Finite Group Databasebeta

← #14908493

Subgroups — #14908493

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079155C211yesmaximal, characteristic, complemented
2#13070780C212yesmaximal, complemented
3#13070773C212yesmaximal, complemented
4#13070763C212yesmaximal, complemented
5#13070758C212yesmaximal, complemented
6#13070402C211yesmaximal, characteristic, complemented
7C2×#10622128C211yesmaximal, characteristic, complemented
8#13070375C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic
10#13070323C211yesmaximal, characteristic
11C11×#2951C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C11×#520—21no—
14#10623050—21no—
15C11×#440—22no—
16C4×C11×Q16C2212yes—
17C4×C11×D8C2212yes—
18C2×C11×#107C2211yescharacteristic
19C11×#417—21no—
20C11×#405C2211yescharacteristic
21#10622734—21no—
22#10622719C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622315—22no—
27#10622296C2212yes—
28#10622295C2212yes—
29#10622202C2211yescharacteristic
30#10622202C2212yes—
31#10622202C2211yescharacteristic
32#10622200C2211yescharacteristic
33#10622200C2212yes—
34#10622200C2211yescharacteristic
35#10622128C2212yes—
36#10622128C2212yes—
37#10622128C2212yes—
38#10622127C2212yes—
39C4⋊(C11⋊C16)C2212yes—
40C4⋊(C11⋊C16)C2212yes—
41C2×C11×#41—21no—
42C11×#135—22no—
43C11×#135Q814yescomplemented
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8C2311yescharacteristic
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×Q8×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11—42no—
52C11×#117—41no—
53C11×#117D411yescharacteristic
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—41no—
56#66979—21no—
57C2×C4⋊Dic11—21no—
58#66943—41no—
59#66941—41no—
60#66931—42no—
61#66923—22no—
62#66922—22no—
63C11×#107—21no—
64C11×#107C2312yes—
65C11×#103—22no—
66C11×#102—22no—
67C11×#97D412yes—
68C4×C8×C11C2312yes—
69#66882—22no—
70#66882—21no—
71#66882C2311yescharacteristic
72#66882C2312yes—
73#66882C2311yescharacteristic
74#66881—22no—
75#66881—21no—
76#66876—22no—
77C2×C11⋊C16—22no—
78C2×C11⋊C16C2312yes—
79C2×C11⋊C16C2311yescharacteristic
80C2×C11⋊C16C2311yescharacteristic
81#33634—111nomaximal, Sylow
82C11×#41—24no—
83C11×#41—42no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—42no—
90C22×C4×C11C2×D411yescharacteristic
91C22×Dic11—41no—
92C2×Dic22—42no—
93C11×Q16—21no—
94C11×Q16C2×Q812yes—
95C11×SD16—24no—
96C11×D8—21no—
97C11×D8C2×Q812yes—
98C11×M16—22no—
99C2×C8×C11C2×D412yes—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×Q812yes—
102C2×C8×C11#4112yes—
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4D811yescharacteristic
108C11×C4⋊C4D811yescharacteristic
109C11×C22⋊C4—42no—
110C11×C22⋊C4D812yes—
111C42×C11—42no—
112C42×C11C2×D412yes—
113C22⋊Dic11—41no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—42no—
118C4⋊Dic11—41no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121C4×Dic11—41no—
122C11⋊C16—21no—
123C11⋊C16—21no—
124C11⋊C16—22no—
125#3164—111no—
126#2951D1111yescharacteristic
127#2229—112no—
128#2228—112no—
129#2226—112no—
130#2225—112no—
131#2159—111no—
132C2×#367—111no—
133#2151—111no—
134#2139—111no—
135#2138—111no—
136C23×C11—41no—
137C23×C11C2×D811yescharacteristic
138Q8×C11—22no—
139Q8×C11—41no—
140D4×C11—22no—
141D4×C11—44no—
142D4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—44no—
145C2×C4×C11—42no—
146C2×C4×C11—162no—
147C2×C4×C11—161no—
148C2×C4×C11C22⋊Q812yes—
149C2×C4×C11C2×D812yes—
150C2×C4×C11C2×D812yes—
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11#13712yes—
153C2×C4×C11C22×D411yescharacteristic
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—42no—
157C2×Dic11—161no—
158Dic22—162no—
159C8×C11—22no—
160C8×C11C22⋊Q812yes—
161C8×C11C22×Q811yescharacteristic
162C8×C11C2×#4111yescharacteristic
163C2×#135C2×D1111yescharacteristic
164#544—221no—
165#520—21no—
166C2×M32—111no—
167C22×C16—111no—
168#501—222no—
169#500—112no—
170#499—112no—
171#440—22no—
172C4×Q16C2×D1112yes—
173C4×D8C2×D1112yes—
174#428—221no—
175#427—111no—
176C2×#107—111no—
177C2×#107C2×D1111yescharacteristic
178#417—21no—
179#405C2×D1111yescharacteristic
180#367—112no—
181#367—112no—
182#367—112no—
183#366—112no—
184C4⋊C16—112no—
185C4⋊C16—112no—
186#358—111no—
187#358—111no—
188#358—112no—
189#357—111no—
190#357—111no—
191#357—112no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#47412yes—
198C22×C11C22×D811yescharacteristic
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—42no—
202C4×C11—82no—
203C4×C11#47412yes—
204C4×C11C2×C22⋊Q811yescharacteristic
205C4×C11C2×#13711yescharacteristic
206Dic11—81no—
207Dic11—82no—
208Dic11—81no—
209C2×#41—21no—
210#135—22no—
211#135Dic2214yescomplemented
212C2×Q16C22×D1111yescharacteristic
213C2×SD16—21no—
214C2×D8C22×D1111yescharacteristic
215C2×M16C22⋊D1111yescharacteristic
216C22×C8C22×D1111yescharacteristic
217C4⋊Q8—222no—
218C4⋊Q8—441no—
219#125—222no—
220#125—441no—
221C22⋊Q8—442no—
222C4×Q8—22no—
223C4×D4—22no—
224C4×D4—42no—
225#117—41no—
226#117—221no—
227#117C22⋊D1111yescharacteristic
228C2×C4⋊C4—21no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—221no—
231M32—222no—
232C2×C16—112no—
233C2×C16—111no—
234C2×C16—111no—
235C2×C16—222no—
236#107—21no—
237#107—111no—
238#107—112no—
239#107—111no—
240#107—221no—
241#107—222no—
242#107C22×D1112yes—
243#106—221no—
244#106—222no—
245#103—22no—
246#102—22no—
247#97C22⋊D1112yes—
248C4×C8C22×D1112yes—
249C2×C11—22no—
250C2×C11—82no—
251C2×C11C2×#47411yescharacteristic
252C2×C11#341611yescharacteristic
253C2×C11#341611yescharacteristic
254#41—24no—
255#41—42no—
256C2×Q8—21no—
257C2×Q8—442no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—441no—
264C22×C4C2×C22⋊D1111yescharacteristic
265Q16—21no—
266Q16C2×Dic2212yes—
267SD16—24no—
268D8—21no—
269D8C2×Dic2212yes—
270M16—22no—
271C2×C8C2×Dic2212yes—
272C2×C8#433912yes—
273C2×C8C2×C22⋊D1112yes—
274C2×C8C2×C22⋊D1111yescharacteristic
275C2×C8C23×D1111yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—221no—
280C4⋊C4—222no—
281C4⋊C4—221no—
282C4⋊C4—441no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C4⋊C4—442no—
286C4⋊C4#432311yescharacteristic
287C4⋊C4#432311yescharacteristic
288C22⋊C4—42no—
289C22⋊C4—441no—
290C22⋊C4#432312yes—
291C42—42no—
292C42—441no—
293C42C2×C22⋊D1112yes—
294C16—221no—
295C16—221no—
296C16—222no—
297C11#3363411yescharacteristic, complemented, Sylow
298C23—41no—
299C23C2×#432311yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—1762no—
303D4—22no—
304D4—44no—
305D4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—162no—
310C2×C4—161no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—442no—
314C2×C4—1761no—
315C2×C4#6697712yes—
316C2×C4C2×#432312yes—
317C2×C4C2×#432312yes—
318C2×C4C2×#432311yescharacteristic
319C2×C4#6700412yes—
320C2×C4C22×C22⋊D1111yescharacteristic
321C8—22no—
322C8#6697712yes—
323C8C22×Dic2211yescharacteristic
324C8C2×#433911yescharacteristic
325C22—21no—
326C22—21no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22#1062262012yes—
331C22C22×#432311yescharacteristic
332C4—22no—
333C4—22no—
334C4—42no—
335C4—82no—
336C4—882no—
337C4—881no—
338C4—881no—
339C4#1062262012yes—
340C4C2×#6697711yescharacteristic
341C4C2×#6700411yescharacteristic
342C2—22no—
343C2—82no—
344C2C2×#1062262011yescharacteristic
345C2#1308176011yescharacteristic
346C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2951C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenter#2951D11
hypocenterC11#33634
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #13079155C2semidirect
2. #13070780C2semidirect
3. #13070773C2semidirect
4. #13070763C2semidirect
5. #13070758C2semidirect
6. #13070402C2semidirect
7. C2×#10622128C2semidirect
8. #13070375C2semidirect
43. C11×#135Q8semidirect
211. #135Dic22semidirect
297. C11#33634semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130707802
#130707732
#130707632
#130707582
#130704022
C2×#106221282
#130703752
#130703282
#130703232
C11×#29512
#3363411