Finite Group Databasebeta

← #14658222

Subgroups — #14658222

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073642C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic
3#13068743C211yesmaximal, characteristic
4#13066500C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic
6#13066455C211yesmaximal, characteristic
7C11×#1947C211yesmaximal, characteristic
8C2×#66941—21no—
9C2×#66922—21no—
10C2×C11×#107—21no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C11×#384C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622598—21no—
15C2×#66872—21no—
16#10622548C2211yescharacteristic
17C4×C4⋊Dic11C2211yescharacteristic
18#10622541—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622269—22no—
22C11×#340—21no—
23#10622167—21no—
24#10622167—22no—
25C22×Dic22—22no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×C4⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D412yes—
40C2×Dic11⋊C4—22no—
41C2×C4×Dic11—21no—
42C22×C11⋊C8—21no—
43C22×C11⋊C8—21no—
44#66941—42no—
45#66941—42no—
46#66922—42no—
47#66922—42no—
48C11×#107—42no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8Q812yescomplemented
51C11×#95—21no—
52C11⋊#95—22no—
53C11⋊#95—21no—
54#66872—42no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)Q812yescomplemented
57C4×C11⋊C8—21no—
58C4×C11⋊C8Q812yescomplemented
59#10575—111nomaximal, Sylow
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—41no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—22no—
69C2×Dic22—44no—
70C2×Dic22—44no—
71C2×Dic22—82no—
72C2×C8×C11—22no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4SD1612yes—
83C11×C4⋊C4SD1612yes—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11C2×Q811yescharacteristic
87C42×C11C2×Q811yescharacteristic
88C42×C11C2×Q811yescharacteristic
89C42×C11#4111yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—42no—
93C4⋊Dic11—44no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11D812yes—
99C4⋊Dic11Q1612yes—
100Dic11⋊C4—44no—
101C4×Dic11—41no—
102C4×Dic11—41no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#2551—111no—
110#1948—111no—
111#1947D1111yescharacteristic
112#1834—111no—
113#1296—111no—
114#1279—111no—
115#1279—111no—
116C23×C11#12011yescharacteristic
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C4⋊Q811yescharacteristic
132C2×C4×C11C4⋊Q811yescharacteristic
133C2×C4×C11C4⋊Q811yescharacteristic
134C2×C4×C11C2×D811yescharacteristic
135C2×C4×C11C2×SD1611yescharacteristic
136C2×C4×C11C2×SD1611yescharacteristic
137C2×C4×C11C2×Q1611yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151Dic22—88no—
152C8×C11—42no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155C2×C4⋊Q8—221no—
156C2×C4⋊Q8—221no—
157C2×#107—21no—
158C2×#106—221no—
159C2×C4⋊C8—111no—
160C2×C4⋊C8C2×D1111yescharacteristic
161C2×C4×C8—111no—
162#395—222no—
163#389—221no—
164#389—221no—
165#384—111no—
166#384C2×D1111yescharacteristic
167C4×C4⋊C4—111no—
168C4×C4⋊C4C2×D1111yescharacteristic
169#340—21no—
170#340—222no—
171#340—221no—
172C22×C11#39511yescharacteristic
173C22×C11#44711yescharacteristic
174C22×C11#44811yescharacteristic
175C22×C11#45011yescharacteristic
176C22×C11#45111yescharacteristic
177C22×C11#45411yescharacteristic
178C22×C11#45511yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—42no—
183C4×C11—161no—
184C4×C11#47411yescharacteristic
185C4×C11#47511yescharacteristic
186C4×C11#47611yescharacteristic
187C4×C11#47711yescharacteristic
188C4×C11#49811yescharacteristic
189C4×C11#50011yescharacteristic
190C4×C11#50111yescharacteristic
191C4×C11#50111yescharacteristic
192Dic11—42no—
193Dic11—42no—
194Dic11—82no—
195C22×Q8—222no—
196C22×C8—21no—
197C22×C8—221no—
198C22×C8—221no—
199C4⋊Q8—442no—
200C4⋊Q8—442no—
201C4⋊Q8—442no—
202C4⋊Q8—442no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—112no—
209C2×C4⋊C4—222no—
210C2×C4⋊C4—222no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C4⋊C4C22⋊D1111yescharacteristic
215C2×C42—21no—
216C2×C42—221no—
217C2×C42C22×D1111yescharacteristic
218#107—42no—
219#106—442no—
220C4⋊C8—21no—
221C4⋊C8—112no—
222C4⋊C8—221no—
223C4⋊C8Dic2212yescomplemented
224C4×C8—112no—
225C4×C8—221no—
226#95—21no—
227#95—222no—
228#95—221no—
229C2×C11#162711yescharacteristic
230C2×C11#163711yescharacteristic
231C2×C11#163911yescharacteristic
232C2×C11#164511yescharacteristic
233C2×C11#205711yescharacteristic
234C2×C11#205811yescharacteristic
235C2×C11#206111yescharacteristic
236C2×Q8—444no—
237C2×Q8—444no—
238C2×Q8—882no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—222no—
245C22×C4D4×D1111yescharacteristic
246C22×C4D4×D1111yescharacteristic
247C22×C4C2×C22⋊D1111yescharacteristic
248C2×C8—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—222no—
252C2×C8—222no—
253C2×C8—441no—
254C2×C8—441no—
255C2×C8—441no—
256C2×C8—441no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—112no—
265C4⋊C4—112no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—442no—
269C4⋊C4—444no—
270C4⋊C4—444no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4#432412yes—
276C4⋊C4#432512yes—
277C42—41no—
278C42—41no—
279C42—441no—
280C42—441no—
281C42C2×Dic2211yescharacteristic
282C42#433911yescharacteristic
283C42Q8×D1111yescharacteristic
284C42Q8×D1111yescharacteristic
285C11#1057511yescharacteristic, complemented, Sylow
286C23#6699011yescharacteristic
287Q8—888no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—222no—
300C2×C4—222no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4#6694111yescharacteristic
309C2×C4#6694111yescharacteristic
310C2×C4#6694911yescharacteristic
311C2×C4#6694911yescharacteristic
312C2×C4D8×D1111yescharacteristic
313C2×C4#6696411yescharacteristic
314C2×C4Q16×D1111yescharacteristic
315C2×C4#6697111yescharacteristic
316C2×C4#6697711yescharacteristic
317C2×C4C2×#432411yescharacteristic
318C2×C4C2×#432511yescharacteristic
319C2×C4#6699711yescharacteristic
320C2×C4#6700211yescharacteristic
321C2×C4#6700411yescharacteristic
322C8—42no—
323C8—442no—
324C8—442no—
325C22#1062259211yescharacteristic
326C22#1062265311yescharacteristic
327C22#1062265911yescharacteristic
328C22#1062276911yescharacteristic
329C22#1062279911yescharacteristic
330C22#1062281411yescharacteristic
331C22#1062281511yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—161no—
337C4—442no—
338C4—442no—
339C4—882no—
340C4#1062248711yescharacteristic
341C4#1062248811yescharacteristic
342C4#1062248911yescharacteristic
343C4#1062250311yescharacteristic
344C4#1062262111yescharacteristic
345C4#1062263311yescharacteristic
346C4#1062267811yescharacteristic
347C4#1062269211yescharacteristic
348C2#1306771811yescharacteristic
349C2#1306777911yescharacteristic
350C2#1306779411yescharacteristic
351C2#1306783511yescharacteristic
352C2#1306994211yescharacteristic
353C2#1306994911yescharacteristic
354C2#1306996411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1947C2
socle, prime radicalC23×C11#120
hypercenter#1947D11
hypocenterC11#10575
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
50. C11×C4⋊C8Q8semidirect
56. C4⋊(C11⋊C8)Q8semidirect
58. C4×C11⋊C8Q8semidirect
223. C4⋊C8Dic22semidirect
285. C11#10575semidirect

Maximal subgroups

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

subgroupindex
#130736422
#130693772
#130687432
#130665002
#130664572
#130664552
C11×#19472
#1057511