Finite Group Databasebeta

← #14737874

Subgroups — #14737874

Order 2816.

586 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078742C212yesmaximal
2C2×#10622292C211yesmaximal, characteristic
3#13068167C214yesmaximal, complemented
4#13068131C212yesmaximal, complemented
5#13068107C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic
7#13067316C212yesmaximal
8C11×#3170C211yesmaximal, characteristic
9C11×#533C2212yes—
10C2×C4×Dic22C2211yescharacteristic
11C11×#500C2211yescharacteristic
12C11×#494C2211yescharacteristic
13C11×#487C2212yes—
14C11×#467—21no—
15C11×#467—21no—
16C4×C11×Q16—21no—
17C4×C11×Q16—21no—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66879—21no—
20C2×Dic11⋊C8—21no—
21#10622707C2214yes—
22#10622703C2214yes—
23#10622663—22no—
24#10622656—22no—
25#10622643—24no—
26#10622539C2212yes—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622292—21no—
29#10622292—21no—
30#10622292C2212yes—
31#10622292C2212yes—
32#10622185C2214yes—
33#10622185C2214yes—
34#10622096C2212yes—
35#10622095C2212yes—
36C22×Dic22D411yescharacteristic
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C11×C4⋊Q8C2312yes—
42C11×C4⋊Q8C2312yes—
43C11×#125—22no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—22no—
46C4×Q8×C11—22no—
47C4×Q8×C11—22no—
48C11×#117—22no—
49C2×C42×C11C2311yescharacteristic
50C2×#4326—24no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22D412yes—
58C4×Dic22C2312yes—
59C11×#107—21no—
60C11×#107—21no—
61C11×#103—22no—
62C11×#103—22no—
63C4×C8×C11D411yescharacteristic
64C4×C8×C11D411yescharacteristic
65C4×C8×C11C2311yescharacteristic
66C4×C8×C11C2311yescharacteristic
67#66899—24no—
68C22⋊(C11⋊C8)—22no—
69#66879—22no—
70#66879—22no—
71Dic11⋊C8—22no—
72Dic11⋊C8—22no—
73#66874—24no—
74#66872—24no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)C2312yes—
77C4⋊(C11⋊C8)C2314yes—
78#66867—22no—
79#19290—111nomaximal, Sylow
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C2×Dic22—21no—
88C2×Dic22—42no—
89C2×Dic22C2×D412yes—
90C11×Q16—42no—
91C11×Q16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C22⋊C4—42no—
105C42×C11—42no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11C2411yescharacteristic
110#4326—48no—
111C4⋊Dic11—21no—
112C4⋊Dic11C2×D412yes—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C2×C11⋊C8—24no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—42no—
120#3170D1111yescharacteristic
121#3113—112no—
122C2×#446—111no—
123#1700—114no—
124#1694—112no—
125#1690—112no—
126#1568—111no—
127#1552—112no—
128C23×C11#12111yescharacteristic
129Q8×C11—42no—
130Q8×C11—44no—
131Q8×C11—42no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C2×#4111yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148Dic22—24no—
149Dic22—42no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—21no—
153C8×C11#13712yes—
154C11⋊C8—42no—
155C11⋊C8—44no—
156#533C2×D1112yes—
157C2×C4×Q8—111no—
158#500C2×D1111yescharacteristic
159#494C2×D1111yescharacteristic
160#487C2×D1112yes—
161#483—222no—
162#475—114no—
163#467—21no—
164#467—21no—
165#462—114no—
166#451—222no—
167#446—112no—
168#446—112no—
169#446—221no—
170#446—221no—
171#441—224no—
172C4×Q16—21no—
173C4×Q16—21no—
174#432—112no—
175C2×C4⋊C8—111no—
176C2×C4⋊C8—221no—
177C2×#97—221no—
178C2×C4×C8C2×D1111yescharacteristic
179#335—112no—
180#334—112no—
181#332—114no—
182#332—114no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11#47312yes—
186C22×C11C2×#12111yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—82no—
192C4×C11—82no—
193C4×C11C2×#13711yescharacteristic
194C4×C11#57512yes—
195C4×C11#57511yescharacteristic
196Dic11—42no—
197Dic11—42no—
198C22×Q8—111no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—224no—
202C22×C8—221no—
203C22×C8C22⋊D1111yescharacteristic
204C22×C8C22⋊D1111yescharacteristic
205C4⋊Q8C22×D1112yes—
206C4⋊Q8C22×D1112yes—
207#125—22no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8—112no—
213C4×Q8—112no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—22no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—221no—
219C2×C42—221no—
220C2×C42C22×D1111yescharacteristic
221#107—21no—
222#107—21no—
223#106—224no—
224C4⋊C8—112no—
225C4⋊C8—114no—
226C4⋊C8—222no—
227C4⋊C8—222no—
228C4⋊C8—221no—
229#103—22no—
230#103—22no—
231#103—224no—
232#103—224no—
233C22⋊C8—222no—
234#97—222no—
235#97—222no—
236#97—222no—
237C4×C8C22⋊D1111yescharacteristic
238C4×C8C22⋊D1111yescharacteristic
239C4×C8C22×D1111yescharacteristic
240C4×C8C22×D1111yescharacteristic
241C2×C11—22no—
242C2×C11#303711yescharacteristic
243C2×C11#305411yescharacteristic
244C2×C11C2×#47311yescharacteristic
245C2×Q8—22no—
246C2×Q8—22no—
247C2×Q8—112no—
248C2×Q8—221no—
249C2×Q8—442no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4D4×D1111yescharacteristic
253C22×C4#434111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255Q16—42no—
256Q16—42no—
257Q16—448no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—224no—
261C2×C8—222no—
262C2×C8—442no—
263C2×C8C2×C22⋊D1111yescharacteristic
264C2×C8C2×C22⋊D1111yescharacteristic
265C2×C8C2×C22⋊D1111yescharacteristic
266C2×C8C2×C22⋊D1111yescharacteristic
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—112no—
274C4⋊C4—221no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C22⋊C4—42no—
278C42—42no—
279C42—222no—
280C42—222no—
281C42D4×D1111yescharacteristic
282C42#434111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C42C23×D1111yescharacteristic
285C11#1929011yescharacteristic, complemented, Sylow
286C23#6699111yescharacteristic
287Q8—44no—
288Q8—42no—
289Q8—42no—
290Q8—224no—
291Q8—442no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4#6699111yescharacteristic
303C2×C4#6699111yescharacteristic
304C2×C4#6699111yescharacteristic
305C2×C4C2×D4×D1111yescharacteristic
306C2×C4C2×#434111yescharacteristic
307C2×C4C22×C22⋊D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—444no—
312C8—442no—
313C8#6700412yes—
314C22—21no—
315C22—21no—
316C22#1062280512yes—
317C22C2×#6699111yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—82no—
323C4—82no—
324C4—442no—
325C4—442no—
326C4#1062329912yes—
327C4#1062335311yescharacteristic
328C4C2×#6700411yescharacteristic
329C2—22no—
330C2#1307808411yescharacteristic
331C2#1307822111yescharacteristic
332C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#3170D11
hypocenterC11#19290
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068167C2semidirect
4. #13068131C2semidirect
5. #13068107C2semidirect
285. C11#19290semidirect

Maximal subgroups

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

subgroupindex
#130787422
C2×#106222922
#130681672
#130681312
#130681072
#130673792
#130673162
C11×#31702
#1929011