Finite Group Databasebeta

← #14822338

Subgroups — #14822338

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073132C211yesmaximal, characteristic
2#13070024C211yesmaximal, characteristic
3#13069997C211yesmaximal, characteristic
4#13069859C211yesmaximal, characteristic
5#13069859C211yesmaximal, characteristic
6#13069295C211yesmaximal, characteristic
7#13069247C211yesmaximal, characteristic
8#13069194C211yesmaximal, characteristic
9#13069194C211yesmaximal, characteristic
10#13069175C211yesmaximal, characteristic
11#13068884C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic
13#13068621C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic
15C11×#2365C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66942—21no—
20C11×#391C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#389—21no—
23C11×#387—21no—
24C11×#387—21no—
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622596—21no—
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622548C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622272—21no—
48#10622266—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—41no—
66C4×Q8×C11—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
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—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66942—44no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66899—22no—
105#66899—22no—
106#66899—22no—
107#66899—22no—
108#66899—22no—
109#66899—22no—
110#66899—41no—
111#66899—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66872—22no—
118#66872—22no—
119C4⋊(C11⋊C8)—41no—
120C4×C11⋊C8—41no—
121#26756—111nomaximal, Sylow
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11#4112yes—
133C2×Q8×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
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—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4SD1614yes—
158C11×C4⋊C4#4112yes—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166C42×C11—42no—
167C42×C11—42no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—42no—
176C4⋊Dic11—42no—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182C4×Dic11—42no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195#2506—111no—
196#2365D1111yescharacteristic
197#2072—111no—
198#2066—111no—
199#2043—111no—
200#2043—111no—
201#1933—111no—
202#1927—111no—
203#1919—111no—
204#1919—111no—
205#1916—111no—
206#1865—111no—
207#1865—111no—
208#1803—111no—
209C4×#103—111no—
210C23×C11C22×D411yescharacteristic
211Q8×C11—22no—
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
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—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C2×SD1612yes—
247C2×C4×C11C2×SD1612yes—
248C2×C4×C11C2×SD1612yes—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—22no—
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—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C2×C4⋊Q8C2×D1111yescharacteristic
272C2×#125—221no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×Q8C2×D1111yescharacteristic
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×#103—111no—
279C2×#103—111no—
280C2×#103—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×C4×C8—111no—
287#400—221no—
288#398—221no—
289#391C2×D1111yescharacteristic
290#391C2×D1111yescharacteristic
291#389—21no—
292#389—111no—
293#389—111no—
294#389—111no—
295#389—111no—
296#387—21no—
297#387—21no—
298#387—221no—
299#384—111no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C4⋊C4C2×D1111yescharacteristic
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314C22×C11#52511yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11#54811yescharacteristic
317C22×C11C22×SD1611yescharacteristic
318C22×C11#57511yescharacteristic
319C22×C11#57811yescharacteristic
320C22×C11#57811yescharacteristic
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—41no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11#52911yescharacteristic
332C4×C11#53911yescharacteristic
333C4×C11#55211yescharacteristic
334C4×C11#55311yescharacteristic
335Dic11—42no—
336Dic11—81no—
337Dic11—81no—
338Dic11—81no—
339C22×Q8C22×D1111yescharacteristic
340C22×Q8C22×D1111yescharacteristic
341C22×C8—111no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—111no—
345C4⋊Q8—22no—
346C4⋊Q8—22no—
347#125—444no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—41no—
351C4×Q8—41no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1111yescharacteristic
377#106—222no—
378#106—222no—
379C4⋊C8—441no—
380#103—222no—
381#103—222no—
382#103—222no—
383#103—222no—
384#103—222no—
385#103—222no—
386#103—441no—
387#103—441no—
388C4×C8—441no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95C22⋊D1111yescharacteristic
400#95C22⋊D1111yescharacteristic
401C2×C11#246011yescharacteristic
402C2×C11#310311yescharacteristic
403C2×C11#312711yescharacteristic
404C2×C11#329811yescharacteristic
405C2×C11#331511yescharacteristic
406C2×C11#335911yescharacteristic
407C2×C11#337711yescharacteristic
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8#433912yes—
419C2×Q8#433912yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4—112no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—442no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4#432514yes—
470C4⋊C4#434112yes—
471C42—21no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—42no—
478C42—42no—
479C42—42no—
480C42—442no—
481C11#2675611yescharacteristic, complemented, Sylow
482C23C22×C22⋊D1111yescharacteristic
483Q8—22no—
484Q8—22no—
485Q8—22no—
486Q8—22no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—222no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C2×#432512yes—
531C2×C4C2×#432512yes—
532C2×C4C2×#432512yes—
533C2×C4C2×#433911yescharacteristic
534C2×C4C2×#433911yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C2×C4#6703711yescharacteristic
537C2×C4#41×D1111yescharacteristic
538C2×C4#6704311yescharacteristic
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C22#1062332211yescharacteristic
544C22#1062333711yescharacteristic
545C22C22×#432511yescharacteristic
546C22#1062335311yescharacteristic
547C22#1062336211yescharacteristic
548C22#1062336911yescharacteristic
549C22#1062336911yescharacteristic
550C4—22no—
551C4—22no—
552C4—22no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—81no—
560C4—442no—
561C4—881no—
562C4—881no—
563C4—881no—
564C4#1062306911yescharacteristic
565C4#1062307111yescharacteristic
566C4#1062307211yescharacteristic
567C4#1062309511yescharacteristic
568C2#1307256211yescharacteristic
569C2#1307864711yescharacteristic
570C2#1307891611yescharacteristic
571C2#1308048111yescharacteristic
572C2#1308071211yescharacteristic
573C2#1308125411yescharacteristic
574C2#1308145211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socle, prime radicalC23×C11C22×D4
hypercenter#2365D11
hypocenterC11#26756
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
481. C11#26756semidirect

Maximal subgroups

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

subgroupindex
#130731322
#130700242
#130699972
#130698592
#130692952
#130692472
#130691942
#130691752
#130688842
#130686212
C4×#668992
C11×#23652
#2675611