Finite Group Databasebeta

← #14650698

Subgroups — #14650698

Order 2816.

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

normal subgroups only

This group has 492 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#13071259C211yesmaximal, characteristic
2#13069561C211yesmaximal, characteristic, complemented
3#13067128C211yesmaximal, characteristic, complemented
4#13067059C211yesmaximal, characteristic
5#13066508C211yesmaximal, characteristic, complemented
6#13066473C211yesmaximal, characteristic, complemented
7C11×#3110C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#484—21no—
11C11×#474C412yescomplemented
12C11×#461C412yescomplemented
13C11×#450—21no—
14C11×#440—22no—
15C11×#432C2211yescharacteristic
16#10622834—21no—
17#10622825—21no—
18#10622824—21no—
19#10622598—21no—
20#10622564—22no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622545C2211yescharacteristic
23#10622539C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622176—21no—
26#10622176—21no—
27D4⋊(C11⋊C8)—22no—
28#10622170—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×SD16—22no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11C2×C412yes—
42C4×D4×C11D412yes—
43C11×#117—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—22no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—22no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11D412yes—
53C2×#4318—21no—
54C11×#107—22no—
55C11×C4⋊C8C2×C412yes—
56C11×#103—22no—
57C11×#102—22no—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11⋊#95—22no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8—21no—
70#9327—111nomaximal, Sylow
71C24×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—42no—
76C2×D4×C11C22⋊C412yes—
77C22×C4×C11—21no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—82no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—22no—
86C22×Dic11—21no—
87C11×SD16—44no—
88C2×C8×C11—22no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4C22⋊C412yes—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—41no—
100C42×C11—41no—
101C42×C11C22×C411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C42×C11#4111yescharacteristic
104C42×C11#4111yescharacteristic
105C22⋊Dic11—82no—
106C22⋊Dic11—82no—
107C4⋊Dic11—42no—
108C4⋊Dic11—82no—
109C4×Dic11—42no—
110C4×Dic11—42no—
111#4318—22no—
112#4318—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8—41no—
115#3110D1111yescharacteristic
116#2319—111no—
117#1986—111no—
118#1506—111no—
119#1490—111no—
120#1300—111no—
121#1285—111no—
122C23×C11—22no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11#12011yescharacteristic
128Q8×C11—42no—
129Q8×C11—81no—
130D4×C11—22no—
131D4×C11—22no—
132D4×C11—42no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—41no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11—82no—
143C2×C4×C11C2×C22⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C8×C11—42no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161#533C2×D1111yescharacteristic
162C2×C4×D4C2×D1111yescharacteristic
163#484—21no—
164#474Dic1112yescomplemented
165#461Dic1112yescomplemented
166#450—21no—
167#440—22no—
168#432—111no—
169#432C2×D1111yescharacteristic
170C4×M16—111no—
171#390—221no—
172#389—221no—
173#388—222no—
174#381—221no—
175#380—221no—
176C4×C4⋊C4—111no—
177#376—111no—
178#339—222no—
179#328—221no—
180#328—221no—
181D4⋊C8—222no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—42no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—82no—
188C22×C11—82no—
189C22×C11#38611yescharacteristic
190C22×C11#45511yescharacteristic
191C22×C11#45611yescharacteristic
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—42no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11#42112yes—
201Dic11—81no—
202Dic11—82no—
203Dic11—81no—
204C22×D4C22⋊D1111yescharacteristic
205C23×C4—21no—
206C2×SD16—22no—
207C2×M16—221no—
208C4⋊Q8C2×Dic1111yescharacteristic
209C4⋊Q8C2×Dic1111yescharacteristic
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—21no—
216C4×D4—21no—
217C4×D4C2×Dic1112yes—
218C4×D4C22⋊D1112yes—
219#117—21no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—222no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—222no—
225C2×C22⋊C4—222no—
226C2×C42—112no—
227C2×C42—221no—
228C2×C42C22×D1111yescharacteristic
229#107—22no—
230C4⋊C8—221no—
231C4⋊C8C2×Dic1112yes—
232#103—22no—
233#102—22no—
234C22⋊C8—21no—
235C22⋊C8—221no—
236#97—21no—
237#97—221no—
238#97—221no—
239C4×C8—221no—
240#95—111no—
241#95—111no—
242#95—222no—
243#95—221no—
244#95—221no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—82no—
248C2×C11#188211yescharacteristic
249C2×C11#189711yescharacteristic
250C2×C11#190411yescharacteristic
251C24—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×D4—21no—
255C2×D4—42no—
256C2×D4C22⋊Dic1112yes—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—82no—
261C22×C4—221no—
262C22×C4—221no—
263C22×C4—222no—
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4C2×C22⋊D1111yescharacteristic
267SD16—44no—
268M16—222no—
269M16—441no—
270C2×C8—22no—
271C2×C8—441no—
272C2×C8—441no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—442no—
281C4⋊C4—882no—
282C4⋊C4C22⋊Dic1112yes—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—41no—
286C22⋊C4—882no—
287C22⋊C4—882no—
288C42—41no—
289C42—442no—
290C42—442no—
291C42#434111yescharacteristic
292C42#434111yescharacteristic
293C42C22×Dic1111yescharacteristic
294C42C2×C22⋊D1111yescharacteristic
295C11#932711yescharacteristic, complemented, Sylow
296C23—22no—
297C23—42no—
298C23—42no—
299C23—41no—
300C23—41no—
301C23#6699011yescharacteristic
302Q8—42no—
303Q8—81no—
304D4—22no—
305D4—22no—
306D4—42no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4—441no—
323C2×C4—442no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4D4×Dic1111yescharacteristic
327C2×C4D4×Dic1111yescharacteristic
328C2×C4#6698811yescharacteristic
329C2×C4#6699211yescharacteristic
330C2×C4#6699211yescharacteristic
331C2×C4C2×C22⋊Dic1111yescharacteristic
332C8—42no—
333C8—442no—
334C8—881no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—82no—
341C22—82no—
342C22#1062281511yescharacteristic
343C22#1062281811yescharacteristic
344C22#1062283311yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—81no—
352C4—81no—
353C4—881no—
354C4—882no—
355C4—881no—
356C4#1062284912yes—
357C2—21no—
358C2—21no—
359C2—82no—
360C2#1306898711yescharacteristic
361C2#1306906511yescharacteristic
362C2#1306910511yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3110C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#3110D11
hypocenterC11#9327
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3110

Complements

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

NH ≅ G/Ntype
2. #13069561C2semidirect
3. #13067128C2semidirect
5. #13066508C2semidirect
6. #13066473C2semidirect
11. C11×#474C4semidirect
12. C11×#461C4semidirect
164. #474Dic11semidirect
165. #461Dic11semidirect
295. C11#9327semidirect

Maximal subgroups

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

subgroupindex
#130712592
#130695612
#130671282
#130670592
#130665082
#130664732
C11×#31102
#932711