Finite Group Databasebeta

← #14910645

Subgroups — #14910645

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#13080963C211yesmaximal, characteristic
2Q16×D44C211yesmaximal, characteristic, complemented
3#13070845C211yesmaximal, characteristic, complemented
4#13070815C212yesmaximal, complemented
5#13070713C212yesmaximal, complemented
6#13070662C211yesmaximal, characteristic, complemented
7#13070534C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9#13070435C211yesmaximal, characteristic, complemented
10D11×#358C212yesmaximal, complemented
11C11×#2225C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2212yes—
13#10623257—21no—
14Q8×D44—21no—
15C11×#500C2211yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C2×#66892C2211yescharacteristic
18#10622700—21no—
19#10622644—21no—
20C2×#66864C2212yes—
21C2×C16×D11C2212yes—
22#10622500C2212yes—
23#10622496C2212yes—
24#10622495—22no—
25D11×#107C2212yes—
26#10622421—22no—
27#10622312C2211yescharacteristic
28C4×D88C2211yescharacteristic
29C8×D44C2211yescharacteristic
30C11×#367C2212yes—
31C11×C4⋊C16C2211yescharacteristic
32C11×#358C2212yes—
33#10622202C2211yescharacteristic
34(C2×D11)⋊C16C2212yes—
35#10622141C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622129C2211yescharacteristic
39#10622128C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4343—41no—
42C2×Q8×D11—22no—
43C2×C11×Q16C2311yescharacteristic
44C11×C4⋊Q8—21no—
45C4×Q8×C11—21no—
46#66999—41no—
47C2×#4326—22no—
48Q16×D11—24no—
49Q16×D11—42no—
50C2×Dic44—21no—
51C2×Dic44C2312yes—
52C2×D88C2311yescharacteristic
53C2×C8×D11C2312yes—
54#66950—22no—
55#66950—42no—
56#66948—22no—
57#66947—42no—
58C4⋊C4×D11—22no—
59C4×D44—21no—
60C4×D44—41no—
61C4×D44D411yescharacteristic
62#66922—21no—
63#66922—41no—
64C2×C11×C16C2312yes—
65C11×#107—21no—
66C11×#107C2312yes—
67C11×#107C2311yescharacteristic
68C11×#103—21no—
69C4×C8×C11C2311yescharacteristic
70#66892—22no—
71#66885—21no—
72(C2×D11)⋊C8D412yes—
73#66882C2311yescharacteristic
74C2×C11⋊C16C2311yescharacteristic
75C2×C11⋊C16C2311yescharacteristic
76#66874—22no—
77#66873—22no—
78#66871—22no—
79C4⋊(C11⋊C8)D411yescharacteristic
80#66864—42no—
81C16×D11—42no—
82#33865—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85#4343—84no—
86Q8×D11—44no—
87Q8×D11—82no—
88C2×D44—21no—
89C2×D44—42no—
90C2×D44D811yescharacteristic
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11—41no—
94C2×C4×D11C2×D412yes—
95C2×Dic22—22no—
96C2×Dic22—42no—
97C11×Q16—21no—
98C11×Q16#4112yescomplemented
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107#4326—44no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4D812yes—
112C4⋊Dic11—21no—
113C4⋊Dic11—42no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11D811yescharacteristic
117Dic11⋊C4—42no—
118C2×C11⋊C8C2×D412yes—
119Dic44—22no—
120Dic44—22no—
121Dic44—81no—
122D88—21no—
123D88—21no—
124C8×D11—22no—
125C8×D11—22no—
126C11×C16—22no—
127C11⋊C16—21no—
128C11⋊C16—21no—
129#3334—111no—
130D4×Q16—111no—
131#2241—111no—
132#2235—112no—
133#2225D1111yescharacteristic, complemented
134#2217—112no—
135#2208—111no—
136#2185—112no—
137C4×SD32—111no—
138D4×C16—111no—
139C2×#358—112no—
140C22×D11—41no—
141C22×D11C2×D812yes—
142Q8×C11—22no—
143Q8×C11—41no—
144Q8×C11—82no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11C2×D812yes—
154D44—41no—
155D44—41no—
156D44—84no—
157D44SD3214yescomplemented
158C4×D11—22no—
159C4×D11—22no—
160C4×D11—84no—
161C4×D11—84no—
162C4×D11—82no—
163Dic22—42no—
164Dic22—42no—
165Dic22—84no—
166C8×C11—21no—
167C8×C11C2×#4111yescharacteristic
168C8×C11H(5,𝔽2)11yescharacteristic
169C11⋊C8—22no—
170C22×Q16—112no—
171D4×Q8—221no—
172#547—221no—
173C2×SD32—111no—
174C2×SD32—112no—
175C22×C16—112no—
176#500C2×D1111yescharacteristic
177#494—111no—
178#480—222no—
179#474—221no—
180#467—112no—
181#466—112no—
182#462—221no—
183#451—222no—
184C4×Q16C2×D1111yescharacteristic
185C4×D8—111no—
186C8×D4—111no—
187C2×#107—112no—
188#367—111no—
189#367C2×D1112yes—
190C4⋊C16C2×D1111yescharacteristic
191#358—111no—
192#358—112no—
193#358—112no—
194#358—112no—
195#358C2×D1112yes—
196#357—111no—
197C22⋊C16—112no—
198C4×C16—111no—
199C22×C11C22×D811yescharacteristic
200C2×D11—22no—
201C2×D11—22no—
202C2×D11—81no—
203C2×D11—81no—
204C2×D11—81no—
205C2×D11C2×SD3214yes—
206C4×C11—21no—
207C4×C11—42no—
208C4×C11—82no—
209C4×C11—81no—
210C4×C11C2×SD3212yes—
211C4×C11#54611yescharacteristic
212C4×C11#57711yescharacteristic
213Dic11—22no—
214Dic11—81no—
215Dic11—82no—
216C2×#41—441no—
217C22×Q8—222no—
218C2×Q16—112no—
219C2×Q16—222no—
220C2×Q16—224no—
221C2×Q16—221no—
222C2×Q16—442no—
223C2×Q16C22×D1111yescharacteristic
224C2×D8—111no—
225C22×C8—112no—
226C4⋊Q8—21no—
227C4⋊Q8—221no—
228C4⋊Q8—441no—
229#123—442no—
230C22⋊Q8—222no—
231C22⋊Q8—442no—
232C22⋊Q8—441no—
233#121—222no—
234C4×Q8—21no—
235C4×D4—111no—
236C4×D4—221no—
237C4×D4—441no—
238C2×C4⋊C4—222no—
239SD32—222no—
240SD32—442no—
241C2×C16—111no—
242C2×C16—111no—
243C2×C16—442no—
244C2×C16C22×D1112yes—
245#107—21no—
246#107—111no—
247#107—222no—
248#107C22×D1111yescharacteristic
249#107C22×D1112yes—
250C4⋊C8—111no—
251#103—21no—
252#103—222no—
253#102—222no—
254#102—221no—
255C22⋊C8—112no—
256C4×C8C22×D1111yescharacteristic
257C2×C11#329411yescharacteristic
258C2×C11C22×SD3211yescharacteristic
259C2×C11#341711yescharacteristic
260D11—24no—
261D11—161no—
262#41—884no—
263C2×Q8—21no—
264C2×Q8—41no—
265C2×Q8—222no—
266C2×Q8—442no—
267C2×Q8—444no—
268C2×Q8—882no—
269C2×D4—111no—
270C2×D4—221no—
271C2×D4—442no—
272C22×C4—112no—
273C22×C4—442no—
274C22×C4—442no—
275C22×C4—441no—
276Q16—21no—
277Q16—222no—
278Q16—222no—
279Q16—444no—
280Q16—881no—
281Q16#434312yescomplemented
282D8—221no—
283D8—221no—
284C2×C8—112no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8D4×D1111yescharacteristic
288C2×C8C23×D1111yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—111no—
294C4⋊C4—221no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C22⋊C4—112no—
300C22⋊C4—442no—
301C22⋊C4—442no—
302C22⋊C4—441no—
303C42—41no—
304C42D4×D1111yescharacteristic
305C16—22no—
306C16—221no—
307C16—221no—
308C11#3386511yescharacteristic, complemented, Sylow
309C23—112no—
310C23—441no—
311Q8—22no—
312Q8—41no—
313Q8—82no—
314Q8—442no—
315Q8—442no—
316Q8—884no—
317D4—114no—
318D4—441no—
319D4—441no—
320D4—884no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—112no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—441no—
328C2×C4—442no—
329C2×C4—884no—
330C2×C4—884no—
331C2×C4—882no—
332C2×C4D8×D1111yescharacteristic
333C2×C4D8×D1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C8—21no—
336C8—222no—
337C8C2×#434311yescharacteristic
338C8#6704211yescharacteristic
339C22—114no—
340C22—222no—
341C22—222no—
342C22—881no—
343C22—881no—
344C22—881no—
345C22C2×D8×D1111yescharacteristic
346C4—21no—
347C4—42no—
348C4—82no—
349C4—81no—
350C4—222no—
351C4—882no—
352C4—881no—
353C4D11×SD3212yes—
354C4#1062316111yescharacteristic
355C4#1062330911yescharacteristic
356C2—224no—
357C2—1761no—
358C2#1308042611yescharacteristic
359C2C2×D11×SD3211yescharacteristic
360C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2225C2
socleC22×C11C22×D8
prime radical#13080963C2
hypercenter#2225D11
hypocenterC11#33865
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
2. Q16×D44C2semidirect
3. #13070845C2semidirect
4. #13070815C2semidirect
5. #13070713C2semidirect
6. #13070662C2semidirect
7. #13070534C2semidirect
8. C4×#66892C2semidirect
9. #13070435C2semidirect
10. D11×#358C2semidirect
11. C11×#2225C2semidirect
98. C11×Q16#41semidirect
133. #2225D11semidirect
157. D44SD32semidirect
281. Q16#4343semidirect
308. C11#33865semidirect

Maximal subgroups

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

subgroupindex
#130809632
Q16×D442
#130708452
#130708152
#130707132
#130706622
#130705342
C4×#668922
#130704352
D11×#3582
C11×#22252
#3386511