Finite Group Databasebeta

← #14910705

Subgroups — #14910705

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080338C211yesmaximal, characteristic, complemented
2#13070845C211yesmaximal, characteristic, complemented
3#13070824C212yesmaximal, complemented
4#13070760C211yesmaximal, characteristic, complemented
5#13070710C212yesmaximal, complemented
6#13070661C211yesmaximal, characteristic, complemented
7#13070537C212yesmaximal, complemented
8C4×#66890C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070321C212yesmaximal, complemented
11C11×#3341C211yesmaximal, characteristic, complemented
12C11×#555—21no—
13C2×#66957C2212yes—
14#10623082—21no—
15C11×#500C2211yescharacteristic
16C11×#482—22no—
17C11×#476—21no—
18C11×#466C2212yes—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C11×#427C2212yes—
22C2×#66891C2212yes—
23C2×#66890C2211yescharacteristic
24#10622729C2212yes—
25C22×C11⋊C16C2212yes—
26#10622454—21no—
27#10622346—22no—
28#10622312C2211yescharacteristic
29C4×D88C2211yescharacteristic
30#10622200C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2212yes—
33#10622130C2212yes—
34#10622130C2212yes—
35#10622129C2211yescharacteristic
36#10622129C2212yes—
37#10622128C2212yes—
38#10622127C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4339—22no—
42C2×C11×D8C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#124—42no—
46C11×#121—22no—
47C11×#121—41no—
48C4×D4×C11—21no—
49C4×D4×C11D411yescharacteristic
50C11×#117—22no—
51C11×#117—41no—
52#66991—41no—
53#66977—22no—
54C2×Dic44—21no—
55C2×Dic44C2312yes—
56#66957—24no—
57#66957—42no—
58C2×D88C2311yescharacteristic
59C2×#4314—22no—
60C4⋊C4×D11—41no—
61#66936—42no—
62C4×D44—21no—
63#66922—21no—
64C11×#107—21no—
65C11×#107C2312yes—
66C11×#107C2311yescharacteristic
67C11×#106—22no—
68C11×C4⋊C8D411yescharacteristic
69C11×#102—21no—
70C11×#102—22no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2311yescharacteristic
73#66891—42no—
74#66890—22no—
75#66885—21no—
76#66882C2311yescharacteristic
77#66880—22no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33870—111nomaximal, Sylow
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—42no—
86C2×D4×C11D811yescharacteristic
87C22×C4×C11—41no—
88C22×C4×C11C2×D412yes—
89C2×C22⋊D11—42no—
90#4339—44no—
91#4339—82no—
92C2×D44—21no—
93C2×C4×D11—41no—
94C2×C4×D11—42no—
95C2×Dic22—22no—
96C11×D8—21no—
97C11×D8—21no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C2×D412yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—21no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4D811yescharacteristic
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4D812yes—
111C42×C11—42no—
112C42×C11C2×D411yescharacteristic
113C22⋊Dic11—42no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118Dic11⋊C4—42no—
119Dic44—22no—
120Dic44—22no—
121Dic44—81no—
122D88—21no—
123D88#4112yes—
124#4314—44no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3341D1111yescharacteristic, complemented
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2226—111no—
133#2217—112no—
134#2208—111no—
135#2186—112no—
136C4×D16—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11—41no—
140C23×C11C2×D812yes—
141C22×D11—41no—
142Q8×C11—161no—
143D4×C11—22no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—162no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—82no—
152C2×C4×C11C2×D812yes—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—84no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159D44—22no—
160D44—41no—
161C4×D11—84no—
162C4×D11—82no—
163Dic22—42no—
164Dic22—42no—
165C8×C11—22no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C2×#135—112no—
170#555—21no—
171#547—221no—
172C2×SD32—112no—
173C2×D16—111no—
174C22×C16—112no—
175#500C2×D1111yescharacteristic
176#494—111no—
177#482—22no—
178#476—21no—
179#467—112no—
180#466C2×D1112yes—
181#461—221no—
182#452—222no—
183C4×D8—111no—
184C4×D8C2×D1111yescharacteristic
185C8×D4C2×D1111yescharacteristic
186#427C2×D1112yes—
187#367—112no—
188#366—111no—
189C4⋊C16—111no—
190#358—112no—
191#358—112no—
192#358—112no—
193#357—111no—
194#357—111no—
195#357—112no—
196C22⋊C16—112no—
197C4×C16—111no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11C22×D811yescharacteristic
205C2×D11—42no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—81no—
211C4×C11—82no—
212C4×C11#50812yes—
213C4×C11#54611yescharacteristic
214C4×C11#57711yescharacteristic
215Dic11—81no—
216Dic11—82no—
217C2×#41—222no—
218#135—224no—
219#135—442no—
220C2×Q16—112no—
221C2×Q16—221no—
222C2×SD16—222no—
223C2×D8—111no—
224C2×D8C22×D1111yescharacteristic
225C22×C8C22×D1112yes—
226C4⋊Q8—21no—
227C4⋊Q8—221no—
228#124—42no—
229#123—442no—
230C22⋊Q8—222no—
231#121—22no—
232#121—41no—
233#121—441no—
234C4×D4—21no—
235C4×D4—221no—
236C4×D4C22⋊D1111yescharacteristic
237#117—22no—
238#117—41no—
239C2×C4⋊C4—441no—
240SD32—442no—
241D16—222no—
242C2×C16—111no—
243C2×C16—111no—
244C2×C16—112no—
245C2×C16—442no—
246#107—21no—
247#107—111no—
248#107C22×D1111yescharacteristic
249#107C22×D1112yes—
250#106—22no—
251C4⋊C8C22⋊D1111yescharacteristic
252#103—222no—
253#102—21no—
254#102—22no—
255#102—221no—
256C22⋊C8C22⋊D1112yes—
257C4×C8C22×D1111yescharacteristic
258C2×C11—42no—
259C2×C11—161no—
260C2×C11#329411yescharacteristic
261C2×C11C2×#50811yescharacteristic
262C2×C11#341611yescharacteristic
263D11—82no—
264#41—444no—
265#41—882no—
266C2×Q8—41no—
267C2×Q8—222no—
268C2×D4—21no—
269C2×D4—42no—
270C2×D4—221no—
271C2×D4—442no—
272C2×D4#432311yescharacteristic
273C22×C4—41no—
274C22×C4—441no—
275C22×C4—442no—
276C22×C4C2×C22⋊D1112yes—
277Q16—222no—
278Q16—222no—
279Q16—881no—
280SD16—444no—
281D8—21no—
282D8—21no—
283D8—112no—
284D8—221no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C2×C22⋊D1112yes—
289C2×C8C23×D1111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—221no—
294C4⋊C4—441no—
295C4⋊C4—442no—
296C4⋊C4—441no—
297C4⋊C4#432311yescharacteristic
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—41no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C22⋊C4#432312yes—
304C42—42no—
305C42C2×C22⋊D1111yescharacteristic
306C16—221no—
307C16—221no—
308C16—222no—
309C11#3387011yescharacteristic, complemented, Sylow
310C23—41no—
311C23—441no—
312C23C2×#432312yes—
313Q8—161no—
314Q8—442no—
315Q8—442no—
316D4—22no—
317D4—41no—
318D4—41no—
319D4—162no—
320D4—222no—
321D4—441no—
322D4—884no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—82no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—884no—
331C2×C4—882no—
332C2×C4C2×#432312yes—
333C2×C4C2×#432311yescharacteristic
334C2×C4C2×#432311yescharacteristic
335C2×C4C22×C22⋊D1111yescharacteristic
336C8—22no—
337C8—21no—
338C8#41×D1111yescharacteristic
339C8#6704211yescharacteristic
340C22—22no—
341C22—22no—
342C22—22no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22—442no—
347C22—881no—
348C22—881no—
349C22C22×#432311yescharacteristic
350C4—22no—
351C4—21no—
352C4—81no—
353C4—82no—
354C4—882no—
355C4—881no—
356C4#1062280712yes—
357C4#1062336011yescharacteristic
358C4#1062336811yescharacteristic
359C2—42no—
360C2—161no—
361C2—882no—
362C2#1308042311yescharacteristic
363C2C2×#1062280711yescharacteristic
364C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3341C2
socleC22×C11C22×D8
hypercenter#3341D11
hypocenterC11#33870
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13080338C2semidirect
2. #13070845C2semidirect
3. #13070824C2semidirect
4. #13070760C2semidirect
5. #13070710C2semidirect
6. #13070661C2semidirect
7. #13070537C2semidirect
8. C4×#66890C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070321C2semidirect
11. C11×#3341C2semidirect
128. #3341D11semidirect
309. C11#33870semidirect

Maximal subgroups

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

subgroupindex
#130803382
#130708452
#130708242
#130707602
#130707102
#130706612
#130705372
C4×#668902
D4×C11⋊C162
#130703212
C11×#33412
#3387011