Finite Group Databasebeta

← C11×#34403 #14611596

Subgroups — C11×#34403 #14611596

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#533C211yesmaximal, characteristic
2C11×#2378C214yesmaximal
3C11×#2370C214yesmaximal, complemented
4C11×#2356C214yesmaximal, complemented
5C11×#2347C212yesmaximal
6C11×#2346C212yesmaximal
7C11×#2332C214yesmaximal
8C11×#2331C212yesmaximal, complemented
9C11×#2331C212yesmaximal, complemented
10C11×#2320C214yesmaximal, complemented
11C11×#2283C211yesmaximal, characteristic
12C11×#2283C211yesmaximal, characteristic
13C11×#533C4116yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125C2212yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2212yes—
21C2×C11×#117C2212yes—
22C22×C42×C11C2211yescharacteristic
23C11×#391C2218yes—
24C11×#391C2218yes—
25C11×#389C2218yes—
26C11×#389C2214yes—
27C11×#389C2214yes—
28C11×#388C2218yes—
29C11×#388C2218yes—
30C11×#387C2218yes—
31C11×#387C2218yes—
32C11×#387C2218yes—
33C11×#387C2218yes—
34C11×#383C2212yes—
35C11×#383C2212yes—
36C11×#383C2214yes—
37C11×#382C2212yes—
38C11×#382C2212yes—
39C11×#382C2214yes—
40C11×#381C2212yes—
41C11×#381C2212yes—
42C11×#380C2212yes—
43C11×#380C2212yes—
44C4×C11×C4⋊C4C2212yes—
45C4×C11×C4⋊C4C2212yes—
46C4×C11×C4⋊C4C2214yes—
47C4×C11×C4⋊C4C2214yes—
48C4×C11×C4⋊C4C2214yes—
49C4×C11×C4⋊C4C2218yes—
50C4×C11×C22⋊C4C2212yes—
51C4×C11×C22⋊C4C2211yescharacteristic
52C4×C11×C22⋊C4C2211yescharacteristic
53C11×#376C2212yes—
54C11×#376C2212yes—
55C11×#376C2214yes—
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C11×C4⋊Q8C2×C418yes—
62C11×C4⋊Q8C2×C418yes—
63C11×#125C2×C4116yes—
64C11×C22⋊Q8C2×C4116yes—
65C11×C22⋊Q8C2×C4116yes—
66C4×Q8×C11C2×C4116yes—
67C4×Q8×C11C2×C4116yes—
68C11×#117C2×C4116yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2318yes—
72C2×C11×C4⋊C4C2318yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2312yes—
81C2×C11×C22⋊C4C2312yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C42×C11C2×C418yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2314yes—
87C2×C42×C11C2318yes—
88C2×C42×C11C2318yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2314yes—
94C11×#95C2312yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11×#95C2314yes—
99C11×#95C2318yes—
100C11×#95C2312yes—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2318yes—
105C11×#95C2318yes—
106C11×#95C2318yes—
107#34403C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11C2411yescharacteristic
109C2×Q8×C11—44no—
110C2×Q8×C11—44no—
111C2×Q8×C11C22×C418yes—
112C2×Q8×C11C22×C418yes—
113C22×C4×C11—24no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C22×C414yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C414yes—
119C22×C4×C11C2414yes—
120C22×C4×C11C2414yes—
121C22×C4×C11C2418yes—
122C22×C4×C11C2411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2414yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C11×C4⋊C4—28no—
131C11×C4⋊C4—48no—
132C11×C4⋊C4—44no—
133C11×C4⋊C4—48no—
134C11×C4⋊C4C22×C418yes—
135C11×C4⋊C4C22×C418yes—
136C11×C4⋊C4C22×C4116yes—
137C11×C4⋊C4C22×C4116yes—
138C11×C4⋊C4C22×C418yes—
139C11×C4⋊C4C22×C418yes—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4C22×C4116yes—
144C42×C11—24no—
145C42×C11—24no—
146C42×C11—44no—
147C42×C11—48no—
148C42×C11—48no—
149C42×C11C22×C414yes—
150C42×C11C22×C414yes—
151C42×C11C22×C414yes—
152C42×C11C22×C414yes—
153C42×C11C22×C4116yes—
154C2×#533C2×C1111yescharacteristic
155#2378C2×C1114yes—
156#2370C2×C1114yescomplemented
157#2356C2×C1114yescomplemented
158#2347C2×C1112yes—
159#2346C2×C1112yes—
160#2332C2×C1114yes—
161#2331C2×C1112yescomplemented
162#2331C2×C1112yescomplemented
163#2320C2×C1114yescomplemented
164#2283C2×C1111yescharacteristic
165#2283C2×C1111yescharacteristic
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11C23×C412yes—
170C23×C11C2511yescharacteristic
171Q8×C11—48no—
172Q8×C11—48no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—28no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—28no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—28no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—28no—
188C2×C4×C11—28no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11C23×C412yes—
194C2×C4×C11C23×C412yes—
195C2×C4×C11C23×C412yes—
196C2×C4×C11C23×C412yes—
197C2×C4×C11C23×C412yes—
198C2×C4×C11C23×C418yes—
199C2×C4×C11C23×C418yes—
200C2×C4×C11C23×C412yes—
201C2×C4×C112−1+414yes—
202#533C4×C11116yescomplemented
203C2×C4⋊Q8C22×C1111yescharacteristic
204C2×C4⋊Q8C22×C1111yescharacteristic
205C2×#125C22×C1112yes—
206C2×C22⋊Q8C22×C1112yes—
207C2×C22⋊Q8C22×C1112yes—
208C2×C4×Q8C22×C1112yes—
209C2×C4×Q8C22×C1112yes—
210C2×#117C22×C1112yes—
211C22×C42C22×C1111yescharacteristic
212#391C22×C1118yes—
213#391C22×C1118yes—
214#389C22×C1118yes—
215#389C22×C1114yes—
216#389C22×C1114yes—
217#388C22×C1118yes—
218#388C22×C1118yes—
219#387C22×C1118yes—
220#387C22×C1118yes—
221#387C22×C1118yes—
222#387C22×C1118yes—
223#383C22×C1112yes—
224#383C22×C1114yes—
225#383C22×C1112yes—
226#382C22×C1112yes—
227#382C22×C1114yes—
228#382C22×C1112yes—
229#381C22×C1112yes—
230#381C22×C1112yes—
231#380C22×C1112yes—
232#380C22×C1112yes—
233C4×C4⋊C4C22×C1114yes—
234C4×C4⋊C4C22×C1114yes—
235C4×C4⋊C4C22×C1114yes—
236C4×C4⋊C4C22×C1118yes—
237C4×C4⋊C4C22×C1112yes—
238C4×C4⋊C4C22×C1112yes—
239C4×C22⋊C4C22×C1112yes—
240C4×C22⋊C4C22×C1111yescharacteristic
241C4×C22⋊C4C22×C1111yescharacteristic
242#376C22×C1114yes—
243#376C22×C1112yes—
244#376C22×C1112yes—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—44no—
249C22×C11C24×C411yescharacteristic
250C22×C11C2×2−1+412yes—
251C22×C11#58512yes—
252C22×C11#58512yes—
253C4×C11—22no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—28no—
259C4×C11—28no—
260C4×C11—44no—
261C4×C11—44no—
262C4×C11—48no—
263C4×C11#51914yes—
264C22×Q8C23×C1112yes—
265C22×Q8C23×C1112yes—
266C23×C4C23×C1111yescharacteristic
267C23×C4C23×C1111yescharacteristic
268C23×C4C23×C1111yescharacteristic
269C4⋊Q8C2×C4×C1118yes—
270C4⋊Q8C2×C4×C1118yes—
271#125C2×C4×C11116yes—
272C22⋊Q8C2×C4×C11116yes—
273C22⋊Q8C2×C4×C11116yes—
274C4×Q8C2×C4×C11116yes—
275C4×Q8C2×C4×C11116yes—
276#117C2×C4×C11116yes—
277C2×C4⋊C4C23×C1114yes—
278C2×C4⋊C4C23×C1114yes—
279C2×C4⋊C4C23×C1118yes—
280C2×C4⋊C4C23×C1118yes—
281C2×C4⋊C4C23×C1112yes—
282C2×C4⋊C4C23×C1112yes—
283C2×C4⋊C4C23×C1114yes—
284C2×C4⋊C4C23×C1114yes—
285C2×C4⋊C4C23×C1112yes—
286C2×C4⋊C4C23×C1112yes—
287C2×C22⋊C4C23×C1114yes—
288C2×C22⋊C4C23×C1112yes—
289C2×C22⋊C4C23×C1112yes—
290C2×C22⋊C4C23×C1114yes—
291C2×C42C2×C4×C1118yes—
292C2×C42C23×C1112yes—
293C2×C42C23×C1112yes—
294C2×C42C23×C1114yes—
295C2×C42C23×C1118yes—
296C2×C42C23×C1118yes—
297C2×C42C23×C1114yes—
298C2×C42C23×C1111yescharacteristic
299C2×C42C23×C1111yescharacteristic
300C2×C42C23×C1111yescharacteristic
301C2×C42C23×C1111yescharacteristic
302#95C23×C1112yes—
303#95C23×C1114yes—
304#95C23×C1114yes—
305#95C23×C1114yes—
306#95C23×C1114yes—
307#95C23×C1118yes—
308#95C23×C1112yes—
309#95C23×C1114yes—
310#95C23×C1114yes—
311#95C23×C1114yes—
312#95C23×C1118yes—
313#95C23×C1118yes—
314#95C23×C1118yes—
315C2×C11—42no—
316C2×C11C2×#51911yescharacteristic
317C2×C11#342811yescharacteristic
318C2×C11#342811yescharacteristic
319C2×C11#356514yes—
320C24C24×C1111yescharacteristic
321C2×Q8—44no—
322C2×Q8—44no—
323C2×Q8C22×C4×C1118yes—
324C2×Q8C22×C4×C1118yes—
325C22×C4—24no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4C22×C4×C1114yes—
329C22×C4C22×C4×C1114yes—
330C22×C4C22×C4×C1114yes—
331C22×C4C24×C1114yes—
332C22×C4C24×C1114yes—
333C22×C4C24×C1118yes—
334C22×C4C24×C1111yescharacteristic
335C22×C4C24×C1111yescharacteristic
336C22×C4C24×C1111yescharacteristic
337C22×C4C24×C1111yescharacteristic
338C22×C4C24×C1114yes—
339C22×C4C24×C1114yes—
340C22×C4C24×C1111yescharacteristic
341C22×C4C24×C1111yescharacteristic
342C4⋊C4—28no—
343C4⋊C4—48no—
344C4⋊C4—44no—
345C4⋊C4—48no—
346C4⋊C4C22×C4×C1118yes—
347C4⋊C4C22×C4×C1118yes—
348C4⋊C4C22×C4×C11116yes—
349C4⋊C4C22×C4×C11116yes—
350C4⋊C4C22×C4×C1118yes—
351C4⋊C4C22×C4×C1118yes—
352C22⋊C4—42no—
353C22⋊C4—44no—
354C22⋊C4—42no—
355C22⋊C4C22×C4×C11116yes—
356C42—24no—
357C42—24no—
358C42—44no—
359C42—48no—
360C42—48no—
361C42C22×C4×C1114yes—
362C42C22×C4×C1114yes—
363C42C22×C4×C1114yes—
364C42C22×C4×C1114yes—
365C42C22×C4×C11116yes—
366C11#3440311yescharacteristic, direct product factor, Sylow
367C23—22no—
368C23—22no—
369C23—22no—
370C23C23×C4×C1112yes—
371C23C25×C1111yescharacteristic
372Q8—48no—
373Q8—48no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—28no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—28no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—28no—
389C2×C4—28no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4C23×C4×C1112yes—
395C2×C4C23×C4×C1112yes—
396C2×C4C23×C4×C1112yes—
397C2×C4C23×C4×C1112yes—
398C2×C4C23×C4×C1112yes—
399C2×C4C23×C4×C1118yes—
400C2×C4C23×C4×C1118yes—
401C2×C4C23×C4×C1112yes—
402C2×C4C11×2−1+414yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—44no—
407C22C24×C4×C1111yescharacteristic
408C22C2×C11×2−1+412yes—
409C22C11×#58512yes—
410C22C11×#58512yes—
411C4—22no—
412C4—22no—
413C4—22no—
414C4—22no—
415C4—22no—
416C4—28no—
417C4—28no—
418C4—44no—
419C4—44no—
420C4—48no—
421C4C11×#51914yes—
422C2—42no—
423C2C2×C11×#51911yescharacteristic
424C2C11×#342811yescharacteristic
425C2C11×#342811yescharacteristic
426C2C11×#356514yes—
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC24×C11C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2370C2semidirect
4. C11×#2356C2semidirect
8. C11×#2331C2semidirect
9. C11×#2331C2semidirect
10. C11×#2320C2semidirect
13. C11×#533C4semidirect
107. #34403C11direct (N × H)
156. #2370C2×C11semidirect
157. #2356C2×C11semidirect
161. #2331C2×C11semidirect
162. #2331C2×C11semidirect
163. #2320C2×C11semidirect
202. #533C4×C11semidirect
366. C11#34403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5332
C11×#23782
C11×#23702
C11×#23562
C11×#23472
C11×#23462
C11×#23322
C11×#23312
C11×#23202
C11×#22832
#3440311