Finite Group Databasebeta

← #14910177

Subgroups — #14910177

Order 2816.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079275C211yesmaximal, characteristic, complemented
2#13070780C211yesmaximal, characteristic, complemented
3#13070773C211yesmaximal, characteristic, complemented
4#13070765C211yesmaximal, characteristic, complemented
5#13070755C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic
7#13070722C211yesmaximal, characteristic, complemented
8#13070710C211yesmaximal, characteristic
9#13070705C211yesmaximal, characteristic, complemented
10#13070675C211yesmaximal, characteristic, complemented
11#13070675C211yesmaximal, characteristic, complemented
12#13070666C211yesmaximal, characteristic, complemented
13#13070661C211yesmaximal, characteristic, complemented
14#13070375C211yesmaximal, characteristic, complemented
15C11×#3175C211yesmaximal, characteristic
16C11×#542—21no—
17#10623049—21no—
18C11×#500C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#489—21no—
21C11×#468—21no—
22C11×#467C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C11×#440—21no—
25C4×C11×Q16C2211yescharacteristic
26C4×C11×D8C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32#10622750—21no—
33#10622729C2211yescharacteristic
34#10622729C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622329—21no—
38#10622316—21no—
39#10622312C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41C4×Dic44C2211yescharacteristic
42#10622296C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622130C2211yescharacteristic
50#10622130C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C2×C11×M16D411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C11×#126—41no—
66C11×#124—21no—
67C11×#124—41no—
68C11×#123—41no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—41no—
71C11×#121—21no—
72C4×Q8×C11—21no—
73C4×D4×C11—21no—
74C11×#117D411yescharacteristic
75#66977—21no—
76#66977—21no—
77C2×Dic44—21no—
78C2×Dic44C2311yescharacteristic
79C2×Dic44C2311yescharacteristic
80#66942—41no—
81#66942—41no—
82#66932—41no—
83#66932—41no—
84#66923—21no—
85#66922—21no—
86C4×Dic22—21no—
87C4×Dic22—21no—
88C11×#107—21no—
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#103—21no—
92C11×#103—21no—
93C11×#102—21no—
94C11×#102—21no—
95C11×#97D411yescharacteristic
96C11×#97D411yescharacteristic
97C4×C8×C11C2311yescharacteristic
98C4×C8×C11C2311yescharacteristic
99#66893—41no—
100#66893—41no—
101#66891—41no—
102#66891—41no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66880—21no—
107#66880—21no—
108#66880—21no—
109#66880—21no—
110#66876—41no—
111C2×C11⋊C16—41no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33824—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—41no—
119C2×D4×C11—21no—
120C2×D4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C2×Dic22—21no—
124C2×Dic22—21no—
125C11×Q16—21no—
126C11×Q16—21no—
127C11×SD16—42no—
128C11×D8—21no—
129C11×D8—21no—
130C11×M16—41no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4D811yescharacteristic
143C11×C4⋊C4D811yescharacteristic
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4D811yescharacteristic
150C11×C22⋊C4D811yescharacteristic
151C42×C11—41no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C22⋊Dic11—41no—
155C22⋊Dic11—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168Dic44—21no—
169Dic44—21no—
170Dic44—21no—
171Dic44—21no—
172Dic44—42no—
173C11⋊C16—21no—
174C11⋊C16—21no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177#3177—111no—
178#3175D1111yescharacteristic
179#2229—111no—
180#2228—111no—
181#2227—111no—
182#2225—111no—
183#2220—111no—
184#2219—111no—
185#2217—111no—
186#2216—111no—
187#2211—111no—
188#2211—111no—
189#2209—111no—
190#2208—111no—
191#2151—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194Q8×C11—41no—
195Q8×C11—41no—
196Q8×C11—161no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—161no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—161no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216Dic22—41no—
217Dic22—41no—
218Dic22—41no—
219Dic22—41no—
220C8×C11—21no—
221C8×C11—21no—
222C8×C11—21no—
223C8×C11H(5,𝔽2)11yescharacteristic
224C8×C112−1+411yescharacteristic
225#542—21no—
226#541—221no—
227C2×Q32—111no—
228C2×Q32—111no—
229C2×SD32—111no—
230C2×SD32—111no—
231C2×M32—111no—
232C22×C16—111no—
233#500C2×D1111yescharacteristic
234#499—111no—
235#495C2×D1111yescharacteristic
236#494—111no—
237#491—221no—
238#489—21no—
239#470—221no—
240#468—21no—
241#467—111no—
242#467—111no—
243#467C2×D1111yescharacteristic
244#466C2×D1111yescharacteristic
245#441—221no—
246#440—21no—
247C4×Q16—111no—
248C4×Q16—111no—
249C4×Q16C2×D1111yescharacteristic
250C4×D8C2×D1111yescharacteristic
251#405C2×D1111yescharacteristic
252#367—111no—
253#367—111no—
254#366—111no—
255#366—111no—
256C4⋊C16—111no—
257C4⋊C16—111no—
258C4⋊C16—111no—
259C4⋊C16—111no—
260#358—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#357—111no—
267#357—111no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11#53711yescharacteristic
284C4×C11#57511yescharacteristic
285Dic11—81no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×Q16—111no—
290C2×Q16—111no—
291C2×Q16—221no—
292C2×Q16C22×D1111yescharacteristic
293C2×SD16—21no—
294C2×D8C22×D1111yescharacteristic
295C2×M16C22⋊D1111yescharacteristic
296C22×C8C22×D1111yescharacteristic
297C4⋊Q8—21no—
298C4⋊Q8—221no—
299#126—41no—
300#126—441no—
301#126—441no—
302#125—221no—
303#125—441no—
304#125—441no—
305#124—21no—
306#124—41no—
307#123—41no—
308C22⋊Q8—21no—
309C22⋊Q8—41no—
310C22⋊Q8—221no—
311C22⋊Q8—221no—
312#121—21no—
313C4×Q8—21no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×D4—21no—
317#117C22⋊D1111yescharacteristic
318Q32—441no—
319Q32—441no—
320SD32—441no—
321SD32—441no—
322M32—441no—
323C2×C16—111no—
324C2×C16—111no—
325C2×C16—111no—
326C2×C16—111no—
327C2×C16—441no—
328#107—21no—
329#107—111no—
330#107—111no—
331#107C22×D1111yescharacteristic
332#107C22×D1111yescharacteristic
333#106—221no—
334#103—21no—
335#103—21no—
336#103—221no—
337#103—221no—
338#103—221no—
339#103—221no—
340#102—21no—
341#102—21no—
342#97C22⋊D1111yescharacteristic
343#97C22⋊D1111yescharacteristic
344C4×C8C22×D1111yescharacteristic
345C4×C8C22×D1111yescharacteristic
346C2×C11—41no—
347C2×C11—161no—
348C2×C11#324511yescharacteristic
349C2×C11#341611yescharacteristic
350C2×C11#341711yescharacteristic
351C2×Q8—21no—
352C2×Q8—41no—
353C2×Q8—221no—
354C2×Q8—221no—
355C2×D4—21no—
356C2×D4—41no—
357C22×C4—41no—
358C22×C4C2×C22⋊D1111yescharacteristic
359Q16—21no—
360Q16—21no—
361Q16—221no—
362Q16—221no—
363Q16—221no—
364Q16—221no—
365Q16—442no—
366SD16—42no—
367D8—21no—
368D8—21no—
369M16—41no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×C22⋊D1111yescharacteristic
373C2×C8C2×C22⋊D1111yescharacteristic
374C2×C8C2×C22⋊D1111yescharacteristic
375C2×C8C23×D1111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4#432311yescharacteristic
392C4⋊C4#432311yescharacteristic
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4#432311yescharacteristic
401C22⋊C4#432311yescharacteristic
402C42—41no—
403C42—441no—
404C42—441no—
405C42C2×C22⋊D1111yescharacteristic
406C42C2×C22⋊D1111yescharacteristic
407C16—221no—
408C16—221no—
409C16—221no—
410C16—221no—
411C11#3382411yescharacteristic, complemented, Sylow
412C23—41no—
413C23C2×#432311yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—161no—
417Q8—441no—
418Q8—441no—
419Q8—441no—
420Q8—441no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—161no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4C2×#432311yescharacteristic
435C2×C4C2×#432311yescharacteristic
436C2×C4C2×#432311yescharacteristic
437C2×C4C2×#432311yescharacteristic
438C2×C4C2×#432311yescharacteristic
439C2×C4C22×C22⋊D1111yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8#6704211yescharacteristic
444C8#6704311yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C22×#432311yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—881no—
461C4—881no—
462C4—881no—
463C4—881no—
464C4#1062335311yescharacteristic
465C4#1062336411yescharacteristic
466C2—41no—
467C2—161no—
468C2#1307992311yescharacteristic
469C2#1308176311yescharacteristic
470C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3175C2
socleC22×C11C22×D8
prime radicalC11×#466C22
hypercenter#3175D11
hypocenterC11#33824
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13079275C2semidirect
2. #13070780C2semidirect
3. #13070773C2semidirect
4. #13070765C2semidirect
5. #13070755C2semidirect
7. #13070722C2semidirect
9. #13070705C2semidirect
10. #13070675C2semidirect
11. #13070675C2semidirect
12. #13070666C2semidirect
13. #13070661C2semidirect
14. #13070375C2semidirect
411. C11#33824semidirect

Maximal subgroups

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

subgroupindex
#130792752
#130707802
#130707732
#130707652
#130707552
#130707272
#130707222
#130707102
#130707052
#130706752
#130706662
#130706612
#130703752
C11×#31752
#3382411