Finite Group Databasebeta

← #15685286

Subgroups — #15685286

Order 2944.

386 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#13093107C211yesmaximal, characteristic, complemented
2#13093076C211yesmaximal, characteristic
3#13092772C211yesmaximal, characteristic, complemented
4#13092759C211yesmaximal, characteristic, complemented
5#13092731C211yesmaximal, characteristic, complemented
6#13092725C211yesmaximal, characteristic, complemented
7#13092658C211yesmaximal, characteristic, complemented
8#13092646C211yesmaximal, characteristic, complemented
9#13092640C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092575C211yesmaximal, characteristic, complemented
12C4×Dic92C211yesmaximal, characteristic, complemented
13#13092414C211yesmaximal, characteristic, complemented
14C2×#10624998C211yesmaximal, characteristic, complemented
15C8×D4×C23C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C22×C8×C23C2211yescharacteristic
19C22×C8×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic
21#10625110—21no—
22#10625106—21no—
23#10625101C2211yescharacteristic
24#10625097C2211yescharacteristic
25C2×C4⋊Dic23C2211yescharacteristic
26#10625095C2211yescharacteristic
27#10625095C2211yescharacteristic
28#10625095C2211yescharacteristic
29C2×Dic92C2211yescharacteristic
30C2×Dic92C2211yescharacteristic
31C2×#67263C2211yescharacteristic
32#10625067—21no—
33#10625060—21no—
34#10625056—21no—
35(C22⋊D23)⋊C4—21no—
36#10625050—21no—
37#10625048—21no—
38#10625046C2211yescharacteristic
39#10625041C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41C4×Dic46C2211yescharacteristic
42C23×C4⋊C8C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44C23×C22⋊C8C2211yescharacteristic
45C4×C8×C23C2211yescharacteristic
46#10625003C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49#10625000C2211yescharacteristic
50#10625000C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624998C2211yescharacteristic
53#10624998C2211yescharacteristic
54#10624998C2211yescharacteristic
55#10624998C2211yescharacteristic
56#10624998C2211yescharacteristic
57#10624998C2211yescharacteristic
58#10624998C2211yescharacteristic
59C2×D4×C23D411yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C22×C4×C23C2311yescharacteristic
62C2×C22⋊D23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65C22×Dic23—21no—
66#67288—22no—
67#67288—41no—
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×Dic46—22no—
71C2×Dic46—21no—
72C2×Dic46—41no—
73C2×Dic46C2311yescharacteristic
74C2×Dic46C2311yescharacteristic
75C2×Dic46C2311yescharacteristic
76C2×C8×C23—41no—
77C2×C8×C23—41no—
78C2×C8×C23C2311yescharacteristic
79C2×C8×C23C2311yescharacteristic
80C2×C8×C23C2311yescharacteristic
81C2×C8×C23C2311yescharacteristic
82C4⋊C4×C23D411yescharacteristic
83C22⋊C4×C23D411yescharacteristic
84C22⋊C4×C23D411yescharacteristic
85C42×C23C2311yescharacteristic
86C22⋊Dic23—21no—
87C22⋊Dic23—21no—
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23C2311yescharacteristic
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103Dic23⋊C4—21no—
104Dic23⋊C4—21no—
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23—21no—
108Dic92—22no—
109Dic92—41no—
110#67263—41no—
111C23×C23C2×D411yescharacteristic
112C23×C23C2×D411yescharacteristic
113C22×D23—21no—
114D4×C23—22no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2411yescharacteristic
124C22⋊D23—42no—
125C22⋊D23—42no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—21no—
133C2×Dic23—42no—
134C2×Dic23—42no—
135D92—21no—
136D92—21no—
137C4×D23—42no—
138Dic46—21no—
139Dic46—21no—
140Dic46—21no—
141Dic46—21no—
142Dic46—21no—
143Dic46—42no—
144Dic46#4112yes—
145C8×C23—21no—
146C8×C23—21no—
147C8×C23—21no—
148C8×C23—21no—
149#3300—231nomaximal, Sylow
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—21no—
154C22×C23—21no—
155C22×C23#13512yes—
156C22×C23C22×D411yescharacteristic
157C2×D23—41no—
158C2×D23—41no—
159C2×D23—41no—
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—21no—
163C4×C23—21no—
164C4×C23C2×#4111yescharacteristic
165C4×C23H(5,𝔽2)11yescharacteristic
166Dic23—22no—
167Dic23—41no—
168Dic23—41no—
169Dic23—41no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173#552—231no—
174#548—231no—
175#488—231no—
176#485—231no—
177#480—231no—
178#479—231no—
179#467—231no—
180#465—231no—
181#464—231no—
182#452—231no—
183#451—231no—
184C4×Q16—231no—
185C8×D4D2311yescharacteristic, complemented
186#416—231no—
187C2×#103—231no—
188C2×C23—22no—
189C2×C23—41no—
190C2×C23#54611yescharacteristic
191C2×C23C2×#13511yescharacteristic
192C2×C23#57811yescharacteristic
193D23—81no—
194C2×#41—231no—
195C22×Q8—231no—
196C2×Q16—231no—
197C2×Q16—231no—
198C2×SD16—231no—
199C22×C8C2×D2311yescharacteristic
200C22×C8C2×D2311yescharacteristic
201#126—461no—
202#125—231no—
203#125—461no—
204#124—231no—
205#124—461no—
206#123—461no—
207C22⋊Q8—231no—
208C22⋊Q8—231no—
209C22⋊Q8—231no—
210C22⋊Q8—461no—
211#121—231no—
212#121—461no—
213C4×Q8—231no—
214C4×Q8—231no—
215C4×D4—461no—
216C4×D4C2×D2311yescharacteristic
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220#107—231no—
221#107—231no—
222#106—231no—
223C4⋊C8C2×D2311yescharacteristic
224#103—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103—231no—
229#103—231no—
230#103—231no—
231#102—231no—
232#102—231no—
233#102—231no—
234C22⋊C8C2×D2311yescharacteristic
235C22⋊C8C2×D2311yescharacteristic
236C4×C8C2×D2311yescharacteristic
237C23#330011yescharacteristic, complemented, Sylow
238#41—462no—
239#41—921no—
240C2×Q8—231no—
241C2×Q8—231no—
242C2×Q8—231no—
243C2×Q8—462no—
244C2×Q8—461no—
245C2×Q8—921no—
246C2×D4—231no—
247C2×D4—461no—
248C2×D4—461no—
249C2×D4D9211yescharacteristic
250C22×C4—461no—
251C22×C4—461no—
252C22×C4—461no—
253C22×C4C22×D2311yescharacteristic
254C22×C4C22×D2311yescharacteristic
255Q16—462no—
256Q16—921no—
257SD16—921no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C22×D2311yescharacteristic
261C2×C8C22×D2311yescharacteristic
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C4⋊C4—231no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—461no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4—461no—
276C4⋊C4D9211yescharacteristic
277C22⋊C4—461no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4D9211yescharacteristic
285C22⋊C4D9211yescharacteristic
286C42—461no—
287C42—461no—
288C42—461no—
289C42C22×D2311yescharacteristic
290C23—461no—
291C23C2×D9211yescharacteristic
292C23C2×D9211yescharacteristic
293Q8—232no—
294Q8—461no—
295Q8—461no—
296Q8—461no—
297Q8—461no—
298Q8—461no—
299Q8—922no—
300D4—22no—
301D4—461no—
302D4—461no—
303D4—922no—
304D4—922no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—461no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—922no—
317C2×C4—922no—
318C2×C4—922no—
319C2×C4C2×D9211yescharacteristic
320C2×C4C2×D9211yescharacteristic
321C2×C4C2×D9211yescharacteristic
322C2×C4C2×D9211yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—921no—
334C22—921no—
335C22—921no—
336C22#1062507512yes—
337C22C22×D9211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—462no—
343C4—921no—
344C4—921no—
345C4—921no—
346C4—921no—
347C4—921no—
348C4—921no—
349C4#1062515511yescharacteristic
350C4#41×D2311yescharacteristic
351C2—22no—
352C2—41no—
353C2—1841no—
354C2#1309306211yescharacteristic
355C2C2×#1062507511yescharacteristic
356C2#1309323411yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC8×D4×C23C2
socleC22×C23C22×D4
prime radical#13093076C2
hypercenterC8×D4D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #13093107C2semidirect
3. #13092772C2semidirect
4. #13092759C2semidirect
5. #13092731C2semidirect
6. #13092725C2semidirect
7. #13092658C2semidirect
8. #13092646C2semidirect
9. #13092640C2semidirect
10. #13092581C2semidirect
11. #13092575C2semidirect
12. C4×Dic92C2semidirect
13. #13092414C2semidirect
14. C2×#10624998C2semidirect
15. C8×D4×C23C2semidirect
185. C8×D4D23semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130931072
#130930762
#130927722
#130927592
#130927312
#130927252
#130926582
#130926462
#130926402
#130925812
#130925752
C4×Dic922
#130924142
C2×#106249982
C8×D4×C232
#330023