Finite Group Databasebeta

← #14786693

Subgroups — #14786693

Order 2816.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078545C211yesmaximal, characteristic, complemented
2#13077135C211yesmaximal, characteristic, complemented
3#13073079C211yesmaximal, characteristic, complemented
4#13069842C211yesmaximal, characteristic, complemented
5#13069837C211yesmaximal, characteristic, complemented
6#13069823C211yesmaximal, characteristic, complemented
7#13069823C211yesmaximal, characteristic, complemented
8#13069080C211yesmaximal, characteristic, complemented
9#13068919C211yesmaximal, characteristic, complemented
10#13068849C211yesmaximal, characteristic, complemented
11#13068842C211yesmaximal, characteristic, complemented
12#13068570C211yesmaximal, characteristic, complemented
13#13068570C211yesmaximal, characteristic, complemented
14#13068560C211yesmaximal, characteristic, complemented
15C11×#3488C211yesmaximal, characteristic
16C2×C11×H(5,𝔽2)C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18C11×#550—21no—
19C11×#548—21no—
20C11×#546—21no—
21C11×#546—22no—
22D42×C11—22no—
23D42×C11—21no—
24C11×#537—21no—
25C11×#537C2211yescharacteristic
26C11×#535—21no—
27C11×#535C2211yescharacteristic
28C11×#525—21no—
29C11×#525C2211yescharacteristic
30C2×C11×#121—21no—
31C2×C11×#121C2211yescharacteristic
32C11×#520C2211yescharacteristic
33C2×#66979C2211yescharacteristic, complemented
34C22×#4318C2211yescharacteristic, complemented
35C2×#66901C2211yescharacteristic
36C2×#66901C2211yescharacteristic
37C2×#66901C2211yescharacteristic, complemented
38C2×#66901C2211yescharacteristic, complemented
39C2×#66901C2211yescharacteristic, complemented
40C2×#66901C2211yescharacteristic, complemented
41#10622846—21no—
42#10622846—21no—
43#10622845C2211yescharacteristic
44#10622845C2211yescharacteristic
45#10622845C2211yescharacteristic, complemented
46#10622845C2211yescharacteristic, complemented
47#10622845C2211yescharacteristic, complemented
48#10622845C2211yescharacteristic, complemented
49#10622838—21no—
50#10622835—22no—
51#10622834C2211yescharacteristic, complemented
52#10622834C2211yescharacteristic, complemented
53C2×#66897C2211yescharacteristic, complemented
54C2×#66897C2211yescharacteristic, complemented
55#10622828—21no—
56C4×C22⋊Dic11C2211yescharacteristic, complemented
57#10622820C2211yescharacteristic, complemented
58#10622658—21no—
59#10622658—21no—
60#10622648—21no—
61#10622648—21no—
62#10622608C2211yescharacteristic, complemented
63#10622608C2211yescharacteristic, complemented
64#10622590C2211yescharacteristic, complemented
65#10622589C2211yescharacteristic, complemented
66#10622557—22no—
67#10622170C2211yescharacteristic, complemented
68#10622170C2211yescharacteristic, complemented
69#10622168C2211yescharacteristic, complemented
70#10622168C2211yescharacteristic, complemented
71C11×H(5,𝔽2)—22no—
72C11×H(5,𝔽2)—22no—
73C11×H(5,𝔽2)—41no—
74C11×H(5,𝔽2)—41no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41—21no—
78C2×C11×#41—21no—
79C2×C11×#41—22no—
80C2×C11×#41—22no—
81C2×C11×#41—41no—
82C2×C11×#41—41no—
83C2×C11×#41D411yescharacteristic
84C2×C11×#41D411yescharacteristic
85C2×C11×#41C2311yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C22×Q8×C11D411yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—22no—
91C22×D4×C11—22no—
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11D411yescharacteristic
95C22×D4×C11D412yes—
96C22×D4×C11C2311yescharacteristic
97C23×C4×C11—21no—
98C23×C4×C11C2311yescharacteristic
99C11×#127—22no—
100C11×#127—21no—
101C11×#124—22no—
102C11×#124—21no—
103C11×#123—22no—
104C11×#123—21no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8D411yescharacteristic
109C11×C22⋊Q8D411yescharacteristic
110C11×#121—22no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121—22no—
114C11×#121—22no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121—21no—
118C11×#121—21no—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—22no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121D411yescharacteristic
125C11×#121D411yescharacteristic
126C11×#120—22no—
127C11×#120—22no—
128C11×#120—22no—
129C11×#120—21no—
130C11×#120—22no—
131C4×Q8×C11—21no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—21no—
135C4×D4×C11—22no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C11×#117—21no—
139C11×#117C2311yescharacteristic
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4—22no—
143C2×C11×C22⋊C4D412yes—
144C2×C22⋊Dic11—21no—
145C2×C22⋊Dic11—22no—
146C2×C22⋊Dic11—21no—
147C2×C22⋊Dic11—22no—
148#66979—21no—
149#66979—21no—
150#66979—21no—
151#66979—21no—
152C2×C4⋊Dic11C2311yescharacteristic
153C2×C4⋊Dic11C2311yescharacteristic
154C2×Dic11⋊C4—22no—
155C2×C4×Dic11—21no—
156C2×C4×Dic11C2311yescharacteristic
157C2×C4×Dic11C2311yescharacteristic
158C2×#4318—21no—
159C2×#4318—41no—
160C2×#4318—41no—
161C2×#4318C2311yescharacteristic
162C2×#4318C2311yescharacteristic
163C2×#4318C2311yescharacteristic
164C2×#4318C2311yescharacteristic
165C22×C11⋊C8—21no—
166#66901—22no—
167#66901—22no—
168#66901—41no—
169#66901—41no—
170#66901—41no—
171#66901—41no—
172#66899—21no—
173#66899—21no—
174#66899—21no—
175#66899—21no—
176#66899—21no—
177#66899—21no—
178#66897—41no—
179#66897—41no—
180#66896—21no—
181#66896—21no—
182#66896—21no—
183#66896—21no—
184#66896—21no—
185#66896—21no—
186C11⋊#95—21no—
187C11⋊#95—22no—
188C22⋊(C11⋊C8)—21no—
189C22⋊(C11⋊C8)—21no—
190#66872—21no—
191#66872—21no—
192#66871—21no—
193#66871—21no—
194#24031—111nomaximal, Sylow
195C24×C11—22no—
196C24×C11—21no—
197C24×C11C2×D412yes—
198C24×C11C2×D411yescharacteristic
199C11×#41—21no—
200C11×#41—21no—
201C11×#41—22no—
202C11×#41—22no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—21no—
207C11×#41—21no—
208C11×#41—21no—
209C11×#41—21no—
210C11×#41—21no—
211C11×#41—42no—
212C11×#41—42no—
213C11×#41—41no—
214C11×#41—41no—
215C11×#41—42no—
216C11×#41—42no—
217C11×#41—42no—
218C11×#41—42no—
219C11×#41—42no—
220C11×#41—42no—
221C11×#41#4112yes—
222C11×#41#4112yes—
223C2×Q8×C11—21no—
224C2×Q8×C11—22no—
225C2×Q8×C11—41no—
226C2×Q8×C11C2×D411yescharacteristic
227C2×Q8×C11C2×D411yescharacteristic
228C2×Q8×C11C2×D411yescharacteristic
229C2×D4×C11—21no—
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—21no—
235C2×D4×C11—21no—
236C2×D4×C11—21no—
237C2×D4×C11—21no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—21no—
243C2×D4×C11—22no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—21no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—41no—
252C2×D4×C11—42no—
253C2×D4×C11—42no—
254C2×D4×C11—42no—
255C2×D4×C11—42no—
256C2×D4×C11—44no—
257C2×D4×C11—44no—
258C2×D4×C11—42no—
259C2×D4×C11—42no—
260C2×D4×C11—82no—
261C2×D4×C11—84no—
262C2×D4×C11C2×D411yescharacteristic
263C2×D4×C11C2×D411yescharacteristic
264C2×D4×C11C2×D411yescharacteristic
265C22×C4×C11—21no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—22no—
271C22×C4×C11—21no—
272C22×C4×C11—22no—
273C22×C4×C11—21no—
274C22×C4×C11—21no—
275C22×C4×C11—21no—
276C22×C4×C11—21no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11C2×D411yescharacteristic
280C22×C4×C11C2×D411yescharacteristic
281C22×C4×C11C2×D411yescharacteristic
282C22×C4×C11C2×D411yescharacteristic
283C22×C4×C11C2×D411yescharacteristic
284C22×C4×C11C2×D412yes—
285C22×C4×C11C2411yescharacteristic
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4—21no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D411yescharacteristic
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—22no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—21no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—21no—
310C42×C11—22no—
311C42×C11—21no—
312C22⋊Dic11—42no—
313C22⋊Dic11—44no—
314C22⋊Dic11—41no—
315C22⋊Dic11—41no—
316C22⋊Dic11—82no—
317C4⋊Dic11—21no—
318C4⋊Dic11—21no—
319C4⋊Dic11—21no—
320C4⋊Dic11—21no—
321Dic11⋊C4—82no—
322C4×Dic11—21no—
323C4×Dic11—21no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326C4×Dic11—41no—
327C4×Dic11—41no—
328#4318—21no—
329#4318—21no—
330#4318—21no—
331#4318—21no—
332#4318—21no—
333#4318—21no—
334#4318—21no—
335#4318—21no—
336#4318—42no—
337C2×C11⋊C8—21no—
338C2×C11⋊C8—21no—
339C2×C11⋊C8—21no—
340C2×C11⋊C8—21no—
341C2×C11⋊C8—42no—
342#3488D1111yescharacteristic
343#3093—111no—
344#2896—111no—
345#2500—111no—
346#2040—111no—
347#2039—111no—
348#2037—111no—
349#2037—111no—
350#1900—111no—
351#1871—111no—
352#1860—111no—
353#1859—111no—
354#1792—111no—
355#1792—111no—
356#1789—111no—
357C23×C11—21no—
358C23×C11—21no—
359C23×C11—21no—
360C23×C11—22no—
361C23×C11—21no—
362C23×C11—21no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11—44no—
370C23×C11—42no—
371C23×C11—42no—
372C23×C11—81no—
373C23×C11—82no—
374C23×C11—82no—
375C23×C11#12011yescharacteristic
376C23×C11#12011yescharacteristic
377C23×C11C22×D411yescharacteristic
378Q8×C11—21no—
379Q8×C11—21no—
380Q8×C11—21no—
381Q8×C11—21no—
382Q8×C11—21no—
383Q8×C11—42no—
384Q8×C11#12312yes—
385D4×C11—22no—
386D4×C11—22no—
387D4×C11—21no—
388D4×C11—21no—
389D4×C11—21no—
390D4×C11—21no—
391D4×C11—21no—
392D4×C11—42no—
393D4×C11—42no—
394D4×C11—44no—
395D4×C11—42no—
396D4×C11—44no—
397D4×C11—44no—
398D4×C11—42no—
399D4×C11—41no—
400D4×C11—41no—
401D4×C11—41no—
402D4×C11—41no—
403D4×C11—41no—
404D4×C11—41no—
405D4×C11—41no—
406D4×C11—41no—
407D4×C11—81no—
408D4×C11—82no—
409D4×C11—82no—
410D4×C11—82no—
411D4×C11—82no—
412D4×C11#12312yes—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—21no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—21no—
427C2×C4×C11—22no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—42no—
432C2×C4×C11—42no—
433C2×C4×C11—42no—
434C2×C4×C11—44no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—42no—
440C2×C4×C11—82no—
441C2×C4×C11#12011yescharacteristic
442C2×C4×C11#12011yescharacteristic
443C2×C4×C11C22×D411yescharacteristic
444C2×C4×C11C22×D411yescharacteristic
445C2×C4×C11C2×#4111yescharacteristic
446C2×C4×C11C2×#4111yescharacteristic
447C2×C4×C11H(5,𝔽2)11yescharacteristic
448C2×C4×C11H(5,𝔽2)11yescharacteristic
449C2×Dic11—22no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—42no—
453C2×Dic11—41no—
454C2×Dic11—42no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C11⋊C8—41no—
460C11⋊C8—41no—
461C11⋊C8—41no—
462C11⋊C8—41no—
463C2×H(5,𝔽2)C2×D1111yescharacteristic
464C22×#41C2×D1111yescharacteristic
465C22×M16—111no—
466#550—21no—
467#548—21no—
468#546—21no—
469#546—22no—
470D42—22no—
471D42—21no—
472#537—21no—
473#537C2×D1111yescharacteristic
474#535—21no—
475#535C2×D1111yescharacteristic
476#525—21no—
477#525C2×D1111yescharacteristic
478C2×#121—21no—
479C2×#121C2×D1111yescharacteristic
480#520C2×D1111yescharacteristic
481C2×#117—111no—
482#485—221no—
483#485—221no—
484#482—221no—
485#482—221no—
486#428—111no—
487#428—111no—
488C2×#104—111no—
489C2×#104—111no—
490C2×#104—111no—
491C2×#104—111no—
492C2×#104—111no—
493C2×#104—111no—
494#419—221no—
495#418—221no—
496#417—111no—
497#417—111no—
498#417—111no—
499#417—111no—
500#417—111no—
501#417—111no—
502#416—221no—
503#416—221no—
504C2×#100—111no—
505C2×#100—111no—
506#407—111no—
507#394—222no—
508#390—111no—
509#390—111no—
510#388—222no—
511#384—111no—
512#382—111no—
513C4×C22⋊C4—111no—
514#343—111no—
515#343—111no—
516#339—111no—
517#339—111no—
518C22×C11—21no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—22no—
523C22×C11—21no—
524C22×C11—21no—
525C22×C11—21no—
526C22×C11—21no—
527C22×C11—41no—
528C22×C11—41no—
529C22×C11—41no—
530C22×C11—41no—
531C22×C11—42no—
532C22×C11—41no—
533C22×C11—42no—
534C22×C11—41no—
535C22×C11—42no—
536C22×C11—41no—
537C22×C11—41no—
538C22×C11—81no—
539C22×C11—81no—
540C22×C11—82no—
541C22×C11—82no—
542C22×C11—84no—
543C22×C11—164no—
544C22×C11C2×#12011yescharacteristic
545C22×C11#54611yescharacteristic
546C22×C11#54611yescharacteristic
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—22no—
550C4×C11—41no—
551C4×C11—41no—
552C4×C11—41no—
553C4×C11—42no—
554C4×C11—41no—
555C4×C11C2×#12311yescharacteristic
556C4×C11#53411yescharacteristic
557C4×C11#54611yescharacteristic
558C4×C11#54611yescharacteristic
559Dic11—42no—
560Dic11—81no—
561Dic11—81no—
562Dic11—81no—
563H(5,𝔽2)—22no—
564H(5,𝔽2)—22no—
565H(5,𝔽2)—41no—
566H(5,𝔽2)—41no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—22no—
572C2×#41—22no—
573C2×#41—41no—
574C2×#41—41no—
575C2×#41C22⋊D1111yescharacteristic
576C2×#41C22⋊D1111yescharacteristic
577C2×#41C22×D1111yescharacteristic
578C2×#41C22×D1111yescharacteristic
579C2×#41C22×D1111yescharacteristic
580C22×Q8C22⋊D1111yescharacteristic
581C22×D4—21no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4C22⋊D1111yescharacteristic
587C22×D4C22⋊D1112yes—
588C22×D4C22×D1111yescharacteristic
589C23×C4—21no—
590C23×C4C22×D1111yescharacteristic
591C2×M16—111no—
592C2×M16—111no—
593C2×M16—111no—
594C2×M16—111no—
595C2×M16—221no—
596C2×M16—441no—
597C2×M16—441no—
598C22×C8—221no—
599#127—22no—
600#127—21no—
601#124—22no—
602#124—21no—
603#123—22no—
604#123—21no—
605C22⋊Q8—22no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8C22⋊D1111yescharacteristic
609C22⋊Q8C22⋊D1111yescharacteristic
610#121—22no—
611#121—22no—
612#121—22no—
613#121—22no—
614#121—22no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—22no—
622#121—21no—
623#121—21no—
624#121C22⋊D1111yescharacteristic
625#121C22⋊D1111yescharacteristic
626#120—22no—
627#120—22no—
628#120—22no—
629#120—21no—
630#120—22no—
631C4×Q8—21no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—21no—
635C4×D4—22no—
636C4×D4—21no—
637C4×D4—21no—
638#117—21no—
639#117—221no—
640#117—221no—
641#117—221no—
642#117—221no—
643#117C22×D1111yescharacteristic
644C2×C4⋊C4—21no—
645C2×C4⋊C4—111no—
646C2×C4⋊C4—111no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C22⋊C4—22no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—222no—
653C2×C22⋊C4—222no—
654C2×C22⋊C4C22⋊D1112yes—
655C2×C42—111no—
656C2×C42—111no—
657C2×C42—221no—
658#107—221no—
659#107—221no—
660#106—221no—
661#106—221no—
662#104—222no—
663#104—222no—
664#104—441no—
665#104—441no—
666#104—441no—
667#104—441no—
668#103—221no—
669#103—221no—
670#103—221no—
671#103—221no—
672#103—221no—
673#103—221no—
674#102—221no—
675#102—221no—
676#102—221no—
677#102—221no—
678#102—221no—
679#102—221no—
680#100—441no—
681#100—441no—
682C22⋊C8—221no—
683C22⋊C8—221no—
684#95—221no—
685#95—222no—
686C2×C11—21no—
687C2×C11—21no—
688C2×C11—41no—
689C2×C11—41no—
690C2×C11—42no—
691C2×C11—81no—
692C2×C11—82no—
693C2×C11—81no—
694C2×C11#240511yescharacteristic
695C2×C11#301811yescharacteristic
696C2×C11#301911yescharacteristic
697C24—22no—
698C24—21no—
699C24C2×C22⋊D1112yes—
700C24C2×C22⋊D1111yescharacteristic
701#41—21no—
702#41—21no—
703#41—22no—
704#41—22no—
705#41—21no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—42no—
714#41—42no—
715#41—41no—
716#41—41no—
717#41—42no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41#434112yes—
724#41#434112yes—
725C2×Q8—21no—
726C2×Q8—22no—
727C2×Q8—41no—
728C2×Q8C2×C22⋊D1111yescharacteristic
729C2×Q8C2×C22⋊D1111yescharacteristic
730C2×Q8C2×C22⋊D1111yescharacteristic
731C2×D4—21no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—41no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—82no—
763C2×D4—84no—
764C2×D4C2×C22⋊D1111yescharacteristic
765C2×D4C2×C22⋊D1111yescharacteristic
766C2×D4C2×C22⋊D1111yescharacteristic
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4C2×C22⋊D1111yescharacteristic
786C22×C4C2×C22⋊D1111yescharacteristic
787C22×C4C2×C22⋊D1111yescharacteristic
788C22×C4C2×C22⋊D1111yescharacteristic
789C22×C4C2×C22⋊D1111yescharacteristic
790C22×C4C2×C22⋊D1112yes—
791C22×C4C23×D1111yescharacteristic
792M16—221no—
793M16—221no—
794M16—221no—
795M16—221no—
796M16—221no—
797M16—221no—
798M16—221no—
799M16—221no—
800M16—442no—
801C2×C8—221no—
802C2×C8—221no—
803C2×C8—221no—
804C2×C8—221no—
805C2×C8—442no—
806C4⋊C4—22no—
807C4⋊C4—22no—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—221no—
813C4⋊C4—221no—
814C4⋊C4—221no—
815C4⋊C4—221no—
816C4⋊C4—882no—
817C4⋊C4C2×C22⋊D1111yescharacteristic
818C4⋊C4C2×C22⋊D1111yescharacteristic
819C22⋊C4—22no—
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—21no—
831C22⋊C4—442no—
832C22⋊C4—444no—
833C22⋊C4—441no—
834C22⋊C4—441no—
835C22⋊C4—882no—
836C42—22no—
837C42—21no—
838C42—221no—
839C42—221no—
840C42—221no—
841C42—221no—
842C42—441no—
843C42—441no—
844C11#2403111yescharacteristic, complemented, Sylow
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#6700611yescharacteristic
864C23#6700611yescharacteristic
865C23C22×C22⋊D1111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#6698812yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—82no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#6698812yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—44no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—82no—
929C2×C4—222no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—442no—
934C2×C4—441no—
935C2×C4—442no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4#6700611yescharacteristic
940C2×C4#6700611yescharacteristic
941C2×C4C2×#434111yescharacteristic
942C2×C4C2×#434111yescharacteristic
943C2×C4#6703711yescharacteristic
944C2×C4#6703711yescharacteristic
945C2×C4C22×C22⋊D1111yescharacteristic
946C2×C4C22×C22⋊D1111yescharacteristic
947C8—441no—
948C8—441no—
949C8—441no—
950C8—441no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22#1062333711yescharacteristic
978C22#1062333711yescharacteristic
979C22C2×#6700611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—42no—
987C4—41no—
988C4—442no—
989C4—881no—
990C4—881no—
991C4—881no—
992C4C2×#6698811yescharacteristic
993C4#1062333511yescharacteristic
994C4#1062333711yescharacteristic
995C4#1062333711yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#1307193911yescharacteristic
1005C2#1307796511yescharacteristic
1006C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3488C2
socleC22×C11C2×#120
hypercenter#3488D11
hypocenterC11#24031
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #13078545C2semidirect
2. #13077135C2semidirect
3. #13073079C2semidirect
4. #13069842C2semidirect
5. #13069837C2semidirect
6. #13069823C2semidirect
7. #13069823C2semidirect
8. #13069080C2semidirect
9. #13068919C2semidirect
10. #13068849C2semidirect
11. #13068842C2semidirect
12. #13068570C2semidirect
13. #13068570C2semidirect
14. #13068560C2semidirect
33. C2×#66979C22semidirect
34. C22×#4318C22semidirect
37. C2×#66901C22semidirect
38. C2×#66901C22semidirect
39. C2×#66901C22semidirect
40. C2×#66901C22semidirect
45. #10622845C22semidirect
46. #10622845C22semidirect
47. #10622845C22semidirect
48. #10622845C22semidirect
51. #10622834C22semidirect
52. #10622834C22semidirect
53. C2×#66897C22semidirect
54. C2×#66897C22semidirect
56. C4×C22⋊Dic11C22semidirect
57. #10622820C22semidirect
62. #10622608C22semidirect
63. #10622608C22semidirect
64. #10622590C22semidirect
65. #10622589C22semidirect
67. #10622170C22semidirect
68. #10622170C22semidirect
69. #10622168C22semidirect
70. #10622168C22semidirect
844. C11#24031semidirect

Maximal subgroups

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

subgroupindex
#130785452
#130771352
#130730792
#130698422
#130698372
#130698232
#130690802
#130689192
#130688492
#130688422
#130685702
#130685602
C11×#34882
#2403111