Finite Group Databasebeta

← C11×#12176 #14589369

Subgroups — C11×#12176 #14589369

Order 2816.

486 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2677C211yesmaximal, characteristic, complemented
2C11×#2044C211yesmaximal, characteristic
3C11×#1613C211yesmaximal, characteristic
4C11×#1601C211yesmaximal, characteristic
5C11×#1352C211yesmaximal, characteristic, complemented
6C11×#1351C211yesmaximal, characteristic, complemented
7C11×#1326C211yesmaximal, characteristic, complemented
8C11×#534C2211yescharacteristic
9C2×C11×C4⋊Q8—21no—
10C2×C11×C22⋊Q8—21no—
11C11×#481—21no—
12C11×#448—21no—
13C2×C11×#99—21no—
14C11×#399C2211yescharacteristic
15C11×#398—21no—
16C11×#395—21no—
17C11×#393C2211yescharacteristic
18C11×#388—21no—
19C11×#387—21no—
20C11×#386—21no—
21C11×#385C2211yescharacteristic
22C11×#342C2211yescharacteristic
23C11×#327—21no—
24C11×#327—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×Q8×C11—21no—
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11—21no—
30C23×C4×C11D411yescharacteristic
31C2×C11×SD16—41no—
32C11×C4⋊Q8—44no—
33C11×#123—41no—
34C11×C22⋊Q8—44no—
35C11×#121—21no—
36C11×#121—21no—
37C11×#120—41no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—41no—
49C2×C11×C22⋊C4D411yescharacteristic
50C2×C11×C22⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C11×#106—41no—
53C11×#103—41no—
54C11×#102—41no—
55C11×#99—42no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—41no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65#12176C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C2×Q8×C11—42no—
69C2×Q8×C11—42no—
70C2×Q8×C11—42no—
71C2×Q8×C11—41no—
72C2×Q8×C11—81no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—42no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C11×SD16—82no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—21no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—82no—
114C11×C22⋊C4SD1612yescomplemented
115C42×C11—42no—
116#2677C2×C1111yescharacteristic, complemented
117#2044C2×C1111yescharacteristic
118#1613C2×C1111yescharacteristic
119#1601C2×C1111yescharacteristic
120#1352C2×C1111yescharacteristic, complemented
121#1351C2×C1111yescharacteristic, complemented
122#1326C2×C1111yescharacteristic, complemented
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11#12011yescharacteristic
133C23×C11C2×SD1611yescharacteristic
134C23×C11#13711yescharacteristic
135Q8×C11—42no—
136Q8×C11—81no—
137Q8×C11—84no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—81no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C8×C11—81no—
175C8×C11—81no—
176#534C22×C1111yescharacteristic
177C2×C4⋊Q8—21no—
178C2×C22⋊Q8—21no—
179#481—21no—
180#448—21no—
181C2×#99—21no—
182#399C22×C1111yescharacteristic
183#398—21no—
184#395—21no—
185#393C22×C1111yescharacteristic
186#388—21no—
187#387—21no—
188#386—21no—
189#385C22×C1111yescharacteristic
190#342C22×C1111yescharacteristic
191#327—21no—
192#327—21no—
193#323C22×C1111yescharacteristic
194#323C22×C1111yescharacteristic
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—81no—
204C22×C11—82no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—161no—
209C22×C11#44811yescharacteristic
210C22×C11#45411yescharacteristic
211C22×C11B(4,𝔽2)11yescharacteristic
212C4×C11—42no—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—161no—
222C22×Q8—21no—
223C22×Q8D4×C1111yescharacteristic
224C22×D4—21no—
225C23×C4D4×C1111yescharacteristic
226C2×SD16—41no—
227C4⋊Q8—44no—
228#123—41no—
229C22⋊Q8—44no—
230#121—21no—
231#121—21no—
232#120—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4D4×C1111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—41no—
244C2×C22⋊C4D4×C1111yescharacteristic
245C2×C22⋊C4C23×C1111yescharacteristic
246C2×C42—21no—
247#106—41no—
248#103—41no—
249#102—41no—
250#99—42no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—41no—
258#95D4×C1111yescharacteristic
259#95D4×C1111yescharacteristic
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—41no—
263C2×C11—41no—
264C2×C11—161no—
265C2×C11#159911yescharacteristic
266C2×C11#219611yescharacteristic
267C2×C11#220111yescharacteristic
268C24—21no—
269C24C2×D4×C1111yescharacteristic
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×Q8—81no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295SD16—82no—
296C2×C8—41no—
297C2×C8—41no—
298C4⋊C4—24no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C22⋊C4—21no—
308C22⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—82no—
316C22⋊C4C11×SD1612yescomplemented
317C42—42no—
318C11#1217611yescharacteristic, direct product factor, Sylow
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—81no—
327C23—81no—
328C23C11×#12011yescharacteristic
329C23C2×C11×SD1611yescharacteristic
330C23C11×#13711yescharacteristic
331Q8—42no—
332Q8—81no—
333Q8—84no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—81no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C8—81no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—82no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—161no—
386C22C11×#44811yescharacteristic
387C22C11×#45411yescharacteristic
388C22C11×B(4,𝔽2)11yescharacteristic
389C4—42no—
390C4—42no—
391C4—41no—
392C4—42no—
393C4—42no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—161no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—161no—
404C2C11×#159911yescharacteristic
405C2C11×#219611yescharacteristic
406C2C11×#220111yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2677C2semidirect
5. C11×#1352C2semidirect
6. C11×#1351C2semidirect
7. C11×#1326C2semidirect
65. #12176C11direct (N × H)
114. C11×C22⋊C4SD16semidirect
116. #2677C2×C11semidirect
120. #1352C2×C11semidirect
121. #1351C2×C11semidirect
122. #1326C2×C11semidirect
316. C22⋊C4C11×SD16semidirect
318. C11#12176direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26772
C11×#20442
C11×#16132
C11×#16012
C11×#13522
C11×#13512
C11×#13262
#1217611