Finite Group Databasebeta

← C11×#13462 #14590655

Subgroups — C11×#13462 #14590655

Order 2816.

476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2748C211yesmaximal, characteristic
2C11×#1867C211yesmaximal, characteristic
3C11×#1867C211yesmaximal, characteristic
4C11×#1856C211yesmaximal, characteristic
5C11×#1393C211yesmaximal, characteristic
6C11×#1390C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic
8C11×#518C2211yescharacteristic
9C11×#428—21no—
10C2×C11×#100C2211yescharacteristic
11C2×C11×#99C2211yescharacteristic
12C2×C11×#99C2211yescharacteristic
13C11×#399—21no—
14C11×#398—21no—
15C11×#396—21no—
16C11×#390C2211yescharacteristic
17C11×#387—21no—
18C11×#386C2211yescharacteristic
19C11×#386C2211yescharacteristic
20C11×#385—21no—
21C11×#385—21no—
22C11×#385—21no—
23C11×#380—21no—
24C11×#342—21no—
25C11×#342—21no—
26C11×#339—21no—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C2×C11×M16—21no—
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C11×#117—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—41no—
40C2×C11×C4⋊C4—41no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4D411yescharacteristic
51C2×C11×C22⋊C4D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C11×#107—41no—
54C11×#106—41no—
55C11×#100—21no—
56C11×#100Q812yes—
57C11×#99—21no—
58C11×#99—21no—
59C11×#99Q812yes—
60C11×#99Q812yes—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—41no—
67C11×#95—41no—
68#13462C1111yesmaximal, characteristic, direct product factor, Sylow
69C24×C11C2×D411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11C2×Q811yescharacteristic
74C2×D4×C11C2×Q811yescharacteristic
75C2×D4×C11C2×Q811yescharacteristic
76C2×D4×C11#4111yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—81no—
93C22×C4×C11C2×D411yescharacteristic
94C11×M16—22no—
95C11×M16—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—81no—
102C11×C4⋊C4—81no—
103C11×C4⋊C4—81no—
104C11×C4⋊C4—81no—
105C11×C4⋊C4—82no—
106C11×C4⋊C4—82no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—81no—
118C11×C22⋊C4—81no—
119C11×C22⋊C4—81no—
120C42×C11—41no—
121C42×C11—41no—
122#2748C2×C1111yescharacteristic
123#1867C2×C1111yescharacteristic
124#1867C2×C1111yescharacteristic
125#1856C2×C1111yescharacteristic
126#1393C2×C1111yescharacteristic
127#1390C2×C1111yescharacteristic
128#1390C2×C1111yescharacteristic
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11#12011yescharacteristic
138C23×C11C22⋊Q811yescharacteristic
139C23×C11C22⋊Q811yescharacteristic
140C23×C11C4⋊Q811yescharacteristic
141C23×C11C4⋊Q811yescharacteristic
142D4×C11—41no—
143D4×C11—41no—
144D4×C11—41no—
145D4×C11—41no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11C22⋊Q811yescharacteristic
183C2×C4×C11C4⋊Q811yescharacteristic
184C8×C11—42no—
185#518C22×C1111yescharacteristic
186#428—21no—
187C2×#100C22×C1111yescharacteristic
188C2×#99C22×C1111yescharacteristic
189C2×#99C22×C1111yescharacteristic
190#399—21no—
191#398—21no—
192#396—21no—
193#390C22×C1111yescharacteristic
194#387—21no—
195#386C22×C1111yescharacteristic
196#386C22×C1111yescharacteristic
197#385—21no—
198#385—21no—
199#385—21no—
200#380—21no—
201#342—21no—
202#342—21no—
203#339—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39511yescharacteristic
221C22×C11B(4,𝔽2)11yescharacteristic
222C22×C11#45811yescharacteristic
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11—81no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—82no—
230C4×C11—82no—
231C4×C11—81no—
232C4×C11—81no—
233C4×C11—81no—
234C4×C11—81no—
235C22×D4C23×C1111yescharacteristic
236C23×C4D4×C1111yescharacteristic
237C23×C4D4×C1111yescharacteristic
238C2×M16—21no—
239C4×D4—41no—
240C4×D4—41no—
241#117—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4D4×C1111yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4D4×C1111yescharacteristic
259C2×C22⋊C4D4×C1111yescharacteristic
260C2×C42D4×C1111yescharacteristic
261#107—41no—
262#106—41no—
263#100—21no—
264#100Q8×C1112yes—
265#99—21no—
266#99—21no—
267#99Q8×C1112yes—
268#99Q8×C1112yes—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—41no—
275#95—41no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—41no—
279C2×C11—41no—
280C2×C11—41no—
281C2×C11—41no—
282C2×C11#206211yescharacteristic
283C2×C11#219711yescharacteristic
284C2×C11#220011yescharacteristic
285C24C2×D4×C1111yescharacteristic
286C24C2×D4×C1111yescharacteristic
287C2×D4—41no—
288C2×D4—41no—
289C2×D4C2×Q8×C1111yescharacteristic
290C2×D4C2×Q8×C1111yescharacteristic
291C2×D4C2×Q8×C1111yescharacteristic
292C2×D4C11×#4111yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—81no—
309C22×C4C2×D4×C1111yescharacteristic
310M16—22no—
311M16—41no—
312C2×C8—41no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—81no—
318C4⋊C4—81no—
319C4⋊C4—81no—
320C4⋊C4—81no—
321C4⋊C4—82no—
322C4⋊C4—82no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—42no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C42—41no—
337C42—41no—
338C11#1346211yescharacteristic, direct product factor, Sylow
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23C11×#12011yescharacteristic
348C23C11×C22⋊Q811yescharacteristic
349C23C11×C22⋊Q811yescharacteristic
350C23C11×C4⋊Q811yescharacteristic
351C23C11×C4⋊Q811yescharacteristic
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4C11×C22⋊Q811yescharacteristic
393C2×C4C11×C4⋊Q811yescharacteristic
394C8—42no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22C11×#39511yescharacteristic
412C22C11×B(4,𝔽2)11yescharacteristic
413C22C11×#45811yescharacteristic
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—82no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—81no—
425C4—81no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2—41no—
431C2—41no—
432C2C11×#206211yescharacteristic
433C2C11×#219711yescharacteristic
434C2C11×#220011yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
68. #13462C11direct (N × H)
338. C11#13462direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#27482
C11×#18672
C11×#18562
C11×#13932
C11×#13902
#1346211