Finite Group Databasebeta

← C11×#10088 #14587281

Subgroups — C11×#10088 #14587281

Order 2816.

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

normal subgroups only

This group has 770 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×#3213C211yesmaximal, characteristic, complemented
2C11×#3151C211yesmaximal, characteristic, complemented
3C11×#2657C211yesmaximal, characteristic, complemented
4C11×#1555C211yesmaximal, characteristic, complemented
5C11×#1527C211yesmaximal, characteristic, complemented
6C11×#1505C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—22no—
9C11×#532C2211yescharacteristic
10C2×C11×#127—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C11×#124—21no—
13C2×C11×#124C2211yescharacteristic
14C11×#496—21no—
15C11×#496—22no—
16C11×#493—21no—
17C11×#492—21no—
18C11×#489—21no—
19C11×#463—22no—
20C11×#448—21no—
21C11×#447—21no—
22C11×#432C2211yescharacteristic
23C11×#432C2211yescharacteristic
24C4×C11×M16C2211yescharacteristic
25C11×#392—22no—
26C11×#392—22no—
27C11×#376C2211yescharacteristic
28C11×#331—22no—
29C11×#329—22no—
30C11×#327—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11—24no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11D411yescharacteristic
37C22×D4×C11D412yes—
38C11×AGL(1,ℤ/8)—48no—
39C2×C11×SD16—24no—
40C2×C11×SD16—22no—
41C2×C11×D8—24no—
42C2×C11×D8—22no—
43C2×C11×M16—21no—
44C11×C4⋊Q8D411yescharacteristic, complemented
45C11×#127—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—44no—
50C11×#127D411yescharacteristic, complemented
51C11×#124—21no—
52C11×#124—21no—
53C11×#124—21no—
54C11×#124—21no—
55C11×#124—21no—
56C11×#124—44no—
57C11×#121—21no—
58C11×#121—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yescomplemented
68C11×#103—22no—
69C11×#102—22no—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—21no—
72C11×#97—21no—
73C11×#97—21no—
74C11×#97D412yescomplemented
75C4×C8×C11—21no—
76C11×#95—21no—
77C11×#95D412yes—
78#10088C1111yesmaximal, characteristic, direct product factor, Sylow
79C24×C11—22no—
80C24×C11—21no—
81C11×#41—44no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—42no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—22no—
93C2×D4×C11—44no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—48no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—82no—
104C2×D4×C11—84no—
105C2×D4×C11—84no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C11×SD16—48no—
113C11×SD16—82no—
114C11×D8—48no—
115C11×D8—82no—
116C11×M16—24no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—41no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C22⋊C4—48no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11—24no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134#3213C2×C1111yescharacteristic, complemented
135#3151C2×C1111yescharacteristic, complemented
136#2657C2×C1111yescharacteristic, complemented
137#1555C2×C1111yescharacteristic, complemented
138#1527C2×C1111yescharacteristic, complemented
139#1505C2×C1111yescharacteristic, complemented
140#1300C2×C1111yescharacteristic, complemented
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—44no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—42no—
149C23×C11—44no—
150C23×C11—42no—
151C23×C11#12011yescharacteristic
152Q8×C11—42no—
153Q8×C11—42no—
154Q8×C11—81no—
155D4×C11—42no—
156D4×C11—44no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—81no—
160D4×C11—82no—
161D4×C11—81no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—816no—
166D4×C11—82no—
167D4×C11—82no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—82no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C8×C11—24no—
185C8×C11—42no—
186C8×C11—81no—
187C2×AGL(1,ℤ/8)—22no—
188#532C22×C1111yescharacteristic
189C2×#127—21no—
190C2×#127C22×C1111yescharacteristic
191C2×#124—21no—
192C2×#124C22×C1111yescharacteristic
193#496—21no—
194#496—22no—
195#493—21no—
196#492—21no—
197#489—21no—
198#463—22no—
199#448—21no—
200#447—21no—
201#432C22×C1111yescharacteristic
202#432C22×C1111yescharacteristic
203C4×M16C22×C1111yescharacteristic
204#392—22no—
205#392—22no—
206#376C22×C1111yescharacteristic
207#331—22no—
208#329—22no—
209#327—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—84no—
213C22×C11—84no—
214C22×C11—84no—
215C22×C11—81no—
216C22×C11—82no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—82no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11#39211yescharacteristic
225C22×C11#45312yes—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—44no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11#45312yes—
235C2×#41—21no—
236C22×Q8D4×C1111yescharacteristic
237C22×D4—24no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4D4×C1111yescharacteristic
241C22×D4D4×C1112yes—
242AGL(1,ℤ/8)—48no—
243C2×SD16—24no—
244C2×SD16—22no—
245C2×D8—24no—
246C2×D8—22no—
247C2×M16—21no—
248C4⋊Q8D4×C1111yescharacteristic, complemented
249#127—21no—
250#127—21no—
251#127—21no—
252#127—21no—
253#127—44no—
254#127D4×C1111yescharacteristic, complemented
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259#124—21no—
260#124—44no—
261#121—21no—
262#121—21no—
263C4×D4—21no—
264C4×D4—21no—
265C2×C22⋊C4—24no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C42—21no—
269C2×C42C23×C1111yescharacteristic
270C4⋊C8—21no—
271C4⋊C8D4×C1112yescomplemented
272#103—22no—
273#102—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276#97—21no—
277#97—21no—
278#97D4×C1112yescomplemented
279C4×C8—21no—
280#95—21no—
281#95D4×C1112yes—
282C2×C11—22no—
283C2×C11—161no—
284C2×C11—161no—
285C2×C11—162no—
286C2×C11#200211yescharacteristic
287C2×C11#200211yescharacteristic
288C2×C11#200811yescharacteristic
289C24—22no—
290C24—21no—
291#41—44no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—22no—
303C2×D4—44no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—48no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—82no—
314C2×D4—84no—
315C2×D4—84no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4C2×D4×C1111yescharacteristic
320C22×C4C2×D4×C1111yescharacteristic
321C22×C4C2×D4×C1111yescharacteristic
322SD16—48no—
323SD16—82no—
324D8—48no—
325D8—82no—
326M16—24no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—41no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C22⋊C4—48no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—24no—
340C42C2×D4×C1111yescharacteristic
341C42C2×D4×C1111yescharacteristic
342C42C2×D4×C1111yescharacteristic
343C42C11×#4111yescharacteristic
344C11#1008811yescharacteristic, direct product factor, Sylow
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—44no—
350C23—41no—
351C23—41no—
352C23—42no—
353C23—44no—
354C23—42no—
355C23C11×#12011yescharacteristic
356Q8—42no—
357Q8—42no—
358Q8—81no—
359D4—42no—
360D4—44no—
361D4—42no—
362D4—42no—
363D4—81no—
364D4—82no—
365D4—81no—
366D4—82no—
367D4—82no—
368D4—82no—
369D4—816no—
370D4—82no—
371D4—82no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—82no—
382C2×C4C11×#12011yescharacteristic
383C2×C4C11×#12011yescharacteristic
384C2×C4C11×#12111yescharacteristic
385C2×C4C11×#12111yescharacteristic
386C2×C4C11×#12111yescharacteristic
387C2×C4C11×#12711yescharacteristic
388C8—24no—
389C8—42no—
390C8—81no—
391C22—21no—
392C22—21no—
393C22—84no—
394C22—84no—
395C22—84no—
396C22—81no—
397C22—82no—
398C22—81no—
399C22—81no—
400C22—82no—
401C22—81no—
402C22—82no—
403C22—81no—
404C22—81no—
405C22C11×#39211yescharacteristic
406C22C11×#45312yes—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—44no—
413C4—81no—
414C4—81no—
415C4C11×#45312yes—
416C2—22no—
417C2—161no—
418C2—162no—
419C2—161no—
420C2C11×#200211yescharacteristic
421C2C11×#200211yescharacteristic
422C2C11×#200811yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
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×#3213C2semidirect
2. C11×#3151C2semidirect
3. C11×#2657C2semidirect
4. C11×#1555C2semidirect
5. C11×#1527C2semidirect
6. C11×#1505C2semidirect
7. C11×#1300C2semidirect
44. C11×C4⋊Q8D4semidirect
50. C11×#127D4semidirect
67. C11×C4⋊C8D4semidirect
74. C11×#97D4semidirect
78. #10088C11direct (N × H)
134. #3213C2×C11semidirect
135. #3151C2×C11semidirect
136. #2657C2×C11semidirect
137. #1555C2×C11semidirect
138. #1527C2×C11semidirect
139. #1505C2×C11semidirect
140. #1300C2×C11semidirect
248. C4⋊Q8D4×C11semidirect
254. #127D4×C11semidirect
271. C4⋊C8D4×C11semidirect
278. #97D4×C11semidirect
344. C11#10088direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32132
C11×#31512
C11×#26572
C11×#15552
C11×#15272
C11×#15052
C11×#13002
#1008811