Finite Group Databasebeta

← #14772713

Subgroups — #14772713

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×Dic22C211yesmaximal, characteristic
2#13071568C212yesmaximal
3#13069387C212yesmaximal
4#13069382C212yesmaximal
5#13069373C212yesmaximal
6#13068745C211yesmaximal, characteristic
7#13068742C211yesmaximal, characteristic
8C4×#66882C211yesmaximal, characteristic
9#13068508C211yesmaximal, characteristic
10#13068504C211yesmaximal, characteristic
11C11×#1835C211yesmaximal, characteristic
12C2×C4×Dic22C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C11×#382C2212yes—
15C2×#66882C2212yes—
16C2×Dic11⋊C8C2211yescharacteristic
17C2×Dic11⋊C8C2211yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C2×C8×Dic11C2211yescharacteristic
20#10622590C2212yes—
21#10622589C2212yes—
22C4⋊C4×Dic11C2212yes—
23C4⋊C4×Dic11C2212yes—
24C2×#66872C2212yes—
25C2×#66871C2212yes—
26C4×C4⋊Dic11C2212yes—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C8×Dic22C418yescomplemented
29#10622266—22no—
30#10622265—22no—
31#10622262—22no—
32#10622259—22no—
33C11×#340C2212yes—
34C11×#340C2211yescharacteristic
35C11×#340C2211yescharacteristic
36#10622189C2211yescharacteristic
37#10622189C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40C22×Dic22D411yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C22×C8×C11C2311yescharacteristic
43C2×C11×C4⋊C4C2312yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C42×C11C2311yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11C2312yes—
48C2×C4⋊Dic11C2312yes—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4—22no—
51C2×Dic11⋊C4D411yescharacteristic
52C2×Dic11⋊C4D411yescharacteristic
53C2×C4×Dic11—22no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11C2311yescharacteristic
57C2×C4×Dic11C2311yescharacteristic
58C22×C11⋊C8C2311yescharacteristic
59C22×C11⋊C8C2311yescharacteristic
60C4×Dic22C2×C414yes—
61C4×Dic22Q814yes—
62C4×C8×C11C2×C414yes—
63C11×#95—22no—
64C11×#95—22no—
65C11⋊#95—22no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#66882—24no—
71Dic11⋊C8C2×C414yes—
72Dic11⋊C8C2×C414yes—
73C8×Dic11C2×C414yes—
74C8×Dic11C2×C414yes—
75#66872—24no—
76#66871—24no—
77C4⋊(C11⋊C8)C2×C414yes—
78#22739—111nomaximal, Sylow
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11C2×D411yescharacteristic
87C22×Dic11C2×D411yescharacteristic
88C22×Dic11C2×D411yescharacteristic
89C22×Dic11C2×D411yescharacteristic
90C2×Dic22—24no—
91C2×Dic22C4⋊C414yes—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11C22×C412yes—
95C2×C8×C11C22×C412yes—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C42×C11C22×C412yes—
101C42×C11C2×Q812yes—
102C4⋊Dic11—22no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11C4⋊C414yes—
106C4⋊Dic11#4114yes—
107Dic11⋊C4—44no—
108Dic11⋊C4—82no—
109Dic11⋊C4C4⋊C414yes—
110Dic11⋊C4C4⋊C414yes—
111C4×Dic11—44no—
112C4×Dic11—82no—
113C4×Dic11—82no—
114C4×Dic11C22×C412yes—
115C4×Dic11C22×C412yes—
116C4×Dic11C2×Q812yes—
117C4×Dic11C2×Q812yes—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8C22×C412yes—
121C2×C11⋊C8C22×C412yes—
122C2×C8×Q8—111no—
123#2355—112no—
124#1949—112no—
125#1949—112no—
126#1947—112no—
127#1835—111no—
128#1835D1111yescharacteristic
129#1834—111no—
130C4×#107—111no—
131C4×#107—111no—
132C4×#106—111no—
133C23×C11C22×D411yescharacteristic
134C2×C4×C11—22no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—42no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11C2×C4⋊C412yes—
144C2×C4×C11C2×C4⋊C412yes—
145C2×C4×C11C23×C411yescharacteristic
146C2×C4×C11C22×Q811yescharacteristic
147C2×C4×C11C2×#4112yes—
148C2×C4×C112−1+412yes—
149C2×Dic11—22no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—24no—
155C2×Dic11—42no—
156C2×Dic11—42no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11C2×C4⋊C412yes—
161C2×Dic11C2×C4⋊C412yes—
162C2×Dic11C2×C4⋊C412yes—
163C2×Dic11C2×C4⋊C412yes—
164C2×Dic11#13514yes—
165Dic22—28no—
166C8×C11—22no—
167C8×C11—22no—
168C11⋊C8—22no—
169C11⋊C8—22no—
170C2×C4×Q8—111no—
171C8×Q8—118no—
172C2×#107—112no—
173C2×#107—112no—
174C2×#106—112no—
175C2×C4⋊C8—111no—
176C2×C4⋊C8—111no—
177C2×C4⋊C8—111no—
178C2×C4×C8—111no—
179C2×C4×C8—111no—
180C2×C4×C8C2×D1111yescharacteristic
181#391—222no—
182#387—222no—
183#387—222no—
184#384—112no—
185#382—112no—
186#382C2×D1112yes—
187C4×C4⋊C4—112no—
188C4×C4⋊C4—112no—
189C4×C4⋊C4—112no—
190C4×C4⋊C4—222no—
191#340—111no—
192#340—111no—
193#340—112no—
194#340—112no—
195#340C2×D1111yescharacteristic
196#340C2×D1111yescharacteristic
197#340C2×D1112yes—
198C22×C11C22×C4⋊C411yescharacteristic
199C22×C11#54812yes—
200C22×C11C2×#13512yes—
201C22×C11#57611yescharacteristic
202C22×C11#57811yescharacteristic
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—82no—
206C4×C11—82no—
207C4×C11C4×#4111yescharacteristic
208C4×C11#51911yescharacteristic
209C4×C11#55712yes—
210Dic11—22no—
211Dic11—22no—
212Dic11—22no—
213Dic11—44no—
214Dic11—82no—
215Dic11#42714yes—
216C22×Q8—111no—
217C22×C8—111no—
218C22×C8—111no—
219C22×C8C22×D1111yescharacteristic
220C22×C8C22×D1111yescharacteristic
221C4×Q8—114no—
222C4×Q8—114no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—112no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4—222no—
229C2×C4⋊C4—222no—
230C2×C4⋊C4C22×D1112yes—
231C2×C4⋊C4C22×D1112yes—
232C2×C42—111no—
233C2×C42—111no—
234C2×C42—222no—
235C2×C42—222no—
236C2×C42—222no—
237C2×C42C22×D1111yescharacteristic
238#107—224no—
239#107—224no—
240#106—224no—
241C4⋊C8—114no—
242C4⋊C8—114no—
243C4⋊C8—114no—
244C4×C8—114no—
245C4×C8—114no—
246C4×C8C4×D1114yes—
247#95—22no—
248#95—22no—
249#95—222no—
250#95—222no—
251#95—222no—
252#95—222no—
253#95—222no—
254C2×C11#235111yescharacteristic
255C2×C11C2×#42711yescharacteristic
256C2×C11#291311yescharacteristic
257C2×C11#336112yes—
258C2×C11#336412yes—
259C2×Q8—114no—
260C2×Q8—224no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—222no—
268C22×C4—222no—
269C22×C4D4×D1111yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4C23×D1111yescharacteristic
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—112no—
275C2×C8—112no—
276C2×C8—222no—
277C2×C8—222no—
278C2×C8C2×C4×D1112yes—
279C2×C8C2×C4×D1112yes—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—114no—
285C4⋊C4—114no—
286C4⋊C4—114no—
287C4⋊C4—114no—
288C4⋊C4—222no—
289C4⋊C4—222no—
290C4⋊C4—222no—
291C4⋊C4—444no—
292C4⋊C4—882no—
293C42—112no—
294C42—112no—
295C42—112no—
296C42—112no—
297C42—444no—
298C42—882no—
299C42—882no—
300C42C2×C4×D1112yes—
301C42Q8×D1112yes—
302C11#2273911yescharacteristic, complemented, Sylow
303C23C2×D4×D1111yescharacteristic
304Q8—228no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—112no—
315C2×C4—114no—
316C2×C4—112no—
317C2×C4—112no—
318C2×C4—112no—
319C2×C4—222no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—224no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4C4⋊C4×D1112yes—
331C2×C4C4⋊C4×D1112yes—
332C2×C4C22×C4×D1111yescharacteristic
333C2×C4C2×Q8×D1111yescharacteristic
334C2×C4#41×D1112yes—
335C2×C4#6704312yes—
336C8—22no—
337C8—22no—
338C8—222no—
339C8—222no—
340C22C2×C4⋊C4×D1111yescharacteristic
341C22#1062320812yes—
342C22D11×#13512yes—
343C22#1062330011yescharacteristic
344C22#1062330211yescharacteristic
345C4—22no—
346C4—22no—
347C4—82no—
348C4—82no—
349C4—114no—
350C4—222no—
351C4—222no—
352C4—222no—
353C4—444no—
354C4—882no—
355C4#1062304711yescharacteristic
356C4#1062305311yescharacteristic
357C4#1062321612yes—
358C2#1307153311yescharacteristic
359C2D11×#42711yescharacteristic
360C2#1307721311yescharacteristic
361C2#1308127312yes—
362C2#1308129812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1835C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1835D11
hypocenterC11#22739
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1835

Complements

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

NH ≅ G/Ntype
28. C8×Dic22C4semidirect
302. C11#22739semidirect

Maximal subgroups

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

subgroupindex
C2×C8×Dic222
#130715682
#130693872
#130693822
#130693732
#130687452
#130687422
C4×#668822
#130685082
#130685042
C11×#18352
#2273911