Finite Group Databasebeta

← C11×#33789 #14610982

Subgroups — C11×#33789 #14610982

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3177C211yesmaximal, characteristic, complemented
2C11×#3156C211yesmaximal, characteristic
3C11×#2251C211yesmaximal, characteristic, complemented
4C11×#2247C211yesmaximal, characteristic, complemented
5C11×#2245C211yesmaximal, characteristic, complemented
6C11×#2242C211yesmaximal, characteristic, complemented
7C11×#2211C212yesmaximal, complemented
8C11×#2209C212yesmaximal, complemented
9C11×#2189C212yesmaximal
10C11×#2188C212yesmaximal, complemented
11C11×#2164C211yesmaximal, characteristic, complemented
12C2×C11×#137—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×Q16C2211yescharacteristic
15C11×#541—21no—
16C11×#536—21no—
17C2×C11×Q32C2212yes—
18C2×C11×Q32C2212yes—
19C2×C11×Q32C2212yes—
20C2×C11×SD32C2212yes—
21C11×#499C2211yescharacteristic
22C11×#497—21no—
23C11×#497—21no—
24C11×#495C2211yescharacteristic
25C11×#495C2211yescharacteristic
26C11×#494C2211yescharacteristic
27C11×#494C2211yescharacteristic
28C11×#494C2211yescharacteristic
29C11×#491—21no—
30C11×#470—21no—
31C11×#467C2212yes—
32C11×#441—21no—
33C4×C11×Q16C2212yes—
34C11×#405C2211yescharacteristic
35C11×C4⋊C16C2212yes—
36C11×#358C2212yes—
37C11×#358C2212yes—
38C11×#358C2212yes—
39C11×#357C2212yes—
40C11×C22⋊C16C2212yes—
41C11×#346C2211yescharacteristic
42C4×C11×C16C2211yescharacteristic
43C2×C11×#41—21no—
44C22×Q8×C11—21no—
45C11×#137—44no—
46C11×#135—42no—
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C2×C11×Q16—21no—
51C2×C11×Q16—42no—
52C2×C11×Q16C2311yescharacteristic
53C2×C11×Q16C2311yescharacteristic
54C2×C11×Q16C2311yescharacteristic
55C2×C11×Q16C2312yes—
56C2×C11×SD16—21no—
57C2×C11×SD16—21no—
58C2×C11×SD16—21no—
59C2×C11×D8C2311yescharacteristic
60C2×C11×M16D411yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×#126—42no—
66C11×#125—21no—
67C11×#125—42no—
68C11×#124—21no—
69C11×#124—21no—
70C11×#123—42no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—42no—
73C4×Q8×C11—22no—
74C11×#117D411yescharacteristic
75C11×Q32—42no—
76C11×Q32—42no—
77C11×Q32—42no—
78C11×SD32—42no—
79C2×C11×C16C2312yes—
80C2×C11×C16C2312yes—
81C11×#107C2312yes—
82C11×#106—21no—
83C11×#103—22no—
84C11×#103—22no—
85C11×#97D411yescharacteristic
86C11×#97D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#33789C1111yesmaximal, characteristic, direct product factor, Sylow
90C11×#41—42no—
91C11×#41—42no—
92C2×Q8×C11—22no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—41no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C11×Q16—22no—
105C11×Q16—22no—
106C11×Q16—22no—
107C11×Q16—22no—
108C11×Q16—22no—
109C11×Q16—42no—
110C11×Q16—42no—
111C11×Q16—42no—
112C11×Q16—42no—
113C11×SD16—42no—
114C11×SD16—42no—
115C11×SD16—42no—
116C11×D8—22no—
117C11×M16—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4D812yes—
131C11×C22⋊C4—42no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4D812yes—
135C42×C11—42no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C11×C16—22no—
139C11×C16—22no—
140#3177C2×C1111yescharacteristic, complemented
141#3156C2×C1111yescharacteristic
142#2251C2×C1111yescharacteristic, complemented
143#2247C2×C1111yescharacteristic, complemented
144#2245C2×C1111yescharacteristic, complemented
145#2242C2×C1111yescharacteristic, complemented
146#2211C2×C1112yescomplemented
147#2209C2×C1112yescomplemented
148#2189C2×C1112yes—
149#2188C2×C1112yescomplemented
150#2164C2×C1111yescharacteristic, complemented
151C23×C11—41no—
152C23×C11C2×D811yescharacteristic
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—41no—
156Q8×C11—42no—
157Q8×C11—41no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11—42no—
161Q8×C11—82no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—82no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11C2×D812yes—
175C2×C4×C11C2×D812yes—
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C8×C11—21no—
179C8×C11—21no—
180C8×C11AGL(1,ℤ/8)12yes—
181C8×C11H(5,𝔽2)12yes—
182C2×#137—21no—
183C2×#135C22×C1111yescharacteristic
184C22×Q16C22×C1111yescharacteristic
185#541—21no—
186#536—21no—
187C2×Q32C22×C1112yes—
188C2×Q32C22×C1112yes—
189C2×Q32C22×C1112yes—
190C2×SD32C22×C1112yes—
191#499C22×C1111yescharacteristic
192#497—21no—
193#497—21no—
194#495C22×C1111yescharacteristic
195#495C22×C1111yescharacteristic
196#494C22×C1111yescharacteristic
197#494C22×C1111yescharacteristic
198#494C22×C1111yescharacteristic
199#491—21no—
200#470—21no—
201#467C22×C1112yes—
202#441—21no—
203C4×Q16C22×C1112yes—
204#405C22×C1111yescharacteristic
205C4⋊C16C22×C1112yes—
206#358C22×C1112yes—
207#358C22×C1112yes—
208#358C22×C1112yes—
209#357C22×C1112yes—
210C22⋊C16C22×C1112yes—
211#346C22×C1111yescharacteristic
212C4×C16C22×C1111yescharacteristic
213C22×C11—22no—
214C22×C11—21no—
215C22×C11—82no—
216C22×C11—81no—
217C22×C11C22×D811yescharacteristic
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—82no—
226C4×C11#53511yescharacteristic
227C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C2×#41—21no—
229C22×Q8—21no—
230#137—44no—
231#135—42no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—21no—
235C2×Q16—21no—
236C2×Q16—42no—
237C2×Q16C23×C1111yescharacteristic
238C2×Q16C23×C1111yescharacteristic
239C2×Q16C23×C1111yescharacteristic
240C2×Q16C23×C1112yes—
241C2×SD16—21no—
242C2×SD16—21no—
243C2×SD16—21no—
244C2×D8C23×C1111yescharacteristic
245C2×M16D4×C1111yescharacteristic
246C22×C8C23×C1111yescharacteristic
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250#126—42no—
251#125—21no—
252#125—42no—
253#124—21no—
254#124—21no—
255#123—42no—
256C22⋊Q8—22no—
257C22⋊Q8—42no—
258C4×Q8—22no—
259#117D4×C1111yescharacteristic
260Q32—42no—
261Q32—42no—
262Q32—42no—
263SD32—42no—
264C2×C16C23×C1112yes—
265C2×C16C23×C1112yes—
266#107C23×C1112yes—
267#106—21no—
268#103—22no—
269#103—22no—
270#97D4×C1111yescharacteristic
271#97D4×C1111yescharacteristic
272C4×C8C23×C1111yescharacteristic
273C4×C8C23×C1111yescharacteristic
274C2×C11—41no—
275C2×C11—161no—
276C2×C11#320511yescharacteristic
277C2×C11#341712yes—
278#41—42no—
279#41—42no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C2×D4×C1111yescharacteristic
292Q16—22no—
293Q16—22no—
294Q16—22no—
295Q16—22no—
296Q16—22no—
297Q16—42no—
298Q16—42no—
299Q16—42no—
300Q16—42no—
301SD16—42no—
302SD16—42no—
303SD16—42no—
304D8—22no—
305M16—22no—
306C2×C8—22no—
307C2×C8C2×D4×C1111yescharacteristic
308C2×C8C2×D4×C1111yescharacteristic
309C2×C8C2×D4×C1111yescharacteristic
310C2×C8C24×C1111yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4C11×D812yes—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4C11×D812yes—
323C42—42no—
324C42C2×D4×C1111yescharacteristic
325C42C2×D4×C1111yescharacteristic
326C16—22no—
327C16—22no—
328C11#3378911yescharacteristic, direct product factor, Sylow
329C23—41no—
330C23C2×C11×D811yescharacteristic
331Q8—41no—
332Q8—41no—
333Q8—41no—
334Q8—42no—
335Q8—41no—
336Q8—41no—
337Q8—41no—
338Q8—42no—
339Q8—82no—
340D4—41no—
341D4—41no—
342D4—82no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4C2×C11×D812yes—
353C2×C4C2×C11×D812yes—
354C2×C4C2×C11×D811yescharacteristic
355C2×C4C22×D4×C1111yescharacteristic
356C8—21no—
357C8—21no—
358C8C11×AGL(1,ℤ/8)12yes—
359C8C11×H(5,𝔽2)12yes—
360C22—22no—
361C22—21no—
362C22—82no—
363C22—81no—
364C22C22×C11×D811yescharacteristic
365C4—22no—
366C4—22no—
367C4—21no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—82no—
373C4C11×#53511yescharacteristic
374C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
375C2—41no—
376C2—161no—
377C2C11×#320511yescharacteristic
378C2C11×#341712yes—
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC2×C11×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3177C2semidirect
3. C11×#2251C2semidirect
4. C11×#2247C2semidirect
5. C11×#2245C2semidirect
6. C11×#2242C2semidirect
7. C11×#2211C2semidirect
8. C11×#2209C2semidirect
10. C11×#2188C2semidirect
11. C11×#2164C2semidirect
89. #33789C11direct (N × H)
140. #3177C2×C11semidirect
142. #2251C2×C11semidirect
143. #2247C2×C11semidirect
144. #2245C2×C11semidirect
145. #2242C2×C11semidirect
146. #2211C2×C11semidirect
147. #2209C2×C11semidirect
149. #2188C2×C11semidirect
150. #2164C2×C11semidirect
328. C11#33789direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31772
C11×#31562
C11×#22512
C11×#22472
C11×#22452
C11×#22422
C11×#22112
C11×#22092
C11×#21892
C11×#21882
C11×#21642
#3378911