Finite Group Databasebeta

← #15675870

Subgroups — #15675870

Order 2944.

500 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625058C211yesmaximal, characteristic
2#13092321C211yesmaximal, characteristic
3#13092321C211yesmaximal, characteristic
4#13092314C211yesmaximal, characteristic
5#13092312C211yesmaximal, characteristic
6#13092303C211yesmaximal, characteristic
7#13092301C211yesmaximal, characteristic
8#13092299C211yesmaximal, characteristic
9C4⋊C4×Dic23C211yesmaximal, characteristic
10#13092268C211yesmaximal, characteristic
11#13092268C211yesmaximal, characteristic
12#13092262C211yesmaximal, characteristic
13#13092262C211yesmaximal, characteristic
14C42×Dic23C211yesmaximal, characteristic
15C23×#387C211yesmaximal, characteristic
16C22×Dic46C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18C2×C4⋊C4×C23C2211yescharacteristic
19C2×C42×C23C2211yescharacteristic
20C2×C4⋊Dic23C2211yescharacteristic
21C2×Dic23⋊C4C2211yescharacteristic
22C2×Dic23⋊C4C2211yescharacteristic
23C2×Dic23⋊C4C2211yescharacteristic
24C2×Dic23⋊C4C2211yescharacteristic
25C2×Dic23⋊C4C2211yescharacteristic
26C2×Dic23⋊C4C2211yescharacteristic
27C2×C4×Dic23C2211yescharacteristic
28C2×C4×Dic23C2211yescharacteristic
29C2×C4×Dic23C2211yescharacteristic
30C2×C4×Dic23C2211yescharacteristic
31C2×C4×Dic23C2211yescharacteristic
32C2×C4×Dic23C2211yescharacteristic
33C2×C4×Dic23C2211yescharacteristic
34C2×C4×Dic23C2211yescharacteristic
35C2×C4×Dic23C2211yescharacteristic
36C2×C4×Dic23C2211yescharacteristic
37#10625058C418yescomplemented
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
52C22×C4×C23C2311yescharacteristic
53C22×C4×C23C2311yescharacteristic
54C22×C4×C23C2311yescharacteristic
55C22×C4×C23C2311yescharacteristic
56C22×C4×C23C2311yescharacteristic
57C22×C4×C23C2311yescharacteristic
58C22×C4×C23C2311yescharacteristic
59C22×Dic23C2311yescharacteristic
60C22×Dic23C2311yescharacteristic
61C22×Dic23C2311yescharacteristic
62C22×Dic23C2311yescharacteristic
63C22×Dic23C2311yescharacteristic
64C22×Dic23C2311yescharacteristic
65C22×Dic23C2311yescharacteristic
66C22×Dic23C2311yescharacteristic
67C2×Dic46—22no—
68C2×Dic46—22no—
69C2×Dic46C2×C414yes—
70C4⋊C4×C23—22no—
71C4⋊C4×C23C2×C414yes—
72C42×C23—22no—
73C4⋊Dic23—22no—
74Dic23⋊C4—22no—
75Dic23⋊C4—22no—
76Dic23⋊C4—22no—
77Dic23⋊C4—22no—
78Dic23⋊C4C2×C414yes—
79Dic23⋊C4C2×C414yes—
80C4×Dic23—22no—
81C4×Dic23—22no—
82C4×Dic23—22no—
83C4×Dic23—22no—
84C4×Dic23—22no—
85C4×Dic23—22no—
86C4×Dic23C2×C414yes—
87C4×Dic23C2×C414yes—
88C4×Dic23C2×C414yes—
89C4×Dic23Q814yescomplemented
90C23×C23C2411yescharacteristic
91C2×C4×C23—21no—
92C2×C4×C23—21no—
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×C23C22×C412yes—
108C2×C4×C23C22×C412yes—
109C2×C4×C23C22×C412yes—
110C2×C4×C23C2×Q812yes—
111C2×C4×C23#4112yes—
112C2×Dic23—21no—
113C2×Dic23—21no—
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×Dic23C22×C412yes—
127C2×Dic23C22×C412yes—
128C2×Dic23C22×C412yes—
129C2×Dic23C22×C412yes—
130C2×Dic23C2×Q812yes—
131C2×Dic23C2×Q812yes—
132C2×Dic23#4112yes—
133C2×Dic23#4112yes—
134C2×Dic23#4112yes—
135C2×Dic23#4112yes—
136Dic46—28no—
137#2295—231nomaximal, Sylow
138C22×C23C23×C411yescharacteristic
139C22×C23C22×Q811yescharacteristic
140C22×C23C2×#4111yescharacteristic
141C22×C23C2×#4111yescharacteristic
142C22×C23C2×#4111yescharacteristic
143C22×C23C2×#4111yescharacteristic
144C22×C23C2×#4111yescharacteristic
145C4×C23—22no—
146C4×C23—22no—
147C4×C23—22no—
148C4×C23—22no—
149C4×C23—22no—
150C4×C23—41no—
151C4×C23—41no—
152Dic23—22no—
153Dic23—22no—
154Dic23—22no—
155Dic23—22no—
156Dic23—41no—
157Dic23—41no—
158Dic23#11714yes—
159Dic23C4×Q814yes—
160C2×C4×Q8—231no—
161#391—231no—
162#391—231no—
163#389—231no—
164#389—231no—
165#387—231no—
166#387—231no—
167#387—231no—
168#387D2311yescharacteristic
169C4×C4⋊C4—231no—
170C4×C4⋊C4—231no—
171C4×C4⋊C4—231no—
172#376—231no—
173#376—231no—
174C43—231no—
175C2×C23C2×#11711yescharacteristic
176C2×C23C2×C4×Q811yescharacteristic
177C2×C23C4×#4111yescharacteristic
178C2×C23#52911yescharacteristic
179C2×C23#52911yescharacteristic
180C2×C23#53311yescharacteristic
181C2×C23#53311yescharacteristic
182C22×Q8—231no—
183C4×Q8—238no—
184C2×C4⋊C4—231no—
185C2×C4⋊C4—231no—
186C2×C4⋊C4—231no—
187C2×C4⋊C4—231no—
188C2×C4⋊C4—231no—
189C2×C4⋊C4—231no—
190C2×C4⋊C4—231no—
191C2×C4⋊C4C2×D2311yescharacteristic
192C2×C4⋊C4C2×D2311yescharacteristic
193C2×C42—231no—
194C2×C42—231no—
195C2×C42—231no—
196C2×C42—231no—
197C2×C42—231no—
198C2×C42—231no—
199C2×C42—231no—
200C2×C42—231no—
201C2×C42—231no—
202C2×C42—231no—
203C2×C42C2×D2311yescharacteristic
204#95—231no—
205#95—231no—
206#95—231no—
207#95—231no—
208#95—231no—
209#95—231no—
210#95—231no—
211#95—231no—
212#95—231no—
213#95—231no—
214#95C2×D2311yescharacteristic
215#95C2×D2311yescharacteristic
216#95C2×D2311yescharacteristic
217#95C2×D2311yescharacteristic
218C23#229511yescharacteristic, complemented, Sylow
219C2×Q8—234no—
220C2×Q8—462no—
221C2×Q8—462no—
222C22×C4—231no—
223C22×C4—231no—
224C22×C4—231no—
225C22×C4—231no—
226C22×C4—231no—
227C22×C4—231no—
228C22×C4—231no—
229C22×C4—231no—
230C22×C4C22×D2311yescharacteristic
231C22×C4C22×D2311yescharacteristic
232C22×C4C22×D2311yescharacteristic
233C22×C4C22×D2311yescharacteristic
234C22×C4C22×D2311yescharacteristic
235C22×C4C22×D2311yescharacteristic
236C22×C4C22×D2311yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—234no—
239C4⋊C4—234no—
240C4⋊C4—462no—
241C4⋊C4—462no—
242C4⋊C4—462no—
243C4⋊C4—462no—
244C4⋊C4—462no—
245C4⋊C4C4×D2314yes—
246C42—22no—
247C42—234no—
248C42—234no—
249C42—234no—
250C42—234no—
251C42—462no—
252C42—462no—
253C42—462no—
254C42—462no—
255C42—462no—
256C42—462no—
257C23C23×D2311yescharacteristic
258Q8—468no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
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—232no—
276C2×C4—232no—
277C2×C4—232no—
278C2×C4—232no—
279C2×C4—232no—
280C2×C4—232no—
281C2×C4—232no—
282C2×C4—232no—
283C2×C4—232no—
284C2×C4—232no—
285C2×C4—461no—
286C2×C4—461no—
287C2×C4—461no—
288C2×C4—461no—
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×C4C2×C4×D2312yes—
300C2×C4C2×C4×D2312yes—
301C2×C4C2×C4×D2312yes—
302C2×C4#6729012yes—
303C2×C4Q8×D2312yes—
304C22C22×C4×D2311yescharacteristic
305C22C2×#6729011yescharacteristic
306C22C2×Q8×D2311yescharacteristic
307C22#41×D2311yescharacteristic
308C22#41×D2311yescharacteristic
309C22#41×D2311yescharacteristic
310C22#41×D2311yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—234no—
319C4—234no—
320C4—462no—
321C4—462no—
322C4—462no—
323C4—462no—
324C4—921no—
325C4—921no—
326C2#117×D2311yescharacteristic
327C2C4×Q8×D2311yescharacteristic
328C2C4×#6729011yescharacteristic
329C2#1309294411yescharacteristic
330C2#1309295011yescharacteristic
331C2#1309296911yescharacteristic
332C2#1309297311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#387C2
socle, prime radical, cosocleC23×C23C24
hypercenter#387D23
hypocenterC23#2295
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
37. #10625058C4semidirect
89. C4×Dic23Q8semidirect
218. C23#2295semidirect

Maximal subgroups

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

subgroupindex
C2×#106250582
#130923212
#130923142
#130923122
#130923032
#130923012
#130922992
C4⋊C4×Dic232
#130922682
#130922622
C42×Dic232
C23×#3872
#229523