Finite Group Databasebeta

← C11×#33759 #14610952

Subgroups — C11×#33759 #14610952

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic, complemented
2C2×C11×#466C211yesmaximal, characteristic
3C11×#2236C212yesmaximal, complemented
4C11×#2232C212yesmaximal, complemented
5C11×#2220C214yesmaximal, complemented
6C11×#2187C212yesmaximal, complemented
7C11×#2185C212yesmaximal, complemented
8C11×#2112C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic, complemented
10C22×C11×D8C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×C22⋊Q8—21no—
13C2×C11×#121—21no—
14C2×C11×SD32C2214yescomplemented
15C2×C11×M32C2212yescomplemented
16C11×#467—21no—
17C11×#467—21no—
18C11×#467C2212yes—
19C11×#467C2212yescomplemented
20C11×#466—21no—
21C11×#466—21no—
22C11×#466C2212yes—
23C11×#466C2212yes—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic, complemented
26C2×C11×#103—21no—
27C2×C11×#102—21no—
28C11×#366C2214yescomplemented
29C11×#358C2214yescomplemented
30C11×#357C2214yescomplemented
31C11×C22⋊C16C2212yes—
32C11×C22⋊C16C2212yescomplemented
33C22×Q8×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—41no—
36C23×C4×C11D411yescharacteristic
37C2×C11×Q16—21no—
38C2×C11×Q16—42no—
39C2×C11×Q16C2312yes—
40C2×C11×D8—21no—
41C2×C11×D8—42no—
42C2×C11×D8C2312yes—
43C22×C8×C11—42no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11D411yescharacteristic
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—41no—
53C11×C22⋊Q8—41no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—41no—
57C11×#121—41no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—41no—
61C2×C11×C22⋊C4—41no—
62C2×C11×C22⋊C4—41no—
63C11×SD32—44no—
64C11×M32—42no—
65C2×C11×C16C2314yes—
66C11×#107—21no—
67C11×#107—21no—
68C11×#107C2312yes—
69C11×#107C2312yes—
70C11×#103—22no—
71C11×#103—22no—
72C11×#102—22no—
73C11×#102—22no—
74#33759C1111yesmaximal, characteristic, direct product factor, Sylow
75C24×C11—41no—
76C24×C11D811yescharacteristic
77C2×Q8×C11—22no—
78C2×Q8×C11—42no—
79C2×Q8×C11—42no—
80C2×Q8×C11—41no—
81C2×D4×C11—22no—
82C2×D4×C11—42no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—41no—
87C2×D4×C11—84no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11D811yescharacteristic
94C22×C4×C11D811yescharacteristic
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C11×Q16—24no—
100C11×Q16—42no—
101C11×D8—24no—
102C11×D8—42no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—42no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—42no—
121C11×C22⋊C4—42no—
122C11×C22⋊C4—42no—
123C11×C16—24no—
124C2×#467C2×C1111yescharacteristic, complemented
125C2×#466C2×C1111yescharacteristic
126#2236C2×C1112yescomplemented
127#2232C2×C1112yescomplemented
128#2220C2×C1114yescomplemented
129#2187C2×C1112yescomplemented
130#2185C2×C1112yescomplemented
131#2112C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—82no—
137C23×C11—82no—
138C23×C11—82no—
139C23×C11C2×D811yescharacteristic
140C23×C11C2×D811yescharacteristic
141C23×C11C2×D811yescharacteristic
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—82no—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—82no—
148D4×C11—84no—
149D4×C11—84no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C8×C11—21no—
170C8×C11—21no—
171C8×C11—21no—
172C8×C11H(5,𝔽2)12yes—
173C22×Q16C22×C1111yescharacteristic, complemented
174C22×D8C22×C1111yescharacteristic
175C23×C8C22×C1111yescharacteristic
176C2×C22⋊Q8—21no—
177C2×#121—21no—
178C2×SD32C22×C1114yescomplemented
179C2×M32C22×C1112yescomplemented
180#467—21no—
181#467—21no—
182#467C22×C1112yes—
183#467C22×C1112yescomplemented
184#466—21no—
185#466—21no—
186#466C22×C1112yes—
187#466C22×C1112yes—
188C2×#107C22×C1111yescharacteristic
189C2×#107C22×C1111yescharacteristic, complemented
190C2×#103—21no—
191C2×#102—21no—
192#366C22×C1114yescomplemented
193#358C22×C1114yescomplemented
194#357C22×C1114yescomplemented
195C22⋊C16C22×C1112yes—
196C22⋊C16C22×C1112yescomplemented
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—44no—
205C22×C11—82no—
206C22×C11—82no—
207C22×C11—82no—
208C22×C11—164no—
209C22×C11#50912yes—
210C22×C11#51012yes—
211C22×C11C22×D811yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—82no—
216C4×C11—82no—
217C4×C11—82no—
218C4×C11#53411yescharacteristic
219C4×C11#57511yescharacteristic
220C22×Q8—21no—
221C22×D4—21no—
222C22×D4—41no—
223C23×C4D4×C1111yescharacteristic
224C2×Q16—21no—
225C2×Q16—42no—
226C2×Q16C23×C1112yes—
227C2×D8—21no—
228C2×D8—42no—
229C2×D8C23×C1112yes—
230C22×C8—42no—
231C22×C8D4×C1111yescharacteristic
232C22×C8D4×C1111yescharacteristic
233C22×C8D4×C1111yescharacteristic
234C22×C8C23×C1111yescharacteristic
235C22×C8C23×C1111yescharacteristic
236C22×C8C23×C1111yescharacteristic
237C22⋊Q8—22no—
238C22⋊Q8—22no—
239C22⋊Q8—41no—
240C22⋊Q8—41no—
241#121—22no—
242#121—22no—
243#121—41no—
244#121—41no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—41no—
248C2×C22⋊C4—41no—
249C2×C22⋊C4—41no—
250SD32—44no—
251M32—42no—
252C2×C16C23×C1114yes—
253#107—21no—
254#107—21no—
255#107C23×C1112yes—
256#107C23×C1112yes—
257#103—22no—
258#103—22no—
259#102—22no—
260#102—22no—
261C2×C11—22no—
262C2×C11—22no—
263C2×C11—41no—
264C2×C11—162no—
265C2×C11#318611yescharacteristic
266C2×C11C2×#50911yescharacteristic
267C2×C11C2×#51011yescharacteristic
268C24—41no—
269C24C11×D811yescharacteristic
270C2×Q8—22no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—41no—
274C2×D4—22no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—84no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C11×D811yescharacteristic
287C22×C4C11×D811yescharacteristic
288C22×C4C11×D811yescharacteristic
289C22×C4C2×D4×C1111yescharacteristic
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292Q16—24no—
293Q16—42no—
294D8—24no—
295D8—42no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8C2×D4×C1111yescharacteristic
303C2×C8C2×D4×C1111yescharacteristic
304C2×C8C2×D4×C1111yescharacteristic
305C2×C8C24×C1111yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C16—24no—
317C11#3375911yescharacteristic, direct product factor, Sylow
318C23—22no—
319C23—22no—
320C23—41no—
321C23—42no—
322C23—82no—
323C23—82no—
324C23—82no—
325C23C2×C11×D811yescharacteristic
326C23C2×C11×D811yescharacteristic
327C23C2×C11×D811yescharacteristic
328Q8—42no—
329Q8—42no—
330Q8—82no—
331D4—42no—
332D4—42no—
333D4—82no—
334D4—84no—
335D4—84no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4C2×C11×D811yescharacteristic
352C2×C4C2×C11×D811yescharacteristic
353C2×C4C2×C11×D811yescharacteristic
354C2×C4C22×D4×C1111yescharacteristic
355C8—21no—
356C8—21no—
357C8—21no—
358C8C11×H(5,𝔽2)12yes—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—164no—
371C22C11×#50912yes—
372C22C11×#51012yes—
373C22C22×C11×D811yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—82no—
378C4—82no—
379C4—82no—
380C4C11×#53411yescharacteristic
381C4C11×#57511yescharacteristic
382C2—22no—
383C2—22no—
384C2—41no—
385C2—162no—
386C2C11×#318611yescharacteristic
387C2C2×C11×#50911yescharacteristic
388C2C2×C11×#51011yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC2×C11×#466C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#467C2semidirect
3. C11×#2236C2semidirect
4. C11×#2232C2semidirect
5. C11×#2220C2semidirect
6. C11×#2187C2semidirect
7. C11×#2185C2semidirect
8. C11×#2112C2semidirect
9. C22×C11×Q16C22semidirect
14. C2×C11×SD32C22semidirect
15. C2×C11×M32C22semidirect
19. C11×#467C22semidirect
25. C2×C11×#107C22semidirect
28. C11×#366C22semidirect
29. C11×#358C22semidirect
30. C11×#357C22semidirect
32. C11×C22⋊C16C22semidirect
74. #33759C11direct (N × H)
124. C2×#467C2×C11semidirect
126. #2236C2×C11semidirect
127. #2232C2×C11semidirect
128. #2220C2×C11semidirect
129. #2187C2×C11semidirect
130. #2185C2×C11semidirect
131. #2112C2×C11semidirect
173. C22×Q16C22×C11semidirect
178. C2×SD32C22×C11semidirect
179. C2×M32C22×C11semidirect
183. #467C22×C11semidirect
189. C2×#107C22×C11semidirect
192. #366C22×C11semidirect
193. #358C22×C11semidirect
194. #357C22×C11semidirect
196. C22⋊C16C22×C11semidirect
317. C11#33759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C11×#4662
C11×#22362
C11×#22322
C11×#22202
C11×#21872
C11×#21852
C11×#21122
#3375911