Finite Group Databasebeta

← C11×#10008 #14587201

Subgroups — C11×#10008 #14587201

Order 2816.

654 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3215C211yesmaximal, characteristic, complemented
2C11×#3110C211yesmaximal, characteristic, complemented
3C11×#2540C211yesmaximal, characteristic
4C11×#1986C211yesmaximal, characteristic, complemented
5C11×#1527C211yesmaximal, characteristic, complemented
6C11×#1490C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C2×C11×C22⋊Q8—21no—
11C2×C11×#121—21no—
12C2×C4×D4×C11C2211yescharacteristic
13C11×#497—21no—
14C11×#489—21no—
15C11×#484—21no—
16C11×#474—21no—
17C11×#464—22no—
18C11×#461—21no—
19C11×#451—21no—
20C11×#450—21no—
21C11×#450—21no—
22C11×#440—22no—
23C11×#432C2211yescharacteristic
24C11×#432C2211yescharacteristic
25C4×C11×M16C2211yescharacteristic
26C11×#399—21no—
27C11×#392—21no—
28C11×#390—22no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C11×#339—22no—
31C11×#329—22no—
32C11×D4⋊C8—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11D411yescharacteristic
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C2×C11×Q16—22no—
39C2×C11×SD16—22no—
40C2×C11×SD16—22no—
41C2×C11×M16—21no—
42C11×C4⋊Q8D411yescharacteristic, complemented
43C11×C4⋊Q8D411yescharacteristic, complemented
44C11×#125—21no—
45C11×#124—21no—
46C11×#124—21no—
47C11×#124—21no—
48C11×#124—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—44no—
52C11×#121—44no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11—21no—
59C11×#117—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C42×C11D412yes—
69C2×C42×C11C2311yescharacteristic
70C11×#107—22no—
71C11×C4⋊C8—21no—
72C11×C4⋊C8D412yescomplemented
73C11×#103—22no—
74C11×#103—22no—
75C11×#102—22no—
76C11×#102—22no—
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×#97—21no—
80C11×#97—21no—
81C11×#97D412yescomplemented
82C4×C8×C11—21no—
83C11×#95—21no—
84#10008C1111yesmaximal, characteristic, direct product factor, Sylow
85C24×C11—21no—
86C24×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—42no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—42no—
97C2×D4×C11—44no—
98C2×D4×C11—42no—
99C2×D4×C11—44no—
100C2×D4×C11—82no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C11×Q16—82no—
112C11×SD16—44no—
113C11×SD16—82no—
114C11×M16—22no—
115C11×M16—41no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—41no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—44no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C22⋊C4—44no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11—42no—
139C42×C11—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144#3215C2×C1111yescharacteristic, complemented
145#3110C2×C1111yescharacteristic, complemented
146#2540C2×C1111yescharacteristic
147#1986C2×C1111yescharacteristic, complemented
148#1527C2×C1111yescharacteristic, complemented
149#1490C2×C1111yescharacteristic, complemented
150#1285C2×C1111yescharacteristic, complemented
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11#12011yescharacteristic
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—42no—
167Q8×C11—81no—
168D4×C11—22no—
169D4×C11—22no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—42no—
173D4×C11—81no—
174D4×C11—88no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12711yescharacteristic
197C8×C11—42no—
198C8×C11—42no—
199C8×C11—42no—
200#533C22×C1111yescharacteristic
201C2×#124C22×C1111yescharacteristic
202C2×C22⋊Q8—21no—
203C2×#121—21no—
204C2×C4×D4C22×C1111yescharacteristic
205#497—21no—
206#489—21no—
207#484—21no—
208#474—21no—
209#464—22no—
210#461—21no—
211#451—21no—
212#450—21no—
213#450—21no—
214#440—22no—
215#432C22×C1111yescharacteristic
216#432C22×C1111yescharacteristic
217C4×M16C22×C1111yescharacteristic
218#399—21no—
219#392—21no—
220#390—22no—
221C4×C4⋊C4C22×C1111yescharacteristic
222#339—22no—
223#329—22no—
224D4⋊C8—22no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—82no—
233C22×C11—82no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11#39211yescharacteristic
240C22×C11#45511yescharacteristic
241C22×C11#45611yescharacteristic
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—44no—
248C4×C11—81no—
249C4×C11—81no—
250C4×C11—81no—
251C4×C11—81no—
252C4×C11#45312yes—
253C22×Q8D4×C1111yescharacteristic
254C22×D4—22no—
255C22×D4D4×C1111yescharacteristic
256C22×D4D4×C1111yescharacteristic
257C23×C4—21no—
258C2×Q16—22no—
259C2×SD16—22no—
260C2×SD16—22no—
261C2×M16—21no—
262C4⋊Q8D4×C1111yescharacteristic, complemented
263C4⋊Q8D4×C1111yescharacteristic, complemented
264#125—21no—
265#124—21no—
266#124—21no—
267#124—21no—
268#124—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—44no—
272#121—44no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279#117—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4D4×C1111yescharacteristic
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C42D4×C1112yes—
289C2×C42C23×C1111yescharacteristic
290#107—22no—
291C4⋊C8—21no—
292C4⋊C8D4×C1112yescomplemented
293#103—22no—
294#103—22no—
295#102—22no—
296#102—22no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299#97—21no—
300#97—21no—
301#97D4×C1112yescomplemented
302C4×C8—21no—
303#95—21no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—82no—
307C2×C11—161no—
308C2×C11#200211yescharacteristic
309C2×C11#200711yescharacteristic
310C2×C11#201011yescharacteristic
311C24—21no—
312C24—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8—42no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—42no—
323C2×D4—44no—
324C2×D4—42no—
325C2×D4—44no—
326C2×D4—82no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C2×D4×C1111yescharacteristic
335C22×C4C2×D4×C1111yescharacteristic
336C22×C4C2×D4×C1111yescharacteristic
337Q16—82no—
338SD16—44no—
339SD16—82no—
340M16—22no—
341M16—41no—
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—41no—
345C4⋊C4—24no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—44no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C22⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C42—42no—
365C42—41no—
366C42C2×D4×C1111yescharacteristic
367C42C2×D4×C1111yescharacteristic
368C42C2×D4×C1111yescharacteristic
369C42C11×#4111yescharacteristic
370C11#1000811yescharacteristic, direct product factor, Sylow
371C23—22no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—42no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23C11×#12011yescharacteristic
384Q8—42no—
385Q8—42no—
386Q8—42no—
387Q8—81no—
388D4—22no—
389D4—22no—
390D4—41no—
391D4—41no—
392D4—42no—
393D4—81no—
394D4—88no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4C11×#12011yescharacteristic
412C2×C4C11×#12011yescharacteristic
413C2×C4C11×#12111yescharacteristic
414C2×C4C11×#12111yescharacteristic
415C2×C4C11×#12111yescharacteristic
416C2×C4C11×#12711yescharacteristic
417C8—42no—
418C8—42no—
419C8—42no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22C11×#39211yescharacteristic
435C22C11×#45511yescharacteristic
436C22C11×#45611yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—44no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4C11×#45312yes—
448C2—21no—
449C2—21no—
450C2—82no—
451C2—161no—
452C2C11×#200211yescharacteristic
453C2C11×#200711yescharacteristic
454C2C11×#201011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#2540C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3215C2semidirect
2. C11×#3110C2semidirect
4. C11×#1986C2semidirect
5. C11×#1527C2semidirect
6. C11×#1490C2semidirect
7. C11×#1285C2semidirect
42. C11×C4⋊Q8D4semidirect
43. C11×C4⋊Q8D4semidirect
72. C11×C4⋊C8D4semidirect
81. C11×#97D4semidirect
84. #10008C11direct (N × H)
144. #3215C2×C11semidirect
145. #3110C2×C11semidirect
147. #1986C2×C11semidirect
148. #1527C2×C11semidirect
149. #1490C2×C11semidirect
150. #1285C2×C11semidirect
262. C4⋊Q8D4×C11semidirect
263. C4⋊Q8D4×C11semidirect
292. C4⋊C8D4×C11semidirect
301. #97D4×C11semidirect
370. C11#10008direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32152
C11×#31102
C11×#25402
C11×#19862
C11×#15272
C11×#14902
C11×#12852
#1000811