Finite Group Databasebeta

← C11×#10500 #14587693

Subgroups — C11×#10500 #14587693

Order 2816.

508 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3205C211yesmaximal, characteristic
2C11×#1982C211yesmaximal, characteristic, complemented
3C11×#1980C211yesmaximal, characteristic, complemented
4C11×#1965C211yesmaximal, characteristic, complemented
5C11×#1565C211yesmaximal, characteristic, complemented
6C11×#1547C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C11×#493—21no—
11C11×#486—21no—
12C11×#459—21no—
13C11×#459—21no—
14C11×#447—22no—
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#104—21no—
19C2×C11×#104—21no—
20C2×C11×#102—22no—
21C2×C11×#100—21no—
22C2×C11×#100—21no—
23C4×C11×M16C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C11×#335—21no—
26C11×#334—21no—
27C11×#332—21no—
28C11×#331—21no—
29C2×C11×#41—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D412yes—
33C2×C11×D8—22no—
34C2×C11×D8—22no—
35C2×C11×M16—21no—
36C2×C11×M16D411yescharacteristic
37C2×C11×M16D411yescharacteristic
38C22×C8×C11—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127D411yescharacteristic
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D411yescharacteristic
58C11×C4⋊C8D411yescharacteristic
59C11×#104—42no—
60C11×#104—42no—
61C11×#102—22no—
62C11×#102—22no—
63C11×#102—44no—
64C11×#100—42no—
65C11×#100—42no—
66C11×C22⋊C8—21no—
67C11×#97—21no—
68C4×C8×C11—21no—
69C4×C8×C11—21no—
70C11×#95—21no—
71#10500C1111yesmaximal, characteristic, direct product factor, Sylow
72C24×C11—22no—
73C11×#41—41no—
74C11×#41—41no—
75C11×#41—41no—
76C11×#41—41no—
77C2×Q8×C11—21no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—22no—
82C2×D4×C11—21no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
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—41no—
94C2×D4×C11—82no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C11×D8—82no—
101C11×D8—82no—
102C11×M16—21no—
103C11×M16—21no—
104C11×M16—21no—
105C11×M16—41no—
106C11×M16—41no—
107C11×M16D812yescomplemented
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—42no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—41no—
122C42×C11—41no—
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C42×C11#4111yescharacteristic
127#3205C2×C1111yescharacteristic
128#1982C2×C1111yescharacteristic, complemented
129#1980C2×C1111yescharacteristic, complemented
130#1965C2×C1111yescharacteristic, complemented
131#1565C2×C1111yescharacteristic, complemented
132#1547C2×C1111yescharacteristic, complemented
133#1303C2×C1111yescharacteristic, complemented
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—82no—
139C23×C11—82no—
140C23×C11#12111yescharacteristic
141Q8×C11—41no—
142Q8×C11—41no—
143D4×C11—44no—
144D4×C11—41no—
145D4×C11—42no—
146D4×C11—41no—
147D4×C11—42no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—81no—
151D4×C11—82no—
152D4×C11—82no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×C4×C11#12411yescharacteristic
174C2×C4×C11C2×D811yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C8×C11—22no—
179C8×C11—41no—
180C8×C11—41no—
181C8×C11—41no—
182C8×C11—81no—
183C8×C11—81no—
184#532C22×C1111yescharacteristic
185C2×#127C22×C1111yescharacteristic
186#493—21no—
187#486—21no—
188#459—21no—
189#459—21no—
190#447—22no—
191#431C22×C1111yescharacteristic
192#423C22×C1111yescharacteristic
193C2×C4⋊C8C22×C1111yescharacteristic
194C2×#104—21no—
195C2×#104—21no—
196C2×#102—22no—
197C2×#100—21no—
198C2×#100—21no—
199C4×M16C22×C1111yescharacteristic
200C4×C4⋊C4C22×C1111yescharacteristic
201#335—21no—
202#334—21no—
203#332—21no—
204#331—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—82no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—81no—
213C22×C11—162no—
214C22×C11—162no—
215C22×C11#39411yescharacteristic
216C22×C11#45911yescharacteristic
217C22×C11#46311yescharacteristic
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11#45311yescharacteristic
224C4×C11#45511yescharacteristic
225C4×C11#45911yescharacteristic
226C4×C11#46311yescharacteristic
227C4×C11#46611yescharacteristic
228C4×C11#46911yescharacteristic
229C2×#41—21no—
230C22×D4—21no—
231C22×D4—21no—
232C22×D4D4×C1112yes—
233C2×D8—22no—
234C2×D8—22no—
235C2×M16—21no—
236C2×M16D4×C1111yescharacteristic
237C2×M16D4×C1111yescharacteristic
238C22×C8—21no—
239C4⋊Q8D4×C1111yescharacteristic
240#127—21no—
241#127—21no—
242#127—21no—
243#127—21no—
244#127D4×C1111yescharacteristic
245#124—21no—
246#121—21no—
247#121—21no—
248C4×D4—21no—
249C4×D4—21no—
250C2×C4⋊C4—21no—
251C2×C42—21no—
252C2×C42C23×C1111yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8D4×C1111yescharacteristic
258C4⋊C8D4×C1111yescharacteristic
259#104—42no—
260#104—42no—
261#102—22no—
262#102—22no—
263#102—44no—
264#100—42no—
265#100—42no—
266C22⋊C8—21no—
267#97—21no—
268C4×C8—21no—
269C4×C8—21no—
270#95—21no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11—161no—
274C2×C11—162no—
275C2×C11#203711yescharacteristic
276C2×C11#204811yescharacteristic
277C2×C11#205411yescharacteristic
278C24—22no—
279#41—41no—
280#41—41no—
281#41—41no—
282#41—41no—
283C2×Q8—21no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—82no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C1111yescharacteristic
304C22×C4C2×D4×C1111yescharacteristic
305C22×C4C11×#4111yescharacteristic
306D8—82no—
307D8—82no—
308M16—21no—
309M16—21no—
310M16—21no—
311M16—41no—
312M16—41no—
313M16C11×D812yescomplemented
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—42no—
319C2×C8—41no—
320C2×C8—41no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C42—41no—
328C42—41no—
329C42C2×D4×C1111yescharacteristic
330C42C2×D4×C1111yescharacteristic
331C42C11×#4111yescharacteristic
332C42C11×#4111yescharacteristic
333C11#1050011yescharacteristic, direct product factor, Sylow
334C23—41no—
335C23—42no—
336C23—42no—
337C23—42no—
338C23—82no—
339C23—82no—
340C23C11×#12111yescharacteristic
341Q8—41no—
342Q8—41no—
343D4—44no—
344D4—41no—
345D4—42no—
346D4—41no—
347D4—42no—
348D4—41no—
349D4—41no—
350D4—81no—
351D4—82no—
352D4—82no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4C11×#12011yescharacteristic
369C2×C4C11×#12111yescharacteristic
370C2×C4C11×#12111yescharacteristic
371C2×C4C11×#12311yescharacteristic
372C2×C4C11×#12311yescharacteristic
373C2×C4C11×#12411yescharacteristic
374C2×C4C2×C11×D811yescharacteristic
375C2×C4C11×#13511yescharacteristic
376C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
377C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
378C8—22no—
379C8—41no—
380C8—41no—
381C8—41no—
382C8—81no—
383C8—81no—
384C22—21no—
385C22—21no—
386C22—82no—
387C22—81no—
388C22—82no—
389C22—81no—
390C22—81no—
391C22—82no—
392C22—162no—
393C22—162no—
394C22C11×#39411yescharacteristic
395C22C11×#45911yescharacteristic
396C22C11×#46311yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—82no—
401C4—81no—
402C4C11×#45311yescharacteristic
403C4C11×#45511yescharacteristic
404C4C11×#45911yescharacteristic
405C4C11×#46311yescharacteristic
406C4C11×#46611yescharacteristic
407C4C11×#46911yescharacteristic
408C2—21no—
409C2—21no—
410C2—162no—
411C2—161no—
412C2C11×#203711yescharacteristic
413C2C11×#204811yescharacteristic
414C2C11×#205411yescharacteristic
subgroupG/H
center, socleC22×C11#394
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#3205C2
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×#1982C2semidirect
3. C11×#1980C2semidirect
4. C11×#1965C2semidirect
5. C11×#1565C2semidirect
6. C11×#1547C2semidirect
7. C11×#1303C2semidirect
71. #10500C11direct (N × H)
107. C11×M16D8semidirect
128. #1982C2×C11semidirect
129. #1980C2×C11semidirect
130. #1965C2×C11semidirect
131. #1565C2×C11semidirect
132. #1547C2×C11semidirect
133. #1303C2×C11semidirect
313. M16C11×D8semidirect
333. C11#10500direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32052
C11×#19822
C11×#19802
C11×#19652
C11×#15652
C11×#15472
C11×#13032
#1050011