Finite Group Databasebeta

← #14910642

Subgroups — #14910642

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic44C211yesmaximal, characteristic, complemented
2#13070845C211yesmaximal, characteristic, complemented
3#13070813C212yesmaximal, complemented
4#13070755C211yesmaximal, characteristic, complemented
5#13070710C212yesmaximal, complemented
6#13070661C211yesmaximal, characteristic, complemented
7#13070532C212yesmaximal, complemented
8C4×#66891C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10C2×#10622130C212yesmaximal, complemented
11C11×#3334C211yesmaximal, characteristic
12C11×#547—21no—
13C22×Dic44C2212yes—
14D4×Dic22—21no—
15C11×#500C2211yescharacteristic
16C11×#480—22no—
17C11×#474—21no—
18C11×#466C2212yes—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×C11×#107C2212yes—
22C2×#66891C2211yescharacteristic
23C2×#66891C2212yes—
24#10622729C2212yes—
25C22×C11⋊C16C2212yes—
26#10622462—21no—
27#10622352—22no—
28#10622312C2211yescharacteristic
29C4×Dic44C2211yescharacteristic
30#10622200C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2212yes—
33#10622130C2212yes—
34#10622130C2211yescharacteristic
35#10622130C2212yes—
36#10622130C2212yes—
37#10622128C2212yes—
38#10622128C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—41no—
42C22×Dic22—22no—
43C2×C11×D8C2311yescharacteristic
44C22×C8×C11C2312yes—
45C11×C4⋊Q8—21no—
46C11×#123—42no—
47C11×C22⋊Q8—41no—
48C11×#121—22no—
49C4×D4×C11—21no—
50C4×D4×C11D411yescharacteristic
51C2×C11×C4⋊C4—22no—
52D4×Dic11—41no—
53#66977—22no—
54C2×Dic44—24no—
55C2×Dic44—22no—
56C2×Dic44—21no—
57C2×Dic44—42no—
58C2×Dic44C2312yes—
59C2×Dic44C2311yescharacteristic
60#66941—41no—
61#66931—42no—
62#66922—21no—
63C4×Dic22—21no—
64C11×#107—21no—
65C11×#107—22no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×C4⋊C8D411yescharacteristic
69C11×#102—21no—
70C11×#102—22no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2311yescharacteristic
73#66891—22no—
74#66891—42no—
75#66882C2311yescharacteristic
76#66880—22no—
77#66880—21no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33865—111nomaximal, Sylow
83C11×#41—84no—
84C2×Q8×C11—41no—
85C2×D4×C11—21no—
86C2×D4×C11—42no—
87C2×D4×C11D811yescharacteristic
88C22×C4×C11—42no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D412yes—
91C22×Dic11—42no—
92C2×Dic22—21no—
93C2×Dic22—22no—
94C2×Dic22—44no—
95C2×Dic22—42no—
96C2×Dic22—82no—
97C11×D8—21no—
98C11×D8—21no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D412yes—
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4D811yescharacteristic
109C11×C22⋊C4—41no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4D812yes—
112C42×C11C2×D411yescharacteristic
113C22⋊Dic11—42no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—42no—
119C4×Dic11—41no—
120Dic44—22no—
121Dic44—21no—
122Dic44—22no—
123Dic44—44no—
124Dic44—81no—
125Dic44#4112yescomplemented
126C11⋊C16—21no—
127C11⋊C16—21no—
128C11⋊C16—22no—
129#3334D1111yescharacteristic
130D4×Q16—111no—
131#2241—111no—
132#2235—112no—
133#2225—111no—
134#2217—112no—
135#2208—111no—
136#2185—112no—
137C4×SD32—111no—
138D4×C16—111no—
139C2×#358—112no—
140C23×C11—41no—
141C23×C11C2×D812yes—
142Q8×C11—82no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—84no—
146D4×C11SD3214yescomplemented
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—84no—
152C2×C4×C11—82no—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×D812yes—
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—84no—
161Dic22—22no—
162Dic22—41no—
163Dic22—42no—
164Dic22—42no—
165Dic22—84no—
166C8×C11—22no—
167C8×C11—21no—
168C8×C11C2×#4111yescharacteristic
169C8×C11H(5,𝔽2)11yescharacteristic
170C22×Q16—112no—
171D4×Q8—221no—
172#547—21no—
173C2×SD32—111no—
174C2×SD32—112no—
175C22×C16—112no—
176#500C2×D1111yescharacteristic
177#494—111no—
178#480—22no—
179#474—21no—
180#467—112no—
181#466C2×D1112yes—
182#462—221no—
183#451—222no—
184C4×Q16—111no—
185C4×D8C2×D1111yescharacteristic
186C8×D4C2×D1111yescharacteristic
187C2×#107C2×D1112yes—
188#367—111no—
189#367—112no—
190C4⋊C16—111no—
191#358—111no—
192#358—112no—
193#358—112no—
194#358—112no—
195#358—112no—
196#357—111no—
197C22⋊C16—112no—
198C4×C16—111no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11C2×SD3214yes—
205C22×C11C22×D811yescharacteristic
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—81no—
209C4×C11—82no—
210C4×C11C2×SD3212yes—
211C4×C11#54611yescharacteristic
212C4×C11#57711yescharacteristic
213Dic11—42no—
214Dic11—81no—
215Dic11—82no—
216C2×#41—41no—
217C22×Q8—222no—
218C2×Q16—111no—
219C2×Q16—112no—
220C2×Q16—224no—
221C2×Q16—222no—
222C2×Q16—221no—
223C2×Q16—442no—
224C2×D8C22×D1111yescharacteristic
225C22×C8C22×D1112yes—
226C4⋊Q8—21no—
227C4⋊Q8—221no—
228C4⋊Q8—441no—
229#123—42no—
230C22⋊Q8—41no—
231C22⋊Q8—222no—
232C22⋊Q8—442no—
233#121—22no—
234C4×Q8—221no—
235C4×D4—21no—
236C4×D4—441no—
237C4×D4C22⋊D1111yescharacteristic
238C2×C4⋊C4—22no—
239SD32—222no—
240SD32—442no—
241C2×C16—111no—
242C2×C16—111no—
243C2×C16—112no—
244C2×C16—442no—
245#107—22no—
246#107—21no—
247#107—111no—
248#107C22×D1111yescharacteristic
249#107C22×D1112yes—
250C4⋊C8C22⋊D1111yescharacteristic
251#103—221no—
252#103—222no—
253#102—21no—
254#102—22no—
255C22⋊C8C22⋊D1112yes—
256C4×C8C22×D1111yescharacteristic
257C2×C11—24no—
258C2×C11—161no—
259C2×C11#329411yescharacteristic
260C2×C11C22×SD3211yescharacteristic
261C2×C11#341711yescharacteristic
262#41—84no—
263C2×Q8—41no—
264C2×Q8—221no—
265C2×Q8—222no—
266C2×Q8—444no—
267C2×Q8—442no—
268C2×Q8—882no—
269C2×D4—21no—
270C2×D4—42no—
271C2×D4#432311yescharacteristic
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—442no—
275C22×C4C2×C22⋊D1112yes—
276Q16—112no—
277Q16—222no—
278Q16—221no—
279Q16—222no—
280Q16—444no—
281Q16—881no—
282D8—21no—
283D8—21no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8C2×C22⋊D1111yescharacteristic
287C2×C8C2×C22⋊D1112yes—
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—221no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—442no—
297C4⋊C4—441no—
298C4⋊C4#432311yescharacteristic
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—442no—
302C22⋊C4#432312yes—
303C42—441no—
304C42C2×C22⋊D1111yescharacteristic
305C16—221no—
306C16—221no—
307C16—222no—
308C11#3386511yescharacteristic, complemented, Sylow
309C23—41no—
310C23C2×#432312yes—
311Q8—82no—
312Q8—222no—
313Q8—441no—
314Q8—442no—
315Q8—442no—
316Q8—884no—
317D4—41no—
318D4—41no—
319D4—84no—
320D4#6689114yescomplemented
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—84no—
326C2×C4—82no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—884no—
331C2×C4C2×#432311yescharacteristic
332C2×C4C2×#432312yes—
333C2×C4C2×#432311yescharacteristic
334C2×C4C22×C22⋊D1111yescharacteristic
335C8—22no—
336C8—21no—
337C8#41×D1111yescharacteristic
338C8#6704211yescharacteristic
339C22—22no—
340C22—22no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22C2×#6689114yes—
345C22C22×#432311yescharacteristic
346C4—22no—
347C4—21no—
348C4—81no—
349C4—82no—
350C4—442no—
351C4—882no—
352C4—881no—
353C4C2×#6689112yes—
354C4#1062336011yescharacteristic
355C4#1062336811yescharacteristic
356C2—24no—
357C2—161no—
358C2#1308042311yescharacteristic
359C2C22×#6689111yescharacteristic
360C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. D4×Dic44C2semidirect
2. #13070845C2semidirect
3. #13070813C2semidirect
4. #13070755C2semidirect
5. #13070710C2semidirect
6. #13070661C2semidirect
7. #13070532C2semidirect
8. C4×#66891C2semidirect
9. D4×C11⋊C16C2semidirect
10. C2×#10622130C2semidirect
125. Dic44#41semidirect
146. D4×C11SD32semidirect
308. C11#33865semidirect
320. D4#66891semidirect

Maximal subgroups

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

subgroupindex
D4×Dic442
#130708452
#130708132
#130707552
#130707102
#130706612
#130705322
C4×#668912
D4×C11⋊C162
C2×#106221302
C11×#33342
#3386511