Finite Group Databasebeta

← #14910660

Subgroups — #14910660

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
2D4×Dic44C211yesmaximal, characteristic
3#13070844C211yesmaximal, characteristic, complemented
4#13070819C212yesmaximal, complemented
5#13070769C211yesmaximal, characteristic, complemented
6#13070707C212yesmaximal, complemented
7#13070667C211yesmaximal, characteristic, complemented
8#13070552C212yesmaximal, complemented
9C4×Dic88C211yesmaximal, characteristic, complemented
10C2×#10622141C212yesmaximal, complemented
11D4×C11×C16C211yesmaximal, characteristic
12C22×Dic44C2212yes—
13#10623074—21no—
14D4×Dic22—21no—
15C22×C11×C16C2212yes—
16C8×D4×C11C2211yescharacteristic
17#10622729C2212yes—
18#10622729C2212yes—
19C2×#66882C2212yes—
20C2×Dic88C2211yescharacteristic
21C2×Dic88C2212yes—
22#10622463—21no—
23#10622462—21no—
24#10622352—22no—
25#10622335—22no—
26#10622312C2211yescharacteristic
27C4×Dic44C2211yescharacteristic
28C4×Dic44C2211yescharacteristic
29#10622295C2211yescharacteristic
30C11×C4⋊C16C2211yescharacteristic
31C11×C22⋊C16C2212yes—
32C4×C11×C16C2211yescharacteristic
33#10622142C2212yes—
34#10622142C2211yescharacteristic
35#10622141C2212yes—
36#10622141C2211yescharacteristic
37#10622141C2212yes—
38#10622141C2211yescharacteristic
39#10622141C2212yes—
40#10622141C2212yes—
41C22×Dic22—22no—
42C22×C8×C11C2312yes—
43C4×D4×C11D411yescharacteristic
44D4×Dic11—41no—
45D4×Dic11—41no—
46C2×C4⋊Dic11—22no—
47#66977—22no—
48#66977—22no—
49C2×Dic44—24no—
50C2×Dic44—22no—
51C2×Dic44—21no—
52C2×Dic44—42no—
53C2×Dic44C2311yescharacteristic
54C2×Dic44C2312yes—
55C2×Dic44C2311yescharacteristic
56#66943—41no—
57#66941—41no—
58#66931—42no—
59#66931—42no—
60#66922—21no—
61#66922—21no—
62C4×Dic22—21no—
63C4×Dic22—21no—
64C2×C11×C16—42no—
65C2×C11×C16C2311yescharacteristic
66C2×C11×C16C2312yes—
67C2×C11×C16C2311yescharacteristic
68C11×C4⋊C8D411yescharacteristic
69C11×C22⋊C8D412yes—
70C4×C8×C11C2311yescharacteristic
71#66882—21no—
72#66882—22no—
73#66882C2311yescharacteristic
74#66882C2312yes—
75#66882C2311yescharacteristic
76#66880—22no—
77#66880—22no—
78#66880—21no—
79#66880—21no—
80Dic88—22no—
81Dic88—42no—
82#33866—111nomaximal, Sylow
83C2×D4×C11D811yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C2×Dic22—21no—
88C2×Dic22—21no—
89C2×Dic22—22no—
90C2×Dic22—44no—
91C2×Dic22—42no—
92C2×Dic22—41no—
93C2×Dic22—82no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D412yes—
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4D811yescharacteristic
100C11×C22⋊C4D812yes—
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—22no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—42no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113Dic11⋊C4—42no—
114Dic11⋊C4—42no—
115C4×Dic11—41no—
116C4×Dic11—41no—
117Dic44—21no—
118Dic44—22no—
119Dic44—21no—
120Dic44—21no—
121Dic44—22no—
122Dic44—44no—
123Dic44—81no—
124Dic44#4112yes—
125C11×C16—21no—
126C11×C16—22no—
127C11×C16—21no—
128#3338—111no—
129D4×Q16—111no—
130#2241—111no—
131#2236—112no—
132#2227—111no—
133#2216—112no—
134#2209—111no—
135#2188—112no—
136C4×Q32—111no—
137D4×C16D1111yescharacteristic
138C2×#358—112no—
139C23×C11C2×D812yes—
140D4×C11Q3214yescomplemented
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—84no—
154C2×Dic11—162no—
155Dic22—22no—
156Dic22—41no—
157Dic22—42no—
158Dic22—41no—
159Dic22—42no—
160Dic22—41no—
161Dic22—84no—
162Dic22—161no—
163C8×C11—22no—
164C8×C11—21no—
165C8×C11C2×#4111yescharacteristic
166C8×C11H(5,𝔽2)11yescharacteristic
167C22×Q16—112no—
168#554—221no—
169D4×Q8—221no—
170C2×Q32—111no—
171C2×Q32—112no—
172C22×C16C2×D1112yes—
173#500—111no—
174#494—111no—
175#484—222no—
176#477—221no—
177#467—112no—
178#467—112no—
179#462—221no—
180#451—222no—
181C4×Q16—111no—
182C4×Q16—111no—
183C8×D4C2×D1111yescharacteristic
184C2×#107—112no—
185#366—111no—
186#366—112no—
187C4⋊C16C2×D1111yescharacteristic
188#358—111no—
189#358—112no—
190#358—112no—
191#358—112no—
192#358—111no—
193#358—112no—
194C22⋊C16C2×D1112yes—
195C4×C16C2×D1111yescharacteristic
196C22×C11—22no—
197C22×C11—22no—
198C22×C11C2×Q3214yes—
199C22×C11C22×D811yescharacteristic
200C4×C11—21no—
201C4×C11—22no—
202C4×C11C2×Q3212yes—
203C4×C11#54611yescharacteristic
204C4×C11#57711yescharacteristic
205Dic11—42no—
206Dic11—82no—
207Dic11—81no—
208Dic11—81no—
209Dic11—82no—
210Dic11—81no—
211C22×Q8—222no—
212C2×Q16—111no—
213C2×Q16—112no—
214C2×Q16—111no—
215C2×Q16—224no—
216C2×Q16—222no—
217C2×Q16—221no—
218C2×Q16—442no—
219C22×C8C22×D1112yes—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—441no—
223#125—441no—
224C22⋊Q8—222no—
225C22⋊Q8—222no—
226C22⋊Q8—442no—
227C22⋊Q8—442no—
228C4×Q8—221no—
229C4×Q8—221no—
230C4×D4—441no—
231C4×D4—441no—
232C4×D4D4411yescharacteristic
233C2×C4⋊C4—222no—
234Q32—222no—
235Q32—442no—
236C2×C16—42no—
237C2×C16C22×D1111yescharacteristic
238C2×C16C22×D1111yescharacteristic
239C2×C16C22×D1112yes—
240#107—111no—
241#107—112no—
242#107—111no—
243#107—222no—
244#107—221no—
245C4⋊C8D4411yescharacteristic
246#103—221no—
247#103—221no—
248#103—222no—
249#103—222no—
250C22⋊C8D4412yes—
251C4×C8C22×D1111yescharacteristic
252C2×C11—24no—
253C2×C11#329411yescharacteristic
254C2×C11C22×Q3211yescharacteristic
255C2×C11#341611yescharacteristic
256C2×Q8—221no—
257C2×Q8—221no—
258C2×Q8—222no—
259C2×Q8—444no—
260C2×Q8—442no—
261C2×Q8—441no—
262C2×Q8—882no—
263C2×D4D8811yescharacteristic
264C22×C4—442no—
265C22×C4—442no—
266C22×C4C2×D4412yes—
267Q16—112no—
268Q16—221no—
269Q16—221no—
270Q16—222no—
271Q16—221no—
272Q16—222no—
273Q16—444no—
274Q16—881no—
275C2×C8—22no—
276C2×C8—22no—
277C2×C8C2×D4411yescharacteristic
278C2×C8C2×D4412yes—
279C2×C8C23×D1111yescharacteristic
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—222no—
283C4⋊C4—442no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—442no—
289C4⋊C4—442no—
290C4⋊C4—441no—
291C4⋊C4D8811yescharacteristic
292C22⋊C4—442no—
293C22⋊C4—442no—
294C22⋊C4D8812yes—
295C42—441no—
296C42—441no—
297C42C2×D4411yescharacteristic
298C16—21no—
299C16—22no—
300C16—21no—
301C11#3386611yescharacteristic, complemented, Sylow
302C23C2×D8812yes—
303Q8—222no—
304Q8—441no—
305Q8—442no—
306Q8—441no—
307Q8—442no—
308Q8—441no—
309Q8—884no—
310Q8—1761no—
311D4Dic8814yescomplemented
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—884no—
321C2×C4—1762no—
322C2×C4C2×D8811yescharacteristic
323C2×C4C2×D8812yes—
324C2×C4C2×D8811yescharacteristic
325C2×C4C22×D4411yescharacteristic
326C8—21no—
327C8—22no—
328C8#6703711yescharacteristic
329C8#41×D1111yescharacteristic
330C22—22no—
331C22—22no—
332C22C2×Dic8814yes—
333C22C22×D8811yescharacteristic
334C4—22no—
335C4—21no—
336C4—442no—
337C4—882no—
338C4—881no—
339C4—881no—
340C4—882no—
341C4—881no—
342C4C2×Dic8812yes—
343C4#1062308511yescharacteristic
344C4#1062328211yescharacteristic
345C2—24no—
346C2#1308043011yescharacteristic
347C2C22×Dic8811yescharacteristic
348C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenterD4×C16D11
hypocenterC11#33866
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
3. #13070844C2semidirect
4. #13070819C2semidirect
5. #13070769C2semidirect
6. #13070707C2semidirect
7. #13070667C2semidirect
8. #13070552C2semidirect
9. C4×Dic88C2semidirect
10. C2×#10622141C2semidirect
140. D4×C11Q32semidirect
301. C11#33866semidirect
311. D4Dic88semidirect

Maximal subgroups

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

subgroupindex
#130810092
D4×Dic442
#130708442
#130708192
#130707692
#130707072
#130706672
#130705522
C4×Dic882
C2×#106221412
D4×C11×C162
#3386611