Finite Group Databasebeta

← #14803242

Subgroups — #14803242

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622316C211yesmaximal, characteristic
2C2×#10622442C211yesmaximal, characteristic
3#13073604C211yesmaximal, characteristic
4#13071710C211yesmaximal, characteristic
5#13070010C211yesmaximal, characteristic
6#13069996C211yesmaximal, characteristic
7#13069863C211yesmaximal, characteristic
8#13069863C211yesmaximal, characteristic
9#13069538C211yesmaximal, characteristic
10#13069538C211yesmaximal, characteristic
11#13069538C211yesmaximal, characteristic
12#13069258C211yesmaximal, characteristic
13#13069251C211yesmaximal, characteristic
14#13068447C211yesmaximal, characteristic
15C11×#1940C211yesmaximal, characteristic
16C2×#66923C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40#10622598—21no—
41#10622598—21no—
42#10622591—21no—
43#10622585—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622442—24no—
52#10622316—24no—
53#10622274—21no—
54#10622274—21no—
55#10622265—21no—
56#10622262—21no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93#66923—22no—
94#66923D414yes—
95#66922—22no—
96#66922—22no—
97#66922—22no—
98#66922—22no—
99#66922—41no—
100#66922—41no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8—41no—
105C11×C4⋊C8—41no—
106C11×#97—22no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66882—22no—
119#66881—22no—
120#66880—22no—
121#66880—22no—
122#66880—22no—
123#66880—22no—
124#66880—22no—
125#66880—22no—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—41no—
131#66880—41no—
132#25290—111nomaximal, Sylow
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—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#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
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—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11C2×D412yes—
185C42×C11#4112yes—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11C2×D412yes—
200C4⋊Dic11C2×D412yes—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—81no—
210C4×Dic11—81no—
211C2×#491—111no—
212C2×#479—111no—
213#2546—111no—
214#2370—111no—
215#2068—111no—
216#2066—111no—
217#2043—111no—
218#2043—111no—
219#1981—111no—
220#1981—111no—
221#1981—111no—
222#1940D1111yescharacteristic
223#1928—111no—
224#1927—111no—
225#1763—111no—
226C23×C11C22×D411yescharacteristic
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
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#12112yes—
242C2×C4×C11#12112yes—
243C2×C4×C11#13712yes—
244C2×C4×C11#13712yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
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—
275Dic22—22no—
276Dic22—22no—
277Dic22—41no—
278Dic22—41no—
279Dic22—41no—
280Dic22—41no—
281Dic22—41no—
282Dic22—41no—
283Dic22—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287C8×C11—41no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11—41no—
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8—111no—
293C2×C4⋊Q8—111no—
294C2×#125—111no—
295C2×C4×Q8—111no—
296#491—224no—
297#479—224no—
298C2×#107—111no—
299C2×#106—111no—
300C2×C4⋊C8C2×D1111yescharacteristic
301C2×C4⋊C8C2×D1111yescharacteristic
302C2×C4⋊C8C2×D1111yescharacteristic
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#97C2×D1111yescharacteristic
316#398—221no—
317#398—221no—
318#391—111no—
319#391—111no—
320#389—111no—
321#389—111no—
322#389—221no—
323#389—221no—
324#389—221no—
325#387—221no—
326#387—221no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—221no—
331C4×C4⋊C4C2×D1111yescharacteristic
332#340—111no—
333#340—111no—
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336C22×C11C2×#12111yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C22×C11C2×#13711yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11#52911yescharacteristic
350C4×C11#54211yescharacteristic
351C4×C11#54811yescharacteristic
352C4×C11#55011yescharacteristic
353Dic11—42no—
354Dic11—42no—
355Dic11—42no—
356Dic11—42no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361C22×Q8—111no—
362C22×Q8—111no—
363C22×Q8—111no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C22×C8C22×D1111yescharacteristic
368C4⋊Q8—222no—
369C4⋊Q8—222no—
370C4⋊Q8—222no—
371C4⋊Q8—222no—
372C4⋊Q8—441no—
373C4⋊Q8—441no—
374#125—114no—
375#125—222no—
376C4×Q8—222no—
377C4×Q8—222no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4D4411yescharacteristic
395C2×C4⋊C4D4411yescharacteristic
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403#107—222no—
404#106—222no—
405C4⋊C8—22no—
406C4⋊C8—41no—
407C4⋊C8—41no—
408#103—222no—
409#103—222no—
410#103—222no—
411#103—222no—
412#103—222no—
413#103—222no—
414#103—222no—
415#103—222no—
416#103—222no—
417#103—222no—
418#103—441no—
419#103—441no—
420#97—22no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95D4411yescharacteristic
431#95D4411yescharacteristic
432C2×C11#242611yescharacteristic
433C2×C11#303911yescharacteristic
434C2×C11#304611yescharacteristic
435C2×C11#331211yescharacteristic
436C2×C11#332011yescharacteristic
437C2×C11#337211yescharacteristic
438C2×C11#337411yescharacteristic
439C2×Q8—112no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C2×D4411yescharacteristic
470C22×C4C2×D4411yescharacteristic
471C22×C4C23×D1111yescharacteristic
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—881no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—442no—
512C42—442no—
513C42—881no—
514C42—881no—
515C42D4×D1112yes—
516C42#434312yes—
517C11#2529011yescharacteristic, complemented, Sylow
518C23C22×D4411yescharacteristic
519Q8—222no—
520Q8—222no—
521Q8—441no—
522Q8—441no—
523Q8—441no—
524Q8—441no—
525Q8—441no—
526Q8—441no—
527Q8—441no—
528Q8—441no—
529Q8—441no—
530Q8—441no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4#6694812yes—
570C2×C4#6694812yes—
571C2×C4#6696212yes—
572C2×C4#6696212yes—
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#6703711yescharacteristic
575C2×C4C2×#434311yescharacteristic
576C2×C4#6704011yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C22C2×#6694811yescharacteristic
584C22#1062308511yescharacteristic
585C22#1062310711yescharacteristic
586C22C2×#6696211yescharacteristic
587C22C2×#6696211yescharacteristic
588C22#1062328211yescharacteristic
589C22#1062328411yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—442no—
597C4—442no—
598C4—442no—
599C4—442no—
600C4—881no—
601C4—881no—
602C4—881no—
603C4—881no—
604C4#1062313011yescharacteristic
605C4#1062316411yescharacteristic
606C4#1062322211yescharacteristic
607C4#1062326411yescharacteristic
608C2#1307218011yescharacteristic
609C2#1307810411yescharacteristic
610C2#1307816811yescharacteristic
611C2#1308066911yescharacteristic
612C2#1308078911yescharacteristic
613C2#1308139911yescharacteristic
614C2#1308142111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1940C2
socle, prime radicalC23×C11C22×D4
hypercenter#1940D11
hypocenterC11#25290
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
517. C11#25290semidirect

Maximal subgroups

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

subgroupindex
C2×#106223162
C2×#106224422
#130736042
#130717102
#130700102
#130699962
#130698632
#130695382
#130692582
#130692512
#130684472
C11×#19402
#2529011