Finite Group Databasebeta

← #14653880

Subgroups — #14653880

Order 2816.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076978C211yesmaximal, characteristic
2#13068470C211yesmaximal, characteristic
3#13068364C211yesmaximal, characteristic
4#13066498C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×#66943C411yescharacteristic
9C2×#66943C411yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×Dic11⋊C8—21no—
14#10622589C411yescharacteristic
15#10622589C411yescharacteristic
16#10622549C2211yescharacteristic
17C42×Dic11C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19C2×#66867C2211yescharacteristic
20#10622260—21no—
21#10622260—21no—
22#10622260—21no—
23#10622260—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×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11C2×C411yescharacteristic
43C2×C4×Dic11C2×C411yescharacteristic
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66943—42no—
51#66943—42no—
52C11×#97—21no—
53C11×#97—21no—
54C11×#97—21no—
55C11×#97Q812yes—
56C11×#95—21no—
57C11×#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60Dic11⋊C8—24no—
61#66867—21no—
62#66867—21no—
63#66867—21no—
64#66867Q812yes—
65#9894—111nomaximal, Sylow
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×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C42×C11C2×Q811yescharacteristic
86C42×C11C2×Q811yescharacteristic
87C42×C11#4111yescharacteristic
88C42×C11#4111yescharacteristic
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—42no—
98Dic11⋊C4—42no—
99C4×Dic11—22no—
100C4×Dic11—22no—
101C4×Dic11—22no—
102C4×Dic11—41no—
103C4×Dic11—41no—
104C4×Dic11—41no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2859—111no—
112#1767—111no—
113#1745—111no—
114#1295—111no—
115#1295—111no—
116#1295—111no—
117#1295D1111yescharacteristic
118C23×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11C4×Q811yescharacteristic
132C2×C4×C11C4×Q811yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11C4⋊Q811yescharacteristic
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11#10012yes—
153C2×Dic11#10112yes—
154C2×Dic11#10412yes—
155C8×C11—42no—
156C8×C11—42no—
157C11⋊C8—42no—
158C11⋊C8—42no—
159C2×#125—111no—
160C2×#125—111no—
161C2×C4⋊C8—221no—
162C2×#97—111no—
163C2×#97—111no—
164C2×#97C2×D1111yescharacteristic
165C2×#97C2×D1111yescharacteristic
166#389—221no—
167#389—221no—
168#389—221no—
169#389—221no—
170#384—111no—
171#384—111no—
172#382—111no—
173#382C2×D1111yescharacteristic
174C43—111no—
175#336—221no—
176#336—221no—
177#336—221no—
178C22×C11#39111yescharacteristic
179C22×C11C2×#10011yescharacteristic
180C22×C11C2×#10111yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C22×C11#42111yescharacteristic
183C22×C11#42111yescharacteristic
184C22×C11#42111yescharacteristic
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—81no—
192C4×C11—81no—
193Dic11—22no—
194Dic11—22no—
195Dic11—22no—
196Dic11—41no—
197Dic11—81no—
198Dic11—81no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—221no—
202C22×C8—221no—
203#125—442no—
204#125—442no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4C4×D1111yescharacteristic
216C2×C4⋊C4C4×D1111yescharacteristic
217C2×C42—111no—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42—111no—
221C2×C42—111no—
222C2×C42—111no—
223C2×C42C22×D1111yescharacteristic
224C4⋊C8—224no—
225#97—21no—
226#97—21no—
227#97—21no—
228#97—112no—
229#97—221no—
230#97—221no—
231#97—221no—
232#97Dic2212yes—
233#95—21no—
234#95—21no—
235#95—221no—
236#95—221no—
237C2×C11#152811yescharacteristic
238C2×C11#153011yescharacteristic
239C2×C11#153411yescharacteristic
240C2×C11#153611yescharacteristic
241C2×C11#198611yescharacteristic
242C2×C11#199511yescharacteristic
243C2×C11#199711yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—111no—
249C22×C4—111no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4D4×D1111yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—222no—
262C2×C8—222no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8—441no—
266C2×C8—441no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—442no—
279C42—222no—
280C42—222no—
281C42—222no—
282C42—441no—
283C42—441no—
284C42—441no—
285C42C2×Dic2211yescharacteristic
286C42#433911yescharacteristic
287C42#434111yescharacteristic
288C42Q8×D1111yescharacteristic
289C11#989411yescharacteristic, complemented, Sylow
290C23C22⋊C4×D1111yescharacteristic
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—112no—
304C2×C4—112no—
305C2×C4—112no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4C4×Dic2211yescharacteristic
322C2×C4#6693111yescharacteristic
323C2×C4#6693811yescharacteristic
324C2×C4#6694011yescharacteristic
325C2×C4#6694111yescharacteristic
326C2×C4#6694911yescharacteristic
327C8—42no—
328C8—42no—
329C8—442no—
330C8—442no—
331C22#1062225911yescharacteristic
332C22D11×#10011yescharacteristic
333C22D11×#10111yescharacteristic
334C22D11×#10411yescharacteristic
335C22#1062243411yescharacteristic
336C22#1062243411yescharacteristic
337C22#1062243411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—81no—
345C4—81no—
346C4—222no—
347C4—222no—
348C4—222no—
349C4—441no—
350C4—881no—
351C4—881no—
352C2#1306721611yescharacteristic
353C2#1306722511yescharacteristic
354C2#1306724111yescharacteristic
355C2#1306724911yescharacteristic
356C2#1306955811yescharacteristic
357C2#1306959511yescharacteristic
358C2#1306960311yescharacteristic
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#9894
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
289. C11#9894semidirect

Maximal subgroups

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

subgroupindex
#130769782
#130684702
#130683642
#130664982
#130664972
C11×#12952
#989411