Finite Group Databasebeta

← #14653862

Subgroups — #14653862

Order 2816.

484 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076992C211yesmaximal, characteristic
2#13068470C211yesmaximal, characteristic
3#97×Dic11C211yesmaximal, characteristic
4#13066498C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×#66941C411yescharacteristic
9C2×#66941C411yescharacteristic
10C2×C11×#97C2211yescharacteristic
11C2×C11×#97C2211yescharacteristic
12C11×#382C2211yescharacteristic
13C2×#66879—21no—
14C2×Dic11⋊C8—21no—
15C2×C8×Dic11—21no—
16#10622590C411yescharacteristic
17#10622590C411yescharacteristic
18#10622549C2211yescharacteristic
19C42×Dic11C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22#10622259—21no—
23#10622259—21no—
24#10622259—21no—
25#10622259—21no—
26#10622188—21no—
27C22×Dic22—21no—
28C22×Dic22—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C42×C11C2311yescharacteristic
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—
46#66941—42no—
47#66941—42no—
48C11×#97—21no—
49C11×#97—21no—
50C11×#97—21no—
51C11×#97Q812yescomplemented
52C11×#95—21no—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60#66879—24no—
61Dic11⋊C8—24no—
62C8×Dic11—24no—
63#66867—21no—
64#66867—21no—
65#66867—21no—
66#66867Q812yescomplemented
67#9890—111nomaximal, Sylow
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C2×Dic22—42no—
84C2×Dic22—42no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C42×C11C2×Q811yescharacteristic
94C42×C11C2×Q811yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99Dic11⋊C4—42no—
100Dic11⋊C4—42no—
101C4×Dic11—22no—
102C4×Dic11—22no—
103C4×Dic11—22no—
104C4×Dic11—22no—
105C4×Dic11—22no—
106C4×Dic11—41no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2862—111no—
114#1767—111no—
115C4×#97—111no—
116#1295—111no—
117#1295—111no—
118#1295—111no—
119#1295D1111yescharacteristic
120C23×C11C2×C22⋊C411yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11C4×Q811yescharacteristic
134C2×C4×C11C4×Q811yescharacteristic
135C2×C4×C11C22⋊Q811yescharacteristic
136C2×C4×C11C22⋊Q811yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11C4⋊Q811yescharacteristic
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—
155C2×Dic11#10412yes—
156C2×Dic11#10412yes—
157Dic22—84no—
158Dic22—84no—
159C8×C11—24no—
160C8×C11—42no—
161C11⋊C8—24no—
162C11⋊C8—42no—
163C2×C4⋊Q8—111no—
164C2×C4⋊Q8—111no—
165C2×C4⋊C8—221no—
166C2×#97—111no—
167C2×#97—111no—
168C2×#97—221no—
169C2×#97C2×D1111yescharacteristic
170C2×#97C2×D1111yescharacteristic
171C2×C4×C8—221no—
172#391—221no—
173#391—221no—
174#391—221no—
175#391—221no—
176#382—111no—
177#382—111no—
178#382—111no—
179#382C2×D1111yescharacteristic
180C43—111no—
181#336—221no—
182C22×C11#39111yescharacteristic
183C22×C11C2×#10011yescharacteristic
184C22×C11C2×#10111yescharacteristic
185C22×C11C2×#10411yescharacteristic
186C22×C11C2×#10411yescharacteristic
187C22×C11C2×#10411yescharacteristic
188C22×C11#42111yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—81no—
196C4×C11—81no—
197Dic11—22no—
198Dic11—22no—
199Dic11—41no—
200Dic11—81no—
201Dic11—81no—
202Dic11#32914yes—
203C22×Q8—221no—
204C22×Q8—221no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—221no—
208C22×C8—221no—
209C4⋊Q8—442no—
210C4⋊Q8—442no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
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—224no—
230#97—221no—
231#97—221no—
232#97—221no—
233#97Dic2212yescomplemented
234C4×C8—224no—
235#95—21no—
236#95—21no—
237#95—221no—
238#95—221no—
239#95—221no—
240#95—221no—
241#95—221no—
242#95—221no—
243C2×C11C2×#32911yescharacteristic
244C2×C11#152611yescharacteristic
245C2×C11#152711yescharacteristic
246C2×C11#153111yescharacteristic
247C2×C11#198611yescharacteristic
248C2×C11#199411yescharacteristic
249C2×C11#199711yescharacteristic
250C2×Q8—442no—
251C2×Q8—442no—
252C2×Q8—442no—
253C2×Q8—442no—
254C2×Q8—442no—
255C2×Q8—442no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—111no—
259C22×C4—111no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—221no—
263C22×C4—221no—
264C22×C4C2×C4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—222no—
274C2×C8—222no—
275C2×C8—222no—
276C2×C8—222no—
277C2×C8—441no—
278C2×C8—441no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—442no—
284C4⋊C4—442no—
285C42—222no—
286C42—222no—
287C42—222no—
288C42—222no—
289C42—222no—
290C42—441no—
291C42C2×Dic2211yescharacteristic
292C42#433911yescharacteristic
293C42#434111yescharacteristic
294C42Q8×D1111yescharacteristic
295C11#989011yescharacteristic, complemented, Sylow
296C23C22⋊C4×D1111yescharacteristic
297Q8—884no—
298Q8—884no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—112no—
312C2×C4—112no—
313C2×C4—112no—
314C2×C4—112no—
315C2×C4—112no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4C4×Dic2211yescharacteristic
330C2×C4#6693111yescharacteristic
331C2×C4#6693811yescharacteristic
332C2×C4#6694011yescharacteristic
333C2×C4#6694111yescharacteristic
334C2×C4#6694911yescharacteristic
335C8—24no—
336C8—42no—
337C8—224no—
338C8—442no—
339C22#1062225911yescharacteristic
340C22D11×#10011yescharacteristic
341C22D11×#10111yescharacteristic
342C22D11×#10411yescharacteristic
343C22D11×#10411yescharacteristic
344C22D11×#10411yescharacteristic
345C22#1062243411yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—81no—
354C4—114no—
355C4—222no—
356C4—222no—
357C4—441no—
358C4—881no—
359C4—881no—
360C2D11×#32911yescharacteristic
361C2#1306720911yescharacteristic
362C2#1306721211yescharacteristic
363C2#1306722911yescharacteristic
364C2#1306955811yescharacteristic
365C2#1306959111yescharacteristic
366C2#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#9890
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
51. C11×#97Q8semidirect
66. #66867Q8semidirect
233. #97Dic22semidirect
295. C11#9890semidirect

Maximal subgroups

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

subgroupindex
#130769922
#130684702
#97×Dic112
#130664982
#130664972
C11×#12952
#989011