Finite Group Databasebeta

← #14737025

Subgroups — #14737025

Order 2816.

582 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
1#13079769C211yesmaximal, characteristic
2#13079767C211yesmaximal, characteristic
3C2×#10622691C211yesmaximal, characteristic
4#13077546C211yesmaximal, characteristic
5#13068143C214yesmaximal, complemented
6#13068019C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic
8#13067298C211yesmaximal, characteristic
9C11×#1548C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11#10623001C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C11×#423C2211yescharacteristic
15#10622735—21no—
16#10622732—21no—
17#10622706—21no—
18#10622704C2214yes—
19#10622691—21no—
20#10622691—21no—
21#10622691—21no—
22#10622691C2212yes—
23#10622691C2212yes—
24#10622583—22no—
25C2×#66871—21no—
26C2×#66871—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622463C2214yes—
30#10622444—21no—
31#10622444C2212yes—
32#10622443—21no—
33#10622443C2212yes—
34#10622335—22no—
35#10622295—21no—
36#10622294—21no—
37C11×#333C2214yes—
38#10622119C2214yes—
39#10622118C2212yes—
40#10622117C2212yes—
41C22×Q8×C11—21no—
42C22×Dic22—21no—
43C2×C11×M16—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51#66979—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54#66977—21no—
55#66977D412yes—
56C22×C11⋊C8D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58#66923—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922D411yescharacteristic
63#66922D411yescharacteristic
64#66922C2312yes—
65C4×Dic22—21no—
66C4×Dic22C2312yes—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C4×C8×C11—21no—
72C22⋊(C11⋊C8)—21no—
73#66882—24no—
74#66880—24no—
75#66879—22no—
76Dic11⋊C8—22no—
77Dic11⋊C8—22no—
78C8×Dic11—22no—
79#66874—24no—
80#66871—24no—
81#66871—22no—
82#66871—22no—
83#66871—22no—
84#66871—22no—
85C4⋊(C11⋊C8)C2312yes—
86C4×C11⋊C8—21no—
87C4×C11⋊C8D411yescharacteristic
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8C2311yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91#19209—111nomaximal, Sylow
92C2×Q8×C11—22no—
93C2×Q8×C11—41no—
94C2×Q8×C11—82no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C22×Dic11—41no—
100C2×Dic22—21no—
101C2×Dic22—22no—
102C2×Dic22—41no—
103C2×Dic22—82no—
104C2×Dic22C2×D412yes—
105C11×M16—42no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11C2411yescharacteristic
116C22⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11C2×D412yes—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127C4×Dic11—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8Q1614yes—
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135#3230—111no—
136#3230—111no—
137C2×#500—111no—
138#2960—111no—
139#1696—114no—
140#1676—114no—
141#1564—111no—
142#1548—111no—
143#1548D1111yescharacteristic
144C23×C11#12111yescharacteristic
145Q8×C11—82no—
146Q8×C11—82no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—42no—
150C2×C4×C11—82no—
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11C2×Q1612yes—
155C2×C4×C11#13712yes—
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C2×#4111yescharacteristic
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—82no—
163Dic22—24no—
164Dic22—42no—
165Dic22—82no—
166Dic22—82no—
167C8×C11—42no—
168C8×C11—42no—
169C11⋊C8—21no—
170C11⋊C8—21no—
171C11⋊C8—42no—
172C11⋊C8C2×Q1612yes—
173C11⋊C8C2×Q1612yes—
174#533—111no—
175C2×C4⋊Q8—111no—
176C2×C4⋊Q8C2×D1111yescharacteristic
177#500—112no—
178#500—112no—
179#500—221no—
180#500—221no—
181#500—221no—
182#500—221no—
183#487—221no—
184#487—221no—
185#484—222no—
186#484—222no—
187#477—114no—
188#477—114no—
189#446—112no—
190#446—221no—
191C8×Q8—112no—
192C8×Q8—221no—
193#431—111no—
194#431C2×D1111yescharacteristic
195C2×#107—221no—
196C2×#107—221no—
197#424—221no—
198#423C2×D1111yescharacteristic
199#405—221no—
200C2×C4×C8—111no—
201#335—112no—
202#334—112no—
203#333—114no—
204#333C2×D1114yes—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11#46212yes—
208C22×C11C2×#12111yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—82no—
212C4×C11#46212yes—
213C4×C11#47212yes—
214C4×C11C22×Q1611yescharacteristic
215C4×C11C2×#13711yescharacteristic
216C4×C11#57812yes—
217Dic11—42no—
218Dic11—42no—
219Dic11—82no—
220C22×Q8—21no—
221C22×Q8—221no—
222C2×M16—21no—
223C22×C8—111no—
224C22×C8—111no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—111no—
229C4⋊Q8—111no—
230C4⋊Q8—112no—
231C4⋊Q8—221no—
232C4⋊Q8—221no—
233C4⋊Q8—221no—
234C4⋊Q8C22×D1112yes—
235#125—221no—
236C22⋊Q8—112no—
237C22⋊Q8—221no—
238C4×Q8—112no—
239C4×Q8—221no—
240#117—221no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C42C22×D1111yescharacteristic
246#107—224no—
247#107—222no—
248#107—222no—
249#107—222no—
250#107—222no—
251#107—224no—
252C4⋊C8—21no—
253C4⋊C8—112no—
254C4⋊C8—222no—
255C4⋊C8—222no—
256C4⋊C8C22×D1112yes—
257C4⋊C8C22×D1112yes—
258#103—224no—
259#103—224no—
260C22⋊C8—21no—
261C22⋊C8—221no—
262#97—222no—
263C4×C8—21no—
264C4×C8—111no—
265C4×C8—111no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—222no—
269C4×C8—221no—
270C2×C11—22no—
271C2×C11C2×#46211yescharacteristic
272C2×C11#305911yescharacteristic
273C2×C11C2×#47211yescharacteristic
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—82no—
277C2×Q8—112no—
278C2×Q8—221no—
279C2×Q8—222no—
280C2×Q8—441no—
281C2×Q8—882no—
282C22×C4—41no—
283C22×C4—441no—
284C22×C4#433911yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4D4×D1111yescharacteristic
287M16—42no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—114no—
291C2×C8—111no—
292C2×C8—111no—
293C2×C8—111no—
294C2×C8—111no—
295C2×C8—222no—
296C2×C8—222no—
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—112no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4—221no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—222no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C22⋊C4—222no—
312C42—222no—
313C42#433911yescharacteristic
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C42C23×D1111yescharacteristic
317C11#1920911yescharacteristic, complemented, Sylow
318C23#6693711yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—224no—
322Q8—442no—
323Q8—882no—
324Q8—882no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—442no—
332C2×C4—882no—
333C2×C4#6693711yescharacteristic
334C2×C4#6693711yescharacteristic
335C2×C4#6693711yescharacteristic
336C2×C4#6696812yes—
337C2×C4Q16×D1112yes—
338C2×C4C2×#433911yescharacteristic
339C2×C4C2×D4×D1111yescharacteristic
340C2×C4C2×D4×D1111yescharacteristic
341C8—42no—
342C8—42no—
343C8—112no—
344C8—112no—
345C8—221no—
346C8—221no—
347C8—442no—
348C22—21no—
349C22—21no—
350C22#1062240612yes—
351C22C2×#6693711yescharacteristic
352C4—21no—
353C4—21no—
354C4—82no—
355C4—442no—
356C4—442no—
357C4—882no—
358C4#1062236212yes—
359C4#1062240612yes—
360C4C2×#6696811yescharacteristic
361C4C2×Q16×D1111yescharacteristic
362C4#1062331012yes—
363C2—22no—
364C2C2×#1062240611yescharacteristic
365C2#1307827011yescharacteristic
366C2C2×#1062236211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#1548D11
hypocenterC11#19209
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
5. #13068143C2semidirect
6. #13068019C2semidirect
317. C11#19209semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130797672
C2×#106226912
#130775462
#130681432
#130680192
#130673622
#130672982
C11×#15482
#1920911