Finite Group Databasebeta

← #14656914

Subgroups — #14656914

Order 2816.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13071924C211yesmaximal, characteristic
2#13069598C211yesmaximal, characteristic
3#13067115C211yesmaximal, characteristic
4#13066519C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1503C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C4×C11×C4⋊C4C2211yescharacteristic
11#10622599—21no—
12#10622597—21no—
13C4×C4⋊Dic11—21no—
14C4×C4⋊Dic11C2211yescharacteristic
15#10622545C2211yescharacteristic
16C4×Dic11⋊C4—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622274—21no—
20#10622273—21no—
21C11×#328—21no—
22C11×#328—21no—
23#10622176—21no—
24#10622176—21no—
25#10622170—21no—
26#10622170—21no—
27C11×C4⋊Q8Q811yescharacteristic
28C11×C4⋊Q8Q811yescharacteristic
29C11×#125—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C11×#117—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C4×C8×C11—21no—
50C11×#95D411yescharacteristic
51C11×#95D411yescharacteristic
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65#10373—111nomaximal, Sylow
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
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×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—41no—
86C42×C11—41no—
87C42×C11—41no—
88C42×C11—41no—
89C42×C11C2×Q811yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C42×C11#4111yescharacteristic
93C4⋊Dic11—42no—
94C4⋊Dic11—42no—
95C4⋊Dic11—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—42no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—41no—
103C4×Dic11—41no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2402—111no—
109#1995—111no—
110#1503—111no—
111#1503D1111yescharacteristic
112#1303—111no—
113#1303—111no—
114#1274—111no—
115C23×C11#12011yescharacteristic
116Q8×C11—81no—
117Q8×C11—81no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×C4×C11#13711yescharacteristic
138C2×Dic11—22no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C8×C11—81no—
151C11⋊C8—81no—
152C11⋊C8—81no—
153#533C2×D1111yescharacteristic
154#431—111no—
155#431C2×D1111yescharacteristic
156#423—111no—
157#400—221no—
158#400—221no—
159#398—221no—
160#398—221no—
161C4×C4⋊C4—111no—
162C4×C4⋊C4—221no—
163C4×C4⋊C4—221no—
164C4×C4⋊C4C2×D1111yescharacteristic
165#376—111no—
166#339—221no—
167#339—221no—
168#328—21no—
169#328—21no—
170#328—221no—
171#328—221no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11#39311yescharacteristic
175C22×C11#45211yescharacteristic
176C22×C11#45211yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—81no—
183C4×C11—81no—
184C4×C11—81no—
185C4×C11#47911yescharacteristic
186C4×C11#47911yescharacteristic
187C4×C11#48811yescharacteristic
188C4×C11#49111yescharacteristic
189Dic11—42no—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193C2×M16—221no—
194C4⋊Q8Dic2211yescharacteristic
195C4⋊Q8Dic2211yescharacteristic
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C42—21no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42—221no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—221no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C22⋊C8—21no—
218C22⋊C8—221no—
219C4×C8—21no—
220C4×C8—221no—
221#95—111no—
222#95—111no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95C22⋊D1111yescharacteristic
230#95C22⋊D1111yescharacteristic
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#202611yescharacteristic
234C2×C11#203111yescharacteristic
235C2×C11#203111yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4D4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247M16—441no—
248M16—441no—
249C2×C8—41no—
250C2×C8—441no—
251C2×C8—441no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C4⋊C4—442no—
263C4⋊C4—442no—
264C22⋊C4—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—221no—
272C42—441no—
273C42—441no—
274C42C2×Dic2211yescharacteristic
275C42#433911yescharacteristic
276C42#434111yescharacteristic
277C42#434111yescharacteristic
278C11#1037311yescharacteristic, complemented, Sylow
279C23#6699011yescharacteristic
280Q8—81no—
281Q8—81no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—222no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4#6693111yescharacteristic
305C2×C4#6693111yescharacteristic
306C2×C4#6693811yescharacteristic
307C2×C4#6693811yescharacteristic
308C2×C4#6696811yescharacteristic
309C2×C4#6696911yescharacteristic
310C2×C4#6697111yescharacteristic
311C2×C4#6697211yescharacteristic
312C2×C4#6697711yescharacteristic
313C2×C4#6698911yescharacteristic
314C8—81no—
315C8—881no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22#1062256011yescharacteristic
320C22#1062278611yescharacteristic
321C22#1062280011yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—442no—
331C4—881no—
332C4—881no—
333C4—881no—
334C4#1062240911yescharacteristic
335C4#1062241011yescharacteristic
336C4#1062241211yescharacteristic
337C4#1062241311yescharacteristic
338C2—21no—
339C2—21no—
340C2#1306976511yescharacteristic
341C2#1306978811yescharacteristic
342C2#1306979011yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1503C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1503D11
hypocenterC11#10373
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
278. C11#10373semidirect

Maximal subgroups

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

subgroupindex
#130719242
#130695982
#130671152
#130665192
#130665182
#130664442
C11×#15032
#1037311