Finite Group Databasebeta

← C11×#61935 #14639128

Subgroups — C11×#61935 #14639128

Order 2816.

1746 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic, complemented
2C11×#3509C211yesmaximal, characteristic, complemented
3C11×#3397C214yesmaximal, complemented
4C11×#3392C214yesmaximal, complemented
5C11×#3372C214yesmaximal, complemented
6C11×#3360C214yesmaximal, complemented
7C11×#3221C214yesmaximal, complemented
8C11×#3206C212yesmaximal, complemented
9C11×#3126C214yesmaximal, complemented
10C11×#3106C212yesmaximal, complemented
11C11×#2986C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#557C2214yes—
14C11×#556C2214yes—
15C11×#554C2214yes—
16C11×#552—24no—
17C11×#550C2214yes—
18C11×#547—22no—
19C11×#541—22no—
20C11×#540C2214yes—
21C11×#537—24no—
22C11×#536C2212yes—
23C11×#533—22no—
24C11×#533C2211yescharacteristic
25C11×#532C2212yes—
26C2×C11×C4⋊Q8C2211yescharacteristic
27C11×#519C2212yes—
28C4×C11×#41C2211yescharacteristic
29C11×#496C2214yes—
30C11×#492C2214yes—
31C11×#492C2214yes—
32C11×#491C2214yes—
33C11×#488C2214yes—
34C11×#487C2214yes—
35C11×#482C2214yes—
36C11×#479C2218yes—
37C11×#477C2212yes—
38C11×#476C2212yes—
39C11×#463C2218yes—
40C11×#461C2214yes—
41C11×#461C2214yes—
42C11×#461C2218yes—
43C11×#460C2212yes—
44C11×#460C2218yes—
45C11×#459C2212yes—
46C11×#449C2214yes—
47C11×#448C2218yes—
48C11×#446C2214yes—
49C8×Q8×C11C2214yes—
50C11×#440C2218yes—
51C4×C11×SD16C2218yes—
52C4×C11×SD16C2214yes—
53C4×C11×D8C2214yes—
54C11×#433C2214yes—
55C11×#431C2212yes—
56C2×C11×#41—24no—
57C2×C11×#41—22no—
58C2×C11×#41C2311yescharacteristic
59C22×Q8×C11C2312yes—
60C2×C11×SD16C2318yes—
61C2×C11×SD16C2314yes—
62C2×C11×SD16C2318yes—
63C2×C11×D8C2314yes—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8D412yes—
67C11×C4⋊Q8C2314yes—
68C11×C4⋊Q8C2314yes—
69C11×C4⋊Q8C2312yes—
70C11×#127C2312yes—
71C11×#127C2314yes—
72C11×#126—28no—
73C11×#125—24no—
74C11×#125—28no—
75C11×#125D412yes—
76C11×#125C2314yes—
77C11×#124—22no—
78C11×#124C2314yes—
79C11×#123—28no—
80C11×#123—24no—
81C11×C22⋊Q8—24no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8D414yes—
86C11×#121—22no—
87C11×#121—24no—
88C11×#121—28no—
89C11×#121—28no—
90C11×#121C2314yes—
91C4×Q8×C11—24no—
92C4×Q8×C11—24no—
93C4×Q8×C11C2312yes—
94C4×Q8×C11C2318yes—
95C4×Q8×C11C2314yes—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11C2312yes—
99C4×D4×C11C2314yes—
100C4×D4×C11C2318yes—
101C11×#117—24no—
102C11×#117—24no—
103C11×#117—21no—
104C11×#117C2311yescharacteristic
105C11×#117C2312yes—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—24no—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110C11×#107C2314yes—
111C11×#106C2314yes—
112C11×C4⋊C8C2312yes—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2318yes—
115C11×#103C2314yes—
116C11×#103C2318yes—
117C11×#103C2318yes—
118C11×#102C2314yes—
119C11×#102C2314yes—
120C11×#102C2314yes—
121C11×C22⋊C8C2314yes—
122C11×#97C2314yes—
123C4×C8×C11C2314yes—
124C4×C8×C11C2314yes—
125#61935C1111yesmaximal, characteristic, direct product factor, Sylow
126C11×#41—42no—
127C11×#41—84no—
128C11×#41—88no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—44no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2414yes—
134C2×Q8×C11C2411yescharacteristic
135C2×D4×C11—21no—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—28no—
139C2×D4×C11—22no—
140C2×D4×C11C2411yescharacteristic
141C2×D4×C11C2414yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—28no—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2411yescharacteristic
149C11×SD16—48no—
150C11×SD16—48no—
151C11×SD16—44no—
152C11×D8—44no—
153C2×C8×C11C2414yes—
154C2×C8×C11C2414yes—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4C2×D414yes—
163C11×C4⋊C4C2×D414yes—
164C11×C4⋊C4C2×D418yes—
165C11×C4⋊C4C2412yes—
166C11×C4⋊C4C2414yes—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4C2×D414yes—
174C42×C11—21no—
175C42×C11—22no—
176C42×C11—28no—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2412yes—
180C42×C11C2414yes—
181#3548C2×C1111yescharacteristic, complemented
182#3509C2×C1111yescharacteristic, complemented
183#3397C2×C1114yescomplemented
184#3392C2×C1114yescomplemented
185#3372C2×C1114yescomplemented
186#3360C2×C1114yescomplemented
187#3221C2×C1114yescomplemented
188#3206C2×C1112yescomplemented
189#3126C2×C1114yescomplemented
190#3106C2×C1112yescomplemented
191#2986C2×C1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11—24no—
194C23×C11C22×D411yescharacteristic
195Q8×C11—28no—
196Q8×C11—28no—
197Q8×C11—22no—
198Q8×C11—44no—
199Q8×C11—82no—
200D4×C11—22no—
201D4×C11—24no—
202D4×C11—24no—
203D4×C11—42no—
204D4×C11—44no—
205D4×C11—82no—
206D4×C11—88no—
207D4×C11—84no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—48no—
218C2×C4×C11—88no—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D418yes—
221C2×C4×C11C22×D412yes—
222C2×C4×C11C22×D412yes—
223C2×C4×C11C2511yescharacteristic
224C8×C11—24no—
225C8×C11—24no—
226#562—22no—
227#557C22×C1114yes—
228#556C22×C1114yes—
229#554C22×C1114yes—
230#552—24no—
231#550C22×C1114yes—
232#547—22no—
233#541—22no—
234#540C22×C1114yes—
235#537—24no—
236#536C22×C1112yes—
237#533—22no—
238#533C22×C1111yescharacteristic
239#532C22×C1112yes—
240C2×C4⋊Q8C22×C1111yescharacteristic
241#519C22×C1112yes—
242C4×#41C22×C1111yescharacteristic
243#496C22×C1114yes—
244#492C22×C1114yes—
245#492C22×C1114yes—
246#491C22×C1114yes—
247#488C22×C1114yes—
248#487C22×C1114yes—
249#482C22×C1114yes—
250#479C22×C1118yes—
251#477C22×C1112yes—
252#476C22×C1112yes—
253#463C22×C1118yes—
254#461C22×C1114yes—
255#461C22×C1118yes—
256#461C22×C1114yes—
257#460C22×C1112yes—
258#460C22×C1118yes—
259#459C22×C1112yes—
260#449C22×C1114yes—
261#448C22×C1118yes—
262#446C22×C1114yes—
263C8×Q8C22×C1114yes—
264#440C22×C1118yes—
265C4×SD16C22×C1118yes—
266C4×SD16C22×C1114yes—
267C4×D8C22×C1114yes—
268#433C22×C1114yes—
269#431C22×C1112yes—
270C22×C11—21no—
271C22×C11—22no—
272C22×C11—41no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—44no—
277C22×C11C23×D411yescharacteristic
278C4×C11—21no—
279C4×C11—22no—
280C4×C11—28no—
281C4×C11—41no—
282C4×C11—44no—
283C4×C11—42no—
284C4×C11—44no—
285C4×C11#57714yes—
286C4×C11#58512yes—
287C2×#41—24no—
288C2×#41—22no—
289C2×#41C23×C1111yescharacteristic
290C22×Q8C23×C1112yes—
291C2×SD16C23×C1118yes—
292C2×SD16C23×C1114yes—
293C2×SD16C23×C1118yes—
294C2×D8C23×C1114yes—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8D4×C1112yes—
298C4⋊Q8C23×C1114yes—
299C4⋊Q8C23×C1114yes—
300C4⋊Q8C23×C1112yes—
301#127C23×C1112yes—
302#127C23×C1114yes—
303#126—28no—
304#125—24no—
305#125—28no—
306#125D4×C1112yes—
307#125C23×C1114yes—
308#124—22no—
309#124C23×C1114yes—
310#123—28no—
311#123—24no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—28no—
316C22⋊Q8D4×C1114yes—
317#121—22no—
318#121—24no—
319#121—28no—
320#121—28no—
321#121C23×C1114yes—
322C4×Q8—24no—
323C4×Q8—24no—
324C4×Q8C23×C1112yes—
325C4×Q8C23×C1118yes—
326C4×Q8C23×C1114yes—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4C23×C1112yes—
330C4×D4C23×C1114yes—
331C4×D4C23×C1118yes—
332#117—24no—
333#117—24no—
334#117—21no—
335#117C23×C1111yescharacteristic
336#117C23×C1112yes—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C42—21no—
340C2×C42C23×C1111yescharacteristic
341#107C23×C1114yes—
342#106C23×C1114yes—
343C4⋊C8C23×C1112yes—
344C4⋊C8C23×C1112yes—
345C4⋊C8C23×C1118yes—
346#103C23×C1118yes—
347#103C23×C1114yes—
348#103C23×C1118yes—
349#102C23×C1114yes—
350#102C23×C1114yes—
351#102C23×C1114yes—
352C22⋊C8C23×C1114yes—
353#97C23×C1114yes—
354C4×C8C23×C1114yes—
355C4×C8C23×C1114yes—
356C2×C11—41no—
357C2×C11—81no—
358C2×C11—84no—
359C2×C11#348711yescharacteristic
360C2×C11C2×#57712yes—
361#41—42no—
362#41—84no—
363#41—88no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—44no—
367C2×Q8C2×D4×C1114yes—
368C2×Q8C24×C1114yes—
369C2×Q8C24×C1111yescharacteristic
370C2×D4—21no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—28no—
374C2×D4—22no—
375C2×D4C24×C1111yescharacteristic
376C2×D4C24×C1114yes—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—24no—
381C22×C4—28no—
382C22×C4C2×D4×C1112yes—
383C22×C4C24×C1111yescharacteristic
384SD16—48no—
385SD16—48no—
386SD16—44no—
387D8—44no—
388C2×C8C24×C1114yes—
389C2×C8C24×C1114yes—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—28no—
393C4⋊C4—24no—
394C4⋊C4—22no—
395C4⋊C4—28no—
396C4⋊C4—28no—
397C4⋊C4C2×D4×C1114yes—
398C4⋊C4C2×D4×C1114yes—
399C4⋊C4C2×D4×C1118yes—
400C4⋊C4C24×C1112yes—
401C4⋊C4C24×C1114yes—
402C22⋊C4—21no—
403C22⋊C4—22no—
404C22⋊C4—28no—
405C22⋊C4—24no—
406C22⋊C4—28no—
407C22⋊C4—24no—
408C22⋊C4C2×D4×C1114yes—
409C42—21no—
410C42—22no—
411C42—28no—
412C42C2×D4×C1111yescharacteristic
413C42C2×D4×C1111yescharacteristic
414C42C24×C1112yes—
415C42C24×C1114yes—
416C11#6193511yescharacteristic, direct product factor, Sylow
417C23—21no—
418C23—24no—
419C23C22×D4×C1111yescharacteristic
420Q8—28no—
421Q8—28no—
422Q8—22no—
423Q8—44no—
424Q8—82no—
425D4—22no—
426D4—24no—
427D4—24no—
428D4—42no—
429D4—44no—
430D4—82no—
431D4—88no—
432D4—84no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—21no—
438C2×C4—24no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—48no—
443C2×C4—88no—
444C2×C4C22×D4×C1111yescharacteristic
445C2×C4C22×D4×C1118yes—
446C2×C4C22×D4×C1112yes—
447C2×C4C22×D4×C1112yes—
448C2×C4C25×C1111yescharacteristic
449C8—24no—
450C8—24no—
451C22—21no—
452C22—22no—
453C22—41no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—44no—
458C22C23×D4×C1111yescharacteristic
459C4—21no—
460C4—22no—
461C4—28no—
462C4—41no—
463C4—44no—
464C4—44no—
465C4—42no—
466C4C11×#57714yes—
467C4C11×#58512yes—
468C2—41no—
469C2—81no—
470C2—84no—
471C2C11×#348711yescharacteristic
472C2C2×C11×#57712yes—
subgroupG/H
center, socleC22×C11C23×D4
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3548C2semidirect
2. C11×#3509C2semidirect
3. C11×#3397C2semidirect
4. C11×#3392C2semidirect
5. C11×#3372C2semidirect
6. C11×#3360C2semidirect
7. C11×#3221C2semidirect
8. C11×#3206C2semidirect
9. C11×#3126C2semidirect
10. C11×#3106C2semidirect
11. C11×#2986C2semidirect
125. #61935C11direct (N × H)
181. #3548C2×C11semidirect
182. #3509C2×C11semidirect
183. #3397C2×C11semidirect
184. #3392C2×C11semidirect
185. #3372C2×C11semidirect
186. #3360C2×C11semidirect
187. #3221C2×C11semidirect
188. #3206C2×C11semidirect
189. #3126C2×C11semidirect
190. #3106C2×C11semidirect
191. #2986C2×C11semidirect
416. C11#61935direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#35092
C11×#33972
C11×#33922
C11×#33722
C11×#33602
C11×#32212
C11×#32062
C11×#31262
C11×#31062
C11×#29862
#6193511