Finite Group Databasebeta

← C11×#10074 #14587267

Subgroups — C11×#10074 #14587267

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#498C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic
3C11×#2547C211yesmaximal, characteristic
4C11×#1981C211yesmaximal, characteristic, complemented
5C2×C11×#332C211yesmaximal, characteristic, complemented
6C2×C11×D4⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#124—21no—
11C2×C4×D4×C11C2211yescharacteristic
12C11×#498—22no—
13C11×#498—22no—
14C11×#474—22no—
15C11×#474—22no—
16C2×C11×#107—21no—
17C2×C11×#106—22no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103—22no—
21C2×C11×#102—21no—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#397—22no—
24C11×#391—21no—
25C11×#380—22no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#332—22no—
28C11×D4⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8D412yes—
44C11×#124—42no—
45C11×#124—42no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C22⋊C4—24no—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C11×#107—24no—
61C11×#106—28no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8D412yes—
66C11×#103—44no—
67C11×#102—24no—
68C4×C8×C11—21no—
69C4×C8×C11D412yes—
70C11×#95—24no—
71C11×#95—21no—
72#10074C1111yesmaximal, characteristic, direct product factor, Sylow
73C24×C11—21no—
74C2×Q8×C11—22no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11SD1612yes—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C2×C8×C11—24no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C22⋊C4—48no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124C42×C11—41no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C2×#498C2×C1111yescharacteristic, complemented
130C2×#474C2×C1111yescharacteristic
131#2547C2×C1111yescharacteristic
132#1981C2×C1111yescharacteristic, complemented
133C2×#332C2×C1111yescharacteristic, complemented
134C2×D4⋊C8C2×C1111yescharacteristic
135#1279C2×C1111yescharacteristic, complemented
136C23×C11—22no—
137C23×C11—41no—
138C23×C11—42no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11#12011yescharacteristic
142Q8×C11—44no—
143Q8×C11—81no—
144Q8×C11—81no—
145Q8×C11—81no—
146Q8×C11—81no—
147Q8×C11—81no—
148Q8×C11—81no—
149D4×C11—22no—
150D4×C11—22no—
151D4×C11—41no—
152D4×C11—41no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×SD1611yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11#13512yes—
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)12yes—
178C2×C4×C11#13711yescharacteristic
179C8×C11—24no—
180C8×C11—42no—
181C8×C11—81no—
182C2×C4⋊Q8C22×C1111yescharacteristic
183C2×C4⋊Q8C22×C1111yescharacteristic
184C2×#124—21no—
185C2×C4×D4C22×C1111yescharacteristic
186#498—22no—
187#498—22no—
188#474—22no—
189#474—22no—
190C2×#107—21no—
191C2×#106—22no—
192C2×C4⋊C8C22×C1111yescharacteristic
193C2×C4⋊C8C22×C1111yescharacteristic
194C2×#103—22no—
195C2×#102—21no—
196C2×C4×C8C22×C1111yescharacteristic
197#397—22no—
198#391—21no—
199#380—22no—
200C4×C4⋊C4C22×C1111yescharacteristic
201#332—22no—
202D4⋊C8—22no—
203C22×C11—44no—
204C22×C11—42no—
205C22×C11—82no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39211yescharacteristic
209C22×C11#44912yes—
210C22×C11#45011yescharacteristic
211C22×C11#45211yescharacteristic
212C22×C11#45612yes—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—82no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11#44811yescharacteristic
220C4×C11#44911yescharacteristic
221C4×C11#46312yes—
222C4×C11#46511yescharacteristic
223C4×C11#46811yescharacteristic
224C4×C11#49511yescharacteristic
225C4×C11#49611yescharacteristic
226C22×Q8—21no—
227C22×Q8—21no—
228C22×D4D4×C1111yescharacteristic
229C23×C4—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8D4×C1112yes—
241#124—42no—
242#124—42no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4D4×C1111yescharacteristic
251C2×C4⋊C4D4×C1112yes—
252C2×C4⋊C4D4×C1112yes—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42C23×C1111yescharacteristic
257#107—24no—
258#106—28no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8D4×C1112yes—
263#103—44no—
264#102—24no—
265C4×C8—21no—
266C4×C8D4×C1112yes—
267#95—24no—
268#95—21no—
269C2×C11—82no—
270C2×C11#165212yes—
271C2×C11#165412yes—
272C2×C11#200011yescharacteristic
273C2×C11#200511yescharacteristic
274C2×C11#201211yescharacteristic
275C24—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4C11×SD1612yes—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1111yescharacteristic
302C22×C4C2×D4×C1111yescharacteristic
303C2×C8—24no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—42no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C22⋊C4—48no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C42—41no—
326C42—41no—
327C42C2×D4×C1111yescharacteristic
328C42C2×D4×C1111yescharacteristic
329C42C2×D4×C1111yescharacteristic
330C42C11×#4111yescharacteristic
331C11#1007411yescharacteristic, direct product factor, Sylow
332C23—22no—
333C23—41no—
334C23—42no—
335C23—41no—
336C23—42no—
337C23C11×#12011yescharacteristic
338Q8—44no—
339Q8—81no—
340Q8—81no—
341Q8—81no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—82no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—82no—
363C2×C4C11×#12011yescharacteristic
364C2×C4C11×#12011yescharacteristic
365C2×C4C11×#12111yescharacteristic
366C2×C4C11×#12111yescharacteristic
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12711yescharacteristic
369C2×C4C2×C11×SD1611yescharacteristic
370C2×C4C11×#13512yes—
371C2×C4C11×#13511yescharacteristic
372C2×C4C11×AGL(1,ℤ/8)12yes—
373C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
374C2×C4C11×#13711yescharacteristic
375C8—24no—
376C8—42no—
377C8—81no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22C11×#39211yescharacteristic
384C22C11×#44912yes—
385C22C11×#45011yescharacteristic
386C22C11×#45211yescharacteristic
387C22C11×#45612yes—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—82no—
392C4—81no—
393C4—82no—
394C4C11×#44811yescharacteristic
395C4C11×#44911yescharacteristic
396C4C11×#46312yes—
397C4C11×#46511yescharacteristic
398C4C11×#46811yescharacteristic
399C4C11×#49511yescharacteristic
400C4C11×#49611yescharacteristic
401C2—82no—
402C2C11×#165212yes—
403C2C11×#165412yes—
404C2C11×#200011yescharacteristic
405C2C11×#200511yescharacteristic
406C2C11×#201211yescharacteristic
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#498C2semidirect
4. C11×#1981C2semidirect
5. C2×C11×#332C2semidirect
7. C11×#1279C2semidirect
72. #10074C11direct (N × H)
129. C2×#498C2×C11semidirect
132. #1981C2×C11semidirect
133. C2×#332C2×C11semidirect
135. #1279C2×C11semidirect
331. C11#10074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4982
C2×C11×#4742
C11×#25472
C11×#19812
C2×C11×#3322
C2×C11×D4⋊C82
C11×#12792
#1007411