Finite Group Databasebeta

← #14655691

Subgroups — #14655691

Order 2816.

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

normal subgroups only

This group has 574 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#13079538C211yesmaximal, characteristic
2#13079076C211yesmaximal, characteristic
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13069604C211yesmaximal, characteristic, complemented
5#13067289C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67004—22no—
10C2×#66922C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66880—22no—
15#10622706—21no—
16#10622705—21no—
17#10622689—21no—
18#10622689—21no—
19#10622673—22no—
20#10622653—22no—
21#10622632—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622294—22no—
25#10622294—22no—
26C11×D4⋊C8—22no—
27#10622192—22no—
28#10622120—22no—
29C2×C11×#41—21no—
30C22×Dic22—21no—
31C22×Dic22D412yes—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42#67004—44no—
43#67004—44no—
44C2×#4326—24no—
45C2×#4324—24no—
46C2×#4324—24no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×#4318D412yes—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922D412yes—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C4×C8×C11—21no—
63C4×C8×C11D412yes—
64C22⋊(C11⋊C8)—21no—
65#66880—28no—
66#66874—24no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10170—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—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—41no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—22no—
88C2×Dic22—44no—
89C2×Dic22—41no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—42no—
95C2×C8×C11—41no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104#4326—48no—
105#4324—48no—
106#4324—84no—
107C4⋊Dic11—22no—
108C4⋊Dic11—22no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115#4318—22no—
116#4318SD1614yescomplemented
117C2×C11⋊C8—22no—
118C2×C11⋊C8—22no—
119#3206—111no—
120#3152—111no—
121C2×#487—111no—
122#1997—111no—
123#1546—111no—
124#1492D1111yescharacteristic
125#1278—111no—
126C23×C11—41no—
127C23×C11#12111yescharacteristic
128Q8×C11—42no—
129D4×C11—42no—
130D4×C11—42no—
131D4×C11—42no—
132D4×C11—82no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12711yescharacteristic
144C2×C4×C11C2×SD1612yes—
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—82no—
149C2×Dic11—82no—
150Dic22—44no—
151Dic22—44no—
152Dic22—44no—
153Dic22—81no—
154Dic22—81no—
155C8×C11—42no—
156C8×C11—81no—
157C11⋊C8—24no—
158C11⋊C8—42no—
159C2×#137—222no—
160#532C2×D1111yescharacteristic
161C2×C4⋊Q8—111no—
162C2×C4⋊Q8—111no—
163#497—222no—
164#494—221no—
165#492—221no—
166#492—221no—
167#487—222no—
168#487—221no—
169#487—222no—
170#461—222no—
171#448—222no—
172#431—111no—
173#423C2×D1111yescharacteristic
174C2×#103—222no—
175C4×M16—111no—
176C2×C4×C8C2×D1111yescharacteristic
177#343—222no—
178#332—222no—
179D4⋊C8—22no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11#39211yescharacteristic
186C22×C11#46012yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11#45012yes—
191C4×C11#45512yes—
192C4×C11#47312yes—
193C4×C11#49211yescharacteristic
194C4×C11#49611yescharacteristic
195Dic11—82no—
196Dic11—82no—
197C2×#41—21no—
198C22×Q8—112no—
199C22×Q8—221no—
200#137—444no—
201#137—444no—
202C2×Q16—224no—
203C2×SD16—224no—
204C2×SD16—224no—
205C2×M16—21no—
206C2×M16—112no—
207C22×C8—21no—
208C4⋊Q8—112no—
209C4⋊Q8—221no—
210C4⋊Q8—221no—
211C4⋊Q8—221no—
212C4⋊Q8—221no—
213C4⋊Q8—221no—
214C4⋊Q8—221no—
215C4⋊Q8—221no—
216C4⋊Q8D4411yescharacteristic
217#127D4411yescharacteristic
218#124—21no—
219#121—21no—
220#121—21no—
221C4×D4—21no—
222C4×D4—21no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C42C22×D1111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—112no—
231#103—224no—
232#103—228no—
233C22⋊C8—221no—
234#97—221no—
235C4×C8—21no—
236C4×C8—221no—
237C4×C8—221no—
238C4×C8C22⋊D1112yes—
239C2×C11—22no—
240C2×C11—161no—
241C2×C11#200411yescharacteristic
242C2×C11#201411yescharacteristic
243C2×C11#202011yescharacteristic
244#41—42no—
245#41—42no—
246C2×Q8—21no—
247C2×Q8—222no—
248C2×Q8—222no—
249C2×Q8—222no—
250C2×Q8—444no—
251C2×Q8—441no—
252C2×Q8—442no—
253C2×Q8—442no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—41no—
259C22×C4—222no—
260C22×C4—441no—
261C22×C4#433911yescharacteristic
262C22×C4D4×D1111yescharacteristic
263C22×C4D4×D1111yescharacteristic
264Q16—448no—
265SD16—448no—
266SD16—884no—
267M16—42no—
268M16—114no—
269M16—222no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—41no—
273C2×C8—222no—
274C2×C8—222no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—222no—
278C4⋊C4—222no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42C2×D4411yescharacteristic
288C42D4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42C2×C22⋊D1111yescharacteristic
291C11#1017011yescharacteristic, complemented, Sylow
292C23—41no—
293C23#6693711yescharacteristic
294Q8—42no—
295Q8—444no—
296Q8—444no—
297Q8—444no—
298Q8—881no—
299Q8—881no—
300D4—42no—
301D4—42no—
302D4—42no—
303D4—82no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—882no—
312C2×C4—882no—
313C2×C4#6693511yescharacteristic
314C2×C4#6693511yescharacteristic
315C2×C4#6693711yescharacteristic
316C2×C4#6696412yes—
317C2×C4SD16×D1112yes—
318C2×C4#6698311yescharacteristic
319C2×C4#6699011yescharacteristic
320C2×C4#6699311yescharacteristic
321C8—42no—
322C8—81no—
323C8—224no—
324C8—442no—
325C22—21no—
326C22—21no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22#1062237512yes—
331C22#1062257311yescharacteristic
332C4—21no—
333C4—21no—
334C4—81no—
335C4—882no—
336C4—882no—
337C4#1062238912yes—
338C4#1062243812yes—
339C4#1062275612yes—
340C4#1062276711yescharacteristic
341C4#1062278811yescharacteristic
342C2—22no—
343C2—161no—
344C2#1306964411yescharacteristic
345C2#1306970511yescharacteristic
346C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1492D11
hypocenterC11#10170
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
3. C2×#10622294C2semidirect
4. #13069604C2semidirect
5. #13067289C2semidirect
6. #13066453C2semidirect
116. #4318SD16semidirect
291. C11#10170semidirect

Maximal subgroups

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

subgroupindex
#130795382
#130790762
C2×#106222942
#130696042
#130672892
#130664532
C11×#14922
#1017011