Finite Group Databasebeta

← C11×#10179 #14587372

Subgroups — C11×#10179 #14587372

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3208C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C2×C11×#460C211yesmaximal, characteristic
4C11×#1545C211yesmaximal, characteristic
5C11×#1481C211yesmaximal, characteristic, complemented
6C11×#1461C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C11×#533C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C11×#492—21no—
13C11×#486—21no—
14C11×#479—22no—
15C11×#477—21no—
16C11×#475—21no—
17C11×#460—22no—
18C11×#460—22no—
19C11×#460—22no—
20C11×#450—22no—
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C11×#428—21no—
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#419—21no—
27C2×C11×#102—21no—
28C11×#331—22no—
29C11×Q8⋊C8—22no—
30C11×#324—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C2×C11×SD16—24no—
36C2×C11×SD16—24no—
37C2×C11×SD16—42no—
38C2×C11×SD16—42no—
39C2×C11×M16—21no—
40C22×C8×C11—21no—
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127D412yes—
47C11×#125—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C4×Q8×C11—21no—
51C4×Q8×C11—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C11×#117—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C11×#107—22no—
62C11×#106—22no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8D412yes—
69C11×#103—22no—
70C11×#103—22no—
71C11×#102—24no—
72C11×#102—24no—
73C11×C22⋊C8—21no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11—21no—
77#10179C1111yesmaximal, characteristic, direct product factor, Sylow
78C24×C11—41no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11SD1612yescomplemented
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—82no—
98C2×D4×C11—82no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C11×SD16—48no—
105C11×SD16—84no—
106C11×M16—41no—
107C11×M16—41no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C42×C11—41no—
126C42×C11—41no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#3208C2×C1111yescharacteristic
133#3078C2×C1111yescharacteristic, complemented
134C2×#460C2×C1111yescharacteristic
135#1545C2×C1111yescharacteristic
136#1481C2×C1111yescharacteristic, complemented
137#1461C2×C1111yescharacteristic, complemented
138#1301C2×C1111yescharacteristic, complemented
139C23×C11—42no—
140C23×C11—82no—
141C23×C11—82no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11#12111yescharacteristic
145Q8×C11—22no—
146Q8×C11—22no—
147Q8×C11—42no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—42no—
151D4×C11—44no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—82no—
155D4×C11—82no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—82no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12711yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11#13711yescharacteristic
178C8×C11—42no—
179C8×C11—42no—
180C8×C11—42no—
181C8×C11—81no—
182C22×SD16—21no—
183#533C22×C1111yescharacteristic
184C2×#127C22×C1111yescharacteristic
185C2×C4×Q8C22×C1111yescharacteristic
186#492—21no—
187#486—21no—
188#479—22no—
189#477—21no—
190#475—21no—
191#460—22no—
192#460—22no—
193#460—22no—
194#450—22no—
195#431C22×C1111yescharacteristic
196#431C22×C1111yescharacteristic
197#428—21no—
198#423C22×C1111yescharacteristic
199C2×C4⋊C8C22×C1111yescharacteristic
200#419—21no—
201C2×#102—21no—
202#331—22no—
203Q8⋊C8—22no—
204#324—22no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—162no—
211C22×C11—162no—
212C22×C11#39211yescharacteristic
213C22×C11#46511yescharacteristic
214C22×C11#46811yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11#44811yescharacteristic
223C4×C11#44911yescharacteristic
224C4×C11#45011yescharacteristic
225C4×C11#45211yescharacteristic
226C4×C11#47112yes—
227C22×Q8D4×C1111yescharacteristic
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C2×SD16—24no—
232C2×SD16—24no—
233C2×SD16—42no—
234C2×SD16—42no—
235C2×M16—21no—
236C22×C8—21no—
237C4⋊Q8D4×C1111yescharacteristic
238C4⋊Q8D4×C1111yescharacteristic
239#127—21no—
240#127—21no—
241#127—21no—
242#127D4×C1112yes—
243#125—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252#117—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4×C1111yescharacteristic
255C2×C42—21no—
256C2×C42C23×C1111yescharacteristic
257#107—22no—
258#106—22no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8D4×C1112yes—
264C4⋊C8D4×C1112yes—
265#103—22no—
266#103—22no—
267#102—24no—
268#102—24no—
269C22⋊C8—21no—
270C22⋊C8D4×C1112yes—
271C4×C8—21no—
272C4×C8—21no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—162no—
276C2×C11#200011yescharacteristic
277C2×C11#200811yescharacteristic
278C2×C11#201911yescharacteristic
279C24—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8C11×SD1612yescomplemented
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—82no—
299C2×D4—82no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C11×#4111yescharacteristic
305SD16—48no—
306SD16—84no—
307M16—41no—
308M16—41no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42C2×D4×C1111yescharacteristic
330C42C2×D4×C1111yescharacteristic
331C42C2×D4×C1111yescharacteristic
332C42C2×D4×C1111yescharacteristic
333C11#1017911yescharacteristic, direct product factor, Sylow
334C23—42no—
335C23—82no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23C11×#12111yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—42no—
343Q8—41no—
344Q8—41no—
345Q8—42no—
346D4—44no—
347D4—42no—
348D4—42no—
349D4—82no—
350D4—82no—
351D4—81no—
352D4—81no—
353D4—82no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4C11×#12011yescharacteristic
364C2×C4C11×#12011yescharacteristic
365C2×C4C11×#12011yescharacteristic
366C2×C4C11×#12111yescharacteristic
367C2×C4C11×#12111yescharacteristic
368C2×C4C11×#12711yescharacteristic
369C2×C4C2×C11×SD1611yescharacteristic
370C2×C4C11×#13511yescharacteristic
371C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
372C2×C4C11×#13711yescharacteristic
373C8—42no—
374C8—42no—
375C8—42no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22C11×#39211yescharacteristic
385C22C11×#46511yescharacteristic
386C22C11×#46811yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—81no—
393C4—81no—
394C4C11×#44811yescharacteristic
395C4C11×#44911yescharacteristic
396C4C11×#45011yescharacteristic
397C4C11×#45211yescharacteristic
398C4C11×#47112yes—
399C2—21no—
400C2—21no—
401C2—162no—
402C2C11×#200011yescharacteristic
403C2C11×#200811yescharacteristic
404C2C11×#201911yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC2×C11×#127C22
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
2. C11×#3078C2semidirect
5. C11×#1481C2semidirect
6. C11×#1461C2semidirect
7. C11×#1301C2semidirect
77. #10179C11direct (N × H)
86. C2×Q8×C11SD16semidirect
133. #3078C2×C11semidirect
136. #1481C2×C11semidirect
137. #1461C2×C11semidirect
138. #1301C2×C11semidirect
287. C2×Q8C11×SD16semidirect
333. C11#10179direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32082
C11×#30782
C2×C11×#4602
C11×#15452
C11×#14812
C11×#14612
C11×#13012
#1017911