Finite Group Databasebeta

← #14672458

Subgroups — #14672458

Order 2816.

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

normal subgroups only

This group has 420 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#13073826C211yesmaximal, characteristic
2#13068610C211yesmaximal, characteristic
3#101×Dic11C211yesmaximal, characteristic
4#13066743C211yesmaximal, characteristic
5#13066742C211yesmaximal, characteristic
6#13066742C211yesmaximal, characteristic
7C11×#1394C211yesmaximal, characteristic
8C2×Q8×Dic11C2211yescharacteristic
9C2×#66941C411yescharacteristic
10C2×C11×#101C2211yescharacteristic
11C2×C11×#101C2211yescharacteristic
12C11×#391C2211yescharacteristic
13#10622843C2211yescharacteristic
14C2×#66900C2211yescharacteristic
15C2×#66900C2211yescharacteristic
16#10622731—21no—
17M16×Dic11—21no—
18#10622589C411yescharacteristic
19#10622548C411yescharacteristic
20C4×Dic11⋊C4C411yescharacteristic
21#10622269—21no—
22#10622269—21no—
23#10622260—21no—
24#10622260—21no—
25#10622192—21no—
26#10622192—21no—
27C22×Q8×C11C2311yescharacteristic
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33Q8×Dic11—41no—
34Q8×Dic11—41no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×#4318—21no—
50C2×#4318—21no—
51#66941—41no—
52#66941—41no—
53C11×#101—21no—
54C11×#101—21no—
55C11×#101—21no—
56C11×#101Q812yescomplemented
57C11×#95—21no—
58C11×#95—21no—
59#66900—21no—
60#66900—21no—
61#66900—21no—
62#66900Q812yescomplemented
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66#66879—41no—
67Dic11⋊C8—41no—
68Dic11⋊C8—41no—
69C8×Dic11—41no—
70#13302—111nomaximal, Sylow
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11C2×Q811yescharacteristic
74C2×Q8×C11C2×Q811yescharacteristic
75C2×Q8×C11#4111yescharacteristic
76C2×Q8×C11#4111yescharacteristic
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C2×Dic22—42no—
89C2×Dic22—81no—
90C2×Dic22—81no—
91C11×M16—22no—
92C11×M16—41no—
93C11×M16—41no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C42×C11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—81no—
104C4⋊Dic11—81no—
105Dic11⋊C4—24no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108Dic11⋊C4—81no—
109Dic11⋊C4—81no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—41no—
117#4318—22no—
118#4318—41no—
119#4318—41no—
120#4318—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123#2567—111no—
124#1801—111no—
125C4×#101—111no—
126#1394—111no—
127#1394—111no—
128#1394—111no—
129#1394D1111yescharacteristic
130C23×C11C2×C22⋊C411yescharacteristic
131Q8×C11—41no—
132Q8×C11—41no—
133Q8×C11—41no—
134Q8×C11—41no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11C4×Q811yescharacteristic
148C2×C4×C11C4×Q811yescharacteristic
149C2×C4×C11C22⋊Q811yescharacteristic
150C2×C4×C11C22⋊Q811yescharacteristic
151C2×C4×C11#12411yescharacteristic
152C2×C4×C11C4⋊Q811yescharacteristic
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11#9911yescharacteristic
167C2×Dic11#9911yescharacteristic
168Dic22—84no—
169C8×C11—42no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—81no—
173C2×C4⋊Q8—111no—
174C2×C4×Q8—111no—
175#423—221no—
176C2×#101—111no—
177C2×#101—111no—
178C2×#101C2×D1111yescharacteristic
179C2×#101C2×D1111yescharacteristic
180C4×M16—221no—
181#395—221no—
182#395—221no—
183#391—111no—
184#391C2×D1111yescharacteristic
185#389—221no—
186#389—221no—
187#384—111no—
188#384—111no—
189C4×C4⋊C4—111no—
190#343—221no—
191#343—221no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#39111yescharacteristic
195C22×C11C2×#9911yescharacteristic
196C22×C11#41011yescharacteristic
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—42no—
204C4×C11—81no—
205Dic11—21no—
206Dic11—42no—
207Dic11—41no—
208Dic11—41no—
209Dic11—41no—
210Dic11—81no—
211Dic11#35612yes—
212C22×Q8—221no—
213C22×Q8C22×D1111yescharacteristic
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—221no—
217C2×M16—221no—
218C4⋊Q8—441no—
219C4⋊Q8—441no—
220C4×Q8—441no—
221C4×Q8—441no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4C4×D1111yescharacteristic
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42C4×D1111yescharacteristic
238C4⋊C8—441no—
239C4⋊C8—441no—
240#101—21no—
241#101—21no—
242#101—21no—
243#101—112no—
244#101—221no—
245#101—221no—
246#101—221no—
247#101Dic2212yescomplemented
248#97—441no—
249C4×C8—441no—
250#95—21no—
251#95—21no—
252#95—221no—
253#95—221no—
254#95—221no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11#199611yescharacteristic
258C2×C11C2×#35611yescharacteristic
259C2×C11#213411yescharacteristic
260C2×Q8—41no—
261C2×Q8—41no—
262C2×Q8—442no—
263C2×Q8—881no—
264C2×Q8—881no—
265C2×Q8C2×Dic2211yescharacteristic
266C2×Q8#433911yescharacteristic
267C2×Q8#434111yescharacteristic
268C2×Q8Q8×D1111yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—222no—
285M16—441no—
286M16—441no—
287M16—441no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—41no—
293C4⋊C4—224no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C4⋊C4—441no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—881no—
301C4⋊C4—881no—
302C4⋊C4—881no—
303C4⋊C4—881no—
304C42—41no—
305C42—221no—
306C42—221no—
307C42—221no—
308C42—221no—
309C42—221no—
310C42—221no—
311C42—441no—
312C11#1330211yescharacteristic, complemented, Sylow
313C23C22⋊C4×D1111yescharacteristic
314Q8—41no—
315Q8—41no—
316Q8—41no—
317Q8—41no—
318Q8—884no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—111no—
332C2×C4—111no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4C4×Dic2211yescharacteristic
347C2×C4#6693111yescharacteristic
348C2×C4#6693811yescharacteristic
349C2×C4#6694011yescharacteristic
350C2×C4#6694111yescharacteristic
351C2×C4#6694911yescharacteristic
352C8—42no—
353C8—81no—
354C8—442no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22#1062225911yescharacteristic
359C22#1062235311yescharacteristic
360C22D11×#9911yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—81no—
369C4—112no—
370C4—221no—
371C4—442no—
372C4—441no—
373C4—441no—
374C4—441no—
375C4—881no—
376C2—21no—
377C2—21no—
378C2#1306959911yescharacteristic
379C2D11×#35611yescharacteristic
380C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#1394C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenter#1394D11
hypocenterC11#13302
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
56. C11×#101Q8semidirect
62. #66900Q8semidirect
247. #101Dic22semidirect
312. C11#13302semidirect

Maximal subgroups

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

subgroupindex
#130738262
#130686102
#101×Dic112
#130667432
#130667422
C11×#13942
#1330211