Finite Group Databasebeta

← #14658211

Subgroups — #14658211

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073642C211yesmaximal, characteristic
2#13069375C211yesmaximal, characteristic
3#13069374C211yesmaximal, characteristic
4#13068776C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×#66941—21no—
9C2×#66922—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66882—21no—
14C2×#66882—22no—
15#10622598—21no—
16C2×#66871—21no—
17#10622548C2211yescharacteristic
18#10622548C2211yescharacteristic
19C4×C4⋊Dic11C2211yescharacteristic
20#10622541—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622269—22no—
23#10622189—21no—
24#10622167—21no—
25C22×Dic22—22no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D412yes—
41C2×Dic11⋊C4—22no—
42C2×C4×Dic11—21no—
43C22×C11⋊C8—21no—
44#66941—42no—
45#66941—42no—
46#66922—42no—
47#66922—42no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8Q812yescomplemented
50C4×C8×C11—21no—
51C4×C8×C11Q812yescomplemented
52C11×#95—21no—
53C11⋊#95—22no—
54C11⋊#95—21no—
55#66882—44no—
56#66882—42no—
57#66871—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)Q812yescomplemented
60#10573—111nomaximal, Sylow
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×Dic11—21no—
67C22×Dic11—21no—
68C22×Dic11—22no—
69C22×Dic11—41no—
70C2×Dic22—44no—
71C2×Dic22—44no—
72C2×Dic22—82no—
73C2×C8×C11—22no—
74C2×C8×C11—22no—
75C2×C8×C11—22no—
76C2×C8×C11—22no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4D812yes—
82C11×C4⋊C4Q1612yes—
83C42×C11—41no—
84C42×C11—41no—
85C42×C11C2×Q811yescharacteristic
86C42×C11C2×Q811yescharacteristic
87C42×C11C2×Q811yescharacteristic
88C42×C11#4111yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—44no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11D812yes—
103C4⋊Dic11Q1612yes—
104Dic11⋊C4—44no—
105C4×Dic11—41no—
106C4×Dic11—41no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110#2551—111no—
111#1947—111no—
112#1947—111no—
113#1845—111no—
114#1296—111no—
115#1279—111no—
116#1279D1111yescharacteristic
117C23×C11#12011yescharacteristic
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C4⋊Q811yescharacteristic
130C2×C4×C11C4⋊Q811yescharacteristic
131C2×C4×C11C4⋊Q811yescharacteristic
132C2×C4×C11C2×D811yescharacteristic
133C2×C4×C11C2×D811yescharacteristic
134C2×C4×C11C2×Q1611yescharacteristic
135C2×C4×C11C2×Q1611yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—22no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152Dic22—88no—
153C8×C11—24no—
154C8×C11—42no—
155C11⋊C8—42no—
156C2×C4⋊Q8—221no—
157C2×C4⋊Q8—221no—
158C2×#107—222no—
159C2×#107—221no—
160C2×#107—221no—
161C2×C4⋊C8—111no—
162C2×C4⋊C8C2×D1111yescharacteristic
163C2×C4×C8C2×D1111yescharacteristic
164#395—222no—
165#389—221no—
166#389—221no—
167#384—111no—
168#384—111no—
169C4×C4⋊C4—111no—
170C4×C4⋊C4C2×D1111yescharacteristic
171#340—221no—
172#340—221no—
173C22×C11#39511yescharacteristic
174C22×C11#44711yescharacteristic
175C22×C11#44711yescharacteristic
176C22×C11#45111yescharacteristic
177C22×C11#45111yescharacteristic
178C22×C11#45311yescharacteristic
179C22×C11#45611yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—42no—
184C4×C11#47411yescharacteristic
185C4×C11#47411yescharacteristic
186C4×C11#47711yescharacteristic
187C4×C11#47711yescharacteristic
188C4×C11#50011yescharacteristic
189C4×C11#50011yescharacteristic
190C4×C11#50111yescharacteristic
191C4×C11#50111yescharacteristic
192Dic11—42no—
193Dic11—42no—
194Dic11—82no—
195Dic11—161no—
196C22×Q8—222no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—221no—
200C4⋊Q8—442no—
201C4⋊Q8—442no—
202C4⋊Q8—442no—
203C4⋊Q8—442no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—112no—
207C2×C4⋊C4—222no—
208C2×C4⋊C4—222no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4D4411yescharacteristic
215C2×C4⋊C4D4411yescharacteristic
216C2×C42—21no—
217C2×C42—221no—
218C2×C42C22×D1111yescharacteristic
219#107—442no—
220#107—444no—
221#107—442no—
222C4⋊C8—21no—
223C4⋊C8—112no—
224C4⋊C8—221no—
225C4⋊C8Dic2212yescomplemented
226C4×C8—21no—
227C4×C8Dic2212yescomplemented
228#95—21no—
229#95—222no—
230#95—221no—
231C2×C11#161911yescharacteristic
232C2×C11#163311yescharacteristic
233C2×C11#164911yescharacteristic
234C2×C11#164911yescharacteristic
235C2×C11#205711yescharacteristic
236C2×C11#205711yescharacteristic
237C2×C11#206011yescharacteristic
238C2×Q8—444no—
239C2×Q8—444no—
240C2×Q8—882no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—222no—
246C22×C4—441no—
247C22×C4C2×D4411yescharacteristic
248C22×C4D4×D1111yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—222no—
257C2×C8—441no—
258C2×C8—441no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—112no—
262C4⋊C4—112no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—442no—
266C4⋊C4—444no—
267C4⋊C4—442no—
268C4⋊C4—444no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—441no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4D8812yes—
278C4⋊C4Dic4412yes—
279C42—41no—
280C42—41no—
281C42—441no—
282C42—441no—
283C42C2×Dic2211yescharacteristic
284C42C2×Dic2211yescharacteristic
285C42#434111yescharacteristic
286C42Q8×D1111yescharacteristic
287C11#1057311yescharacteristic, complemented, Sylow
288C23#6693511yescharacteristic
289Q8—888no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4—881no—
310C2×C4#6692211yescharacteristic
311C2×C4#6693111yescharacteristic
312C2×C4#6693111yescharacteristic
313C2×C4#6694111yescharacteristic
314C2×C4#6694111yescharacteristic
315C2×C4#6695011yescharacteristic
316C2×C4C2×D8811yescharacteristic
317C2×C4C2×Dic4411yescharacteristic
318C2×C4#6696111yescharacteristic
319C2×C4#6696211yescharacteristic
320C2×C4D8×D1111yescharacteristic
321C2×C4#6696711yescharacteristic
322C2×C4#6696811yescharacteristic
323C2×C4Q16×D1111yescharacteristic
324C8—24no—
325C8—42no—
326C8—442no—
327C22#1062226911yescharacteristic
328C22#1062234511yescharacteristic
329C22#1062235211yescharacteristic
330C22#1062238611yescharacteristic
331C22#1062242111yescharacteristic
332C22#1062243511yescharacteristic
333C22#1062243911yescharacteristic
334C4—21no—
335C4—21no—
336C4—42no—
337C4—42no—
338C4—442no—
339C4—442no—
340C4—882no—
341C4—1761no—
342C4#1062229511yescharacteristic
343C4#1062231511yescharacteristic
344C4#1062237211yescharacteristic
345C4#1062240711yescharacteristic
346C4#1062245911yescharacteristic
347C4#1062246311yescharacteristic
348C4#1062246911yescharacteristic
349C4#1062248711yescharacteristic
350C2#1306767211yescharacteristic
351C2#1306775811yescharacteristic
352C2#1306786711yescharacteristic
353C2#1306786811yescharacteristic
354C2#1306994311yescharacteristic
355C2#1306994511yescharacteristic
356C2#1306996011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socle, prime radicalC23×C11#120
hypercenter#1279D11
hypocenterC11#10573
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
49. C11×C4⋊C8Q8semidirect
51. C4×C8×C11Q8semidirect
59. C4⋊(C11⋊C8)Q8semidirect
225. C4⋊C8Dic22semidirect
227. C4×C8Dic22semidirect
287. C11#10573semidirect

Maximal subgroups

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

subgroupindex
#130736422
#130693752
#130693742
#130687762
#130665002
#130664562
C11×#12792
#1057311