Finite Group Databasebeta

← C11×#9174 #14586367

Subgroups — C11×#9174 #14586367

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3038C211yesmaximal, characteristic
2C11×#2925C211yesmaximal, characteristic, complemented
3C11×#1545C211yesmaximal, characteristic, complemented
4C2×C11×#331C211yesmaximal, characteristic, complemented
5C11×#1477C211yesmaximal, characteristic, complemented
6C11×#1301C211yesmaximal, characteristic, complemented
7C11×#1292C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C2×C11×#127C2211yescharacteristic
10C4×C11×#41C2211yescharacteristic
11C11×#460—21no—
12C11×#460C412yes—
13C11×#459—21no—
14C11×#459C412yes—
15C11×#433—22no—
16C11×#432—21no—
17C11×#431—21no—
18C11×#431C2211yescharacteristic
19C11×#423C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#418—21no—
24C11×#408—21no—
25C11×#405—21no—
26C11×#331—21no—
27C11×#331—21no—
28C11×#331—22no—
29C11×Q8⋊C8—21no—
30C11×D4⋊C8—21no—
31C2×C11×#41D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C11×AGL(1,ℤ/8)—42no—
36C11×AGL(1,ℤ/8)—42no—
37C2×C11×SD16—22no—
38C2×C11×D8—22no—
39C2×C11×M16—21no—
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127C2×C412yes—
47C4×Q8×C11C2×C411yescharacteristic
48C4×Q8×C11D411yescharacteristic
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11C2×C411yescharacteristic
52C4×D4×C11D411yescharacteristic
53C11×#117—21no—
54C11×#117D411yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8C2×C412yes—
64C11×C4⋊C8D411yescharacteristic
65C11×C4⋊C8D411yescharacteristic
66C11×C4⋊C8D412yes—
67C11×#102—22no—
68C11×#102—22no—
69C11×C22⋊C8—22no—
70C11×C22⋊C8—22no—
71C11×C22⋊C8—21no—
72C11×#97—22no—
73C4×C8×C11—22no—
74C4×C8×C11—21no—
75#9174C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—41no—
77C11×#41—21no—
78C11×#41—21no—
79C11×#41—21no—
80C11×#41—21no—
81C2×Q8×C11C22⋊C411yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—22no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—81no—
94C2×D4×C11—81no—
95C2×D4×C11—82no—
96C2×D4×C11C22⋊C411yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C11×SD16—44no—
104C11×D8—44no—
105C11×M16—41no—
106C11×M16—41no—
107C11×M16—41no—
108C11×M16—41no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—22no—
112C2×C8×C11—21no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—81no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4C22⋊C411yescharacteristic
121C11×C4⋊C4C22⋊C411yescharacteristic
122C11×C22⋊C4—21no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—21no—
125C42×C11—21no—
126C42×C11—21no—
127C42×C11—21no—
128C42×C11C22×C411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132#3038C2×C1111yescharacteristic
133#2925C2×C1111yescharacteristic, complemented
134#1545C2×C1111yescharacteristic, complemented
135C2×#331C2×C1111yescharacteristic, complemented
136#1477C2×C1111yescharacteristic, complemented
137#1301C2×C1111yescharacteristic, complemented
138#1292C2×C1111yescharacteristic, complemented
139C23×C11—21no—
140C23×C11—42no—
141C23×C11—82no—
142C23×C11—82no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11#12311yescharacteristic
146Q8×C11—21no—
147Q8×C11—21no—
148D4×C11—21no—
149D4×C11—21no—
150D4×C11—41no—
151D4×C11—41no—
152D4×C11—42no—
153D4×C11—42no—
154D4×C11—82no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—81no—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11C4×D411yescharacteristic
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#13511yescharacteristic
179C2×C4×C11#13511yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
182C8×C11—42no—
183C8×C11—41no—
184C8×C11—41no—
185C8×C11—42no—
186C8×C11—81no—
187C8×C11—81no—
188C2×AGL(1,ℤ/8)—21no—
189C2×#127C22×C1111yescharacteristic
190C4×#41C22×C1111yescharacteristic
191#460—21no—
192#460C4×C1112yes—
193#459—21no—
194#459C4×C1112yes—
195#433—22no—
196#432—21no—
197#431—21no—
198#431C22×C1111yescharacteristic
199#423C22×C1111yescharacteristic
200#423C22×C1111yescharacteristic
201C2×C4⋊C8C22×C1111yescharacteristic
202C2×C4⋊C8C22×C1111yescharacteristic
203#418—21no—
204#408—21no—
205#405—21no—
206#331—21no—
207#331—21no—
208#331—22no—
209Q8⋊C8—21no—
210D4⋊C8—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—82no—
217C22×C11—82no—
218C22×C11—82no—
219C22×C11—162no—
220C22×C11—162no—
221C22×C11#38611yescharacteristic
222C22×C11#48211yescharacteristic
223C22×C11#48211yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11#41611yescharacteristic
231C4×C11#41811yescharacteristic
232C4×C11#44911yescharacteristic
233C4×C11#44911yescharacteristic
234C4×C11#47111yescharacteristic
235C4×C11#47211yescharacteristic
236C2×#41D4×C1111yescharacteristic
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240AGL(1,ℤ/8)—42no—
241AGL(1,ℤ/8)—42no—
242C2×SD16—22no—
243C2×D8—22no—
244C2×M16—21no—
245C2×M16—21no—
246C22×C8—21no—
247C22×C8—21no—
248#127—21no—
249#127—21no—
250#127—21no—
251#127C2×C4×C1112yes—
252C4×Q8C2×C4×C1111yescharacteristic
253C4×Q8D4×C1111yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C2×C4×C1111yescharacteristic
257C4×D4D4×C1111yescharacteristic
258#117—21no—
259#117D4×C1111yescharacteristic
260C2×C42—21no—
261C2×C42C23×C1111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8C2×C4×C1112yes—
269C4⋊C8D4×C1111yescharacteristic
270C4⋊C8D4×C1111yescharacteristic
271C4⋊C8D4×C1112yes—
272#102—22no—
273#102—22no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8—21no—
277#97—22no—
278C4×C8—22no—
279C4×C8—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—81no—
283C2×C11—162no—
284C2×C11#187511yescharacteristic
285C2×C11#190311yescharacteristic
286C2×C11#190711yescharacteristic
287C24—41no—
288#41—21no—
289#41—21no—
290#41—21no—
291#41—21no—
292C2×Q8C11×C22⋊C411yescharacteristic
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—81no—
305C2×D4—81no—
306C2×D4—82no—
307C2×D4C11×C22⋊C411yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C11×#4111yescharacteristic
313C22×C4C11×#4111yescharacteristic
314SD16—44no—
315D8—44no—
316M16—41no—
317M16—41no—
318M16—41no—
319M16—41no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—22no—
323C2×C8—21no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—81no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4C11×C22⋊C411yescharacteristic
332C4⋊C4C11×C22⋊C411yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C42—21no—
337C42—21no—
338C42—21no—
339C42C22×C4×C1111yescharacteristic
340C42C2×D4×C1111yescharacteristic
341C42C2×D4×C1111yescharacteristic
342C42C2×D4×C1111yescharacteristic
343C11#917411yescharacteristic, direct product factor, Sylow
344C23—21no—
345C23—42no—
346C23—82no—
347C23—82no—
348C23—81no—
349C23—81no—
350C23C11×#12311yescharacteristic
351Q8—21no—
352Q8—21no—
353D4—21no—
354D4—21no—
355D4—41no—
356D4—41no—
357D4—42no—
358D4—42no—
359D4—82no—
360D4—82no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4C2×C11×C22⋊C411yescharacteristic
378C2×C4C4×D4×C1111yescharacteristic
379C2×C4C4×D4×C1111yescharacteristic
380C2×C4C11×#12011yescharacteristic
381C2×C4C11×#12111yescharacteristic
382C2×C4C11×#12111yescharacteristic
383C2×C4C11×#13511yescharacteristic
384C2×C4C11×#13511yescharacteristic
385C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
386C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
387C8—42no—
388C8—41no—
389C8—41no—
390C8—42no—
391C8—81no—
392C8—81no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—82no—
399C22—82no—
400C22—82no—
401C22—162no—
402C22—162no—
403C22C11×#38611yescharacteristic
404C22C11×#48211yescharacteristic
405C22C11×#48211yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4C11×#41611yescharacteristic
413C4C11×#41811yescharacteristic
414C4C11×#44911yescharacteristic
415C4C11×#44911yescharacteristic
416C4C11×#47111yescharacteristic
417C4C11×#47211yescharacteristic
418C2—21no—
419C2—21no—
420C2—81no—
421C2—162no—
422C2C11×#187511yescharacteristic
423C2C11×#190311yescharacteristic
424C2C11×#190711yescharacteristic
subgroupG/H
center, socleC22×C11#386
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3038C2
LCSG ▷ 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×#2925C2semidirect
3. C11×#1545C2semidirect
4. C2×C11×#331C2semidirect
5. C11×#1477C2semidirect
6. C11×#1301C2semidirect
7. C11×#1292C2semidirect
75. #9174C11direct (N × H)
133. #2925C2×C11semidirect
134. #1545C2×C11semidirect
135. C2×#331C2×C11semidirect
136. #1477C2×C11semidirect
137. #1301C2×C11semidirect
138. #1292C2×C11semidirect
343. C11#9174direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30382
C11×#29252
C11×#15452
C2×C11×#3312
C11×#14772
C11×#13012
C11×#12922
#917411