Finite Group Databasebeta

← C11×#18375 #14595568

Subgroups — C11×#18375 #14595568

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#3236C211yesmaximal, characteristic, complemented
3C11×#3234C211yesmaximal, characteristic, complemented
4C11×#2633C211yesmaximal, characteristic, complemented
5C11×#1618C214yesmaximal, complemented
6C11×#1612C214yesmaximal, complemented
7C11×#1515C211yesmaximal, characteristic, complemented
8C11×#1514C211yesmaximal, characteristic, complemented
9C11×#1466C211yesmaximal, characteristic, complemented
10C11×#559—22no—
11C11×#556—21no—
12C11×#555—21no—
13C11×#553—22no—
14C11×#550—21no—
15C11×#547—21no—
16C11×#538C2214yes—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C11×#525—22no—
22C11×#520—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C11×#501—21no—
25C11×#501—21no—
26C11×#491—21no—
27C11×#490—21no—
28C11×#484C2212yes—
29C11×#483C2212yes—
30C11×#481C2212yes—
31C11×#480C2212yes—
32C11×#479—22no—
33C11×#478—22no—
34C11×#432C2211yescharacteristic
35C11×#432C2211yescharacteristic
36C11×#399C2212yes—
37C11×#398—21no—
38C11×#397C2212yes—
39C11×#394—21no—
40C11×#385—22no—
41C11×#383C2211yescharacteristic
42C11×#328C2214yes—
43C11×#327C2214yes—
44C11×#323C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11D412yes—
49C11×C4⋊Q8D411yescharacteristic
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×#127—22no—
53C11×#127D411yescharacteristic
54C11×#126—24no—
55C11×#125—21no—
56C11×#125—21no—
57C11×#125—21no—
58C11×#125—21no—
59C11×#125—21no—
60C11×#124—22no—
61C11×#124—24no—
62C11×#124—21no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8C2312yes—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—22no—
71C11×#121—24no—
72C11×#121—21no—
73C11×#121C2312yes—
74C11×#120—24no—
75C4×Q8×C11—22no—
76C4×Q8×C11—21no—
77C4×Q8×C11D412yes—
78C4×D4×C11—22no—
79C4×D4×C11—24no—
80C4×D4×C11—24no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11D412yes—
87C11×#117—22no—
88C11×#117—22no—
89C11×#117—21no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4C2312yes—
100C2×C42×C11C2311yescharacteristic
101C11×#107—22no—
102C11×#107—22no—
103C11×#106—22no—
104C11×#106—22no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×C22⋊C8C2312yes—
112C11×C22⋊C8C2312yes—
113C11×#97—21no—
114C11×#97—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—22no—
118C11×#95C2312yes—
119#18375C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11C2×D412yes—
121C11×#41—44no—
122C11×#41—84no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—22no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—42no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—82no—
167C11×C4⋊C4C2×D412yes—
168C11×C4⋊C4C2×D412yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—44no—
178C11×C22⋊C4—82no—
179C42×C11—24no—
180C42×C11—22no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185#3506C2×C1111yescharacteristic
186#3236C2×C1111yescharacteristic, complemented
187#3234C2×C1111yescharacteristic, complemented
188#2633C2×C1111yescharacteristic, complemented
189#1618C2×C1114yescomplemented
190#1612C2×C1114yescomplemented
191#1515C2×C1111yescharacteristic, complemented
192#1514C2×C1111yescharacteristic, complemented
193#1466C2×C1111yescharacteristic, complemented
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11C22×D411yescharacteristic
201Q8×C11—42no—
202Q8×C11—42no—
203Q8×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—44no—
210D4×C11—84no—
211D4×C11—84no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—82no—
231C2×C4×C11—84no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C8×C11—42no—
239C8×C11—42no—
240#559—22no—
241#556—21no—
242#555—21no—
243#553—22no—
244#550—21no—
245#547—21no—
246#538C22×C1114yes—
247#535—21no—
248#533C22×C1111yescharacteristic
249#532C22×C1111yescharacteristic
250C2×#125C22×C1111yescharacteristic
251#525—22no—
252#520—21no—
253C2×C4×D4C22×C1111yescharacteristic
254#501—21no—
255#501—21no—
256#491—21no—
257#490—21no—
258#484C22×C1112yes—
259#483C22×C1112yes—
260#481C22×C1112yes—
261#480C22×C1112yes—
262#479—22no—
263#478—22no—
264#432C22×C1111yescharacteristic
265#432C22×C1111yescharacteristic
266#399C22×C1112yes—
267#398—21no—
268#397C22×C1112yes—
269#394—21no—
270#385—22no—
271#383C22×C1111yescharacteristic
272#328C22×C1114yes—
273#327C22×C1114yes—
274#323C22×C1114yes—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—44no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—82no—
285C22×C11C2×#12011yescharacteristic
286C22×C11#57512yes—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11—82no—
298C4×C11—81no—
299C4×C11—81no—
300C2×#41—22no—
301C2×#41—21no—
302C22×D4D4×C1111yescharacteristic
303C23×C4D4×C1112yes—
304C4⋊Q8D4×C1111yescharacteristic
305C4⋊Q8D4×C1111yescharacteristic
306C4⋊Q8D4×C1111yescharacteristic
307#127—22no—
308#127D4×C1111yescharacteristic
309#126—24no—
310#125—21no—
311#125—21no—
312#125—21no—
313#125—21no—
314#125—21no—
315#124—22no—
316#124—24no—
317#124—21no—
318#123—24no—
319#123—24no—
320C22⋊Q8—22no—
321C22⋊Q8—21no—
322C22⋊Q8C23×C1112yes—
323#121—22no—
324#121—22no—
325#121—22no—
326#121—24no—
327#121—21no—
328#121C23×C1112yes—
329#120—24no—
330C4×Q8—22no—
331C4×Q8—21no—
332C4×Q8D4×C1112yes—
333C4×D4—22no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4D4×C1112yes—
342#117—22no—
343#117—22no—
344#117—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4D4×C1111yescharacteristic
350C2×C4⋊C4C23×C1111yescharacteristic
351C2×C4⋊C4C23×C1111yescharacteristic
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4C23×C1112yes—
355C2×C42C23×C1111yescharacteristic
356#107—22no—
357#107—22no—
358#106—22no—
359#106—22no—
360C4⋊C8—21no—
361C4⋊C8—21no—
362#103—22no—
363#103—22no—
364#102—22no—
365#102—22no—
366C22⋊C8C23×C1112yes—
367C22⋊C8C23×C1112yes—
368#97—21no—
369#97—21no—
370#95—21no—
371#95—21no—
372#95—22no—
373#95C23×C1112yes—
374C2×C11—22no—
375C2×C11—82no—
376C2×C11—82no—
377C2×C11#300511yescharacteristic
378C2×C11#301911yescharacteristic
379C2×C11#302811yescharacteristic
380C24C2×D4×C1112yes—
381#41—44no—
382#41—84no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8C2×D4×C1112yes—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—42no—
394C2×D4C2×D4×C1112yes—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—82no—
403C22×C4C2×D4×C1111yescharacteristic
404C22×C4C2×D4×C1112yes—
405C22×C4C2×D4×C1111yescharacteristic
406C22×C4C24×C1111yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C4⋊C4—24no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—82no—
427C4⋊C4C2×D4×C1112yes—
428C4⋊C4C2×D4×C1112yes—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—44no—
438C22⋊C4—82no—
439C42—24no—
440C42—22no—
441C42C2×D4×C1111yescharacteristic
442C42C2×D4×C1111yescharacteristic
443C42C2×D4×C1111yescharacteristic
444C42C2×D4×C1111yescharacteristic
445C11#1837511yescharacteristic, direct product factor, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—42no—
451C23—42no—
452C23C22×D4×C1111yescharacteristic
453Q8—42no—
454Q8—42no—
455Q8—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—44no—
462D4—84no—
463D4—84no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—82no—
483C2×C4—84no—
484C2×C4C11×#12011yescharacteristic
485C2×C4C11×#12011yescharacteristic
486C2×C4C11×#12011yescharacteristic
487C2×C4C11×#12011yescharacteristic
488C2×C4C22×D4×C1111yescharacteristic
489C2×C4C22×D4×C1111yescharacteristic
490C8—42no—
491C8—42no—
492C22—21no—
493C22—21no—
494C22—44no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—82no—
502C22C2×C11×#12011yescharacteristic
503C22C11×#57512yes—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—82no—
515C4—81no—
516C4—81no—
517C2—22no—
518C2—82no—
519C2—82no—
520C2C11×#300511yescharacteristic
521C2C11×#301911yescharacteristic
522C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3506C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3236C2semidirect
3. C11×#3234C2semidirect
4. C11×#2633C2semidirect
5. C11×#1618C2semidirect
6. C11×#1612C2semidirect
7. C11×#1515C2semidirect
8. C11×#1514C2semidirect
9. C11×#1466C2semidirect
119. #18375C11direct (N × H)
186. #3236C2×C11semidirect
187. #3234C2×C11semidirect
188. #2633C2×C11semidirect
189. #1618C2×C11semidirect
190. #1612C2×C11semidirect
191. #1515C2×C11semidirect
192. #1514C2×C11semidirect
193. #1466C2×C11semidirect
445. C11#18375direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#32362
C11×#32342
C11×#26332
C11×#16182
C11×#16122
C11×#15152
C11×#15142
C11×#14662
#1837511