Finite Group Databasebeta

← #14653203

Subgroups — #14653203

Order 2816.

396 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068367C211yesmaximal, characteristic, complemented
2#13067379C211yesmaximal, characteristic, complemented
3#13067231C211yesmaximal, characteristic, complemented
4#13067227C211yesmaximal, characteristic
5#13067128C211yesmaximal, characteristic, complemented
6#13067124C211yesmaximal, characteristic
7C11×#3167C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#532C2211yescharacteristic
10C11×#498C411yescharacteristic, complemented
11C11×#492C411yescharacteristic, complemented
12C11×#487C411yescharacteristic, complemented
13C11×#486C411yescharacteristic, complemented
14C11×#465—21no—
15C11×#465—21no—
16C4×C11×SD16—21no—
17C4×C11×SD16—21no—
18C2×C4×C8×C11C2211yescharacteristic
19#10622545C2211yescharacteristic
20#10622539C2211yescharacteristic
21#10622539C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23#10622188—21no—
24#10622188—21no—
25#10622181—22no—
26#10622178—22no—
27#10622176—22no—
28#10622175—22no—
29#10622096—21no—
30#10622095—21no—
31C2×C11×#41—21no—
32C2×C11×SD16—21no—
33C2×C11×SD16—21no—
34C22×C8×C11D411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C11×C4⋊Q8C2×C411yescharacteristic
37C11×C4⋊Q8C2×C411yescharacteristic
38C11×C4⋊Q8C2×C411yescharacteristic
39C11×#127C2×C411yescharacteristic
40C11×#125—21no—
41C11×#124—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C11×#117—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C4×Dic11—21no—
53C22×C11⋊C8—21no—
54C11×#106—21no—
55C11×#106—21no—
56C11×#103—21no—
57C11×#103—21no—
58C11×#102—21no—
59C11×#102—21no—
60C4×C8×C11C2×C411yescharacteristic
61C4×C8×C11C2×C411yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11D411yescharacteristic
64C11⋊#95—21no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70#66867—21no—
71#66867—21no—
72#66867—21no—
73#66867D412yes—
74#9766—111nomaximal, Sylow
75C11×#41—82no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—22no—
88C11×SD16—42no—
89C11×SD16—42no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11C22⋊C411yescharacteristic
93C2×C8×C11C22⋊C411yescharacteristic
94C2×C8×C11C22⋊C411yescharacteristic
95C2×C8×C11C22⋊C411yescharacteristic
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11C22×C411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C4×Dic11—41no—
113C4×Dic11—41no—
114C2×C11⋊C8—22no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#3167D1111yescharacteristic
120#1746—111no—
121#1568—111no—
122#1531—111no—
123#1530—111no—
124#1506—111no—
125#1505—111no—
126C23×C11—41no—
127C23×C11#12111yescharacteristic
128Q8×C11—41no—
129Q8×C11—41no—
130Q8×C11—81no—
131Q8×C11—81no—
132D4×C11—41no—
133D4×C11—41no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—82no—
137C2×C4×C11—22no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—82no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11#12711yescharacteristic
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C8×C11—21no—
155C8×C11—21no—
156C8×C11—21no—
157C8×C11—21no—
158C11⋊C8—42no—
159C11⋊C8—81no—
160C11⋊C8—81no—
161#533C2×D1111yescharacteristic
162#532C2×D1111yescharacteristic
163#498Dic1111yescharacteristic, complemented
164#492Dic1111yescharacteristic, complemented
165#487Dic1111yescharacteristic, complemented
166#486Dic1111yescharacteristic, complemented
167#465—21no—
168#465—21no—
169C4×SD16—21no—
170C4×SD16—21no—
171#432—111no—
172#432—111no—
173C2×#97—111no—
174C2×C4×C8C2×D1111yescharacteristic
175#376—111no—
176#336—221no—
177#336—221no—
178#335—221no—
179#334—221no—
180#330—222no—
181#329—222no—
182#328—222no—
183#327—222no—
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—81no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11#42111yescharacteristic
200C4×C11#42111yescharacteristic
201Dic11—82no—
202C2×#41—21no—
203C2×SD16—21no—
204C2×SD16—21no—
205C22×C8—221no—
206C22×C8C22⋊D1111yescharacteristic
207C22×C8C22⋊D1111yescharacteristic
208C4⋊Q8C2×Dic1111yescharacteristic
209C4⋊Q8C2×Dic1111yescharacteristic
210C4⋊Q8C2×Dic1111yescharacteristic
211#127C2×Dic1111yescharacteristic
212#125—21no—
213#124—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216#121—21no—
217#121—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×D4—21no—
221C4×D4—21no—
222#117—21no—
223C2×C42—221no—
224C2×C42C22×D1111yescharacteristic
225#106—21no—
226#106—21no—
227C4⋊C8—221no—
228C4⋊C8—221no—
229#103—21no—
230#103—21no—
231#102—21no—
232#102—21no—
233C22⋊C8—221no—
234C22⋊C8—221no—
235#97—112no—
236#97—221no—
237#97—221no—
238#97—221no—
239C4×C8C2×Dic1111yescharacteristic
240C4×C8C2×Dic1111yescharacteristic
241C4×C8C22⋊D1111yescharacteristic
242C4×C8C22⋊D1111yescharacteristic
243#95—112no—
244#95—221no—
245C2×C11—22no—
246C2×C11—161no—
247C2×C11#196311yescharacteristic
248C2×C11#197611yescharacteristic
249C2×C11#197711yescharacteristic
250#41—82no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C22×C4—41no—
259C22×C4—222no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263SD16—42no—
264SD16—42no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—222no—
268C2×C8—441no—
269C2×C8—441no—
270C2×C8—441no—
271C2×C8—441no—
272C2×C8C22⋊Dic1111yescharacteristic
273C2×C8C22⋊Dic1111yescharacteristic
274C2×C8C22⋊Dic1111yescharacteristic
275C2×C8C22⋊Dic1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—41no—
288C42—441no—
289C42—441no—
290C42D4×D1111yescharacteristic
291C42#434111yescharacteristic
292C42C22×Dic1111yescharacteristic
293C42C2×C22⋊D1111yescharacteristic
294C11#976611yescharacteristic, complemented, Sylow
295C23—41no—
296C23#6699111yescharacteristic
297Q8—41no—
298Q8—41no—
299Q8—81no—
300Q8—81no—
301D4—41no—
302D4—41no—
303D4—81no—
304D4—81no—
305D4—82no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—82no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4D4×Dic1111yescharacteristic
318C2×C4D4×Dic1111yescharacteristic
319C2×C4#6698911yescharacteristic
320C2×C4#6699111yescharacteristic
321C2×C4#6699311yescharacteristic
322C2×C4C2×C22⋊Dic1111yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—21no—
327C8—442no—
328C8—881no—
329C8—881no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#1062279012yes—
336C22#1062283411yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—882no—
346C4#1062284911yescharacteristic
347C4#1062284911yescharacteristic
348C2—22no—
349C2—161no—
350C2#1306944911yescharacteristic
351C2#1306951511yescharacteristic
352C2#1306952111yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3167C2
socleC22×C11#390
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3167D11
hypocenterC11#9766
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #13068367C2semidirect
2. #13067379C2semidirect
3. #13067231C2semidirect
5. #13067128C2semidirect
10. C11×#498C4semidirect
11. C11×#492C4semidirect
12. C11×#487C4semidirect
13. C11×#486C4semidirect
163. #498Dic11semidirect
164. #492Dic11semidirect
165. #487Dic11semidirect
166. #486Dic11semidirect
294. C11#9766semidirect

Maximal subgroups

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

subgroupindex
#130683672
#130673792
#130672312
#130672272
#130671282
#130671242
C11×#31672
#976611