Finite Group Databasebeta

← #14738386

Subgroups — #14738386

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C212yesmaximal
2#13077329C211yesmaximal, characteristic
3#13068126C212yesmaximal, complemented
4#13068102C212yesmaximal, complemented
5#13068036C214yesmaximal, complemented
6#13067372C211yesmaximal, characteristic, complemented
7#13067354C212yesmaximal, complemented
8C11×#3170C211yesmaximal, characteristic, complemented
9C11×#533C2212yes—
10C2×#66954—21no—
11#10623008C2211yescharacteristic
12C11×#500C2211yescharacteristic
13C11×#494C2211yescharacteristic
14C11×#487C2212yes—
15C11×#467—21no—
16C11×#467—21no—
17C4×C11×Q16—21no—
18C4×C11×Q16—21no—
19C2×C4×C8×C11C2211yescharacteristic
20#10622723—21no—
21#10622700C2214yes—
22#10622696C2214yes—
23#10622662—24no—
24#10622640—22no—
25#10622634—22no—
26#10622537C2211yescharacteristic
27#10622537C2212yes—
28#10622301—21no—
29#10622301C2212yes—
30C8×D44—21no—
31C8×D44C2212yes—
32#10622185C2214yes—
33#10622185C2214yes—
34#10622095C2212yes—
35#10622095C2212yes—
36C2×#4339—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C11×C4⋊Q8C2312yes—
42C11×C4⋊Q8C2312yes—
43C11×#125—22no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—22no—
46C4×Q8×C11—22no—
47C4×Q8×C11—22no—
48C11×#117—22no—
49C2×C42×C11C2311yescharacteristic
50C2×#4325—24no—
51#66983—21no—
52#66983D412yes—
53C2×#4318—21no—
54C2×#4318—22no—
55#66954—44no—
56C2×#4313—22no—
57C2×C8×D11—22no—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44C2312yes—
62#66922D411yescharacteristic
63C11×#107—21no—
64C11×#107—21no—
65C11×#103—22no—
66C11×#103—22no—
67C4×C8×C11D411yescharacteristic
68C4×C8×C11D411yescharacteristic
69C4×C8×C11C2311yescharacteristic
70C4×C8×C11C2311yescharacteristic
71#66899—24no—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66873—24no—
75#66871—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2314yes—
80#19338—111nomaximal, Sylow
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—22no—
87#4339—42no—
88#4339—42no—
89C2×D44—21no—
90C2×D44—21no—
91C2×D44C2×D412yes—
92C2×C4×D11—22no—
93C2×Dic22—21no—
94C11×Q16—42no—
95C11×Q16—42no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11C2×D411yescharacteristic
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—42no—
108C11×C22⋊C4—42no—
109C42×C11—42no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11C2411yescharacteristic
114#4325—84no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11C2×D412yes—
119#4318—42no—
120#4318—82no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—22no—
123#4313—44no—
124C8×D11—44no—
125#3254—112no—
126#3170D1111yescharacteristic, complemented
127#2931—111no—
128#1693—112no—
129#1689—112no—
130#1679—114no—
131#1566—111no—
132#1561—112no—
133C23×C11#12111yescharacteristic
134C22×D11—22no—
135Q8×C11—42no—
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—42no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×D411yescharacteristic
150C2×C4×C11C2×#4111yescharacteristic
151C22⋊D11—44no—
152C2×Dic11—22no—
153D44—24no—
154D44—42no—
155D44—42no—
156C4×D11—42no—
157C4×D11—42no—
158Dic22—42no—
159C8×C11—21no—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11AGL(1,ℤ/8)12yes—
163C11⋊C8—42no—
164C11⋊C8—44no—
165C2×#131—221no—
166#533C2×D1112yes—
167#532—111no—
168#500C2×D1111yescharacteristic
169#494C2×D1111yescharacteristic
170#487C2×D1112yes—
171#477—222no—
172#474—114no—
173#468—224no—
174#467—21no—
175#467—21no—
176#461—114no—
177#460—222no—
178C4×Q16—21no—
179C4×Q16—21no—
180#436—112no—
181#436—221no—
182C8×D4—112no—
183C8×D4—221no—
184#423—111no—
185#423—112no—
186#408—221no—
187C2×C4×C8C2×D1111yescharacteristic
188#334—112no—
189#334—112no—
190#332—114no—
191#332—114no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11C2×#12111yescharacteristic
196C2×D11—42no—
197C2×D11—42no—
198C2×D11—42no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—82no—
203C4×C11—82no—
204C4×C11#47312yes—
205C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
206C4×C11#57511yescharacteristic
207C4×C11#57712yes—
208Dic11—42no—
209C2×#41—221no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×SD16—224no—
213#131—444no—
214C2×M16—221no—
215C2×M16—222no—
216C2×M16—222no—
217C22×C8—222no—
218C22×C8C22⋊D1111yescharacteristic
219C22×C8C22⋊D1111yescharacteristic
220C4⋊Q8—111no—
221C4⋊Q8C22×D1112yes—
222C4⋊Q8C22×D1112yes—
223#127—111no—
224#125—22no—
225#124—221no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228#121—112no—
229#121—221no—
230C4×Q8—22no—
231C4×Q8—22no—
232C4×D4—112no—
233C4×D4—221no—
234#117—22no—
235C2×C42C22×D1111yescharacteristic
236#107—21no—
237#107—21no—
238#107—224no—
239C4⋊C8—112no—
240C4⋊C8—114no—
241C4⋊C8—222no—
242C4⋊C8—221no—
243#103—22no—
244#103—22no—
245#103—224no—
246#102—224no—
247C22⋊C8—222no—
248C22⋊C8—222no—
249C4×C8C22⋊D1111yescharacteristic
250C4×C8C22⋊D1111yescharacteristic
251C4×C8C22×D1111yescharacteristic
252C4×C8C22×D1111yescharacteristic
253C2×C11—41no—
254C2×C11#303611yescharacteristic
255C2×C11#306011yescharacteristic
256C2×C11C2×#47311yescharacteristic
257D11—82no—
258#41—442no—
259#41—442no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—221no—
263C2×D4—112no—
264C2×D4—222no—
265C2×D4—221no—
266C2×D4—221no—
267C22×C4—222no—
268C22×C4D4×D1111yescharacteristic
269C22×C4#434111yescharacteristic
270C22×C4C2×C22⋊D1111yescharacteristic
271Q16—42no—
272Q16—42no—
273SD16—884no—
274M16—442no—
275M16—444no—
276M16—882no—
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—224no—
280C2×C8—222no—
281C2×C8—444no—
282C2×C8C2×C22⋊D1111yescharacteristic
283C2×C8C2×C22⋊D1111yescharacteristic
284C2×C8C2×C22⋊D1111yescharacteristic
285C2×C8C2×C22⋊D1111yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—112no—
293C4⋊C4—221no—
294C22⋊C4—42no—
295C22⋊C4—222no—
296C22⋊C4—222no—
297C42—42no—
298C42D4×D1111yescharacteristic
299C42#434111yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C42C23×D1111yescharacteristic
302C11#1933811yescharacteristic, complemented, Sylow
303C23—222no—
304C23#6699111yescharacteristic
305Q8—42no—
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—442no—
310D4—224no—
311D4—442no—
312D4—444no—
313D4—442no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—222no—
321C2×C4—442no—
322C2×C4—442no—
323C2×C4#6699111yescharacteristic
324C2×C4#6699111yescharacteristic
325C2×C4#6699111yescharacteristic
326C2×C4C2×D4×D1111yescharacteristic
327C2×C4C2×#434111yescharacteristic
328C2×C4C22×C22⋊D1111yescharacteristic
329C8—21no—
330C8—21no—
331C8—21no—
332C8—444no—
333C8—442no—
334C8#6700212yes—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—442no—
339C22—442no—
340C22—442no—
341C22C2×#6699111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—82no—
347C4—442no—
348C4#1062280512yes—
349C4#1062330112yes—
350C4C2×#6700211yescharacteristic
351C4#1062335311yescharacteristic
352C2—41no—
353C2—882no—
354C2#1307807611yescharacteristic
355C2#1307827411yescharacteristic
356C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3170D11
hypocenterC11#19338
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068126C2semidirect
4. #13068102C2semidirect
5. #13068036C2semidirect
6. #13067372C2semidirect
7. #13067354C2semidirect
8. C11×#3170C2semidirect
126. #3170D11semidirect
302. C11#19338semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130773292
#130681262
#130681022
#130680362
#130673722
#130673542
C11×#31702
#1933811