Finite Group Databasebeta

← C11×#9211 #14586404

Subgroups — C11×#9211 #14586404

Order 2816.

536 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×#3106C211yesmaximal, characteristic
2C4×C11×#131C211yesmaximal, characteristic, complemented
3C11×#1525C211yesmaximal, characteristic, complemented
4C11×#1492C211yesmaximal, characteristic, complemented
5C11×#1489C211yesmaximal, characteristic, complemented
6C11×#1299C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C2×C11×#131—21no—
9C11×#532C2211yescharacteristic
10C4×C11×#41C2211yescharacteristic
11C11×#482—21no—
12C11×#477C411yescharacteristic
13C11×#476C411yescharacteristic
14C11×#460C411yescharacteristic
15C11×#459C411yescharacteristic
16C11×#449—21no—
17C4×C11×SD16—21no—
18C4×C11×D8—21no—
19C11×#431C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C11×#405—21no—
22C11×#405—22no—
23C4×C11×M16—21no—
24C4×C11×M16C2211yescharacteristic
25C4×C11×M16C2211yescharacteristic
26C2×C4×C8×C11—21no—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#329—22no—
29C11×Q8⋊C8—21no—
30C11×D4⋊C8—21no—
31C11×D4⋊C8—21no—
32C11×D4⋊C8—21no—
33C2×C11×#41—21no—
34C2×C11×#41D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×D8—21no—
37C11×#131—24no—
38C11×#131—24no—
39C2×C11×M16—22no—
40C2×C11×M16—21no—
41C2×C11×M16—21no—
42C2×C11×M16—21no—
43C22×C8×C11—22no—
44C22×C8×C11—21no—
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×#127C2×C411yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×Q8×C11C2×C411yescharacteristic
51C4×Q8×C11D411yescharacteristic
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11C2×C411yescharacteristic
57C4×D4×C11D411yescharacteristic
58C11×#117—21no—
59C11×#117D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C11×#107—21no—
63C11×#106—21no—
64C11×C4⋊C8—21no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8C2×C411yescharacteristic
67C11×C4⋊C8C2×C411yescharacteristic
68C11×#103—21no—
69C11×#102—21no—
70C11×#102—21no—
71C11×#102—21no—
72C11×C22⋊C8—21no—
73C11×#97—22no—
74C11×#97—21no—
75C11×#97D412yes—
76C4×C8×C11—22no—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79C4×C8×C11—21no—
80C4×C8×C11—21no—
81C4×C8×C11D411yescharacteristic
82C4×C8×C11D411yescharacteristic
83#9211C1111yesmaximal, characteristic, direct product factor, Sylow
84C11×#41—22no—
85C11×#41—22no—
86C11×#41—81no—
87C11×#41—81no—
88C2×Q8×C11—21no—
89C2×Q8×C11C22⋊C411yescharacteristic
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11C22⋊C411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C11×SD16—42no—
104C11×D8—42no—
105C11×M16—28no—
106C11×M16—22no—
107C11×M16—22no—
108C11×M16—22no—
109C11×M16—41no—
110C11×M16—81no—
111C2×C8×C11—28no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4C22⋊C411yescharacteristic
126C11×C4⋊C4C22⋊C411yescharacteristic
127C11×C22⋊C4—21no—
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C42×C11—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11C22×C411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139#3106C2×C1111yescharacteristic
140C4×#131C2×C1111yescharacteristic, complemented
141#1525C2×C1111yescharacteristic, complemented
142#1492C2×C1111yescharacteristic, complemented
143#1489C2×C1111yescharacteristic, complemented
144#1299C2×C1111yescharacteristic, complemented
145#1278C2×C1111yescharacteristic, complemented
146C23×C11—21no—
147C23×C11—41no—
148C23×C11#12311yescharacteristic
149Q8×C11—21no—
150Q8×C11—81no—
151Q8×C11#10412yes—
152D4×C11—24no—
153D4×C11—21no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—41no—
157D4×C11—41no—
158D4×C11—81no—
159D4×C11—82no—
160D4×C11#10412yes—
161C2×C4×C11—24no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11C2×C22⋊C411yescharacteristic
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C8×C11—22no—
185C8×C11—24no—
186C8×C11—22no—
187C8×C11—42no—
188C8×C11—41no—
189C8×C11—41no—
190C8×C11—81no—
191C2×#131—21no—
192#532C22×C1111yescharacteristic
193C4×#41C22×C1111yescharacteristic
194#482—21no—
195#477C4×C1111yescharacteristic
196#476C4×C1111yescharacteristic
197#460C4×C1111yescharacteristic
198#459C4×C1111yescharacteristic
199#449—21no—
200C4×SD16—21no—
201C4×D8—21no—
202#431C22×C1111yescharacteristic
203#423C22×C1111yescharacteristic
204#405—21no—
205#405—22no—
206C4×M16—21no—
207C4×M16C22×C1111yescharacteristic
208C4×M16C22×C1111yescharacteristic
209C2×C4×C8—21no—
210C2×C4×C8C22×C1111yescharacteristic
211#329—22no—
212Q8⋊C8—21no—
213D4⋊C8—21no—
214D4⋊C8—21no—
215D4⋊C8—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—22no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11#38611yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—22no—
229C4×C11—21no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—81no—
233C4×C11C2×#10411yescharacteristic
234C4×C11C2×#10411yescharacteristic
235C4×C11#44311yescharacteristic
236C4×C11#44411yescharacteristic
237C4×C11#47111yescharacteristic
238C4×C11#47211yescharacteristic
239C2×#41—21no—
240C2×#41D4×C1111yescharacteristic
241C2×SD16—21no—
242C2×D8—21no—
243#131—24no—
244#131—24no—
245C2×M16—22no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C22×C8—22no—
250C22×C8—21no—
251C4⋊Q8C2×C4×C1111yescharacteristic
252#127C2×C4×C1111yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×Q8C2×C4×C1111yescharacteristic
257C4×Q8D4×C1111yescharacteristic
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4C2×C4×C1111yescharacteristic
263C4×D4D4×C1111yescharacteristic
264#117—21no—
265#117D4×C1111yescharacteristic
266C2×C42—21no—
267C2×C42C23×C1111yescharacteristic
268#107—21no—
269#106—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8C2×C4×C1111yescharacteristic
273C4⋊C8C2×C4×C1111yescharacteristic
274#103—21no—
275#102—21no—
276#102—21no—
277#102—21no—
278C22⋊C8—21no—
279#97—22no—
280#97—21no—
281#97D4×C1112yes—
282C4×C8—22no—
283C4×C8—21no—
284C4×C8—21no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8D4×C1111yescharacteristic
288C4×C8D4×C1111yescharacteristic
289C2×C11—41no—
290C2×C11—42no—
291C2×C11—161no—
292C2×C11#187611yescharacteristic
293C2×C11#189611yescharacteristic
294C2×C11#190711yescharacteristic
295#41—22no—
296#41—22no—
297#41—81no—
298#41—81no—
299C2×Q8—21no—
300C2×Q8C11×C22⋊C411yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4C11×C22⋊C411yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—41no—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C11×#4111yescharacteristic
313C22×C4C11×#4111yescharacteristic
314SD16—42no—
315D8—42no—
316M16—28no—
317M16—22no—
318M16—22no—
319M16—22no—
320M16—41no—
321M16—81no—
322C2×C8—28no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—22no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8—41no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4C11×C22⋊C411yescharacteristic
337C4⋊C4C11×C22⋊C411yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—21no—
344C42—21no—
345C42—21no—
346C42C22×C4×C1111yescharacteristic
347C42C2×D4×C1111yescharacteristic
348C42C2×D4×C1111yescharacteristic
349C42C2×D4×C1111yescharacteristic
350C11#921111yescharacteristic, direct product factor, Sylow
351C23—21no—
352C23—41no—
353C23C11×#12311yescharacteristic
354Q8—21no—
355Q8—81no—
356Q8C11×#10412yes—
357D4—24no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—82no—
365D4C11×#10412yes—
366C2×C4—24no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4C2×C11×C22⋊C411yescharacteristic
384C2×C4C4×D4×C1111yescharacteristic
385C2×C4C4×D4×C1111yescharacteristic
386C2×C4C11×#12011yescharacteristic
387C2×C4C11×#12111yescharacteristic
388C2×C4C11×#12111yescharacteristic
389C8—22no—
390C8—24no—
391C8—22no—
392C8—42no—
393C8—41no—
394C8—41no—
395C8—81no—
396C22—21no—
397C22—21no—
398C22—22no—
399C22—21no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C11×#38611yescharacteristic
406C4—21no—
407C4—21no—
408C4—22no—
409C4—21no—
410C4—41no—
411C4—41no—
412C4—81no—
413C4C2×C11×#10411yescharacteristic
414C4C2×C11×#10411yescharacteristic
415C4C11×#44311yescharacteristic
416C4C11×#44411yescharacteristic
417C4C11×#47111yescharacteristic
418C4C11×#47211yescharacteristic
419C2—41no—
420C2—42no—
421C2—161no—
422C2C11×#187611yescharacteristic
423C2C11×#189611yescharacteristic
424C2C11×#190711yescharacteristic
subgroupG/H
centerC2×C4×C11#121
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
socleC22×C11#386
prime radicalC11×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C11×#131C2semidirect
3. C11×#1525C2semidirect
4. C11×#1492C2semidirect
5. C11×#1489C2semidirect
6. C11×#1299C2semidirect
7. C11×#1278C2semidirect
83. #9211C11direct (N × H)
140. C4×#131C2×C11semidirect
141. #1525C2×C11semidirect
142. #1492C2×C11semidirect
143. #1489C2×C11semidirect
144. #1299C2×C11semidirect
145. #1278C2×C11semidirect
350. C11#9211direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31062
C4×C11×#1312
C11×#15252
C11×#14922
C11×#14892
C11×#12992
C11×#12782
#921111