Finite Group Databasebeta

← #14816656

Subgroups — #14816656

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622484C211yesmaximal, characteristic, complemented
2C2×#10622494C211yesmaximal, characteristic, complemented
3#13072343C211yesmaximal, characteristic, complemented
4#13071656C211yesmaximal, characteristic
5#13070140C211yesmaximal, characteristic, complemented
6#13070120C211yesmaximal, characteristic, complemented
7#13069989C211yesmaximal, characteristic, complemented
8#13069953C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13069053C211yesmaximal, characteristic
11#13068932C211yesmaximal, characteristic
12#13068860C211yesmaximal, characteristic, complemented
13#13068814C211yesmaximal, characteristic, complemented
14#13068797C211yesmaximal, characteristic, complemented
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66948C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C11×#382C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622600C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622586C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622552—21no—
41#10622552C2211yescharacteristic
42C4×(C2×D11)⋊C4—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622494—24no—
46#10622484—24no—
47#10622283—21no—
48#10622281—21no—
49#10622280—21no—
50#10622278—21no—
51#10622271—21no—
52#10622270—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—22no—
96C2×#4313—22no—
97C2×#4313—22no—
98#66948—22no—
99#66948Q814yes—
100#66946—22no—
101#66946—41no—
102#66945—22no—
103#66945—41no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—41no—
106#66943—22no—
107#66943—41no—
108C11×#107—22no—
109C11×#106—22no—
110C11×C4⋊C8—22no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66885—22no—
121#66885—22no—
122(C2×D11)⋊C8—22no—
123#66881—22no—
124Dic11⋊C8—22no—
125#66873—22no—
126#66873—41no—
127#66872—22no—
128#66871—41no—
129#66871D414yescomplemented
130#26363—111nomaximal, Sylow
131C23×D11—21no—
132C23×D11C2×D411yescharacteristic
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C2×D44—24no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—81no—
153C2×D44—81no—
154C2×D44C2×Q812yes—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11C2×Q812yes—
166C2×C4×D11#4112yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11#4112yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×Q812yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—81no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11—81no—
199C4⋊Dic11C2×D412yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—81no—
203Dic11⋊C4—81no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213#4313—28no—
214C2×#478—111no—
215C2×#428—111no—
216#2442—111no—
217#2363—111no—
218#2092—111no—
219#2088—111no—
220#2065—111no—
221#2059—111no—
222#1949D1111yescharacteristic, complemented
223#1918—111no—
224#1895—111no—
225#1874—111no—
226#1862—111no—
227#1854—111no—
228#1851—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11C22⋊Q812yes—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11C22⋊Q812yes—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290D44—84no—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—84no—
296C4×D11—84no—
297C8×C11—22no—
298C8×C11—41no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C22×M16—111no—
302C2×#125—111no—
303C2×#121—111no—
304C2×C4×D4—111no—
305C2×#117—111no—
306C22×C4⋊C4—111no—
307#478—224no—
308#428—224no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#107C2×D1111yescharacteristic
312C2×#106—111no—
313C2×#106—111no—
314C2×#106C2×D1111yescharacteristic
315C2×C4⋊C8—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C22⋊C8—111no—
322#400—221no—
323#398—221no—
324#390—111no—
325#390—221no—
326#389—111no—
327#389—111no—
328#389—111no—
329#388—221no—
330#386—221no—
331#385—221no—
332#382C2×D1111yescharacteristic
333#380—111no—
334#380—221no—
335C4×C4⋊C4C2×D1111yescharacteristic
336C4×C22⋊C4—111no—
337C4×C22⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346C22×C11C2×C22⋊Q811yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11#54711yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57711yescharacteristic
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11#52511yescharacteristic
374C4×C11#53911yescharacteristic
375C4×C11D4×Q811yescharacteristic
376C4×C11#55411yescharacteristic
377Dic11—22no—
378Dic11—41no—
379Dic11—41no—
380Dic11—42no—
381Dic11—81no—
382Dic11—81no—
383C22×D4—111no—
384C22×D4—221no—
385C23×C4—111no—
386C23×C4—221no—
387C23×C4—221no—
388C2×M16—222no—
389C2×M16—222no—
390C2×M16—222no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#125—222no—
396#125—441no—
397#121—114no—
398#121—222no—
399C4×D4—222no—
400C4×D4—441no—
401#117—222no—
402#117—441no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—441no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—21no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430#107—22no—
431#107—114no—
432#107—441no—
433#106—22no—
434#106—222no—
435#106—222no—
436C4⋊C8—22no—
437C4⋊C8—222no—
438#102—222no—
439#102—222no—
440#102—222no—
441#102—441no—
442C22⋊C8—222no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—111no—
447#95—111no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11#244911yescharacteristic
453C2×C11#308011yescharacteristic
454C2×C11#308111yescharacteristic
455C2×C11#327111yescharacteristic
456C2×C11#327311yescharacteristic
457C2×C11#334811yescharacteristic
458C2×C11#335511yescharacteristic
459D11—42no—
460D11—82no—
461C24—111no—
462C24—221no—
463C2×D4—112no—
464C2×D4—224no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—881no—
471C2×D4—881no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497M16—228no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8#433912yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C4⋊C4—881no—
527C4⋊C4—881no—
528C4⋊C4D4×D1112yes—
529C4⋊C4Q8×D1112yes—
530C22⋊C4—224no—
531C22⋊C4—441no—
532C22⋊C4—441no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C42—21no—
539C42—21no—
540C42—81no—
541C42—221no—
542C42—221no—
543C42—442no—
544C11#2636311yescharacteristic, complemented, Sylow
545C23—112no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—222no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23C2×D4×D1111yescharacteristic
560D4—222no—
561D4—222no—
562D4—441no—
563D4—441no—
564D4—884no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—112no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—222no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—884no—
606C2×C4—884no—
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×Q8×D1111yescharacteristic
610C2×C4#6704011yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704211yescharacteristic
613C8—22no—
614C8—41no—
615C8—222no—
616C8—441no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—881no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22#1062303811yescharacteristic
632C22#1062314011yescharacteristic
633C22D11×C22⋊Q811yescharacteristic
634C22#1062329911yescharacteristic
635C22#1062330111yescharacteristic
636C22#1062330511yescharacteristic
637C22#1062330811yescharacteristic
638C4—41no—
639C4—41no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—81no—
644C4—222no—
645C4—441no—
646C4—441no—
647C4—442no—
648C4—881no—
649C4—881no—
650C4#1062307811yescharacteristic
651C4#1062311011yescharacteristic
652C4#1062322311yescharacteristic
653C4#1062325811yescharacteristic
654C2—442no—
655C2—882no—
656C2#1307243211yescharacteristic
657C2#1307843511yescharacteristic
658C2#1307844611yescharacteristic
659C2#1308020711yescharacteristic
660C2#1308022211yescharacteristic
661C2#1308112711yescharacteristic
662C2#1308121811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1949D11
hypocenterC11#26363
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#10622484C2semidirect
2. C2×#10622494C2semidirect
3. #13072343C2semidirect
5. #13070140C2semidirect
6. #13070120C2semidirect
7. #13069989C2semidirect
8. #13069953C2semidirect
9. #13069187C2semidirect
12. #13068860C2semidirect
13. #13068814C2semidirect
14. #13068797C2semidirect
15. C11×#1949C2semidirect
129. #66871D4semidirect
222. #1949D11semidirect
544. C11#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#106224842
C2×#106224942
#130723432
#130716562
#130701402
#130701202
#130699892
#130699532
#130691872
#130690532
#130689322
#130688602
#130688142
#130687972
C11×#19492
#2636311