Finite Group Databasebeta

← #14652895

Subgroups — #14652895

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3C2×#10622090C214yesmaximal
4C4×C11×#95C211yesmaximal, characteristic
5C22×C42×C11—21no—
6C22×C42×C11C2211yescharacteristic
7C2×#66977C2212yes—
8C2×#66922C411yescharacteristic, complemented
9C2×C11×#95—21no—
10C2×C11×#95C2212yes—
11#10622825—21no—
12#10622825—21no—
13C2×C22⋊(C11⋊C8)C2212yes—
14#10622548C411yescharacteristic, complemented
15#10622542C412yescomplemented
16#10622541—21no—
17#10622541—21no—
18C2×C4⋊(C11⋊C8)—21no—
19#10622162—21no—
20#10622090—28no—
21C23×C4×C11—22no—
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C22×Dic22C2×C412yes—
26C2×C42×C11—24no—
27C2×C42×C11—42no—
28C2×C42×C11—42no—
29C2×C42×C11—42no—
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C412yes—
40#66977—24no—
41#66977—24no—
42C2×Dic11⋊C4—22no—
43C22×C11⋊C8—22no—
44#66922—42no—
45C11×#95—24no—
46C11×#95—22no—
47C11×#95D414yes—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C22⋊(C11⋊C8)—24no—
51C4⋊(C11⋊C8)—42no—
52#9711—111nomaximal, Sylow
53C24×C11C2×D411yescharacteristic
54C22×C4×C11—22no—
55C22×C4×C11—22no—
56C22×C4×C11—24no—
57C22×C4×C11—24no—
58C22×C4×C11—24no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22⋊C411yescharacteristic
72C22×C4×C11SD1612yes—
73C22×C4×C11Q1612yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D412yes—
77C22×C4×C11#4112yes—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C2×Dic22—24no—
81C2×Dic22—42no—
82C2×Dic22—42no—
83C42×C11—22no—
84C42×C11—22no—
85C42×C11—41no—
86C42×C11—41no—
87C42×C11—48no—
88C22⋊Dic11—44no—
89C4⋊Dic11—24no—
90C4⋊Dic11—42no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98C2×C11⋊C8—42no—
99#2857—111no—
100#1797—111no—
101C2×#328—114no—
102C4×#95D1111yescharacteristic
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11C2×C22⋊C411yescharacteristic
108C23×C11#12112yes—
109C23×C11C2×SD1611yescharacteristic
110C23×C11C2×Q1611yescharacteristic
111C23×C11#13712yes—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—28no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
134C2×C4×C11—44no—
135C2×C4×C11#9912yes—
136C2×C4×C11#10312yes—
137C2×C4×C11#10312yes—
138C2×C4×C11#10412yes—
139C2×C4×C11#10412yes—
140C2×C4×C11C4×D412yes—
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11#12711yescharacteristic
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149Dic22—84no—
150C11⋊C8—82no—
151C2×C4⋊Q8—111no—
152C2×C22⋊Q8—112no—
153C22×C42—21no—
154C22×C42C2×D1111yescharacteristic
155C2×C4⋊C8—221no—
156C2×C22⋊C8—112no—
157#391—112no—
158#389—221no—
159#389—221no—
160#384—111no—
161#380—221no—
162#380—221no—
163C2×#95—21no—
164C2×#95C2×D1112yes—
165#336—221no—
166#328—228no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11#39011yescharacteristic
176C22×C11C2×#9911yescharacteristic
177C22×C11#41011yescharacteristic
178C22×C11C2×#10311yescharacteristic
179C22×C11#41911yescharacteristic
180C22×C11C2×#10411yescharacteristic
181C22×C11C2×#10411yescharacteristic
182C22×C11#46112yes—
183C22×C11#46212yes—
184C4×C11—22no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—22no—
188C4×C11—22no—
189C4×C11—48no—
190C4×C11—41no—
191C4×C11#32814yescomplemented
192Dic11—82no—
193Dic11—82no—
194C22×Q8—112no—
195C23×C4—22no—
196C23×C4C22⋊D1111yescharacteristic
197C23×C4C22⋊D1111yescharacteristic
198C23×C4C22×D1111yescharacteristic
199C22×C8—222no—
200C4⋊Q8—442no—
201C22⋊Q8—224no—
202C22⋊Q8—224no—
203C2×C4⋊C4—112no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—222no—
209C2×C22⋊C4—222no—
210C2×C42—24no—
211C2×C42—42no—
212C2×C42—42no—
213C2×C42—42no—
214C2×C42C4×D1111yescharacteristic
215C2×C42C4×D1111yescharacteristic
216C2×C42D4411yescharacteristic
217C2×C42D4411yescharacteristic
218C4⋊C8—442no—
219C22⋊C8—224no—
220#95—24no—
221#95—22no—
222#95—222no—
223#95—222no—
224#95D4414yes—
225C2×C11—22no—
226C2×C11—22no—
227C2×C11C2×#32811yescharacteristic
228C2×C11#150311yescharacteristic
229C2×C11#150611yescharacteristic
230C2×C11#150811yescharacteristic
231C2×C11#196211yescharacteristic
232C2×C11#196411yescharacteristic
233C2×C11#198111yescharacteristic
234C24C2×C22⋊D1111yescharacteristic
235C2×Q8—224no—
236C2×Q8—442no—
237C2×Q8—442no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—222no—
253C22×C4—222no—
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4(C2×D11)⋊C411yescharacteristic
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4#432412yes—
259C22×C4#432612yes—
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4C2×D4412yes—
263C22×C4#433912yes—
264C2×C8—442no—
265C2×C8—442no—
266C2×C8—442no—
267C4⋊C4—224no—
268C4⋊C4—442no—
269C4⋊C4—442no—
270C4⋊C4—442no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C22⋊C4—444no—
275C42—22no—
276C42—22no—
277C42—41no—
278C42—41no—
279C42—48no—
280C11#971111yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23C2×(C2×D11)⋊C411yescharacteristic
286C23#6698312yes—
287C23C2×#432411yescharacteristic
288C23C2×#432611yescharacteristic
289C23#6700412yes—
290Q8—884no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—28no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4—442no—
319C2×C4—442no—
320C2×C4#6686912yes—
321C2×C4#6686912yes—
322C2×C4#6687012yes—
323C2×C4#6687412yes—
324C2×C4#6687412yes—
325C2×C4C4×D4412yes—
326C2×C4#6692711yescharacteristic
327C2×C4#6692811yescharacteristic
328C8—882no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22C2×#6686911yescharacteristic
338C22C2×#6686911yescharacteristic
339C22#1062255211yescharacteristic
340C22C2×#6687011yescharacteristic
341C22C2×#6687411yescharacteristic
342C22#1062261711yescharacteristic
343C22#1062261911yescharacteristic
344C22#1062263212yes—
345C22#1062264412yes—
346C4—22no—
347C4—22no—
348C4—21no—
349C4—22no—
350C4—21no—
351C4—48no—
352C4—41no—
353C4—882no—
354C4—882no—
355C4#1062209014yescomplemented
356C2—22no—
357C2—22no—
358C2C2×#1062209011yescharacteristic
359C2#1306711411yescharacteristic
360C2#1306712711yescharacteristic
361C2#1306713511yescharacteristic
362C2#1306944411yescharacteristic
363C2#1306945211yescharacteristic
364C2#1306953911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×#95C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4×#95D11
hypocenterC11#9711
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
8. C2×#66922C4semidirect
14. #10622548C4semidirect
15. #10622542C4semidirect
191. C4×C11#328semidirect
280. C11#9711semidirect
355. C4#10622090semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130685962
C2×#106220902
C4×C11×#952
#971111