Finite Group Databasebeta

← C11×#10378 #14587571

Subgroups — C11×#10378 #14587571

Order 2816.

398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 90 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
1C11×#2605C211yesmaximal, characteristic, complemented
2C11×#1980C211yesmaximal, characteristic
3C11×#1514C211yesmaximal, characteristic
4C11×#1505C211yesmaximal, characteristic
5C11×#1300C211yesmaximal, characteristic, complemented
6C11×#1288C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C2×C11×#104—21no—
12C2×C11×#104—21no—
13C4×C11×M16C2211yescharacteristic
14C11×#400—21no—
15C11×#395—21no—
16C11×#391—21no—
17C11×#391—21no—
18C11×#387—21no—
19C11×#387—21no—
20C11×#383C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#376C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#327—21no—
26C11×#327—21no—
27C2×C11×#41—21no—
28C22×Q8×C11—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8Q811yescharacteristic, complemented
31C11×#127Q811yescharacteristic, complemented
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11D411yescharacteristic
43C2×C42×C11D411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×#104—42no—
48C11×#104—42no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C11×#97—21no—
53C11×#97—21no—
54C4×C8×C11—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65C11×#95D411yescharacteristic
66C11×#95D411yescharacteristic
67#10378C1111yesmaximal, characteristic, direct product factor, Sylow
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×Q8×C11—42no—
74C2×Q8×C11—42no—
75C2×Q8×C11—81no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C11×M16—22no—
91C11×M16—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—42no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—42no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11C2×Q811yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110#2605C2×C1111yescharacteristic, complemented
111#1980C2×C1111yescharacteristic
112#1514C2×C1111yescharacteristic
113#1505C2×C1111yescharacteristic
114#1300C2×C1111yescharacteristic, complemented
115#1288C2×C1111yescharacteristic, complemented
116#1285C2×C1111yescharacteristic, complemented
117C23×C11—41no—
118C23×C11#12011yescharacteristic
119Q8×C11—41no—
120Q8×C11—41no—
121Q8×C11—84no—
122D4×C11—41no—
123D4×C11—41no—
124D4×C11—81no—
125D4×C11—81no—
126D4×C11—81no—
127D4×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11C22⋊Q811yescharacteristic
154C2×C4×C11C22⋊Q811yescharacteristic
155C2×C4×C11C22⋊Q811yescharacteristic
156C2×C4×C11#12411yescharacteristic
157C2×C4×C11#12411yescharacteristic
158C2×C4×C11#12411yescharacteristic
159C8×C11—42no—
160C8×C11—81no—
161C8×C11—81no—
162#532C22×C1111yescharacteristic
163#432C22×C1111yescharacteristic
164#432C22×C1111yescharacteristic
165C2×#104—21no—
166C2×#104—21no—
167C4×M16C22×C1111yescharacteristic
168#400—21no—
169#395—21no—
170#391—21no—
171#391—21no—
172#387—21no—
173#387—21no—
174#383C22×C1111yescharacteristic
175C4×C4⋊C4C22×C1111yescharacteristic
176#376C22×C1111yescharacteristic
177#327—21no—
178#327—21no—
179#327—21no—
180#327—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#39311yescharacteristic
187C22×C11#45311yescharacteristic
188C22×C11#45411yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—42no—
196C4×C11—42no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11—81no—
202C2×#41—21no—
203C22×Q8—21no—
204C2×M16—21no—
205C4⋊Q8Q8×C1111yescharacteristic, complemented
206#127Q8×C1111yescharacteristic, complemented
207#124—21no—
208#121—21no—
209#121—21no—
210C4×D4—21no—
211C4×D4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C42—21no—
217C2×C42D4×C1111yescharacteristic
218C2×C42D4×C1111yescharacteristic
219C2×C42C23×C1111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222#104—42no—
223#104—42no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226#97—21no—
227#97—21no—
228#97—21no—
229C4×C8—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95D4×C1111yescharacteristic
239#95D4×C1111yescharacteristic
240#95D4×C1111yescharacteristic
241#95D4×C1111yescharacteristic
242C2×C11—21no—
243C2×C11—21no—
244C2×C11—161no—
245C2×C11#202711yescharacteristic
246C2×C11#203111yescharacteristic
247C2×C11#203111yescharacteristic
248#41—41no—
249#41—41no—
250#41—41no—
251#41—41no—
252C2×Q8—21no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—81no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4C2×D4×C1111yescharacteristic
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1111yescharacteristic
270M16—22no—
271M16—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C42—41no—
285C42—42no—
286C42C2×Q8×C1111yescharacteristic
287C42C11×#4111yescharacteristic
288C42C11×#4111yescharacteristic
289C42C11×#4111yescharacteristic
290C11#1037811yescharacteristic, direct product factor, Sylow
291C23—41no—
292C23C11×#12011yescharacteristic
293Q8—41no—
294Q8—41no—
295Q8—84no—
296D4—41no—
297D4—41no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C11×C22⋊Q811yescharacteristic
328C2×C4C11×C22⋊Q811yescharacteristic
329C2×C4C11×C22⋊Q811yescharacteristic
330C2×C4C11×#12411yescharacteristic
331C2×C4C11×#12411yescharacteristic
332C2×C4C11×#12411yescharacteristic
333C8—42no—
334C8—81no—
335C8—81no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C11×#39311yescharacteristic
342C22C11×#45311yescharacteristic
343C22C11×#45411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—42no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—81no—
357C2—21no—
358C2—21no—
359C2—161no—
360C2C11×#202711yescharacteristic
361C2C11×#203111yescharacteristic
362C2C11×#203111yescharacteristic
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2605C2semidirect
5. C11×#1300C2semidirect
6. C11×#1288C2semidirect
7. C11×#1285C2semidirect
30. C11×C4⋊Q8Q8semidirect
31. C11×#127Q8semidirect
67. #10378C11direct (N × H)
110. #2605C2×C11semidirect
114. #1300C2×C11semidirect
115. #1288C2×C11semidirect
116. #1285C2×C11semidirect
205. C4⋊Q8Q8×C11semidirect
206. #127Q8×C11semidirect
290. C11#10378direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26052
C11×#19802
C11×#15142
C11×#15052
C11×#13002
C11×#12882
C11×#12852
#1037811