Finite Group Databasebeta

← #14776268

Subgroups — #14776268

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622462C211yesmaximal, characteristic
2C2×#10622329C211yesmaximal, characteristic
3C2×C4×Dic44C211yesmaximal, characteristic
4#13071672C211yesmaximal, characteristic
5#13071536C211yesmaximal, characteristic
6#13069436C211yesmaximal, characteristic
7#13069386C211yesmaximal, characteristic
8#13069306C211yesmaximal, characteristic
9#13069292C211yesmaximal, characteristic
10#13068956C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic
12#13068887C211yesmaximal, characteristic
13#13068873C211yesmaximal, characteristic
14#13068447C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic
16C22×Dic44C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C4⋊C4×Dic11—21no—
40#10622586—21no—
41#10622585—21no—
42#10622585—21no—
43#10622549C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622462C418yescomplemented
50#10622329—24no—
51C4×Dic44—24no—
52#10622267—21no—
53#10622267—21no—
54#10622263—21no—
55#10622262—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×Dic44—22no—
95C2×Dic44—22no—
96C2×Dic44—22no—
97C2×Dic44—22no—
98C2×Dic44C2×C414yes—
99C2×Dic44C2×C414yes—
100#66922—22no—
101#66922C2×C414yes—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C4×Dic22—22no—
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C4×Dic22—41no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C4×Dic22C2×C414yes—
112C11×C4⋊C8C2×C414yes—
113C11×#97—22no—
114C11×#97—22no—
115C4×C8×C11—22no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66882—22no—
128#66881—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—41no—
133#66880—41no—
134#66880C2×C414yes—
135#66880C2×C414yes—
136#66880D414yes—
137#23014—111nomaximal, Sylow
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C22×C412yes—
167C2×Dic22C22×C412yes—
168C2×Dic22C22×C412yes—
169C2×Dic22C2×D412yes—
170C2×Dic22#4112yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C22×C412yes—
182C2×C8×C11C2×D412yes—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—41no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11C22×C412yes—
190C42×C11#4112yes—
191C4⋊Dic11—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C412yes—
202C4⋊Dic11C2×D412yes—
203Dic11⋊C4—24no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210C4×Dic11—24no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216Dic44—28no—
217Dic44—28no—
218C2×#462—111no—
219C2×#441—111no—
220C2×C4×Q16—111no—
221#2365—111no—
222#2351—111no—
223#1960—111no—
224#1949—111no—
225#1935—111no—
226#1933—111no—
227#1878—111no—
228#1878—111no—
229#1865—111no—
230#1863—111no—
231#1771D1111yescharacteristic
232#1763—111no—
233C23×C11C22×D411yescharacteristic
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11C4×D412yes—
250C2×C4×C11C4×D412yes—
251C2×C4×C11#13712yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282Dic22—22no—
283Dic22—22no—
284Dic22—22no—
285Dic22—22no—
286Dic22—22no—
287Dic22—22no—
288Dic22—22no—
289Dic22—41no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22C4×D414yes—
294C8×C11—22no—
295C8×C11—22no—
296C8×C11—22no—
297C8×C11—41no—
298C22×Q16—111no—
299C22×Q16—111no—
300C2×C4⋊Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8—111no—
306#462—118no—
307#441—224no—
308C4×Q16—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#97C2×D1111yescharacteristic
321C2×#97C2×D1111yescharacteristic
322C2×C4×C8C2×D1111yescharacteristic
323#391—111no—
324#391—111no—
325#389—111no—
326#389—111no—
327#389—221no—
328#389—221no—
329#389—221no—
330#387—221no—
331#387—221no—
332#382—111no—
333#382—221no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—221no—
336C4×C4⋊C4—221no—
337C4×C4⋊C4C2×D1111yescharacteristic
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336C2×D1111yescharacteristic
343#336C2×D1111yescharacteristic
344C22×C11C2×C4×D411yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57811yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11C2×C4×D411yescharacteristic
358C4×C11#52011yescharacteristic
359C4×C11#54711yescharacteristic
360C4×C11#55311yescharacteristic
361Dic11—24no—
362Dic11—42no—
363Dic11—42no—
364Dic11—42no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8—111no—
370C22×Q8—111no—
371C22×Q8—111no—
372C2×Q16—114no—
373C2×Q16—114no—
374C2×Q16—222no—
375C2×Q16—222no—
376C2×Q16—222no—
377C2×Q16—222no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—114no—
383C4⋊Q8—222no—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×Q8—222no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—441no—
391C4×Q8—441no—
392C4×Q8—441no—
393C4×Q8—441no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4D4411yescharacteristic
409C2×C4⋊C4D4411yescharacteristic
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#107—222no—
420#106—222no—
421C4⋊C8C4×D1114yes—
422#103—114no—
423#103—114no—
424#103—114no—
425#103—222no—
426#103—222no—
427#103—222no—
428#103—441no—
429#103—441no—
430#97—22no—
431#97—22no—
432C4×C8—22no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95D4411yescharacteristic
443#95D4411yescharacteristic
444C2×C11#236111yescharacteristic
445C2×C11C4×#13711yescharacteristic
446C2×C11#295011yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#327011yescharacteristic
449C2×C11#337411yescharacteristic
450C2×C11#337711yescharacteristic
451C2×Q8—112no—
452C2×Q8—112no—
453C2×Q8—112no—
454C2×Q8—112no—
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4C2×D4411yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4C23×D1111yescharacteristic
484Q16—228no—
485Q16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C2×C4×D1112yes—
496C2×C8C2×C4×D1112yes—
497C2×C8D4×D1112yes—
498C4⋊C4—22no—
499C4⋊C4—41no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—224no—
524C42—442no—
525C42—442no—
526C42—442no—
527C42—442no—
528C42—442no—
529C42C2×C4×D1112yes—
530C42#433912yes—
531C11#2301411yescharacteristic, complemented, Sylow
532C23C22×D4411yescharacteristic
533Q8—114no—
534Q8—222no—
535Q8—222no—
536Q8—222no—
537Q8—222no—
538Q8—222no—
539Q8—222no—
540Q8—222no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544Q8—441no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4C4×D4412yes—
585C2×C4C4×D4412yes—
586C2×C4#6696212yes—
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4#6704011yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#6704211yescharacteristic
593C8—22no—
594C8—22no—
595C8—22no—
596C8—41no—
597C22C2×C4×D4411yescharacteristic
598C22D4×D4411yescharacteristic
599C22#1062310711yescharacteristic
600C22C2×#6696211yescharacteristic
601C22#1062327911yescharacteristic
602C22#1062328411yescharacteristic
603C22#1062328411yescharacteristic
604C4—22no—
605C4—22no—
606C4—22no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—224no—
611C4—442no—
612C4—442no—
613C4—442no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4—881no—
618C4#1062303811yescharacteristic
619C4#1062306111yescharacteristic
620C4C4×D4×D1111yescharacteristic
621C4#1062310511yescharacteristic
622C2#1307163411yescharacteristic
623C2C4×#6696211yescharacteristic
624C2#1307748511yescharacteristic
625C2#1308017611yescharacteristic
626C2#1308019111yescharacteristic
627C2#1308142111yescharacteristic
628C2#1308146011yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1771C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#23014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
49. #10622462C4semidirect
531. C11#23014semidirect

Maximal subgroups

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

subgroupindex
C2×#106224622
C2×#106223292
C2×C4×Dic442
#130716722
#130715362
#130694362
#130693862
#130693062
#130692922
#130689562
#130688872
#130688732
#130684472
C11×#17712
#2301411