Finite Group Databasebeta

← #14752424

Subgroups — #14752424

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622314C212yesmaximal
2C42×Dic22C211yesmaximal, characteristic
3#13068490C212yesmaximal
4#13068488C212yesmaximal
5C8×Dic11⋊C4C212yesmaximal
6#13068470C211yesmaximal, characteristic
7#13068470C211yesmaximal, characteristic
8#13068469C211yesmaximal, characteristic
9#97×Dic11C211yesmaximal, characteristic
10#97×Dic11C211yesmaximal, characteristic
11C4×C11×#97C211yesmaximal, characteristic
12C2×C4×Dic22C412yes—
13C2×C4×Dic22C2211yescharacteristic
14C2×C11×#97C2211yescharacteristic
15C2×C11×#97C2212yes—
16C2×C11×#97C2211yescharacteristic
17C2×C4×C8×C11C2212yes—
18C43×C11C2211yescharacteristic
19C2×#66879C2212yes—
20C2×#66879C2212yes—
21C2×Dic11⋊C8C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×C8×Dic11C2212yes—
24C2×C8×Dic11C2212yes—
25C4×C4⋊Dic11C412yes—
26C4×C4⋊Dic11C2211yescharacteristic
27C4×Dic11⋊C4C412yes—
28C4×Dic11⋊C4C412yes—
29C4×Dic11⋊C4C2211yescharacteristic
30C4×Dic11⋊C4C2211yescharacteristic
31C42×Dic11C2211yescharacteristic
32C42×Dic11C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×#66867C2211yescharacteristic
35C2×#66867C2211yescharacteristic
36#10622314C4116yescomplemented
37#10622188C2212yes—
38#10622188C2212yes—
39#10622162C2212yes—
40C22×Dic22C2×C411yescharacteristic
41C22×C8×C11C2312yes—
42C22×C8×C11C2312yes—
43C2×C42×C11C2×C412yes—
44C2×C42×C11C2×C412yes—
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11C2×C412yes—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×Dic11⋊C4C2×C412yes—
51C2×Dic11⋊C4C2×C411yescharacteristic
52C2×Dic11⋊C4C2×C411yescharacteristic
53C2×Dic11⋊C4C2×C412yes—
54C2×C4×Dic11C2×C412yes—
55C2×C4×Dic11C2×C412yes—
56C2×C4×Dic11C2×C412yes—
57C2×C4×Dic11C2×C412yes—
58C2×C4×Dic11C2311yescharacteristic
59C2×C4×Dic11C2311yescharacteristic
60C2×C4×Dic11C2311yescharacteristic
61C2×C4×Dic11C2311yescharacteristic
62C22×C11⋊C8C2312yes—
63C22×C11⋊C8C2312yes—
64C4×Dic22—28no—
65C4×Dic22C2×C418yes—
66C11×#97—22no—
67C11×#97C2×C418yes—
68C11×#97Q814yescomplemented
69C4×C8×C11—24no—
70C11⋊#95C2×C412yes—
71C11⋊#95C2×C412yes—
72C11⋊#95C2×C412yes—
73#66879—24no—
74#66879C2×C418yes—
75Dic11⋊C8C2×C418yes—
76Dic11⋊C8C2×C418yes—
77C8×Dic11—24no—
78C8×Dic11C2×C418yes—
79C4⋊(C11⋊C8)C2×C418yes—
80#66867—22no—
81#66867—22no—
82#20520—111nomaximal, Sylow
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C22×C412yes—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C2411yescharacteristic
88C22×Dic11C22×C412yes—
89C22×Dic11C22×C411yescharacteristic
90C22×Dic11C22×C411yescharacteristic
91C22×Dic11C22×C411yescharacteristic
92C22×Dic11C22×C412yes—
93C22×Dic11C22×C411yescharacteristic
94C2×Dic22—24no—
95C2×Dic22C4214yes—
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11C22×C414yes—
99C2×C8×C11C22×C414yes—
100C2×C8×C11C2×Q814yes—
101C2×C8×C11#4114yes—
102C42×C11—24no—
103C42×C11—22no—
104C42×C11—42no—
105C42×C11C22×C414yes—
106C42×C11C2×Q812yes—
107C42×C11#4112yes—
108C4⋊Dic11—24no—
109C4⋊Dic11C4214yes—
110Dic11⋊C4—24no—
111Dic11⋊C4C4214yes—
112Dic11⋊C4C4214yes—
113Dic11⋊C4M1618yes—
114C4×Dic11—24no—
115C4×Dic11—24no—
116C4×Dic11—22no—
117C4×Dic11—22no—
118C4×Dic11—42no—
119C4×Dic11—42no—
120C4×Dic11C22×C414yes—
121C4×Dic11C22×C414yes—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8C22×C414yes—
127C2×C11⋊C8C22×C414yes—
128C2×#446—112no—
129C42×Q8—111no—
130#1771—112no—
131#1771—112no—
132C8×C4⋊C4—112no—
133#1767—111no—
134#1767—111no—
135#1767—111no—
136C4×#97—111no—
137C4×#97—111no—
138C4×#97D1111yescharacteristic
139C23×C11C23×C411yescharacteristic
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11C2×C4212yes—
147C2×C4×C11C2×C4212yes—
148C2×C4×C11C4×Q814yes—
149C2×C4×C11C2×M1614yes—
150C2×C4×C11C23×C412yes—
151C2×C4×C11C22×Q811yescharacteristic
152C2×C4×C11C2×#4112yes—
153C2×C4×C11C2×#4111yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11C2×C4212yes—
163C2×Dic11C2×C4212yes—
164C2×Dic11C2×C4212yes—
165C2×Dic11C2×C4212yes—
166C2×Dic11C2×M1614yes—
167C2×Dic11C2×M1614yes—
168Dic22—28no—
169C8×C11—24no—
170C8×C11C4×Q818yescomplemented
171C11⋊C8—24no—
172C11⋊C8—24no—
173C2×C4×Q8—111no—
174C2×C4×Q8—112no—
175#446—1116no—
176C2×C4⋊C8—112no—
177C2×C4⋊C8—112no—
178C2×C4⋊C8—112no—
179C2×#97—112no—
180C2×#97—112no—
181C2×#97—111no—
182C2×#97—111no—
183C2×#97C2×D1111yescharacteristic
184C2×#97C2×D1111yescharacteristic
185C2×#97C2×D1112yes—
186C2×C4×C8—112no—
187C2×C4×C8—112no—
188C2×C4×C8C2×D1112yes—
189C4×C4⋊C4—111no—
190C4×C4⋊C4—111no—
191C4×C4⋊C4—111no—
192C4×C4⋊C4—112no—
193C4×C4⋊C4—112no—
194C4×C4⋊C4—112no—
195C43—111no—
196C43—111no—
197C43C2×D1111yescharacteristic
198#336—112no—
199#336—112no—
200#336—112no—
201C22×C11C22×C4211yescharacteristic
202C22×C11C2×C4×Q811yescharacteristic
203C22×C11C4×#4111yescharacteristic
204C22×C11C22×M1612yes—
205C22×C11#56812yes—
206C4×C11—22no—
207C4×C11—22no—
208C4×C11—24no—
209C4×C11—24no—
210C4×C11C2×C4×Q812yes—
211C4×C11C4×#4112yes—
212Dic11—22no—
213Dic11—22no—
214Dic11—22no—
215Dic11—24no—
216Dic11—42no—
217Dic11C4×M1614yes—
218C22×Q8—111no—
219C22×C8—112no—
220C22×C8—112no—
221C22×C8C22×D1112yes—
222C22×C8C22×D1112yes—
223C4×Q8—118no—
224C4×Q8—228no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—111no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—112no—
231C2×C42—111no—
232C2×C42—111no—
233C2×C42—112no—
234C2×C42—112no—
235C2×C42—111no—
236C2×C42—111no—
237C2×C42—112no—
238C2×C42—112no—
239C2×C42C4×D1112yes—
240C2×C42C4×D1112yes—
241C2×C42C22×D1111yescharacteristic
242C2×C42C22×D1111yescharacteristic
243C2×C42C22×D1111yescharacteristic
244C4⋊C8—118no—
245C4⋊C8—118no—
246C4⋊C8—118no—
247#97—22no—
248#97—118no—
249#97—224no—
250#97—222no—
251#97—222no—
252#97Dic2214yescomplemented
253#97C4×D1118yes—
254C4×C8—24no—
255C4×C8—118no—
256C4×C8—224no—
257#95—112no—
258#95—112no—
259#95—112no—
260C2×C11C42×Q811yescharacteristic
261C2×C11C2×C4×M1611yescharacteristic
262C2×C11#287511yescharacteristic
263C2×C11Q8×M1612yes—
264C2×C11#297012yes—
265C2×Q8—114no—
266C2×Q8—224no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—112no—
271C22×C4—111no—
272C22×C4—112no—
273C22×C4C2×C4×D1112yes—
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4C2×C4×D1112yes—
277C22×C4C23×D1111yescharacteristic
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—114no—
281C2×C8—114no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—222no—
286C2×C8C2×Dic2214yes—
287C2×C8C2×C4×D1114yes—
288C2×C8C2×C4×D1114yes—
289C2×C8#433914yes—
290C4⋊C4—114no—
291C4⋊C4—114no—
292C4⋊C4—114no—
293C4⋊C4—118no—
294C4⋊C4—224no—
295C4⋊C4—224no—
296C42—24no—
297C42—22no—
298C42—42no—
299C42—114no—
300C42—114no—
301C42—224no—
302C42—224no—
303C42—222no—
304C42—222no—
305C42—442no—
306C42—442no—
307C42C2×Dic2212yes—
308C42C2×C4×D1114yes—
309C42#433912yes—
310C11#2052011yescharacteristic, complemented, Sylow
311C23C22×C4×D1111yescharacteristic
312Q8—228no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—112no—
320C2×C4—114no—
321C2×C4—112no—
322C2×C4—112no—
323C2×C4—112no—
324C2×C4—114no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4C4×Dic2214yes—
334C2×C4C42×D1112yes—
335C2×C4C42×D1112yes—
336C2×C4M16×D1114yes—
337C2×C4C22×Dic2211yescharacteristic
338C2×C4C22×C4×D1112yes—
339C2×C4C2×#433912yes—
340C2×C4C2×#433911yescharacteristic
341C8—24no—
342C8—224no—
343C8—224no—
344C8C4×Dic2218yescomplemented
345C22C2×C4×Dic2211yescharacteristic
346C22C2×C42×D1111yescharacteristic
347C22C4×#433911yescharacteristic
348C22C2×M16×D1112yes—
349C22#1062327612yes—
350C4—22no—
351C4—22no—
352C4—24no—
353C4—24no—
354C4—114no—
355C4—222no—
356C4—222no—
357C4—222no—
358C4—224no—
359C4—442no—
360C4C2×C4×Dic2212yes—
361C4C4×#433912yes—
362C2C42×Dic2211yescharacteristic
363C2C4×M16×D1111yescharacteristic
364C2#1307704511yescharacteristic
365C2M16×Dic2212yes—
366C2#1307762712yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×#97C2
socle, prime radicalC23×C11C23×C4
cosocleC22×C4×C11C24
hypercenterC4×#97D11
hypocenterC11#20520
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
36. #10622314C4semidirect
68. C11×#97Q8semidirect
170. C8×C11C4×Q8semidirect
252. #97Dic22semidirect
310. C11#20520semidirect
344. C8C4×Dic22semidirect

Maximal subgroups

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

subgroupindex
C2×#106223142
C42×Dic222
#130684902
#130684882
C8×Dic11⋊C42
#130684702
#130684692
#97×Dic112
C4×C11×#972
#2052011