Finite Group Databasebeta

← #14660277

Subgroups — #14660277

Order 2816.

1434 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
1C22×#66900C212yesmaximal, complemented
2C2×#10622820C212yesmaximal
3C2×#10622168C212yesmaximal, complemented
4C22×C11×C22⋊Q8C211yesmaximal, characteristic
5C23×Q8×C11C2211yescharacteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—24no—
8C2×C11×C22⋊Q8—24no—
9C2×C11×C22⋊Q8—24no—
10C22×C11×C4⋊C4C412yes—
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C412yes—
13C22×#4318C2214yes—
14C2×#66900—24no—
15C2×#66900—28no—
16#10622820—28no—
17C2×C22⋊(C11⋊C8)—24no—
18#10622168—24no—
19C25×C11C2×C411yescharacteristic
20C22×Q8×C11—24no—
21C22×Q8×C11—22no—
22C22×Q8×C11—22no—
23C22×Q8×C11—24no—
24C22×Q8×C11D414yes—
25C23×C4×C11—24no—
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—24no—
29C23×C4×C11C2×C412yes—
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C412yes—
32C23×C4×C11D414yes—
33C23×C4×C11C2311yescharacteristic
34C11×C22⋊Q8—232no—
35C2×C11×C4⋊C4—24no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4D414yes—
41C2×C11×C22⋊C4—24no—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—24no—
44C2×#4318—24no—
45C2×#4318—24no—
46C2×#4318—24no—
47C2×#4318—24no—
48C2×#4318—24no—
49C2×#4318D418yes—
50C22×C11⋊C8—24no—
51#66900—216no—
52C22⋊(C11⋊C8)—216no—
53#10968—111nomaximal, Sylow
54C24×C11—24no—
55C24×C11—21no—
56C24×C11—21no—
57C24×C11—24no—
58C24×C11—42no—
59C24×C11C22⋊C412yes—
60C24×C11C22×C411yescharacteristic
61C2×Q8×C11—24no—
62C2×Q8×C11—28no—
63C2×Q8×C11—28no—
64C2×Q8×C11—24no—
65C2×Q8×C11—42no—
66C2×Q8×C11—44no—
67C2×Q8×C11—44no—
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—42no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—24no—
78C22×C4×C11—28no—
79C22×C4×C11—24no—
80C22×C4×C11—28no—
81C22×C4×C11—28no—
82C22×C4×C11—24no—
83C22×C4×C11—42no—
84C22×C4×C11—44no—
85C22×C4×C11—44no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—44no—
90C22×C4×C11C22⋊C414yes—
91C22×C4×C11C22⋊C412yes—
92C22×C4×C11C22⋊C414yes—
93C22×C4×C11C2×D412yes—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D414yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11#4114yes—
98C11×C4⋊C4—216no—
99C11×C4⋊C4—28no—
100C11×C22⋊C4—216no—
101#4318—28no—
102#4318—28no—
103#4318—44no—
104#4318—44no—
105C2×C11⋊C8—28no—
106C2×C11⋊C8—44no—
107C2×C11⋊C8—44no—
108C22×C22⋊Q8D1111yescharacteristic
109C22×#101—112no—
110C2×#407—112no—
111C2×#343—112no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—24no—
115C23×C11—24no—
116C23×C11—22no—
117C23×C11—24no—
118C23×C11—22no—
119C23×C11—24no—
120C23×C11—416no—
121C23×C11—42no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11#10114yescomplemented
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11C4×D414yes—
130Q8×C11—48no—
131Q8×C11—48no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—28no—
137C2×C4×C11—44no—
138C2×C4×C11—42no—
139C2×C4×C11—44no—
140C2×C4×C11—42no—
141C2×C4×C11—44no—
142C2×C4×C11—44no—
143C2×C4×C11—48no—
144C2×C4×C11—48no—
145C2×C4×C11—44no—
146C2×C4×C11#12012yes—
147C2×C4×C11#12012yes—
148C2×C4×C11#12014yes—
149C2×C4×C11#12114yes—
150C2×C4×C11#12114yes—
151C2×C4×C11#12114yes—
152C2×C4×C11#12312yes—
153C2×C4×C11#12312yes—
154C2×C4×C11#12412yes—
155C2×C4×C11#12712yes—
156C11⋊C8—48no—
157C23×Q8C2×D1111yescharacteristic
158C24×C4C2×D1111yescharacteristic
159C22×M16—114no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—24no—
163C22×C4⋊C4Dic1112yes—
164C22×C4⋊C4C2×D1111yescharacteristic
165C22×C22⋊C4Dic1112yes—
166C2×#101—228no—
167C2×#101—224no—
168#407—228no—
169C2×C22⋊C8—224no—
170#343—224no—
171C22×C11—28no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—28no—
177C22×C11—24no—
178C22×C11—48no—
179C22×C11—48no—
180C22×C11—44no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11#37911yescharacteristic
184C22×C11#38612yes—
185C22×C11#38612yes—
186C22×C11#39012yes—
187C22×C11C2×#10112yes—
188C22×C11#41312yes—
189C4×C11—42no—
190C4×C11—44no—
191C4×C11—44no—
192C4×C11#39214yes—
193C4×C11#39414yes—
194C25C2×Dic1111yescharacteristic
195C22×Q8—24no—
196C22×Q8—24no—
197C22×Q8—22no—
198C22×Q8—22no—
199C22×Q8C22⋊D1114yes—
200C23×C4—24no—
201C23×C4—24no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4C2×Dic1112yes—
205C23×C4C2×Dic1111yescharacteristic
206C23×C4C2×Dic1112yes—
207C23×C4C22⋊D1114yes—
208C23×C4C22×D1111yescharacteristic
209C2×M16—118no—
210C2×M16—224no—
211C2×M16—224no—
212C2×M16—224no—
213C2×M16—224no—
214C2×M16—224no—
215C22×C8—224no—
216C22⋊Q8—232no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4C22⋊D1114yes—
223C2×C22⋊C4—24no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—24no—
226#101—2216no—
227C22⋊C8—2216no—
228C2×C11—22no—
229C2×C11—22no—
230C2×C11—44no—
231C2×C11#143811yescharacteristic
232C2×C11#178411yescharacteristic
233C2×C11#178511yescharacteristic
234C2×C11#190114yes—
235C24—24no—
236C24—21no—
237C24—21no—
238C24—24no—
239C24—42no—
240C24C22⋊Dic1112yes—
241C24C22×Dic1111yescharacteristic
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—28no—
245C2×Q8—28no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—44no—
250C2×Q8—44no—
251C2×Q8—42no—
252C22×C4—24no—
253C22×C4—28no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—42no—
270C22×C4—44no—
271C22×C4C22⋊Dic1114yes—
272C22×C4C22⋊Dic1112yes—
273C22×C4C22⋊Dic1114yes—
274C22×C4D4×D1114yes—
275C22×C4#434114yes—
276C22×C4C2×C22⋊D1112yes—
277C22×C4C2×C22⋊D1112yes—
278C22×C4C2×C22⋊D1112yes—
279M16—228no—
280M16—228no—
281M16—444no—
282M16—444no—
283C2×C8—228no—
284C2×C8—444no—
285C2×C8—444no—
286C4⋊C4—216no—
287C4⋊C4—28no—
288C22⋊C4—216no—
289C11#1096811yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23—24no—
293C23—24no—
294C23—24no—
295C23—22no—
296C23—24no—
297C23—22no—
298C23—416no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#6690014yescomplemented
304C23D4×Dic1114yes—
305C23C2×C22⋊Dic1111yescharacteristic
306C23C2×C22⋊Dic1111yescharacteristic
307C23C2×C22⋊Dic1111yescharacteristic
308Q8—48no—
309Q8—48no—
310C2×C4—24no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—48no—
322C2×C4—48no—
323C2×C4—44no—
324C2×C4#6698812yes—
325C2×C4#6698812yes—
326C2×C4#6698912yes—
327C2×C4#6699012yes—
328C2×C4#6699012yes—
329C2×C4#6699114yes—
330C2×C4#6699214yes—
331C2×C4#6699214yes—
332C2×C4#6699312yes—
333C2×C4#6700614yes—
334C8—448no—
335C22—21no—
336C22—21no—
337C22—28no—
338C22—21no—
339C22—21no—
340C22—28no—
341C22—24no—
342C22—48no—
343C22—48no—
344C22—42no—
345C22—44no—
346C22—42no—
347C22#1062283312yes—
348C22#1062283312yes—
349C22#1062283412yes—
350C22C2×#6690012yes—
351C22#1062285012yes—
352C22#1062286011yescharacteristic
353C4—44no—
354C4—42no—
355C4—44no—
356C4#1062283514yes—
357C4#1062283614yes—
358C2—22no—
359C2—22no—
360C2—44no—
361C2#1306685711yescharacteristic
362C2#1306854011yescharacteristic
363C2#1306854411yescharacteristic
364C2#1306908514yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC23×C4×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11#10968
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66900C2semidirect
3. C2×#10622168C2semidirect
125. C23×C11#101semidirect
289. C11#10968semidirect
303. C23#66900semidirect

Maximal subgroups

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

subgroupindex
C22×#669002
C2×#106228202
C2×#106221682
C22×C11×C22⋊Q82
#1096811