Finite Group Databasebeta

← #14910694

Subgroups — #14910694

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080338C211yesmaximal, characteristic
2#13070845C211yesmaximal, characteristic, complemented
3#13070824C212yesmaximal, complemented
4#13070750C211yesmaximal, characteristic, complemented
5#13070705C212yesmaximal, complemented
6#13070666C211yesmaximal, characteristic, complemented
7#13070554C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10#13070321C212yesmaximal, complemented
11C11×#3342C211yesmaximal, characteristic, complemented
12C11×#556—21no—
13C2×#66957C2212yes—
14#10623082—21no—
15C11×#500C2211yescharacteristic
16C11×#485—22no—
17C11×#475—21no—
18C11×#467C2212yes—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C11×#427C2212yes—
22C2×#66893C2212yes—
23C2×#66892C2211yescharacteristic
24#10622729C2212yes—
25C22×C11⋊C16C2212yes—
26#10622454—21no—
27#10622346—22no—
28#10622312C2211yescharacteristic
29C4×D88C2211yescharacteristic
30#10622202C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622130C2212yes—
33#10622130C2212yes—
34#10622130C2212yes—
35#10622129C2211yescharacteristic
36#10622129C2212yes—
37#10622128C2211yescharacteristic
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4339—22no—
42C2×C11×Q16C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#126—42no—
46C11×#124—41no—
47C11×C22⋊Q8—22no—
48C4×Q8×C11—21no—
49C4×Q8×C11—41no—
50C4×D4×C11D411yescharacteristic
51C11×#117—22no—
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×#103—21no—
70C11×#103—22no—
71C11×C22⋊C8D412yes—
72C4×C8×C11C2311yescharacteristic
73#66893—42no—
74#66892—22no—
75#66885—21no—
76#66882C2311yescharacteristic
77#66880—22no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33869—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×D4×C11D811yescharacteristic
86C22×C4×C11C2×D412yes—
87C2×C22⋊D11—42no—
88#4339—44no—
89#4339—82no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×C4×D11—42no—
93C2×Dic22—22no—
94C11×Q16—21no—
95C11×Q16—21no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11C2×D412yes—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4D811yescharacteristic
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4D812yes—
110C42×C11—42no—
111C42×C11—41no—
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#3342D1111yescharacteristic, complemented
129#3283—111no—
130#2241—111no—
131#2237—112no—
132#2224—111no—
133#2216—112no—
134#2209—111no—
135#2189—112no—
136C4×SD32—111no—
137D4×C16—111no—
138#2138—112no—
139C23×C11C2×D812yes—
140C22×D11—41no—
141Q8×C11—41no—
142Q8×C11—41no—
143Q8×C11—82no—
144D4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11C2×D812yes—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—84no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157D44—22no—
158D44—41no—
159C4×D11—84no—
160C4×D11—82no—
161Dic22—42no—
162Dic22—42no—
163C8×C11—22no—
164C8×C11—21no—
165C8×C11C2×#4111yescharacteristic
166C8×C11H(5,𝔽2)11yescharacteristic
167C2×#135—112no—
168#556—21no—
169#547—221no—
170C2×Q32—112no—
171C2×SD32—111no—
172C22×C16—112no—
173#500C2×D1111yescharacteristic
174#494—111no—
175#485—22no—
176#475—21no—
177#467—112no—
178#467C2×D1112yes—
179#461—221no—
180#452—222no—
181C4×Q16C2×D1111yescharacteristic
182C4×D8—111no—
183C8×D4C2×D1111yescharacteristic
184#427C2×D1112yes—
185#367—111no—
186#366—112no—
187C4⋊C16—111no—
188#358—111no—
189#358—112no—
190#358—112no—
191#358—112no—
192#357—111no—
193#357—112no—
194C22⋊C16—112no—
195C4×C16—111no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11C22×D811yescharacteristic
200C2×D11—42no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—22no—
205C4×C11—82no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11#50812yes—
209C4×C11#54611yescharacteristic
210C4×C11#57711yescharacteristic
211Dic11—81no—
212Dic11—82no—
213C2×#41—222no—
214#135—224no—
215#135—442no—
216C2×Q16—112no—
217C2×Q16—221no—
218C2×Q16C22×D1111yescharacteristic
219C2×SD16—222no—
220C2×D8—111no—
221C22×C8C22×D1112yes—
222C4⋊Q8—21no—
223C4⋊Q8—221no—
224#126—42no—
225#124—41no—
226#123—442no—
227C22⋊Q8—22no—
228C22⋊Q8—222no—
229#121—441no—
230C4×Q8—21no—
231C4×Q8—41no—
232C4×D4—221no—
233C4×D4C22⋊D1111yescharacteristic
234#117—22no—
235C2×C4⋊C4—441no—
236Q32—442no—
237SD32—222no—
238C2×C16—111no—
239C2×C16—111no—
240C2×C16—112no—
241C2×C16—442no—
242#107—21no—
243#107—111no—
244#107C22×D1112yes—
245#107C22×D1111yescharacteristic
246#106—22no—
247C4⋊C8C22⋊D1111yescharacteristic
248#103—21no—
249#103—22no—
250#103—222no—
251#102—221no—
252C22⋊C8C22⋊D1112yes—
253C4×C8C22×D1111yescharacteristic
254C2×C11—42no—
255C2×C11#329411yescharacteristic
256C2×C11C2×#50811yescharacteristic
257C2×C11#341711yescharacteristic
258D11—82no—
259#41—444no—
260#41—882no—
261C2×Q8—21no—
262C2×Q8—41no—
263C2×Q8—222no—
264C2×D4—221no—
265C2×D4—442no—
266C2×D4#432311yescharacteristic
267C22×C4—441no—
268C22×C4—442no—
269C22×C4C2×C22⋊D1112yes—
270Q16—21no—
271Q16—21no—
272Q16—222no—
273Q16—222no—
274Q16—881no—
275SD16—444no—
276D8—112no—
277D8—221no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C2×C22⋊D1111yescharacteristic
281C2×C8C2×C22⋊D1112yes—
282C2×C8C23×D1111yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—41no—
288C4⋊C4—221no—
289C4⋊C4—441no—
290C4⋊C4—442no—
291C4⋊C4—441no—
292C4⋊C4#432311yescharacteristic
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—442no—
296C22⋊C4—441no—
297C22⋊C4#432312yes—
298C42—42no—
299C42—41no—
300C42C2×C22⋊D1111yescharacteristic
301C16—221no—
302C16—221no—
303C16—222no—
304C11#3386911yescharacteristic, complemented, Sylow
305C23—441no—
306C23C2×#432312yes—
307Q8—41no—
308Q8—41no—
309Q8—82no—
310Q8—442no—
311Q8—442no—
312D4—22no—
313D4—222no—
314D4—441no—
315D4—884no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—441no—
322C2×C4—442no—
323C2×C4—884no—
324C2×C4—882no—
325C2×C4C2×#432312yes—
326C2×C4C2×#432311yescharacteristic
327C2×C4C2×#432311yescharacteristic
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—22no—
330C8—21no—
331C8#41×D1111yescharacteristic
332C8#6704211yescharacteristic
333C22—22no—
334C22—22no—
335C22—22no—
336C22—442no—
337C22—881no—
338C22—881no—
339C22C22×#432311yescharacteristic
340C4—22no—
341C4—21no—
342C4—81no—
343C4—82no—
344C4—81no—
345C4—882no—
346C4—881no—
347C4#1062280712yes—
348C4#1062336011yescharacteristic
349C4#1062336811yescharacteristic
350C2—42no—
351C2—882no—
352C2#1308042311yescharacteristic
353C2C2×#1062280711yescharacteristic
354C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3342C2
socleC22×C11C22×D8
prime radical#13080338C2
hypercenter#3342D11
hypocenterC11#33869
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3342

Complements

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

NH ≅ G/Ntype
2. #13070845C2semidirect
3. #13070824C2semidirect
4. #13070750C2semidirect
5. #13070705C2semidirect
6. #13070666C2semidirect
7. #13070554C2semidirect
8. C4×#66892C2semidirect
9. D4×C11⋊C16C2semidirect
10. #13070321C2semidirect
11. C11×#3342C2semidirect
128. #3342D11semidirect
304. C11#33869semidirect

Maximal subgroups

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

subgroupindex
#130803382
#130708452
#130708242
#130707502
#130707052
#130706662
#130705542
C4×#668922
D4×C11⋊C162
#130703212
C11×#33422
#3386911