Finite Group Databasebeta

← #14652147

Subgroups — #14652147

Order 2816.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069567C211yesmaximal, characteristic
2#13069417C211yesmaximal, characteristic
3#13069377C211yesmaximal, characteristic
4#13068486C211yesmaximal, characteristic
5C2×#10622120C211yesmaximal, characteristic
6#13066450C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C11×#384C2211yescharacteristic
12C2×#66879—21no—
13C2×#66874—21no—
14C2×#66874—21no—
15C2×#66872—21no—
16C4×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622189—21no—
20#10622189—21no—
21#10622188—21no—
22#10622167—21no—
23#10622120C414yescomplemented
24C22×Dic22—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11D411yescharacteristic
34C2×C4⋊Dic11D411yescharacteristic
35C2×C4×Dic11—21no—
36C22×C11⋊C8—21no—
37C22×C11⋊C8D411yescharacteristic
38C22×C11⋊C8D411yescharacteristic
39#66922—21no—
40#66922—21no—
41#66922—21no—
42#66922C2×C412yes—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8C2×C412yes—
47C11⋊#95—21no—
48#66879—42no—
49#66874—42no—
50#66874—42no—
51#66872—42no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)C2×C412yes—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56#9570—111nomaximal, Sylow
57C22×C4×C11—41no—
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×Dic11—21no—
62C22×Dic11—21no—
63C22×Dic11—41no—
64C2×Dic22—22no—
65C2×Dic22—41no—
66C2×Dic22—41no—
67C2×Dic22—41no—
68C2×Dic22—41no—
69C2×Dic22—41no—
70C2×C8×C11—22no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—81no—
81C42×C11C22×C411yescharacteristic
82C42×C11#4111yescharacteristic
83C42×C11#4111yescharacteristic
84C42×C11#4111yescharacteristic
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4×Dic11—41no—
94C4×Dic11—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8SD1612yes—
104#1988—111no—
105#1956—111no—
106#1948—111no—
107#1770—111no—
108C2×#332—111no—
109#1296D1111yescharacteristic
110#1277—111no—
111C23×C11#12111yescharacteristic
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11#11711yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12311yescharacteristic
121C2×C4×C11#12411yescharacteristic
122C2×C4×C11#12611yescharacteristic
123C2×C4×C11C2×SD1611yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×C4×C11#13711yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—42no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140Dic22—42no—
141Dic22—42no—
142Dic22—81no—
143Dic22—81no—
144C8×C11—42no—
145C8×C11—81no—
146C11⋊C8—22no—
147C11⋊C8—42no—
148C11⋊C8—41no—
149C2×C4⋊Q8—111no—
150C2×#106—221no—
151C2×C4⋊C8—111no—
152C2×C4⋊C8C2×D1111yescharacteristic
153C2×C4⋊C8C2×D1111yescharacteristic
154C2×#103—221no—
155C2×#103—221no—
156C2×#97—221no—
157C2×C4×C8—111no—
158#384C2×D1111yescharacteristic
159C4×C4⋊C4—111no—
160#340—221no—
161#340—221no—
162#340—221no—
163#336—221no—
164#332—114no—
165C22×C11#38811yescharacteristic
166C22×C11#46011yescharacteristic
167C22×C11#46311yescharacteristic
168C22×C11#46811yescharacteristic
169C22×C11#47011yescharacteristic
170C22×C11#47111yescharacteristic
171C22×C11#47311yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—161no—
175C4×C11C4×SD1611yescharacteristic
176C4×C11#44011yescharacteristic
177C4×C11#44111yescharacteristic
178C4×C11#44211yescharacteristic
179C4×C11#48111yescharacteristic
180C4×C11#48211yescharacteristic
181C4×C11#48911yescharacteristic
182C4×C11#49111yescharacteristic
183Dic11—82no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—221no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—111no—
190C22×C8—111no—
191C22×C8—221no—
192C4⋊Q8—112no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C42—221no—
204C2×C42C22×D1111yescharacteristic
205#106—442no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—112no—
210C4⋊C8—221no—
211C4⋊C8C4×D1112yes—
212#103—442no—
213#103—442no—
214#97—442no—
215C4×C8—221no—
216C4×C8—221no—
217#95—221no—
218C2×C11#168611yescharacteristic
219C2×C11#169011yescharacteristic
220C2×C11#169911yescharacteristic
221C2×C11#170311yescharacteristic
222C2×C11#192611yescharacteristic
223C2×C11#193011yescharacteristic
224C2×C11#193511yescharacteristic
225C2×Q8—222no—
226C2×Q8—441no—
227C2×Q8—441no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C22×C4—41no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—441no—
235C22×C4#433911yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—112no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—222no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—441no—
252C2×C8—441no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—222no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—441no—
265C4⋊C4—441no—
266C42—441no—
267C42—441no—
268C42C2×C4×D1111yescharacteristic
269C42#433911yescharacteristic
270C42#434111yescharacteristic
271C42#434311yescharacteristic
272C11#957011yescharacteristic, complemented, Sylow
273C23#6693711yescharacteristic
274Q8—442no—
275Q8—442no—
276Q8—881no—
277Q8—881no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—442no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—881no—
291C2×C4—881no—
292C2×C4#6692511yescharacteristic
293C2×C4(C22⋊D11)⋊C411yescharacteristic
294C2×C4#6693811yescharacteristic
295C2×C4#6694611yescharacteristic
296C2×C4#6694711yescharacteristic
297C2×C4#6695111yescharacteristic
298C2×C4#6696411yescharacteristic
299C2×C4#6696411yescharacteristic
300C2×C4SD16×D1111yescharacteristic
301C2×C4#6696711yescharacteristic
302C2×C4#6696811yescharacteristic
303C2×C4#6696811yescharacteristic
304C2×C4#6697111yescharacteristic
305C2×C4#6697211yescharacteristic
306C8—42no—
307C8—81no—
308C8—222no—
309C8—441no—
310C8—442no—
311C22#1062228211yescharacteristic
312C22#1062236111yescharacteristic
313C22#1062236811yescharacteristic
314C22#1062237511yescharacteristic
315C22#1062239311yescharacteristic
316C22#1062242911yescharacteristic
317C22#1062243211yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—881no—
322C4—881no—
323C4—882no—
324C4#1062237811yescharacteristic
325C4#1062239811yescharacteristic
326C4#1062240111yescharacteristic
327C4#1062241011yescharacteristic
328C4#1062246611yescharacteristic
329C4#1062247611yescharacteristic
330C4#1062249811yescharacteristic
331C4#1062250211yescharacteristic
332C2#1306808711yescharacteristic
333C2#1306810911yescharacteristic
334C2#1306816611yescharacteristic
335C2#1306819411yescharacteristic
336C2#1306924111yescharacteristic
337C2#1306926911yescharacteristic
338C2#1306930411yescharacteristic
subgroupG/H
centerC23#66937
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socle, prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#9570
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
23. #10622120C4semidirect
272. C11#9570semidirect

Maximal subgroups

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

subgroupindex
#130695672
#130694172
#130693772
#130684862
C2×#106221202
#130664502
C11×#12962
#957011