Finite Group Databasebeta

← #14656905

Subgroups — #14656905

Order 2816.

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

normal subgroups only

This group has 416 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#13071910C211yesmaximal, characteristic
2#13069596C211yesmaximal, characteristic
3#13067116C211yesmaximal, characteristic
4#13067114C211yesmaximal, characteristic
5#13066517C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×C4×Dic22—21no—
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622597—21no—
14#10622592—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622545C2211yescharacteristic
17C4×Dic11⋊C4—21no—
18#10622538C2211yescharacteristic
19#10622270—21no—
20#10622269—21no—
21#10622193—21no—
22#10622193—21no—
23#10622105—21no—
24#10622105—21no—
25#10622090—21no—
26#10622090—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32#66979—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35#66977—21no—
36#66977—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44#66923—21no—
45#66922Q811yescharacteristic, complemented
46#66922Q811yescharacteristic, complemented
47C4×Dic22—21no—
48C4×Dic22—21no—
49C4×Dic22—42no—
50C4×Dic22—42no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C11⋊#95D411yescharacteristic
64C22⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67#10371—111nomaximal, Sylow
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C11×M16—41no—
83C11×M16—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C11×C4⋊C4—42no—
87C42×C11—41no—
88C42×C11—41no—
89C42×C11C2×Q811yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C22⋊Dic11—41no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—42no—
99C4⋊Dic11—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C4×Dic11—41no—
111C4×Dic11SD1612yes—
112C4×Dic11Q1612yes—
113C2×C11⋊C8—41no—
114#2399—111no—
115#1995—111no—
116#1503—111no—
117#1503—111no—
118#1303—111no—
119#1303D1111yescharacteristic
120#1274—111no—
121C23×C11#12011yescharacteristic
122C2×C4×C11—22no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11C22⋊Q811yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11C2×Q1611yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154Dic22—48no—
155Dic22—81no—
156Dic22—81no—
157C8×C11—81no—
158C8×C11—81no—
159C11⋊C8—81no—
160#533—111no—
161C2×C4×Q8—221no—
162#431—111no—
163#431C2×D1111yescharacteristic
164#423C2×D1111yescharacteristic
165#398—221no—
166#398—221no—
167#395—221no—
168#395—221no—
169C4×C4⋊C4—111no—
170C4×C4⋊C4—221no—
171C4×C4⋊C4C2×D1111yescharacteristic
172#376—111no—
173#339—221no—
174#339—221no—
175#328—221no—
176#328—221no—
177#328—221no—
178#328—221no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39311yescharacteristic
182C22×C11#45011yescharacteristic
183C22×C11#45111yescharacteristic
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—42no—
189C4×C11—81no—
190C4×C11#47511yescharacteristic
191C4×C11#47711yescharacteristic
192C4×C11#48711yescharacteristic
193C4×C11#48911yescharacteristic
194Dic11—42no—
195Dic11—42no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200C22×Q8—221no—
201C2×M16—21no—
202C4⋊Q8—111no—
203C4⋊Q8—111no—
204#125—221no—
205C22⋊Q8—221no—
206C22⋊Q8—221no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×Q8—442no—
210C4×Q8—442no—
211#117—221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C42—21no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—221no—
223C2×C42C22×D1111yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—221no—
228C22⋊C8—21no—
229C22⋊C8—221no—
230C4×C8—21no—
231C4×C8—221no—
232#95—111no—
233#95—111no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95D4411yescharacteristic
239#95D4411yescharacteristic
240C2×C11—21no—
241C2×C11—21no—
242C2×C11#202411yescharacteristic
243C2×C11#203111yescharacteristic
244C2×C11#203111yescharacteristic
245C2×Q8—221no—
246C2×Q8—221no—
247C2×Q8—442no—
248C2×Q8—442no—
249C2×Q8—442no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4C2×D4411yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259M16—41no—
260M16—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—441no—
264C4⋊C4—42no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—441no—
278C42—41no—
279C42—41no—
280C42—112no—
281C42—112no—
282C42—221no—
283C42—221no—
284C42—441no—
285C42—441no—
286C42—441no—
287C42#433911yescharacteristic
288C42#433911yescharacteristic
289C42#434111yescharacteristic
290C42Q8×D1111yescharacteristic
291C11#1037111yescharacteristic, complemented, Sylow
292C23#6693511yescharacteristic
293Q8—448no—
294Q8—881no—
295Q8—881no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4#6692811yescharacteristic
319C2×C4#6693811yescharacteristic
320C2×C4#6693811yescharacteristic
321C2×C4#6694911yescharacteristic
322C2×C4#6694911yescharacteristic
323C2×C4#6695011yescharacteristic
324C2×C4#6696411yescharacteristic
325C2×C4SD16×D1111yescharacteristic
326C2×C4#6696811yescharacteristic
327C2×C4Q16×D1111yescharacteristic
328C8—81no—
329C8—81no—
330C8—881no—
331C22—21no—
332C22—21no—
333C22#1062228611yescharacteristic
334C22#1062238911yescharacteristic
335C22#1062242111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—442no—
343C4—442no—
344C4—442no—
345C4—881no—
346C4—881no—
347C4—881no—
348C4#1062237811yescharacteristic
349C4#1062240511yescharacteristic
350C4#1062246711yescharacteristic
351C4#1062248811yescharacteristic
352C2—21no—
353C2—21no—
354C2#1306975611yescharacteristic
355C2#1306978911yescharacteristic
356C2#1306979111yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1303D11
hypocenterC11#10371
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
45. #66922Q8semidirect
46. #66922Q8semidirect
291. C11#10371semidirect

Maximal subgroups

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

subgroupindex
#130719102
#130695962
#130671162
#130671142
#130665172
#130664442
C11×#13032
#1037111