Finite Group Databasebeta

← #14646348

Subgroups — #14646348

Order 2816.

1062 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069070C214yesmaximal, complemented
2#13068690C211yesmaximal, characteristic, complemented
3#13066865C211yesmaximal, characteristic, complemented
4C11×#3490C211yesmaximal, characteristic
5C11×#551—24no—
6C11×#546—24no—
7C11×#543C411yescharacteristic, complemented
8C11×#538—22no—
9C11×#534C411yescharacteristic, complemented
10C11×#525—22no—
11C2×C11×#120C2212yes—
12C11×#518C412yescomplemented
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15#10622860C2212yes—
16C2×#66898—24no—
17C2×C11⋊#95—22no—
18#10622164—24no—
19#10622164—22no—
20C25×C11C2311yescharacteristic
21C2×C11×#41—22no—
22C22×D4×C11C2×C412yes—
23C22×D4×C11D414yes—
24C23×C4×C11D412yes—
25C23×Dic11—22no—
26C11×#126—24no—
27C11×#124—24no—
28C11×#123—24no—
29C11×#123—24no—
30C11×#123—22no—
31C11×C22⋊Q8—22no—
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—24no—
34C11×#121—22no—
35C11×#121—24no—
36C11×#121—22no—
37C11×#120—22no—
38C11×#120—22no—
39C11×#120—22no—
40C11×#120—24no—
41C4×D4×C11—24no—
42C4×D4×C11—24no—
43C4×D4×C11—24no—
44C11×#117—22no—
45C11×#117—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—24no—
48C2×C11×C22⋊C4C2×C411yescharacteristic
49C2×C11×C22⋊C4C2×C411yescharacteristic
50C2×C11×C22⋊C4C2×C412yes—
51C2×C11×C22⋊C4D412yes—
52C2×C11×C22⋊C4D414yes—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—44no—
57#66898—48no—
58C11⋊#95—44no—
59#8535—111nomaximal, Sylow
60C24×C11—42no—
61C24×C11—42no—
62C24×C11—42no—
63C24×C11C22⋊C412yes—
64C24×C11C22×C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C24×C11C2×D414yes—
67C24×C11C2×D411yescharacteristic
68C11×#41—82no—
69C11×#41—82no—
70C2×Q8×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—24no—
74C2×D4×C11—22no—
75C2×D4×C11—24no—
76C2×D4×C11—44no—
77C2×D4×C11—44no—
78C2×D4×C11—44no—
79C22×C4×C11—22no—
80C22×C4×C11—24no—
81C22×C4×C11—22no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11C22⋊C412yes—
85C22×C4×C11C22⋊C414yes—
86C22×C4×C11C22⋊C412yes—
87C22×C4×C11C22⋊C412yes—
88C22×Dic11—24no—
89C22×Dic11—42no—
90C22×Dic11—42no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—24no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—24no—
109C42×C11—24no—
110C22⋊Dic11—28no—
111C22⋊Dic11—44no—
112C22⋊Dic11—44no—
113C22⋊Dic11—44no—
114C22⋊Dic11—44no—
115#3490D1111yescharacteristic
116#1898—114no—
117#1819—111no—
118#1440—111no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—24no—
125C23×C11—24no—
126C23×C11—22no—
127C23×C11—42no—
128C23×C11—44no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11—42no—
132C23×C11—44no—
133C23×C11—82no—
134C23×C11—82no—
135C23×C11—82no—
136C23×C11—82no—
137C23×C11C2×C22⋊C412yes—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11#12012yes—
140C23×C11#12012yes—
141Q8×C11—82no—
142D4×C11—44no—
143D4×C11—44no—
144D4×C11—44no—
145D4×C11—44no—
146D4×C11—84no—
147D4×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—24no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—44no—
158C2×C4×C11—82no—
159C2×C4×C11—84no—
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—82no—
164C2×Dic11—82no—
165C2×Dic11—82no—
166C2×Dic11—82no—
167C2×Dic11—82no—
168C2×Dic11—84no—
169#551—24no—
170#546—24no—
171#543Dic1111yescharacteristic, complemented
172#538—22no—
173#534Dic1111yescharacteristic, complemented
174#525—22no—
175C2×#120C2×D1112yes—
176#518Dic1112yescomplemented
177C22×C22⋊C4—112no—
178C22×C22⋊C4C2×D1111yescharacteristic
179C2×#99—224no—
180#379—112no—
181C2×#95—222no—
182#342—222no—
183#342—224no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—24no—
194C22×C11—24no—
195C22×C11—42no—
196C22×C11—44no—
197C22×C11—84no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—84no—
201C22×C11—162no—
202C22×C11#37911yescharacteristic
203C22×C11#41012yes—
204C22×C11B(4,𝔽2)12yes—
205C22×C11#45812yes—
206C4×C11—42no—
207C4×C11—42no—
208C4×C11—42no—
209C4×C11—44no—
210Dic11—84no—
211Dic11—162no—
212C25C22×D1111yescharacteristic
213C2×#41—22no—
214C22×D4C2×Dic1112yes—
215C22×D4C22⋊D1114yes—
216C23×C4—222no—
217C23×C4C22⋊D1112yes—
218#126—24no—
219#124—24no—
220#123—24no—
221#123—24no—
222#123—22no—
223C22⋊Q8—22no—
224C22⋊Q8—22no—
225C22⋊Q8—24no—
226#121—22no—
227#121—24no—
228#121—22no—
229#120—22no—
230#120—22no—
231#120—22no—
232#120—24no—
233C4×D4—24no—
234C4×D4—24no—
235C4×D4—24no—
236#117—22no—
237#117—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—24no—
240C2×C22⋊C4—224no—
241C2×C22⋊C4—222no—
242C2×C22⋊C4—224no—
243C2×C22⋊C4—444no—
244C2×C22⋊C4C2×Dic1111yescharacteristic
245C2×C22⋊C4C2×Dic1111yescharacteristic
246C2×C22⋊C4C2×Dic1112yes—
247C2×C22⋊C4C22⋊D1112yes—
248C2×C22⋊C4C22⋊D1114yes—
249#99—448no—
250#95—444no—
251C2×C11—22no—
252C2×C11—22no—
253C2×C11—22no—
254C2×C11—42no—
255C2×C11—42no—
256C2×C11—82no—
257C2×C11#178211yescharacteristic
258C2×C11#179012yes—
259C24—42no—
260C24—42no—
261C24—42no—
262C24C22⋊Dic1112yes—
263C24C22×Dic1111yescharacteristic
264C24C2×C22⋊D1111yescharacteristic
265C24C2×C22⋊D1114yes—
266C24C2×C22⋊D1111yescharacteristic
267#41—82no—
268#41—82no—
269C2×Q8—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—24no—
273C2×D4—22no—
274C2×D4—24no—
275C2×D4—44no—
276C2×D4—44no—
277C2×D4—44no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—224no—
284C22×C4—442no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4—442no—
291C22×C4C22⋊Dic1112yes—
292C22×C4C22⋊Dic1114yes—
293C22×C4C22⋊Dic1112yes—
294C22×C4C22⋊Dic1112yes—
295C4⋊C4—24no—
296C4⋊C4—22no—
297C4⋊C4—22no—
298C4⋊C4—24no—
299C22⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C22⋊C4—24no—
308C22⋊C4—228no—
309C22⋊C4—444no—
310C22⋊C4—444no—
311C22⋊C4—444no—
312C22⋊C4—444no—
313C42—24no—
314C11#853511yescharacteristic, complemented, Sylow
315C23—22no—
316C23—22no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—24no—
321C23—24no—
322C23—22no—
323C23—42no—
324C23—42no—
325C23—44no—
326C23—44no—
327C23—44no—
328C23—42no—
329C23—82no—
330C23—82no—
331C23—82no—
332C23—82no—
333C23C2×C22⋊Dic1112yes—
334C23C2×C22⋊Dic1111yescharacteristic
335C23#6700612yes—
336C23#6700612yes—
337Q8—82no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—44no—
342D4—84no—
343D4—82no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—84no—
356C2×C4—444no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—882no—
360C2×C4—882no—
361C2×C4—882no—
362C2×C4—882no—
363C2×C4—884no—
364C2×C4—882no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—24no—
373C22—24no—
374C22—22no—
375C22—22no—
376C22—44no—
377C22—42no—
378C22—84no—
379C22—82no—
380C22—82no—
381C22—84no—
382C22—162no—
383C22#1062285312yes—
384C22#1062285612yes—
385C22#1062285712yes—
386C22#1062286011yescharacteristic
387C4—42no—
388C4—42no—
389C4—44no—
390C4—42no—
391C4—884no—
392C4—1762no—
393C2—22no—
394C2—22no—
395C2—22no—
396C2—42no—
397C2—42no—
398C2—82no—
399C2#1306853411yescharacteristic
400C2#1306856412yes—
subgroupG/H
centerC22#10622860
commutatorC24×C11C22×C4
FrattiniC25C22×D11
Fitting, prime radicalC11×#3490C2
socleC22×C11#379
cosocleC25×C11C23
hypercenter#3490D11
hypocenterC11#8535
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #3490

Complements

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

NH ≅ G/Ntype
1. #13069070C2semidirect
2. #13068690C2semidirect
3. #13066865C2semidirect
7. C11×#543C4semidirect
9. C11×#534C4semidirect
12. C11×#518C4semidirect
171. #543Dic11semidirect
173. #534Dic11semidirect
176. #518Dic11semidirect
314. C11#8535semidirect

Maximal subgroups

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

subgroupindex
#130690702
#130686902
#130668652
C11×#34902
#853511