Finite Group Databasebeta

← C11×#33666 #14610859

Subgroups — C11×#33666 #14610859

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3169C211yesmaximal, characteristic, complemented
2C4×C11×#135C211yesmaximal, characteristic, complemented
3C11×#2234C212yesmaximal, complemented
4C11×#2227C211yesmaximal, characteristic, complemented
5C11×#2226C211yesmaximal, characteristic, complemented
6C11×#2207C211yesmaximal, characteristic, complemented
7C11×#2206C211yesmaximal, characteristic, complemented
8C11×#2186C212yesmaximal, complemented
9C4×C11×SD32C212yesmaximal, complemented
10C4×C11×D16C212yesmaximal, complemented
11C11×#2162C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C11×#532—21no—
14C4×C11×#41—21no—
15C2×C11×SD32C2212yes—
16C2×C11×D16C2212yes—
17C11×#500C2211yescharacteristic
18C11×#493C2211yescharacteristic
19C11×#486—21no—
20C11×#466—21no—
21C11×#466C2212yes—
22C4×C11×Q16C2211yescharacteristic
23C4×C11×Q16C2211yescharacteristic
24C4×C11×SD16—21no—
25C4×C11×SD16—21no—
26C4×C11×D8—21no—
27C4×C11×D8C2212yes—
28C4×C11×D8C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C11×#427C2211yescharacteristic
31C11×#416—21no—
32C2×C4×C8×C11C2211yescharacteristic
33C11×#367C2212yes—
34C11×#366C2212yes—
35C11×C4⋊C16C2211yescharacteristic
36C11×C4⋊C16C2211yescharacteristic
37C11×#358C2212yes—
38C11×#357C2212yes—
39C11×#357C2212yes—
40C11×#357C2212yes—
41C11×C22⋊C16C2212yes—
42C4×C11×C16C2212yes—
43C2×C11×#41—21no—
44C2×C11×#41—41no—
45C11×#135—22no—
46C11×#135—22no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×D8—21no—
50C2×C11×D8C2312yes—
51C2×C11×D8C2311yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C11×C4⋊Q8—21no—
55C11×#127—21no—
56C11×#124—41no—
57C11×#121—22no—
58C11×#121—41no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—22no—
64C4×D4×C11—41no—
65C4×D4×C11—41no—
66C4×D4×C11—41no—
67C11×#117—21no—
68C11×#117—41no—
69C2×C42×C11—41no—
70C2×C42×C11D411yescharacteristic
71C11×SD32—24no—
72C11×D16—24no—
73C2×C11×C16C2312yes—
74C2×C11×C16C2312yes—
75C11×#107—21no—
76C11×#107C2312yes—
77C11×#107C2311yescharacteristic
78C11×#107C2311yescharacteristic
79C11×#106—21no—
80C11×#103—21no—
81C11×#103—21no—
82C11×#102—21no—
83C11×#102—21no—
84C11×#102—22no—
85C11×#102—22no—
86C4×C8×C11D411yescharacteristic
87C4×C8×C11D411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90#33666C1111yesmaximal, characteristic, direct product factor, Sylow
91C11×#41—24no—
92C11×#41—42no—
93C11×#41—84no—
94C2×Q8×C11—21no—
95C2×Q8×C11—41no—
96C2×D4×C11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—41no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—42no—
106C22×C4×C11D811yescharacteristic
107C22×C4×C11D811yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C11×Q16—21no—
110C11×Q16#4112yescomplemented
111C11×SD16—24no—
112C11×D8—21no—
113C11×D8—22no—
114C11×D8—22no—
115C11×D8—42no—
116C11×D8#4112yescomplemented
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—41no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—42no—
134C11×C22⋊C4—42no—
135C42×C11—41no—
136C42×C11—41no—
137C42×C11—41no—
138C42×C11D811yescharacteristic
139C42×C11D811yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C11×C16—22no—
143C11×C16—22no—
144#3169C2×C1111yescharacteristic, complemented
145C4×#135C2×C1111yescharacteristic, complemented
146#2234C2×C1112yescomplemented
147#2227C2×C1111yescharacteristic, complemented
148#2226C2×C1111yescharacteristic, complemented
149#2207C2×C1111yescharacteristic, complemented
150#2206C2×C1111yescharacteristic, complemented
151#2186C2×C1112yescomplemented
152C4×SD32C2×C1112yescomplemented
153C4×D16C2×C1112yescomplemented
154#2162C2×C1111yescharacteristic, complemented
155C23×C11—41no—
156C23×C11—42no—
157C23×C11C2×D811yescharacteristic
158Q8×C11—22no—
159Q8×C11—41no—
160Q8×C11—82no—
161D4×C11—22no—
162D4×C11—44no—
163D4×C11—42no—
164D4×C11—41no—
165D4×C11—42no—
166D4×C11—82no—
167D4×C11—84no—
168D4×C11—82no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—44no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11—84no—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C8×C11—21no—
188C8×C11—21no—
189C8×C11—21no—
190C8×C11C2×#4111yescharacteristic
191C8×C11C2×#4111yescharacteristic
192C2×#135C22×C1111yescharacteristic
193#532—21no—
194C4×#41—21no—
195C2×SD32C22×C1112yes—
196C2×D16C22×C1112yes—
197#500C22×C1111yescharacteristic
198#493C22×C1111yescharacteristic
199#486—21no—
200#466—21no—
201#466C22×C1112yes—
202C4×Q16C22×C1111yescharacteristic
203C4×Q16C22×C1111yescharacteristic
204C4×SD16—21no—
205C4×SD16—21no—
206C4×D8—21no—
207C4×D8C22×C1112yes—
208C4×D8C22×C1111yescharacteristic
209C4×D8C22×C1111yescharacteristic
210#427C22×C1111yescharacteristic
211#416—21no—
212C2×C4×C8C22×C1111yescharacteristic
213#367C22×C1112yes—
214#366C22×C1112yes—
215C4⋊C16C22×C1111yescharacteristic
216C4⋊C16C22×C1111yescharacteristic
217#358C22×C1112yes—
218#357C22×C1112yes—
219#357C22×C1112yes—
220#357C22×C1112yes—
221C22⋊C16C22×C1112yes—
222C4×C16C22×C1112yes—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—42no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11C22×D811yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—42no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—82no—
240C4×C11#50812yes—
241C4×C11#50912yes—
242C4×C11#52511yescharacteristic
243C4×C11#57511yescharacteristic
244C2×#41—21no—
245C2×#41—41no—
246#135—22no—
247#135—22no—
248C2×Q16C23×C1111yescharacteristic
249C2×SD16—21no—
250C2×D8—21no—
251C2×D8C23×C1112yes—
252C2×D8C23×C1111yescharacteristic
253C22×C8D4×C1111yescharacteristic
254C22×C8C23×C1111yescharacteristic
255C4⋊Q8—21no—
256#127—21no—
257#124—41no—
258#121—22no—
259#121—41no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—22no—
265C4×D4—41no—
266C4×D4—41no—
267C4×D4—41no—
268#117—21no—
269#117—41no—
270C2×C42—41no—
271C2×C42D4×C1111yescharacteristic
272SD32—24no—
273D16—24no—
274C2×C16C23×C1112yes—
275C2×C16C23×C1112yes—
276#107—21no—
277#107C23×C1111yescharacteristic
278#107C23×C1111yescharacteristic
279#107C23×C1112yes—
280#106—21no—
281#103—21no—
282#103—21no—
283#102—21no—
284#102—21no—
285#102—22no—
286#102—22no—
287C4×C8D4×C1111yescharacteristic
288C4×C8D4×C1111yescharacteristic
289C4×C8C23×C1111yescharacteristic
290C4×C8C23×C1111yescharacteristic
291C2×C11—41no—
292C2×C11—82no—
293C2×C11—162no—
294C2×C11#310011yescharacteristic
295C2×C11C2×#50811yescharacteristic
296C2×C11C2×#50911yescharacteristic
297#41—24no—
298#41—42no—
299#41—84no—
300C2×Q8—21no—
301C2×Q8—41no—
302C2×D4—21no—
303C2×D4—22no—
304C2×D4—41no—
305C2×D4—42no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4C11×D811yescharacteristic
313C22×C4C11×D811yescharacteristic
314C22×C4C2×D4×C1111yescharacteristic
315Q16—21no—
316Q16C11×#4112yescomplemented
317SD16—24no—
318D8—21no—
319D8—22no—
320D8—22no—
321D8—42no—
322D8C11×#4112yescomplemented
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8C2×D4×C1111yescharacteristic
327C2×C8C2×D4×C1111yescharacteristic
328C2×C8C2×D4×C1111yescharacteristic
329C2×C8C24×C1111yescharacteristic
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C42—41no—
342C42—41no—
343C42—41no—
344C42C11×D811yescharacteristic
345C42C11×D811yescharacteristic
346C42C2×D4×C1111yescharacteristic
347C42C2×D4×C1111yescharacteristic
348C16—22no—
349C16—22no—
350C11#3366611yescharacteristic, direct product factor, Sylow
351C23—41no—
352C23—42no—
353C23C2×C11×D811yescharacteristic
354Q8—22no—
355Q8—41no—
356Q8—82no—
357D4—22no—
358D4—44no—
359D4—42no—
360D4—41no—
361D4—42no—
362D4—82no—
363D4—84no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—44no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—84no—
377C2×C4C2×C11×D811yescharacteristic
378C2×C4C2×C11×D811yescharacteristic
379C2×C4C2×C11×D811yescharacteristic
380C2×C4C2×C11×D811yescharacteristic
381C2×C4C2×C11×D811yescharacteristic
382C2×C4C22×D4×C1111yescharacteristic
383C8—21no—
384C8—21no—
385C8—21no—
386C8C2×C11×#4111yescharacteristic
387C8C2×C11×#4111yescharacteristic
388C22—21no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—81no—
393C22—81no—
394C22—82no—
395C22—82no—
396C22—82no—
397C22C22×C11×D811yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—42no—
402C4—81no—
403C4—82no—
404C4—81no—
405C4C11×#50812yes—
406C4C11×#50912yes—
407C4C11×#52511yescharacteristic
408C4C11×#57511yescharacteristic
409C2—41no—
410C2—82no—
411C2—162no—
412C2C11×#310011yescharacteristic
413C2C2×C11×#50811yescharacteristic
414C2C2×C11×#50911yescharacteristic
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. C4×C11×#135C2semidirect
3. C11×#2234C2semidirect
4. C11×#2227C2semidirect
5. C11×#2226C2semidirect
6. C11×#2207C2semidirect
7. C11×#2206C2semidirect
8. C11×#2186C2semidirect
9. C4×C11×SD32C2semidirect
10. C4×C11×D16C2semidirect
11. C11×#2162C2semidirect
90. #33666C11direct (N × H)
110. C11×Q16#41semidirect
116. C11×D8#41semidirect
144. #3169C2×C11semidirect
145. C4×#135C2×C11semidirect
146. #2234C2×C11semidirect
147. #2227C2×C11semidirect
148. #2226C2×C11semidirect
149. #2207C2×C11semidirect
150. #2206C2×C11semidirect
151. #2186C2×C11semidirect
152. C4×SD32C2×C11semidirect
153. C4×D16C2×C11semidirect
154. #2162C2×C11semidirect
316. Q16C11×#41semidirect
322. D8C11×#41semidirect
350. C11#33666direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31692
C4×C11×#1352
C11×#22342
C11×#22272
C11×#22262
C11×#22072
C11×#22062
C11×#21862
C4×C11×SD322
C4×C11×D162
C11×#21622
#3366611