Finite Group Databasebeta

← #14664938

Subgroups — #14664938

Order 2816.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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#13073820C211yesmaximal, characteristic
2#13068611C211yesmaximal, characteristic
3#13066938C211yesmaximal, characteristic
4#13066647C211yesmaximal, characteristic
5#13066646C211yesmaximal, characteristic
6#13066645C211yesmaximal, characteristic
7C11×#1354C211yesmaximal, characteristic
8C2×#66997C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C11×#395C2211yescharacteristic
11#10622842C411yescharacteristic
12C2×#66888—21no—
13#10622731—21no—
14#10622592C2211yescharacteristic
15#10622589—21no—
16#10622585—21no—
17#10622331—21no—
18#10622269C411yescharacteristic
19#10622262C411yescharacteristic
20#10622260—21no—
21#10622259—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×Dic22D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4C2311yescharacteristic
33#66997—41no—
34#66997—41no—
35C2×C4⋊Dic11—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4C2×C411yescharacteristic
42C2×Dic11⋊C4D411yescharacteristic
43C2×C4×Dic11—21no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48#66940—41no—
49#66940—41no—
50C11×C22⋊C8—21no—
51C11×#95—21no—
52C11×#95C2×C411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66888—42no—
59Dic11⋊C8—41no—
60Dic11⋊C8—41no—
61Dic11⋊C8—41no—
62C8×Dic11—41no—
63#11908—111nomaximal, Sylow
64C2×Q8×C11—41no—
65C2×Q8×C11—81no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C2×Dic22—41no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—81no—
81C2×Dic22SD1612yes—
82C2×Dic22Q1612yes—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—81no—
89C4⋊Dic11—81no—
90Dic11⋊C4—24no—
91Dic11⋊C4—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—42no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96Dic11⋊C4—81no—
97Dic11⋊C4—81no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—42no—
105#4318—41no—
106#4318—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2567—111no—
110#1801—111no—
111#1461—111no—
112#1354—111no—
113#1354—111no—
114#1354—111no—
115#1354D1111yescharacteristic
116C23×C11C2×C22⋊C411yescharacteristic
117Q8×C11—82no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
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×C11C2×SD1611yescharacteristic
131C2×C4×C11C2×Q1611yescharacteristic
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—21no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11#9911yescharacteristic
146C2×Dic11#9911yescharacteristic
147C2×Dic11#10312yes—
148C2×Dic11#10312yes—
149Dic22—42no—
150Dic22—42no—
151Dic22—82no—
152C8×C11—81no—
153C8×C11—81no—
154C11⋊C8—81no—
155C11⋊C8—81no—
156C2×C4⋊Q8—111no—
157C2×C4×Q8—111no—
158#431—221no—
159#423—221no—
160C2×#101—221no—
161#395—111no—
162#395—111no—
163#395—111no—
164#395C2×D1111yescharacteristic
165#391—221no—
166#389—221no—
167#389—221no—
168#384—221no—
169C4×C4⋊C4—111no—
170#343—111no—
171#343C2×D1111yescharacteristic
172#324—111no—
173#324—221no—
174#324C2×D1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11C2×#9911yescharacteristic
178C22×C11C2×#10311yescharacteristic
179C22×C11#42111yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—81no—
186Dic11—21no—
187Dic11—22no—
188Dic11—22no—
189Dic11—42no—
190Dic11—41no—
191Dic11—81no—
192Dic11#35612yes—
193C22×Q8—111no—
194C22×Q8—111no—
195C22×Q8C4×D1111yescharacteristic
196C2×M16—21no—
197C2×M16—221no—
198C4⋊Q8—441no—
199C4⋊Q8—441no—
200C4×Q8—441no—
201C4×Q8—441no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—111no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C22×D1111yescharacteristic
212C2×C42—111no—
213C2×C42—111no—
214C2×C42—111no—
215C2×C42—221no—
216C4⋊C8—441no—
217C4⋊C8—441no—
218C4⋊C8—441no—
219#101—442no—
220C22⋊C8—21no—
221C22⋊C8—221no—
222C4×C8—441no—
223#95—21no—
224#95—111no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95C4×D1111yescharacteristic
229C2×C11—21no—
230C2×C11—21no—
231C2×C11#152011yescharacteristic
232C2×C11#212211yescharacteristic
233C2×C11C2×#35611yescharacteristic
234C2×Q8—41no—
235C2×Q8—81no—
236C2×Q8—112no—
237C2×Q8—112no—
238C2×Q8—441no—
239C2×Q8—441no—
240C2×Q8—441no—
241C2×Q8—881no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253M16—41no—
254M16—41no—
255M16—441no—
256M16—441no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—441no—
260C2×C8—441no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—224no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4—442no—
269C4⋊C4—881no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42—221no—
278C42—442no—
279C11#1190811yescharacteristic, complemented, Sylow
280C23C22⋊C4×D1111yescharacteristic
281Q8—82no—
282Q8—442no—
283Q8—442no—
284Q8—882no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—112no—
300C2×C4—112no—
301C2×C4—222no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—222no—
307C2×C4—221no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4SD16×D1111yescharacteristic
315C2×C4Q16×D1111yescharacteristic
316C8—81no—
317C8—81no—
318C8—881no—
319C8—881no—
320C22—21no—
321C22—21no—
322C22D11×#9911yescharacteristic
323C22D11×#10311yescharacteristic
324C22#1062243411yescharacteristic
325C4—21no—
326C4—21no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—112no—
332C4—222no—
333C4—222no—
334C4—221no—
335C4—442no—
336C4—441no—
337C4—881no—
338C2—21no—
339C2—21no—
340C2#1306718611yescharacteristic
341C2#1307026411yescharacteristic
342C2D11×#35611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11908
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
279. C11#11908semidirect

Maximal subgroups

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

subgroupindex
#130738202
#130686112
#130669382
#130666472
#130666462
#130666452
C11×#13542
#1190811