Finite Group Databasebeta

← #14786656

Subgroups — #14786656

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 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#13073070C211yesmaximal, characteristic, complemented
4#13069842C211yesmaximal, characteristic, complemented
5#13069837C211yesmaximal, characteristic, complemented
6#13069830C211yesmaximal, characteristic, complemented
7#13069830C211yesmaximal, characteristic, complemented
8#13069085C211yesmaximal, characteristic, complemented
9#13068919C211yesmaximal, characteristic, complemented
10#13068849C211yesmaximal, characteristic, complemented
11#13068842C211yesmaximal, characteristic, complemented
12#13068575C211yesmaximal, characteristic, complemented
13#13068575C211yesmaximal, characteristic, complemented
14#13068560C211yesmaximal, characteristic, complemented
15C11×#3489C211yesmaximal, characteristic
16C2×C11×2−1+4C2211yescharacteristic
17C22×C11×#41C2211yescharacteristic
18D4×Q8×C11—21no—
19C11×#548—21no—
20C11×#547—21no—
21C11×#547—22no—
22C11×#546—21no—
23C11×#546—22no—
24C11×#537—21no—
25C11×#537C2211yescharacteristic
26C11×#536—21no—
27C11×#536C2211yescharacteristic
28C11×#525—21no—
29C11×#525C2211yescharacteristic
30C2×C11×C22⋊Q8—21no—
31C2×C11×C22⋊Q8C2211yescharacteristic
32C11×#520C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66901C2211yescharacteristic
36C2×#66901C2211yescharacteristic
37C2×#66901C2211yescharacteristic
38C2×#66901C2211yescharacteristic
39C2×#66901C2211yescharacteristic, complemented
40C2×#66901C2211yescharacteristic, complemented
41#10622846—21no—
42#10622846—21no—
43#10622845C2211yescharacteristic
44#10622845C2211yescharacteristic
45#10622845C2211yescharacteristic
46#10622845C2211yescharacteristic
47#10622845C2211yescharacteristic, complemented
48#10622845C2211yescharacteristic, complemented
49#10622843C2211yescharacteristic, complemented
50#10622843C2211yescharacteristic, complemented
51C2×#66900C2211yescharacteristic, complemented
52C2×#66900C2211yescharacteristic, complemented
53#10622838—21no—
54#10622828—21no—
55C4×C22⋊Dic11C2211yescharacteristic
56#10622820C2211yescharacteristic
57#10622658—21no—
58#10622658—21no—
59#10622648—21no—
60#10622648—21no—
61#10622608C2211yescharacteristic, complemented
62#10622608C2211yescharacteristic, complemented
63#10622591—22no—
64#10622590C2211yescharacteristic, complemented
65#10622589C2211yescharacteristic, complemented
66#10622565—22no—
67#10622170C2211yescharacteristic, complemented
68#10622170C2211yescharacteristic, complemented
69#10622168C2211yescharacteristic, complemented
70#10622168C2211yescharacteristic, complemented
71C11×2−1+4—22no—
72C11×2−1+4—22no—
73C11×2−1+4—41no—
74C11×2−1+4—41no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41—21no—
78C2×C11×#41—22no—
79C2×C11×#41—21no—
80C2×C11×#41—22no—
81C2×C11×#41—22no—
82C2×C11×#41—41no—
83C2×C11×#41—41no—
84C2×C11×#41D411yescharacteristic
85C2×C11×#41D411yescharacteristic
86C2×C11×#41C2311yescharacteristic
87C2×C11×#41C2311yescharacteristic
88C2×C11×#41C2311yescharacteristic
89C22×Q8×C11—21no—
90C22×Q8×C11—21no—
91C22×Q8×C11D411yescharacteristic
92C22×Q8×C11C2311yescharacteristic
93C22×D4×C11—21no—
94C22×D4×C11D411yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C11×C4⋊Q8—22no—
98C11×C4⋊Q8—21no—
99C11×#124—22no—
100C11×#124—21no—
101C11×#123—22no—
102C11×#123—22no—
103C11×#123—22no—
104C11×#123—21no—
105C11×#123—22no—
106C11×C22⋊Q8—22no—
107C11×C22⋊Q8—22no—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—21no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—21no—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8D411yescharacteristic
118C11×C22⋊Q8D411yescharacteristic
119C11×#121—22no—
120C11×#121—22no—
121C11×#121—22no—
122C11×#121—21no—
123C11×#121—21no—
124C11×#121—22no—
125C11×#121D411yescharacteristic
126C11×#121D411yescharacteristic
127C11×#120—22no—
128C11×#120—21no—
129C4×Q8×C11—21no—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—21no—
133C4×D4×C11—22no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C11×#117—21no—
137C11×#117C2311yescharacteristic
138C2×C11×C4⋊C4—22no—
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4D412yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4—22no—
143C2×C11×C22⋊C4D412yes—
144C2×C22⋊Dic11—21no—
145C2×C22⋊Dic11—21no—
146#66979—21no—
147#66979—21no—
148#66979—21no—
149#66979—21no—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4—22no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C2×#4318—21no—
157C2×#4318—41no—
158C2×#4318—41no—
159C2×#4318C2311yescharacteristic
160C2×#4318C2311yescharacteristic
161C2×#4318C2311yescharacteristic
162C2×#4318C2311yescharacteristic
163C22×C11⋊C8—21no—
164#66901—22no—
165#66901—22no—
166#66901—41no—
167#66901—41no—
168#66901—41no—
169#66901—41no—
170#66900—41no—
171#66900—41no—
172#66899—21no—
173#66899—21no—
174#66899—21no—
175#66899—21no—
176#66899—21no—
177#66899—21no—
178#66896—21no—
179#66896—21no—
180#66896—21no—
181#66896—21no—
182#66896—21no—
183#66896—21no—
184C11⋊#95—22no—
185C11⋊#95—22no—
186C11⋊#95—22no—
187C11⋊#95—21no—
188C22⋊(C11⋊C8)—21no—
189C22⋊(C11⋊C8)—21no—
190#66872—21no—
191#66872—21no—
192#66871—21no—
193#66871—21no—
194#24028—111nomaximal, Sylow
195C24×C11—21no—
196C24×C11C2×D411yescharacteristic
197C11×#41—21no—
198C11×#41—21no—
199C11×#41—22no—
200C11×#41—22no—
201C11×#41—21no—
202C11×#41—21no—
203C11×#41—21no—
204C11×#41—21no—
205C11×#41—21no—
206C11×#41—21no—
207C11×#41—21no—
208C11×#41—21no—
209C11×#41—42no—
210C11×#41—42no—
211C11×#41—41no—
212C11×#41—41no—
213C11×#41—42no—
214C11×#41—42no—
215C11×#41—42no—
216C11×#41—42no—
217C11×#41—44no—
218C11×#41—44no—
219C11×#41—42no—
220C11×#41—42no—
221C11×#41#4112yes—
222C11×#41#4112yes—
223C2×Q8×C11—22no—
224C2×Q8×C11—21no—
225C2×Q8×C11—21no—
226C2×Q8×C11—21no—
227C2×Q8×C11—21no—
228C2×Q8×C11—21no—
229C2×Q8×C11—21no—
230C2×Q8×C11—21no—
231C2×Q8×C11—22no—
232C2×Q8×C11—41no—
233C2×Q8×C11—42no—
234C2×Q8×C11—42no—
235C2×Q8×C11—42no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D411yescharacteristic
239C2×Q8×C11C2×D411yescharacteristic
240C2×D4×C11—21no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—21no—
245C2×D4×C11—21no—
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11—22no—
249C2×D4×C11—21no—
250C2×D4×C11—21no—
251C2×D4×C11—41no—
252C2×D4×C11—42no—
253C2×D4×C11—42no—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2×D411yescharacteristic
256C2×D4×C11C2×D411yescharacteristic
257C22×C4×C11—21no—
258C22×C4×C11—21no—
259C22×C4×C11—21no—
260C22×C4×C11—21no—
261C22×C4×C11—21no—
262C22×C4×C11—22no—
263C22×C4×C11—22no—
264C22×C4×C11—21no—
265C22×C4×C11—22no—
266C22×C4×C11—21no—
267C22×C4×C11—21no—
268C22×C4×C11—21no—
269C22×C4×C11—21no—
270C22×C4×C11—42no—
271C22×C4×C11—42no—
272C22×C4×C11C2×D412yes—
273C22×C4×C11C2×D411yescharacteristic
274C22×C4×C11C2×D411yescharacteristic
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D411yescharacteristic
277C22×C4×C11C2×D411yescharacteristic
278C22×C4×C11C2×D412yes—
279C22×C4×C11C2411yescharacteristic
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—21no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—21no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4—21no—
294C11×C4⋊C4C2×D411yescharacteristic
295C11×C4⋊C4C2×D411yescharacteristic
296C11×C22⋊C4—22no—
297C11×C22⋊C4—22no—
298C11×C22⋊C4—22no—
299C11×C22⋊C4—22no—
300C11×C22⋊C4—22no—
301C11×C22⋊C4—21no—
302C11×C22⋊C4—22no—
303C11×C22⋊C4—22no—
304C11×C22⋊C4—21no—
305C11×C22⋊C4—21no—
306C11×C22⋊C4—21no—
307C11×C22⋊C4—21no—
308C42×C11—22no—
309C42×C11—21no—
310C22⋊Dic11—42no—
311C22⋊Dic11—41no—
312C22⋊Dic11—41no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11—21no—
316C4⋊Dic11—21no—
317Dic11⋊C4—44no—
318C4×Dic11—21no—
319C4×Dic11—21no—
320C4×Dic11—21no—
321C4×Dic11—21no—
322C4×Dic11—41no—
323C4×Dic11—41no—
324#4318—21no—
325#4318—21no—
326#4318—21no—
327#4318—21no—
328#4318—21no—
329#4318—21no—
330#4318—21no—
331#4318—21no—
332#4318—42no—
333C2×C11⋊C8—21no—
334C2×C11⋊C8—21no—
335C2×C11⋊C8—21no—
336C2×C11⋊C8—21no—
337C2×C11⋊C8—42no—
338#3489D1111yescharacteristic
339#3093—111no—
340#2896—111no—
341#2499—111no—
342#2040—111no—
343#2039—111no—
344#2038—111no—
345#2038—111no—
346#1901—111no—
347#1871—111no—
348#1860—111no—
349#1859—111no—
350#1793—111no—
351#1793—111no—
352#1789—111no—
353C23×C11—21no—
354C23×C11—21no—
355C23×C11—21no—
356C23×C11—21no—
357C23×C11—21no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—81no—
363C23×C11#12011yescharacteristic
364C23×C11#12011yescharacteristic
365C23×C11C22×D411yescharacteristic
366Q8×C11—21no—
367Q8×C11—21no—
368Q8×C11—21no—
369Q8×C11—21no—
370Q8×C11—21no—
371Q8×C11—42no—
372Q8×C11—44no—
373Q8×C11—41no—
374Q8×C11—41no—
375Q8×C11—41no—
376Q8×C11—41no—
377Q8×C11#12312yes—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—21no—
381D4×C11—21no—
382D4×C11—21no—
383D4×C11—21no—
384D4×C11—21no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—42no—
388D4×C11—42no—
389D4×C11—44no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—41no—
394D4×C11—81no—
395D4×C11—82no—
396D4×C11#12312yes—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—21no—
401C2×C4×C11—21no—
402C2×C4×C11—21no—
403C2×C4×C11—21no—
404C2×C4×C11—21no—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—21no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—42no—
419C2×C4×C11—42no—
420C2×C4×C11—42no—
421C2×C4×C11—44no—
422C2×C4×C11—44no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—42no—
428C2×C4×C11—82no—
429C2×C4×C11#12011yescharacteristic
430C2×C4×C11#12011yescharacteristic
431C2×C4×C11C22×D411yescharacteristic
432C2×C4×C11C22×D411yescharacteristic
433C2×C4×C11C2×#4111yescharacteristic
434C2×C4×C11C2×#4111yescharacteristic
435C2×C4×C11H(5,𝔽2)11yescharacteristic
436C2×C4×C11H(5,𝔽2)11yescharacteristic
437C2×Dic11—22no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—42no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—42no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C11⋊C8—41no—
448C11⋊C8—41no—
449C11⋊C8—41no—
450C11⋊C8—41no—
451C2×2−1+4C2×D1111yescharacteristic
452C22×#41C2×D1111yescharacteristic
453C22×M16—111no—
454D4×Q8—21no—
455#548—21no—
456#547—21no—
457#547—22no—
458#546—21no—
459#546—22no—
460#537—21no—
461#537C2×D1111yescharacteristic
462#536—21no—
463#536C2×D1111yescharacteristic
464#525—21no—
465#525C2×D1111yescharacteristic
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8C2×D1111yescharacteristic
468#520C2×D1111yescharacteristic
469C2×#117—111no—
470#485—221no—
471#485—221no—
472#482—221no—
473#482—221no—
474#428—111no—
475#428—111no—
476C2×#104—111no—
477C2×#104—111no—
478C2×#104—111no—
479C2×#104—111no—
480C2×#104—111no—
481C2×#104—111no—
482#419—221no—
483#418—221no—
484#417—111no—
485#417—111no—
486#417—111no—
487#417—111no—
488#417—111no—
489#417—111no—
490#416—221no—
491#416—221no—
492C2×#101—111no—
493C2×#101—111no—
494#407—111no—
495#397—222no—
496#391—111no—
497#391—111no—
498#387—222no—
499#384—111no—
500#382—111no—
501C4×C22⋊C4—111no—
502#343—111no—
503#343—111no—
504#339—111no—
505#339—111no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—22no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—41no—
516C22×C11—41no—
517C22×C11—41no—
518C22×C11—41no—
519C22×C11—41no—
520C22×C11—41no—
521C22×C11—41no—
522C22×C11—41no—
523C22×C11—81no—
524C22×C11—81no—
525C22×C11—84no—
526C22×C11C2×#12011yescharacteristic
527C22×C11#54611yescharacteristic
528C22×C11#54611yescharacteristic
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—42no—
533C4×C11—41no—
534C4×C11—41no—
535C4×C11—42no—
536C4×C11—41no—
537C4×C11—41no—
538C4×C11C2×#12311yescharacteristic
539C4×C11#53411yescharacteristic
540C4×C11#54611yescharacteristic
541C4×C11#54611yescharacteristic
542Dic11—42no—
543Dic11—81no—
544Dic11—81no—
545Dic11—81no—
5462−1+4—22no—
5472−1+4—22no—
5482−1+4—41no—
5492−1+4—41no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—22no—
554C2×#41—21no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—41no—
558C2×#41—41no—
559C2×#41C22⋊D1111yescharacteristic
560C2×#41C22⋊D1111yescharacteristic
561C2×#41C22×D1111yescharacteristic
562C2×#41C22×D1111yescharacteristic
563C2×#41C22×D1111yescharacteristic
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8C22⋊D1111yescharacteristic
567C22×Q8C22×D1111yescharacteristic
568C22×D4—21no—
569C22×D4C22⋊D1111yescharacteristic
570C23×C4—21no—
571C23×C4C22×D1111yescharacteristic
572C2×M16—111no—
573C2×M16—111no—
574C2×M16—111no—
575C2×M16—111no—
576C2×M16—221no—
577C2×M16—441no—
578C2×M16—441no—
579C22×C8—221no—
580C4⋊Q8—22no—
581C4⋊Q8—21no—
582#124—22no—
583#124—21no—
584#123—22no—
585#123—22no—
586#123—22no—
587#123—21no—
588#123—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8C22⋊D1111yescharacteristic
601C22⋊Q8C22⋊D1111yescharacteristic
602#121—22no—
603#121—22no—
604#121—22no—
605#121—21no—
606#121—21no—
607#121—22no—
608#121C22⋊D1111yescharacteristic
609#121C22⋊D1111yescharacteristic
610#120—22no—
611#120—21no—
612C4×Q8—21no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—21no—
616C4×D4—22no—
617C4×D4—21no—
618C4×D4—21no—
619#117—21no—
620#117—221no—
621#117—221no—
622#117—221no—
623#117—221no—
624#117C22×D1111yescharacteristic
625C2×C4⋊C4—22no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—222no—
630C2×C4⋊C4C22⋊D1112yes—
631C2×C4⋊C4C22×D1111yescharacteristic
632C2×C22⋊C4—22no—
633C2×C22⋊C4—221no—
634C2×C22⋊C4—221no—
635C2×C22⋊C4C22⋊D1112yes—
636C2×C42—111no—
637C2×C42—111no—
638C2×C42—221no—
639#107—221no—
640#107—221no—
641#106—221no—
642#106—221no—
643#104—222no—
644#104—222no—
645#104—441no—
646#104—441no—
647#104—441no—
648#104—441no—
649#103—221no—
650#103—221no—
651#103—221no—
652#103—221no—
653#103—221no—
654#103—221no—
655#102—221no—
656#102—221no—
657#102—221no—
658#102—221no—
659#102—221no—
660#102—221no—
661#101—441no—
662#101—441no—
663C22⋊C8—221no—
664C22⋊C8—221no—
665#95—221no—
666#95—222no—
667#95—222no—
668#95—222no—
669C2×C11—21no—
670C2×C11—21no—
671C2×C11—41no—
672C2×C11—41no—
673C2×C11—42no—
674C2×C11—81no—
675C2×C11—81no—
676C2×C11#240511yescharacteristic
677C2×C11#301811yescharacteristic
678C2×C11#302011yescharacteristic
679C24—21no—
680C24C2×C22⋊D1111yescharacteristic
681#41—21no—
682#41—21no—
683#41—22no—
684#41—22no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—21no—
689#41—21no—
690#41—21no—
691#41—21no—
692#41—21no—
693#41—42no—
694#41—42no—
695#41—41no—
696#41—41no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41—42no—
701#41—44no—
702#41—44no—
703#41—42no—
704#41—42no—
705#41#434112yes—
706#41#434112yes—
707C2×Q8—22no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—22no—
716C2×Q8—41no—
717C2×Q8—42no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—42no—
721C2×Q8C2×C22⋊D1111yescharacteristic
722C2×Q8C2×C22⋊D1111yescharacteristic
723C2×Q8C2×C22⋊D1111yescharacteristic
724C2×D4—21no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—41no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4C2×C22⋊D1111yescharacteristic
739C2×D4C2×C22⋊D1111yescharacteristic
740C2×D4C2×C22⋊D1111yescharacteristic
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4C2×C22⋊D1112yes—
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1111yescharacteristic
763C22×C4C2×C22⋊D1111yescharacteristic
764C22×C4C2×C22⋊D1111yescharacteristic
765C22×C4C2×C22⋊D1111yescharacteristic
766C22×C4C2×C22⋊D1112yes—
767C22×C4C23×D1111yescharacteristic
768M16—221no—
769M16—221no—
770M16—221no—
771M16—221no—
772M16—221no—
773M16—221no—
774M16—221no—
775M16—221no—
776M16—442no—
777C2×C8—221no—
778C2×C8—221no—
779C2×C8—221no—
780C2×C8—221no—
781C2×C8—442no—
782C4⋊C4—22no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—21no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—221no—
793C4⋊C4—221no—
794C4⋊C4—221no—
795C4⋊C4—221no—
796C4⋊C4—444no—
797C4⋊C4C2×C22⋊D1111yescharacteristic
798C4⋊C4C2×C22⋊D1111yescharacteristic
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—21no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—442no—
812C22⋊C4—441no—
813C22⋊C4—441no—
814C42—22no—
815C42—21no—
816C42—221no—
817C42—221no—
818C42—221no—
819C42—221no—
820C42—441no—
821C42—441no—
822C11#2402811yescharacteristic, complemented, Sylow
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—41no—
829C23—41no—
830C23—42no—
831C23—42no—
832C23—81no—
833C23#6700611yescharacteristic
834C23#6700611yescharacteristic
835C23C22×C22⋊D1111yescharacteristic
836Q8—21no—
837Q8—21no—
838Q8—21no—
839Q8—21no—
840Q8—21no—
841Q8—42no—
842Q8—44no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8#6698812yes—
848D4—22no—
849D4—22no—
850D4—21no—
851D4—21no—
852D4—21no—
853D4—21no—
854D4—21no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—81no—
865D4—82no—
866D4#6698812yes—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—42no—
898C2×C4—82no—
899C2×C4—222no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—442no—
904C2×C4—441no—
905C2×C4—442no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4#6700611yescharacteristic
910C2×C4#6700611yescharacteristic
911C2×C4C2×#434111yescharacteristic
912C2×C4C2×#434111yescharacteristic
913C2×C4#6703711yescharacteristic
914C2×C4#6703711yescharacteristic
915C2×C4C22×C22⋊D1111yescharacteristic
916C2×C4C22×C22⋊D1111yescharacteristic
917C8—441no—
918C8—441no—
919C8—441no—
920C8—441no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—22no—
926C22—21no—
927C22—21no—
928C22—21no—
929C22—21no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—81no—
939C22—81no—
940C22—84no—
941C22#1062333711yescharacteristic
942C22#1062333711yescharacteristic
943C22C2×#6700611yescharacteristic
944C4—21no—
945C4—21no—
946C4—22no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—42no—
951C4—41no—
952C4—41no—
953C4—442no—
954C4—881no—
955C4—881no—
956C4—881no—
957C4C2×#6698811yescharacteristic
958C4#1062333511yescharacteristic
959C4#1062333711yescharacteristic
960C4#1062333711yescharacteristic
961C2—21no—
962C2—21no—
963C2—41no—
964C2—41no—
965C2—42no—
966C2—81no—
967C2—81no—
968C2#1307193911yescharacteristic
969C2#1307796511yescharacteristic
970C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3489C2
socleC22×C11C2×#120
hypercenter#3489D11
hypocenterC11#24028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #13078545C2semidirect
2. #13077135C2semidirect
3. #13073070C2semidirect
4. #13069842C2semidirect
5. #13069837C2semidirect
6. #13069830C2semidirect
7. #13069830C2semidirect
8. #13069085C2semidirect
9. #13068919C2semidirect
10. #13068849C2semidirect
11. #13068842C2semidirect
12. #13068575C2semidirect
13. #13068575C2semidirect
14. #13068560C2semidirect
39. C2×#66901C22semidirect
40. C2×#66901C22semidirect
47. #10622845C22semidirect
48. #10622845C22semidirect
49. #10622843C22semidirect
50. #10622843C22semidirect
51. C2×#66900C22semidirect
52. C2×#66900C22semidirect
61. #10622608C22semidirect
62. #10622608C22semidirect
64. #10622590C22semidirect
65. #10622589C22semidirect
67. #10622170C22semidirect
68. #10622170C22semidirect
69. #10622168C22semidirect
70. #10622168C22semidirect
822. C11#24028semidirect

Maximal subgroups

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

subgroupindex
#130785452
#130771352
#130730702
#130698422
#130698372
#130698302
#130690852
#130689192
#130688492
#130688422
#130685752
#130685602
C11×#34892
#2402811