—21no—
271#4318—21no—
272#4318—21no—
273#4318—21no—
274#4318—21no—
275#4318—42no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—42no—
281Dic44—41no—
282Dic44—41no—
283D88—41no—
284D88—41no—
285#4314—41no—
286#4314—41no—
287#4314—41no—
288#4314—41no—
289#4313—42no—
290C8×D11—42no—
291#3002—111no—
292#2930—111no—
293#2879—111no—
294#1975—111no—
295#1974—111no—
296#1938—111no—
297#1937—111no—
298#1929—111no—
299#1929—111no—
300#1876—111no—
301#1876—111no—
302#1871—111no—
303#1855—111no—
304#1789—111no—
305#1753D1111yescharacteristic, complemented
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C4×D411yescharacteristic
311C23×C11C4×D411yescharacteristic
312C23×C11C2×#4111yescharacteristic
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—42no—
317C22×D11—81no—
318C22×D11—81no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—22no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11C4×D411yescharacteristic
336C2×C4×C11C4×D411yescharacteristic
337C2×C4×C11C23×C411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11H(5,𝔽2)11yescharacteristic
340C2×C4×C11H(5,𝔽2)11yescharacteristic
341C2×C4×C11H(5,𝔽2)11yescharacteristic
342C2×C4×C11H(5,𝔽2)11yescharacteristic
343C22⋊D11—42no—
344C22⋊D11—42no—
345C22⋊D11—41no—
346C22⋊D11—41no—
347C22⋊D11—41no—
348C22⋊D11—41no—
349C22⋊D11—41no—
350C22⋊D11—41no—
351C22⋊D11—81no—
352C22⋊D11—81no—
353C2×Dic11—21no—
354C2×Dic11—21no—
355C2×Dic11—21no—
356C2×Dic11—21no—
357C2×Dic11—21no—
358C2×Dic11—42no—
359D44—21no—
360D44—21no—
361D44—21no—
362D44—21no—
363D44—21no—
364D44—21no—
365D44—42no—
366C4×D11—42no—
367C4×D11—42no—
368C4×D11—41no—
369C4×D11—41no—
370C4×D11—41no—
371C4×D11—41no—
372C4×D11—41no—
373C4×D11—41no—
374Dic22—21no—
375Dic22—21no—
376Dic22—21no—
377Dic22—21no—
378Dic22—21no—
379Dic22—21no—
380Dic22—42no—
381C8×C11—21no—
382C8×C11—21no—
383C8×C11—21no—
384C8×C11—21no—
385C8×C11—21no—
386C8×C11—21no—
387C8×C11—21no—
388C8×C11—21no—
389C11⋊C8—41no—
390C11⋊C8—41no—
391C11⋊C8—41no—
392C11⋊C8—41no—
393C22×#41—111no—
394C2×#135—111no—
395C2×#135—111no—
396C2×#131—111no—
397C22×M16—111no—
398C22×M16C2×D1111yescharacteristic
399#525—111no—
400#452—111no—
401#452—111no—
402#451—111no—
403#450—111no—
404#449—111no—
405#449—111no—
406#448—111no—
407#447—111no—
408#436—221no—
409#436—221no—
410#435—221no—
411#435—221no—
412C2×#108—111no—
413C2×#108—111no—
414#424—111no—
415C2×#104—111no—
416C2×#104—111no—
417C2×#104—111no—
418C2×#104—111no—
419C2×#104—111no—
420C2×#104—111no—
421#416—111no—
422#416—111no—
423#408—111no—
424#408—111no—
425#408—111no—
426#408—111no—
427#408—111no—
428#408—221no—
429#408—221no—
430#407—111no—
431#407—221no—
432#407—221no—
433C2×C22⋊C8C2×D1111yescharacteristic
434#405—111no—
435C2×#97C2×D1111yescharacteristic, complemented
436C2×C4×C8C2×D1111yescharacteristic, complemented
437C4×C22⋊C4C2×D1111yescharacteristic
438#341—111no—
439#341—111no—
440#339—111no—
441#339—111no—
442#336C2×D1111yescharacteristic, complemented
443#336C2×D1111yescharacteristic, complemented
444C22×C11—21no—
445C22×C11—21no—
446C22×C11—21no—
447C22×C11—21no—
448C22×C11—21no—
449C22×C11—21no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11C2×C4×D411yescharacteristic
455C22×C11#53811yescharacteristic
456C22×C11#53811yescharacteristic
457C2×D11—41no—
458C2×D11—41no—
459C2×D11—41no—
460C2×D11—41no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—41no—
466C2×D11—84no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—42no—
470C4×C11—81no—
471C4×C11#51811yescharacteristic
472C4×C11#51811yescharacteristic
473C4×C11#53411yescharacteristic
474C4×C11#53511yescharacteristic
475Dic11—41no—
476Dic11—41no—
477Dic11—41no—
478Dic11—41no—
479Dic11—41no—
480C2×#41—111no—
481C2×#41—111no—
482C2×#41—111no—
483C2×#41—111no—
484C2×#41—111no—
485C2×#41—221no—
486C2×#41—221no—
487C2×#41—441no—
488C2×#41—441no—
489C2×#41—441no—
490C2×#41—441no—
491C22×Q8—111no—
492C22×D4—111no—
493C22×D4—221no—
494C23×C4—221no—
495C23×C4C22×D1111yescharacteristic
496#135—441no—
497#135—441no—
498#135—441no—
499#135—441no—
500C2×Q16—111no—
501C2×Q16—111no—
502C2×SD16—111no—
503C2×SD16—111no—
504C2×SD16—111no—
505C2×SD16—111no—
506C2×D8—111no—
507C2×D8—111no—
508#131—441no—
509#131—441no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16—111no—
513C2×M16—111no—
514C2×M16—111no—
515C2×M16—111no—
516C2×M16—221no—
517C2×M16—221no—
518C2×M16—441no—
519C2×M16—441no—
520C2×M16D4411yescharacteristic
521C2×M16D4411yescharacteristic
522C2×M16D4411yescharacteristic
523C2×M16D4411yescharacteristic
524C22×C8—221no—
525C22×C8—221no—
526C22×C8C22×D1111yescharacteristic
527C22×C8C22×D1111yescharacteristic
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#123—221no—
531C22⋊Q8—111no—
532C22⋊Q8—111no—
533#121—111no—
534#121—111no—
535#120—221no—
536C4×D4—221no—
537C4×D4—221no—
538#117—111no—
539C2×C22⋊C4—21no—
540C2×C42C22×D1111yescharacteristic
541C2×C42C22×D1111yescharacteristic
542#108—441no—
543#108—441no—
544C4⋊C8—221no—
545C4⋊C8—221no—
546#104—441no—
547#104—441no—
548#104—441no—
549#104—441no—
550#104—441no—
551#104—441no—
552#103—111no—
553#103—111no—
554#103—111no—
555#103—111no—
556#102—111no—
557#102—111no—
558#102—111no—
559#102—111no—
560C22⋊C8—221no—
561C22⋊C8—221no—
562C22⋊C8—221no—
563C22⋊C8—221no—
564C22⋊C8—221no—
565C22⋊C8—221no—
566C22⋊C8—221no—
567C22⋊C8—221no—
568C22⋊C8—221no—
569C22⋊C8—221no—
570C22⋊C8—221no—
571C22⋊C8—221no—
572C22⋊C8C4×D1111yescharacteristic
573C22⋊C8C4×D1111yescharacteristic
574C22⋊C8C4×D1111yescharacteristic
575C22⋊C8C4×D1111yescharacteristic
576#97—41no—
577#97—221no—
578C4×C8—41no—
579C4×C8—221no—
580#95—21no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—41no—
584C2×C11—41no—
585C2×C11#232111yescharacteristic
586C2×C11#295611yescharacteristic
587C2×C11#295711yescharacteristic
588D11—81no—
589D11—81no—
590D11—81no—
591C24—221no—
592C24#433911yescharacteristic
593#41—221no—
594#41—221no—
595#41—221no—
596#41—221no—
597#41—221no—
598#41—221no—
599#41—221no—
600#41—221no—
601#41—221no—
602#41—221no—
603#41—221no—
604#41—221no—
605#41—441no—
606#41—441no—
607#41—441no—
608#41—441no—
609#41—442no—
610#41—442no—
611#41—442no—
612#41—442no—
613C2×Q8—111no—
614C2×Q8—111no—
615C2×Q8—111no—
616C2×Q8—221no—
617C2×Q8—441no—
618C2×Q8—441no—
619C2×D4—111no—
620C2×D4—111no—
621C2×D4—111no—
622C2×D4—221no—
623C2×D4—221no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—441no—
631C2×D4—441no—
632C2×D4—442no—
633C2×D4—442no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—221no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4C2×C4×D1111yescharacteristic
649C22×C4C2×C4×D1111yescharacteristic
650C22×C4C2×D4411yescharacteristic
651C22×C4C2×D4411yescharacteristic
652C22×C4#433911yescharacteristic
653C22×C4C23×D1111yescharacteristic
654Q16—441no—
655Q16—441no—
656SD16—441no—
657SD16—441no—
658SD16—441no—
659SD16—441no—
660D8—441no—
661D8—441no—
662M16—41no—
663M16—41no—
664M16—41no—
665M16—41no—
666M16—221no—
667M16—221no—
668M16—221no—
669M16—221no—
670M16—221no—
671M16—221no—
672M16—221no—
673M16—221no—
674M16—442no—
675M16—442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—442no—
689C2×C8—442no—
690C2×C8C2×C4×D1111yescharacteristic
691C2×C8C2×C4×D1111yescharacteristic
692C2×C8C2×C4×D1111yescharacteristic
693C2×C8C2×C4×D1111yescharacteristic
694C2×C8C2×D4411yescharacteristic
695C2×C8C2×D4411yescharacteristic
696C2×C8C2×D4411yescharacteristic
697C2×C8C2×D4411yescharacteristic
698C4⋊C4—111no—
699C4⋊C4—111no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C22⋊C4—42no—
703C22⋊C4—221no—
704C22⋊C4—221no—
705C22⋊C4—221no—
706C22⋊C4—221no—
707C22⋊C4—221no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—221no—
713C11#2206211yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—41no—
717C23—41no—
718C23—221no—
719C23—221no—
720C23—221no—
721C23—442no—
722C23—881no—
723C23—881no—
724C23C4×D4411yescharacteristic
725C23C4×D4411yescharacteristic
726C23C2×#433911yescharacteristic
727Q8—221no—
728Q8—221no—
729Q8—221no—
730Q8—221no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—221no—
735D4—221no—
736D4—221no—
737D4—221no—
738D4—221no—
739D4—221no—
740D4—442no—
741D4—442no—
742D4—442no—
743D4—441no—
744D4—441no—
745D4—441no—
746D4—441no—
747D4—441no—
748D4—441no—
749D4—881no—
750D4—881no—
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—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—221no—
770C2×C4—221no—
771C2×C4—221no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4C4×D4411yescharacteristic
782C2×C4C4×D4411yescharacteristic
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4C22×D4411yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6703711yescharacteristic
787C2×C4#6704211yescharacteristic
788C2×C4#6704211yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—441no—
798C8—441no—
799C8—441no—
800C8—441no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—81no—
810C22—81no—
811C22—441no—
812C22—441no—
813C22—441no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22C2×C4×D4411yescharacteristic
822C22#1062309111yescharacteristic
823C22#1062309111yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—81no—
828C4—441no—
829C4—441no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4#1062302411yescharacteristic
834C4#1062305611yescharacteristic
835C4#1062307611yescharacteristic
836C4#1062307611yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—881no—
842C2—881no—
843C2—881no—
844C2#1307127611yescharacteristic
845C2#1307752711yescharacteristic
846C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC22×C11C2×C4×D4
prime radical#13077838C2
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. #13077319C2semidirect
3. #13077060C2semidirect
4. #13069509C2semidirect
5. #13069504C2semidirect
6. #13069327C2semidirect
7. #13069320C2semidirect
8. #13069265C2semidirect
9. #13069265C2semidirect
10. #13068942C2semidirect
11. #13068942C2semidirect
12. #13068916C2semidirect
13. #13068823C2semidirect
14. #13068561C2semidirect
15. C11×#1753C2semidirect
22. C2×#66954C22semidirect
24. C2×C11×#97C22semidirect
25. C2×C4×C8×C11C22semidirect
42. #10622723C22semidirect
43. C2×#66883C22semidirect
44. C2×#66883C22semidirect
45. #10622715C22semidirect
46. #10622714C22semidirect
51. C2×#66869C22semidirect
52. C2×#66869C22semidirect
53. #10622352C4semidirect
54. #10622351C4semidirect
55. #10622347C4semidirect
56. #10622347C4semidirect
57. #10622346C4semidirect
58. #10622346C4semidirect
59. #10622345C4semidirect
60. #10622344C4semidirect
61. C11×#336C22semidirect
62. C11×#336C22semidirect
63. #10622190C22semidirect
64. #10622190C22semidirect
65. #10622161C22semidirect
66. #10622161C22semidirect
305. #1753D11semidirect
435. C2×#97C2×D11semidirect
436. C2×C4×C8C2×D11semidirect
442. #336C2×D11semidirect
443. #336C2×D11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130778382
#130773192
#130770602
#130695092
#130695042
#130693272
#130693202
#130692652
#130689422
#130689162
#130688232
#130685612
C11×#17532
#2206211