Finite Group Databasebeta

← #14656832

Subgroups — #14656832

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073647C211yesmaximal, characteristic
2#13069577C211yesmaximal, characteristic
3#13069567C211yesmaximal, characteristic
4#13069539C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×#66943—21no—
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622598—21no—
14C2×#66874—21no—
15C2×#66874—21no—
16#10622548—21no—
17#10622548C2211yescharacteristic
18C4×C4⋊Dic11C2211yescharacteristic
19#10622541—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622274—22no—
22#10622189—22no—
23#10622189—21no—
24#10622189—21no—
25C22×Dic22—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—22no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D412yes—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44#66943—42no—
45#66943—42no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922Q812yes—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C11×#95—21no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57#66874—42no—
58#66874—42no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61#10356—111nomaximal, Sylow
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—21no—
69C22×Dic11—22no—
70C22×Dic11—41no—
71C2×Dic22—22no—
72C2×Dic22—41no—
73C2×Dic22—41no—
74C2×Dic22—41no—
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—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4D812yes—
86C11×C4⋊C4SD1612yes—
87C42×C11—41no—
88C42×C11—41no—
89C42×C11C2×Q811yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C4⋊Dic11—22no—
94C4⋊Dic11—22no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—42no—
100C4⋊Dic11—44no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—82no—
108Dic11⋊C4—44no—
109C4×Dic11—41no—
110C4×Dic11—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2552—111no—
115#1990—111no—
116#1988—111no—
117#1981—111no—
118#1296—111no—
119#1279—111no—
120#1279D1111yescharacteristic
121C23×C11#12011yescharacteristic
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—42no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—42no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156Dic22—42no—
157Dic22—42no—
158Dic22—81no—
159Dic22—81no—
160C8×C11—42no—
161C8×C11—81no—
162C11⋊C8—81no—
163C2×C4⋊Q8—111no—
164C2×#125—221no—
165C2×C4⋊C8—111no—
166C2×C4⋊C8C2×D1111yescharacteristic
167C2×#103—221no—
168C2×#103—221no—
169C2×C4×C8C2×D1111yescharacteristic
170#398—222no—
171#389—221no—
172#389—221no—
173#384—111no—
174#384—221no—
175C4×C4⋊C4—111no—
176C4×C4⋊C4C2×D1111yescharacteristic
177#340—221no—
178#340—221no—
179#340—222no—
180C22×C11#39311yescharacteristic
181C22×C11#44711yescharacteristic
182C22×C11#44811yescharacteristic
183C22×C11#45211yescharacteristic
184C22×C11#45211yescharacteristic
185C22×C11#45511yescharacteristic
186C22×C11#45611yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11—42no—
191C4×C11#47411yescharacteristic
192C4×C11#47611yescharacteristic
193C4×C11#47911yescharacteristic
194C4×C11#47911yescharacteristic
195C4×C11#48611yescharacteristic
196C4×C11#48811yescharacteristic
197C4×C11#48911yescharacteristic
198C4×C11#49111yescharacteristic
199Dic11—81no—
200Dic11—82no—
201Dic11—81no—
202Dic11—82no—
203C22×Q8—221no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—221no—
207C4⋊Q8—112no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211#125—442no—
212#125—442no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4—112no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—222no—
219C2×C4⋊C4—222no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—222no—
223C2×C4⋊C4D4411yescharacteristic
224C2×C4⋊C4D4411yescharacteristic
225C2×C42—21no—
226C2×C42—221no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—221no—
231C4⋊C8—221no—
232#103—442no—
233#103—442no—
234C4×C8—21no—
235C4×C8—21no—
236#95—21no—
237#95—222no—
238#95—221no—
239C2×C11#164111yescharacteristic
240C2×C11#164311yescharacteristic
241C2×C11#164711yescharacteristic
242C2×C11#165311yescharacteristic
243C2×C11#202311yescharacteristic
244C2×C11#202611yescharacteristic
245C2×C11#202811yescharacteristic
246C2×Q8—222no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—222no—
257C22×C4—441no—
258C22×C4C2×D4411yescharacteristic
259C22×C4D4×D1111yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—442no—
279C4⋊C4—444no—
280C4⋊C4—444no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C4⋊C4—882no—
288C4⋊C4#431412yes—
289C4⋊C4D8812yes—
290C42—41no—
291C42—41no—
292C42—441no—
293C42—441no—
294C42#433911yescharacteristic
295C42#433911yescharacteristic
296C42#434111yescharacteristic
297C42Q8×D1111yescharacteristic
298C11#1035611yescharacteristic, complemented, Sylow
299C23#6693511yescharacteristic
300Q8—442no—
301Q8—442no—
302Q8—881no—
303Q8—881no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—442no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—442no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4#6692811yescharacteristic
325C2×C4#6693811yescharacteristic
326C2×C4#6693811yescharacteristic
327C2×C4#6694911yescharacteristic
328C2×C4#6694911yescharacteristic
329C2×C4#6695011yescharacteristic
330C2×C4C2×#431411yescharacteristic
331C2×C4C2×D8811yescharacteristic
332C2×C4#6696111yescharacteristic
333C2×C4#6696211yescharacteristic
334C2×C4#6696511yescharacteristic
335C2×C4#6696811yescharacteristic
336C2×C4#6696911yescharacteristic
337C2×C4#6697111yescharacteristic
338C8—42no—
339C8—81no—
340C8—881no—
341C22#1062228611yescharacteristic
342C22#1062234511yescharacteristic
343C22#1062235111yescharacteristic
344C22#1062239611yescharacteristic
345C22#1062242311yescharacteristic
346C22#1062243811yescharacteristic
347C22#1062243911yescharacteristic
348C4—21no—
349C4—21no—
350C4—42no—
351C4—42no—
352C4—881no—
353C4—882no—
354C4—881no—
355C4—882no—
356C4#1062230711yescharacteristic
357C4#1062232711yescharacteristic
358C4#1062238111yescharacteristic
359C4#1062241011yescharacteristic
360C4#1062245511yescharacteristic
361C4#1062245911yescharacteristic
362C4#1062247011yescharacteristic
363C4#1062249011yescharacteristic
364C2#1306781111yescharacteristic
365C2#1306782511yescharacteristic
366C2#1306785311yescharacteristic
367C2#1306789511yescharacteristic
368C2#1306975311yescharacteristic
369C2#1306976611yescharacteristic
370C2#1306977611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socle, prime radicalC23×C11#120
hypercenter#1279D11
hypocenterC11#10356
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
298. C11#10356semidirect

Maximal subgroups

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

subgroupindex
#130736472
#130695772
#130695672
#130695392
#130665002
#130664562
C11×#12792
#1035611