Finite Group Databasebeta

← #14910648

Subgroups — #14910648

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
1#13080964C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic, complemented
3#13070811C212yesmaximal, complemented
4#13070758C211yesmaximal, characteristic, complemented
5#13070714C212yesmaximal, complemented
6#13070658C211yesmaximal, characteristic, complemented
7#13070533C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10C2×#10622202C212yesmaximal, complemented
11D4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2212yes—
13D4×Q8×C11—21no—
14#10623086—21no—
15C11×#494C2211yescharacteristic
16C11×#467C2212yes—
17C11×#462—21no—
18C11×#451—22no—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66892C2211yescharacteristic
22C2×#66892C2212yes—
23#10622728C2212yes—
24C2×#66882C2212yes—
25C22×C11⋊C16C2212yes—
26#10622459—21no—
27#10622349—22no—
28C4×D88C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2212yes—
31#10622202C2212yes—
32#10622202C2211yescharacteristic
33#10622202C2212yes—
34#10622202C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622129C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C22×Q8×C11—22no—
42C2×#4341—41no—
43C2×C11×Q16—24no—
44C2×C11×Q16—22no—
45C2×C11×Q16—21no—
46C2×C11×Q16—42no—
47C2×C11×Q16C2312yes—
48C2×C11×Q16C2311yescharacteristic
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—41no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—42no—
54C4×Q8×C11—21no—
55C4×D4×C11—41no—
56C4×D4×C11D411yescharacteristic
57#66983—22no—
58C2×C4⋊Dic11—22no—
59C2×D88C2311yescharacteristic
60#66950—41no—
61#66939—42no—
62C4×D44—21no—
63#66922—21no—
64C11×#107C2311yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×#103—21no—
67C11×#103—22no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2311yescharacteristic
70#66892—22no—
71#66892—42no—
72#66885—22no—
73#66885—21no—
74#66882—21no—
75#66882—22no—
76#66882C2312yes—
77#66882C2311yescharacteristic
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33865—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—22no—
85C2×Q8×C11—44no—
86C2×Q8×C11—42no—
87C2×Q8×C11—82no—
88C2×D4×C11D811yescharacteristic
89C22×C4×C11—42no—
90C22×C4×C11C2×D412yes—
91C2×C22⋊D11—42no—
92C22×Dic11—42no—
93#4341—84no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—41no—
97C11×Q16—21no—
98C11×Q16—22no—
99C11×Q16—22no—
100C11×Q16—44no—
101C11×Q16—81no—
102C11×Q16#4112yescomplemented
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D412yes—
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—21no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4D811yescharacteristic
114C11×C22⋊C4—42no—
115C11×C22⋊C4D812yes—
116C42×C11—41no—
117C42×C11C2×D411yescharacteristic
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4⋊Dic11—42no—
124D88—21no—
125D88—21no—
126C11⋊C16—21no—
127C11⋊C16—21no—
128C11⋊C16—22no—
129#3334—111no—
130D4×Q16D1111yescharacteristic, complemented
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×C11C2×D812yes—
141C22×D11—41no—
142Q8×C11—22no—
143Q8×C11—41no—
144Q8×C11—42no—
145Q8×C11—42no—
146Q8×C11—84no—
147D4×C11SD3214yescomplemented
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—84no—
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×D812yes—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C22×D411yescharacteristic
158C22⋊D11—84no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—84no—
162D44—41no—
163D44—41no—
164C4×D11—82no—
165Dic22—82no—
166C8×C11—22no—
167C8×C11—21no—
168C8×C11C2×#4111yescharacteristic
169C8×C11H(5,𝔽2)11yescharacteristic
170C22×Q16C2×D1112yes—
171D4×Q8—21no—
172#547—221no—
173C2×SD32—111no—
174C2×SD32—112no—
175C22×C16—112no—
176#500—111no—
177#494C2×D1111yescharacteristic
178#480—222no—
179#474—221no—
180#467C2×D1112yes—
181#466—112no—
182#462—21no—
183#451—22no—
184C4×Q16C2×D1111yescharacteristic
185C4×D8—111no—
186C8×D4C2×D1111yescharacteristic
187C2×#107—112no—
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×C11C2×SD3214yes—
202C22×C11C22×D811yescharacteristic
203C2×D11—81no—
204C2×D11—81no—
205C2×D11—81no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—42no—
209C4×C11—81no—
210C4×C11—82no—
211C4×C11C2×SD3212yes—
212C4×C11#54611yescharacteristic
213C4×C11#57711yescharacteristic
214Dic11—82no—
215Dic11—81no—
216C2×#41—441no—
217C22×Q8—22no—
218C2×Q16—24no—
219C2×Q16—22no—
220C2×Q16—21no—
221C2×Q16—42no—
222C2×Q16C22×D1112yes—
223C2×Q16C22×D1111yescharacteristic
224C2×D8—111no—
225C22×C8C22×D1112yes—
226C4⋊Q8—21no—
227C4⋊Q8—41no—
228C4⋊Q8—221no—
229#123—442no—
230C22⋊Q8—22no—
231C22⋊Q8—42no—
232C22⋊Q8—441no—
233#121—222no—
234C4×Q8—21no—
235C4×D4—41no—
236C4×D4—221no—
237C4×D4C22⋊D1111yescharacteristic
238C2×C4⋊C4—222no—
239SD32—222no—
240SD32—442no—
241C2×C16—111no—
242C2×C16—111no—
243C2×C16—112no—
244C2×C16—442no—
245#107—111no—
246#107—112no—
247#107—222no—
248#107—221no—
249#107C22×D1111yescharacteristic
250C4⋊C8C22⋊D1111yescharacteristic
251#103—21no—
252#103—22no—
253#102—221no—
254#102—222no—
255C22⋊C8C22⋊D1112yes—
256C4×C8C22×D1111yescharacteristic
257C2×C11—24no—
258C2×C11#329411yescharacteristic
259C2×C11C22×SD3211yescharacteristic
260C2×C11#341711yescharacteristic
261D11—161no—
262#41—884no—
263C2×Q8—21no—
264C2×Q8—22no—
265C2×Q8—44no—
266C2×Q8—42no—
267C2×Q8—82no—
268C2×Q8—441no—
269C2×D4—221no—
270C2×D4—442no—
271C2×D4#432311yescharacteristic
272C22×C4—42no—
273C22×C4—442no—
274C22×C4—441no—
275C22×C4C2×C22⋊D1112yes—
276Q16—22no—
277Q16—21no—
278Q16—22no—
279Q16—44no—
280Q16—81no—
281Q16#434112yescomplemented
282D8—221no—
283D8—221no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8C2×C22⋊D1111yescharacteristic
287C2×C8C2×C22⋊D1112yes—
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—442no—
297C4⋊C4—441no—
298C4⋊C4#432311yescharacteristic
299C22⋊C4—42no—
300C22⋊C4—441no—
301C22⋊C4—442no—
302C22⋊C4#432312yes—
303C42—41no—
304C42C2×C22⋊D1111yescharacteristic
305C16—221no—
306C16—221no—
307C16—222no—
308C11#3386511yescharacteristic, complemented, Sylow
309C23—441no—
310C23C2×#432312yes—
311Q8—22no—
312Q8—41no—
313Q8—42no—
314Q8—42no—
315Q8—84no—
316Q8—882no—
317D4—441no—
318D4—441no—
319D4—884no—
320D4#6689214yescomplemented
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—84no—
327C2×C4—441no—
328C2×C4—442no—
329C2×C4—884no—
330C2×C4—882no—
331C2×C4C2×#432311yescharacteristic
332C2×C4C2×#432312yes—
333C2×C4C2×#432311yescharacteristic
334C2×C4C22×C22⋊D1111yescharacteristic
335C8—22no—
336C8—21no—
337C8C2×#434111yescharacteristic
338C8#6703711yescharacteristic
339C22—22no—
340C22—22no—
341C22—881no—
342C22—881no—
343C22—881no—
344C22C2×#6689214yes—
345C22C22×#432311yescharacteristic
346C4—22no—
347C4—21no—
348C4—42no—
349C4—82no—
350C4—81no—
351C4—881no—
352C4—882no—
353C4C2×#6689212yes—
354C4#1062333711yescharacteristic
355C4#1062336711yescharacteristic
356C2—24no—
357C2—1761no—
358C2#1308042911yescharacteristic
359C2C22×#6689211yescharacteristic
360C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radical#13080964C2
hypercenterD4×Q16D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
2. #13070843C2semidirect
3. #13070811C2semidirect
4. #13070758C2semidirect
5. #13070714C2semidirect
6. #13070658C2semidirect
7. #13070533C2semidirect
8. C4×#66892C2semidirect
9. D4×C11⋊C16C2semidirect
10. C2×#10622202C2semidirect
11. D4×C11×Q16C2semidirect
102. C11×Q16#41semidirect
130. D4×Q16D11semidirect
147. D4×C11SD32semidirect
281. Q16#4341semidirect
308. C11#33865semidirect
320. D4#66892semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130708432
#130708112
#130707582
#130707142
#130706582
#130705332
C4×#668922
D4×C11⋊C162
C2×#106222022
D4×C11×Q162
#3386511