Finite Group Databasebeta

← #14910659

Subgroups — #14910659

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081009C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic, complemented
3#13070816C212yesmaximal, complemented
4#13070768C211yesmaximal, characteristic, complemented
5#13070705C212yesmaximal, complemented
6#13070663C211yesmaximal, characteristic, complemented
7#13070550C212yesmaximal, complemented
8C4×#66893C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic
10C2×#10622202C212yesmaximal, complemented
11D4×C11×Q16C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13D4×Q8×C11—21no—
14#10623074—21no—
15C11×#494C2211yescharacteristic
16C11×#467C2212yes—
17C11×#462—21no—
18C11×#451—22no—
19C4×C11×Q16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21C2×#66893C2211yescharacteristic
22C2×#66893C2212yes—
23#10622729C2212yes—
24C2×#66882C2212yes—
25C22×C11⋊C16C2212yes—
26#10622463—21no—
27#10622335—22no—
28C4×Dic44C2211yescharacteristic
29#10622295C2211yescharacteristic
30#10622202C2212yes—
31#10622202C2212yes—
32#10622202C2211yescharacteristic
33#10622202C2212yes—
34#10622202C2212yes—
35C22⋊(C11⋊C16)C2212yes—
36#10622130C2211yescharacteristic
37#10622127C2212yes—
38#10622127C2211yescharacteristic
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C22×Q8×C11—22no—
42C2×C11×Q16—24no—
43C2×C11×Q16—22no—
44C2×C11×Q16—21no—
45C2×C11×Q16—42no—
46C2×C11×Q16C2312yes—
47C2×C11×Q16C2311yescharacteristic
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—41no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—42no—
53C4×Q8×C11—21no—
54C4×D4×C11—41no—
55C4×D4×C11D411yescharacteristic
56D4×Dic11—41no—
57C2×C4⋊Dic11—22no—
58#66977—22no—
59C2×Dic44C2311yescharacteristic
60#66943—41no—
61#66931—42no—
62#66922—21no—
63C4×Dic22—21no—
64C11×#107C2311yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×#103—21no—
67C11×#103—22no—
68C11×C22⋊C8D412yes—
69C4×C8×C11C2311yescharacteristic
70#66893—22no—
71#66893—42no—
72#66882—21no—
73#66882—22no—
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66880—22no—
77#66880—21no—
78C2×C11⋊C16—42no—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2312yes—
81C2×C11⋊C16C2311yescharacteristic
82#33866—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—
91C22×Dic11—42no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C11×Q16—21no—
95C11×Q16—22no—
96C11×Q16—22no—
97C11×Q16—44no—
98C11×Q16—81no—
99C11×Q16#4112yes—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D412yes—
104C2×C8×C11C2411yescharacteristic
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4D811yescharacteristic
111C11×C22⋊C4—42no—
112C11×C22⋊C4D812yes—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C22⋊Dic11—42no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—42no—
120Dic11⋊C4—41no—
121Dic11⋊C4—42no—
122C4×Dic11—41no—
123Dic44—21no—
124Dic44—21no—
125C11⋊C16—21no—
126C11⋊C16—21no—
127C11⋊C16—22no—
128#3338—111no—
129D4×Q16D1111yescharacteristic
130#2241—111no—
131#2236—112no—
132#2227—111no—
133#2216—112no—
134#2209—111no—
135#2188—112no—
136C4×Q32—111no—
137D4×C16—111no—
138C2×#358—112no—
139C23×C11C2×D812yes—
140Q8×C11—22no—
141Q8×C11—41no—
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—84no—
145D4×C11Q3214yescomplemented
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—84no—
152C2×C4×C11C2×D812yes—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—162no—
160Dic22—41no—
161Dic22—41no—
162Dic22—161no—
163C8×C11—22no—
164C8×C11—21no—
165C8×C11C2×#4111yescharacteristic
166C8×C11H(5,𝔽2)11yescharacteristic
167C22×Q16C2×D1112yes—
168#554—221no—
169D4×Q8—21no—
170C2×Q32—111no—
171C2×Q32—112no—
172C22×C16—112no—
173#500—111no—
174#494C2×D1111yescharacteristic
175#484—222no—
176#477—221no—
177#467—112no—
178#467C2×D1112yes—
179#462—21no—
180#451—22no—
181C4×Q16—111no—
182C4×Q16C2×D1111yescharacteristic
183C8×D4C2×D1111yescharacteristic
184C2×#107—112no—
185#366—111no—
186#366—112no—
187C4⋊C16—111no—
188#358—111no—
189#358—112no—
190#358—112no—
191#358—112no—
192#358—112no—
193#358—111no—
194C22⋊C16—112no—
195C4×C16—111no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11C2×Q3214yes—
199C22×C11C22×D811yescharacteristic
200C4×C11—21no—
201C4×C11—22no—
202C4×C11—42no—
203C4×C11—81no—
204C4×C11—82no—
205C4×C11C2×Q3212yes—
206C4×C11#54611yescharacteristic
207C4×C11#57711yescharacteristic
208Dic11—82no—
209Dic11—81no—
210Dic11—81no—
211C22×Q8—22no—
212C2×Q16—24no—
213C2×Q16—22no—
214C2×Q16—21no—
215C2×Q16—42no—
216C2×Q16—111no—
217C2×Q16C22×D1112yes—
218C2×Q16C22×D1111yescharacteristic
219C22×C8C22×D1112yes—
220C4⋊Q8—21no—
221C4⋊Q8—41no—
222C4⋊Q8—221no—
223#125—441no—
224C22⋊Q8—22no—
225C22⋊Q8—42no—
226C22⋊Q8—222no—
227C22⋊Q8—442no—
228C4×Q8—21no—
229C4×Q8—221no—
230C4×D4—41no—
231C4×D4—441no—
232C4×D4C22⋊D1111yescharacteristic
233C2×C4⋊C4—222no—
234Q32—222no—
235Q32—442no—
236C2×C16—111no—
237C2×C16—111no—
238C2×C16—112no—
239C2×C16—442no—
240#107—111no—
241#107—112no—
242#107—222no—
243#107—221no—
244#107C22×D1111yescharacteristic
245C4⋊C8C22⋊D1111yescharacteristic
246#103—21no—
247#103—22no—
248#103—221no—
249#103—222no—
250C22⋊C8C22⋊D1112yes—
251C4×C8C22×D1111yescharacteristic
252C2×C11—24no—
253C2×C11#329411yescharacteristic
254C2×C11C22×Q3211yescharacteristic
255C2×C11#341611yescharacteristic
256C2×Q8—21no—
257C2×Q8—22no—
258C2×Q8—44no—
259C2×Q8—42no—
260C2×Q8—82no—
261C2×Q8—221no—
262C2×Q8—441no—
263C2×D4#432311yescharacteristic
264C22×C4—42no—
265C22×C4—442no—
266C22×C4C2×C22⋊D1112yes—
267Q16—22no—
268Q16—21no—
269Q16—22no—
270Q16—44no—
271Q16—81no—
272Q16—221no—
273Q16—221no—
274Q16#434112yes—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8C2×C22⋊D1111yescharacteristic
278C2×C8C2×C22⋊D1112yes—
279C2×C8C23×D1111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—41no—
285C4⋊C4—221no—
286C4⋊C4—222no—
287C4⋊C4—442no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—442no—
291C4⋊C4#432311yescharacteristic
292C22⋊C4—42no—
293C22⋊C4—442no—
294C22⋊C4#432312yes—
295C42—41no—
296C42—441no—
297C42C2×C22⋊D1111yescharacteristic
298C16—221no—
299C16—221no—
300C16—222no—
301C11#3386611yescharacteristic, complemented, Sylow
302C23C2×#432312yes—
303Q8—22no—
304Q8—41no—
305Q8—42no—
306Q8—42no—
307Q8—84no—
308Q8—441no—
309Q8—441no—
310Q8—1761no—
311D4#6689314yescomplemented
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—84no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—1762no—
322C2×C4C2×#432311yescharacteristic
323C2×C4C2×#432312yes—
324C2×C4C2×#432311yescharacteristic
325C2×C4C22×C22⋊D1111yescharacteristic
326C8—22no—
327C8—21no—
328C8C2×#434111yescharacteristic
329C8#6703711yescharacteristic
330C22—22no—
331C22—22no—
332C22C2×#6689314yes—
333C22C22×#432311yescharacteristic
334C4—22no—
335C4—21no—
336C4—42no—
337C4—82no—
338C4—81no—
339C4—881no—
340C4—881no—
341C4—882no—
342C4C2×#6689312yes—
343C4#1062333711yescharacteristic
344C4#1062336711yescharacteristic
345C2—24no—
346C2#1308042911yescharacteristic
347C2C22×#6689311yescharacteristic
348C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenterD4×Q16D11
hypocenterC11#33866
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. #13070816C2semidirect
4. #13070768C2semidirect
5. #13070705C2semidirect
6. #13070663C2semidirect
7. #13070550C2semidirect
8. C4×#66893C2semidirect
10. C2×#10622202C2semidirect
145. D4×C11Q32semidirect
301. C11#33866semidirect
311. D4#66893semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130708432
#130708162
#130707682
#130707052
#130706632
#130705502
C4×#668932
D4×C11⋊C162
C2×#106222022
D4×C11×Q162
#3386611