Finite Group Databasebeta

← #14719951

Subgroups — #14719951

Order 2816.

848 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×#10623114C211yesmaximal, characteristic
2#13077700C212yesmaximal, complemented
3#13066984C214yesmaximal
4#13066970C214yesmaximal, complemented
5#13066960C211yesmaximal, characteristic, complemented
6#13066948C212yesmaximal
7C11×#1467C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66999C411yescharacteristic
10C2×#66997C411yescharacteristic
11#10623114—24no—
12#10623114—24no—
13C2×#66951C2212yes—
14C2×#66950C411yescharacteristic
15C2×#66943C411yescharacteristic
16C2×#66942C2212yes—
17C2×#66929C412yes—
18C2×#66925C2211yescharacteristic
19C2×#66923C412yes—
20C2×C4×Dic22C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622441—24no—
24#10622332C2214yes—
25#10622331C2214yes—
26#10622314—24no—
27C11×#324C2214yes—
28#10622166C2214yes—
29#10622107C2214yes—
30#10622106C2214yes—
31C22×Q8×C11C2×C411yescharacteristic
32C22×C4×D11C2×C411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C4×Q8×C11—22no—
35C4×Q8×C11—22no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2312yes—
38C2×C42×C11C2×C412yes—
39C2×C42×C11C2311yescharacteristic
40#66999—24no—
41#66997—24no—
42C2×(C2×D11)⋊C4C2×C411yescharacteristic
43C2×(C2×D11)⋊C4C2×C412yes—
44C2×(C2×D11)⋊C4C2×C412yes—
45C2×(C2×D11)⋊C4C2311yescharacteristic
46C2×C4⋊Dic11C2×C412yes—
47C2×C4⋊Dic11C2×C412yes—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4C2×C411yescharacteristic
50C2×Dic11⋊C4C2×C412yes—
51C2×Dic11⋊C4C2×C412yes—
52C2×Dic11⋊C4C2×C412yes—
53C2×Dic11⋊C4C2×C412yes—
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2311yescharacteristic
56C2×C4×Dic11C2×C411yescharacteristic
57C2×C4×Dic11C2312yes—
58#66951—24no—
59#66951—24no—
60#66950—24no—
61#66943—24no—
62#66942—24no—
63#66942—24no—
64#66929—24no—
65#66929—24no—
66#66925—22no—
67#66925—22no—
68#66923—24no—
69#66923—24no—
70C4×Dic22D414yes—
71C4×Dic22D414yes—
72C11×C4⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C11×#97—22no—
75C22⋊(C11⋊C8)C2314yes—
76#66879—24no—
77Dic11⋊C8—24no—
78Dic11⋊C8—24no—
79C8×Dic11—24no—
80C4⋊(C11⋊C8)—22no—
81#66867—22no—
82#17410—111nomaximal, Sylow
83C23×D11C22×C411yescharacteristic
84C2×Q8×C11—22no—
85C2×Q8×C11—42no—
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2411yescharacteristic
91C22×Dic11C22×C411yescharacteristic
92C22×Dic11C22×C412yes—
93C22×Dic11C22×C411yescharacteristic
94C22×Dic11C22×C411yescharacteristic
95C22×Dic11C22×C412yes—
96C2×C4×D11—22no—
97C2×C4×D11—42no—
98C2×Dic22—42no—
99C2×Dic22C22⋊C414yes—
100C2×C8×C11—24no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11C2×D412yes—
107C42×C11C2×D412yes—
108(C2×D11)⋊C4—24no—
109(C2×D11)⋊C4—24no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—22no—
113C4⋊Dic11—24no—
114C4⋊Dic11—24no—
115C4⋊Dic11C22⋊C414yes—
116Dic11⋊C4—24no—
117Dic11⋊C4—24no—
118Dic11⋊C4—24no—
119Dic11⋊C4—24no—
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122Dic11⋊C4—22no—
123Dic11⋊C4C22⋊C414yes—
124Dic11⋊C4C22⋊C414yes—
125C4×Dic11—22no—
126C4×Dic11C2×D414yes—
127C4×Dic11C2×D414yes—
128C2×C11⋊C8—24no—
129C2×#541—111no—
130#2983—112no—
131#1473—114no—
132#1470—114no—
133#1467—111no—
134#1467D1111yescharacteristic, complemented
135#1464—112no—
136C23×C11C23×C411yescharacteristic
137C22×D11—21no—
138C22×D11—22no—
139C22×D11—41no—
140C22×D11—41no—
141Q8×C11—44no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11C2×C22⋊C412yes—
150C2×C4×C11C2×C22⋊C411yescharacteristic
151C2×C4×C11C2×C22⋊C411yescharacteristic
152C2×C4×C11C22×D412yes—
153C2×Dic11—24no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—22no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11C2×C22⋊C414yes—
162C2×Dic11C2×C22⋊C414yes—
163C4×D11—44no—
164Dic22—44no—
165C8×C11—44no—
166C11⋊C8—44no—
167#541—224no—
168#541—224no—
169C2×C4⋊Q8—111no—
170C2×#126—112no—
171C2×#126—112no—
172C2×#125—112no—
173C2×#125—111no—
174C2×#125—112no—
175C2×C22⋊Q8—111no—
176C2×C22⋊Q8—111no—
177C2×C4×Q8—111no—
178C2×C4×Q8C2×D1111yescharacteristic
179C2×#117—111no—
180#446—224no—
181#446—224no—
182#432—112no—
183#432—114no—
184#432C2×D1112yes—
185#431—114no—
186#324—114no—
187#324—114no—
188#324C2×D1114yes—
189#323—114no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11C22×C22⋊C411yescharacteristic
193C22×C11#56812yes—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—82no—
198C4×C11—22no—
199C4×C11—22no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—42no—
203C4×C11—42no—
204Dic11—24no—
205Dic11—24no—
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209C22×Q8—111no—
210C22×Q8C4×D1111yescharacteristic
211C23×C4—111no—
212C4⋊Q8—224no—
213#126—224no—
214#126—224no—
215#126—224no—
216#126—224no—
217#125—224no—
218#125—224no—
219#125—224no—
220#125—224no—
221#125—224no—
222C22⋊Q8—224no—
223C22⋊Q8—224no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—114no—
227C4×Q8—114no—
228#117—222no—
229#117—222no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—112no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—112no—
235C2×C4⋊C4—112no—
236C2×C4⋊C4—112no—
237C2×C4⋊C4—112no—
238C2×C4⋊C4—112no—
239C2×C4⋊C4—111no—
240C2×C4⋊C4C4×D1111yescharacteristic
241C2×C4⋊C4C22×D1112yes—
242C2×C22⋊C4—111no—
243C2×C22⋊C4—112no—
244C2×C22⋊C4—112no—
245C2×C22⋊C4—111no—
246C2×C42—112no—
247C2×C42—111no—
248C2×C42C4×D1112yes—
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—22no—
251C4⋊C8—224no—
252C4⋊C8—224no—
253C4⋊C8—222no—
254C22⋊C8—114no—
255C22⋊C8C22×D1114yes—
256#97—22no—
257#97—224no—
258#97—222no—
259C4×C8—224no—
260C2×C11—22no—
261C2×C11#287911yescharacteristic
262C2×C11#288411yescharacteristic
263C2×C11#288911yescharacteristic
264D11—81no—
265C24—111no—
266C2×Q8—22no—
267C2×Q8—42no—
268C2×Q8—114no—
269C2×Q8—442no—
270C22×C4—112no—
271C22×C4—112no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—222no—
276C22×C4—442no—
277C22×C4C2×C4×D1112yes—
278C22×C4C2×C4×D1111yescharacteristic
279C22×C4C2×C4×D1112yes—
280C22×C4C2×C4×D1111yescharacteristic
281C22×C4C23×D1111yescharacteristic
282C2×C8—24no—
283C2×C8—224no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—114no—
288C4⋊C4—114no—
289C4⋊C4—114no—
290C4⋊C4—224no—
291C4⋊C4—224no—
292C4⋊C4—224no—
293C4⋊C4—224no—
294C4⋊C4—224no—
295C4⋊C4—224no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—222no—
299C22⋊C4—224no—
300C22⋊C4—224no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—222no—
304C42—22no—
305C42—22no—
306C42—114no—
307C42—114no—
308C42—222no—
309C42D4×D1112yes—
310C42D4×D1112yes—
311C11#1741011yescharacteristic, complemented, Sylow
312C23—221no—
313C23—222no—
314C23—441no—
315C23—441no—
316C23C22×C4×D1111yescharacteristic
317Q8—44no—
318Q8—444no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—114no—
327C2×C4—114no—
328C2×C4—224no—
329C2×C4—221no—
330C2×C4—221no—
331C2×C4—221no—
332C2×C4—222no—
333C2×C4—444no—
334C2×C4—442no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4C22⋊C4×D1111yescharacteristic
338C2×C4C22⋊C4×D1111yescharacteristic
339C2×C4C22⋊C4×D1112yes—
340C2×C4C2×D4×D1112yes—
341C8—44no—
342C8—444no—
343C22—21no—
344C22—21no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—882no—
349C22C2×C22⋊C4×D1111yescharacteristic
350C22#1062327612yes—
351C4—22no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—42no—
357C4—224no—
358C4—224no—
359C4—441no—
360C4—441no—
361C4—441no—
362C2—22no—
363C2—881no—
364C2#1307705911yescharacteristic
365C2#1307707811yescharacteristic
366C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1467C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1467D11
hypocenterC11#17410
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13077700C2semidirect
4. #13066970C2semidirect
5. #13066960C2semidirect
7. C11×#1467C2semidirect
134. #1467D11semidirect
311. C11#17410semidirect

Maximal subgroups

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

subgroupindex
C2×#106231142
#130777002
#130669842
#130669702
#130669602
#130669482
C11×#14672
#1741011