Finite Group Databasebeta

← #14653922

Subgroups — #14653922

Order 2816.

438 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#13076977C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic
3#13068471C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066499C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×#66943—21no—
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66879—21no—
13C2×Dic11⋊C8—21no—
14C2×Dic11⋊C8—21no—
15#10622598—21no—
16#10622598C412yes—
17#10622590—21no—
18#10622586—21no—
19#10622586C412yes—
20#10622548C2211yescharacteristic
21C42×Dic11C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622188—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—22no—
34C2×C4⋊Dic11C2×C412yes—
35C2×Dic11⋊C4—22no—
36C2×C4×Dic11C2×C411yescharacteristic
37C2×C4×Dic11C2×C411yescharacteristic
38C2×C4×Dic11D411yescharacteristic
39C2×C4×Dic11D411yescharacteristic
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66943—42no—
45#66943—42no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8Q812yes—
50C11⋊#95—22no—
51C11⋊#95—22no—
52#66879—42no—
53Dic11⋊C8—42no—
54Dic11⋊C8—42no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)Q812yes—
59#9904—111nomaximal, Sylow
60C22×C4×C11—22no—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×Dic11—22no—
65C22×Dic11C22⋊C411yescharacteristic
66C22×Dic11C22⋊C411yescharacteristic
67C22×Dic11C22⋊C411yescharacteristic
68C22×Dic11C22⋊C411yescharacteristic
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C11×C4⋊C4—42no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C42×C11C2×Q811yescharacteristic
81C42×C11C2×Q811yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C4⋊Dic11—42no—
85C4⋊Dic11—44no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90Dic11⋊C4—44no—
91C4×Dic11—21no—
92C4×Dic11—21no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C4×Dic11—21no—
96C4×Dic11—21no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99C4×Dic11D812yes—
100C4×Dic11SD1612yes—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#2859—111no—
108#1842—111no—
109#1767—111no—
110#1296—111no—
111#1296—111no—
112#1296—111no—
113#1296D1111yescharacteristic
114C23×C11C2×C22⋊C411yescharacteristic
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11C4×Q811yescharacteristic
121C2×C4×C11C4×Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11#12411yescharacteristic
125C2×C4×C11C4⋊Q811yescharacteristic
126C2×C4×C11C2×D811yescharacteristic
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×C4×C11#13711yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×C4×C11#13711yescharacteristic
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—21no—
143C2×Dic11—21no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11#10212yes—
148C2×Dic11#10212yes—
149C8×C11—42no—
150C8×C11—81no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C2×#125—221no—
154C2×C4⋊C8—111no—
155C2×C4⋊C8—111no—
156C2×C4⋊C8—221no—
157C2×C4⋊C8—221no—
158C2×C4⋊C8C2×D1111yescharacteristic
159C2×C4⋊C8C2×D1111yescharacteristic
160C2×#97—221no—
161#389—112no—
162#389—112no—
163#389—221no—
164#389—221no—
165#384—111no—
166#384C2×D1111yescharacteristic
167#382—221no—
168C43—111no—
169#336—221no—
170C22×C11#39111yescharacteristic
171C22×C11#41311yescharacteristic
172C22×C11#41311yescharacteristic
173C22×C11C2×#10211yescharacteristic
174C22×C11#41711yescharacteristic
175C22×C11#41711yescharacteristic
176C22×C11#41911yescharacteristic
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—82no—
180C4×C11#47411yescharacteristic
181C4×C11#47411yescharacteristic
182C4×C11#47511yescharacteristic
183C4×C11#47511yescharacteristic
184C4×C11#49011yescharacteristic
185C4×C11#49111yescharacteristic
186C4×C11#50111yescharacteristic
187C4×C11#50111yescharacteristic
188Dic11—22no—
189Dic11—22no—
190Dic11—41no—
191Dic11—41no—
192Dic11—82no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—221no—
196C22×C8—221no—
197#125—442no—
198#125—442no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—222no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4C4×D1112yes—
207C2×C42—111no—
208C2×C42—111no—
209C2×C42—111no—
210C2×C42—111no—
211C2×C42—111no—
212C2×C42—111no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—112no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221C4⋊C8—442no—
222C4⋊C8—442no—
223C4⋊C8Dic2212yes—
224#97—442no—
225#95—222no—
226#95—222no—
227C2×C11#154711yescharacteristic
228C2×C11#154711yescharacteristic
229C2×C11#155911yescharacteristic
230C2×C11#155911yescharacteristic
231C2×C11#198811yescharacteristic
232C2×C11#199211yescharacteristic
233C2×C11#199811yescharacteristic
234C22×C4—22no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—222no—
240C22×C4C2×C4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—441no—
251C2×C8—441no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—442no—
261C4⋊C4—444no—
262C4⋊C4—444no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C42—112no—
268C42—112no—
269C42—221no—
270C42—221no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42—441no—
276C42—441no—
277C42C2×Dic2211yescharacteristic
278C42#433911yescharacteristic
279C42#434111yescharacteristic
280C42Q8×D1111yescharacteristic
281C11#990411yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1111yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—112no—
289C2×C4—112no—
290C2×C4—221no—
291C2×C4—221no—
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—442no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4C4×Dic2211yescharacteristic
304C2×C4#6693111yescharacteristic
305C2×C4#6693811yescharacteristic
306C2×C4#6694011yescharacteristic
307C2×C4#6694111yescharacteristic
308C2×C4#6694911yescharacteristic
309C2×C4D8×D1111yescharacteristic
310C2×C4#6696411yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C2×C4#6696711yescharacteristic
313C2×C4#6696811yescharacteristic
314C2×C4#6696811yescharacteristic
315C2×C4#6697111yescharacteristic
316C2×C4#6697111yescharacteristic
317C8—42no—
318C8—81no—
319C8—442no—
320C8—881no—
321C22#1062225911yescharacteristic
322C22#1062235811yescharacteristic
323C22#1062236411yescharacteristic
324C22D11×#10211yescharacteristic
325C22#1062238411yescharacteristic
326C22#1062241511yescharacteristic
327C22#1062241611yescharacteristic
328C4—21no—
329C4—21no—
330C4—82no—
331C4—222no—
332C4—222no—
333C4—441no—
334C4—441no—
335C4—882no—
336C4#1062237211yescharacteristic
337C4#1062237711yescharacteristic
338C4#1062240411yescharacteristic
339C4#1062241011yescharacteristic
340C4#1062246711yescharacteristic
341C4#1062246911yescharacteristic
342C4#1062248911yescharacteristic
343C4#1062250311yescharacteristic
344C2#1306729011yescharacteristic
345C2#1306729211yescharacteristic
346C2#1306734311yescharacteristic
347C2#1306734511yescharacteristic
348C2#1306956611yescharacteristic
349C2#1306958311yescharacteristic
350C2#1306960711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9904
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
281. C11#9904semidirect

Maximal subgroups

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

subgroupindex
#130769772
#130687672
#130684712
#130665002
#130664992
C11×#12962
#990411