Finite Group Databasebeta

← #14651963

Subgroups — #14651963

Order 2816.

408 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069553C211yesmaximal, characteristic
2#13068481C211yesmaximal, characteristic
3C4×#66899C211yesmaximal, characteristic
4C2×#10622118C211yesmaximal, characteristic
5#13066456C211yesmaximal, characteristic
6C11⋊#1273C211yesmaximal, characteristic
7C2×C11×Q8⋊C8C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66899C411yescharacteristic
12C2×#66899C411yescharacteristic
13C2×C8×Dic11—21no—
14C4×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18C11×Q8⋊C8—22no—
19#10622188—21no—
20#10622167C411yescharacteristic
21#10622167C411yescharacteristic
22#10622162—21no—
23#10622162—21no—
24#10622118—22no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C4×Q8×C11—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4×Dic11—21no—
39C22×C11⋊C8—21no—
40C22×C11⋊C8C2×C411yescharacteristic
41C22×C11⋊C8C2×C411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C22×C11⋊C8D411yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8D412yes—
46C4×C8×C11—21no—
47C4×C8×C11—21no—
48#66899—22no—
49#66899C814yescomplemented
50C11⋊#95—21no—
51C8×Dic11—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58#9543—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11C2×C812yes—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11—41no—
83C42×C11—41no—
84C42×C11C2×D411yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C42×C11#4111yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2×C812yes—
91C4⋊Dic11M1612yes—
92C4×Dic11—41no—
93C4×Dic11—41no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8C2×C812yes—
108C2×C11⋊C8SD1612yes—
109#1984—111no—
110C8×C4⋊C4—111no—
111C4×#103—111no—
112C2×#334—111no—
113C2×Q8⋊C8D1111yescharacteristic
114#1279—111no—
115#1273—111no—
116C23×C11C4×D411yescharacteristic
117Q8×C11—22no—
118Q8×C11—22no—
119Q8×C11—41no—
120Q8×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#11711yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12611yescharacteristic
135C2×C4×C11C22×C811yescharacteristic
136C2×C4×C11C2×M1611yescharacteristic
137C2×C4×C11#13111yescharacteristic
138C2×C4×C11#13111yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11#13511yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C8×C11—42no—
150C8×C11—42no—
151C11⋊C8—22no—
152C11⋊C8—22no—
153C11⋊C8—41no—
154C11⋊C8—41no—
155C11⋊C8—81no—
156C2×C4×Q8C2×D1111yescharacteristic
157C2×C4⋊C8—111no—
158C2×C4⋊C8C2×D1111yescharacteristic
159C2×#103—111no—
160C2×#103—111no—
161C2×C4×C8—111no—
162C2×C4×C8—111no—
163C2×C4×C8—221no—
164C2×C4×C8C2×D1111yescharacteristic
165C4×C4⋊C4—111no—
166#340—111no—
167#340—111no—
168#336—221no—
169#336—221no—
170#336—221no—
171#334—222no—
172Q8⋊C8—22no—
173C22×C11#38811yescharacteristic
174C22×C11C8×D411yescharacteristic
175C22×C11#43511yescharacteristic
176C22×C11C4×SD1611yescharacteristic
177C22×C11#44111yescharacteristic
178C22×C11#44311yescharacteristic
179C22×C11#44411yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—81no—
184C4×C11#43111yescharacteristic
185C4×C11#43311yescharacteristic
186C4×C11C8×D411yescharacteristic
187C4×C11#43611yescharacteristic
188C4×C11#46111yescharacteristic
189C4×C11#46411yescharacteristic
190C4×C11#48311yescharacteristic
191C4×C11#48511yescharacteristic
192Dic11—42no—
193Dic11—42no—
194C22×Q8C4×D1111yescharacteristic
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—111no—
198C22×C8—111no—
199C22×C8—111no—
200C22×C8—111no—
201C22×C8—221no—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—111no—
209C2×C4⋊C4C4×D1111yescharacteristic
210C2×C42—21no—
211C2×C42—221no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8C22⋊D1112yes—
217#103—114no—
218#103—222no—
219C4×C8—21no—
220C4×C8—21no—
221C4×C8—221no—
222C4×C8—221no—
223C4×C8—221no—
224C4×C8—221no—
225C4×C8—442no—
226#95—221no—
227C2×C11C8×SD1611yescharacteristic
228C2×C11#157911yescharacteristic
229C2×C11#158211yescharacteristic
230C2×C11#158711yescharacteristic
231C2×C11#192311yescharacteristic
232C2×C11#192711yescharacteristic
233C2×C11#192911yescharacteristic
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8C8×D1112yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C22×C4#434111yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—112no—
254C2×C8—112no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—441no—
266C2×C8—441no—
267C2×C8—441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—112no—
273C4⋊C4—112no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C42—41no—
277C42—41no—
278C42—441no—
279C42—441no—
280C42#433911yescharacteristic
281C42#434111yescharacteristic
282C42#434111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#954311yescharacteristic, complemented, Sylow
285C23(C22⋊D11)⋊C411yescharacteristic
286Q8—22no—
287Q8—22no—
288Q8—41no—
289Q8—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4#6693011yescharacteristic
305C2×C4#6693211yescharacteristic
306C2×C4#6693611yescharacteristic
307C2×C4C2×C8×D1111yescharacteristic
308C2×C4#6695411yescharacteristic
309C2×C4M16×D1111yescharacteristic
310C2×C4#6696011yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C2×C4#6696811yescharacteristic
313C2×C4#6697111yescharacteristic
314C2×C4#6697211yescharacteristic
315C2×C4C4×C22⋊D1111yescharacteristic
316C2×C4#6698911yescharacteristic
317C2×C4#6699211yescharacteristic
318C8—42no—
319C8—42no—
320C8—222no—
321C8—222no—
322C8—441no—
323C8—441no—
324C8—881no—
325C22(C22⋊D11)⋊C811yescharacteristic
326C22#1062234111yescharacteristic
327C22#1062240111yescharacteristic
328C22#1062240211yescharacteristic
329C22#1062243611yescharacteristic
330C22#1062243711yescharacteristic
331C22#1062255811yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—442no—
337C4—442no—
338C4#1062233111yescharacteristic
339C4#1062233311yescharacteristic
340C4#1062241811yescharacteristic
341C4#1062242711yescharacteristic
342C4C8×C22⋊D1111yescharacteristic
343C4#1062274111yescharacteristic
344C4#1062277511yescharacteristic
345C4#1062279811yescharacteristic
346C2#1306741311yescharacteristic
347C2#1306743211yescharacteristic
348C2#1306745511yescharacteristic
349C2#1306749011yescharacteristic
350C2#1306922511yescharacteristic
351C2#1306925311yescharacteristic
352C2#1306926711yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socle, prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenterC2×Q8⋊C8D11
hypocenterC11#9543
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
49. #66899C8semidirect
284. C11#9543semidirect

Maximal subgroups

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

subgroupindex
#130695532
#130684812
C4×#668992
C2×#106221182
#130664562
C11⋊#12732
C2×C11×Q8⋊C82
#954311