Finite Group Databasebeta

← #14664241

Subgroups — #14664241

Order 2816.

444 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 71 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#13074194C211yesmaximal, characteristic
2#13068347C211yesmaximal, characteristic
3#13066947C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic
5#13066636C211yesmaximal, characteristic
6#13066616C211yesmaximal, characteristic
7C11×#1344C211yesmaximal, characteristic
8C2×#66940C411yescharacteristic, complemented
9C2×#66930—21no—
10C2×#66930C2211yescharacteristic
11C11×#397C2211yescharacteristic
12#10622593C411yescharacteristic, complemented
13#10622564—21no—
14#10622560C2211yescharacteristic
15#10622559—21no—
16#10622332—21no—
17#10622269C411yescharacteristic, complemented
18#10622267—21no—
19#10622265—21no—
20#10622264C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C23×Dic11D411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—41no—
40C2×Dic11⋊C4C2×C411yescharacteristic
41C2×Dic11⋊C4D411yescharacteristic
42C2×C4×Dic11—21no—
43C2×C4×Dic11—41no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46#66940—41no—
47#66940—41no—
48#66930—24no—
49#66930—41no—
50#66930—41no—
51#66930—42no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95C2×C411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#11756—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—22no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C2×Dic22—41no—
84C2×Dic22—42no—
85C2×C8×C11—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C22⋊Dic11—22no—
93C22⋊Dic11—41no—
94C22⋊Dic11—42no—
95C22⋊Dic11—41no—
96C4⋊Dic11—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—44no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102Dic11⋊C4—42no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—44no—
108C4×Dic11—42no—
109C2×C11⋊C8—41no—
110#2599—111no—
111#1740—111no—
112#1464—111no—
113#1351—111no—
114#1351—111no—
115#1344—111no—
116#1344D1111yescharacteristic
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11AGL(1,ℤ/8)11yescharacteristic
123C23×C11#13711yescharacteristic
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×Dic11—22no—
138C2×Dic11—22no—
139C2×Dic11—22no—
140C2×Dic11—22no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—22no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11#9911yescharacteristic
159C2×Dic11#9911yescharacteristic
160C2×Dic11#10412yes—
161Dic22—42no—
162Dic22—42no—
163C8×C11—81no—
164C11⋊C8—81no—
165C2×C4×Q8—111no—
166C2×#117—111no—
167C2×#117—221no—
168#432—221no—
169#398—111no—
170#397C2×D1111yescharacteristic
171#395—111no—
172#393—111no—
173#388—221no—
174#387—221no—
175#387—221no—
176#385—221no—
177#383—111no—
178#342—111no—
179#342—221no—
180#342C2×D1111yescharacteristic
181#324—221no—
182#323—111no—
183#323C2×D1111yescharacteristic
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—81no—
193C22×C11C2×#9911yescharacteristic
194C22×C11#41711yescharacteristic
195C22×C11C2×#10411yescharacteristic
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—81no—
199C4×C11—82no—
200C4×C11—81no—
201Dic11—21no—
202Dic11—21no—
203Dic11—22no—
204Dic11—42no—
205Dic11—41no—
206Dic11—41no—
207Dic11—81no—
208Dic11—82no—
209C22×Q8—111no—
210C23×C4—111no—
211C4×Q8—441no—
212C4×Q8—441no—
213#117—224no—
214#117—441no—
215#117—441no—
216#117—442no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—441no—
223C2×C4⋊C4C4×D1111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—111no—
227C2×C22⋊C4—221no—
228C2×C22⋊C4—221no—
229C2×C22⋊C4C22×D1111yescharacteristic
230C2×C42—111no—
231C2×C42—111no—
232C2×C42—221no—
233C2×C42—441no—
234C4⋊C8—441no—
235C22⋊C8—21no—
236C22⋊C8—221no—
237#97—441no—
238#95—21no—
239#95—111no—
240#95—221no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95C4×D1111yescharacteristic
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—41no—
249C2×C11—41no—
250C2×C11#150411yescharacteristic
251C2×C11#212011yescharacteristic
252C2×C11#212911yescharacteristic
253C24D4×D1111yescharacteristic
254C2×Q8—441no—
255C2×Q8—442no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—222no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—441no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C2×C8—41no—
274C2×C8—441no—
275C4⋊C4—41no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—444no—
283C22⋊C4—22no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—222no—
289C22⋊C4—441no—
290C22⋊C4—442no—
291C22⋊C4—441no—
292C42—221no—
293C42—221no—
294C42—221no—
295C42—221no—
296C42—442no—
297C42—444no—
298C11#1175611yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23C22⋊C4×D1111yescharacteristic
304C23#6696411yescharacteristic
305C23#6696811yescharacteristic
306Q8—442no—
307Q8—442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—112no—
324C2×C4—222no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—221no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—222no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—442no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—881no—
344C2×C4—881no—
345C8—81no—
346C8—881no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22D11×#9911yescharacteristic
357C22#1062238411yescharacteristic
358C22D11×#10411yescharacteristic
359C4—41no—
360C4—41no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—221no—
365C4—221no—
366C4—222no—
367C4—442no—
368C4—441no—
369C4—441no—
370C4—881no—
371C4—882no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1306711711yescharacteristic
377C2#1307025611yescharacteristic
378C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11756
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
8. C2×#66940C4semidirect
12. #10622593C4semidirect
17. #10622269C4semidirect
20. #10622264C4semidirect
298. C11#11756semidirect

Maximal subgroups

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

subgroupindex
#130741942
#130683472
#130669472
#130666382
#130666362
#130666162
C11×#13442
#1175611