Finite Group Databasebeta

← #14656421

Subgroups — #14656421

Order 2816.

626 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079741C211yesmaximal, characteristic
2#13079538C211yesmaximal, characteristic
3#13077014C211yesmaximal, characteristic, complemented
4#13067302C211yesmaximal, characteristic, complemented
5#13067298C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C11×#1962C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66922—22no—
10C2×#66922C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×#104—22no—
14C43×C11C2211yescharacteristic
15#10622706—21no—
16#10622692—21no—
17#10622689—21no—
18#10622683—21no—
19#10622653—22no—
20#10622647—22no—
21#10622632—22no—
22#10622621—22no—
23#10622548—22no—
24#10622548—22no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622124—22no—
28#10622119—22no—
29C2×C11×#41—21no—
30C22×Dic22—21no—
31C22×Dic22D412yes—
32C2×C11×M16—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C42×C11—21no—
41C2×C42×C11—21no—
42C2×C42×C11D412yes—
43C2×C42×C11C2311yescharacteristic
44C2×#4324—24no—
45C2×C4⋊Dic11—28no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D412yes—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—48no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×#104—44no—
62#66896—24no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66#66872—24no—
67C4⋊(C11⋊C8)D412yes—
68C4⋊(C11⋊C8)D412yes—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10283—111nomaximal, Sylow
72C11×#41—42no—
73C11×#41—42no—
74C2×Q8×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—44no—
89C2×Dic22—44no—
90C2×Dic22—41no—
91C2×Dic22—41no—
92C11×M16—42no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—24no—
99C42×C11—24no—
100C42×C11—22no—
101C42×C11SD1614yescomplemented
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106#4324—84no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—416no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—22no—
118#3227—111no—
119#3206—111no—
120#2868—111no—
121#1962D1111yescharacteristic
122#1549—111no—
123#1548—111no—
124#1276—111no—
125C23×C11—41no—
126C23×C11#12011yescharacteristic
127Q8×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—82no—
132C2×C4×C11—24no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11C2×SD1612yes—
147C2×C4×C11#13712yes—
148C2×Dic11—44no—
149C2×Dic11—44no—
150C2×Dic11—42no—
151C2×Dic11—42no—
152Dic22—44no—
153Dic22—82no—
154Dic22—82no—
155Dic22—82no—
156C8×C11—81no—
157C11⋊C8—42no—
158C11⋊C8—42no—
159#532C2×D1111yescharacteristic
160C2×C4⋊Q8—111no—
161C2×C4⋊Q8—111no—
162C2×C4⋊Q8—222no—
163#498—221no—
164#492—221no—
165#487—221no—
166#486—221no—
167#481—222no—
168#476—222no—
169#461—222no—
170#448—222no—
171#431—111no—
172#431—111no—
173#423C2×D1111yescharacteristic
174C2×#104—22no—
175#384—222no—
176#384—222no—
177C43C2×D1111yescharacteristic
178#333—222no—
179#332—222no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39211yescharacteristic
186C22×C11#44812yes—
187C4×C11—28no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—81no—
191C4×C11#45312yes—
192C4×C11#45612yes—
193C4×C11#46112yes—
194C4×C11#49211yescharacteristic
195C4×C11#49711yescharacteristic
196Dic11—82no—
197Dic11—82no—
198C2×#41—21no—
199C22×Q8—112no—
200C22×Q8—221no—
201C2×SD16—224no—
202C2×M16—21no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—448no—
212C4⋊Q8D4411yescharacteristic
213#127D4411yescharacteristic
214#124—21no—
215#121—21no—
216#121—21no—
217C4×D4—21no—
218C4×D4—21no—
219C2×C4⋊C4—112no—
220C2×C4⋊C4—228no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42C22⋊D1112yes—
227C2×C42C22×D1111yescharacteristic
228#106—224no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—112no—
232C4⋊C8—112no—
233#104—44no—
234#103—224no—
235#102—224no—
236C22⋊C8—221no—
237C22⋊C8—221no—
238C4×C8—221no—
239C4×C8—221no—
240C2×C11—22no—
241C2×C11—161no—
242C2×C11#200211yescharacteristic
243C2×C11#200511yescharacteristic
244C2×C11#201311yescharacteristic
245#41—42no—
246#41—42no—
247C2×Q8—21no—
248C2×Q8—222no—
249C2×Q8—222no—
250C2×Q8—444no—
251C2×Q8—444no—
252C2×Q8—441no—
253C2×Q8—441no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—222no—
261C22×C4—222no—
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264C22×C4C2×C22⋊D1111yescharacteristic
265SD16—884no—
266M16—42no—
267C2×C8—41no—
268C2×C8—222no—
269C2×C8—222no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—222no—
273C4⋊C4—222no—
274C4⋊C4—4416no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—24no—
284C42—24no—
285C42—22no—
286C42#432414yescomplemented
287C42C2×D4411yescharacteristic
288C42#433911yescharacteristic
289C42D4×D1111yescharacteristic
290C42D4×D1111yescharacteristic
291C11#1028311yescharacteristic, complemented, Sylow
292C23—41no—
293C23#6699011yescharacteristic
294Q8—42no—
295Q8—444no—
296Q8—882no—
297Q8—882no—
298Q8—882no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—444no—
312C2×C4—444no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4#6693511yescharacteristic
316C2×C4#6693511yescharacteristic
317C2×C4#6693711yescharacteristic
318C2×C4#6693711yescharacteristic
319C2×C4#6698311yescharacteristic
320C2×C4C2×#432412yes—
321C2×C4#6699311yescharacteristic
322C2×C4#6700412yes—
323C8—81no—
324C8—442no—
325C8—442no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#1062257311yescharacteristic
332C22#1062265312yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—882no—
338C4—882no—
339C4#1062243512yes—
340C4#1062243912yes—
341C4#1062263212yes—
342C4#1062267311yescharacteristic
343C4#1062268911yescharacteristic
344C2—22no—
345C2—161no—
346C2#1306963011yescharacteristic
347C2#1306965111yescharacteristic
348C2#1306969811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1962C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1962D11
hypocenterC11#10283
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
3. #13077014C2semidirect
4. #13067302C2semidirect
5. #13067298C2semidirect
6. #13066449C2semidirect
101. C42×C11SD16semidirect
286. C42#4324semidirect
291. C11#10283semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130795382
#130770142
#130673022
#130672982
#130664492
C11×#19622
#1028311