Finite Group Databasebeta

← #14653204

Subgroups — #14653204

Order 2816.

396 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 93 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#13079171C211yesmaximal, characteristic
2#13068368C211yesmaximal, characteristic, complemented
3#13067377C211yesmaximal, characteristic, complemented
4#13067232C211yesmaximal, characteristic, complemented
5#13067227C211yesmaximal, characteristic
6#13067127C211yesmaximal, characteristic, complemented
7C11×#1505C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622706C411yescharacteristic, complemented
13#10622692C411yescharacteristic, complemented
14#10622689C411yescharacteristic, complemented
15#10622683C411yescharacteristic, complemented
16#10622654—21no—
17#10622654—21no—
18C4×#4324—21no—
19C4×#4324—21no—
20#10622539C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#327—22no—
24#10622178—22no—
25#10622162—21no—
26#10622162—21no—
27#10622118—21no—
28#10622117—21no—
29#10622103—22no—
30#10622090—22no—
31C2×C11×#41—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#124—21no—
35C11×#121—21no—
36C11×#121—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4324—21no—
42C2×#4324—21no—
43#66979—21no—
44#66977—21no—
45#66977—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8D411yescharacteristic
48C22×C11⋊C8D411yescharacteristic
49#66923—21no—
50#66922C2×C411yescharacteristic
51#66922C2×C411yescharacteristic
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#95—21no—
58C11×#95D412yes—
59#66896—21no—
60#66896—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—21no—
63#66874—21no—
64#66872—21no—
65#66872—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69#66867D412yes—
70C4×C11⋊C8C2×C411yescharacteristic
71C4×C11⋊C8C2×C411yescharacteristic
72C4×C11⋊C8D411yescharacteristic
73C4×C11⋊C8D411yescharacteristic
74#9766—111nomaximal, Sylow
75C11×#41—82no—
76C2×Q8×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×Dic22—21no—
87C2×Dic22—21no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C22⋊Dic11—41no—
100#4324—42no—
101#4324—42no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8C22⋊C411yescharacteristic
116C2×C11⋊C8C22⋊C411yescharacteristic
117C2×C11⋊C8C22⋊C411yescharacteristic
118C2×C11⋊C8C22⋊C411yescharacteristic
119#3167—111no—
120#1746—111no—
121#1568—111no—
122#1531—111no—
123#1530—111no—
124#1506—111no—
125#1505D1111yescharacteristic
126C23×C11—41no—
127C23×C11#12111yescharacteristic
128Q8×C11—81no—
129D4×C11—41no—
130D4×C11—41no—
131D4×C11—81no—
132D4×C11—81no—
133D4×C11—82no—
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—82no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×C4×C11#12711yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151Dic22—41no—
152Dic22—41no—
153Dic22—81no—
154C8×C11—81no—
155C11⋊C8—21no—
156C11⋊C8—21no—
157C11⋊C8—21no—
158C11⋊C8—21no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161#533—111no—
162#532C2×D1111yescharacteristic
163#498—111no—
164#492—111no—
165#487—111no—
166#486—111no—
167#465—221no—
168#465—221no—
169C4×SD16—221no—
170C4×SD16—221no—
171#432—111no—
172#432C2×D1111yescharacteristic
173C2×#97—111no—
174C2×C4×C8—111no—
175#376C2×D1111yescharacteristic
176#336—221no—
177#336—221no—
178#335—221no—
179#334—221no—
180#330—222no—
181#329—222no—
182#328—222no—
183#327—22no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—81no—
187C22×C11—81no—
188C22×C11—81no—
189C22×C11#39011yescharacteristic
190C22×C11#47112yes—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—82no—
197C4×C11—81no—
198C4×C11#42111yescharacteristic
199C4×C11#42111yescharacteristic
200Dic11—81no—
201Dic11—81no—
202C2×#41—21no—
203C2×SD16—221no—
204C2×SD16—221no—
205C22×C8—111no—
206C22×C8—111no—
207C22×C8—221no—
208C4⋊Q8—111no—
209C4⋊Q8—111no—
210C4⋊Q8C4×D1111yescharacteristic
211#127C4×D1111yescharacteristic
212#125—221no—
213#124—21no—
214C22⋊Q8—221no—
215C22⋊Q8—221no—
216#121—21no—
217#121—21no—
218C4×Q8—221no—
219C4×Q8—221no—
220C4×D4—21no—
221C4×D4—21no—
222#117—221no—
223C2×C42—21no—
224C2×C42C22×D1111yescharacteristic
225#106—221no—
226#106—221no—
227C4⋊C8—21no—
228C4⋊C8—221no—
229#103—221no—
230#103—221no—
231#102—221no—
232#102—221no—
233C22⋊C8—21no—
234C22⋊C8—221no—
235#97—21no—
236#97—112no—
237#97—221no—
238#97—221no—
239C4×C8—111no—
240C4×C8—111no—
241C4×C8—111no—
242C4×C8—111no—
243#95—21no—
244#95C22⋊D1112yes—
245C2×C11—22no—
246C2×C11—161no—
247C2×C11#196311yescharacteristic
248C2×C11#197611yescharacteristic
249C2×C11#197711yescharacteristic
250#41—82no—
251C2×Q8—21no—
252C2×Q8—221no—
253C2×Q8—221no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263SD16—442no—
264SD16—442no—
265C2×C8—41no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—222no—
271C2×C8—441no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—441no—
287C42—41no—
288C42—41no—
289C42—441no—
290C42C2×C4×D1111yescharacteristic
291C42#433911yescharacteristic
292C42D4×D1111yescharacteristic
293C42D4×D1111yescharacteristic
294C11#976611yescharacteristic, complemented, Sylow
295C23—41no—
296C23#6699211yescharacteristic
297Q8—81no—
298Q8—441no—
299Q8—441no—
300Q8—881no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—82no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—82no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4C22⋊C4×D1111yescharacteristic
318C2×C4(C22⋊D11)⋊C411yescharacteristic
319C2×C4#6693711yescharacteristic
320C2×C4#6693811yescharacteristic
321C2×C4C4×C22⋊D1111yescharacteristic
322C2×C4#6699311yescharacteristic
323C8—81no—
324C8—221no—
325C8—221no—
326C8—221no—
327C8—221no—
328C8—442no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1062257011yescharacteristic
336C22#1062281312yes—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—82no—
343C4—81no—
344C4—881no—
345C4—881no—
346C4#1062243411yescharacteristic
347C4#1062243411yescharacteristic
348C2—22no—
349C2—161no—
350C2#1306944611yescharacteristic
351C2#1306951111yescharacteristic
352C2#1306952211yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1505C2
socleC22×C11#390
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1505D11
hypocenterC11#9766
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1505

Complements

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

NH ≅ G/Ntype
2. #13068368C2semidirect
3. #13067377C2semidirect
4. #13067232C2semidirect
6. #13067127C2semidirect
12. #10622706C4semidirect
13. #10622692C4semidirect
14. #10622689C4semidirect
15. #10622683C4semidirect
294. C11#9766semidirect

Maximal subgroups

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

subgroupindex
#130791712
#130683682
#130673772
#130672322
#130672272
#130671272
C11×#15052
#976611