Finite Group Databasebeta

← #14642962

Subgroups — #14642962

Order 2816.

380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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#13076596C211yesmaximal, characteristic
2#13070173C211yesmaximal, characteristic, complemented
3#13070025C211yesmaximal, characteristic, complemented
4#13066441C211yesmaximal, characteristic, complemented
5#13066440C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic
7C11×#2071C211yesmaximal, characteristic
8C2×C11×#102—21no—
9C11×#390C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622835—21no—
12#10622591—21no—
13C2×#66874—21no—
14#10622566—21no—
15#10622564—21no—
16#10622564—21no—
17#10622560—21no—
18#10622542C2211yescharacteristic
19#10622541C2211yescharacteristic
20C11×#340—21no—
21C11×#336C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C11×#102—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66874—42no—
56#7811—111nomaximal, Sylow
57C24×C11—21no—
58C2×D4×C11—21no—
59C2×D4×C11—21no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22—41no—
74C2×Dic22—41no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—41no—
89C22⋊Dic11—81no—
90C22⋊Dic11—81no—
91C22⋊Dic11—81no—
92C22⋊Dic11—81no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—81no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106#2808—111no—
107#2099—111no—
108#2072—111no—
109#2071D1111yescharacteristic
110#1272—111no—
111#1271—111no—
112#1270—111no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11#12011yescharacteristic
121D4×C11—42no—
122D4×C11—81no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153Dic22—42no—
154Dic22—81no—
155C8×C11—81no—
156C11⋊C8—81no—
157C11⋊C8—81no—
158C2×#103—221no—
159C2×#102—21no—
160#397—221no—
161#394—221no—
162#393—221no—
163#391—111no—
164#390C2×D1111yescharacteristic
165#389—111no—
166#388—221no—
167#388—221no—
168#387—221no—
169#384C2×D1111yescharacteristic
170#340—21no—
171#340—221no—
172#340—221no—
173#340—221no—
174#336—111no—
175#336—111no—
176#336C2×D1111yescharacteristic
177C22×C11—81no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11#44911yescharacteristic
185C22×C11#44911yescharacteristic
186C22×C11#45211yescharacteristic
187C22×C11#45411yescharacteristic
188C22×C11#45511yescharacteristic
189C22×C11#45511yescharacteristic
190C22×C11#45811yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—161no—
199Dic11—81no—
200Dic11—81no—
201Dic11—81no—
202Dic11—81no—
203C22×Q8—111no—
204C22×D4C22⋊D1111yescharacteristic
205C22×C8—21no—
206C22×C8—221no—
207C22×C8—221no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4C22⋊D1111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C42—221no—
223C2×C42C22×D1111yescharacteristic
224#103—442no—
225#102—42no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232C2×C11—161no—
233C2×C11#161211yescharacteristic
234C2×C11#161211yescharacteristic
235C2×C11#161511yescharacteristic
236C2×C11#162811yescharacteristic
237C2×C11#164011yescharacteristic
238C2×C11#164611yescharacteristic
239C2×C11#166211yescharacteristic
240C24—21no—
241C2×Q8—221no—
242C2×Q8—221no—
243C2×Q8—441no—
244C2×Q8—441no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4C2×C22⋊D1111yescharacteristic
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—441no—
262C2×C8—441no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—881no—
284C22⋊C4—881no—
285C22⋊C4—881no—
286C22⋊C4—881no—
287C42—41no—
288C42—881no—
289C11#781111yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#6699011yescharacteristic
298Q8—442no—
299Q8—881no—
300D4—42no—
301D4—81no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4#6696411yescharacteristic
327C2×C4#6696511yescharacteristic
328C2×C4#6696811yescharacteristic
329C2×C4#6696911yescharacteristic
330C2×C4#6698511yescharacteristic
331C2×C4#6700311yescharacteristic
332C8—81no—
333C8—881no—
334C8—881no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#1062265011yescharacteristic
343C22#1062266611yescharacteristic
344C22#1062267411yescharacteristic
345C22#1062277111yescharacteristic
346C22#1062278611yescharacteristic
347C22#1062281411yescharacteristic
348C22#1062281511yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—161no—
357C4—881no—
358C4—881no—
359C4—881no—
360C4—881no—
361C2—161no—
362C2#1306762711yescharacteristic
363C2#1306762811yescharacteristic
364C2#1306764411yescharacteristic
365C2#1306772411yescharacteristic
366C2#1306779911yescharacteristic
367C2#1306784211yescharacteristic
368C2#1306793811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2071C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2071D11
hypocenterC11#7811
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
2. #13070173C2semidirect
3. #13070025C2semidirect
4. #13066441C2semidirect
5. #13066440C2semidirect
289. C11#7811semidirect

Maximal subgroups

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

subgroupindex
#130765962
#130701732
#130700252
#130664412
#130664402
#130664372
C11×#20712
#781111