Finite Group Databasebeta

← #14653877

Subgroups — #14653877

Order 2816.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077001C211yesmaximal, characteristic
2#13068470C211yesmaximal, characteristic
3#13068364C211yesmaximal, characteristic
4#13066498C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×C11×#97C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×Dic11⋊C8—21no—
12#10622598C411yescharacteristic
13#10622598C411yescharacteristic
14#10622586C411yescharacteristic
15#10622586C411yescharacteristic
16#10622549C2211yescharacteristic
17C42×Dic11C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19C2×#66867C2211yescharacteristic
20#10622268—21no—
21#10622268—21no—
22#10622267—21no—
23#10622267—21no—
24#10622188—21no—
25#10622188—21no—
26#10622188—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×C4×Dic11C2×C411yescharacteristic
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C11×#97—21no—
47C11×#97—21no—
48C11×#97—21no—
49C11×#97Q812yes—
50C11×#95—21no—
51C11×#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58Dic11⋊C8—24no—
59#66867—21no—
60#66867—21no—
61#66867—21no—
62#66867Q812yes—
63#9893—111nomaximal, Sylow
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11C22⋊C411yescharacteristic
72C22×Dic11C22⋊C411yescharacteristic
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×C8×C11—22no—
76C2×C8×C11—22no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11C2×Q811yescharacteristic
84C42×C11C2×Q811yescharacteristic
85C42×C11#4111yescharacteristic
86C42×C11#4111yescharacteristic
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—42no—
90C4⋊Dic11—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93C4×Dic11—22no—
94C4×Dic11—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105#2864—111no—
106#1767—111no—
107#1745—111no—
108#1295—111no—
109#1295—111no—
110#1295—111no—
111#1295D1111yescharacteristic
112C23×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
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×C11C4×Q811yescharacteristic
126C2×C4×C11C4×Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11C4⋊Q811yescharacteristic
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11#10412yes—
149C8×C11—42no—
150C8×C11—42no—
151C11⋊C8—42no—
152C11⋊C8—42no—
153C2×C4⋊C8—221no—
154C2×#97—111no—
155C2×#97—111no—
156C2×#97C2×D1111yescharacteristic
157C2×#97C2×D1111yescharacteristic
158#389—111no—
159#389—111no—
160#389—111no—
161#389—111no—
162#387—221no—
163#387—221no—
164#387—221no—
165#387—221no—
166#382—111no—
167#382C2×D1111yescharacteristic
168C43—111no—
169#336—221no—
170#336—221no—
171#336—221no—
172C22×C11#39111yescharacteristic
173C22×C11#41311yescharacteristic
174C22×C11#41311yescharacteristic
175C22×C11C2×#10411yescharacteristic
176C22×C11#42111yescharacteristic
177C22×C11#42111yescharacteristic
178C22×C11#42111yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11—81no—
187Dic11—22no—
188Dic11—41no—
189Dic11—41no—
190Dic11—41no—
191Dic11—81no—
192Dic11—81no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—221no—
196C22×C8—221no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4C4×D1111yescharacteristic
204C2×C4⋊C4C4×D1111yescharacteristic
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—224no—
213#97—21no—
214#97—21no—
215#97—21no—
216#97—112no—
217#97—221no—
218#97—221no—
219#97—221no—
220#97Dic2212yes—
221#95—21no—
222#95—21no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229C2×C11#152911yescharacteristic
230C2×C11#153211yescharacteristic
231C2×C11#153511yescharacteristic
232C2×C11#153511yescharacteristic
233C2×C11#198611yescharacteristic
234C2×C11#199511yescharacteristic
235C2×C11#199811yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4D4×D1111yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—222no—
254C2×C8—222no—
255C2×C8—441no—
256C2×C8—441no—
257C2×C8—441no—
258C2×C8—441no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—442no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C42—222no—
268C42—441no—
269C42—441no—
270C42—441no—
271C42—441no—
272C42—441no—
273C42C2×Dic2211yescharacteristic
274C42#433911yescharacteristic
275C42#434111yescharacteristic
276C42Q8×D1111yescharacteristic
277C11#989311yescharacteristic, complemented, Sylow
278C23C22⋊C4×D1111yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—112no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4C4×Dic2211yescharacteristic
310C2×C4#6693111yescharacteristic
311C2×C4#6693811yescharacteristic
312C2×C4#6694011yescharacteristic
313C2×C4#6694111yescharacteristic
314C2×C4#6694911yescharacteristic
315C8—42no—
316C8—42no—
317C8—442no—
318C8—442no—
319C22#1062225911yescharacteristic
320C22#1062235811yescharacteristic
321C22#1062236411yescharacteristic
322C22D11×#10411yescharacteristic
323C22#1062243411yescharacteristic
324C22#1062243411yescharacteristic
325C22#1062243411yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—222no—
335C4—441no—
336C4—441no—
337C4—441no—
338C4—881no—
339C4—881no—
340C2#1306722011yescharacteristic
341C2#1306723511yescharacteristic
342C2#1306724411yescharacteristic
343C2#1306724611yescharacteristic
344C2#1306955811yescharacteristic
345C2#1306959511yescharacteristic
346C2#1306960711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1295D11
hypocenterC11#9893
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
277. C11#9893semidirect

Maximal subgroups

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

subgroupindex
#130770012
#130684702
#130683642
#130664982
#130664972
C11×#12952
#989311