Finite Group Databasebeta

← #14643098

Subgroups — #14643098

Order 2816.

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

normal subgroups only

This group has 396 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#13070180C211yesmaximal, characteristic, complemented
3#13070153C211yesmaximal, characteristic, complemented
4#13070149C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic, complemented
6#13066438C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic
8C11×#390C2211yescharacteristic
9#10622835—21no—
10C2×#66896—21no—
11C2×#66882—21no—
12C2×#66880—21no—
13#10622591—21no—
14C2×#66872—21no—
15#10622566—21no—
16#10622564—21no—
17#10622564—21no—
18#10622560—21no—
19#10622548C2211yescharacteristic
20#10622542C2211yescharacteristic
21#10622541C2211yescharacteristic
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622189—21no—
25#10622189—21no—
26#10622162C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C42×C11C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C22×C11⋊C8—21no—
48#66896—42no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55#66882—42no—
56#66880—42no—
57#66872—42no—
58#7834—111nomaximal, Sylow
59C24×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
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×C8×C11—22no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—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—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104C4×Dic11—81no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2808—111no—
109#2100—111no—
110#2095—111no—
111#2094—111no—
112#1272—111no—
113#1271—111no—
114#1270D1111yescharacteristic
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123D4×C11—42no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—41no—
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—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155Dic22—42no—
156Dic22—81no—
157C8×C11—42no—
158C8×C11—81no—
159C11⋊C8—42no—
160C2×#107—221no—
161C2×#106—221no—
162C2×#103—221no—
163C2×#102—221no—
164#397—221no—
165#394—221no—
166#393—221no—
167#391—111no—
168#390C2×D1111yescharacteristic
169#389—111no—
170#388—221no—
171#388—221no—
172#387—221no—
173#384—111no—
174#340—221no—
175#340—221no—
176#336—111no—
177#336C2×D1111yescharacteristic
178#336C2×D1111yescharacteristic
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11#45211yescharacteristic
187C22×C11#45211yescharacteristic
188C22×C11#45211yescharacteristic
189C22×C11#45311yescharacteristic
190C22×C11#45311yescharacteristic
191C22×C11#45411yescharacteristic
192C22×C11#45811yescharacteristic
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—81no—
200Dic11—81no—
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204Dic11—161no—
205C22×Q8—111no—
206C22×D4D4411yescharacteristic
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—221no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4D4411yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C42—221no—
225C2×C42C22×D1111yescharacteristic
226#107—442no—
227#106—442no—
228#103—442no—
229#102—442no—
230#95—221no—
231#95—221no—
232#95—221no—
233#95—221no—
234#95—221no—
235#95—221no—
236C2×C11—161no—
237C2×C11#161511yescharacteristic
238C2×C11#161811yescharacteristic
239C2×C11#161811yescharacteristic
240C2×C11#163011yescharacteristic
241C2×C11#163411yescharacteristic
242C2×C11#163811yescharacteristic
243C2×C11#165611yescharacteristic
244C24—21no—
245C2×Q8—221no—
246C2×Q8—221no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—21no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—441no—
259C22×C4C2×D4411yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—222no—
269C2×C8—441no—
270C2×C8—441no—
271C4⋊C4—41no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—442no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—881no—
288C22⋊C4—881no—
289C22⋊C4—881no—
290C22⋊C4—881no—
291C42—41no—
292C42—881no—
293C11#783411yescharacteristic, complemented, Sylow
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#6693511yescharacteristic
302Q8—442no—
303Q8—881no—
304D4—42no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
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—441no—
327C2×C4—881no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4#6695711yescharacteristic
331C2×C4#6696211yescharacteristic
332C2×C4#6696511yescharacteristic
333C2×C4#6696511yescharacteristic
334C2×C4#6696811yescharacteristic
335C2×C4#6696811yescharacteristic
336C8—42no—
337C8—81no—
338C8—442no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1062234611yescharacteristic
347C22#1062235511yescharacteristic
348C22#1062236011yescharacteristic
349C22#1062239611yescharacteristic
350C22#1062239611yescharacteristic
351C22#1062243511yescharacteristic
352C22#1062244011yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—881no—
361C4—881no—
362C4—881no—
363C4—881no—
364C4—1761no—
365C2—161no—
366C2#1306764811yescharacteristic
367C2#1306766511yescharacteristic
368C2#1306766611yescharacteristic
369C2#1306773811yescharacteristic
370C2#1306776311yescharacteristic
371C2#1306779011yescharacteristic
372C2#1306791011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#1270D11
hypocenterC11#7834
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13070180C2semidirect
3. #13070153C2semidirect
5. #13066441C2semidirect
6. #13066438C2semidirect
293. C11#7834semidirect

Maximal subgroups

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

subgroupindex
#130765962
#130701802
#130701532
#130701492
#130664412
#130664382
C11×#12702
#783411