Finite Group Databasebeta

← #14724330

Subgroups — #14724330

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic
2#13077550C211yesmaximal, characteristic
3#13067523C214yesmaximal, complemented
4#13067433C214yesmaximal, complemented
5#13067371C211yesmaximal, characteristic
6#13067071C211yesmaximal, characteristic
7#13067070C211yesmaximal, characteristic
8C2×#10622092C211yesmaximal, characteristic
9C11×#2960C211yesmaximal, characteristic
10C11×#533C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#446—21no—
13C11×#446C2212yes—
14C8×Q8×C11—21no—
15C8×Q8×C11C2212yes—
16C11×#424—21no—
17C11×#423C2211yescharacteristic
18C11×#405—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622715—21no—
21#10622714—21no—
22#10622706C411yescharacteristic
23#10622705C411yescharacteristic
24#10622694C411yescharacteristic
25#10622691C411yescharacteristic
26#10622664C414yes—
27C4×#4326C2214yes—
28#10622537C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622292—21no—
32#10622292C2212yes—
33C8×Dic22—21no—
34C8×Dic22C2212yes—
35Q8⋊(C11⋊C8)C2214yes—
36#10622122C2214yes—
37#10622118C2214yes—
38#10622092C2212yes—
39#10622092C2212yes—
40C2×C11×M16—21no—
41C22×C8×C11D411yescharacteristic
42C22×C8×C11D411yescharacteristic
43C11×C4⋊Q8C2×C411yescharacteristic
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8C2×C412yes—
48C4×Q8×C11—21no—
49C4×Q8×C11C2312yes—
50C11×#117—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326C2×C414yes—
53#66979—21no—
54#66977—21no—
55#66977C2×C412yes—
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8C2×C412yes—
59#66923—21no—
60#66922C2×C411yescharacteristic
61#66922C2×C411yescharacteristic
62C4×Dic22—21no—
63C4×Dic22C2312yes—
64C11×C4⋊C8—22no—
65C11×C4⋊C8—22no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8C2312yes—
68C11×#97—22no—
69C4×C8×C11—22no—
70C4×C8×C11D411yescharacteristic
71C4×C8×C11D411yescharacteristic
72C4×C8×C11C2311yescharacteristic
73C4×C8×C11C2311yescharacteristic
74#66899C2×C414yes—
75#66879—22no—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78C8×Dic11—22no—
79#66874C2×C414yes—
80#66871C2×C414yes—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84C4×C11⋊C8C2×C411yescharacteristic
85C4×C11⋊C8C2×C411yescharacteristic
86C4×C11⋊C8C2312yes—
87C4×C11⋊C8C2312yes—
88#17961—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11C22×C412yes—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×Dic22—21no—
95C2×Dic22C22×C412yes—
96C11×M16—42no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4C22×C412yes—
110C11×C22⋊C4—22no—
111C42×C11—22no—
112C42×C11C22×C411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11C2411yescharacteristic
116C22⋊Dic11—22no—
117#4326—28no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11C22×C412yes—
122Dic11⋊C4—22no—
123Dic11⋊C4—22no—
124C4×Dic11—22no—
125#4318—42no—
126C2×C11⋊C8—24no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—42no—
130C2×C11⋊C8C22×C412yes—
131C2×C11⋊C8C22×C412yes—
132#3170—111no—
133#2960—111no—
134#2960D1111yescharacteristic
135#1593—114no—
136#1579—114no—
137#1566—111no—
138#1493—111no—
139#1493—111no—
140C2×#322—111no—
141C23×C11C4×D411yescharacteristic
142Q8×C11—24no—
143Q8×C11—42no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11#13712yes—
152C2×C4×C11#13712yes—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—22no—
158Dic22—24no—
159Dic22—42no—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—42no—
165C11⋊C8—22no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C11⋊C8#13114yes—
169#533—111no—
170#533C2×D1111yescharacteristic
171#500—111no—
172#494—111no—
173#487—111no—
174#487—111no—
175#467—114no—
176#446—21no—
177#446—112no—
178#446—221no—
179#446C2×D1112yes—
180C8×Q8—21no—
181C8×Q8—112no—
182C8×Q8—221no—
183C8×Q8C2×D1112yes—
184C4×Q16—114no—
185#424—21no—
186#424—221no—
187#423—111no—
188#423C2×D1111yescharacteristic
189#405—21no—
190#405—221no—
191C2×C4×C8—111no—
192C2×C4×C8—111no—
193C2×C4×C8C2×D1111yescharacteristic
194#334—114no—
195Q8⋊C8—114no—
196Q8⋊C8—114no—
197#322—112no—
198#322—112no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11#44112yes—
202C22×C11C2×C4×D411yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11#44112yes—
208C4×C11#44412yes—
209C4×C11C2×#13112yes—
210C4×C11C2×#13711yescharacteristic
211C4×C11C2×#13711yescharacteristic
212Dic11—42no—
213Dic11—42no—
214C2×Q16—114no—
215C2×M16—21no—
216C2×M16—221no—
217C22×C8—112no—
218C22×C8—221no—
219C22×C8C22⋊D1111yescharacteristic
220C22×C8C22⋊D1111yescharacteristic
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223C4⋊Q8C4×D1111yescharacteristic
224C4⋊Q8C4×D1111yescharacteristic
225#125—21no—
226#125—221no—
227C22⋊Q8—21no—
228C22⋊Q8—112no—
229C22⋊Q8—221no—
230C22⋊Q8C4×D1112yes—
231C4×Q8—21no—
232C4×Q8—112no—
233C4×Q8—221no—
234C4×Q8C22×D1112yes—
235#117—21no—
236#117—221no—
237C2×C42C22×D1111yescharacteristic
238#107—114no—
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—21no—
242C4⋊C8—112no—
243C4⋊C8—222no—
244C4⋊C8—222no—
245C4⋊C8—221no—
246C4⋊C8C22×D1112yes—
247#103—114no—
248#103—114no—
249#97—22no—
250#97—222no—
251C4×C8—22no—
252C4×C8—111no—
253C4×C8—111no—
254C4×C8—112no—
255C4×C8—112no—
256C4×C8—222no—
257C4×C8—221no—
258C4×C8C22⋊D1111yescharacteristic
259C4×C8C22⋊D1111yescharacteristic
260C4×C8C22×D1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C2×C11—22no—
263C2×C11#293111yescharacteristic
264C2×C11C2×#44111yescharacteristic
265C2×C11C2×#44411yescharacteristic
266C2×Q8—21no—
267C2×Q8—112no—
268C2×Q8—221no—
269C2×Q8C2×C4×D1112yes—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4#433911yescharacteristic
272C22×C4C2×C22⋊D1111yescharacteristic
273Q16—228no—
274M16—42no—
275M16—442no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—112no—
280C2×C8—112no—
281C2×C8—224no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—442no—
285C2×C8C2×C22⋊D1111yescharacteristic
286C2×C8C2×C22⋊D1111yescharacteristic
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—112no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4C2×C4×D1112yes—
301C22⋊C4—22no—
302C22⋊C4—222no—
303C42—22no—
304C42—222no—
305C42C2×C4×D1111yescharacteristic
306C42#433911yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C42C23×D1111yescharacteristic
309C11#1796111yescharacteristic, complemented, Sylow
310C23C4×C22⋊D1111yescharacteristic
311Q8—24no—
312Q8—42no—
313Q8—224no—
314Q8—442no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4C4×C22⋊D1111yescharacteristic
322C2×C4C4×C22⋊D1111yescharacteristic
323C2×C4C4×C22⋊D1111yescharacteristic
324C2×C4#6699512yes—
325C2×C4#6700412yes—
326C2×C4C22×C4×D1111yescharacteristic
327C2×C4C2×#433911yescharacteristic
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—21no—
330C8—21no—
331C8—21no—
332C8—21no—
333C8—42no—
334C8—114no—
335C8—222no—
336C8—442no—
337C8—442no—
338C22—21no—
339C22—21no—
340C22#1062264312yes—
341C22C2×C4×C22⋊D1111yescharacteristic
342C4—21no—
343C4—21no—
344C4—42no—
345C4—42no—
346C4—442no—
347C4—442no—
348C4#1062264312yes—
349C4#1062275812yes—
350C4D11×#13112yes—
351C4C2×#6699511yescharacteristic
352C4C2×#6700411yescharacteristic
353C2—22no—
354C2#1307732611yescharacteristic
355C2C2×#1062264311yescharacteristic
356C2C2×#1062275811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2960C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#2960D11
hypocenterC11#17961
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2960

Complements

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

NH ≅ G/Ntype
3. #13067523C2semidirect
4. #13067433C2semidirect
309. C11#17961semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130775502
#130675232
#130674332
#130673712
#130670712
#130670702
C2×#106220922
C11×#29602
#1796111