Finite Group Databasebeta

← #14655573

Subgroups — #14655573

Order 2816.

620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079559C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic, complemented
3C2×#10622306C211yesmaximal, characteristic
4#13069456C211yesmaximal, characteristic
5#13067300C211yesmaximal, characteristic, complemented
6#13067072C211yesmaximal, characteristic, complemented
7C11×#1278C211yesmaximal, characteristic, complemented
8C22×#4314—22no—
9C2×#66927C2211yescharacteristic
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66887—22no—
16#10622734—22no—
17#10622537C2211yescharacteristic
18#10622461—22no—
19#10622344—22no—
20#10622315—22no—
21#10622307—21no—
22#10622306—21no—
23#10622306—22no—
24#10622306—22no—
25#10622295—21no—
26#10622293—21no—
27#10622120—22no—
28#10622094—22no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44D412yes—
32C22×Dic22—21no—
33C2×C11×M16D412yes—
34C22×C8×C11—21no—
35C2×C42×C11C2311yescharacteristic
36#66979—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42C2×#4314—28no—
43C2×#4314—24no—
44C2×#4314—48no—
45#66927—21no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66923—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C11×C4⋊C8D412yes—
59C11×C22⋊C8—21no—
60C11×#97—21no—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64C4×C8×C11D412yes—
65#66887—44no—
66#66885—24no—
67#66882—24no—
68#66881—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71#10153—111nomaximal, Sylow
72C23×D11—22no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11#4111yescharacteristic
76C22×Dic11—41no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—44no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—42no—
85C2×D44—42no—
86C2×D44—82no—
87C2×Dic22—21no—
88C2×Dic22—22no—
89C2×Dic22—21no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C11×M16—22no—
93C11×M16SD1614yescomplemented
94C2×C8×C11—24no—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—41no—
103C4⋊Dic11—21no—
104C4⋊Dic11—22no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111Dic11⋊C4—41no—
112Dic11⋊C4—41no—
113C4×Dic11—41no—
114#4318—42no—
115C2×C11⋊C8—41no—
116#4314—416no—
117#4314—84no—
118#3208—111no—
119#3165—111no—
120C2×#492—111no—
121#1965—111no—
122#1549—111no—
123#1493—111no—
124#1278D1111yescharacteristic, complemented
125C23×C11#12111yescharacteristic
126C22×D11—42no—
127C22×D11—44no—
128C22×D11—82no—
129C22×D11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11C2×SD1612yes—
139C2×C4×C11#13712yes—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—82no—
144D44—44no—
145D44—44no—
146D44—82no—
147D44—82no—
148D44—82no—
149D44—81no—
150D44—81no—
151Dic22—44no—
152Dic22—42no—
153Dic22—42no—
154Dic22—82no—
155C8×C11—24no—
156C8×C11—24no—
157C8×C11—42no—
158C11⋊C8—81no—
159C22×SD16—222no—
160#533—111no—
161C2×C4⋊Q8—111no—
162C2×#127—111no—
163#501—222no—
164#500—221no—
165#498—221no—
166#492—222no—
167#492—221no—
168#492—222no—
169#486—221no—
170#460—222no—
171#450—222no—
172#431C2×D1111yescharacteristic
173#428—222no—
174#423—111no—
175C2×#100—222no—
176C4×M16C2×D1111yescharacteristic
177C2×C4×C8C2×D1111yescharacteristic
178#332—222no—
179Q8⋊C8—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39211yescharacteristic
183C22×C11#46112yes—
184C2×D11—82no—
185C2×D11—82no—
186C2×D11—82no—
187C2×D11—164no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11#44812yes—
191C4×C11#45312yes—
192C4×C11#47112yes—
193C4×C11#49211yescharacteristic
194C4×C11#49711yescharacteristic
195Dic11—82no—
196Dic11—81no—
197Dic11—81no—
198C22×Q8—221no—
199C22×D4—112no—
200C22×D4—221no—
201C22×D4—221no—
202C2×SD16—228no—
203C2×SD16—224no—
204C2×SD16—448no—
205C2×M16—221no—
206C2×M16D4412yes—
207C22×C8—21no—
208C4⋊Q8—112no—
209C4⋊Q8—111no—
210C4⋊Q8—111no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214#127—221no—
215#127—221no—
216#127—221no—
217#127—221no—
218#125—221no—
219C22⋊Q8—221no—
220C22⋊Q8—221no—
221C4×Q8—221no—
222C4×Q8—221no—
223#117—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C42C22×D1111yescharacteristic
227#107—224no—
228#106—224no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231C4⋊C8D4412yes—
232#102—224no—
233#100—444no—
234C22⋊C8—21no—
235#97—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8D4412yes—
240C2×C11—22no—
241C2×C11#200211yescharacteristic
242C2×C11#201311yescharacteristic
243C2×C11#201911yescharacteristic
244D11—162no—
245C24—222no—
246C2×Q8—221no—
247C2×Q8—222no—
248C2×Q8—221no—
249C2×Q8—444no—
250C2×Q8—441no—
251C2×D4—222no—
252C2×D4—222no—
253C2×D4—444no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—442no—
259C2×D4—442no—
260C2×D4—882no—
261C22×C4—441no—
262C22×C4C2×D4411yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4#434311yescharacteristic
265SD16—4416no—
266SD16—884no—
267M16—22no—
268M16—442no—
269M16#431414yescomplemented
270C2×C8—24no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—441no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—222no—
278C4⋊C4—221no—
279C4⋊C4—222no—
280C4⋊C4—221no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—441no—
286C42—441no—
287C42C2×D4411yescharacteristic
288C42C2×D4411yescharacteristic
289C42D4×D1111yescharacteristic
290C42D4×D1111yescharacteristic
291C11#1015311yescharacteristic, complemented, Sylow
292C23—442no—
293C23—444no—
294C23—882no—
295C23—882no—
296C23#6694811yescharacteristic
297Q8—444no—
298Q8—442no—
299Q8—442no—
300Q8—882no—
301D4—444no—
302D4—444no—
303D4—882no—
304D4—882no—
305D4—881no—
306D4—881no—
307D4—882no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—882no—
314C2×C4#6692711yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6693511yescharacteristic
317C2×C4#6693511yescharacteristic
318C2×C4#6694811yescharacteristic
319C2×C4#6694811yescharacteristic
320C2×C4C2×#431412yes—
321C2×C4#6696212yes—
322C8—24no—
323C8—24no—
324C8—42no—
325C8—881no—
326C22—21no—
327C22—21no—
328C22—882no—
329C22—882no—
330C22—882no—
331C22—1764no—
332C22#1062228411yescharacteristic
333C22#1062245412yes—
334C4—21no—
335C4—21no—
336C4—882no—
337C4—881no—
338C4—881no—
339C4#1062230611yescharacteristic
340C4#1062232811yescharacteristic
341C4#1062235112yes—
342C4#1062243512yes—
343C4#1062251112yes—
344C2—22no—
345C2—1762no—
346C2#1306963411yescharacteristic
347C2#1306970111yescharacteristic
348C2#1306973311yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1278D11
hypocenterC11#10153
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
2. #13079162C2semidirect
5. #13067300C2semidirect
6. #13067072C2semidirect
7. C11×#1278C2semidirect
93. C11×M16SD16semidirect
124. #1278D11semidirect
269. M16#4314semidirect
291. C11#10153semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130791622
C2×#106223062
#130694562
#130673002
#130670722
C11×#12782
#1015311