Finite Group Databasebeta

← #15676112

Subgroups — #15676112

Order 2944.

516 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625059C211yesmaximal, characteristic
2C2×C4×Dic46C211yesmaximal, characteristic
3C2×#10625058C211yesmaximal, characteristic
4#13092321C211yesmaximal, characteristic
5#13092321C211yesmaximal, characteristic
6#13092304C211yesmaximal, characteristic
7#13092303C211yesmaximal, characteristic
8#13092302C211yesmaximal, characteristic
9#13092301C211yesmaximal, characteristic
10#13092300C211yesmaximal, characteristic
11#13092299C211yesmaximal, characteristic
12#13092298C211yesmaximal, characteristic
13#13092281C211yesmaximal, characteristic
14#13092262C211yesmaximal, characteristic
15C23×#387C211yesmaximal, characteristic
16C22×Dic46C2211yescharacteristic
17C22×Dic46C2211yescharacteristic
18C2×C4⋊C4×C23C2211yescharacteristic
19C2×C4⋊C4×C23C2211yescharacteristic
20C2×C42×C23C2211yescharacteristic
21C2×C4⋊Dic23C2211yescharacteristic
22C2×C4⋊Dic23C2211yescharacteristic
23C2×Dic23⋊C4C2211yescharacteristic
24C2×Dic23⋊C4C2211yescharacteristic
25C2×Dic23⋊C4C2211yescharacteristic
26C2×Dic23⋊C4C2211yescharacteristic
27C2×Dic23⋊C4C2211yescharacteristic
28C2×Dic23⋊C4C2211yescharacteristic
29C2×C4×Dic23C2211yescharacteristic
30C2×C4×Dic23C2211yescharacteristic
31C2×C4×Dic23C2211yescharacteristic
32C2×C4×Dic23C2211yescharacteristic
33C2×C4×Dic23C2211yescharacteristic
34C2×C4×Dic23C2211yescharacteristic
35#10625059C418yescomplemented
36#10625058—24no—
37C4×Dic46—24no—
38C23×#95C2211yescharacteristic
39C23×#95C2211yescharacteristic
40C23×#95C2211yescharacteristic
41C23×#95C2211yescharacteristic
42C23⋊#95C2211yescharacteristic
43C23⋊#95C2211yescharacteristic
44C23⋊#95C2211yescharacteristic
45C23⋊#95C2211yescharacteristic
46C23⋊#95C2211yescharacteristic
47C23⋊#95C2211yescharacteristic
48C23⋊#95C2211yescharacteristic
49C23⋊#95C2211yescharacteristic
50C23⋊#95C2211yescharacteristic
51C23⋊#95C2211yescharacteristic
52C23⋊#95C2211yescharacteristic
53C23⋊#95C2211yescharacteristic
54C22×C4×C23C2311yescharacteristic
55C22×C4×C23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×C4×C23C2311yescharacteristic
60C22×C4×C23C2311yescharacteristic
61C22×Dic23C2311yescharacteristic
62C22×Dic23C2311yescharacteristic
63C22×Dic23C2311yescharacteristic
64C22×Dic23C2311yescharacteristic
65C22×Dic23C2311yescharacteristic
66C22×Dic23C2311yescharacteristic
67C22×Dic23C2311yescharacteristic
68C22×Dic23C2311yescharacteristic
69C2×Dic46—22no—
70C2×Dic46—22no—
71C2×Dic46—22no—
72C2×Dic46—22no—
73C2×Dic46C2×C414yes—
74C2×Dic46C2×C414yes—
75C4⋊C4×C23—22no—
76C4⋊C4×C23C2×C414yes—
77C42×C23—22no—
78C4⋊Dic23—22no—
79C4⋊Dic23C2×C414yes—
80Dic23⋊C4—22no—
81Dic23⋊C4—22no—
82Dic23⋊C4—22no—
83Dic23⋊C4—22no—
84Dic23⋊C4C2×C414yes—
85Dic23⋊C4C2×C414yes—
86C4×Dic23—22no—
87C4×Dic23—22no—
88C4×Dic23—22no—
89C4×Dic23—22no—
90C4×Dic23C2×C414yes—
91C4×Dic23D414yes—
92C23×C23C2411yescharacteristic
93C2×C4×C23—21no—
94C2×C4×C23—21no—
95C2×C4×C23—21no—
96C2×C4×C23—21no—
97C2×C4×C23—21no—
98C2×C4×C23—21no—
99C2×C4×C23—21no—
100C2×C4×C23—21no—
101C2×C4×C23—21no—
102C2×C4×C23—21no—
103C2×C4×C23—21no—
104C2×C4×C23—21no—
105C2×C4×C23—21no—
106C2×C4×C23—21no—
107C2×C4×C23—21no—
108C2×C4×C23—21no—
109C2×C4×C23—21no—
110C2×C4×C23C22×C412yes—
111C2×C4×C23C22×C412yes—
112C2×C4×C23C22×C412yes—
113C2×C4×C23C2×D412yes—
114C2×Dic23—21no—
115C2×Dic23—21no—
116C2×Dic23—21no—
117C2×Dic23—21no—
118C2×Dic23—21no—
119C2×Dic23—21no—
120C2×Dic23—21no—
121C2×Dic23—21no—
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23—21no—
131C2×Dic23C22×C412yes—
132C2×Dic23C22×C412yes—
133C2×Dic23C22×C412yes—
134C2×Dic23C22×C412yes—
135C2×Dic23C2×D412yes—
136C2×Dic23C2×D412yes—
137C2×Dic23#4112yes—
138Dic46—28no—
139Dic46—28no—
140#2327—231nomaximal, Sylow
141C22×C23C23×C411yescharacteristic
142C22×C23C22×D411yescharacteristic
143C22×C23C2×#4111yescharacteristic
144C22×C232−1+411yescharacteristic
145C22×C232−1+411yescharacteristic
146C22×C232−1+411yescharacteristic
147C22×C232−1+411yescharacteristic
148C4×C23—22no—
149C4×C23—22no—
150C4×C23—22no—
151C4×C23—22no—
152C4×C23—41no—
153C4×C23—41no—
154C4×C23—41no—
155Dic23—22no—
156Dic23—22no—
157Dic23—22no—
158Dic23—22no—
159Dic23—41no—
160Dic23—41no—
161Dic23—41no—
162Dic23C4×D414yes—
163C2×C4⋊Q8—231no—
164C2×C4×Q8—231no—
165C2×C4×Q8—231no—
166#391—231no—
167#391—231no—
168#387—231no—
169#387—231no—
170#387—231no—
171#387—231no—
172#387—231no—
173#387—231no—
174#387—231no—
175#387D2311yescharacteristic
176#382—231no—
177#376—231no—
178C2×C23C2×C4×D411yescharacteristic
179C2×C23#51911yescharacteristic
180C2×C23#51911yescharacteristic
181C2×C23#53611yescharacteristic
182C2×C23#53611yescharacteristic
183C2×C23#54111yescharacteristic
184C2×C23#54111yescharacteristic
185C22×Q8—231no—
186C22×Q8—231no—
187C4⋊Q8—238no—
188C4×Q8—464no—
189C4×Q8—464no—
190C2×C4⋊C4—231no—
191C2×C4⋊C4—231no—
192C2×C4⋊C4—231no—
193C2×C4⋊C4—231no—
194C2×C4⋊C4—231no—
195C2×C4⋊C4—231no—
196C2×C4⋊C4—231no—
197C2×C4⋊C4—231no—
198C2×C4⋊C4C2×D2311yescharacteristic
199C2×C4⋊C4C2×D2311yescharacteristic
200C2×C42—231no—
201C2×C42—231no—
202C2×C42—231no—
203C2×C42—231no—
204C2×C42—231no—
205C2×C42—231no—
206C2×C42C2×D2311yescharacteristic
207#95—231no—
208#95—231no—
209#95—231no—
210#95—231no—
211#95—231no—
212#95—231no—
213#95—231no—
214#95—231no—
215#95—231no—
216#95—231no—
217#95—231no—
218#95—231no—
219#95C2×D2311yescharacteristic
220#95C2×D2311yescharacteristic
221#95C2×D2311yescharacteristic
222#95C2×D2311yescharacteristic
223C23#232711yescharacteristic, complemented, Sylow
224C2×Q8—234no—
225C2×Q8—234no—
226C2×Q8—462no—
227C2×Q8—462no—
228C2×Q8—462no—
229C2×Q8—462no—
230C22×C4—231no—
231C22×C4—231no—
232C22×C4—231no—
233C22×C4—231no—
234C22×C4—231no—
235C22×C4—231no—
236C22×C4—231no—
237C22×C4—231no—
238C22×C4C22×D2311yescharacteristic
239C22×C4C22×D2311yescharacteristic
240C22×C4C22×D2311yescharacteristic
241C22×C4C22×D2311yescharacteristic
242C22×C4C22×D2311yescharacteristic
243C22×C4C22×D2311yescharacteristic
244C22×C4C22×D2311yescharacteristic
245C4⋊C4—22no—
246C4⋊C4—234no—
247C4⋊C4—234no—
248C4⋊C4—234no—
249C4⋊C4—462no—
250C4⋊C4—462no—
251C4⋊C4—462no—
252C4⋊C4—462no—
253C4⋊C4—462no—
254C4⋊C4C4×D2314yes—
255C42—22no—
256C42—234no—
257C42—234no—
258C42—462no—
259C42—462no—
260C42—462no—
261C42—462no—
262C23C23×D2311yescharacteristic
263Q8—468no—
264Q8—468no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—232no—
283C2×C4—232no—
284C2×C4—232no—
285C2×C4—232no—
286C2×C4—232no—
287C2×C4—232no—
288C2×C4—232no—
289C2×C4—461no—
290C2×C4—461no—
291C2×C4—461no—
292C2×C4—461no—
293C2×C4—461no—
294C2×C4—461no—
295C2×C4—461no—
296C2×C4—461no—
297C2×C4—461no—
298C2×C4—461no—
299C2×C4—461no—
300C2×C4—461no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4—461no—
305C2×C4—461no—
306C2×C4C2×C4×D2312yes—
307C2×C4C2×C4×D2312yes—
308C2×C4C2×C4×D2312yes—
309C2×C4D4×D2312yes—
310C22C22×C4×D2311yescharacteristic
311C22C2×D4×D2311yescharacteristic
312C22#1062515811yescharacteristic
313C22#41×D2311yescharacteristic
314C22#1062516111yescharacteristic
315C22#1062516111yescharacteristic
316C22#1062516111yescharacteristic
317C4—22no—
318C4—22no—
319C4—22no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—234no—
325C4—462no—
326C4—462no—
327C4—462no—
328C4—462no—
329C4—921no—
330C4—921no—
331C4—921no—
332C2C4×D4×D2311yescharacteristic
333C2#1309289311yescharacteristic
334C2#1309289411yescharacteristic
335C2#1309298911yescharacteristic
336C2#1309299011yescharacteristic
337C2#1309302411yescharacteristic
338C2#1309302611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#387C2
socle, prime radical, cosocleC23×C23C24
hypercenter#387D23
hypocenterC23#2327
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
35. #10625059C4semidirect
223. C23#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#106250592
C2×C4×Dic462
C2×#106250582
#130923212
#130923042
#130923032
#130923022
#130923012
#130923002
#130922992
#130922982
#130922812
#130922622
C23×#3872
#232723