Finite Group Databasebeta

← C11×#33737 #14610930

Subgroups — C11×#33737 #14610930

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3169C211yesmaximal, characteristic, complemented
2C11×#3168C211yesmaximal, characteristic, complemented
3C11×#2255C211yesmaximal, characteristic, complemented
4C11×#2250C211yesmaximal, characteristic, complemented
5C11×#2244C211yesmaximal, characteristic, complemented
6C11×#2243C211yesmaximal, characteristic, complemented
7C11×#2220C212yesmaximal, complemented
8C11×#2218C212yesmaximal, complemented
9C4×C11×SD32C212yesmaximal, complemented
10C4×C11×D16C212yesmaximal, complemented
11C4×C11×M32C211yesmaximal, characteristic, complemented
12C11×#532—21no—
13C11×#529—21no—
14C2×C11×SD32C2212yes—
15C2×C11×D16C2212yes—
16C2×C11×M32C2212yes—
17C11×#500C2211yescharacteristic
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C11×#488—21no—
22C11×#486—21no—
23C11×#467C2211yescharacteristic
24C11×#466—21no—
25C11×#466C2211yescharacteristic
26C11×#466C2212yes—
27C11×#465—21no—
28C4×C11×Q16C2211yescharacteristic
29C4×C11×SD16—21no—
30C4×C11×D8—21no—
31C4×C11×D8C2211yescharacteristic
32C4×C11×D8C2212yes—
33C2×C4×C8×C11C2211yescharacteristic
34C11×#367C2212yes—
35C11×#366C2212yes—
36C11×#358C2212yes—
37C11×#357C2212yes—
38C11×#357C2212yes—
39C11×#357C2212yes—
40C11×#346C2211yescharacteristic
41C11×#346C2211yescharacteristic
42C4×C11×C16C2212yes—
43C2×C11×#41—41no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yes—
48C2×C11×D8C2311yescharacteristic
49C22×C8×C11D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—21no—
52C11×#127—21no—
53C11×#126—41no—
54C11×#125—21no—
55C11×#124—21no—
56C11×#124—41no—
57C11×#123—41no—
58C11×C22⋊Q8—21no—
59C11×#121—21no—
60C11×#121—22no—
61C11×#121—41no—
62C4×Q8×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—22no—
65C4×D4×C11—41no—
66C4×D4×C11—41no—
67C11×#117—41no—
68C2×C42×C11D411yescharacteristic
69C11×SD32—24no—
70C11×D16—24no—
71C11×M32—24no—
72C2×C11×C16C2312yes—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2311yescharacteristic
76C11×#107C2311yescharacteristic
77C11×#107C2312yes—
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—21no—
81C11×#102—22no—
82C11×#102—21no—
83C11×#102—22no—
84C11×#102—21no—
85C4×C8×C11D411yescharacteristic
86C4×C8×C11D411yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89#33737C1111yesmaximal, characteristic, direct product factor, Sylow
90C11×#41—84no—
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×D4×C11—21no—
94C2×D4×C11—22no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—42no—
101C22×C4×C11D811yescharacteristic
102C22×C4×C11D811yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C11×Q16—22no—
105C11×SD16—42no—
106C11×D8—22no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2411yescharacteristic
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—42no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11D811yescharacteristic
133C42×C11D811yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C11×C16—22no—
137C11×C16#4114yescomplemented
138#3169C2×C1111yescharacteristic, complemented
139#3168C2×C1111yescharacteristic, complemented
140#2255C2×C1111yescharacteristic, complemented
141#2250C2×C1111yescharacteristic, complemented
142#2244C2×C1111yescharacteristic, complemented
143#2243C2×C1111yescharacteristic, complemented
144#2220C2×C1112yescomplemented
145#2218C2×C1112yescomplemented
146C4×SD32C2×C1112yescomplemented
147C4×D16C2×C1112yescomplemented
148C4×M32C2×C1111yescharacteristic, complemented
149C23×C11—41no—
150C23×C11—42no—
151C23×C11C2×D811yescharacteristic
152Q8×C11—41no—
153Q8×C11—41no—
154Q8×C11—82no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—82no—
162D4×C11—84no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—82no—
172C2×C4×C11—84no—
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11C2×D811yescharacteristic
176C2×C4×C11C2×D811yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C8×C11—21no—
180C8×C11—21no—
181C8×C11#13512yes—
182C8×C11C2×#4112yes—
183#532—21no—
184#529—21no—
185C2×SD32C22×C1112yes—
186C2×D16C22×C1112yes—
187C2×M32C22×C1112yes—
188#500C22×C1111yescharacteristic
189#499C22×C1111yescharacteristic
190#495C22×C1111yescharacteristic
191#493C22×C1111yescharacteristic
192#488—21no—
193#486—21no—
194#467C22×C1111yescharacteristic
195#466—21no—
196#466C22×C1111yescharacteristic
197#466C22×C1112yes—
198#465—21no—
199C4×Q16C22×C1111yescharacteristic
200C4×SD16—21no—
201C4×D8—21no—
202C4×D8C22×C1111yescharacteristic
203C4×D8C22×C1112yes—
204C2×C4×C8C22×C1111yescharacteristic
205#367C22×C1112yes—
206#366C22×C1112yes—
207#358C22×C1112yes—
208#357C22×C1112yes—
209#357C22×C1112yes—
210#357C22×C1112yes—
211#346C22×C1111yescharacteristic
212#346C22×C1111yescharacteristic
213C4×C16C22×C1112yes—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—82no—
218C22×C11—81no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11C22×D811yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—82no—
230C4×C11—81no—
231C4×C11—81no—
232C4×C11#50912yes—
233C4×C11#53211yescharacteristic
234C4×C11C2×#13511yescharacteristic
235C2×#41—41no—
236C2×Q16C23×C1111yescharacteristic
237C2×SD16—21no—
238C2×D8—21no—
239C2×D8C23×C1112yes—
240C2×D8C23×C1111yescharacteristic
241C22×C8D4×C1111yescharacteristic
242C22×C8C23×C1111yescharacteristic
243C4⋊Q8—21no—
244#127—21no—
245#126—41no—
246#125—21no—
247#124—21no—
248#124—41no—
249#123—41no—
250C22⋊Q8—21no—
251#121—21no—
252#121—22no—
253#121—41no—
254C4×Q8—21no—
255C4×D4—21no—
256C4×D4—22no—
257C4×D4—41no—
258C4×D4—41no—
259#117—41no—
260C2×C42D4×C1111yescharacteristic
261SD32—24no—
262D16—24no—
263M32—24no—
264C2×C16C23×C1112yes—
265C2×C16C23×C1112yes—
266#107—21no—
267#107C23×C1111yescharacteristic
268#107C23×C1111yescharacteristic
269#107C23×C1112yes—
270#106—21no—
271#103—21no—
272#103—21no—
273#102—22no—
274#102—21no—
275#102—22no—
276#102—21no—
277C4×C8D4×C1111yescharacteristic
278C4×C8D4×C1111yescharacteristic
279C4×C8C23×C1111yescharacteristic
280C4×C8C23×C1111yescharacteristic
281C2×C11—41no—
282C2×C11—162no—
283C2×C11—161no—
284C2×C11#316911yescharacteristic
285C2×C11C2×#50911yescharacteristic
286C2×C11#341411yescharacteristic
287#41—84no—
288C2×Q8—21no—
289C2×Q8—41no—
290C2×D4—21no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C22×C4—41no—
297C22×C4—42no—
298C22×C4C11×D811yescharacteristic
299C22×C4C11×D811yescharacteristic
300C22×C4C2×D4×C1111yescharacteristic
301Q16—22no—
302SD16—42no—
303D8—22no—
304D8—22no—
305D8—22no—
306D8—42no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×D4×C1111yescharacteristic
310C2×C8C2×D4×C1111yescharacteristic
311C2×C8C2×D4×C1111yescharacteristic
312C2×C8C24×C1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—41no—
326C22⋊C4—42no—
327C22⋊C4—41no—
328C42—41no—
329C42C11×D811yescharacteristic
330C42C11×D811yescharacteristic
331C42C2×D4×C1111yescharacteristic
332C42C2×D4×C1111yescharacteristic
333C16—22no—
334C16C11×#4114yescomplemented
335C11#3373711yescharacteristic, direct product factor, Sylow
336C23—41no—
337C23—42no—
338C23C2×C11×D811yescharacteristic
339Q8—41no—
340Q8—41no—
341Q8—82no—
342D4—41no—
343D4—42no—
344D4—42no—
345D4—41no—
346D4—82no—
347D4—82no—
348D4—82no—
349D4—84no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—84no—
360C2×C4C2×C11×D811yescharacteristic
361C2×C4C2×C11×D811yescharacteristic
362C2×C4C2×C11×D811yescharacteristic
363C2×C4C2×C11×D811yescharacteristic
364C2×C4C2×C11×D811yescharacteristic
365C2×C4C22×D4×C1111yescharacteristic
366C8—21no—
367C8—21no—
368C8C11×#13512yes—
369C8C2×C11×#4112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—82no—
374C22—81no—
375C22—82no—
376C22—81no—
377C22—82no—
378C22—81no—
379C22C22×C11×D811yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4C11×#50912yes—
389C4C11×#53211yescharacteristic
390C4C2×C11×#13511yescharacteristic
391C2—41no—
392C2—162no—
393C2—161no—
394C2C11×#316911yescharacteristic
395C2C2×C11×#50911yescharacteristic
396C2C11×#341411yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D8
commutator, Frattini, cosocleC2×C8C24×C11
socleC22×C11C22×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3169C2semidirect
2. C11×#3168C2semidirect
3. C11×#2255C2semidirect
4. C11×#2250C2semidirect
5. C11×#2244C2semidirect
6. C11×#2243C2semidirect
7. C11×#2220C2semidirect
8. C11×#2218C2semidirect
9. C4×C11×SD32C2semidirect
10. C4×C11×D16C2semidirect
11. C4×C11×M32C2semidirect
89. #33737C11direct (N × H)
137. C11×C16#41semidirect
138. #3169C2×C11semidirect
139. #3168C2×C11semidirect
140. #2255C2×C11semidirect
141. #2250C2×C11semidirect
142. #2244C2×C11semidirect
143. #2243C2×C11semidirect
144. #2220C2×C11semidirect
145. #2218C2×C11semidirect
146. C4×SD32C2×C11semidirect
147. C4×D16C2×C11semidirect
148. C4×M32C2×C11semidirect
334. C16C11×#41semidirect
335. C11#33737direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31692
C11×#31682
C11×#22552
C11×#22502
C11×#22442
C11×#22432
C11×#22202
C11×#22182
C4×C11×SD322
C4×C11×D162
C4×C11×M322
#3373711