Finite Group Databasebeta

← #14753838

Subgroups — #14753838

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic
3#13068706C212yesmaximal
4#13068631C214yesmaximal, complemented
5#13068551C212yesmaximal
6#13068446C214yesmaximal, complemented
7C22×C4×Q8×C11C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C4×Q8×C11—24no—
10C2×C4×Q8×C11—21no—
11C2×C4×Q8×C11—21no—
12C2×C4×Q8×C11C418yescomplemented
13C2×C4×Q8×C11C2212yes—
14C2×C4×Q8×C11C2212yes—
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11—21no—
18C22×C42×C11C2211yescharacteristic
19C2×#66899C2218yes—
20#10622825C2212yes—
21#10622824—21no—
22C4×C22⋊Dic11—21no—
23C2×C22⋊(C11⋊C8)C2212yes—
24#10622550—21no—
25#10622549C2212yes—
26C4×C4⋊Dic11C2212yes—
27#10622545—21no—
28#10622539—24no—
29C2×C4⋊(C11⋊C8)C2212yes—
30C2×#66867C2212yes—
31#10622167C2218yes—
32C22×Q8×C11—28no—
33C22×Q8×C11—22no—
34C22×Q8×C11—21no—
35C22×Q8×C11C2×C414yes—
36C22×Q8×C11C2312yes—
37C23×C4×C11—21no—
38C23×C4×C11—21no—
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C4×Q8×C11—28no—
43C4×Q8×C11—28no—
44C4×Q8×C11—24no—
45C4×Q8×C11—24no—
46C4×Q8×C11C2×C418yes—
47C4×Q8×C11C2×C418yes—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—28no—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11C2×C414yes—
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D414yes—
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65C2×C4⋊Dic11C2314yes—
66C2×C4×Dic11—22no—
67C22×C11⋊C8C2314yes—
68#66899—216no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—22no—
72C11⋊#95—22no—
73C22⋊(C11⋊C8)—24no—
74C4⋊(C11⋊C8)—24no—
75#66867—24no—
76#20741—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—216no—
79C2×Q8×C11—28no—
80C2×Q8×C11—216no—
81C2×Q8×C11—24no—
82C2×Q8×C11—22no—
83C2×Q8×C11—24no—
84C2×Q8×C11C22×C414yes—
85C2×Q8×C11#4118yes—
86C22×C4×C11—28no—
87C22×C4×C11—24no—
88C22×C4×C11—24no—
89C22×C4×C11—22no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—22no—
93C22×C4×C11—42no—
94C22×C4×C11—44no—
95C22×C4×C11C22⋊C414yes—
96C22×C4×C11C22⋊C414yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—24no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—28no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22×C414yes—
111C42×C11—28no—
112C42×C11—28no—
113C42×C11C22⋊C414yes—
114C42×C11C22⋊C414yes—
115C42×C11C22×C412yes—
116C42×C11C22×C412yes—
117C42×C11C2×D412yes—
118C42×C11C2×D412yes—
119C22⋊Dic11—44no—
120C4⋊Dic11—28no—
121C4×Dic11—44no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—28no—
124C22×C4×Q8D1111yescharacteristic
125C2×#432—111no—
126#2283—111no—
127#1824—112no—
128#1805—114no—
129#1787—112no—
130#1763—114no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11C2×C22⋊C412yes—
134C23×C11#13714yes—
135C23×C11C22×D411yescharacteristic
136Q8×C11—216no—
137Q8×C11—24no—
138Q8×C11—28no—
139Q8×C11#11718yes—
140C2×C4×C11—216no—
141C2×C4×C11—24no—
142C2×C4×C11—28no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—28no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—24no—
152C2×C4×C11—44no—
153C2×C4×C11—48no—
154C2×C4×C11—44no—
155C2×C4×C11C2×C22⋊C412yes—
156C2×C4×C11C2×C22⋊C412yes—
157C2×C4×C11C2×C22⋊C412yes—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11C2×C22⋊C412yes—
160C2×C4×C11C23×C411yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C2×#4114yes—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C11⋊C8—44no—
167C23×Q8C2×D1111yescharacteristic
168C2×C4×Q8—24no—
169C2×C4×Q8—21no—
170C2×C4×Q8—21no—
171C2×C4×Q8Dic1118yescomplemented
172C2×C4×Q8C2×D1112yes—
173C2×C4×Q8C2×D1112yes—
174C22×C4⋊C4—21no—
175C22×C4⋊C4C2×D1111yescharacteristic
176C22×C42—21no—
177C22×C42C2×D1111yescharacteristic
178#432—224no—
179C2×C4⋊C8—112no—
180C2×#103—118no—
181C2×C22⋊C8—112no—
182C2×#97—112no—
183#383—221no—
184#382—112no—
185#381—221no—
186#380—112no—
187C4×C4⋊C4—112no—
188C4×C22⋊C4—221no—
189#376—221no—
190#340—118no—
191C22×C11—28no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11#41914yes—
195C22×C11C22×C22⋊C411yescharacteristic
196C22×C11#52512yes—
197C22×C11C2×#13712yes—
198C22×C11#57512yes—
199C4×C11—22no—
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—28no—
204C4×C11—22no—
205C4×C11—44no—
206C4×C11C2×#11712yes—
207C4×C11#52512yes—
208Dic11—84no—
209C22×Q8—28no—
210C22×Q8—22no—
211C22×Q8—21no—
212C22×Q8C2×Dic1114yes—
213C22×Q8C22×D1112yes—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4C22⋊D1111yescharacteristic
217C23×C4C22⋊D1111yescharacteristic
218C23×C4C22×D1111yescharacteristic
219C22×C8—114no—
220C4×Q8—28no—
221C4×Q8—28no—
222C4×Q8—24no—
223C4×Q8—24no—
224C4×Q8C2×Dic1118yes—
225C4×Q8C2×Dic1118yes—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—114no—
232C2×C4⋊C4C2×Dic1114yes—
233C2×C4⋊C4C22×D1112yes—
234C2×C22⋊C4—222no—
235C2×C42—28no—
236C2×C42—22no—
237C2×C42—22no—
238C2×C42—222no—
239C2×C42C2×Dic1114yes—
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22⋊D1111yescharacteristic
242C2×C42C22⋊D1114yes—
243C2×C42C22×D1111yescharacteristic
244C2×C42C22×D1111yescharacteristic
245C4⋊C8—224no—
246#103—2216no—
247C22⋊C8—224no—
248#97—224no—
249#95—222no—
250#95—222no—
251#95—222no—
252#95—222no—
253C2×C11—24no—
254C2×C11#228011yescharacteristic
255C2×C11C2×#41911yescharacteristic
256C2×C11#289611yescharacteristic
257C2×C11#311714yes—
258C24C2×C22⋊D1111yescharacteristic
259C2×Q8—216no—
260C2×Q8—28no—
261C2×Q8—216no—
262C2×Q8—24no—
263C2×Q8—24no—
264C2×Q8—22no—
265C2×Q8#433918yes—
266C2×Q8C22×Dic1114yes—
267C22×C4—28no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—44no—
276C22×C4—224no—
277C22×C4C22⋊Dic1114yes—
278C22×C4C22⋊Dic1114yes—
279C22×C4C22×Dic1112yes—
280C22×C4C2×C22⋊D1111yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285C22×C4C2×C22⋊D1112yes—
286C22×C4C23×D1111yescharacteristic
287C2×C8—228no—
288C2×C8—224no—
289C4⋊C4—28no—
290C4⋊C4—28no—
291C4⋊C4—24no—
292C4⋊C4—22no—
293C4⋊C4—228no—
294C4⋊C4C22×Dic1114yes—
295C22⋊C4—444no—
296C42—28no—
297C42—28no—
298C42—444no—
299C42C22⋊Dic1114yes—
300C42C22⋊Dic1114yes—
301C42C22×Dic1112yes—
302C42C22×Dic1112yes—
303C42C2×C22⋊D1112yes—
304C42C2×C22⋊D1112yes—
305C11#2074111yescharacteristic, complemented, Sylow
306C23—22no—
307C23—22no—
308C23#6699514yes—
309C23C2×C22⋊Dic1112yes—
310C23C22×C22⋊D1111yescharacteristic
311Q8—216no—
312Q8—24no—
313Q8—28no—
314Q8#6697918yes—
315C2×C4—216no—
316C2×C4—28no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—28no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—44no—
328C2×C4—48no—
329C2×C4—44no—
330C2×C4—444no—
331C2×C4—444no—
332C2×C4—444no—
333C2×C4C2×C22⋊Dic1112yes—
334C2×C4C2×C22⋊Dic1112yes—
335C2×C4C2×C22⋊Dic1112yes—
336C2×C4C2×C22⋊Dic1112yes—
337C2×C4C2×C22⋊Dic1112yes—
338C2×C4C2×#433914yes—
339C2×C4C23×Dic1111yescharacteristic
340C2×C4C22×C22⋊D1111yescharacteristic
341C8—444no—
342C22—28no—
343C22—22no—
344C22—22no—
345C22#1062283814yes—
346C22#1062332212yes—
347C22C2×#6699512yes—
348C22#1062335312yes—
349C22C22×C22⋊Dic1111yescharacteristic
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—28no—
355C4—22no—
356C4—44no—
357C4—884no—
358C4C2×#6697912yes—
359C4#1062332212yes—
360C2—24no—
361C2#1307099911yescharacteristic
362C2C2×#1062283811yescharacteristic
363C2#1307713511yescharacteristic
364C2#1307878714yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11#20741
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
4. #13068631C2semidirect
6. #13068446C2semidirect
12. C2×C4×Q8×C11C4semidirect
171. C2×C4×Q8Dic11semidirect
305. C11#20741semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130710142
#130687062
#130686312
#130685512
#130684462
C22×C4×Q8×C112
#2074111