Finite Group Databasebeta

← #14780376

Subgroups — #14780376

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66997C211yesmaximal, characteristic
2#13069557C211yesmaximal, characteristic
3#13069550C212yesmaximal
4#13069180C212yesmaximal
5#13069178C212yesmaximal
6#13069176C212yesmaximal
7#13069170C212yesmaximal
8#13068758C212yesmaximal
9C11×#1985C211yesmaximal, characteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66997C411yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#97C2211yescharacteristic
15#10622843C411yescharacteristic
16C2×Dic11⋊C8C2212yes—
17C2×C8×Dic11C2212yes—
18#10622589C411yescharacteristic
19#10622587C411yescharacteristic
20#10622585C412yes—
21#10622585C412yes—
22C4×Dic11⋊C4C2212yes—
23C4×Dic11⋊C4C2212yes—
24C42×Dic11C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×#66867C2211yescharacteristic
27C11×#336C2212yes—
28C11×#336C2212yes—
29#10622188C2212yes—
30#10622188C2212yes—
31#10622188C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622162C2212yes—
36#10622162C2212yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Dic22C2×C411yescharacteristic
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C4×Q8×C11—41no—
42C4×Q8×C11—41no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C42×C11C2311yescharacteristic
49#66997—24no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×Dic11⋊C4C2×C412yes—
52C2×Dic11⋊C4C2×C412yes—
53C2×Dic11⋊C4C2×C412yes—
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2×C412yes—
56C2×C4×Dic11C2×C411yescharacteristic
57C2×C4×Dic11C2×C412yes—
58C2×C4×Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2312yes—
60C2×C4×Dic11C2312yes—
61C22×C11⋊C8C2312yes—
62C22×C11⋊C8C2312yes—
63C4×Dic22—41no—
64C4×Dic22—41no—
65C11×C4⋊C8—41no—
66C11×#97—41no—
67C11⋊#95C2×C412yes—
68C11⋊#95C2×C412yes—
69C11⋊#95C2×C412yes—
70C11⋊#95C2×C412yes—
71Dic11⋊C8—42no—
72C8×Dic11—42no—
73C4⋊(C11⋊C8)—41no—
74#66867—41no—
75#23365—111nomaximal, Sylow
76C2×Q8×C11—22no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2411yescharacteristic
86C22×Dic11C22×C412yes—
87C22×Dic11C22×C412yes—
88C22×Dic11C22×C412yes—
89C22×Dic11C22×C412yes—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C2×Dic22M1614yes—
93C2×C8×C11—22no—
94C2×C8×C11—22no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—24no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C42×C11—21no—
102C42×C11—21no—
103C42×C11—21no—
104C42×C11—21no—
105C42×C11—21no—
106C42×C11—21no—
107C4⋊Dic11—41no—
108Dic11⋊C4—24no—
109Dic11⋊C4—24no—
110Dic11⋊C4—24no—
111Dic11⋊C4—24no—
112Dic11⋊C4—42no—
113C4×Dic11—24no—
114C4×Dic11—22no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C4×Dic11—22no—
119C4×Dic11—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—24no—
124C2×C11⋊C8—22no—
125C4×C4⋊Q8—111no—
126#1985—111no—
127#1985D1111yescharacteristic
128#1984—112no—
129#1917—112no—
130#1917—112no—
131#1916—112no—
132#1916—112no—
133#1839—112no—
134C23×C11C23×C411yescharacteristic
135Q8×C11—44no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11C2×M1612yes—
151C2×C4×C11H(5,𝔽2)11yescharacteristic
152C2×C4×C11H(5,𝔽2)11yescharacteristic
153C2×C4×C112−1+412yes—
154C2×C4×C112−1+412yes—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11C2×M1614yes—
166C2×Dic11#13114yes—
167Dic22—44no—
168C8×C11—42no—
169C8×C11—42no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172C2×C4⋊Q8—111no—
173C2×C4×Q8—111no—
174C2×C4×Q8C2×D1111yescharacteristic
175C2×C4⋊C8—112no—
176C2×C4⋊C8—111no—
177C2×C4⋊C8C2×D1111yescharacteristic
178C2×#97—111no—
179C2×#97C2×D1111yescharacteristic
180C2×C4×C8—112no—
181#391—111no—
182#391—111no—
183#389—112no—
184#389—112no—
185#384—111no—
186C4×C4⋊C4—112no—
187C4×C4⋊C4—112no—
188C43—111no—
189#336—112no—
190#336—112no—
191#336—112no—
192#336—112no—
193#336—112no—
194#336—112no—
195#336—112no—
196#336—112no—
197#336C2×D1112yes—
198#336C2×D1112yes—
199C22×C11#51811yescharacteristic
200C22×C11#51912yes—
201C22×C11C22×M1611yescharacteristic
202C22×C11C2×#13112yes—
203C22×C11#56811yescharacteristic
204C4×C11—22no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11#56311yescharacteristic
211C4×C11#56312yes—
212C4×C11#56311yescharacteristic
213Dic11—24no—
214Dic11—24no—
215Dic11—42no—
216Dic11—42no—
217C22×Q8—111no—
218C22×Q8C4×D1111yescharacteristic
219C22×C8—112no—
220C22×C8—112no—
221C22×C8C22×D1112yes—
222C22×C8C22×D1112yes—
223C4⋊Q8—224no—
224C4×Q8—41no—
225C4×Q8—41no—
226C4×Q8—441no—
227C4×Q8—441no—
228C2×C4⋊C4—112no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—112no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4C4×D1111yescharacteristic
235C2×C4⋊C4C4×D1111yescharacteristic
236C2×C4⋊C4C4×D1111yescharacteristic
237C2×C42—111no—
238C2×C42—112no—
239C2×C42—112no—
240C2×C42—112no—
241C2×C42—111no—
242C2×C42C22×D1111yescharacteristic
243C2×C42C22×D1111yescharacteristic
244C2×C42C22×D1111yescharacteristic
245C4⋊C8—41no—
246C4⋊C8—441no—
247C4⋊C8—442no—
248#97—41no—
249#97—441no—
250C4×C8—442no—
251#95—112no—
252#95—112no—
253#95—112no—
254#95—112no—
255C2×C11#238111yescharacteristic
256C2×C11#297311yescharacteristic
257C2×C11#297911yescharacteristic
258C2×C11#298412yes—
259C2×C11#298512yes—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—114no—
264C2×Q8—441no—
265C2×Q8—441no—
266C22×C4—112no—
267C22×C4—112no—
268C22×C4—112no—
269C22×C4—112no—
270C22×C4C2×C4×D1111yescharacteristic
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4C2×C4×D1111yescharacteristic
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4C23×D1111yescharacteristic
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—24no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—224no—
285C2×C8—222no—
286C2×C8—222no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—224no—
291C4⋊C4—224no—
292C4⋊C4—224no—
293C4⋊C4—224no—
294C4⋊C4—442no—
295C4⋊C4—441no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—224no—
303C42—222no—
304C42—222no—
305C42—222no—
306C42—222no—
307C42—222no—
308C42—441no—
309C11#2336511yescharacteristic, complemented, Sylow
310C23C22×C4×D1111yescharacteristic
311Q8—44no—
312Q8—444no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—114no—
328C2×C4—114no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4M16×D1112yes—
340C2×C4#6703711yescharacteristic
341C2×C4#6703711yescharacteristic
342C2×C4#6704012yes—
343C2×C4#6704312yes—
344C8—42no—
345C8—42no—
346C8—442no—
347C8—442no—
348C22#1062301711yescharacteristic
349C22#1062310312yes—
350C22C2×M16×D1111yescharacteristic
351C22#1062327611yescharacteristic
352C22D11×#13112yes—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—224no—
360C4—224no—
361C4—442no—
362C4—442no—
363C4#1062317712yes—
364C4#1062320311yescharacteristic
365C4#1062326611yescharacteristic
366C2#1307179511yescharacteristic
367C2#1307764311yescharacteristic
368C2#1307768011yescharacteristic
369C2#1307770212yes—
370C2#1307770912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socle, prime radicalC23×C11C23×C4
FittingC11×#1985C2
cosocleC22×C4×C11C24
hypercenter#1985D11
hypocenterC11#23365
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
309. C11#23365semidirect

Maximal subgroups

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

subgroupindex
C4×#669972
#130695572
#130695502
#130691802
#130691782
#130691762
#130691702
#130687582
C11×#19852
#2336511