Finite Group Databasebeta

← #15682237

Subgroups — #15682237

Order 2944.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625086C211yesmaximal, characteristic
2#13092896C211yesmaximal, characteristic
3#13092893C211yesmaximal, characteristic, complemented
4#13092525C211yesmaximal, characteristic, complemented
5#13092521C211yesmaximal, characteristic, complemented
6#13092514C211yesmaximal, characteristic, complemented
7#13092511C211yesmaximal, characteristic, complemented
8C4×#67275C211yesmaximal, characteristic, complemented
9SD16×Dic23C211yesmaximal, characteristic, complemented
10C4×#67273C211yesmaximal, characteristic, complemented
11#13092458C211yesmaximal, characteristic, complemented
12#13092410C211yesmaximal, characteristic
13#103×D23C211yesmaximal, characteristic, complemented
14#13092374C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×SD16×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22C2×#67275C2211yescharacteristic
23D4×Dic23C2211yescharacteristic
24C2×#67273C2211yescharacteristic
25C4×C22⋊D23—21no—
26C2×Dic23⋊C4—21no—
27#10625086C418yescomplemented
28C2×Dic92C2211yescharacteristic
29C2×#67262C2211yescharacteristic
30C2×C8×D23C2211yescharacteristic
31#10625063—21no—
32#10625063C2211yescharacteristic
33C4⋊C4×D23C2211yescharacteristic
34#10625058—21no—
35#10625058C2211yescharacteristic
36#10625058C2211yescharacteristic
37(C22⋊D23)⋊C4—21no—
38#10625048—21no—
39#10625043—21no—
40#10625043C2211yescharacteristic
41C4×Dic46—21no—
42C4×Dic46C2211yescharacteristic
43C4×Dic46C2211yescharacteristic
44C23×#107C2211yescharacteristic
45C23×#103C2211yescharacteristic
46C23×#102C2211yescharacteristic
47C23×#97C2211yescharacteristic
48#10625017C2211yescharacteristic
49#10625014C2211yescharacteristic
50#10624999C2211yescharacteristic
51#10624998C2211yescharacteristic
52#10624998C2211yescharacteristic
53#10624997C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624992C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59C4×C23⋊C8C2211yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65C22×Dic23—21no—
66Q8×D23—22no—
67Q8×D23C2×C414yescomplemented
68#67290—22no—
69#67290C2×C414yes—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23C2311yescharacteristic
73C2×Dic46—21no—
74C2×Dic46C2311yescharacteristic
75C2×Dic46C2311yescharacteristic
76SD16×C23C2×C414yescomplemented
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23—21no—
80C4⋊C4×C23C2311yescharacteristic
81C4⋊C4×C23C2311yescharacteristic
82C22⋊C4×C23—21no—
83C42×C23—21no—
84C42×C23C2311yescharacteristic
85C22⋊Dic23—21no—
86#67275C2×C414yescomplemented
87#67273C2×C414yescomplemented
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4D411yescharacteristic
90(C2×D23)⋊C4D411yescharacteristic
91C4⋊Dic23—21no—
92C4⋊Dic23C2311yescharacteristic
93C4⋊Dic23C2311yescharacteristic
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4D411yescharacteristic
100Dic23⋊C4D411yescharacteristic
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110Dic92C2×C414yescomplemented
111#67262C2×C414yescomplemented
112C8×D23—22no—
113C23×C23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23C22×C412yes—
117D4×C23—21no—
118D4×C23C22×C412yes—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—81no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—24no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—24no—
130C2×Dic23—21no—
131C2×Dic23—21no—
132C2×Dic23—81no—
133C2×Dic23C2×D411yescharacteristic
134C2×Dic23C2×D411yescharacteristic
135C2×Dic23C2×D411yescharacteristic
136C4×D23—24no—
137C4×D23—81no—
138C4×D23C22×C412yes—
139C4×D23#4112yes—
140Dic46—21no—
141Dic46—21no—
142Dic46—24no—
143Dic46C22×C412yes—
144Dic46C22×C412yes—
145C8×C23—21no—
146C8×C23C22×C412yes—
147C23⋊C8—21no—
148C23⋊C8C22×C412yes—
149#2947—231nomaximal, Sylow
150C22×C23—22no—
151C22×C23—41no—
152C22×C23—41no—
153C22×C23C22×D411yescharacteristic
154C2×D23—21no—
155C2×D23—21no—
156C2×D23C4×D412yes—
157C4×C23—22no—
158C4×C23—21no—
159C4×C23—21no—
160C4×C23—41no—
161C4×C23—41no—
162C4×C23C23×C411yescharacteristic
163C4×C23C2×#4111yescharacteristic
164Dic23—22no—
165Dic23—22no—
166Dic23—21no—
167Dic23—21no—
168Dic23—41no—
169Dic23—41no—
170Dic23C4×D412yes—
171C2×#137—231no—
172#520—231no—
173#519—231no—
174#441—231no—
175#441—231no—
176#440—231no—
177#440D2311yescharacteristic, complemented
178C4×Q16—231no—
179C4×Q16—231no—
180C4×SD16—231no—
181C4×SD16—231no—
182#428—231no—
183#416—231no—
184C2×#103—231no—
185#405—231no—
186C2×C23—42no—
187C2×C23C2×C4×D411yescharacteristic
188C2×C23#57711yescharacteristic
189C2×C23#57811yescharacteristic
190D23—22no—
191C2×#41—231no—
192C22×Q8—231no—
193#137—238no—
194C2×Q16—231no—
195C2×Q16—231no—
196C2×SD16—231no—
197C2×SD16C2×D2311yescharacteristic
198C2×M16—231no—
199C22×C8—231no—
200C4×Q8—231no—
201C4×Q8—231no—
202C4×Q8—231no—
203C4×Q8—231no—
204C4×Q8—231no—
205C4×Q8—461no—
206C4×Q8—461no—
207C4×Q8C2×D2311yescharacteristic
208C4×D4—231no—
209C4×D4—461no—
210C4×D4—461no—
211C4×D4C2×D2311yescharacteristic
212#117—231no—
213#117—231no—
214#117—461no—
215#117—461no—
216#117—461no—
217C2×C4⋊C4—231no—
218C2×C4⋊C4—461no—
219#107—231no—
220#107C2×D2311yescharacteristic
221#106—231no—
222#106—231no—
223#103—231no—
224#103—231no—
225#103—231no—
226#103—231no—
227#103—231no—
228#103C2×D2311yescharacteristic
229#102—231no—
230#102C2×D2311yescharacteristic
231#97—231no—
232#97C2×D2311yescharacteristic
233C4×C8—231no—
234C4×C8—231no—
235C23#294711yescharacteristic, complemented, Sylow
236#41—234no—
237#41—462no—
238C2×Q8—234no—
239C2×Q8—231no—
240C2×Q8—231no—
241C2×Q8—461no—
242C2×Q8—462no—
243C2×Q8C22×D2311yescharacteristic
244C2×D4—461no—
245C2×D4C22×D2311yescharacteristic
246C22×C4—21no—
247C22×C4—231no—
248C22×C4—461no—
249C22×C4—461no—
250C22×C4—461no—
251C22×C4—461no—
252Q16—234no—
253Q16—234no—
254SD16—234no—
255SD16C4×D2314yescomplemented
256M16—234no—
257C2×C8—231no—
258C2×C8—231no—
259C2×C8—462no—
260C2×C8C22×D2311yescharacteristic
261C2×C8C22×D2311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—231no—
264C4⋊C4—231no—
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⋊C4C22×D2311yescharacteristic
274C4⋊C4C22×D2311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—231no—
277C22⋊C4—231no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C42—21no—
281C42—231no—
282C42—461no—
283C42—461no—
284C42—461no—
285C42—461no—
286C42—461no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C23—21no—
290C23—231no—
291Q8—21no—
292Q8—232no—
293Q8—232no—
294Q8—464no—
295Q8—461no—
296Q8—461no—
297Q8C2×C4×D2312yes—
298D4—21no—
299D4—464no—
300D4C2×C4×D2312yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—231no—
306C2×C4—232no—
307C2×C4—232no—
308C2×C4—231no—
309C2×C4—231no—
310C2×C4—464no—
311C2×C4—464no—
312C2×C4—461no—
313C2×C4—461no—
314C2×C4—461no—
315C2×C4—461no—
316C2×C4—1841no—
317C2×C4—1841no—
318C2×C4D4×D2311yescharacteristic
319C2×C4D4×D2311yescharacteristic
320C2×C4C23×D2311yescharacteristic
321C8—21no—
322C8—232no—
323C8—461no—
324C8C2×C4×D2312yes—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—232no—
329C22—461no—
330C22—461no—
331C22C2×D4×D2311yescharacteristic
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—232no—
338C4—462no—
339C4—462no—
340C4—461no—
341C4—461no—
342C4—921no—
343C4—921no—
344C4C22×C4×D2311yescharacteristic
345C4#41×D2311yescharacteristic
346C2—42no—
347C2—462no—
348C2C4×D4×D2311yescharacteristic
349C2#1309322711yescharacteristic
350C2#1309323311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
prime radicalC2×#67290C22
cosocleC2×C4×C23C24
hypercenter#440D23
hypocenterC23#2947
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #13092893C2semidirect
4. #13092525C2semidirect
5. #13092521C2semidirect
6. #13092514C2semidirect
7. #13092511C2semidirect
8. C4×#67275C2semidirect
9. SD16×Dic23C2semidirect
10. C4×#67273C2semidirect
11. #13092458C2semidirect
13. #103×D23C2semidirect
14. #13092374C2semidirect
15. C23×#440C2semidirect
27. #10625086C4semidirect
67. Q8×D23C2×C4semidirect
76. SD16×C23C2×C4semidirect
86. #67275C2×C4semidirect
87. #67273C2×C4semidirect
110. Dic92C2×C4semidirect
111. #67262C2×C4semidirect
177. #440D23semidirect
235. C23#2947semidirect
255. SD16C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250862
#130928962
#130928932
#130925252
#130925212
#130925142
#130925112
C4×#672752
SD16×Dic232
C4×#672732
#130924582
#130924102
#103×D232
#130923742
C23×#4402
#294723