Finite Group Databasebeta

← #14723243

Subgroups — #14723243

Order 2816.

678 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#13077697C211yesmaximal, characteristic
2#13077696C211yesmaximal, characteristic
3C2×C4×#4326C211yesmaximal, characteristic
4#13067432C214yesmaximal, complemented
5#13067420C214yesmaximal, complemented
6#13067362C211yesmaximal, characteristic
7#13067012C211yesmaximal, characteristic
8#13066900C211yesmaximal, characteristic
9C11×#1479C211yesmaximal, characteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C22×#4326C411yescharacteristic
12C2×C4×Dic22C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C2×#66899C411yescharacteristic
16C4×#4326C412yes—
17C4×#4326C412yes—
18C4×#4326C2212yes—
19C4×#4326C2212yes—
20Q8×C11⋊C8—22no—
21Q8×C11⋊C8C2214yes—
22C2×#66874C411yescharacteristic
23C2×#66871C411yescharacteristic
24#10622538—22no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28#10622443C2214yes—
29#10622331—22no—
30C8×Dic22—22no—
31C11×Q8⋊C8C2214yes—
32#10622118C2212yes—
33#10622117C2212yes—
34#10622094C2214yes—
35#10622092C2212yes—
36C8×C11⋊C8C2212yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Dic22C2×C411yescharacteristic
39C4×Q8×C11—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11C2×C412yes—
42C4×Q8×C11C2312yes—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326C818yescomplemented
48C2×#4326C2×C412yes—
49C2×#4326C2×C412yes—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×Dic11⋊C4—21no—
52C2×C4×Dic11—21no—
53C22×C11⋊C8C2×C411yescharacteristic
54C22×C11⋊C8C2×C411yescharacteristic
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22C2×C412yes—
58C4×Dic22C2312yes—
59C11×C4⋊C8—21no—
60C11×C4⋊C8C2312yes—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C4×C8×C11—21no—
64C4×C8×C11C2312yes—
65#66899C2×C412yes—
66#66899C2×C412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69Dic11⋊C8—24no—
70C8×Dic11—24no—
71#66874C2×C412yes—
72#66874C2×C412yes—
73#66871C2×C412yes—
74#66871C2×C412yes—
75C4⋊(C11⋊C8)—24no—
76C4⋊(C11⋊C8)D412yes—
77C4⋊(C11⋊C8)C2312yes—
78C4×C11⋊C8—21no—
79C4×C11⋊C8—24no—
80C4×C11⋊C8C2×C411yescharacteristic
81C4×C11⋊C8C2×C411yescharacteristic
82C4×C11⋊C8C2311yescharacteristic
83C4×C11⋊C8C2311yescharacteristic
84C4×C11⋊C8C2312yes—
85#17856—111nomaximal, Sylow
86C2×Q8×C11—21no—
87C2×Q8×C11—22no—
88C2×Q8×C11C2×C814yes—
89C2×Q8×C11C22×C412yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×Dic22—21no—
98C2×Dic22—22no—
99C2×Dic22C2×C814yes—
100C2×Dic22C22×C412yes—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4C22×C412yes—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11C2411yescharacteristic
113#4326C2×C818yes—
114#4326C2×C818yes—
115C4⋊Dic11—21no—
116C4⋊Dic11C22×C412yes—
117Dic11⋊C4—22no—
118Dic11⋊C4—22no—
119C4×Dic11—22no—
120C4×Dic11—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8C2×C814yes—
124C2×C11⋊C8C22×C411yescharacteristic
125C2×C11⋊C8C22×C411yescharacteristic
126C2×C11⋊C8C22×C411yescharacteristic
127C2×C11⋊C8C22×C411yescharacteristic
128C2×C11⋊C8C2×D414yes—
129#2982—111no—
130#2982—111no—
131C2×C4×Q16—111no—
132#1579—114no—
133C8×Q16—114no—
134#1564—111no—
135#1479—111no—
136#1479D1111yescharacteristic
137#1450—111no—
138C23×C11C4×D411yescharacteristic
139Q8×C11—22no—
140Q8×C11—24no—
141Q8×C11C22×C814yes—
142C2×C4×C11—22no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11C22×C812yes—
152C2×C4×C11#13112yes—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C2×#4111yescharacteristic
156C2×Dic11—22no—
157C2×Dic11—24no—
158C2×Dic11—22no—
159C2×Dic11—81no—
160Dic22—22no—
161Dic22—24no—
162Dic22C22×C814yes—
163C8×C11—42no—
164C8×C11—42no—
165C11⋊C8—21no—
166C11⋊C8—21no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C11⋊C8C22×C812yes—
170C11⋊C8C22×C812yes—
171C22×Q16—111no—
172C2×C4×Q8—111no—
173C2×C4×Q8C2×D1111yescharacteristic
174C8×Q8—114no—
175C8×Q8—114no—
176C8×Q8—222no—
177C8×Q8—222no—
178C4×Q16—112no—
179C4×Q16—112no—
180C4×Q16—112no—
181C4×Q16—112no—
182#431—111no—
183#431—111no—
184#431—222no—
185#431—222no—
186#431C2×D1111yescharacteristic
187#431C2×D1111yescharacteristic
188C2×#107—111no—
189C2×#103—111no—
190C2×#103—111no—
191C2×C4×C8—111no—
192#335—112no—
193#334—112no—
194Q8⋊C8—114no—
195Q8⋊C8C2×D1114yes—
196#322—112no—
197C82—112no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11C8×D412yes—
201C22×C11C2×C4×D411yescharacteristic
202C4×C11—24no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—42no—
207C4×C11C8×D412yes—
208C4×C11C23×C811yescharacteristic
209C4×C11C2×#13111yescharacteristic
210C4×C11#57812yes—
211Dic11—24no—
212Dic11—42no—
213C22×Q8—111no—
214C22×Q8C4×D1111yescharacteristic
215C2×Q16—118no—
216C2×Q16—112no—
217C2×Q16—112no—
218C22×C8—111no—
219C22×C8—111no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—112no—
223C4×Q8—112no—
224C4×Q8—221no—
225C4×Q8—221no—
226C4×Q8C4×D1112yes—
227C4×Q8C22×D1112yes—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4C4×D1111yescharacteristic
232C2×C42—21no—
233C2×C42—221no—
234C2×C42C22×D1111yescharacteristic
235#107—112no—
236#107—112no—
237C4⋊C8—21no—
238C4⋊C8—112no—
239C4⋊C8—112no—
240C4⋊C8—224no—
241C4⋊C8—224no—
242C4⋊C8C22×D1112yes—
243#103—112no—
244#103—112no—
245#103—112no—
246#103—112no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—112no—
250C22⋊C8—221no—
251C4×C8—21no—
252C4×C8—111no—
253C4×C8—111no—
254C4×C8—111no—
255C4×C8—112no—
256C4×C8—111no—
257C4×C8—224no—
258C4×C8—224no—
259C4×C8—221no—
260C4×C8C22×D1112yes—
261C2×C11—22no—
262C2×C11C2×C8×D411yescharacteristic
263C2×C11#295011yescharacteristic
264C2×C11#295711yescharacteristic
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—114no—
268C2×Q8—112no—
269C2×Q8—221no—
270C2×Q8—222no—
271C2×Q8C8×D1114yes—
272C2×Q8C2×C4×D1112yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4#434111yescharacteristic
280Q16—118no—
281Q16—118no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—114no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8—114no—
290C2×C8—222no—
291C2×C8—222no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—22no—
295C4⋊C4—112no—
296C4⋊C4—221no—
297C4⋊C4—222no—
298C4⋊C4—222no—
299C4⋊C4C2×C4×D1112yes—
300C42—22no—
301C42—22no—
302C42—222no—
303C42—222no—
304C42C2×C4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C42#434111yescharacteristic
307C42C23×D1111yescharacteristic
308C11#1785611yescharacteristic, complemented, Sylow
309C23(C22⋊D11)⋊C411yescharacteristic
310Q8—22no—
311Q8—24no—
312Q8—114no—
313Q8—222no—
314Q8—224no—
315Q8C2×C8×D1114yes—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—222no—
323C2×C4—224no—
324C2×C4—222no—
325C2×C4—881no—
326C2×C4(C22⋊D11)⋊C411yescharacteristic
327C2×C4(C22⋊D11)⋊C411yescharacteristic
328C2×C4(C22⋊D11)⋊C411yescharacteristic
329C2×C4C2×C8×D1112yes—
330C2×C4#6696012yes—
331C2×C4C22×C4×D1111yescharacteristic
332C2×C4C2×D4×D1111yescharacteristic
333C2×C4C2×#434111yescharacteristic
334C8—42no—
335C8—42no—
336C8—112no—
337C8—112no—
338C8—221no—
339C8—221no—
340C8—224no—
341C8—442no—
342C22—21no—
343C22—21no—
344C22(C22⋊D11)⋊C812yes—
345C22C2×(C22⋊D11)⋊C411yescharacteristic
346C4—21no—
347C4—21no—
348C4—24no—
349C4—21no—
350C4—42no—
351C4—224no—
352C4—442no—
353C4(C22⋊D11)⋊C812yes—
354C4C22×C8×D1111yescharacteristic
355C4C2×#6696011yescharacteristic
356C4#1062331012yes—
357C2—22no—
358C2C2×(C22⋊D11)⋊C811yescharacteristic
359C2#1307748011yescharacteristic
360C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1479C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#1479D11
hypocenterC11#17856
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #13067432C2semidirect
5. #13067420C2semidirect
47. C2×#4326C8semidirect
308. C11#17856semidirect

Maximal subgroups

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

subgroupindex
#130776972
#130776962
C2×C4×#43262
#130674322
#130674202
#130673622
#130670122
#130669002
C11×#14792
#1785611