Finite Group Databasebeta

← #15685284

Subgroups — #15685284

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#13092771C211yesmaximal, characteristic, complemented
3#13092755C211yesmaximal, characteristic, complemented
4#13092728C211yesmaximal, characteristic, complemented
5#13092724C211yesmaximal, characteristic, complemented
6#13092656C211yesmaximal, characteristic, complemented
7#13092644C211yesmaximal, characteristic, complemented
8#13092636C211yesmaximal, characteristic, complemented
9#13092579C211yesmaximal, characteristic, complemented
10#13092573C211yesmaximal, characteristic, complemented
11C4×#67275C211yesmaximal, characteristic, complemented
12D4×C23⋊C8C211yesmaximal, characteristic, complemented
13#13092413C211yesmaximal, characteristic, complemented
14C2×#10625017C211yesmaximal, characteristic, complemented
15C23×#548C211yesmaximal, characteristic
16C2×#41×C23C2211yescharacteristic
17C22×Q8×C23C2211yescharacteristic
18C23×#124—21no—
19C23×#124C2211yescharacteristic
20C23×C22⋊Q8—21no—
21C23×C22⋊Q8C2211yescharacteristic
22C23×#121—21no—
23C23×#121C2211yescharacteristic
24C4×Q8×C23C2211yescharacteristic
25C4×D4×C23—21no—
26C4×D4×C23C2211yescharacteristic
27C2×#67275C2211yescharacteristic
28C2×#67275C2211yescharacteristic
29#10625106—21no—
30C2×#67273C2211yescharacteristic
31#10625097C2211yescharacteristic
32C2×C4⋊Dic23C2211yescharacteristic
33#10625095C2211yescharacteristic
34#10625095C2211yescharacteristic
35C22×C23⋊C8C2211yescharacteristic
36C22×C23⋊C8C2211yescharacteristic
37#10625060—21no—
38#10625050—21no—
39#10625048—21no—
40#10625041C2211yescharacteristic
41C4×Dic46C2211yescharacteristic
42#10625017C2211yescharacteristic
43#10625017C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10625014C2211yescharacteristic
51C22⋊(C23⋊C8)C2211yescharacteristic
52C22⋊(C23⋊C8)C2211yescharacteristic
53#10624992C2211yescharacteristic
54#10624990C2211yescharacteristic
55#10624989C2211yescharacteristic
56#10624989C2211yescharacteristic
57C4⋊(C23⋊C8)C2211yescharacteristic
58C4×C23⋊C8C2211yescharacteristic
59#41×C23—22no—
60#41×C23—41no—
61C2×Q8×C23—21no—
62C2×Q8×C23—22no—
63C2×Q8×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×Q8×C23C2311yescharacteristic
66C2×D4×C23—21no—
67C2×D4×C23—21no—
68C2×D4×C23D411yescharacteristic
69C2×D4×C23C2311yescharacteristic
70C22×C4×C23—21no—
71C22×C4×C23—21no—
72C22×C4×C23C2311yescharacteristic
73C22×C4×C23C2311yescharacteristic
74C22×Dic23—21no—
75C2×Dic46C2311yescharacteristic
76C4⋊C4×C23—21no—
77C4⋊C4×C23—21no—
78C4⋊C4×C23D411yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C22⋊C4×C23—21no—
81C22⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C22⋊C4×C23—21no—
84C22⋊C4×C23D411yescharacteristic
85C22⋊C4×C23D411yescharacteristic
86C42×C23—21no—
87C42×C23C2311yescharacteristic
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90C22⋊Dic23—21no—
91#67275—22no—
92#67275—41no—
93#67273—41no—
94C4⋊Dic23—21no—
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4—21no—
103C4×Dic23—21no—
104C4×Dic23—21no—
105C2×C23⋊C8—41no—
106C2×C23⋊C8—41no—
107C2×C23⋊C8C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110C2×C23⋊C8C2311yescharacteristic
111C23×C23—21no—
112C23×C23C2×D411yescharacteristic
113C23×C23C2×D411yescharacteristic
114Q8×C23—21no—
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23—42no—
118Q8×C23#4112yes—
119D4×C23—22no—
120D4×C23—21no—
121D4×C23—21no—
122D4×C23—42no—
123D4×C23—42no—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—21no—
127C2×C4×C23—21no—
128C2×C4×C23—21no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—42no—
132C2×C4×C23—42no—
133C2×C4×C23C2×D411yescharacteristic
134C2×C4×C23C2×D411yescharacteristic
135C2×C4×C23C2×D411yescharacteristic
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2411yescharacteristic
138C2×Dic23—21no—
139C2×Dic23—21no—
140C2×Dic23—21no—
141C2×Dic23—21no—
142C2×Dic23—42no—
143Dic46—21no—
144Dic46—21no—
145C23⋊C8—21no—
146C23⋊C8—21no—
147C23⋊C8—21no—
148C23⋊C8—21no—
149#3300—231nomaximal, Sylow
150C22×C23—21no—
151C22×C23—21no—
152C22×C23—21no—
153C22×C23—21no—
154C22×C23—21no—
155C22×C23—41no—
156C22×C23—41no—
157C22×C23—41no—
158C22×C23#13512yes—
159C22×C23C22×D411yescharacteristic
160C4×C23—21no—
161C4×C23—21no—
162C4×C23—22no—
163C4×C23—21no—
164C4×C23—21no—
165C4×C23—41no—
166C4×C23—41no—
167C4×C23C2×#4111yescharacteristic
168C4×C23H(5,𝔽2)11yescharacteristic
169Dic23—41no—
170Dic23—41no—
171Dic23—41no—
172Dic23—41no—
173#552—231no—
174#548D2311yescharacteristic
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×D4—231no—
186#416—231no—
187C2×#103—231no—
188C2×C23—22no—
189C2×C23—41no—
190C2×C23—81no—
191C2×C23#54611yescharacteristic
192C2×C23C2×#13511yescharacteristic
193C2×C23#57811yescharacteristic
194C2×#41C2×D2311yescharacteristic
195C22×Q8C2×D2311yescharacteristic
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—21no—
205#124C2×D2311yescharacteristic
206#123—461no—
207C22⋊Q8—21no—
208C22⋊Q8—231no—
209C22⋊Q8—231no—
210C22⋊Q8C2×D2311yescharacteristic
211#121—21no—
212#121C2×D2311yescharacteristic
213C4×Q8—231no—
214C4×Q8C2×D2311yescharacteristic
215C4×D4—21no—
216C4×D4C2×D2311yescharacteristic
217#117—231no—
218#117—461no—
219C2×C4⋊C4—231no—
220#107—231no—
221#107—231no—
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#102—231no—
233#102—231no—
234C22⋊C8—231no—
235C22⋊C8—231no—
236C4×C8—231no—
237C23#330011yescharacteristic, complemented, Sylow
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—231no—
244C2×Q8C22×D2311yescharacteristic
245C2×Q8C22×D2311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22⋊D2311yescharacteristic
249C2×D4C22×D2311yescharacteristic
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—461no—
253C22×C4C22×D2311yescharacteristic
254C22×C4C22×D2311yescharacteristic
255Q16—462no—
256Q16—921no—
257SD16—921no—
258C2×C8—231no—
259C2×C8—231no—
260C2×C8—231no—
261C2×C8—231no—
262C2×C8—921no—
263C2×C8—921no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—231no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4—461no—
274C4⋊C4—461no—
275C4⋊C4C22⋊D2311yescharacteristic
276C4⋊C4C22×D2311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—461no—
282C22⋊C4—461no—
283C22⋊C4—461no—
284C22⋊C4C22⋊D2311yescharacteristic
285C22⋊C4C22⋊D2311yescharacteristic
286C42—21no—
287C42—461no—
288C42—461no—
289C42C22×D2311yescharacteristic
290C23—21no—
291C23C2×C22⋊D2311yescharacteristic
292C23C2×C22⋊D2311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—461no—
298Q8—461no—
299Q8#6729012yes—
300D4—22no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—461no—
317C2×C4—461no—
318C2×C4—922no—
319C2×C4C2×C22⋊D2311yescharacteristic
320C2×C4C2×C22⋊D2311yescharacteristic
321C2×C4C2×C22⋊D2311yescharacteristic
322C2×C4C2×C22⋊D2311yescharacteristic
323C2×C4C23×D2311yescharacteristic
324C8—461no—
325C8—461no—
326C8—461no—
327C8—461no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#1062512112yes—
337C22C22×C22⋊D2311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—921no—
346C4—921no—
347C4—921no—
348C4—921no—
349C4C2×#6729011yescharacteristic
350C4#1062515511yescharacteristic
351C2—22no—
352C2—41no—
353C2—81no—
354C2#1309306111yescharacteristic
355C2C2×#1062512111yescharacteristic
356C2#1309323211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
Fitting, prime radicalC23×#548C2
socleC22×C23C22×D4
hypercenter#548D23
hypocenterC23#3300
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #13093107C2semidirect
2. #13092771C2semidirect
3. #13092755C2semidirect
4. #13092728C2semidirect
5. #13092724C2semidirect
6. #13092656C2semidirect
7. #13092644C2semidirect
8. #13092636C2semidirect
9. #13092579C2semidirect
10. #13092573C2semidirect
11. C4×#67275C2semidirect
12. D4×C23⋊C8C2semidirect
13. #13092413C2semidirect
14. C2×#10625017C2semidirect
237. C23#3300semidirect

Maximal subgroups

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

subgroupindex
#130931072
#130927712
#130927552
#130927282
#130927242
#130926562
#130926442
#130926362
#130925792
#130925732
C4×#672752
D4×C23⋊C82
#130924132
C2×#106250172
C23×#5482
#330023