Finite Group Databasebeta

← #14655625

Subgroups — #14655625

Order 2816.

556 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079158C211yesmaximal, characteristic, complemented
3C2×#10622701C211yesmaximal, characteristic
4#13069455C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1548C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66887—22no—
14#10622701—22no—
15#10622701—22no—
16#10622693—22no—
17#10622692—21no—
18#10622691—21no—
19C2×#66873—22no—
20#10622577—22no—
21C4×#4318C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622461—22no—
24#10622344—22no—
25#10622307—21no—
26#10622306—21no—
27C11×#333—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44D412yes—
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42#66977—21no—
43#66977—21no—
44C2×#4318D412yes—
45C22×C11⋊C8—21no—
46C2×#4314—24no—
47#66927—21no—
48#66927—21no—
49#66927—21no—
50#66927—21no—
51#66923—21no—
52#66922D411yescharacteristic
53#66922D411yescharacteristic
54C4×Dic22—21no—
55C4×Dic22—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C22⋊C8—21no—
60C4×C8×C11—21no—
61#66887—44no—
62#66885—24no—
63#66873—28no—
64#66872—24no—
65#66871—24no—
66#66867—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8D412yes—
70#10161—111nomaximal, Sylow
71C23×D11—22no—
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—44no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—82no—
89C2×Dic22—21no—
90C2×Dic22—21no—
91C11×M16—42no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—41no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109C4×Dic11—41no—
110#4318—22no—
111#4318SD1614yescomplemented
112C2×C11⋊C8—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—42no—
115#4314—84no—
116#3208—111no—
117#3165—111no—
118C2×#486—111no—
119#1965—111no—
120#1548D1111yescharacteristic, complemented
121#1493—111no—
122#1278—111no—
123C23×C11#12111yescharacteristic
124C22×D11—42no—
125C22×D11—44no—
126C22×D11—82no—
127C22×D11—82no—
128Q8×C11—82no—
129Q8×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—42no—
133C2×C4×C11—82no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×C4×C11C2×SD1612yes—
141C2×C4×C11#13712yes—
142C2×Dic11—41no—
143C2×Dic11—41no—
144D44—44no—
145D44—44no—
146D44—82no—
147D44—82no—
148D44—82no—
149D44—81no—
150D44—81no—
151Dic22—42no—
152Dic22—42no—
153C8×C11—42no—
154C8×C11—81no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157#533—111no—
158C2×C4⋊Q8C2×D1111yescharacteristic
159C2×#127—111no—
160#501—222no—
161#500—221no—
162#498—221no—
163#492—221no—
164#486—221no—
165#486—222no—
166#486—222no—
167#460—222no—
168#450—222no—
169#431C2×D1111yescharacteristic
170#428—222no—
171#423C2×D1111yescharacteristic
172C2×#102—222no—
173C2×#100—222no—
174C4×M16—111no—
175C2×C4×C8—111no—
176#333—22no—
177Q8⋊C8—222no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#39211yescharacteristic
181C22×C11#46112yes—
182C2×D11—82no—
183C2×D11—82no—
184C2×D11—82no—
185C2×D11—164no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—82no—
189C4×C11#44812yes—
190C4×C11#45512yes—
191C4×C11#47212yes—
192C4×C11#49211yescharacteristic
193C4×C11#49711yescharacteristic
194Dic11—81no—
195Dic11—81no—
196C22×Q8—21no—
197C22×D4—112no—
198C22×D4—221no—
199C22×D4—221no—
200C2×SD16—224no—
201C2×M16—21no—
202C2×M16—112no—
203C22×C8—221no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—111no—
208C4⋊Q8—111no—
209C4⋊Q8D4412yes—
210#127—221no—
211#127—221no—
212#127—221no—
213#127—221no—
214#125—221no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C4×Q8—221no—
218C4×Q8—221no—
219#117—221no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C42C22×D1111yescharacteristic
223#107—224no—
224#106—224no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8C22⋊D1112yes—
228#102—228no—
229#102—224no—
230#100—444no—
231C22⋊C8—21no—
232#97—221no—
233C4×C8—21no—
234C4×C8—112no—
235C4×C8—221no—
236C4×C8—221no—
237C2×C11—22no—
238C2×C11#200411yescharacteristic
239C2×C11#201311yescharacteristic
240C2×C11#201811yescharacteristic
241D11—162no—
242C24—222no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—82no—
246C2×Q8—221no—
247C2×Q8—221no—
248C2×D4—222no—
249C2×D4—222no—
250C2×D4—444no—
251C2×D4—441no—
252C2×D4—441no—
253C2×D4—442no—
254C2×D4—442no—
255C2×D4—441no—
256C2×D4—441no—
257C2×D4—882no—
258C22×C4—41no—
259C22×C4#433911yescharacteristic
260C22×C4D4×D1111yescharacteristic
261C22×C4D4×D1111yescharacteristic
262SD16—884no—
263M16—42no—
264M16—114no—
265M16—222no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—442no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—441no—
282C42—441no—
283C42C2×D4411yescharacteristic
284C42D4×D1111yescharacteristic
285C42D4×D1111yescharacteristic
286C42C2×C22⋊D1111yescharacteristic
287C11#1016111yescharacteristic, complemented, Sylow
288C23—442no—
289C23—444no—
290C23—882no—
291C23—882no—
292C23#6693711yescharacteristic
293Q8—82no—
294Q8—82no—
295Q8—442no—
296Q8—442no—
297D4—444no—
298D4—444no—
299D4—882no—
300D4—881no—
301D4—881no—
302D4—882no—
303D4—882no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4#6693511yescharacteristic
311C2×C4#6693511yescharacteristic
312C2×C4#6693711yescharacteristic
313C2×C4SD16×D1112yes—
314C2×C4#6697112yes—
315C2×C4#6698311yescharacteristic
316C2×C4#6699011yescharacteristic
317C2×C4#6699311yescharacteristic
318C8—42no—
319C8—81no—
320C8—224no—
321C8—442no—
322C22—21no—
323C22—21no—
324C22—882no—
325C22—882no—
326C22—882no—
327C22—1764no—
328C22#1062243112yes—
329C22#1062257311yescharacteristic
330C4—21no—
331C4—21no—
332C4—82no—
333C4—881no—
334C4—881no—
335C4#1062236212yes—
336C4#1062241912yes—
337C4#1062278811yescharacteristic
338C4#1062280311yescharacteristic
339C4#1062281512yes—
340C2—22no—
341C2—1762no—
342C2#1306964611yescharacteristic
343C2#1306970011yescharacteristic
344C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1548D11
hypocenterC11#10161
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
2. #13079158C2semidirect
5. #13067070C2semidirect
6. #13066452C2semidirect
7. C11×#1548C2semidirect
111. #4318SD16semidirect
120. #1548D11semidirect
287. C11#10161semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130791582
C2×#106227012
#130694552
#130670702
#130664522
C11×#15482
#1016111