Finite Group Databasebeta

← C11×#12219 #14589412

Subgroups — C11×#12219 #14589412

Order 2816.

370 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2841C211yesmaximal, characteristic
2C11×#2030C211yesmaximal, characteristic
3C11×#1614C211yesmaximal, characteristic
4C11×#1602C211yesmaximal, characteristic
5C11×#1352C211yesmaximal, characteristic
6C11×#1351C211yesmaximal, characteristic
7C11×#1317C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#484—21no—
10C11×#451—21no—
11C11×#400—21no—
12C11×#399C2211yescharacteristic
13C11×#398—21no—
14C11×#398—21no—
15C11×#396—21no—
16C11×#395—21no—
17C11×#393C2211yescharacteristic
18C11×#381—21no—
19C11×#381C2211yescharacteristic
20C11×#380—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23C11×#328—21no—
24C11×#328—21no—
25C11×#323C2211yescharacteristic
26C11×#323C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C2×C11×Q16—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—41no—
33C11×C22⋊Q8—41no—
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—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4C2311yescharacteristic
47C11×#107—41no—
48C11×#103—41no—
49C11×#103—41no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—41no—
59C11×#95—41no—
60C11×#95D411yescharacteristic
61C11×#95D411yescharacteristic
62#12219C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11Q1612yescomplemented
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C11×Q16—82no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—81no—
92C11×C4⋊C4—81no—
93C11×C4⋊C4—81no—
94C11×C4⋊C4—81no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4—81no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105#2841C2×C1111yescharacteristic
106#2030C2×C1111yescharacteristic
107#1614C2×C1111yescharacteristic
108#1602C2×C1111yescharacteristic
109#1352C2×C1111yescharacteristic
110#1351C2×C1111yescharacteristic
111#1317C2×C1111yescharacteristic
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11#12011yescharacteristic
117C23×C11C2×Q1611yescharacteristic
118C23×C11#13711yescharacteristic
119Q8×C11—42no—
120Q8×C11—81no—
121Q8×C11—81no—
122Q8×C11—81no—
123C2×C4×C11—22no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—81no—
151C2×C4×C11—81no—
152C2×C4×C11—81no—
153C2×C4×C11—81no—
154C8×C11—81no—
155C8×C11—81no—
156#543C22×C1111yescharacteristic
157#484—21no—
158#451—21no—
159#400—21no—
160#399C22×C1111yescharacteristic
161#398—21no—
162#398—21no—
163#396—21no—
164#395—21no—
165#393C22×C1111yescharacteristic
166#381—21no—
167#381C22×C1111yescharacteristic
168#380—21no—
169#342—21no—
170#342C22×C1111yescharacteristic
171#328—21no—
172#328—21no—
173#323C22×C1111yescharacteristic
174#323C22×C1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—81no—
184C22×C11#45111yescharacteristic
185C22×C11#45511yescharacteristic
186C22×C11B(4,𝔽2)11yescharacteristic
187C4×C11—42no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—81no—
191C4×C11—81no—
192C4×C11—81no—
193C4×C11—81no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—161no—
198C22×Q8D4×C1111yescharacteristic
199C23×C4D4×C1111yescharacteristic
200C2×Q16—41no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4D4×C1111yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4D4×C1111yescharacteristic
217C2×C22⋊C4C23×C1111yescharacteristic
218#107—41no—
219#103—41no—
220#103—41no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—41no—
230#95—41no—
231#95D4×C1111yescharacteristic
232#95D4×C1111yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—41no—
236C2×C11—41no—
237C2×C11#160211yescharacteristic
238C2×C11#220011yescharacteristic
239C2×C11#220111yescharacteristic
240C24C2×D4×C1111yescharacteristic
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—81no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C11×Q1612yescomplemented
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260Q16—82no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C11#1221911yescharacteristic, direct product factor, Sylow
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23C11×#12011yescharacteristic
288C23C2×C11×Q1611yescharacteristic
289C23C11×#13711yescharacteristic
290Q8—42no—
291Q8—81no—
292Q8—81no—
293Q8—81no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C8—81no—
326C8—81no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22C11×#45111yescharacteristic
337C22C11×#45511yescharacteristic
338C22C11×B(4,𝔽2)11yescharacteristic
339C4—41no—
340C4—41no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—161no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2C11×#160211yescharacteristic
355C2C11×#220011yescharacteristic
356C2C11×#220111yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
62. #12219C11direct (N × H)
80. C22×C4×C11Q16semidirect
257. C22×C4C11×Q16semidirect
282. C11#12219direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28412
C11×#20302
C11×#16142
C11×#16022
C11×#13522
C11×#13512
C11×#13172
#1221911