Finite Group Databasebeta

← #15682235

Subgroups — #15682235

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×#10625089C211yesmaximal, characteristic
2#13092899C211yesmaximal, characteristic
3#13092893C211yesmaximal, characteristic, complemented
4#13092524C211yesmaximal, characteristic, complemented
5#13092522C211yesmaximal, characteristic, complemented
6#13092516C211yesmaximal, characteristic, complemented
7#13092515C211yesmaximal, characteristic, complemented
8#13092509C211yesmaximal, characteristic, complemented
9C4×#67263C211yesmaximal, characteristic, complemented
10#13092502C211yesmaximal, characteristic, complemented
11#13092458C211yesmaximal, characteristic, complemented
12#13092412C211yesmaximal, characteristic
13#103×D23C211yesmaximal, characteristic, complemented
14#13092371C211yesmaximal, characteristic, complemented
15C4×Q16×C23C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C2×Q16×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20C4×Q8×C23C2211yescharacteristic
21Q8×Dic23C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic
23C2×#67275C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25#10625089C418yescomplemented
26C2×#67263C2211yescharacteristic
27C2×#67262C2211yescharacteristic
28C2×C8×D23C2211yescharacteristic
29#10625064—21no—
30#10625064C2211yescharacteristic
31#10625063—21no—
32#10625063C2211yescharacteristic
33C4⋊C4×D23—21no—
34C4⋊C4×D23C2211yescharacteristic
35#10625058—21no—
36#10625058C2211yescharacteristic
37C4×D92—21no—
38C4×D92C2211yescharacteristic
39#10625043—21no—
40#10625043—21no—
41#10625043C2211yescharacteristic
42C4×Dic46—21no—
43C4×Dic46C2211yescharacteristic
44C23×#107C2211yescharacteristic
45C23×#103C2211yescharacteristic
46C23×#103C2211yescharacteristic
47C4×C8×C23C2211yescharacteristic
48#10625017C2211yescharacteristic
49#10625017C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10624999C2211yescharacteristic
52#10624998C2211yescharacteristic
53#10624997C2211yescharacteristic
54C8×Dic23C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59#10624985C2211yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61C2×Q8×C23C2311yescharacteristic
62#67292—22no—
63#67292C2×C414yes—
64Q8×D23—22no—
65Q8×D23C2×C414yescomplemented
66C2×D92—21no—
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23—21no—
73C2×C4×D23C2311yescharacteristic
74C2×Dic46—21no—
75C2×Dic46C2311yescharacteristic
76Q16×C23C2×C414yescomplemented
77C2×C8×C23C2311yescharacteristic
78C2×C8×C23C2311yescharacteristic
79C4⋊C4×C23—21no—
80C4⋊C4×C23—21no—
81C4⋊C4×C23C2311yescharacteristic
82C4⋊C4×C23C2311yescharacteristic
83C42×C23—21no—
84C42×C23—21no—
85C42×C23C2311yescharacteristic
86#67275C2×C414yescomplemented
87#67274C2×C414yescomplemented
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4D411yescharacteristic
92(C2×D23)⋊C4D411yescharacteristic
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110#67263C2×C414yescomplemented
111#67262C2×C414yescomplemented
112C8×D23—22no—
113C22×D23—21no—
114C22×D23C2×D411yescharacteristic
115Q8×C23—21no—
116Q8×C23—21no—
117Q8×C23C22×C412yes—
118Q8×C23C22×C412yes—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132D92—24no—
133D92—21no—
134D92C22×C412yes—
135C4×D23—24no—
136C4×D23—24no—
137C4×D23—81no—
138C4×D23—81no—
139C4×D23—81no—
140C4×D23C22×C412yes—
141C4×D23#4112yes—
142Dic46—21no—
143Dic46—24no—
144Dic46C22×C412yes—
145C8×C23—21no—
146C8×C23C22×C412yes—
147C23⋊C8—21no—
148C23⋊C8C22×C412yes—
149#2947—231nomaximal, Sylow
150C22×C23C22×D411yescharacteristic
151C2×D23—21no—
152C2×D23—21no—
153C2×D23—22no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23C4×D412yes—
157C4×C23—22no—
158C4×C23—22no—
159C4×C23—21no—
160C4×C23—21no—
161C4×C23—41no—
162C4×C23—41no—
163C4×C23C23×C411yescharacteristic
164C4×C23C2×#4111yescharacteristic
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#440—231no—
178C4×Q16—231no—
179C4×Q16D2311yescharacteristic, complemented
180C4×SD16—231no—
181C4×SD16—231no—
182#428—231no—
183#416—231no—
184C2×#103—231no—
185#405—231no—
186C2×C23C2×C4×D411yescharacteristic
187C2×C23#57711yescharacteristic
188C2×C23#57811yescharacteristic
189D23—22no—
190D23—42no—
191C2×#41—231no—
192C22×Q8—231no—
193#137—238no—
194C2×Q16—231no—
195C2×Q16C2×D2311yescharacteristic
196C2×SD16—231no—
197C2×SD16—231no—
198C2×M16—231no—
199C22×C8—231no—
200C4×Q8—231no—
201C4×Q8—231no—
202C4×Q8—231no—
203C4×Q8—231no—
204C4×Q8—461no—
205C4×Q8—461no—
206C4×Q8C2×D2311yescharacteristic
207C4×Q8C2×D2311yescharacteristic
208C4×D4—231no—
209C4×D4—231no—
210C4×D4—461no—
211C4×D4—461no—
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#103C2×D2311yescharacteristic
228#103C2×D2311yescharacteristic
229#102—231no—
230#102—231no—
231#97—231no—
232#97—231no—
233C4×C8—231no—
234C4×C8C2×D2311yescharacteristic
235C23#294711yescharacteristic, complemented, Sylow
236#41—234no—
237#41—462no—
238C2×Q8—234no—
239C2×Q8—231no—
240C2×Q8—461no—
241C2×Q8—462no—
242C2×Q8C22×D2311yescharacteristic
243C2×Q8C22×D2311yescharacteristic
244C2×D4—231no—
245C2×D4—461no—
246C22×C4—231no—
247C22×C4—461no—
248C22×C4—461no—
249C22×C4—461no—
250C22×C4—461no—
251C22×C4—461no—
252Q16—234no—
253Q16C4×D2314yescomplemented
254SD16—234no—
255SD16—234no—
256M16—234no—
257C2×C8—231no—
258C2×C8—231no—
259C2×C8—462no—
260C2×C8C22×D2311yescharacteristic
261C2×C8C22×D2311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—231no—
265C4⋊C4—231no—
266C4⋊C4—231no—
267C4⋊C4—231no—
268C4⋊C4—461no—
269C4⋊C4—461no—
270C4⋊C4—461no—
271C4⋊C4—461no—
272C4⋊C4—461no—
273C4⋊C4C22×D2311yescharacteristic
274C4⋊C4C22×D2311yescharacteristic
275C22⋊C4—231no—
276C22⋊C4—231no—
277C22⋊C4—461no—
278C22⋊C4—461no—
279C22⋊C4—461no—
280C42—21no—
281C42—21no—
282C42—231no—
283C42—461no—
284C42—461no—
285C42—461no—
286C42—461no—
287C42—461no—
288C42C22×D2311yescharacteristic
289C23—231no—
290C23—461no—
291Q8—21no—
292Q8—21no—
293Q8—232no—
294Q8—464no—
295Q8—461no—
296Q8C2×C4×D2312yes—
297Q8C2×C4×D2312yes—
298D4—232no—
299D4—464no—
300D4—461no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
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—1841no—
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—232no—
326C22—461no—
327C22—461no—
328C22—462no—
329C22—921no—
330C22—921no—
331C22C2×D4×D2311yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—232no—
339C4—462no—
340C4—461no—
341C4—461no—
342C4—921no—
343C4—921no—
344C4C22×C4×D2311yescharacteristic
345C4#41×D2311yescharacteristic
346C2—462no—
347C2—922no—
348C2C4×D4×D2311yescharacteristic
349C2#1309322411yescharacteristic
350C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC4×Q16×C23C2
socleC22×C23C22×D4
prime radicalC2×#67292C22
cosocleC2×C4×C23C24
hypercenterC4×Q16D23
hypocenterC23#2947
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #13092893C2semidirect
4. #13092524C2semidirect
5. #13092522C2semidirect
6. #13092516C2semidirect
7. #13092515C2semidirect
8. #13092509C2semidirect
9. C4×#67263C2semidirect
10. #13092502C2semidirect
11. #13092458C2semidirect
13. #103×D23C2semidirect
14. #13092371C2semidirect
15. C4×Q16×C23C2semidirect
25. #10625089C4semidirect
65. Q8×D23C2×C4semidirect
76. Q16×C23C2×C4semidirect
86. #67275C2×C4semidirect
87. #67274C2×C4semidirect
110. #67263C2×C4semidirect
111. #67262C2×C4semidirect
179. C4×Q16D23semidirect
235. C23#2947semidirect
253. Q16C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250892
#130928992
#130928932
#130925242
#130925222
#130925162
#130925152
#130925092
C4×#672632
#130925022
#130924582
#130924122
#103×D232
#130923712
C4×Q16×C232
#294723