Finite Group Databasebeta

← #14723700

Subgroups — #14723700

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078656C211yesmaximal, characteristic
2#13077546C211yesmaximal, characteristic
3C2×#10622443C211yesmaximal, characteristic
4#13067486C214yesmaximal, complemented
5#13067434C214yesmaximal, complemented
6#13067044C211yesmaximal, characteristic
7#13067018C211yesmaximal, characteristic
8#13066909C211yesmaximal, characteristic
9C11×#1570C211yesmaximal, characteristic
10#10623001C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C2×C11×C4⋊C8C2211yescharacteristic
15#10622735—21no—
16#10622732—21no—
17C2×Dic11⋊C8—21no—
18C2×C8×Dic11—21no—
19#10622538C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622463C412yes—
22#10622462C412yes—
23#10622444—21no—
24#10622444C2212yes—
25#10622443—21no—
26#10622443—21no—
27#10622443—21no—
28#10622443C2212yes—
29#10622443C2212yes—
30#10622443C2212yes—
31#10622352C412yes—
32#10622335C412yes—
33C4×Dic44C2214yes—
34C11×#334C2214yes—
35#10622122C2214yes—
36#10622122C2214yes—
37#10622093C2212yes—
38#10622092C2212yes—
39C22×Dic22C2×C411yescharacteristic
40C2×C11×M16—21no—
41C22×C8×C11—21no—
42C2×C42×C11C2311yescharacteristic
43#66979—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45#66977—21no—
46#66977C2×C412yes—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8D411yescharacteristic
50C22×C11⋊C8D411yescharacteristic
51C2×Dic44C2×C414yes—
52#66923—21no—
53#66922C2×C411yescharacteristic
54#66922C2×C411yescharacteristic
55C4×Dic22—21no—
56C4×Dic22—21no—
57C4×Dic22—21no—
58C4×Dic22C2×C412yes—
59C4×Dic22C2312yes—
60C4×Dic22C2312yes—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8C2×C412yes—
64C11×C4⋊C8C2312yes—
65C11×C4⋊C8C2312yes—
66C11×C22⋊C8C2×C412yes—
67C4×C8×C11C2312yes—
68C22⋊(C11⋊C8)—21no—
69#66882C2×C414yes—
70#66880C2×C414yes—
71#66880C2×C414yes—
72#66879—22no—
73Dic11⋊C8—22no—
74Dic11⋊C8—22no—
75Dic11⋊C8—22no—
76Dic11⋊C8—22no—
77C8×Dic11—22no—
78C8×Dic11—22no—
79C8×Dic11—22no—
80C4⋊(C11⋊C8)—21no—
81C4×C11⋊C8D411yescharacteristic
82C4×C11⋊C8D411yescharacteristic
83C4×C11⋊C8C2312yes—
84C4×C11⋊C8C2311yescharacteristic
85C4×C11⋊C8C2311yescharacteristic
86#17906—111nomaximal, Sylow
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×Dic22—24no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22C22×C412yes—
96C2×Dic22C22×C412yes—
97C11×M16—42no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—42no—
101C2×C8×C11C22×C414yes—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11#4111yescharacteristic
105C42×C11C2411yescharacteristic
106C22⋊Dic11—22no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11C22×C412yes—
112C4⋊Dic11C22×C412yes—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117C4×Dic11—22no—
118C4×Dic11—22no—
119C4×Dic11—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8C2×D411yescharacteristic
124C2×C11⋊C8C2×D411yescharacteristic
125C2×C11⋊C8C2×D411yescharacteristic
126C2×C11⋊C8C2×D411yescharacteristic
127Dic44—28no—
128#3104—111no—
129#2960—111no—
130C2×C8×Q8—111no—
131#1587—114no—
132#1579—114no—
133#1570D1111yescharacteristic
134#1487—111no—
135#1481—111no—
136#1452—111no—
137C23×C11C4×D411yescharacteristic
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11#13712yes—
144C2×C4×C11#13712yes—
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C2×Dic11—24no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—22no—
153C2×Dic11—42no—
154Dic22—24no—
155Dic22—22no—
156Dic22—24no—
157Dic22—42no—
158Dic22#13114yes—
159C8×C11—24no—
160C8×C11—42no—
161C8×C11—42no—
162C11⋊C8—21no—
163C11⋊C8—21no—
164C11⋊C8—21no—
165C11⋊C8—21no—
166C11⋊C8—42no—
167#533—111no—
168C2×C4×Q8—111no—
169#484—112no—
170#477—112no—
171#462—112no—
172#451—112no—
173#446—112no—
174#446—221no—
175C8×Q8—112no—
176C8×Q8—112no—
177C8×Q8—112no—
178C8×Q8—221no—
179C8×Q8—221no—
180C8×Q8—221no—
181C4×Q16—114no—
182#431—111no—
183#431C2×D1111yescharacteristic
184#424—221no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—221no—
187C2×C4⋊C8C2×D1111yescharacteristic
188#405—221no—
189C2×C4×C8—111no—
190C2×C4×C8—221no—
191#334C2×D1114yes—
192Q8⋊C8—114no—
193Q8⋊C8—114no—
194#322—112no—
195#322—112no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#44112yes—
199C22×C11C2×C4×D411yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11#44112yes—
204C4×C11C2×#13112yes—
205C4×C11C2×#13711yescharacteristic
206C4×C11C2×#13711yescharacteristic
207Dic11—24no—
208Dic11—42no—
209Dic11—42no—
210Dic11—42no—
211C22×Q8—111no—
212C2×Q16—114no—
213C2×M16—21no—
214C22×C8—21no—
215C22×C8—111no—
216C22×C8—111no—
217C4⋊Q8—111no—
218C4⋊Q8—111no—
219#125—221no—
220C22⋊Q8—112no—
221C22⋊Q8—221no—
222C4×Q8—112no—
223C4×Q8—112no—
224C4×Q8—112no—
225C4×Q8—221no—
226C4×Q8—221no—
227C4×Q8—221no—
228#117—221no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233#107—114no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—222no—
237C4⋊C8—222no—
238C4⋊C8—222no—
239C4⋊C8—222no—
240C4⋊C8—221no—
241C4⋊C8C4×D1112yes—
242C4⋊C8C22×D1112yes—
243C4⋊C8C22×D1112yes—
244#103—114no—
245#103—114no—
246C22⋊C8—221no—
247C22⋊C8C4×D1112yes—
248#97—222no—
249C4×C8—111no—
250C4×C8—111no—
251C4×C8—111no—
252C4×C8—111no—
253C4×C8—112no—
254C4×C8—222no—
255C4×C8—222no—
256C4×C8—222no—
257C4×C8C22×D1112yes—
258C2×C11—22no—
259C2×C11#292911yescharacteristic
260C2×C11C2×#44111yescharacteristic
261C2×C11#295511yescharacteristic
262C2×Q8—112no—
263C2×Q8—112no—
264C2×Q8—224no—
265C2×Q8—221no—
266C2×Q8—221no—
267C22×C4—221no—
268C22×C4—221no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4#434311yescharacteristic
272Q16—228no—
273M16—42no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—111no—
278C2×C8—111no—
279C2×C8—111no—
280C2×C8—111no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8C2×C4×D1114yes—
285C4⋊C4—112no—
286C4⋊C4—112no—
287C4⋊C4—221no—
288C4⋊C4—222no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—222no—
292C4⋊C4—221no—
293C4⋊C4—222no—
294C4⋊C4—222no—
295C22⋊C4—222no—
296C42—222no—
297C42—222no—
298C42—222no—
299C42C2×C4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42#434311yescharacteristic
302C42C23×D1111yescharacteristic
303C11#1790611yescharacteristic, complemented, Sylow
304C23#6694611yescharacteristic
305Q8—114no—
306Q8—224no—
307Q8—222no—
308Q8—224no—
309Q8—442no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—224no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—442no—
318C2×C4#6694611yescharacteristic
319C2×C4#6694611yescharacteristic
320C2×C4#6694611yescharacteristic
321C2×C4#6696812yes—
322C2×C4#6696812yes—
323C2×C4C22×C4×D1111yescharacteristic
324C2×C4C2×D4×D1111yescharacteristic
325C2×C4C2×#434311yescharacteristic
326C8—24no—
327C8—42no—
328C8—42no—
329C8—221no—
330C8—221no—
331C8—221no—
332C8—221no—
333C8—442no—
334C22—21no—
335C22—21no—
336C22#1062246612yes—
337C22C2×#6694611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—224no—
342C4—442no—
343C4—442no—
344C4—442no—
345C4#1062246612yes—
346C4D11×#13112yes—
347C4C2×#6696811yescharacteristic
348C4C2×#6696811yescharacteristic
349C2—22no—
350C2#1307730911yescharacteristic
351C2C2×#1062246611yescharacteristic
352C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1570C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#1570D11
hypocenterC11#17906
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
4. #13067486C2semidirect
5. #13067434C2semidirect
303. C11#17906semidirect

Maximal subgroups

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

subgroupindex
#130786562
#130775462
C2×#106224432
#130674862
#130674342
#130670442
#130670182
#130669092
C11×#15702
#1790611