Finite Group Databasebeta

← #14648096

Subgroups — #14648096

Order 2816.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077282C211yesmaximal, characteristic
2#13068636C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic, complemented
4#13067372C211yesmaximal, characteristic, complemented
5#13066518C211yesmaximal, characteristic, complemented
6#13066456C211yesmaximal, characteristic, complemented
7C11×#1476C211yesmaximal, characteristic
8C4×C11×#41C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66901—21no—
12#10622847—21no—
13#10622613—22no—
14#10622610—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16#10622539—21no—
17#10622538—21no—
18#10622537C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×Q8⋊C8C411yescharacteristic, complemented
22C11×Q8⋊C8C411yescharacteristic, complemented
23C11×D4⋊C8C411yescharacteristic, complemented
24C11×D4⋊C8C411yescharacteristic, complemented
25#10622170—21no—
26#10622096—21no—
27#10622096—21no—
28#10622095—22no—
29C2×C11×#41D411yescharacteristic
30C22×C8×C11—21no—
31C4×Q8×C11C2×C411yescharacteristic
32C4×Q8×C11Q811yescharacteristic
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11C2×C411yescharacteristic
36C4×D4×C11Q811yescharacteristic
37C11×#117—21no—
38C11×#117D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4×Dic11—21no—
43C2×#4318—21no—
44C2×#4318—21no—
45C22×C11⋊C8—21no—
46C11×C4⋊C8C2×C411yescharacteristic
47C11×C4⋊C8C2×C411yescharacteristic
48C11×C22⋊C8—21no—
49C4×C8×C11—21no—
50C4×C8×C11—21no—
51C4×C8×C11C2×C411yescharacteristic
52C4×C8×C11C2×C411yescharacteristic
53#66901—42no—
54C11⋊#95—21no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D411yescharacteristic
62C4⋊(C11⋊C8)D411yescharacteristic
63C4⋊(C11⋊C8)D412yes—
64#66867—22no—
65C4×C11⋊C8—22no—
66#8905—111nomaximal, Sylow
67C11×#41—21no—
68C11×#41—21no—
69C11×#41—21no—
70C11×#41—21no—
71C2×Q8×C11C4⋊C411yescharacteristic
72C2×D4×C11—21no—
73C2×D4×C11C4⋊C411yescharacteristic
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—41no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—42no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4C4⋊C411yescharacteristic
89C11×C4⋊C4C4⋊C411yescharacteristic
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C42×C11—21no—
94C42×C11—21no—
95C42×C11—21no—
96C42×C11C22×C411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×Q811yescharacteristic
100C4⋊Dic11—22no—
101C4⋊Dic11—41no—
102C4×Dic11—41no—
103C4×Dic11—41no—
104#4318—41no—
105#4318—41no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2925—111no—
115#1806—111no—
116#1571—111no—
117#1566—111no—
118#1476D1111yescharacteristic
119#1303—111no—
120#1279—111no—
121C23×C11—21no—
122C23×C11#12311yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—41no—
128D4×C11—41no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—81no—
140C2×C4×C11C2×C4⋊C411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11C22⋊Q811yescharacteristic
145C2×C4×C11C22⋊Q811yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—42no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C8×C11—22no—
154C8×C11—41no—
155C8×C11—41no—
156C8×C11—41no—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C11⋊C8—42no—
160C11⋊C8—81no—
161C4×#41C2×D1111yescharacteristic
162#433—222no—
163#432—221no—
164#431—221no—
165#431C2×D1111yescharacteristic
166#423—111no—
167#423—111no—
168C2×C4⋊C8—111no—
169C2×#104—221no—
170#408—221no—
171#405—221no—
172C2×C4×C8C2×D1111yescharacteristic
173C4×C4⋊C4—111no—
174#339—221no—
175#335—221no—
176#335—221no—
177#334—222no—
178Q8⋊C8Dic1111yescharacteristic, complemented
179Q8⋊C8Dic1111yescharacteristic, complemented
180D4⋊C8Dic1111yescharacteristic, complemented
181D4⋊C8Dic1111yescharacteristic, complemented
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11#38511yescharacteristic
188C22×C11#48211yescharacteristic
189C22×C11#48511yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11#42711yescharacteristic
197C4×C11#42811yescharacteristic
198C4×C11#44311yescharacteristic
199C4×C11#44411yescharacteristic
200C4×C11#44911yescharacteristic
201C4×C11#45211yescharacteristic
202Dic11—82no—
203C2×#41D4411yescharacteristic
204C2×M16—221no—
205C2×M16—221no—
206C22×C8—21no—
207C22×C8—221no—
208C4×Q8Dic2211yescharacteristic
209C4×Q8C2×Dic1111yescharacteristic
210C4×D4—21no—
211C4×D4—21no—
212C4×D4Dic2211yescharacteristic
213C4×D4C2×Dic1111yescharacteristic
214#117—21no—
215#117D4411yescharacteristic
216C2×C4⋊C4—221no—
217C2×C42—21no—
218C2×C42—221no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—112no—
221C4⋊C8—111no—
222C4⋊C8—111no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C4⋊C8—221no—
227C4⋊C8C2×Dic1111yescharacteristic
228C4⋊C8C2×Dic1111yescharacteristic
229#104—442no—
230C22⋊C8—21no—
231C22⋊C8—222no—
232C22⋊C8—222no—
233#97—222no—
234C4×C8—21no—
235C4×C8—21no—
236C4×C8—222no—
237C4×C8C2×Dic1111yescharacteristic
238C4×C8C2×Dic1111yescharacteristic
239#95—221no—
240C2×C11—21no—
241C2×C11—21no—
242C2×C11—81no—
243C2×C11#185411yescharacteristic
244C2×C11#186111yescharacteristic
245C2×C11#186611yescharacteristic
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250C2×Q8C4⋊Dic1111yescharacteristic
251C2×D4—21no—
252C2×D4C4⋊Dic1111yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—441no—
257C22×C4C2×D4411yescharacteristic
258C22×C4#434111yescharacteristic
259C22×C4#434111yescharacteristic
260M16—441no—
261M16—441no—
262M16—441no—
263M16—441no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—42no—
269C2×C8—221no—
270C2×C8—222no—
271C2×C8—221no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—222no—
278C4⋊C4—441no—
279C4⋊C4C4⋊Dic1111yescharacteristic
280C4⋊C4C4⋊Dic1111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42—21no—
286C42—21no—
287C42—441no—
288C42—441no—
289C42C2×Dic2211yescharacteristic
290C42D4×D1111yescharacteristic
291C42D4×D1111yescharacteristic
292C42C22×Dic1111yescharacteristic
293C11#890511yescharacteristic, complemented, Sylow
294C23—21no—
295C23#6693911yescharacteristic
296Q8—21no—
297Q8—21no—
298D4—21no—
299D4—21no—
300D4—41no—
301D4—41no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—442no—
314C2×C4—881no—
315C2×C4—881no—
316C2×C4#6693111yescharacteristic
317C2×C4#6693111yescharacteristic
318C2×C4#6693511yescharacteristic
319C2×C4#6695711yescharacteristic
320C2×C4#6695711yescharacteristic
321C2×C4#6696111yescharacteristic
322C2×C4#6696211yescharacteristic
323C2×C4C2×C4⋊Dic1111yescharacteristic
324C2×C4D4×Dic1111yescharacteristic
325C2×C4D4×Dic1111yescharacteristic
326C8—22no—
327C8—41no—
328C8—41no—
329C8—41no—
330C8—442no—
331C8—441no—
332C8—441no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#1062233611yescharacteristic
340C22#1062235011yescharacteristic
341C22#1062256311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—882no—
349C4#1062234611yescharacteristic
350C4#1062234711yescharacteristic
351C4#1062271911yescharacteristic
352C4#1062273411yescharacteristic
353C4#1062280911yescharacteristic
354C4#1062281011yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#1306881711yescharacteristic
359C2#1306885811yescharacteristic
360C2#1306889311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1476C2
socleC22×C11#385
prime radicalC2×C11×#41D4
cosocleC2×C42×C11C23
hypercenter#1476D11
hypocenterC11#8905
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
3. #13067391C2semidirect
4. #13067372C2semidirect
5. #13066518C2semidirect
6. #13066456C2semidirect
21. C11×Q8⋊C8C4semidirect
22. C11×Q8⋊C8C4semidirect
23. C11×D4⋊C8C4semidirect
24. C11×D4⋊C8C4semidirect
178. Q8⋊C8Dic11semidirect
179. Q8⋊C8Dic11semidirect
180. D4⋊C8Dic11semidirect
181. D4⋊C8Dic11semidirect
293. C11#8905semidirect

Maximal subgroups

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

subgroupindex
#130772822
#130686362
#130673912
#130673722
#130665182
#130664562
C11×#14762
#890511