Finite Group Databasebeta

← #14669375

Subgroups — #14669375

Order 2816.

790 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 790 conjugacy classes of subgroups — too many to draw. Only its 127 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#13070308C211yesmaximal, characteristic, complemented
2#13070288C211yesmaximal, characteristic, complemented
3#13070266C212yesmaximal, complemented
4#13068720C212yesmaximal, complemented
5C11×#3508C211yesmaximal, characteristic
6C11×#559—22no—
7C11×#550—22no—
8C11×#546—24no—
9C11×#540—22no—
10C11×#535C2211yescharacteristic
11C11×#535C2211yescharacteristic
12C11×#533C411yescharacteristic, complemented
13C11×#532—22no—
14C2×C11×#127C411yescharacteristic, complemented
15C11×#518C411yescharacteristic, complemented
16C11×#518C411yescharacteristic, complemented
17C4×C11×#41C2211yescharacteristic
18#10622853C2212yes—
19#10622850C2212yes—
20#10622183—22no—
21#10622180—22no—
22#10622174—24no—
23#10622169—22no—
24#10622161—22no—
25C2×C11×#41—24no—
26C2×C11×#41C2311yescharacteristic
27C22×D4×C11—22no—
28C22×D4×C11C2×C411yescharacteristic
29C22×D4×C11C2×C411yescharacteristic
30C11×C4⋊Q8—21no—
31C11×#127—22no—
32C11×#127—21no—
33C11×#127—21no—
34C11×#127—21no—
35C11×#127D412yes—
36C11×#125—21no—
37C11×#124—24no—
38C11×#124—21no—
39C11×#124D412yes—
40C11×#123—24no—
41C11×#123—24no—
42C11×C22⋊Q8—22no—
43C11×#121—24no—
44C11×#121—24no—
45C11×#121—24no—
46C11×#121—22no—
47C11×#121—22no—
48C11×#120—22no—
49C11×#120D414yes—
50C4×Q8×C11—21no—
51C4×Q8×C11—22no—
52C4×D4×C11—24no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—21no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C11×#117C2×C411yescharacteristic
60C11×#117C2×C411yescharacteristic
61C11×#117C2×C411yescharacteristic
62C11×#117D412yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C42×C11C2×C411yescharacteristic
66C2×C42×C11D412yes—
67#66979—22no—
68C2×#4318—22no—
69#66900—22no—
70#66898—22no—
71#66898—22no—
72#66897—22no—
73#12722—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11C22⋊C412yes—
76C11×#41—42no—
77C11×#41—88no—
78C2×Q8×C11—22no—
79C2×Q8×C11C2×D411yescharacteristic
80C2×D4×C11—24no—
81C2×D4×C11—24no—
82C2×D4×C11—24no—
83C2×D4×C11—24no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—84no—
90C2×D4×C11C22⋊C412yes—
91C2×D4×C11C2×D411yescharacteristic
92C2×D4×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D412yes—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C22⋊C4—24no—
107C11×C22⋊C4—24no—
108C11×C22⋊C4—21no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—24no—
112C11×C22⋊C4—24no—
113C11×C22⋊C4C22⋊C412yes—
114C42×C11—21no—
115C42×C11—21no—
116C42×C11—22no—
117C42×C11C22⋊C411yescharacteristic
118C42×C11C22⋊C411yescharacteristic
119C42×C11C22⋊C412yes—
120C42×C11C22⋊C412yes—
121C22⋊Dic11—42no—
122C4⋊Dic11—42no—
123C4×Dic11—42no—
124#4318—42no—
125#4318—42no—
126C2×C11⋊C8—42no—
127#3508D1111yescharacteristic
128#2134—111no—
129#2128—111no—
130#2122—112no—
131#1827—112no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—82no—
137C23×C11—82no—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11#12012yes—
140Q8×C11—41no—
141Q8×C11—44no—
142D4×C11—41no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—48no—
147D4×C11—42no—
148D4×C11—42no—
149D4×C11—84no—
150D4×C11—84no—
151D4×C11—84no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—21no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—84no—
163C2×C4×C11—84no—
164C2×C4×C11C2×C22⋊C411yescharacteristic
165C2×C4×C11C2×C22⋊C411yescharacteristic
166C2×C4×C11#12012yes—
167C2×Dic11—82no—
168C11⋊C8—82no—
169#559—22no—
170#550—22no—
171#546—24no—
172#540—22no—
173#535C2×D1111yescharacteristic
174#535C2×D1111yescharacteristic
175#533Dic1111yescharacteristic, complemented
176#532—22no—
177C2×#127Dic1111yescharacteristic, complemented
178#518Dic1111yescharacteristic, complemented
179#518Dic1111yescharacteristic, complemented
180C4×#41C2×D1111yescharacteristic
181#413—112no—
182#410—112no—
183#355—222no—
184#353—222no—
185AΣL(1,𝔽16)—224no—
186#339—222no—
187H(3,ℤ/4)—222no—
188C22×C11—21no—
189C22×C11—22no—
190C22×C11—42no—
191C22×C11—41no—
192C22×C11—44no—
193C22×C11—44no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—162no—
197C22×C11—162no—
198C22×C11#37911yescharacteristic
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—22no—
202C4×C11—42no—
203C4×C11—41no—
204C4×C11—42no—
205C4×C11—42no—
206C4×C11#41012yes—
207Dic11—162no—
208C2×#41—24no—
209C2×#41C22×D1111yescharacteristic
210C22×D4—22no—
211C22×D4C2×Dic1111yescharacteristic
212C22×D4C2×Dic1111yescharacteristic
213C2×M16—222no—
214C4⋊Q8—21no—
215#127—22no—
216#127—21no—
217#127—21no—
218#127—21no—
219#127C22⋊D1112yes—
220#125—21no—
221#124—24no—
222#124—21no—
223#124C22⋊D1112yes—
224#123—24no—
225#123—24no—
226C22⋊Q8—22no—
227#121—24no—
228#121—24no—
229#121—24no—
230#121—22no—
231#121—22no—
232#120—22no—
233#120C22⋊D1114yes—
234C4×Q8—21no—
235C4×Q8—22no—
236C4×D4—24no—
237C4×D4—22no—
238C4×D4—22no—
239C4×D4—21no—
240C4×D4—22no—
241C4×D4—22no—
242C4×D4—22no—
243#117—222no—
244#117C2×Dic1111yescharacteristic
245#117C2×Dic1111yescharacteristic
246#117C2×Dic1111yescharacteristic
247#117C22⋊D1112yes—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C42C2×Dic1111yescharacteristic
251C2×C42C22⋊D1112yes—
252#101—222no—
253#100—222no—
254#99—222no—
255#99—222no—
256C2×C11—21no—
257C2×C11—42no—
258C2×C11—41no—
259C2×C11—82no—
260C2×C11—82no—
261C2×C11#178211yescharacteristic
262C24—21no—
263C24C22⋊Dic1112yes—
264#41—42no—
265#41—88no—
266C2×Q8—22no—
267C2×Q8C2×C22⋊D1111yescharacteristic
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—84no—
278C2×D4C22⋊Dic1112yes—
279C2×D4C2×C22⋊D1111yescharacteristic
280C2×D4C2×C22⋊D1112yes—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4C22×Dic1111yescharacteristic
286C22×C4C2×C22⋊D1112yes—
287M16—442no—
288M16—442no—
289C2×C8—442no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—22no—
297C4⋊C4—442no—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—22no—
303C22⋊C4—24no—
304C22⋊C4—24no—
305C22⋊C4—442no—
306C22⋊C4C22⋊Dic1112yes—
307C42—21no—
308C42—21no—
309C42—22no—
310C42—442no—
311C42C22⋊Dic1112yes—
312C42C22⋊Dic1111yescharacteristic
313C42C22⋊Dic1111yescharacteristic
314C42C22⋊Dic1112yes—
315C11#1272211yescharacteristic, complemented, Sylow
316C23—22no—
317C23—22no—
318C23—42no—
319C23—42no—
320C23—82no—
321C23—82no—
322C23C2×C22⋊Dic1111yescharacteristic
323C23#6700612yes—
324Q8—41no—
325Q8—44no—
326D4—42no—
327D4—41no—
328D4—42no—
329D4—42no—
330D4—48no—
331D4—42no—
332D4—42no—
333D4—84no—
334D4—84no—
335D4—84no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—84no—
347C2×C4—84no—
348C2×C4—882no—
349C2×C4C2×C22⋊Dic1111yescharacteristic
350C2×C4C2×C22⋊Dic1111yescharacteristic
351C2×C4#6700612yes—
352C8—882no—
353C22—22no—
354C22—21no—
355C22—42no—
356C22—41no—
357C22—44no—
358C22—44no—
359C22—42no—
360C22—42no—
361C22—162no—
362C22—162no—
363C22#1062286011yescharacteristic
364C4—22no—
365C4—22no—
366C4—21no—
367C4—42no—
368C4—41no—
369C4—42no—
370C4—42no—
371C4—1762no—
372C4#1062285312yes—
373C2—21no—
374C2—42no—
375C2—41no—
376C2—82no—
377C2—82no—
378C2#1306853411yescharacteristic
subgroupG/H
centerC2#13068534
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
Fitting, prime radicalC11×#3508C2
socleC2×C11#1782
cosocleC2×C11×#41C23
hypercenter#3508D11
hypocenterC11#12722
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×#41 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13070308C2semidirect
2. #13070288C2semidirect
3. #13070266C2semidirect
4. #13068720C2semidirect
12. C11×#533C4semidirect
14. C2×C11×#127C4semidirect
15. C11×#518C4semidirect
16. C11×#518C4semidirect
175. #533Dic11semidirect
177. C2×#127Dic11semidirect
178. #518Dic11semidirect
179. #518Dic11semidirect
315. C11#12722semidirect

Maximal subgroups

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

subgroupindex
#130703082
#130702882
#130702662
#130687202
C11×#35082
#1272211