Finite Group Databasebeta

← #15685282

Subgroups — #15685282

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#13093102C211yesmaximal, characteristic, complemented
2#13093073C211yesmaximal, characteristic
3#13092770C211yesmaximal, characteristic, complemented
4#13092760C211yesmaximal, characteristic, complemented
5#13092723C211yesmaximal, characteristic, complemented
6#13092659C211yesmaximal, characteristic, complemented
7#13092644C211yesmaximal, characteristic, complemented
8#13092638C211yesmaximal, characteristic, complemented
9#13092580C211yesmaximal, characteristic, complemented
10#13092575C211yesmaximal, characteristic, complemented
11#13092511C211yesmaximal, characteristic, complemented
12(C22⋊D23)⋊C8C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14C2×#10624992C211yesmaximal, characteristic, complemented
15C23×#480C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C23×#121C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20#10625110—21no—
21#10625107C2211yescharacteristic
22D4×Dic23—21no—
23C2×#67273C2211yescharacteristic
24#10625100—21no—
25C4×C22⋊D23C2211yescharacteristic
26#10625097—21no—
27#10625095C2211yescharacteristic
28C22×C23⋊C8C2211yescharacteristic
29C2×Dic92C2211yescharacteristic
30C2×Dic92C2211yescharacteristic
31C2×C8×D23C2211yescharacteristic
32#10625069—21no—
33#10625068C2211yescharacteristic
34#10625068C2211yescharacteristic
35#10625063C2211yescharacteristic
36#10625061C2211yescharacteristic
37#10625060—21no—
38#10625058C2211yescharacteristic
39#10625058C2211yescharacteristic
40#10625056—21no—
41#10625049—21no—
42C23×#107C2211yescharacteristic
43C23×#107C2211yescharacteristic
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46C23×C22⋊C8C2211yescharacteristic
47#10625014C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10624998C2211yescharacteristic
50#10624998C2211yescharacteristic
51Dic23⋊C8C2211yescharacteristic
52C8×Dic23C2211yescharacteristic
53#10624992C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624992C2211yescharacteristic
58#10624990C2211yescharacteristic
59C2×D4×C23—21no—
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C22×C4×C23C2311yescharacteristic
63C2×C22⋊D23—21no—
64C2×C22⋊D23D411yescharacteristic
65C22×Dic23—21no—
66C22×Dic23—21no—
67#67290—22no—
68#67290—41no—
69C2×C4×D23C2311yescharacteristic
70C2×Dic46—22no—
71C2×Dic46—21no—
72C2×Dic46—41no—
73C2×Dic46C2311yescharacteristic
74C2×Dic46C2311yescharacteristic
75C2×Dic46C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C2×C8×C23C2311yescharacteristic
78C4⋊C4×C23—21no—
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C4⋊C4×C23C2311yescharacteristic
82C22⋊C4×C23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85C22⋊Dic23—21no—
86C22⋊Dic23D411yescharacteristic
87#67273—41no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4D411yescharacteristic
92C4⋊Dic23—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23C2311yescharacteristic
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8—41no—
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108Dic92—22no—
109Dic92—41no—
110C8×D23—41no—
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C22×D23C2×D411yescharacteristic
114D4×C23—21no—
115D4×C23—21no—
116D4×C23—42no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—42no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—22no—
126C22⋊D23—42no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23—42no—
132C2×Dic23—42no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135C2×Dic23C2×D411yescharacteristic
136C4×D23—21no—
137C4×D23—21no—
138Dic46—21no—
139Dic46—21no—
140Dic46—21no—
141Dic46—21no—
142Dic46—21no—
143Dic46—42no—
144Dic46#4112yes—
145C8×C23—21no—
146C8×C23—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149#3300—231nomaximal, Sylow
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—41no—
153C22×C23—41no—
154C22×C23—41no—
155C22×C23#13512yes—
156C22×C23C22×D411yescharacteristic
157C2×D23—21no—
158C2×D23—21no—
159C2×D23—21no—
160C4×C23—21no—
161C4×C23—41no—
162C4×C23—41no—
163C4×C23—41no—
164C4×C23C2×#4111yescharacteristic
165C4×C23H(5,𝔽2)11yescharacteristic
166Dic23—22no—
167Dic23—21no—
168Dic23—21no—
169Dic23—21no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173#552—231no—
174#548—231no—
175#488—231no—
176#485—231no—
177#480D2311yescharacteristic, complemented
178#479—231no—
179#467—231no—
180#465—231no—
181#464—231no—
182#452—231no—
183#451—231no—
184C4×Q16—231no—
185C8×D4—231no—
186#416—231no—
187C2×#103—231no—
188C2×C23—22no—
189C2×C23—81no—
190C2×C23#54611yescharacteristic
191C2×C23C2×#13511yescharacteristic
192C2×C23#57811yescharacteristic
193D23—41no—
194C2×#41—231no—
195C22×Q8—231no—
196C2×Q16—231no—
197C2×Q16—231no—
198C2×SD16—231no—
199C22×C8—231no—
200C22×C8—231no—
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—461no—
212#121C2×D2311yescharacteristic
213C4×Q8—231no—
214C4×Q8—231no—
215C4×D4—231no—
216C4×D4—461no—
217#117—231no—
218#117—461no—
219C2×C4⋊C4C2×D2311yescharacteristic
220#107C2×D2311yescharacteristic
221#107C2×D2311yescharacteristic
222#106—231no—
223C4⋊C8—231no—
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#102C2×D2311yescharacteristic
233#102C2×D2311yescharacteristic
234C22⋊C8—231no—
235C22⋊C8C2×D2311yescharacteristic
236C4×C8—231no—
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—21no—
247C2×D4—231no—
248C2×D4—461no—
249C2×D4C22×D2311yescharacteristic
250C22×C4—21no—
251C22×C4—231no—
252C22×C4—461no—
253C22×C4—461no—
254C22×C4C22×D2311yescharacteristic
255Q16—462no—
256Q16—921no—
257SD16—921no—
258C2×C8—231no—
259C2×C8—231no—
260C2×C8—921no—
261C2×C8—921no—
262C2×C8C22×D2311yescharacteristic
263C2×C8C22×D2311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—461no—
268C4⋊C4—461no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4C22×D2311yescharacteristic
275C4⋊C4C22×D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—231no—
279C22⋊C4—231no—
280C22⋊C4—461no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4—461no—
285C22⋊C4—461no—
286C42—231no—
287C42—461no—
288C42—461no—
289C42—461no—
290C23—21no—
291C23—231no—
292C23D4×D2311yescharacteristic
293Q8—232no—
294Q8—461no—
295Q8—461no—
296Q8—461no—
297Q8—461no—
298Q8—461no—
299Q8—922no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—462no—
304D4—922no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—231no—
312C2×C4—231no—
313C2×C4—231no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—461no—
319C2×C4—461no—
320C2×C4—922no—
321C2×C4—922no—
322C2×C4D4×D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—21no—
325C8—21no—
326C8—461no—
327C8—461no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—461no—
334C22—461no—
335C22—461no—
336C22#1062508312yes—
337C22C2×D4×D2311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—461no—
343C4—461no—
344C4—461no—
345C4—462no—
346C4—921no—
347C4—921no—
348C4—921no—
349C4#41×D2311yescharacteristic
350C4#1062516011yescharacteristic
351C2—22no—
352C2—81no—
353C2—921no—
354C2#1309305911yescharacteristic
355C2C2×#1062508311yescharacteristic
356C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#480C2
socleC22×C23C22×D4
prime radical#13093073C2
hypercenter#480D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #13093102C2semidirect
3. #13092770C2semidirect
4. #13092760C2semidirect
5. #13092723C2semidirect
6. #13092659C2semidirect
7. #13092644C2semidirect
8. #13092638C2semidirect
9. #13092580C2semidirect
10. #13092575C2semidirect
11. #13092511C2semidirect
12. (C22⋊D23)⋊C8C2semidirect
13. #13092410C2semidirect
14. C2×#10624992C2semidirect
15. C23×#480C2semidirect
177. #480D23semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130931022
#130930732
#130927702
#130927602
#130927232
#130926592
#130926442
#130926382
#130925802
#130925752
#130925112
(C22⋊D23)⋊C82
#130924102
C2×#106249922
C23×#4802
#330023