Finite Group Databasebeta

← #14737006

Subgroups — #14737006

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079767C211yesmaximal, characteristic
2#13079564C211yesmaximal, characteristic
3#13077550C211yesmaximal, characteristic
4#13068119C214yesmaximal, complemented
5#13067995C214yesmaximal, complemented
6#13067364C211yesmaximal, characteristic
7#13067301C211yesmaximal, characteristic
8#13067297C211yesmaximal, characteristic
9C2×C11×#498C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12#10623001C2211yescharacteristic
13C11×#498—21no—
14C11×#498—21no—
15C11×#498C2212yes—
16C11×#498C2212yes—
17C2×C11×#106—21no—
18C2×C11×#106—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622841—22no—
21#10622715—21no—
22#10622714—21no—
23#10622706—21no—
24#10622705—21no—
25#10622704C2214yes—
26#10622703C2214yes—
27#10622694—21no—
28#10622691—21no—
29#10622583—22no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622292—21no—
34#10622292C2212yes—
35C8×Dic22—21no—
36C8×Dic22C2212yes—
37#10622185C2214yes—
38#10622184C2214yes—
39#10622096C2212yes—
40#10622095C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×C8×C11D411yescharacteristic
44C22×C8×C11D411yescharacteristic
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8C2312yes—
52C11×C4⋊Q8C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4326—24no—
59#66979—21no—
60#66977—21no—
61#66977D412yes—
62C2×#4318—21no—
63#66923—21no—
64#66922D411yescharacteristic
65#66922D411yescharacteristic
66C4×Dic22—21no—
67C4×Dic22C2312yes—
68C11×#106—22no—
69C11×#106—22no—
70C11×#106—22no—
71C11×#106—22no—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66899—24no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79#66879—22no—
80Dic11⋊C8—22no—
81Dic11⋊C8—22no—
82C8×Dic11—22no—
83#66874—24no—
84#66871—24no—
85C4⋊(C11⋊C8)—21no—
86C4⋊(C11⋊C8)C2312yes—
87C4⋊(C11⋊C8)C2312yes—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8—21no—
91#19207—111nomaximal, Sylow
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—41no—
96C2×Q8×C11—82no—
97C2×Q8×C11—82no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×Dic22—21no—
104C2×Dic22C2×D412yes—
105C2×C8×C11—22no—
106C2×C8×C11Q1614yescomplemented
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123C22⋊Dic11—22no—
124#4326—84no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129Dic11⋊C4—22no—
130Dic11⋊C4—22no—
131C4×Dic11—22no—
132#4318—42no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136#3230—111no—
137#3209—111no—
138C2×#498D1111yescharacteristic
139#2960—111no—
140#1692—114no—
141#1672—114no—
142#1564—111no—
143#1549—111no—
144#1548—111no—
145C23×C11#12111yescharacteristic
146Q8×C11—44no—
147Q8×C11—82no—
148Q8×C11—82no—
149Q8×C11—82no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—82no—
155C2×C4×C11—82no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11C2×Q1612yes—
160C2×C4×C11#13712yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—22no—
166Dic22—24no—
167Dic22—42no—
168C8×C11—21no—
169C8×C11—21no—
170C8×C11C2×Q1612yes—
171C8×C11C2×Q1612yes—
172C11⋊C8—42no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175#533—111no—
176C2×C4⋊Q8C2×D1111yescharacteristic
177C2×C4⋊Q8C2×D1111yescharacteristic
178#500—221no—
179#498—21no—
180#498—21no—
181#498C2×D1112yes—
182#498C2×D1112yes—
183#494—221no—
184#487—221no—
185#487—221no—
186#484—222no—
187#477—114no—
188#462—114no—
189#451—222no—
190#446—112no—
191#446—221no—
192C8×Q8—112no—
193C8×Q8—221no—
194#431—111no—
195#431—111no—
196C2×#106—21no—
197C2×#106—21no—
198#424—221no—
199#423—111no—
200#405—221no—
201C2×C4×C8C2×D1111yescharacteristic
202#335—112no—
203#334—112no—
204#333—114no—
205#332—114no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11#46212yes—
209C22×C11C2×#12111yescharacteristic
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—82no—
213C4×C11—82no—
214C4×C11#46212yes—
215C4×C11#47112yes—
216C4×C11C22×Q1611yescharacteristic
217C4×C11C2×#13711yescharacteristic
218C4×C11#57712yes—
219Dic11—42no—
220Dic11—42no—
221C22×Q8—21no—
222C22×Q8—21no—
223C2×Q16—224no—
224C2×M16—221no—
225C22×C8C22⋊D1111yescharacteristic
226C22×C8C22⋊D1111yescharacteristic
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—111no—
234C4⋊Q8—111no—
235C4⋊Q8C22×D1112yes—
236C4⋊Q8C22×D1112yes—
237#125—221no—
238C22⋊Q8—112no—
239C22⋊Q8—221no—
240C4×Q8—112no—
241C4×Q8—221no—
242#117—221no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42C22×D1111yescharacteristic
248#107—224no—
249#106—22no—
250#106—22no—
251#106—22no—
252#106—22no—
253C4⋊C8—112no—
254C4⋊C8—112no—
255C4⋊C8—112no—
256C4⋊C8—222no—
257C4⋊C8—222no—
258C4⋊C8—221no—
259#103—224no—
260#103—224no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263#97—222no—
264C4×C8—222no—
265C4×C8—221no—
266C4×C8—221no—
267C4×C8C22⋊D1111yescharacteristic
268C4×C8C22⋊D1111yescharacteristic
269C4×C8C22×D1111yescharacteristic
270C4×C8C22×D1111yescharacteristic
271C2×C11—22no—
272C2×C11C2×#46211yescharacteristic
273C2×C11#305711yescharacteristic
274C2×C11C2×#47111yescharacteristic
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—82no—
280C2×Q8—82no—
281C2×Q8—112no—
282C2×Q8—221no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—884no—
289M16—442no—
290C2×C8—22no—
291C2×C8—222no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8#432614yescomplemented
295C2×C8C2×C22⋊D1111yescharacteristic
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—112no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—221no—
312C4⋊C4—222no—
313C22⋊C4—222no—
314C42—222no—
315C42D4×D1111yescharacteristic
316C42#434111yescharacteristic
317C42C2×C22⋊D1111yescharacteristic
318C42C23×D1111yescharacteristic
319C11#1920711yescharacteristic, complemented, Sylow
320C23#6699111yescharacteristic
321Q8—44no—
322Q8—82no—
323Q8—82no—
324Q8—82no—
325Q8—224no—
326Q8—442no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—222no—
334C2×C4—222no—
335C2×C4#6699111yescharacteristic
336C2×C4#6699111yescharacteristic
337C2×C4#6699111yescharacteristic
338C2×C4#6699512yes—
339C2×C4C2×#432612yes—
340C2×C4C2×D4×D1111yescharacteristic
341C2×C4C2×#434111yescharacteristic
342C2×C4C22×C22⋊D1111yescharacteristic
343C8—21no—
344C8—21no—
345C8—442no—
346C8—442no—
347C8—442no—
348C8C2×#432612yes—
349C8C2×#432612yes—
350C22—21no—
351C22—21no—
352C22#1062270312yes—
353C22C2×#6699111yescharacteristic
354C4—21no—
355C4—21no—
356C4—82no—
357C4—82no—
358C4—442no—
359C4—442no—
360C4#1062270312yes—
361C4#1062279012yes—
362C4#1062329312yes—
363C4C2×#6699511yescharacteristic
364C4C22×#432611yescharacteristic
365C2—22no—
366C2C2×#1062270311yescharacteristic
367C2#1307825111yescharacteristic
368C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#498C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenterC2×#498D11
hypocenterC11#19207
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
4. #13068119C2semidirect
5. #13067995C2semidirect
106. C2×C8×C11Q16semidirect
294. C2×C8#4326semidirect
319. C11#19207semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130795642
#130775502
#130681192
#130679952
#130673642
#130673012
#130672972
C2×C11×#4982
#1920711