Finite Group Databasebeta

← #14725205

Subgroups — #14725205

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077631C212yesmaximal, complemented
2C4×#66957C211yesmaximal, characteristic
3#13067514C212yesmaximal, complemented
4#13067454C214yesmaximal, complemented
5C8×D88C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067051C212yesmaximal, complemented
8C8×C11×M16C211yesmaximal, characteristic, complemented
9C2×#66957C411yescharacteristic
10C4×#4339C2212yes—
11C11×#431C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622740—24no—
15#10622726C412yes—
16#10622719C411yescharacteristic
17#10622539C2212yes—
18#10622318—22no—
19D11×#97—22no—
20C4×Dic44C411yescharacteristic
21C4×Dic44C2211yescharacteristic
22C4×D88C411yescharacteristic
23C4×D88C2211yescharacteristic
24C4×#4314C412yes—
25C4×#4314C2212yes—
26C8×D44C2214yes—
27#10622292C2214yes—
28C11×#322C2212yes—
29C82×C11C2212yes—
30#10622097C2214yes—
31#10622096C2212yes—
32#10622095C2212yes—
33#10622094C2214yes—
34C2×#4339C2×C412yes—
35C2×C11×M16D412yes—
36C22×C8×C11C2×C411yescharacteristic
37C22×C8×C11C2×C411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C4×C22⋊D11—22no—
40C4×C22⋊D11—22no—
41#66979C2×C412yes—
42C2×Dic44C2×C411yescharacteristic
43#66957—24no—
44C2×D88C2×C411yescharacteristic
45C2×#4314C2×C412yes—
46C2×C8×D11—24no—
47C4×D44C2×C412yes—
48C4×D44C2312yes—
49#66925—22no—
50C42×D11—22no—
51C4×Dic22C2×C412yes—
52C4×Dic22C2312yes—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×#97D411yescharacteristic
56C11×#97D411yescharacteristic
57C4×C8×C11C2×C411yescharacteristic
58C4×C8×C11C2×C411yescharacteristic
59C4×C8×C11C2312yes—
60C4×C8×C11C2311yescharacteristic
61C4×C8×C11C2311yescharacteristic
62C4×C8×C11C2312yes—
63C22⋊(C11⋊C8)—22no—
64#66885C2×C412yes—
65#66885C2×C412yes—
66(C2×D11)⋊C8—24no—
67#66882C2×C411yescharacteristic
68#66882C2×C411yescharacteristic
69#66881C2×C412yes—
70#66880C2×C412yes—
71#66880C2×C412yes—
72#66879—24no—
73Dic11⋊C8—24no—
74C4⋊(C11⋊C8)C2314yes—
75#66867—22no—
76#18035—111nomaximal, Sylow
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—22no—
81#4339—24no—
82#4339—42no—
83C2×D44C22×C412yes—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×C4×D11—22no—
87C2×Dic22C22×C412yes—
88C11×M16—24no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C22×C411yescharacteristic
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D412yes—
98C42×C11C22×C411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11C2411yescharacteristic
102C22⋊Dic11—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—22no—
105C4⋊Dic11C22×C412yes—
106C4⋊Dic11C22×C412yes—
107Dic11⋊C4—22no—
108Dic11⋊C4—22no—
109C4×Dic11—22no—
110C4×Dic11—22no—
111C4×Dic11—22no—
112C2×C11⋊C8—24no—
113Dic44—22no—
114D88M1614yescomplemented
115#4314—24no—
116C8×D11—48no—
117#2970—112no—
118C4×#135—111no—
119#1591—112no—
120#1582—114no—
121C8×D8—112no—
122#1568—111no—
123#1488—112no—
124C8×M16D1111yescharacteristic, complemented
125C23×C11C4×D411yescharacteristic
126C22×D11—22no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C23×C411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C2×#4111yescharacteristic
137C22⋊D11—44no—
138C2×Dic11—22no—
139C2×Dic11—22no—
140C2×Dic11—22no—
141D44—22no—
142D44C2×M1614yes—
143C4×D11—44no—
144C4×D11—44no—
145C4×D11—82no—
146Dic22—22no—
147Dic22—22no—
148C8×C11—21no—
149C8×C11—21no—
150C8×C11—21no—
151C8×C11—22no—
152C8×C11—42no—
153C8×C11C2×M1612yes—
154C8×C11#13514yescomplemented
155C11⋊C8—44no—
156C2×#135—111no—
157C4×#41—112no—
158#446—114no—
159C4×Q16—111no—
160C4×Q16—111no—
161C4×SD16—112no—
162C4×SD16—112no—
163C4×D8—111no—
164C4×D8—111no—
165#435—224no—
166C8×D4—114no—
167#432—112no—
168#432—222no—
169#431C2×D1111yescharacteristic
170#427—111no—
171#416—112no—
172C4×M16C2×D1111yescharacteristic
173C2×#97—222no—
174C2×C4×C8C2×D1111yescharacteristic
175#335—112no—
176#334—112no—
177Q8⋊C8—114no—
178D4⋊C8—114no—
179#322C2×D1112yes—
180C82C2×D1112yes—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11C2×C4×D411yescharacteristic
185C2×D11—24no—
186C2×D11—42no—
187C2×D11—42no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11C22×M1611yescharacteristic
193C4×C11#56811yescharacteristic
194C4×C11C2×#13512yes—
195Dic11—42no—
196Dic11—42no—
197Dic11—42no—
198C2×#41—112no—
199#135—224no—
200C2×Q16—111no—
201C2×SD16—112no—
202C2×D8—111no—
203C2×M16D4412yes—
204C22×C8—224no—
205C22×C8C4×D1111yescharacteristic
206C22×C8C4×D1111yescharacteristic
207C4×Q8—112no—
208C4×Q8—112no—
209C4×D4—112no—
210C4×D4—112no—
211C4×D4—222no—
212C4×D4—222no—
213#117—112no—
214#117—222no—
215C2×C42—222no—
216C2×C42C22×D1111yescharacteristic
217#107—111no—
218#107—111no—
219#106—112no—
220C4⋊C8—21no—
221C4⋊C8—114no—
222C4⋊C8—224no—
223#103—112no—
224#103—112no—
225#102—112no—
226#102—112no—
227C22⋊C8—21no—
228C22⋊C8—222no—
229C22⋊C8—224no—
230#97—224no—
231#97—222no—
232#97D4411yescharacteristic
233#97D4411yescharacteristic
234C4×C8C4×D1111yescharacteristic
235C4×C8C4×D1111yescharacteristic
236C4×C8C22×D1112yes—
237C4×C8C22×D1111yescharacteristic
238C4×C8C22×D1111yescharacteristic
239C4×C8C22×D1112yes—
240C2×C11—41no—
241C2×C11D4×M1611yescharacteristic
242C2×C11C4×#13511yescharacteristic
243C2×C11#295711yescharacteristic
244D11—44no—
245#41—224no—
246#41—442no—
247C2×Q8—112no—
248C2×D4—112no—
249C2×D4—222no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—222no—
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×D4411yescharacteristic
255C22×C4#433911yescharacteristic
256Q16—222no—
257SD16—224no—
258D8—114no—
259M16—24no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—224no—
264C2×C8—448no—
265C2×C8C2×C4×D1111yescharacteristic
266C2×C8C2×C4×D1111yescharacteristic
267C2×C8C2×C4×D1111yescharacteristic
268C2×C8C2×C4×D1111yescharacteristic
269C2×C8C2×D4412yes—
270C2×C8C2×D4412yes—
271C4⋊C4—112no—
272C4⋊C4—112no—
273C4⋊C4—222no—
274C4⋊C4—222no—
275C22⋊C4—222no—
276C22⋊C4—222no—
277C22⋊C4—222no—
278C42—222no—
279C42—222no—
280C42—222no—
281C42C2×C4×D1111yescharacteristic
282C42C2×D4411yescharacteristic
283C42#433911yescharacteristic
284C42C23×D1111yescharacteristic
285C11#1803511yescharacteristic, complemented, Sylow
286C23—222no—
287C23C4×D4411yescharacteristic
288Q8—222no—
289Q8—222no—
290D4—114no—
291D4—222no—
292D4—444no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—222no—
298C2×C4—222no—
299C2×C4—222no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4—882no—
303C2×C4C4×D4411yescharacteristic
304C2×C4C4×D4411yescharacteristic
305C2×C4C4×D4411yescharacteristic
306C2×C4C22×C4×D1111yescharacteristic
307C2×C4C22×D4411yescharacteristic
308C2×C4C2×#433911yescharacteristic
309C8—22no—
310C8—21no—
311C8—21no—
312C8—21no—
313C8—42no—
314C8—444no—
315C8#6695714yescomplemented
316C8M16×D1112yes—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—224no—
321C22—442no—
322C22—442no—
323C22C2×C4×D4411yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—442no—
329C4—442no—
330C4—442no—
331C4C2×#6695712yes—
332C4C2×M16×D1111yescharacteristic
333C4#1062327611yescharacteristic
334C2—41no—
335C2—444no—
336C2M16×D4411yescharacteristic
337C2C4×#6695711yescharacteristic
338C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenterC8×M16D11
hypocenterC11#18035
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
1. #13077631C2semidirect
3. #13067514C2semidirect
4. #13067454C2semidirect
5. C8×D88C2semidirect
6. #13067379C2semidirect
7. #13067051C2semidirect
8. C8×C11×M16C2semidirect
114. D88M16semidirect
124. C8×M16D11semidirect
154. C8×C11#135semidirect
285. C11#18035semidirect
315. C8#66957semidirect

Maximal subgroups

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

subgroupindex
#130776312
C4×#669572
#130675142
#130674542
C8×D882
#130673792
#130670512
C8×C11×M162
#1803511