Finite Group Databasebeta

← C11×#10185 #14587378

Subgroups — C11×#10185 #14587378

Order 2816.

550 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×#3226C211yesmaximal, characteristic
2C11×#3037C211yesmaximal, characteristic
3C2×C11×#462C211yesmaximal, characteristic, complemented
4C11×#1546C211yesmaximal, characteristic, complemented
5C11×#1480C211yesmaximal, characteristic
6C11×#1461C211yesmaximal, characteristic, complemented
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C22×C11×Q16—21no—
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C11×#500—21no—
14C11×#486—21no—
15C11×#480—22no—
16C11×#474—22no—
17C11×#464—22no—
18C11×#462—22no—
19C11×#462—21no—
20C11×#462—22no—
21C11×#460—21no—
22C11×#431C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#423C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#417—21no—
27C2×C11×#103—21no—
28C11×#332—22no—
29C11×D4⋊C8—22no—
30C11×#324—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11D411yescharacteristic
34C11×#137—42no—
35C11×#137—42no—
36C2×C11×Q16—24no—
37C2×C11×Q16—22no—
38C2×C11×Q16—42no—
39C2×C11×Q16—42no—
40C2×C11×SD16—22no—
41C2×C11×M16—21no—
42C22×C8×C11—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8D411yescharacteristic
47C11×C4⋊Q8D412yes—
48C11×#127D411yescharacteristic
49C11×#124—21no—
50C11×#121—21no—
51C11×#121—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#107—24no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yes—
70C11×C4⋊C8D412yes—
71C11×#103—24no—
72C11×#103—22no—
73C11×#102—22no—
74C11×#102—24no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8D412yes—
77C4×C8×C11—21no—
78C4×C8×C11—21no—
79#10185C1111yesmaximal, characteristic, direct product factor, Sylow
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—22no—
89C2×Q8×C11—21no—
90C2×Q8×C11—21no—
91C2×Q8×C11—41no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11D812yes—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—41no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C11×Q16—48no—
109C11×Q16—44no—
110C11×SD16—44no—
111C11×M16—41no—
112C11×M16—41no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137#3226C2×C1111yescharacteristic
138#3037C2×C1111yescharacteristic
139C2×#462C2×C1111yescharacteristic, complemented
140#1546C2×C1111yescharacteristic, complemented
141#1480C2×C1111yescharacteristic
142#1461C2×C1111yescharacteristic, complemented
143#1301C2×C1111yescharacteristic, complemented
144C23×C11—41no—
145C23×C11#12111yescharacteristic
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—42no—
151Q8×C11—41no—
152Q8×C11—42no—
153Q8×C11—41no—
154Q8×C11—81no—
155Q8×C11—81no—
156D4×C11—42no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—42no—
160D4×C11—81no—
161D4×C11—81no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11#12011yescharacteristic
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12711yescharacteristic
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C8×C11—42no—
186C8×C11—42no—
187C8×C11—42no—
188C8×C11—81no—
189C2×#137—21no—
190C22×Q16—21no—
191#532C22×C1111yescharacteristic
192C2×C4⋊Q8C22×C1111yescharacteristic
193C2×C4×Q8C22×C1111yescharacteristic
194#500—21no—
195#486—21no—
196#480—22no—
197#474—22no—
198#464—22no—
199#462—22no—
200#462—21no—
201#462—22no—
202#460—21no—
203#431C22×C1111yescharacteristic
204#431C22×C1111yescharacteristic
205#423C22×C1111yescharacteristic
206C2×C4⋊C8C22×C1111yescharacteristic
207#417—21no—
208C2×#103—21no—
209#332—22no—
210D4⋊C8—22no—
211#324—22no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11#39211yescharacteristic
218C22×C11#46611yescharacteristic
219C22×C11#46911yescharacteristic
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—81no—
225C4×C11—82no—
226C4×C11—81no—
227C4×C11#44711yescharacteristic
228C4×C11#44711yescharacteristic
229C4×C11#44911yescharacteristic
230C4×C11#44911yescharacteristic
231C4×C11#47312yes—
232C2×#41—21no—
233C22×Q8—21no—
234C22×Q8D4×C1111yescharacteristic
235#137—42no—
236#137—42no—
237C2×Q16—24no—
238C2×Q16—22no—
239C2×Q16—42no—
240C2×Q16—42no—
241C2×SD16—22no—
242C2×M16—21no—
243C22×C8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C1112yes—
248C4⋊Q8D4×C1111yescharacteristic
249#127D4×C1111yescharacteristic
250#124—21no—
251#121—21no—
252#121—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4D4×C1111yescharacteristic
263C2×C42—21no—
264C2×C42C23×C1111yescharacteristic
265#107—24no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8D4×C1112yes—
271C4⋊C8D4×C1112yes—
272#103—24no—
273#103—22no—
274#102—22no—
275#102—24no—
276C22⋊C8—21no—
277C22⋊C8D4×C1112yes—
278C4×C8—21no—
279C4×C8—21no—
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—161no—
283C2×C11#199911yescharacteristic
284C2×C11#200911yescharacteristic
285C2×C11#202011yescharacteristic
286#41—41no—
287#41—41no—
288#41—41no—
289#41—41no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—22no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8C11×D812yes—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C1111yescharacteristic
312C22×C4C2×D4×C1111yescharacteristic
313C22×C4C11×#4111yescharacteristic
314Q16—48no—
315Q16—44no—
316SD16—44no—
317M16—41no—
318M16—41no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42—41no—
338C42—41no—
339C42C2×D4×C1111yescharacteristic
340C42C2×D4×C1111yescharacteristic
341C42C2×D4×C1111yescharacteristic
342C42C2×D4×C1111yescharacteristic
343C11#1018511yescharacteristic, direct product factor, Sylow
344C23—41no—
345C23C11×#12111yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350Q8—42no—
351Q8—41no—
352Q8—42no—
353Q8—41no—
354Q8—81no—
355Q8—81no—
356D4—42no—
357D4—41no—
358D4—41no—
359D4—42no—
360D4—81no—
361D4—81no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C11×#12011yescharacteristic
376C2×C4C11×#12011yescharacteristic
377C2×C4C11×#12011yescharacteristic
378C2×C4C11×#12111yescharacteristic
379C2×C4C11×#12111yescharacteristic
380C2×C4C11×#12711yescharacteristic
381C2×C4C2×C11×D811yescharacteristic
382C2×C4C11×#13511yescharacteristic
383C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
384C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
385C8—42no—
386C8—42no—
387C8—42no—
388C8—81no—
389C22—21no—
390C22—21no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22C11×#39211yescharacteristic
395C22C11×#46611yescharacteristic
396C22C11×#46911yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—81no—
402C4—82no—
403C4—81no—
404C4C11×#44711yescharacteristic
405C4C11×#44711yescharacteristic
406C4C11×#44911yescharacteristic
407C4C11×#44911yescharacteristic
408C4C11×#47312yes—
409C2—21no—
410C2—21no—
411C2—161no—
412C2C11×#199911yescharacteristic
413C2C11×#200911yescharacteristic
414C2C11×#202011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC11×#532C22
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
3. C2×C11×#462C2semidirect
4. C11×#1546C2semidirect
6. C11×#1461C2semidirect
7. C11×#1301C2semidirect
79. #10185C11direct (N × H)
139. C2×#462C2×C11semidirect
140. #1546C2×C11semidirect
142. #1461C2×C11semidirect
143. #1301C2×C11semidirect
343. C11#10185direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32262
C11×#30372
C2×C11×#4622
C11×#15462
C11×#14802
C11×#14612
C11×#13012
#1018511