Finite Group Databasebeta

← #14900653

Subgroups — #14900653

Order 2816.

628 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 127 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#13069793C212yesmaximal, complemented
3#13069783C211yesmaximal, characteristic, complemented
4#13069159C212yesmaximal
5#13069075C212yesmaximal, complemented
6#13069030C212yesmaximal, complemented
7#13068722C212yesmaximal, complemented
8#13068691C211yesmaximal, characteristic, complemented
9C11×#2022C211yesmaximal, characteristic
10C11×#534C2211yescharacteristic
11C2×C11×#123C2212yes—
12#10623329C2212yes—
13C2×#66979C2211yescharacteristic
14#10623014C2211yescharacteristic
15C2×C11×#99C2212yes—
16C11×#381C2211yescharacteristic
17C2×#66898C2212yes—
18C2×#66898C2212yes—
19C2×#66898C2212yes—
20#10622824C2212yes—
21#10622824C2211yescharacteristic
22C11×#342C2211yescharacteristic
23#10622165C2212yes—
24#10622165C2212yes—
25#10622165C2212yes—
26#10622165C2212yes—
27#10622165C2212yes—
28#10622164C2212yes—
29#10622164C2212yes—
30#10622164C2211yescharacteristic
31C22×D4×C11C2312yes—
32C23×C4×C11C2311yescharacteristic
33C11×#123—22no—
34C11×#123—22no—
35C11×#123—22no—
36C11×#123—42no—
37C11×#121—41no—
38C11×#120—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4C2311yescharacteristic
42C2×C11×C22⋊C4C2312yes—
43C2×C11×C22⋊C4C2311yescharacteristic
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11C2312yes—
46C2×C22⋊Dic11C2312yes—
47C2×C22⋊Dic11C2312yes—
48C2×C22⋊Dic11C2312yes—
49D4×Dic11—42no—
50D4×Dic11—42no—
51#66979—22no—
52#66979—41no—
53#66979—41no—
54C2×C4⋊Dic11—21no—
55#66977—41no—
56C2×C4×Dic11—21no—
57#66931—42no—
58C11×#99—42no—
59C11×#95—41no—
60#66898—42no—
61#66898—42no—
62#66898—42no—
63C11⋊#95—42no—
64C11⋊#95—41no—
65#32701—111nomaximal, Sylow
66C24×C11#4112yes—
67C24×C11C2411yescharacteristic
68C2×D4×C11—22no—
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—41no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4112yes—
85C22×Dic11—22no—
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—42no—
90C2×Dic22—41no—
91C11×C4⋊C4—42no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C22⋊Dic11—22no—
102C22⋊Dic11—22no—
103C22⋊Dic11—22no—
104C22⋊Dic11—22no—
105C22⋊Dic11—22no—
106C22⋊Dic11—22no—
107C22⋊Dic11—22no—
108C22⋊Dic11—22no—
109C22⋊Dic11—42no—
110C4⋊Dic11—42no—
111C4⋊Dic11—42no—
112C4⋊Dic11—41no—
113Dic11⋊C4—42no—
114C4×Dic11—42no—
115C4×Dic11—42no—
116#2104—112no—
117#2032—112no—
118#2030—111no—
119#2022D1111yescharacteristic
120#1913—112no—
121#1899—112no—
122#1890—112no—
123#1828—112no—
124#1820—111no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—81no—
129C23×C11—82no—
130C23×C11C2×#4112yes—
131C23×C11C2×#4111yescharacteristic
132C23×C11H(5,𝔽2)11yescharacteristic
133C23×C11H(5,𝔽2)12yes—
134C23×C11H(5,𝔽2)11yescharacteristic
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—161no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161C2×Dic11—82no—
162C2×Dic11—82no—
163C2×Dic11—82no—
164C2×Dic11—162no—
165Dic22—161no—
166#543—111no—
167#534C2×D1111yescharacteristic
168C2×#123C2×D1112yes—
169#518—112no—
170C2×#117—111no—
171C2×#99—112no—
172C2×#99—112no—
173C2×#99—112no—
174C2×#99C2×D1112yes—
175#381—111no—
176#381—112no—
177#381C2×D1111yescharacteristic
178#342—112no—
179#342—112no—
180#342—111no—
181#342—112no—
182#342—112no—
183#342—112no—
184#342—112no—
185#342—112no—
186#342C2×D1111yescharacteristic
187C22×C11—41no—
188C22×C11—42no—
189C22×C11—41no—
190C22×C11—42no—
191C22×C11—41no—
192C22×C11—42no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11#53811yescharacteristic
197C22×C11#53812yes—
198C22×C11#55112yes—
199C22×C11#55111yescharacteristic
200C22×C11#56011yescharacteristic
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—42no—
204C4×C11—82no—
205C4×C11—81no—
206C4×C11—81no—
207Dic11—82no—
208Dic11—82no—
209Dic11—82no—
210Dic11—82no—
211C22×D4C22×D1112yes—
212C23×C4C22×D1111yescharacteristic
213#123—22no—
214#123—22no—
215#123—22no—
216#123—42no—
217C22⋊Q8—442no—
218C22⋊Q8—441no—
219#121—41no—
220#120—22no—
221C4×D4—442no—
222C4×D4—442no—
223#117—222no—
224#117—441no—
225#117—441no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—221no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—112no—
230C2×C22⋊C4—112no—
231C2×C22⋊C4—112no—
232C2×C22⋊C4—112no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4C22×D1112yes—
235C2×C22⋊C4C22×D1111yescharacteristic
236C2×C22⋊C4C22×D1111yescharacteristic
237C2×C42—221no—
238#99—42no—
239#99—442no—
240#99—442no—
241#99—442no—
242#95—41no—
243#95—442no—
244#95—441no—
245C2×C11—21no—
246C2×C11—22no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—22no—
250C2×C11—82no—
251C2×C11#276011yescharacteristic
252C24#434112yes—
253C24C23×D1111yescharacteristic
254C2×Q8—441no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—222no—
270C22×C4—222no—
271C22×C4—222no—
272C22×C4—222no—
273C22×C4—442no—
274C22×C4#434111yescharacteristic
275C22×C4#434112yes—
276C22×C4#434111yescharacteristic
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—442no—
281C4⋊C4—442no—
282C4⋊C4—442no—
283C4⋊C4—441no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—222no—
292C22⋊C4—222no—
293C22⋊C4—222no—
294C22⋊C4—222no—
295C22⋊C4—222no—
296C22⋊C4—222no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C22⋊C4—442no—
300C42—442no—
301C42—442no—
302C11#3270111yescharacteristic, complemented, Sylow
303C23—22no—
304C23—22no—
305C23—22no—
306C23—81no—
307C23—82no—
308C23C2×#434111yescharacteristic
309C23C2×#434112yes—
310C23#6703712yes—
311C23#6703711yescharacteristic
312C23#6704211yescharacteristic
313Q8—1761no—
314D4—42no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—161no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—82no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—882no—
340C2×C4—882no—
341C2×C4—882no—
342C2×C4—882no—
343C2×C4—1762no—
344C22—41no—
345C22—42no—
346C22—41no—
347C22—42no—
348C22—41no—
349C22—42no—
350C22—82no—
351C22—82no—
352C22—82no—
353C22#1062311812yes—
354C22#1062311811yescharacteristic
355C22#1062314811yescharacteristic
356C22#1062314812yes—
357C22#1062325111yescharacteristic
358C4—41no—
359C4—41no—
360C4—42no—
361C4—81no—
362C4—81no—
363C4—82no—
364C4—882no—
365C4—882no—
366C4—882no—
367C4—882no—
368C2—21no—
369C2—21no—
370C2—22no—
371C2—22no—
372C2—21no—
373C2—82no—
374C2#1307599511yescharacteristic
subgroupG/H
centerC2#13075995
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#2022C2
socleC2×C11#2760
prime radicalC11×#534C22
hypercenter#2022D11
hypocenterC11#32701
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C24 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. C11⋊#2104C2semidirect
2. #13069793C2semidirect
3. #13069783C2semidirect
5. #13069075C2semidirect
6. #13069030C2semidirect
7. #13068722C2semidirect
8. #13068691C2semidirect
302. C11#32701semidirect

Maximal subgroups

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

subgroupindex
C11⋊#21042
#130697932
#130697832
#130691592
#130690752
#130690302
#130687222
#130686912
C11×#20222
#3270111