Finite Group Databasebeta

← #15617546

Subgroups — #15617546

Order 2816.

2122 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
1#13077267C218yesmaximal, complemented
2#13077260C218yesmaximal, complemented
3#13077254C214yesmaximal, complemented
4#13077249C214yesmaximal, complemented
5#13077180C212yesmaximal, complemented
6#13077061C212yesmaximal
7C2×C4×#4318C212yesmaximal, complemented
8C2×C4×C11×#41C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C4×C11×#41C418yes—
11C4×C11×#41C2214yes—
12C4×C11×#41C2214yes—
13C2×C4×Q8×C11C412yes—
14C2×C4×D4×C11C414yes—
15C2×C4×D4×C11C412yes—
16C2×C11×#117C2212yes—
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×#4318C2214yes—
21#10622847C22116yes—
22#10622820C2218yes—
23#10622613C22132yescomplemented
24#10622612C22116yescomplemented
25#10622539C22116yescomplemented
26#10622538C22116yescomplemented
27#10622537C2218yes—
28C4×#4318C2214yes—
29C4×#4318C2214yes—
30C4×#4318C2214yescomplemented
31C4×#4318C2214yescomplemented
32C2×#66867C2214yescomplemented
33C2×C4×C11⋊C8C2214yescomplemented
34C2×C11×#41—28no—
35C2×C11×#41C2×C414yes—
36C2×C11×#41C2314yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C414yes—
41C23×C4×C11C2×C412yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C4×Q8×C11C2×C418yes—
45C4×Q8×C11C2×C418yes—
46C4×D4×C11C2×C4116yes—
47C4×D4×C11C2×C418yes—
48C4×D4×C11C2×C4116yes—
49C4×D4×C11C2×C418yes—
50C11×#117C2×C418yes—
51C11×#117C2×C414yes—
52C11×#117C2314yes—
53C11×#117C2318yes—
54C2×C11×C4⋊C4C2×C414yes—
55C2×C11×C4⋊C4C2×C412yes—
56C2×C11×C22⋊C4C2×C414yes—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C42×C11C2×C414yes—
59C2×C42×C11C2×C412yes—
60C2×C42×C11C2×C418yes—
61C2×C42×C11C2×C414yes—
62C2×C42×C11C2312yes—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2312yes—
67C2×C42×C11C2314yes—
68C2×C42×C11C2314yes—
69C2×#4318—216no—
70C2×#4318C2318yes—
71C2×#4318C2318yes—
72C22×C11⋊C8C2318yes—
73C22⋊(C11⋊C8)C23132yes—
74C4⋊(C11⋊C8)C23132yes—
75#66867C2318yes—
76#66867C2318yes—
77C4×C11⋊C8C2318yes—
78C4×C11⋊C8C2318yes—
79#60123—111nomaximal, Sylow
80C24×C11C22×C412yes—
81C24×C11C22×C411yescharacteristic
82C11×#41—216no—
83C11×#41—216no—
84C2×Q8×C11—24no—
85C2×Q8×C11C22×C414yes—
86C2×D4×C11—28no—
87C2×D4×C11—24no—
88C2×D4×C11C22×C418yes—
89C2×D4×C11C22×C414yes—
90C22×C4×C11—28no—
91C22×C4×C11—44no—
92C22×C4×C11—48no—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C22×C414yes—
96C22×C4×C11C22×C418yes—
97C22×C4×C11C22×C414yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C22×C418yes—
101C22×C4×C11C22×C414yes—
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C412yes—
104C22×C4×C11#4118yes—
105C22×C4×C11C2414yes—
106C22×C4×C11C2412yes—
107C22×C4×C11C2411yescharacteristic
108C11×C4⋊C4C22×C4116yes—
109C11×C4⋊C4C22×C418yes—
110C11×C22⋊C4C22×C4116yes—
111C11×C22⋊C4C22×C418yes—
112C42×C11C22×C412yes—
113C42×C11C22×C412yes—
114C42×C11C22×C414yes—
115C42×C11C22×C418yes—
116C42×C11C22×C414yes—
117C42×C11C22×C418yes—
118C42×C11C22×C414yes—
119C42×C11C2412yes—
120C42×C11C2411yescharacteristic
121C42×C11C2414yes—
122C42×C11C2411yescharacteristic
123#4318—216no—
124#4318—216no—
125C2×C11⋊C8—216no—
126C2×C11⋊C8C24116yes—
127C2×C4×#41D1111yescharacteristic
128#2923—118no—
129#2922—118no—
130#2921—114no—
131#2920—114no—
132#2905—112no—
133#2879—112no—
134C2×C4×M16—112no—
135C23×C11—24no—
136C23×C11—42no—
137C23×C11—44no—
138C23×C11#11714yes—
139C23×C11C23×C414yes—
140C23×C11C23×C412yes—
141C23×C11C23×C411yescharacteristic
142Q8×C11—28no—
143D4×C11—216no—
144D4×C11—28no—
145C2×C4×C11—24no—
146C2×C4×C11—28no—
147C2×C4×C11—24no—
148C2×C4×C11—28no—
149C2×C4×C11—216no—
150C2×C4×C11—28no—
151C2×C4×C11—44no—
152C2×C4×C11—48no—
153C2×C4×C11—42no—
154C2×C4×C11—44no—
155C2×C4×C11#11714yes—
156C2×C4×C11#11718yes—
157C2×C4×C11C23×C412yes—
158C2×C4×C11C23×C414yes—
159C2×C4×C11C23×C414yes—
160C2×C4×C11C23×C418yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C23×C412yes—
163C2×C4×C11C23×C412yes—
164C2×C4×C11C2×#4118yes—
165C2×C4×C11C2×#4114yes—
166C2×C4×C11C2511yescharacteristic
167C11⋊C8—216no—
168C22×#41C2×D1111yescharacteristic
169C22×M16—114no—
170C4×#41Dic1118yes—
171C4×#41C2×D1114yes—
172C4×#41C2×D1114yes—
173C2×C4×Q8Dic1112yes—
174C2×C4×D4Dic1114yes—
175C2×C4×D4Dic1112yes—
176C2×#117C2×D1111yescharacteristic
177C2×#117C2×D1112yes—
178C22×C42C2×D1111yescharacteristic
179C22×C42C2×D1112yes—
180#433—1132no—
181#432—1116no—
182#431—1116no—
183#424—1116no—
184#423—118no—
185#408—1116no—
186#407—118no—
187C4×M16—114no—
188C4×M16—114no—
189C4×M16—114no—
190C4×M16—114no—
191C2×#97—114no—
192C2×C4×C8—114no—
193C22×C11—22no—
194C22×C11—24no—
195C22×C11—24no—
196C22×C11—28no—
197C22×C11—44no—
198C22×C11—48no—
199C22×C11C2×#11712yes—
200C22×C11C2×#11714yes—
201C22×C11C24×C411yescharacteristic
202C4×C11—24no—
203C4×C11—22no—
204C4×C11—24no—
205C4×C11—28no—
206C4×C11C2×#11712yes—
207C4×C11C2×#11714yes—
208C4×C11#56814yes—
209C4×C11C22×#4112yes—
210C2×#41—28no—
211C2×#41C2×Dic1114yes—
212C2×#41C22×D1114yes—
213C22×Q8C2×Dic1111yescharacteristic
214C22×D4C2×Dic1112yes—
215C22×D4C2×Dic1111yescharacteristic
216C23×C4C2×Dic1114yes—
217C23×C4C2×Dic1112yes—
218C23×C4C22×D1112yes—
219C23×C4C22×D1111yescharacteristic
220C2×M16—118no—
221C2×M16—118no—
222C2×M16—2216no—
223C22×C8—118no—
224C4×Q8C2×Dic1118yes—
225C4×Q8C2×Dic1118yes—
226C4×D4C2×Dic11116yes—
227C4×D4C2×Dic1118yes—
228C4×D4C2×Dic11116yes—
229C4×D4C2×Dic1118yes—
230#117C2×Dic1118yes—
231#117C2×Dic1114yes—
232#117C22×D1114yes—
233#117C22×D1118yes—
234C2×C4⋊C4C2×Dic1114yes—
235C2×C4⋊C4C2×Dic1112yes—
236C2×C22⋊C4C2×Dic1114yes—
237C2×C22⋊C4C2×Dic1112yes—
238C2×C42C2×Dic1114yes—
239C2×C42C2×Dic1112yes—
240C2×C42C2×Dic1118yes—
241C2×C42C2×Dic1114yes—
242C2×C42C22×D1111yescharacteristic
243C2×C42C22×D1112yes—
244C2×C42C22×D1112yes—
245C2×C42C22×D1114yes—
246C2×C42C22×D1112yes—
247C2×C42C22×D1114yes—
248C2×C42C22×D1111yescharacteristic
249C4⋊C8—1132no—
250C22⋊C8—1132no—
251#97—118no—
252#97—118no—
253C4×C8—118no—
254C4×C8—118no—
255C2×C11—22no—
256C2×C11—24no—
257C2×C11—44no—
258C2×C11C22×#11711yescharacteristic
259C2×C11C2×#56812yes—
260C24C22×Dic1112yes—
261C24C22×Dic1111yescharacteristic
262#41—216no—
263#41—216no—
264C2×Q8—24no—
265C2×Q8C22×Dic1114yes—
266C2×D4—28no—
267C2×D4—24no—
268C2×D4C22×Dic1118yes—
269C2×D4C22×Dic1114yes—
270C22×C4—28no—
271C22×C4—44no—
272C22×C4—48no—
273C22×C4#433918yes—
274C22×C4C22×Dic1112yes—
275C22×C4C22×Dic1118yes—
276C22×C4C22×Dic1114yes—
277C22×C4C22×Dic1112yes—
278C22×C4C22×Dic1114yes—
279C22×C4C22×Dic1112yes—
280C22×C4C22×Dic1114yes—
281C22×C4C22×Dic1118yes—
282C22×C4C22×Dic1114yes—
283C22×C4C22×Dic1111yescharacteristic
284C22×C4C22×Dic1112yes—
285C22×C4C23×D1114yes—
286C22×C4C23×D1111yescharacteristic
287C22×C4C23×D1112yes—
288M16—2216no—
289M16—2216no—
290C2×C8—1116no—
291C2×C8—2216no—
292C4⋊C4C22×Dic11116yes—
293C4⋊C4C22×Dic1118yes—
294C22⋊C4C22×Dic11116yes—
295C22⋊C4C22×Dic1118yes—
296C42C22×Dic1112yes—
297C42C22×Dic1112yes—
298C42C22×Dic1114yes—
299C42C22×Dic1118yes—
300C42C22×Dic1114yes—
301C42C22×Dic1118yes—
302C42C22×Dic1114yes—
303C42C23×D1112yes—
304C42C23×D1111yescharacteristic
305C42C23×D1114yes—
306C42C23×D1111yescharacteristic
307C11#6012311yescharacteristic, complemented, Sylow
308C23—24no—
309C23—42no—
310C23—44no—
311C23#6697914yes—
312C23C23×Dic1114yes—
313C23C23×Dic1112yes—
314C23C23×Dic1111yescharacteristic
315Q8—28no—
316D4—216no—
317D4—28no—
318C2×C4—24no—
319C2×C4—28no—
320C2×C4—24no—
321C2×C4—28no—
322C2×C4—216no—
323C2×C4—28no—
324C2×C4—44no—
325C2×C4—48no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4#6697914yes—
329C2×C4#6697918yes—
330C2×C4C2×#433918yes—
331C2×C4C2×#433914yes—
332C2×C4C23×Dic1112yes—
333C2×C4C23×Dic1114yes—
334C2×C4C23×Dic1114yes—
335C2×C4C23×Dic1118yes—
336C2×C4C23×Dic1111yescharacteristic
337C2×C4C23×Dic1112yes—
338C2×C4C23×Dic1112yes—
339C2×C4C24×D1111yescharacteristic
340C8—2216no—
341C22—22no—
342C22—24no—
343C22—24no—
344C22—28no—
345C22—44no—
346C22—48no—
347C22C2×#6697912yes—
348C22C2×#6697914yes—
349C22C24×Dic1111yescharacteristic
350C4—24no—
351C4—22no—
352C4—24no—
353C4—28no—
354C4C2×#6697912yes—
355C4C2×#6697914yes—
356C4#1062335014yes—
357C4C22×#433912yes—
358C2—22no—
359C2—24no—
360C2—44no—
361C2C22×#6697911yescharacteristic
362C2C2×#1062335012yes—
subgroupG/H
centerC42C23×D11
commutator, socleC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C4×C11×#41C2
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC2×C4×#41D11
hypocenterC11#60123
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13077267C2semidirect
2. #13077260C2semidirect
3. #13077254C2semidirect
4. #13077249C2semidirect
5. #13077180C2semidirect
7. C2×C4×#4318C2semidirect
23. #10622613C22semidirect
24. #10622612C22semidirect
25. #10622539C22semidirect
26. #10622538C22semidirect
30. C4×#4318C22semidirect
31. C4×#4318C22semidirect
32. C2×#66867C22semidirect
33. C2×C4×C11⋊C8C22semidirect
307. C11#60123semidirect

Maximal subgroups

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

subgroupindex
#130772672
#130772602
#130772542
#130772492
#130771802
#130770612
C2×C4×#43182
C2×C4×C11×#412
#6012311