Finite Group Databasebeta

← #14765190

Subgroups — #14765190

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#13077832C211yesmaximal, characteristic
2#13077060C211yesmaximal, characteristic, complemented
3#13069508C211yesmaximal, characteristic, complemented
4#13069503C211yesmaximal, characteristic, complemented
5#13069326C211yesmaximal, characteristic, complemented
6#13069319C211yesmaximal, characteristic, complemented
7#13069264C211yesmaximal, characteristic, complemented
8#13069264C211yesmaximal, characteristic, complemented
9#13068943C211yesmaximal, characteristic, complemented
10#13068943C211yesmaximal, characteristic, complemented
11#13068919C211yesmaximal, characteristic, complemented
12#13068820C211yesmaximal, characteristic, complemented
13#13068559C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#2930C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic, complemented
18C22×C11×M16C2211yescharacteristic
19C11×#525C2211yescharacteristic
20C2×#67003C2211yescharacteristic
21C2×#67003C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#436—21no—
24C11×#436—21no—
25C11×#435—21no—
26C11×#435—21no—
27C11×#424C2211yescharacteristic, complemented
28C11×#408C2211yescharacteristic, complemented
29C11×#407C2211yescharacteristic
30C11×#405C2211yescharacteristic, complemented
31C2×#66901C2211yescharacteristic, complemented
32C2×#66901C2211yescharacteristic, complemented
33C4×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66889C2211yescharacteristic
36C2×#66889C2211yescharacteristic
37C2×#66889C2211yescharacteristic
38C2×#66889C2211yescharacteristic
39#10622742—21no—
40#10622742—21no—
41#10622739—21no—
42#10622739—21no—
43C2×#66886C2211yescharacteristic, complemented
44C2×#66886C2211yescharacteristic, complemented
45#10622723C2211yescharacteristic
46#10622723C2211yescharacteristic
47#10622723C2211yescharacteristic
48#10622723C2211yescharacteristic
49C2×#66879C2211yescharacteristic, complemented
50C2×C8×Dic11C2211yescharacteristic, complemented
51#10622663C411yescharacteristic, complemented
52#10622660C411yescharacteristic, complemented
53#10622660C411yescharacteristic, complemented
54#10622659C411yescharacteristic, complemented
55#10622653C411yescharacteristic, complemented
56#10622650C411yescharacteristic, complemented
57#10622650C411yescharacteristic, complemented
58#10622649C411yescharacteristic, complemented
59#10622615C2211yescharacteristic
60#10622615C2211yescharacteristic
61#10622196C2211yescharacteristic, complemented
62#10622196C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64#10622188C2211yescharacteristic, complemented
65#10622170C2211yescharacteristic, complemented
66#10622170C2211yescharacteristic, complemented
67C2×C11×#41C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339—41no—
73C2×#4339—41no—
74C2×#4339—41no—
75C2×#4339—41no—
76C2×#4339C2×C411yescharacteristic
77C2×#4339C2×C411yescharacteristic
78C2×#4339C2311yescharacteristic
79C2×#4339C2311yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—21no—
82C22×Dic22C2×C411yescharacteristic
83C11×#131—41no—
84C11×#131—41no—
85C2×C11×M16—21no—
86C2×C11×M16—41no—
87C2×C11×M16—41no—
88C2×C11×M16D411yescharacteristic
89C2×C11×M16D411yescharacteristic
90C2×C11×M16D411yescharacteristic
91C2×C11×M16D411yescharacteristic
92C2×C11×M16C2311yescharacteristic
93C2×C11×M16C2311yescharacteristic
94C22×C8×C11—21no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×#123—21no—
98C11×C22⋊Q8C2×C411yescharacteristic
99C11×C22⋊Q8C2×C411yescharacteristic
100C11×#121C2×C411yescharacteristic
101C11×#121C2×C411yescharacteristic
102C11×#120—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C11×#117C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#67003—41no—
108#67003—41no—
109#67003—41no—
110#67003—41no—
111C2×#4326C2×C411yescharacteristic
112C2×#4326C2×C411yescharacteristic
113C2×#4325C2×C411yescharacteristic
114C2×#4325C2×C411yescharacteristic
115C2×#4324C2×C411yescharacteristic
116C2×#4324C2×C411yescharacteristic
117C2×#4323C2×C411yescharacteristic
118C2×#4323C2×C411yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2311yescharacteristic
121C2×#4318—21no—
122C2×#4318—41no—
123C2×#4318—41no—
124C2×#4318C2311yescharacteristic
125C2×#4318C2311yescharacteristic
126C22×C11⋊C8—21no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C11×C4⋊C8—21no—
130C11×C4⋊C8—21no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×#97—21no—
136C4×C8×C11—21no—
137#66901—41no—
138#66901—41no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)C2×C411yescharacteristic
141C22⋊(C11⋊C8)C2×C411yescharacteristic
142C22⋊(C11⋊C8)C2×C411yescharacteristic
143C22⋊(C11⋊C8)C2×C411yescharacteristic
144#66889—41no—
145#66889—41no—
146#66889—41no—
147#66889—41no—
148#66886—41no—
149#66886—41no—
150(C2×D11)⋊C8—21no—
151(C2×D11)⋊C8—21no—
152(C2×D11)⋊C8—21no—
153(C2×D11)⋊C8—21no—
154(C2×D11)⋊C8—21no—
155(C2×D11)⋊C8—21no—
156(C2×D11)⋊C8—21no—
157(C2×D11)⋊C8—21no—
158#66879—41no—
159C8×Dic11—41no—
160#66874C2×C411yescharacteristic
161#66874C2×C411yescharacteristic
162#66874C2×C411yescharacteristic
163#66874C2×C411yescharacteristic
164#66873C2×C411yescharacteristic
165#66873C2×C411yescharacteristic
166#66873C2×C411yescharacteristic
167#66873C2×C411yescharacteristic
168#22062—111nomaximal, Sylow
169C24×C11#4111yescharacteristic
170C23×D11—21no—
171C11×#41—21no—
172C11×#41—21no—
173C11×#41—21no—
174C11×#41—21no—
175C2×Q8×C11C22×C411yescharacteristic
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11C22×C411yescharacteristic
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11C22×C411yescharacteristic
186C22×C4×C11C22×C411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11#4111yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—21no—
192C2×C22⋊D11—21no—
193C2×C22⋊D11—21no—
194C2×C22⋊D11—21no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200#4339—21no—
201#4339—21no—
202#4339—21no—
203#4339—21no—
204#4339—21no—
205#4339—21no—
206#4339—21no—
207#4339—21no—
208#4339—41no—
209#4339—41no—
210#4339—41no—
211#4339—41no—
212#4339—42no—
213#4339—42no—
214#4339—42no—
215#4339—42no—
216C2×D44—21no—
217C2×D44—41no—
218C2×D44—41no—
219C2×D44C22×C411yescharacteristic
220C2×D44C22×C411yescharacteristic
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×Dic22—21no—
228C2×Dic22—41no—
229C2×Dic22—41no—
230C2×Dic22C22×C411yescharacteristic
231C2×Dic22C22×C411yescharacteristic
232C11×M16—21no—
233C11×M16—21no—
234C11×M16—21no—
235C11×M16—21no—
236C11×M16—41no—
237C11×M16—41no—
238C11×M16—41no—
239C11×M16—41no—
240C11×M16—42no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—42no—
248C2×C8×C11C2×D411yescharacteristic
249C2×C8×C11C2×D411yescharacteristic
250C2×C8×C11C2×D411yescharacteristic
251C2×C8×C11C2×D411yescharacteristic
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C22×C411yescharacteristic
255C11×C4⋊C4C22×C411yescharacteristic
256C11×C22⋊C4—21no—
257C11×C22⋊C4—21no—
258C11×C22⋊C4—21no—
259C11×C22⋊C4—21no—
260C11×C22⋊C4—21no—
261C42×C11—21no—
262C22⋊Dic11—42no—
263#4326—41no—
264#4326—41no—
265#4325—41no—
266#4325—41no—
267#4324—41no—
268#4324—41no—
269#4323—41no—
270#4323—41no—
271C4×Dic11—21no—
272C4×Dic11—21no—
273C4×Dic11—21no—
274C4×Dic11—21no—
275#4318—21no—
276#4318—21no—
277#4318—21no—
278#4318—21no—
279#4318—42no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—42no—
287C2×C11⋊C8C22×C411yescharacteristic
288C2×C11⋊C8C22×C411yescharacteristic
289C2×C11⋊C8C22×C411yescharacteristic
290C2×C11⋊C8C22×C411yescharacteristic
291#3002—111no—
292#2930D1111yescharacteristic, complemented
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#1753—111no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11C4×D411yescharacteristic
312C23×C11C4×D411yescharacteristic
313C23×C11C2×#4111yescharacteristic
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—42no—
317C22×D11—81no—
318C22×D11—81no—
319Q8×C11—21no—
320Q8×C11—21no—
321D4×C11—21no—
322D4×C11—21no—
323D4×C11—41no—
324D4×C11—41no—
325D4×C11—81no—
326D4×C11—81no—
327C2×C4×C11—21no—
328C2×C4×C11—21no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11C4×D411yescharacteristic
343C2×C4×C11C4×D411yescharacteristic
344C2×C4×C11C23×C411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11H(5,𝔽2)11yescharacteristic
347C2×C4×C11H(5,𝔽2)11yescharacteristic
348C2×C4×C11H(5,𝔽2)11yescharacteristic
349C2×C4×C11H(5,𝔽2)11yescharacteristic
350C22⋊D11—42no—
351C22⋊D11—42no—
352C22⋊D11—41no—
353C22⋊D11—41no—
354C22⋊D11—41no—
355C22⋊D11—41no—
356C2×Dic11—22no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—42no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365D44—21no—
366D44—21no—
367D44—21no—
368D44—21no—
369D44—42no—
370C4×D11—42no—
371C4×D11—42no—
372C4×D11—41no—
373C4×D11—41no—
374C4×D11—41no—
375C4×D11—41no—
376Dic22—21no—
377Dic22—21no—
378Dic22—21no—
379Dic22—21no—
380Dic22—42no—
381C8×C11—21no—
382C8×C11—21no—
383C8×C11—21no—
384C8×C11—21no—
385C8×C11—41no—
386C8×C11—41no—
387C11⋊C8—21no—
388C11⋊C8—21no—
389C11⋊C8—21no—
390C11⋊C8—21no—
391C11⋊C8—41no—
392C11⋊C8—41no—
393C22×#41—111no—
394C2×#135—111no—
395C2×#135—111no—
396C2×#131C2×D1111yescharacteristic, complemented
397C22×M16—111no—
398C22×M16C2×D1111yescharacteristic
399#525C2×D1111yescharacteristic
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—21no—
409#436—21no—
410#435—21no—
411#435—21no—
412C2×#108—111no—
413C2×#108—111no—
414#424C2×D1111yescharacteristic, complemented
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—221no—
428#408—221no—
429#408C2×D1111yescharacteristic, complemented
430#407—221no—
431#407—221no—
432#407C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434#405C2×D1111yescharacteristic, complemented
435C2×#97—111no—
436C2×C4×C8—111no—
437C4×C22⋊C4—111no—
438#341—111no—
439#341—111no—
440#339—111no—
441#339—111no—
442#336—111no—
443#336—111no—
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—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11C2×C4×D411yescharacteristic
458C22×C11#53811yescharacteristic
459C22×C11#53811yescharacteristic
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—41no—
470C4×C11—41no—
471C4×C11—41no—
472C4×C11#51811yescharacteristic
473C4×C11#51811yescharacteristic
474C4×C11#53411yescharacteristic
475C4×C11#53511yescharacteristic
476Dic11—42no—
477Dic11—41no—
478Dic11—41no—
479Dic11—81no—
480C2×#41—111no—
481C2×#41—111no—
482C2×#41—111no—
483C2×#41—111no—
484C2×#41—221no—
485C2×#41—221no—
486C2×#41—441no—
487C2×#41—441no—
488C2×#41—441no—
489C2×#41—441no—
490C2×#41C22×D1111yescharacteristic
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—41no—
509#131—41no—
510C2×M16—21no—
511C2×M16—41no—
512C2×M16—41no—
513C2×M16—111no—
514C2×M16—111no—
515C2×M16—221no—
516C2×M16—441no—
517C2×M16—441no—
518C2×M16C22⋊D1111yescharacteristic
519C2×M16C22⋊D1111yescharacteristic
520C2×M16C22⋊D1111yescharacteristic
521C2×M16C22⋊D1111yescharacteristic
522C2×M16C22×D1111yescharacteristic
523C2×M16C22×D1111yescharacteristic
524C22×C8—21no—
525C22×C8—111no—
526C22×C8—111no—
527C22×C8—221no—
528C22×C8C22×D1111yescharacteristic
529C22×C8C22×D1111yescharacteristic
530#123—21no—
531C22⋊Q8C4×D1111yescharacteristic
532C22⋊Q8C4×D1111yescharacteristic
533#121C4×D1111yescharacteristic
534#121C4×D1111yescharacteristic
535#120—21no—
536C4×D4—21no—
537C4×D4—21no—
538#117C22×D1111yescharacteristic
539C2×C22⋊C4—221no—
540C2×C42—111no—
541C2×C42—111no—
542#108—441no—
543#108—441no—
544C4⋊C8—21no—
545C4⋊C8—21no—
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—21no—
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—21no—
564C22⋊C8—111no—
565C22⋊C8—111no—
566C22⋊C8—111no—
567C22⋊C8—111no—
568C22⋊C8—221no—
569C22⋊C8—221no—
570C22⋊C8—221no—
571C22⋊C8—221no—
572C22⋊C8—221no—
573C22⋊C8—221no—
574C22⋊C8—221no—
575C22⋊C8—221no—
576#97—21no—
577#97—441no—
578C4×C8—21no—
579C4×C8—441no—
580#95—221no—
581C2×C11—21no—
582C2×C11—21no—
583C2×C11—41no—
584C2×C11—41no—
585C2×C11—81no—
586C2×C11#232111yescharacteristic
587C2×C11#295611yescharacteristic
588C2×C11#295711yescharacteristic
589D11—81no—
590D11—81no—
591C24—221no—
592C24#433911yescharacteristic
593#41—21no—
594#41—21no—
595#41—21no—
596#41—21no—
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—221no—
616C2×Q8—441no—
617C2×Q8—441no—
618C2×Q8C2×C4×D1111yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—111no—
623C2×D4—111no—
624C2×D4—221no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—441no—
630C2×D4—441no—
631C2×D4—442no—
632C2×D4—442no—
633C2×D4C2×C4×D1111yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—221no—
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×C4#433911yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654Q16—441no—
655Q16—441no—
656SD16—441no—
657SD16—441no—
658SD16—441no—
659SD16—441no—
660D8—441no—
661D8—441no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—41no—
667M16—41no—
668M16—41no—
669M16—41no—
670M16—42no—
671M16—221no—
672M16—221no—
673M16—221no—
674M16—221no—
675M16—442no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—42no—
683C2×C8—111no—
684C2×C8—111no—
685C2×C8—111no—
686C2×C8—111no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—442no—
694C2×C8C2×C22⋊D1111yescharacteristic
695C2×C8C2×C22⋊D1111yescharacteristic
696C2×C8C2×C22⋊D1111yescharacteristic
697C2×C8C2×C22⋊D1111yescharacteristic
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4C2×C4×D1111yescharacteristic
701C4⋊C4C2×C4×D1111yescharacteristic
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—442no—
708C42—21no—
709C42—221no—
710C42—221no—
711C42—221no—
712C42—221no—
713C11#2206211yescharacteristic, complemented, Sylow
714C23—21no—
715C23—21no—
716C23—21no—
717C23—41no—
718C23—41no—
719C23—221no—
720C23—221no—
721C23—442no—
722C23—881no—
723C23—881no—
724C23C4×C22⋊D1111yescharacteristic
725C23C4×C22⋊D1111yescharacteristic
726C23C2×#433911yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—221no—
730Q8—221no—
731Q8—221no—
732Q8—221no—
733Q8—442no—
734D4—21no—
735D4—21no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—221no—
741D4—221no—
742D4—221no—
743D4—221no—
744D4—442no—
745D4—442no—
746D4—442no—
747D4—441no—
748D4—441no—
749D4—441no—
750D4—441no—
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—41no—
765C2×C4—41no—
766C2×C4—222no—
767C2×C4—221no—
768C2×C4—221no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4—441no—
775C2×C4—441no—
776C2×C4—441no—
777C2×C4—441no—
778C2×C4—441no—
779C2×C4—441no—
780C2×C4—441no—
781C2×C4C4×C22⋊D1111yescharacteristic
782C2×C4C4×C22⋊D1111yescharacteristic
783C2×C4C22×C4×D1111yescharacteristic
784C2×C4#6703711yescharacteristic
785C2×C4#6703711yescharacteristic
786C2×C4#6704211yescharacteristic
787C2×C4#6704211yescharacteristic
788C2×C4C22×C22⋊D1111yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—221no—
796C8—221no—
797C8—221no—
798C8—221no—
799C8—441no—
800C8—441no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—81no—
813C22—81no—
814C22—441no—
815C22—441no—
816C22—441no—
817C22—441no—
818C22—441no—
819C22—441no—
820C22—884no—
821C22#1062309111yescharacteristic
822C22#1062309111yescharacteristic
823C22C2×C4×C22⋊D1111yescharacteristic
824C4—21no—
825C4—21no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—442no—
830C4—441no—
831C4—441no—
832C4—881no—
833C4#1062307611yescharacteristic
834C4#1062307611yescharacteristic
835C4#1062333511yescharacteristic
836C4#1062336111yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—881no—
843C2—881no—
844C2#1307127011yescharacteristic
845C2#1307752311yescharacteristic
846C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2930C2
socleC22×C11C2×C4×D4
prime radical#13077832C2
cosocleC22×C4×C11C24
hypercenter#2930D11
hypocenterC11#22062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #13077060C2semidirect
3. #13069508C2semidirect
4. #13069503C2semidirect
5. #13069326C2semidirect
6. #13069319C2semidirect
7. #13069264C2semidirect
8. #13069264C2semidirect
9. #13068943C2semidirect
10. #13068943C2semidirect
11. #13068919C2semidirect
12. #13068820C2semidirect
13. #13068559C2semidirect
14. #13068397C2semidirect
15. C11×#2930C2semidirect
17. C2×C11×#131C22semidirect
27. C11×#424C22semidirect
28. C11×#408C22semidirect
30. C11×#405C22semidirect
31. C2×#66901C22semidirect
32. C2×#66901C22semidirect
43. C2×#66886C22semidirect
44. C2×#66886C22semidirect
49. C2×#66879C22semidirect
50. C2×C8×Dic11C22semidirect
51. #10622663C4semidirect
52. #10622660C4semidirect
53. #10622660C4semidirect
54. #10622659C4semidirect
55. #10622653C4semidirect
56. #10622650C4semidirect
57. #10622650C4semidirect
58. #10622649C4semidirect
61. #10622196C22semidirect
62. #10622196C22semidirect
63. #10622188C22semidirect
64. #10622188C22semidirect
65. #10622170C22semidirect
66. #10622170C22semidirect
292. #2930D11semidirect
396. C2×#131C2×D11semidirect
414. #424C2×D11semidirect
429. #408C2×D11semidirect
434. #405C2×D11semidirect
713. C11#22062semidirect

Maximal subgroups

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

subgroupindex
#130778322
#130770602
#130695082
#130695032
#130693262
#130693192
#130692642
#130689432
#130689192
#130688202
#130685592
#130683972
C11×#29302
#2206211