Finite Group Databasebeta

← #14653870

Subgroups — #14653870

Order 2816.

432 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077001C211yesmaximal, characteristic
2#13068470C211yesmaximal, characteristic
3#97×Dic11C211yesmaximal, characteristic
4#13066498C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×C11×#97C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66879—21no—
12C2×Dic11⋊C8—21no—
13C2×C8×Dic11—21no—
14#10622598C411yescharacteristic
15#10622598C411yescharacteristic
16#10622586C411yescharacteristic
17#10622586C411yescharacteristic
18#10622549C2211yescharacteristic
19C42×Dic11C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22#10622268—21no—
23#10622268—21no—
24#10622267—21no—
25#10622267—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—
58#66879—24no—
59Dic11⋊C8—24no—
60C8×Dic11—24no—
61#66867—21no—
62#66867—21no—
63#66867—21no—
64#66867Q812yes—
65#9892—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—22no—
80C2×C8×C11—22no—
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—
95C4×Dic11—22no—
96C4×Dic11—22no—
97C4×Dic11—22no—
98C4×Dic11—41no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2864—111no—
108#1767—111no—
109C4×#97—111no—
110#1295—111no—
111#1295—111no—
112#1295—111no—
113#1295D1111yescharacteristic
114C23×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
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×C11C4×Q811yescharacteristic
128C2×C4×C11C4×Q811yescharacteristic
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11C4⋊Q811yescharacteristic
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—
149C2×Dic11#10412yes—
150C2×Dic11#10412yes—
151C8×C11—24no—
152C8×C11—42no—
153C11⋊C8—24no—
154C11⋊C8—42no—
155C2×C4⋊C8—221no—
156C2×#97—111no—
157C2×#97—111no—
158C2×#97—221no—
159C2×#97C2×D1111yescharacteristic
160C2×#97C2×D1111yescharacteristic
161C2×C4×C8—221no—
162#389—111no—
163#389—111no—
164#389—111no—
165#389—111no—
166#387—221no—
167#387—221no—
168#387—221no—
169#387—221no—
170#382—111no—
171#382C2×D1111yescharacteristic
172C43—111no—
173#336—221no—
174C22×C11#39111yescharacteristic
175C22×C11#41311yescharacteristic
176C22×C11#41311yescharacteristic
177C22×C11C2×#10411yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11C2×#10411yescharacteristic
180C22×C11#42111yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—81no—
188C4×C11—81no—
189Dic11—22no—
190Dic11—22no—
191Dic11—22no—
192Dic11—41no—
193Dic11—81no—
194Dic11—81no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—221no—
198C22×C8—221no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C4×D1111yescharacteristic
206C2×C4⋊C4C4×D1111yescharacteristic
207C2×C42—111no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42—111no—
212C2×C42—111no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—224no—
215#97—21no—
216#97—21no—
217#97—21no—
218#97—112no—
219#97—224no—
220#97—221no—
221#97—221no—
222#97—221no—
223#97Dic2212yes—
224C4×C8—224no—
225#95—21no—
226#95—21no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95—221no—
233C2×C11#152411yescharacteristic
234C2×C11#152411yescharacteristic
235C2×C11#152911yescharacteristic
236C2×C11#153211yescharacteristic
237C2×C11#198611yescharacteristic
238C2×C11#199411yescharacteristic
239C2×C11#199811yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—222no—
259C2×C8—222no—
260C2×C8—222no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C42—222no—
272C42—222no—
273C42—222no—
274C42—441no—
275C42—441no—
276C42—441no—
277C42C2×Dic2211yescharacteristic
278C42#433911yescharacteristic
279C42#434111yescharacteristic
280C42Q8×D1111yescharacteristic
281C11#989211yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1111yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—112no—
296C2×C4—112no—
297C2×C4—112no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4C4×Dic2211yescharacteristic
314C2×C4#6693111yescharacteristic
315C2×C4#6693811yescharacteristic
316C2×C4#6694011yescharacteristic
317C2×C4#6694111yescharacteristic
318C2×C4#6694911yescharacteristic
319C8—24no—
320C8—42no—
321C8—224no—
322C8—442no—
323C22#1062225911yescharacteristic
324C22#1062235811yescharacteristic
325C22#1062236411yescharacteristic
326C22D11×#10411yescharacteristic
327C22D11×#10411yescharacteristic
328C22D11×#10411yescharacteristic
329C22#1062243411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—222no—
339C4—222no—
340C4—222no—
341C4—441no—
342C4—881no—
343C4—881no—
344C2#1306720111yescharacteristic
345C2#1306720311yescharacteristic
346C2#1306722211yescharacteristic
347C2#1306723311yescharacteristic
348C2#1306955811yescharacteristic
349C2#1306959111yescharacteristic
350C2#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#9892
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
281. C11#9892semidirect

Maximal subgroups

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

subgroupindex
#130770012
#130684702
#97×Dic112
#130664982
#130664972
C11×#12952
#989211