Finite Group Databasebeta

← #14672454

Subgroups — #14672454

Order 2816.

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

normal subgroups only

This group has 404 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#13073833C211yesmaximal, 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#10622590C411yescharacteristic
19#10622549C411yescharacteristic
20C4×Dic11⋊C4C411yescharacteristic
21#10622273—21no—
22#10622273—21no—
23#10622259—21no—
24#10622259—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⋊Dic11C2×C411yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11C2×C411yescharacteristic
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×#4318—21no—
46C2×#4318—21no—
47#66941—41no—
48#66941—41no—
49C11×#101—21no—
50C11×#101—21no—
51C11×#101—21no—
52C11×#101Q812yescomplemented
53C11×#95—21no—
54C11×#95—21no—
55#66900—21no—
56#66900—21no—
57#66900—21no—
58#66900Q812yescomplemented
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66#66879—41no—
67Dic11⋊C8—41no—
68Dic11⋊C8—41no—
69C8×Dic11—41no—
70#13301—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—44no—
89C2×Dic22—41no—
90C2×Dic22—41no—
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—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—41no—
112#4318—22no—
113#4318—41no—
114#4318—41no—
115#4318—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—41no—
118#2568—111no—
119#1801—111no—
120C4×#101—111no—
121#1394—111no—
122#1394—111no—
123#1394—111no—
124#1394D1111yescharacteristic
125C23×C11C2×C22⋊C411yescharacteristic
126Q8×C11—41no—
127Q8×C11—41no—
128Q8×C11—41no—
129Q8×C11—41no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11C4×Q811yescharacteristic
142C2×C4×C11C4×Q811yescharacteristic
143C2×C4×C11C22⋊Q811yescharacteristic
144C2×C4×C11C22⋊Q811yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11C4⋊Q811yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11#9911yescharacteristic
160C2×Dic11#9911yescharacteristic
161Dic22—82no—
162Dic22—82no—
163C8×C11—42no—
164C8×C11—81no—
165C11⋊C8—42no—
166C11⋊C8—81no—
167C2×C4⋊Q8—111no—
168C2×C4×Q8—111no—
169#423—221no—
170C2×#101—111no—
171C2×#101—111no—
172C2×#101C2×D1111yescharacteristic
173C2×#101C2×D1111yescharacteristic
174C4×M16—221no—
175#400—221no—
176#400—221no—
177#391—111no—
178#391—221no—
179#391—221no—
180#391C2×D1111yescharacteristic
181#382—111no—
182#382—111no—
183C4×C4⋊C4—111no—
184#343—221no—
185#343—221no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11#39111yescharacteristic
189C22×C11C2×#9911yescharacteristic
190C22×C11#41011yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—81no—
198C4×C11—81no—
199Dic11—21no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—81no—
204Dic11—81no—
205Dic11#35512yes—
206C22×Q8—221no—
207C22×Q8C22×D1111yescharacteristic
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—221no—
211C2×M16—221no—
212C4⋊Q8—441no—
213C4⋊Q8—441no—
214C4×Q8—441no—
215C4×Q8—441no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—111no—
218C2×C4⋊C4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C4×D1111yescharacteristic
223C2×C42—111no—
224C2×C42—111no—
225C2×C42—111no—
226C2×C42—111no—
227C2×C42C4×D1111yescharacteristic
228C4⋊C8—441no—
229C4⋊C8—441no—
230#101—21no—
231#101—21no—
232#101—21no—
233#101—112no—
234#101—221no—
235#101—221no—
236#101—221no—
237#101Dic2212yescomplemented
238#97—441no—
239C4×C8—441no—
240#95—21no—
241#95—21no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248#95—221no—
249C2×C11—21no—
250C2×C11—21no—
251C2×C11#199611yescharacteristic
252C2×C11C2×#35511yescharacteristic
253C2×C11#213511yescharacteristic
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×Q8—444no—
259C2×Q8C2×Dic2211yescharacteristic
260C2×Q8#433911yescharacteristic
261C2×Q8#434111yescharacteristic
262C2×Q8Q8×D1111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4D4×D1111yescharacteristic
274M16—22no—
275M16—41no—
276M16—41no—
277M16—41no—
278M16—222no—
279M16—441no—
280M16—441no—
281M16—441no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—441no—
285C2×C8—441no—
286C4⋊C4—41no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—442no—
292C4⋊C4—442no—
293C42—41no—
294C42—221no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42—221no—
300C42—441no—
301C11#1330111yescharacteristic, complemented, Sylow
302C23C22⋊C4×D1111yescharacteristic
303Q8—41no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—882no—
308Q8—882no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—222no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—442no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4C4×Dic2211yescharacteristic
335C2×C4#6693111yescharacteristic
336C2×C4#6693811yescharacteristic
337C2×C4#6694011yescharacteristic
338C2×C4#6694111yescharacteristic
339C2×C4#6694911yescharacteristic
340C8—42no—
341C8—81no—
342C8—442no—
343C8—881no—
344C22—21no—
345C22—21no—
346C22#1062225911yescharacteristic
347C22#1062235311yescharacteristic
348C22D11×#9911yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—112no—
358C4—221no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4—881no—
363C4—881no—
364C2—21no—
365C2—21no—
366C2#1306959911yescharacteristic
367C2D11×#35511yescharacteristic
368C2#1307030911yescharacteristic
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#13301
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
52. C11×#101Q8semidirect
58. #66900Q8semidirect
237. #101Dic22semidirect
301. C11#13301semidirect

Maximal subgroups

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

subgroupindex
#130738332
#130686102
#101×Dic112
#130667432
#130667422
C11×#13942
#1330111