Finite Group Databasebeta

← #14642232

Subgroups — #14642232

Order 2816.

448 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 109 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#13076991C211yesmaximal, characteristic
2#13068468C211yesmaximal, characteristic
3#13068360C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066441C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic
8C2×#66997C411yescharacteristic
9C2×#66941C411yescharacteristic
10C11×#391C2211yescharacteristic
11#10622843C411yescharacteristic
12C2×#66879—21no—
13C2×Dic11⋊C8—21no—
14C2×C8×Dic11—21no—
15#10622587C411yescharacteristic
16C42×Dic11C2211yescharacteristic
17#10622542C2211yescharacteristic
18#10622263—21no—
19#10622263—21no—
20#10622259—21no—
21#10622259—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11C2×C411yescharacteristic
28C22×Dic22—21no—
29C22×Dic22C2×C411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C42×C11C2311yescharacteristic
34#66997—42no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47#66941—42no—
48C11×#95—21no—
49C11×#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56#66879—42no—
57Dic11⋊C8—24no—
58C8×Dic11—24no—
59#7682—111nomaximal, Sylow
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—41no—
89C42×C11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94C4×Dic11—22no—
95C4×Dic11—22no—
96C4×Dic11—22no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11SD1612yes—
102C4×Dic11Q1612yes—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2862—111no—
110#1767—111no—
111#1744—111no—
112#1272—111no—
113#1272—111no—
114#1272—111no—
115#1272D1111yescharacteristic
116C23×C11C2×C22⋊C411yescharacteristic
117Q8×C11—81no—
118Q8×C11—81no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#13111yescharacteristic
132C2×C4×C11#13111yescharacteristic
133C2×C4×C11C2×SD1611yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11#10012yes—
151C2×Dic11#10312yes—
152C2×Dic11#10312yes—
153C2×Dic11#10412yes—
154C2×Dic11#10412yes—
155Dic22—84no—
156Dic22—81no—
157Dic22—81no—
158C8×C11—42no—
159C8×C11—42no—
160C11⋊C8—42no—
161C11⋊C8—42no—
162C2×C4⋊Q8—111no—
163C2×C4⋊Q8—111no—
164C2×C4⋊C8—221no—
165C2×#97—221no—
166C2×C4×C8—221no—
167#391—111no—
168#391—111no—
169#391—111no—
170#391—221no—
171#391—221no—
172#391C2×D1111yescharacteristic
173#382—221no—
174#382—221no—
175C43—111no—
176#336—111no—
177#336—111no—
178#336—221no—
179#336C2×D1111yescharacteristic
180#336C2×D1111yescharacteristic
181C22×C11#40811yescharacteristic
182C22×C11#41011yescharacteristic
183C22×C11C2×#10011yescharacteristic
184C22×C11C2×#10311yescharacteristic
185C22×C11#41911yescharacteristic
186C22×C11C2×#10411yescharacteristic
187C22×C11C2×#10411yescharacteristic
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—81no—
195C4×C11—81no—
196Dic11—22no—
197Dic11—22no—
198Dic11—41no—
199Dic11—81no—
200Dic11—81no—
201Dic11#32914yes—
202C22×Q8—111no—
203C22×Q8—221no—
204C22×Q8C4×D1111yescharacteristic
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—221no—
208C22×C8—221no—
209C4⋊Q8—442no—
210C4⋊Q8—442no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4C4×D1111yescharacteristic
216C2×C42—111no—
217C2×C42—111no—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42C22×D1111yescharacteristic
223C4⋊C8—224no—
224#97—442no—
225C4×C8—224no—
226#95—21no—
227#95—21no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234C2×C11#146911yescharacteristic
235C2×C11#148511yescharacteristic
236C2×C11#149311yescharacteristic
237C2×C11#150311yescharacteristic
238C2×C11#150611yescharacteristic
239C2×C11C2×#32911yescharacteristic
240C2×C11#154811yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—221no—
246C2×Q8—221no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—442no—
250C2×Q8—442no—
251C2×Q8—442no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—111no—
257C22×C4—111no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C4⋊C4—41no—
276C4⋊C4—441no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C42—41no—
281C42—112no—
282C42—112no—
283C42—222no—
284C42—222no—
285C42—222no—
286C42—221no—
287C42—221no—
288C42—221no—
289C42—221no—
290C11#768211yescharacteristic, complemented, Sylow
291C23C22⋊C4×D1111yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—881no—
295Q8—881no—
296Q8—884no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—112no—
310C2×C4—112no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—112no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4#6695411yescharacteristic
328C2×C4#6696011yescharacteristic
329C2×C4SD16×D1111yescharacteristic
330C2×C4#6696811yescharacteristic
331C2×C4Q16×D1111yescharacteristic
332C2×C4#6697111yescharacteristic
333C8—42no—
334C8—42no—
335C8—442no—
336C8—442no—
337C22#1062234011yescharacteristic
338C22#1062235311yescharacteristic
339C22D11×#10011yescharacteristic
340C22D11×#10311yescharacteristic
341C22#1062241511yescharacteristic
342C22D11×#10411yescharacteristic
343C22D11×#10411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—81no—
351C4—81no—
352C4—114no—
353C4—222no—
354C4—222no—
355C4—441no—
356C4—881no—
357C4—881no—
358C2#1306696611yescharacteristic
359C2#1306703511yescharacteristic
360C2#1306706911yescharacteristic
361C2#1306711311yescharacteristic
362C2#1306712611yescharacteristic
363C2D11×#32911yescharacteristic
364C2#1306729511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1272D11
hypocenterC11#7682
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
290. C11#7682semidirect

Maximal subgroups

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

subgroupindex
#130769912
#130684682
#130683602
#130664422
#130664412
C11×#12722
#768211