Finite Group Databasebeta

← #14911134

Subgroups — #14911134

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080964C211yesmaximal, characteristic
2#13070896C211yesmaximal, characteristic, complemented
3#13070811C212yesmaximal, complemented
4#13070801C212yesmaximal, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070758C211yesmaximal, characteristic, complemented
7#13070714C212yesmaximal, complemented
8C4×#66892C211yesmaximal, characteristic, complemented
9D4×C11⋊C16C211yesmaximal, characteristic, complemented
10C2×#10622128C212yesmaximal, complemented
11C11×#3338C211yesmaximal, characteristic, complemented
12C11×#554—21no—
13#10623086—21no—
14C11×#500C2211yescharacteristic
15C11×#484—22no—
16C11×#477—21no—
17C11×#467C2212yes—
18C4×C11×Q16C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×#66892C2211yescharacteristic
22#10622728C2212yes—
23C2×#66882C2212yes—
24C22×C11⋊C16C2212yes—
25#10622459—21no—
26#10622349—22no—
27C4×D88C2211yescharacteristic
28#10622295C2211yescharacteristic
29#10622202C2212yes—
30#10622202C2211yescharacteristic
31C22⋊(C11⋊C16)C2212yes—
32#10622129C2212yes—
33#10622129C2211yescharacteristic
34#10622128C2212yes—
35#10622128C2212yes—
36#10622128C2211yescharacteristic
37#10622128C2212yes—
38#10622128C2212yes—
39C4⋊(C11⋊C16)C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4341—41no—
42C2×C11×Q16C2311yescharacteristic
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—21no—
45C11×#125—41no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—42no—
48C4×Q8×C11—21no—
49C4×D4×C11—41no—
50C4×D4×C11D411yescharacteristic
51C2×C11×C4⋊C4—22no—
52#66983—22no—
53C2×C4⋊Dic11—22no—
54C2×D88C2311yescharacteristic
55#66950—41no—
56#66939—42no—
57C4×D44—21no—
58#66922—21no—
59C11×#107—21no—
60C11×#107—22no—
61C11×#107C2312yes—
62C11×#107C2311yescharacteristic
63C11×C4⋊C8D411yescharacteristic
64C11×#103—21no—
65C11×#103—22no—
66C11×C22⋊C8D412yes—
67C4×C8×C11C2311yescharacteristic
68#66892—22no—
69#66885—22no—
70#66885—21no—
71#66882—21no—
72#66882—22no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75C2×C11⋊C16—24no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33902—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×D4×C11D811yescharacteristic
83C22×C4×C11—42no—
84C22×C4×C11C2×D412yes—
85C2×C22⋊D11—42no—
86C22×Dic11—42no—
87#4341—84no—
88C2×D44—21no—
89C2×C4×D11—41no—
90C2×Dic22—41no—
91C11×Q16—21no—
92C11×Q16—21no—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4D811yescharacteristic
105C11×C22⋊C4—42no—
106C11×C22⋊C4D812yes—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—41no—
114C4⋊Dic11—42no—
115D88—21no—
116D88—21no—
117C11⋊C16—22no—
118C11⋊C16—21no—
119C11⋊C16#4112yescomplemented
120#3338D1111yescharacteristic, complemented
121#3334—111no—
122#2254—111no—
123#2235—112no—
124#2233—112no—
125#2226—111no—
126#2225—111no—
127#2217—112no—
128C4×SD32—111no—
129D4×C16—111no—
130C2×#367—112no—
131C23×C11C2×D812yes—
132C22×D11—41no—
133Q8×C11—41no—
134Q8×C11—41no—
135Q8×C11—161no—
136D4×C11SD3214yescomplemented
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—162no—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×D812yes—
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C22⋊D11—84no—
148C2×Dic11—42no—
149C2×Dic11—41no—
150C2×Dic11—84no—
151D44—41no—
152D44—41no—
153C4×D11—82no—
154Dic22—82no—
155C8×C11—22no—
156C8×C11—21no—
157C8×C11C2×#4111yescharacteristic
158C8×C112−1+411yescharacteristic
159#554—21no—
160#547—221no—
161C2×SD32—111no—
162C22×C16—112no—
163#500—111no—
164#500C2×D1111yescharacteristic
165#484—22no—
166#480—222no—
167#477—21no—
168#474—221no—
169#467C2×D1112yes—
170#466—112no—
171C4×Q16C2×D1111yescharacteristic
172C4×D8—111no—
173C8×D4C2×D1111yescharacteristic
174C2×#107—112no—
175C2×#107C2×D1112yes—
176#367—111no—
177#367—112no—
178#367—112no—
179#367—112no—
180#367—112no—
181C4⋊C16—111no—
182#358—111no—
183#358—112no—
184#357—111no—
185#357—112no—
186C22⋊C16—112no—
187C4×C16—111no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11C2×SD3214yes—
191C22×C11C22×D811yescharacteristic
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—22no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—82no—
200C4×C11C2×SD3212yes—
201C4×C11#54711yescharacteristic
202C4×C11#57811yescharacteristic
203Dic11—82no—
204Dic11—81no—
205C2×#41—441no—
206C2×Q16C22×D1111yescharacteristic
207C2×D8—111no—
208C22×C8C22×D1112yes—
209C4⋊Q8—21no—
210C4⋊Q8—221no—
211#125—41no—
212#123—442no—
213C22⋊Q8—22no—
214C22⋊Q8—42no—
215C22⋊Q8—441no—
216#121—222no—
217C4×Q8—21no—
218C4×D4—41no—
219C4×D4—221no—
220C4×D4C22⋊D1111yescharacteristic
221C2×C4⋊C4—22no—
222C2×C4⋊C4—222no—
223SD32—222no—
224C2×C16—111no—
225C2×C16—111no—
226C2×C16—112no—
227C2×C16—224no—
228#107—22no—
229#107—21no—
230#107—111no—
231#107—112no—
232#107—222no—
233#107—221no—
234#107C22×D1111yescharacteristic
235#107C22×D1112yes—
236C4⋊C8C22⋊D1111yescharacteristic
237#103—21no—
238#103—22no—
239#102—221no—
240#102—222no—
241C22⋊C8C22⋊D1112yes—
242C4×C8C22×D1111yescharacteristic
243C2×C11—24no—
244C2×C11#333411yescharacteristic
245C2×C11C22×SD3211yescharacteristic
246C2×C11#341611yescharacteristic
247D11—161no—
248#41—884no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—441no—
252C2×D4—221no—
253C2×D4—442no—
254C2×D4#432311yescharacteristic
255C22×C4—42no—
256C22×C4—442no—
257C22×C4—441no—
258C22×C4C2×C22⋊D1112yes—
259Q16—21no—
260Q16—21no—
261D8—221no—
262D8—221no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8C2×C22⋊D1111yescharacteristic
266C2×C8C2×C22⋊D1112yes—
267C2×C8C23×D1111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4#432311yescharacteristic
279C22⋊C4—42no—
280C22⋊C4—441no—
281C22⋊C4—442no—
282C22⋊C4#432312yes—
283C42—41no—
284C42C2×C22⋊D1111yescharacteristic
285C16—112no—
286C16—222no—
287C16—221no—
288C11#3390211yescharacteristic, complemented, Sylow
289C23—441no—
290C23C2×#432312yes—
291Q8—41no—
292Q8—41no—
293Q8—161no—
294Q8—882no—
295D4—441no—
296D4—441no—
297D4—884no—
298D4#6689214yescomplemented
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—162no—
305C2×C4—441no—
306C2×C4—442no—
307C2×C4—884no—
308C2×C4—882no—
309C2×C4C2×#432311yescharacteristic
310C2×C4C2×#432312yes—
311C2×C4C2×#432311yescharacteristic
312C2×C4C22×C22⋊D1111yescharacteristic
313C8—22no—
314C8—21no—
315C8#41×D1111yescharacteristic
316C8#6704311yescharacteristic
317C22—22no—
318C22—22no—
319C22—881no—
320C22—881no—
321C22—881no—
322C22C2×#6689214yes—
323C22C22×#432311yescharacteristic
324C4—22no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—82no—
329C4—881no—
330C4—882no—
331C4C2×#6689212yes—
332C4#1062335511yescharacteristic
333C4#1062336911yescharacteristic
334C2—24no—
335C2—1761no—
336C2#1308095911yescharacteristic
337C2C22×#6689211yescharacteristic
338C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3338C2
socleC22×C11C22×D8
prime radical#13080964C2
hypercenter#3338D11
hypocenterC11#33902
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3338

Complements

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

NH ≅ G/Ntype
2. #13070896C2semidirect
3. #13070811C2semidirect
4. #13070801C2semidirect
5. #13070760C2semidirect
6. #13070758C2semidirect
7. #13070714C2semidirect
8. C4×#66892C2semidirect
9. D4×C11⋊C16C2semidirect
10. C2×#10622128C2semidirect
11. C11×#3338C2semidirect
119. C11⋊C16#41semidirect
120. #3338D11semidirect
136. D4×C11SD32semidirect
288. C11#33902semidirect
298. D4#66892semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130708962
#130708112
#130708012
#130707602
#130707582
#130707142
C4×#668922
D4×C11⋊C162
C2×#106221282
C11×#33382
#3390211