Finite Group Databasebeta

← #14642971

Subgroups — #14642971

Order 2816.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#13076609C211yesmaximal, characteristic
2#13070158C211yesmaximal, characteristic
3#13070026C211yesmaximal, characteristic
4#13070024C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic
6#13066441C211yesmaximal, characteristic
7C11×#1272C211yesmaximal, characteristic
8C11×#391C2211yescharacteristic
9#10622843—21no—
10C2×#66899—21no—
11C2×#66881—21no—
12C2×#66880—21no—
13C2×#66880—21no—
14#10622592—21no—
15#10622548C2211yescharacteristic
16#10622542C2211yescharacteristic
17#10622542C2211yescharacteristic
18#10622269—21no—
19#10622269—21no—
20#10622259—21no—
21#10622259—21no—
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622167—21no—
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Dic22—21no—
29C22×Dic22D411yescharacteristic
30C22×Dic22D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2311yescharacteristic
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C22×C11⋊C8—21no—
45C11×#95—21no—
46C11×#95—21no—
47#66899—42no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66881—42no—
56#66880—42no—
57#66880—42no—
58#7812—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11SD1612yes—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—81no—
80C2×Dic22—81no—
81C2×Dic22—81no—
82C2×Dic22SD1612yes—
83C2×Dic22Q1612yes—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—41no—
91C42×C11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—81no—
101Dic11⋊C4—81no—
102Dic11⋊C4—81no—
103C4×Dic11—81no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2811—111no—
108#2096—111no—
109#2072—111no—
110#2072—111no—
111#1272—111no—
112#1272—111no—
113#1272D1111yescharacteristic
114C23×C11#12011yescharacteristic
115Q8×C11—42no—
116Q8×C11—81no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11C2×SD1611yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11C2×Q1611yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×C4×C11#13711yescharacteristic
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150Dic22—42no—
151Dic22—42no—
152Dic22—81no—
153Dic22—81no—
154Dic22—84no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—81no—
158C2×#106—221no—
159C2×#103—221no—
160C2×#103—221no—
161C2×#103—221no—
162#395—221no—
163#395—221no—
164#395—221no—
165#391—111no—
166#391—111no—
167#391—221no—
168#391—221no—
169#391—221no—
170#391C2×D1111yescharacteristic
171#384—111no—
172#340—221no—
173#340—221no—
174#336—111no—
175#336C2×D1111yescharacteristic
176#336C2×D1111yescharacteristic
177C22×C11#44811yescharacteristic
178C22×C11#44811yescharacteristic
179C22×C11#45111yescharacteristic
180C22×C11#45311yescharacteristic
181C22×C11#45511yescharacteristic
182C22×C11#45511yescharacteristic
183C22×C11#45811yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11—81no—
192Dic11—42no—
193Dic11—42no—
194Dic11—81no—
195Dic11—81no—
196Dic11—161no—
197C22×Q8—111no—
198C22×Q8—111no—
199C22×Q8—221no—
200C22×Q8D4411yescharacteristic
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—221no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4D4411yescharacteristic
213C2×C42—221no—
214C2×C42C22×D1111yescharacteristic
215#106—442no—
216#103—442no—
217#103—442no—
218#103—442no—
219#95—21no—
220#95—21no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228C2×C11#160811yescharacteristic
229C2×C11#160811yescharacteristic
230C2×C11#161411yescharacteristic
231C2×C11#162311yescharacteristic
232C2×C11#164511yescharacteristic
233C2×C11#164511yescharacteristic
234C2×C11#165911yescharacteristic
235C2×Q8—21no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—112no—
239C2×Q8—112no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×Q8—441no—
243C2×Q8—441no—
244C2×Q8—441no—
245C2×Q8—441no—
246C2×Q8—881no—
247C2×Q8—881no—
248C2×Q8—881no—
249C2×Q8#431412yes—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—441no—
257C22×C4C2×D4411yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—441no—
267C2×C8—441no—
268C2×C8—441no—
269C4⋊C4—41no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—881no—
279C4⋊C4—881no—
280C4⋊C4—881no—
281C42—41no—
282C42—881no—
283C11#781211yescharacteristic, complemented, Sylow
284C23#6693511yescharacteristic
285Q8—42no—
286Q8—81no—
287Q8—442no—
288Q8—442no—
289Q8—881no—
290Q8—881no—
291Q8—884no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4C2×#431411yescharacteristic
320C2×C4#6696211yescharacteristic
321C2×C4SD16×D1111yescharacteristic
322C2×C4#6696811yescharacteristic
323C2×C4Q16×D1111yescharacteristic
324C2×C4#6697111yescharacteristic
325C8—42no—
326C8—81no—
327C8—881no—
328C22#1062235111yescharacteristic
329C22#1062235511yescharacteristic
330C22#1062235911yescharacteristic
331C22#1062241911yescharacteristic
332C22#1062242111yescharacteristic
333C22#1062243511yescharacteristic
334C22#1062243811yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—442no—
344C4—442no—
345C4—881no—
346C4—881no—
347C4—1761no—
348C2#1306760811yescharacteristic
349C2#1306760911yescharacteristic
350C2#1306764211yescharacteristic
351C2#1306769611yescharacteristic
352C2#1306783811yescharacteristic
353C2#1306783911yescharacteristic
354C2#1306792411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11#120
hypercenter#1272D11
hypocenterC11#7812
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
283. C11#7812semidirect

Maximal subgroups

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

subgroupindex
#130766092
#130701582
#130700262
#130700242
#130664412
C11×#12722
#781211