Finite Group Databasebeta

← #14816945

Subgroups — #14816945

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622403C211yesmaximal, characteristic
2#13072473C211yesmaximal, characteristic
3#13071534C211yesmaximal, characteristic
4#13070161C211yesmaximal, characteristic
5#13070101C211yesmaximal, characteristic
6#13070010C211yesmaximal, characteristic
7#13069951C211yesmaximal, characteristic
8#13069347C211yesmaximal, characteristic
9#13069170C211yesmaximal, characteristic
10#13068957C211yesmaximal, characteristic
11#13068955C211yesmaximal, characteristic
12#13068882C211yesmaximal, characteristic
13#13068881C211yesmaximal, characteristic
14#13068872C211yesmaximal, characteristic
15C2×C11×#479C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C11×#479—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622597—21no—
35#10622595—21no—
36#10622591—21no—
37#10622590—21no—
38#10622590C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622586—21no—
41#10622586—21no—
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622541—21no—
51#10622541C2211yescharacteristic
52#10622403—24no—
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#125—22no—
66C11×#125—41no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81C2×#4326—22no—
82C2×#4326—22no—
83C2×#4326Q814yes—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66940—22no—
104#66940—41no—
105C11×#107—22no—
106C11×#106—22no—
107C11×C4⋊C8—22no—
108C11×#103—22no—
109C11×#103D414yes—
110#66899—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66882—22no—
124#66880—22no—
125#66880—22no—
126C8×Dic11—22no—
127#66874—41no—
128#66872—41no—
129#66871—22no—
130#26383—111nomaximal, Sylow
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×Q812yes—
136C2×Q8×C11#4112yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22C2×Q812yes—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×D412yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C2×D412yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176#4326—28no—
177C4⋊Dic11—24no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11#4112yes—
186Dic11⋊C4—22no—
187Dic11⋊C4—41no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—24no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C2×Q812yes—
205C2×#479D1111yescharacteristic
206C2×C4×Q16—111no—
207#2453—111no—
208#2351—111no—
209#2097—111no—
210#2085—111no—
211#2068—111no—
212#2059—111no—
213#1942—111no—
214#1916—111no—
215#1878—111no—
216#1878—111no—
217#1865—111no—
218#1865—111no—
219#1863—111no—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11C22⋊Q814yes—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
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—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×Q811yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
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#13512yes—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—22no—
278C8×C11—41no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C22×Q16—111no—
282C2×#125C2×D1111yescharacteristic
283C2×C4×Q8—111no—
284C2×C4×Q8—111no—
285C2×C4×Q8—111no—
286C2×C4×Q8C2×D1111yescharacteristic
287#479—24no—
288C4×Q16—224no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#107C2×D1111yescharacteristic
292C2×#106—111no—
293C2×#106C2×D1111yescharacteristic
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103C2×D1111yescharacteristic
300C2×#103C2×D1111yescharacteristic
301C2×C4×C8—111no—
302#400—221no—
303#398—221no—
304#391—111no—
305#391—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#389—221no—
311#389—221no—
312#389—221no—
313#387—221no—
314#382—111no—
315#382—221no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—221no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326C22×C11#52511yescharacteristic
327C22×C11D4211yescharacteristic
328C22×C11D4×Q811yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57811yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—24no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×C22⋊Q811yescharacteristic
340C4×C11#53911yescharacteristic
341C4×C11#54711yescharacteristic
342C4×C11#55411yescharacteristic
343Dic11—22no—
344Dic11—41no—
345Dic11—42no—
346Dic11—41no—
347Dic11—42no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×Q8C22×D1111yescharacteristic
353C2×Q16—114no—
354C2×Q16—222no—
355C2×Q16—222no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360#125—22no—
361#125—41no—
362C4×Q8—22no—
363C4×Q8—41no—
364C4×Q8—222no—
365C4×Q8—222no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×Q8—441no—
369C4×Q8—441no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C42—21no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395#107—22no—
396#107—222no—
397#107—222no—
398#106—22no—
399#106—441no—
400C4⋊C8—22no—
401#103—22no—
402#103—222no—
403#103—222no—
404#103—222no—
405#103—441no—
406#103C22⋊D1114yes—
407C4×C8—222no—
408#95—111no—
409#95—111no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420C2×C11#244911yescharacteristic
421C2×C11#310211yescharacteristic
422C2×C11#312711yescharacteristic
423C2×C11#326911yescharacteristic
424C2×C11#328511yescharacteristic
425C2×C11#338311yescharacteristic
426C2×C11#339011yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8Q8×D1112yes—
437C2×Q8#434312yes—
438C2×Q8C2×C22⋊D1112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454Q16—228no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—112no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8C2×C22⋊D1112yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—112no—
476C4⋊C4—222no—
477C4⋊C4—224no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—441no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4C2×C22⋊D1112yes—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—224no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—442no—
500C42—442no—
501C11#2638311yescharacteristic, complemented, Sylow
502C23C2×D4×D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—22no—
506Q8—222no—
507Q8—222no—
508Q8—441no—
509Q8—441no—
510Q8#6699914yes—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—112no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—222no—
541C2×C4—221no—
542C2×C4—222no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4#6703711yescharacteristic
554C2×C4C2×Q8×D1111yescharacteristic
555C2×C4C2×#434311yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704311yescharacteristic
558C2×C4C22×C22⋊D1111yescharacteristic
559C8—22no—
560C8—41no—
561C8—222no—
562C8—441no—
563C22#1062315811yescharacteristic
564C22#1062316311yescharacteristic
565C22D11×#13511yescharacteristic
566C22#1062330211yescharacteristic
567C22#1062330811yescharacteristic
568C22#1062331011yescharacteristic
569C22D4×C22⋊D1111yescharacteristic
570C4—24no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—222no—
577C4—442no—
578C4—441no—
579C4—441no—
580C4—442no—
581C4—441no—
582C4—881no—
583C4—881no—
584C4#1062316711yescharacteristic
585C4#1062317611yescharacteristic
586C4C2×#6699911yescharacteristic
587C4#1062335511yescharacteristic
588C2#1307242111yescharacteristic
589C2#1307864111yescharacteristic
590C2#1307891811yescharacteristic
591C2#1308016511yescharacteristic
592C2#1308035111yescharacteristic
593C2#1308150211yescharacteristic
594C2#1308158211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#479D11
hypocenterC11#26383
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
501. C11#26383semidirect

Maximal subgroups

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

subgroupindex
C2×#106224032
#130724732
#130715342
#130701612
#130701012
#130700102
#130699512
#130693472
#130691702
#130689572
#130689552
#130688822
#130688812
#130688722
C2×C11×#4792
#2638311