Finite Group Databasebeta

← C11×#10002 #14587195

Subgroups — C11×#10002 #14587195

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3104C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic
3C11×#2580C211yesmaximal, characteristic
4C11×#1518C211yesmaximal, characteristic, complemented
5C11×#1487C211yesmaximal, characteristic, complemented
6C11×#1478C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#484—21no—
12C11×#478—22no—
13C11×#477—21no—
14C11×#476—21no—
15C11×#474—21no—
16C11×#462—21no—
17C11×#451—21no—
18C4×C11×Q16—22no—
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21C11×#428—21no—
22C11×#423C2211yescharacteristic
23C11×#418—21no—
24C11×#399—21no—
25C11×#393—21no—
26C11×#390—21no—
27C11×#389—21no—
28C11×#385—22no—
29C11×#382C2211yescharacteristic
30C11×#328—22no—
31C11×Q8⋊C8—22no—
32C11×D4⋊C8—22no—
33C22×Q8×C11D411yescharacteristic
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C2×C11×Q16—22no—
37C2×C11×M16—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C11×#117—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C11×#107—22no—
65C11×#107—22no—
66C11×#106—22no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×#103—22no—
72C11×#103—22no—
73C11×#102—22no—
74C11×#102—22no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8—21no—
77C4×C8×C11—21no—
78C4×C8×C11D412yes—
79C11×#95—22no—
80C11×#95—21no—
81C11×#95D412yes—
82#10002C1111yesmaximal, characteristic, direct product factor, Sylow
83C24×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—42no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11Q1612yescomplemented
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—82no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C11×Q16—44no—
106C11×M16—41no—
107C11×M16—41no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—82no—
126C11×C22⋊C4—44no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—82no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11—41no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138#3104C2×C1111yescharacteristic, complemented
139#3077C2×C1111yescharacteristic
140#2580C2×C1111yescharacteristic
141#1518C2×C1111yescharacteristic, complemented
142#1487C2×C1111yescharacteristic, complemented
143#1478C2×C1111yescharacteristic
144#1286C2×C1111yescharacteristic, complemented
145C23×C11—22no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151Q8×C11—22no—
152Q8×C11—22no—
153Q8×C11—41no—
154Q8×C11—41no—
155Q8×C11—42no—
156Q8×C11—81no—
157D4×C11—22no—
158D4×C11—22no—
159D4×C11—41no—
160D4×C11—41no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12711yescharacteristic
184C2×C4×C11C2×Q1611yescharacteristic
185C2×C4×C11#13511yescharacteristic
186C2×C4×C11#13711yescharacteristic
187C2×C4×C11#13711yescharacteristic
188C8×C11—42no—
189C8×C11—42no—
190C8×C11—81no—
191#533C22×C1111yescharacteristic
192C2×C4×Q8C22×C1111yescharacteristic
193C2×C4×D4C22×C1111yescharacteristic
194#484—21no—
195#478—22no—
196#477—21no—
197#476—21no—
198#474—21no—
199#462—21no—
200#451—21no—
201C4×Q16—22no—
202#431C22×C1111yescharacteristic
203#431C22×C1111yescharacteristic
204#428—21no—
205#423C22×C1111yescharacteristic
206#418—21no—
207#399—21no—
208#393—21no—
209#390—21no—
210#389—21no—
211#385—22no—
212#382C22×C1111yescharacteristic
213#328—22no—
214Q8⋊C8—22no—
215D4⋊C8—22no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—44no—
219C22×C11—42no—
220C22×C11—82no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11#39211yescharacteristic
224C22×C11#45111yescharacteristic
225C22×C11#45211yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231C4×C11—82no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235C4×C11—81no—
236C4×C11#45111yescharacteristic
237C4×C11#45211yescharacteristic
238C4×C11#46711yescharacteristic
239C4×C11#47011yescharacteristic
240C22×Q8D4×C1111yescharacteristic
241C22×D4D4×C1111yescharacteristic
242C23×C4—21no—
243C2×Q16—22no—
244C2×M16—21no—
245C4⋊Q8D4×C1111yescharacteristic
246C4⋊Q8D4×C1111yescharacteristic
247#125—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260#117—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4D4×C1111yescharacteristic
265C2×C4⋊C4D4×C1111yescharacteristic
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—22no—
269C2×C42—21no—
270C2×C42C23×C1111yescharacteristic
271#107—22no—
272#107—22no—
273#106—22no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8D4×C1112yes—
278#103—22no—
279#103—22no—
280#102—22no—
281#102—22no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C4×C8—21no—
285C4×C8D4×C1112yes—
286#95—22no—
287#95—21no—
288#95D4×C1112yes—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—82no—
292C2×C11#200111yescharacteristic
293C2×C11#200811yescharacteristic
294C2×C11#201011yescharacteristic
295C24—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—42no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4C11×Q1612yescomplemented
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—82no—
314C22×C4C2×D4×C1111yescharacteristic
315C22×C4C2×D4×C1111yescharacteristic
316C22×C4C2×D4×C1111yescharacteristic
317Q16—44no—
318M16—41no—
319M16—41no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—41no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—82no—
338C22⋊C4—44no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—82no—
343C42—41no—
344C42—41no—
345C42—41no—
346C42C2×D4×C1111yescharacteristic
347C42C2×D4×C1111yescharacteristic
348C42C2×D4×C1111yescharacteristic
349C42C11×#4111yescharacteristic
350C11#1000211yescharacteristic, direct product factor, Sylow
351C23—22no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23C11×#12011yescharacteristic
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—81no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4C11×#12011yescharacteristic
385C2×C4C11×#12011yescharacteristic
386C2×C4C11×#12111yescharacteristic
387C2×C4C11×#12111yescharacteristic
388C2×C4C11×#12111yescharacteristic
389C2×C4C11×#12711yescharacteristic
390C2×C4C2×C11×Q1611yescharacteristic
391C2×C4C11×#13511yescharacteristic
392C2×C4C11×#13711yescharacteristic
393C2×C4C11×#13711yescharacteristic
394C8—42no—
395C8—42no—
396C8—81no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—42no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22C11×#39211yescharacteristic
405C22C11×#45111yescharacteristic
406C22C11×#45211yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—82no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4C11×#45111yescharacteristic
418C4C11×#45211yescharacteristic
419C4C11×#46711yescharacteristic
420C4C11×#47011yescharacteristic
421C2—21no—
422C2—21no—
423C2—82no—
424C2C11×#200111yescharacteristic
425C2C11×#200811yescharacteristic
426C2C11×#201011yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC2×C42C23×C11
prime radicalC22×D4×C11D4
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
1. C11×#3104C2semidirect
4. C11×#1518C2semidirect
5. C11×#1487C2semidirect
7. C11×#1286C2semidirect
82. #10002C11direct (N × H)
94. C2×D4×C11Q16semidirect
138. #3104C2×C11semidirect
141. #1518C2×C11semidirect
142. #1487C2×C11semidirect
144. #1286C2×C11semidirect
306. C2×D4C11×Q16semidirect
350. C11#10002direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31042
C11×#30772
C11×#25802
C11×#15182
C11×#14872
C11×#14782
C11×#12862
#1000211