Finite Group Databasebeta

← #14816748

Subgroups — #14816748

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622379C211yesmaximal, characteristic, complemented
2#13072482C211yesmaximal, characteristic, complemented
3#13071521C211yesmaximal, characteristic, complemented
4#13070135C211yesmaximal, characteristic, complemented
5#13070100C211yesmaximal, characteristic, complemented
6#13070002C211yesmaximal, characteristic, complemented
7#13069952C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069173C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic
11#13068966C211yesmaximal, characteristic
12#13068877C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068865C211yesmaximal, characteristic, complemented
15C2×C4×C11×D8C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C4×C11×D8—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825—21no—
34#10622823—21no—
35#10622823—21no—
36C2×C11⋊#95—21no—
37C2×#66882C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622590C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622562—21no—
46#10622561—21no—
47#10622559—21no—
48#10622555—21no—
49C4×Dic11⋊C4C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622379—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C2×C11×D8—22no—
68C2×C11×D8—22no—
69C2×C11×D8Q814yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—41no—
75C4×D4×C11—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87D4×Dic11—22no—
88D4×Dic11—22no—
89D4×Dic11—22no—
90D4×Dic11—41no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4D411yescharacteristic
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66943—22no—
108#66943—41no—
109C11×#107—22no—
110C11×#102—22no—
111C11×#102D414yes—
112C4×C8×C11—22no—
113#66896—22no—
114#66896—22no—
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66882—22no—
126#66882—22no—
127Dic11⋊C8—22no—
128#66872—22no—
129#66872—41no—
130#26370—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×Q812yes—
143C2×D4×C11C2×Q812yes—
144C2×D4×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—24no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C22×Dic11—81no—
165C22×Dic11—81no—
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C11×D8—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×Q812yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4C2×D412yes—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C42×C11—21no—
184C42×C11—21no—
185C22⋊Dic11—24no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—81no—
189C22⋊Dic11—81no—
190C22⋊Dic11—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—81no—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—22no—
202Dic11⋊C4—41no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205Dic11⋊C4—81no—
206Dic11⋊C4—81no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×#478—111no—
218C2×C4×D8D1111yescharacteristic
219#2454—111no—
220#2349—111no—
221#2092—111no—
222#2085—111no—
223#2067—111no—
224#2059—111no—
225#1942—111no—
226#1916—111no—
227#1879—111no—
228#1879—111no—
229#1864—111no—
230#1864—111no—
231#1862—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11C22⋊Q814yes—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—84no—
267C2×C4×C11—84no—
268C2×C4×C11#13512yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—84no—
300C2×Dic11—84no—
301C8×C11—22no—
302C8×C11—22no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C22×D8C2×D1111yescharacteristic
306C2×#125—111no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4C2×D1111yescharacteristic
310C2×C4×D4C2×D1111yescharacteristic
311#478—224no—
312C4×D8—24no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107C2×D1111yescharacteristic
316C2×#106—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102C2×D1111yescharacteristic
324C2×#102C2×D1111yescharacteristic
325C2×C4×C8C2×D1111yescharacteristic
326#399—221no—
327#396—221no—
328#390—111no—
329#390—111no—
330#389—111no—
331#389—111no—
332#389—111no—
333#389—111no—
334#385—221no—
335#385—221no—
336#385—221no—
337#382—111no—
338#380—221no—
339#380—221no—
340C4×C4⋊C4—111no—
341C2×#95—221no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#336—111no—
347#336—111no—
348#336—111no—
349#336—111no—
350C22×C11—24no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11#52511yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11D4×Q811yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57611yescharacteristic
370C22×C11#57611yescharacteristic
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—81no—
375C4×C11C2×C22⋊Q811yescharacteristic
376C4×C11#53911yescharacteristic
377C4×C11#54711yescharacteristic
378C4×C11#55411yescharacteristic
379Dic11—41no—
380Dic11—41no—
381Dic11—42no—
382Dic11—41no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387C22×D4C22×D1111yescharacteristic
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—221no—
392C23×C4—221no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8Dic2214yes—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#125—222no—
401#125—441no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—41no—
405C4×D4—41no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—441no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42C22×D1111yescharacteristic
435#107—22no—
436#107—222no—
437#107—222no—
438#106—222no—
439#106—441no—
440C4⋊C8—222no—
441#102—22no—
442#102—222no—
443#102—222no—
444#102—222no—
445#102—441no—
446#102C22⋊D1114yes—
447C4×C8—22no—
448#95—111no—
449#95—111no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—44no—
457C2×C11—82no—
458C2×C11#244911yescharacteristic
459C2×C11#310211yescharacteristic
460C2×C11#312211yescharacteristic
461C2×C11#326811yescharacteristic
462C2×C11#328011yescharacteristic
463C2×C11#338011yescharacteristic
464C2×C11#338911yescharacteristic
465C24—21no—
466C24—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4C2×Dic2212yes—
476C2×D4C2×Dic2212yes—
477C2×D4#433912yes—
478C2×D4C2×C22⋊D1112yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—221no—
492C22×C4—224no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4—881no—
501C22×C4D4×D1111yescharacteristic
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504D8—28no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8C2×Dic2212yes—
516C2×C8C2×C22⋊D1112yes—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—112no—
521C4⋊C4—222no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—441no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—881no—
533C4⋊C4—881no—
534C4⋊C4—881no—
535C4⋊C4—881no—
536C4⋊C4C2×C22⋊D1112yes—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—224no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C22⋊C4—881no—
545C42—21no—
546C42—21no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42—221no—
551C11#2637011yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×D4×D1111yescharacteristic
567D4—22no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4#6697714yes—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—84no—
587C2×C4—84no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—884no—
613C2×C4—884no—
614C2×C4#6696512yes—
615C2×C4C22×Dic2211yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4#6703711yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C2×C4#6704311yescharacteristic
620C2×C4C22×C22⋊D1111yescharacteristic
621C8—22no—
622C8—22no—
623C8—441no—
624C8—441no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22D4×Dic2211yescharacteristic
640C22#1062307811yescharacteristic
641C22C2×#6696511yescharacteristic
642C22#1062328811yescharacteristic
643C22#1062329911yescharacteristic
644C22#1062330011yescharacteristic
645C22D4×C22⋊D1111yescharacteristic
646C4—22no—
647C4—41no—
648C4—42no—
649C4—81no—
650C4—441no—
651C4—442no—
652C4—441no—
653C4—441no—
654C4—441no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4#1062307011yescharacteristic
659C4#1062309511yescharacteristic
660C4C2×#6697711yescharacteristic
661C4#1062335511yescharacteristic
662C2—44no—
663C2—82no—
664C2#1307241911yescharacteristic
665C2#1307863011yescharacteristic
666C2#1307885611yescharacteristic
667C2#1308015611yescharacteristic
668C2#1308030111yescharacteristic
669C2#1308148111yescharacteristic
670C2#1308157211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11#26370
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10622379C2semidirect
2. #13072482C2semidirect
3. #13071521C2semidirect
4. #13070135C2semidirect
5. #13070100C2semidirect
6. #13070002C2semidirect
7. #13069952C2semidirect
8. #13069349C2semidirect
9. #13069173C2semidirect
12. #13068877C2semidirect
13. #13068877C2semidirect
14. #13068865C2semidirect
551. C11#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#106223792
#130724822
#130715212
#130701352
#130701002
#130700022
#130699522
#130693492
#130691732
#130689662
#130688772
#130688652
C2×C4×C11×D82
#2637011