Finite Group Databasebeta

← #14900654

Subgroups — #14900654

Order 2816.

628 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 123 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⋊#2104C212yesmaximal, complemented
2#13069792C212yesmaximal, complemented
3#13069747C211yesmaximal, characteristic
4#13069157C212yesmaximal
5#13069072C212yesmaximal, complemented
6#13069026C212yesmaximal, complemented
7#13068723C212yesmaximal, complemented
8#13068691C211yesmaximal, characteristic, complemented
9C11×#2030C211yesmaximal, characteristic, complemented
10C11×#543C2211yescharacteristic
11C2×#66982C2212yes—
12C2×#66979C2211yescharacteristic
13#10623024C2211yescharacteristic
14#10623017C2212yes—
15C11×#381C2212yes—
16C11×#381C2211yescharacteristic
17#10622824C2211yescharacteristic
18C2×#66870C2212yes—
19C2×#66870C2212yes—
20C2×#66870C2212yes—
21C2×#66870C2212yes—
22C11×#342C2212yes—
23C11×#342C2211yescharacteristic
24#10622165C2212yes—
25#10622165C2212yes—
26#10622165C2212yes—
27#10622165C2212yes—
28#10622165C2212yes—
29#10622164C2211yescharacteristic
30#10622164C2212yes—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11C2312yes—
33C11×C22⋊Q8—42no—
34C11×C22⋊Q8—41no—
35C2×C11×C22⋊C4C2312yes—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C11×C22⋊C4C2312yes—
38C2×C11×C22⋊C4C2311yescharacteristic
39C2×C22⋊Dic11C2312yes—
40C2×C22⋊Dic11C2312yes—
41C2×C22⋊Dic11C2312yes—
42#66983—41no—
43#66982—22no—
44#66982—22no—
45#66982—42no—
46C4×C22⋊D11—42no—
47C2×(C2×D11)⋊C4—22no—
48#66979—41no—
49#66979—41no—
50C2×C4⋊Dic11—21no—
51C2×Dic11⋊C4—22no—
52C2×C4×Dic11—21no—
53#66939—22no—
54#66935—22no—
55(C22⋊D11)⋊C4—42no—
56C22⋊C4×D11—22no—
57#66930—22no—
58C11×#95—41no—
59C11×#95—42no—
60C11⋊#95—41no—
61#66870—42no—
62#66870—42no—
63#66870—42no—
64#66870—42no—
65#32701—111nomaximal, Sylow
66C24×C11C2411yescharacteristic
67C23×D11#4112yes—
68C2×Q8×C11—41no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—22no—
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11#4112yes—
89C2×D44—41no—
90C2×C4×D11—42no—
91C11×C4⋊C4—43no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C22⋊Dic11—22no—
99C22⋊Dic11—22no—
100C22⋊Dic11—22no—
101C22⋊Dic11—22no—
102C22⋊Dic11—22no—
103C22⋊Dic11—22no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108C4⋊Dic11—42no—
109C4⋊Dic11—41no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—42no—
114C4×Dic11—42no—
115#2104—112no—
116#2032—112no—
117#2030D1111yescharacteristic, complemented
118#2022—111no—
119#1913—112no—
120#1899—112no—
121#1890—112no—
122#1828—112no—
123#1820—111no—
124C23×C11—81no—
125C23×C11C2×#4111yescharacteristic
126C23×C11C2×#4112yes—
127C23×C11H(5,𝔽2)12yes—
128C23×C11H(5,𝔽2)11yescharacteristic
129C23×C11H(5,𝔽2)11yescharacteristic
130C22×D11—22no—
131C22×D11—22no—
132C22×D11—22no—
133C22×D11—82no—
134Q8×C11—161no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—81no—
147C2×C4×C11—82no—
148C2×C4×C11—82no—
149C2×C4×C11—81no—
150C22⋊D11—42no—
151C22⋊D11—42no—
152C22⋊D11—42no—
153C22⋊D11—42no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C2×Dic11—82no—
163D44—161no—
164C4×D11—162no—
165#543C2×D1111yescharacteristic
166#534—111no—
167C2×#123—112no—
168#518—112no—
169C2×#117—111no—
170C2×#99—112no—
171C2×#99—112no—
172C2×#99—112no—
173C2×#99—112no—
174#381—111no—
175#381C2×D1111yescharacteristic
176#381C2×D1112yes—
177#342—112no—
178#342—112no—
179#342—112no—
180#342—112no—
181#342—111no—
182#342—112no—
183#342—112no—
184#342C2×D1111yescharacteristic
185#342C2×D1112yes—
186C22×C11—41no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11#53811yescharacteristic
192C22×C11#53812yes—
193C22×C11#55112yes—
194C22×C11#55111yescharacteristic
195C22×C11#56011yescharacteristic
196C2×D11—42no—
197C2×D11—82no—
198C2×D11—82no—
199C2×D11—82no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—81no—
203C4×C11—82no—
204C4×C11—82no—
205C4×C11—81no—
206Dic11—42no—
207Dic11—82no—
208Dic11—82no—
209Dic11—82no—
210C22×D4—112no—
211C23×C4C22×D1111yescharacteristic
212#123—222no—
213#123—222no—
214#123—222no—
215#123—442no—
216C22⋊Q8—42no—
217C22⋊Q8—41no—
218#121—441no—
219#120—222no—
220C4×D4—442no—
221C4×D4—442no—
222#117—222no—
223#117—441no—
224#117—441no—
225C2×C4⋊C4—222no—
226C2×C4⋊C4—221no—
227C2×C22⋊C4—112no—
228C2×C22⋊C4—112no—
229C2×C22⋊C4—112no—
230C2×C22⋊C4—222no—
231C2×C22⋊C4—222no—
232C2×C22⋊C4C22×D1112yes—
233C2×C22⋊C4C22×D1111yescharacteristic
234C2×C22⋊C4C22×D1111yescharacteristic
235C2×C22⋊C4C22×D1112yes—
236C2×C42—221no—
237#99—442no—
238#99—442no—
239#99—442no—
240#99—442no—
241#95—41no—
242#95—42no—
243#95—441no—
244C2×C11—21no—
245C2×C11—22no—
246C2×C11—22no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11#276011yescharacteristic
250D11—82no—
251C24—112no—
252C24C23×D1111yescharacteristic
253C2×Q8—41no—
254C2×D4—222no—
255C2×D4—222no—
256C2×D4—222no—
257C2×D4—222no—
258C2×D4—222no—
259C2×D4—222no—
260C2×D4—441no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—112no—
270C22×C4—222no—
271C22×C4—222no—
272C22×C4—222no—
273C22×C4—442no—
274C22×C4#434311yescharacteristic
275C22×C4#434311yescharacteristic
276C4⋊C4—43no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C4⋊C4—442no—
280C4⋊C4—441no—
281C4⋊C4—442no—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—222no—
289C22⋊C4—222no—
290C22⋊C4—222no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—222no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—442no—
297C22⋊C4—442no—
298C42—442no—
299C42—442no—
300C11#3270111yescharacteristic, complemented, Sylow
301C23—81no—
302C23—222no—
303C23—222no—
304C23—222no—
305C23—882no—
306C23#6703712yes—
307C23#6703711yescharacteristic
308C23C2×#434311yescharacteristic
309C23#41×D1112yes—
310C23#6704211yescharacteristic
311Q8—161no—
312D4—442no—
313D4—442no—
314D4—442no—
315D4—442no—
316D4—1761no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—82no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4—81no—
332C2×C4—222no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—882no—
339C2×C4—882no—
340C2×C4—882no—
341C2×C4—1762no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—442no—
348C22—882no—
349C22—882no—
350C22—882no—
351C22#1062312611yescharacteristic
352C22#1062316812yes—
353C22#1062317511yescharacteristic
354C22#1062320912yes—
355C22#1062321011yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—81no—
360C4—81no—
361C4—82no—
362C4—442no—
363C4—882no—
364C4—882no—
365C4—882no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—21no—
370C2—22no—
371C2—882no—
372C2#1307599111yescharacteristic
subgroupG/H
centerC2#13075991
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2030C2
socleC2×C11#2760
prime radical#10623024C22
hypercenter#2030D11
hypocenterC11#32701
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C24 ◁ #2030

Complements

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

NH ≅ G/Ntype
1. C11⋊#2104C2semidirect
2. #13069792C2semidirect
5. #13069072C2semidirect
6. #13069026C2semidirect
7. #13068723C2semidirect
8. #13068691C2semidirect
9. C11×#2030C2semidirect
117. #2030D11semidirect
300. C11#32701semidirect

Maximal subgroups

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

subgroupindex
C11⋊#21042
#130697922
#130697472
#130691572
#130690722
#130690262
#130687232
#130686912
C11×#20302
#3270111