Finite Group Databasebeta

← C11×#33651 #14610844

Subgroups — C11×#33651 #14610844

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3059C211yesmaximal, characteristic
2C11×#2913C211yesmaximal, characteristic
3C11×#2237C212yesmaximal, complemented
4C11×#2237C212yesmaximal, complemented
5C11×#2236C212yesmaximal, complemented
6C11×#2235C212yesmaximal, complemented
7C11×#2159C211yesmaximal, characteristic, complemented
8C11×#2158C211yesmaximal, characteristic, complemented
9C11×#2141C211yesmaximal, characteristic, complemented
10C2×C11×#358C211yesmaximal, characteristic, complemented
11C11×#2113C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic
14C11×#536—21no—
15C11×#520—21no—
16C2×C11×M32C2211yescharacteristic
17C22×C11×C16C2211yescharacteristic
18C11×#470—22no—
19C11×#467C2212yes—
20C11×#467C2212yes—
21C11×#428—21no—
22C11×#428—22no—
23C11×#427C2211yescharacteristic
24C11×#427C2212yes—
25C11×#427C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C11×#107C2212yes—
28C11×#419—21no—
29C11×#367C2211yescharacteristic
30C11×#367C2211yescharacteristic
31C11×#367C2212yes—
32C11×#366C2211yescharacteristic
33C11×#366C2211yescharacteristic
34C11×#366C2212yes—
35C11×#358C2212yes—
36C11×#358C2212yes—
37C11×#358C2212yes—
38C11×#358C2212yes—
39C11×C22⋊C16C2212yes—
40C11×C22⋊C16C2212yes—
41C2×C11×#41D411yescharacteristic
42C22×Q8×C11—21no—
43C2×C11×Q16—21no—
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2312yes—
47C11×#131—22no—
48C11×#131—22no—
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D412yes—
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C11×C4⋊Q8—41no—
54C11×#124—41no—
55C11×#123—42no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C4×Q8×C11—41no—
59C4×D4×C11—42no—
60C4×D4×C11—41no—
61C11×#117—22no—
62C11×#117—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C11×M32—22no—
67C2×C11×C16—22no—
68C2×C11×C16C2311yescharacteristic
69C2×C11×C16C2311yescharacteristic
70C2×C11×C16C2312yes—
71C11×#107—22no—
72C11×#107—21no—
73C11×#107C2312yes—
74C11×#107C2311yescharacteristic
75C11×#107C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—22no—
79C11×#106—21no—
80C11×#106—21no—
81C11×#103—22no—
82C11×#103—22no—
83#33651C1111yesmaximal, characteristic, direct product factor, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11D811yescharacteristic
91C2×D4×C11D812yes—
92C2×D4×C11D811yescharacteristic
93C22×C4×C11—41no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C11×Q16—22no—
99C11×Q16—22no—
100C11×Q16—42no—
101C11×M16—24no—
102C11×M16—22no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11C2×D412yes—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11#4112yes—
108C2×C8×C11#4112yes—
109C2×C8×C11C2411yescharacteristic
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—42no—
118C11×C4⋊C4—42no—
119C11×C22⋊C4—42no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—42no—
123C11×C22⋊C4—42no—
124C42×C11—42no—
125C42×C11—41no—
126C42×C11—41no—
127C11×C16—21no—
128C11×C16—21no—
129C11×C16—22no—
130#3059C2×C1111yescharacteristic
131#2913C2×C1111yescharacteristic
132#2237C2×C1112yescomplemented
133#2237C2×C1112yescomplemented
134#2236C2×C1112yescomplemented
135#2235C2×C1112yescomplemented
136#2159C2×C1111yescharacteristic, complemented
137#2158C2×C1111yescharacteristic, complemented
138#2141C2×C1111yescharacteristic, complemented
139C2×#358C2×C1111yescharacteristic, complemented
140#2113C2×C1111yescharacteristic
141C23×C11C2×D812yes—
142C23×C11C2×D811yescharacteristic
143Q8×C11—22no—
144Q8×C11—42no—
145Q8×C11—42no—
146Q8×C11—82no—
147D4×C11—24no—
148D4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11—161no—
159C2×C4×C11—162no—
160C2×C4×C11#12312yes—
161C2×C4×C11C2×D812yes—
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D411yescharacteristic
165C8×C11—22no—
166C8×C11#12312yes—
167C8×C11C2×#4111yescharacteristic
168C8×C11C2×#4111yescharacteristic
169C22×Q16C22×C1111yescharacteristic
170C2×#131C22×C1111yescharacteristic
171#536—21no—
172#520—21no—
173C2×M32C22×C1111yescharacteristic
174C22×C16C22×C1111yescharacteristic
175#470—22no—
176#467C22×C1112yes—
177#467C22×C1112yes—
178#428—21no—
179#428—22no—
180#427C22×C1111yescharacteristic
181#427C22×C1112yes—
182#427C22×C1111yescharacteristic
183C2×#107C22×C1111yescharacteristic
184C2×#107C22×C1112yes—
185#419—21no—
186#367C22×C1111yescharacteristic
187#367C22×C1111yescharacteristic
188#367C22×C1112yes—
189#366C22×C1111yescharacteristic
190#366C22×C1111yescharacteristic
191#366C22×C1112yes—
192#358C22×C1112yes—
193#358C22×C1112yes—
194#358C22×C1112yes—
195#358C22×C1112yes—
196C22⋊C16C22×C1112yes—
197C22⋊C16C22×C1112yes—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11#48012yes—
204C22×C11C22×D811yescharacteristic
205C4×C11—22no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—82no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11—81no—
212C4×C11#48012yes—
213C4×C11C2×#12311yescharacteristic
214C4×C11C2×#13711yescharacteristic
215C2×#41D4×C1111yescharacteristic
216C22×Q8—21no—
217C2×Q16—21no—
218C2×Q16—22no—
219C2×Q16—22no—
220C2×Q16C23×C1112yes—
221#131—22no—
222#131—22no—
223C2×M16D4×C1111yescharacteristic
224C2×M16D4×C1112yes—
225C22×C8C23×C1112yes—
226C22×C8C23×C1111yescharacteristic
227C4⋊Q8—41no—
228#124—41no—
229#123—42no—
230C22⋊Q8—22no—
231C22⋊Q8—22no—
232C4×Q8—41no—
233C4×D4—42no—
234C4×D4—41no—
235#117—22no—
236#117—21no—
237#117—21no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240M32—22no—
241C2×C16—22no—
242C2×C16C23×C1111yescharacteristic
243C2×C16C23×C1112yes—
244C2×C16C23×C1111yescharacteristic
245#107—22no—
246#107—21no—
247#107C23×C1112yes—
248#107C23×C1111yescharacteristic
249#107C23×C1111yescharacteristic
250#107C23×C1111yescharacteristic
251#107C23×C1111yescharacteristic
252#106—22no—
253#106—21no—
254#106—21no—
255#103—22no—
256#103—22no—
257C2×C11—22no—
258C2×C11—42no—
259C2×C11C2×#48011yescharacteristic
260C2×C11#341611yescharacteristic
261C2×C11#341711yescharacteristic
262#41—22no—
263#41—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8C11×D811yescharacteristic
269C2×D4C11×D812yes—
270C2×D4C11×D811yescharacteristic
271C22×C4—41no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4C2×D4×C1112yes—
275C22×C4C2×D4×C1111yescharacteristic
276Q16—22no—
277Q16—22no—
278Q16—42no—
279M16—22no—
280M16—24no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8C2×D4×C1112yes—
284C2×C8C2×D4×C1111yescharacteristic
285C2×C8C11×#4112yes—
286C2×C8C11×#4112yes—
287C2×C8C24×C1111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C42—42no—
303C42—41no—
304C42—41no—
305C16—21no—
306C16—21no—
307C16—22no—
308C11#3365111yescharacteristic, direct product factor, Sylow
309C23C2×C11×D812yes—
310C23C2×C11×D811yescharacteristic
311Q8—22no—
312Q8—42no—
313Q8—42no—
314Q8—82no—
315D4—24no—
316D4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—161no—
327C2×C4—162no—
328C2×C4C11×#12312yes—
329C2×C4C2×C11×D812yes—
330C2×C4C2×C11×D811yescharacteristic
331C2×C4C11×#13712yes—
332C2×C4C22×D4×C1111yescharacteristic
333C8—22no—
334C8C11×#12312yes—
335C8C2×C11×#4111yescharacteristic
336C8C2×C11×#4111yescharacteristic
337C22—21no—
338C22—21no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22C11×#48012yes—
343C22C22×C11×D811yescharacteristic
344C4—22no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—82no—
351C4C11×#48012yes—
352C4C2×C11×#12311yescharacteristic
353C4C2×C11×#13711yescharacteristic
354C2—22no—
355C2—42no—
356C2C2×C11×#48011yescharacteristic
357C2C11×#341611yescharacteristic
358C2C11×#341711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC2×C11×#41D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2237C2semidirect
4. C11×#2237C2semidirect
5. C11×#2236C2semidirect
6. C11×#2235C2semidirect
7. C11×#2159C2semidirect
8. C11×#2158C2semidirect
9. C11×#2141C2semidirect
10. C2×C11×#358C2semidirect
83. #33651C11direct (N × H)
132. #2237C2×C11semidirect
133. #2237C2×C11semidirect
134. #2236C2×C11semidirect
135. #2235C2×C11semidirect
136. #2159C2×C11semidirect
137. #2158C2×C11semidirect
138. #2141C2×C11semidirect
139. C2×#358C2×C11semidirect
308. C11#33651direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30592
C11×#29132
C11×#22372
C11×#22362
C11×#22352
C11×#21592
C11×#21582
C11×#21412
C2×C11×#3582
C11×#21132
#3365111