Finite Group Databasebeta

← #15682616

Subgroups — #15682616

Order 2944.

764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67290C211yesmaximal, characteristic, complemented
2C2×#10625087C212yesmaximal, complemented
3#13092930C211yesmaximal, characteristic, complemented
4#13092576C212yesmaximal, complemented
5#13092572C211yesmaximal, characteristic, complemented
6#13092563C212yesmaximal, complemented
7#13092558C211yesmaximal, characteristic, complemented
8#13092551C211yesmaximal, characteristic, complemented
9#13092410C212yesmaximal, complemented
10C22⋊C8×D23C211yesmaximal, characteristic, complemented
11C23×#450C211yesmaximal, characteristic, complemented
12C22×D4×C23C2211yescharacteristic
13C22×C22⋊D23—21no—
14C23×Dic23—21no—
15C2×#67292C2211yescharacteristic, complemented
16C2×#67290—28no—
17C2×#67290—21no—
18C2×#67290—21no—
19C2×#67290C2212yes—
20C2×#67290C2212yes—
21C22×C4×D23C2211yescharacteristic
22C22×Dic46C2211yescharacteristic
23C2×SD16×C23C2212yescomplemented
24C23×C22⋊Q8C2211yescharacteristic
25#10625117C2211yescharacteristic, complemented
26C2×#67275C2212yescomplemented
27C2×#67272C2212yescomplemented
28#10625101C2211yescharacteristic
29#10625087—28no—
30C2×#67263C2212yescomplemented
31C2×C8×D23C2212yescomplemented
32#10625066C2211yescharacteristic, complemented
33#10625065—21no—
34#10625064—21no—
35#10625063C2211yescharacteristic, complemented
36#10625053—21no—
37(C22⋊D23)⋊C4—21no—
38C23×#102C2212yescomplemented
39C23×C22⋊C8C2211yescharacteristic
40#10625014C2212yescomplemented
41C22⋊(C23⋊C8)C2211yescharacteristic
42(C2×D23)⋊C8C2212yescomplemented
43#10624998C2212yescomplemented
44#10624992C2212yescomplemented
45C24×C23—21no—
46C23×D23D411yescharacteristic
47C2×Q8×C23C2311yescharacteristic
48C2×D4×C23—24no—
49C2×D4×C23—21no—
50C2×D4×C23C2312yes—
51C22×C4×C23C2311yescharacteristic
52C2×C22⋊D23—28no—
53C2×C22⋊D23—22no—
54C2×C22⋊D23—22no—
55C2×C22⋊D23—21no—
56C22×Dic23—28no—
57C22×Dic23—21no—
58C22×Dic23—22no—
59C22×Dic23—22no—
60C22×Dic23D411yescharacteristic
61#67292—24no—
62#67290—28no—
63#67290—28no—
64#67290—24no—
65#67290—24no—
66#67290—24no—
67#67290D418yescomplemented
68C2×D92—21no—
69C2×D92—21no—
70C2×D92C2311yescharacteristic
71C2×C4×D23—24no—
72C2×C4×D23—21no—
73C2×C4×D23D411yescharacteristic
74C2×C4×D23D411yescharacteristic
75C2×C4×D23C2311yescharacteristic
76C2×C4×D23C2311yescharacteristic
77C2×Dic46—21no—
78C2×Dic46—24no—
79C2×Dic46C2312yes—
80SD16×C23—24no—
81C2×C8×C23C2312yes—
82C4⋊C4×C23—21no—
83C4⋊C4×C23C2311yescharacteristic
84C22⋊C4×C23—21no—
85#67275—24no—
86#67272—24no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91C4⋊Dic23C2311yescharacteristic
92Dic23⋊C4—21no—
93C4×Dic23—21no—
94C2×C23⋊C8C2312yes—
95#67263—24no—
96C8×D23—24no—
97C23×C23—24no—
98C23×C23—22no—
99C23×C23—42no—
100C23×C23—42no—
101C23×C23C2×D411yescharacteristic
102C22×D23—22no—
103C22×D23—22no—
104C22×D23—21no—
105C22×D23—41no—
106C22×D23C2×D411yescharacteristic
107C22×D23C2×D411yescharacteristic
108Q8×C23—22no—
109D4×C23—24no—
110D4×C23—22no—
111D4×C23C2×D414yes—
112C2×C4×C23—22no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23C2×D411yescharacteristic
116C2×C4×C23C2411yescharacteristic
117C22⋊D23—28no—
118C22⋊D23—28no—
119C22⋊D23—42no—
120C2×Dic23—24no—
121C2×Dic23—28no—
122C2×Dic23—22no—
123C2×Dic23—22no—
124C2×Dic23—28no—
125C2×Dic23—21no—
126C2×Dic23C2×D411yescharacteristic
127C2×Dic23C2×D411yescharacteristic
128D92—22no—
129D92—42no—
130D92—42no—
131C4×D23—22no—
132C4×D23—22no—
133C4×D23—22no—
134C4×D23—42no—
135C4×D23C2×D414yes—
136Dic46—24no—
137Dic46—22no—
138Dic46C2×D414yes—
139C8×C23—22no—
140C23⋊C8—22no—
141#3002—231nomaximal, Sylow
142C22×C23—21no—
143C22×C23—21no—
144C22×C23—24no—
145C22×C23—48no—
146C22×C23—42no—
147C22×C23—42no—
148C22×C23#13512yescomplemented
149C22×C23C22×D411yescharacteristic
150C2×D23—21no—
151C2×D23—21no—
152C2×D23—21no—
153C2×D23—21no—
154C2×D23—21no—
155C2×D23—44no—
156C2×D23—41no—
157C2×D23—41no—
158C2×D23—41no—
159C2×D23#12012yes—
160C4×C23—21no—
161C4×C23—41no—
162C4×C23—41no—
163C4×C23C22×D412yes—
164Dic23—24no—
165Dic23—21no—
166Dic23—41no—
167Dic23#12012yes—
168C22×#41—231no—
169C2×#135—232no—
170#525—231no—
171#452—232no—
172#451—231no—
173#450D2311yescharacteristic, complemented
174#449—232no—
175#448—231no—
176#447—231no—
177#416—232no—
178C2×C22⋊C8—231no—
179C2×C23—22no—
180C2×C23—44no—
181C2×C23C2×#12011yescharacteristic
182C2×C23C2×#13511yescharacteristic
183C2×C23#57511yescharacteristic
184D23—22no—
185D23—41no—
186D23—81no—
187C2×#41—231no—
188C2×#41—232no—
189C2×#41—232no—
190C2×#41—461no—
191C2×#41—461no—
192C2×#41—468no—
193C22×Q8—231no—
194C22×D4—461no—
195C22×D4C2×D2311yescharacteristic
196C23×C4—231no—
197C23×C4—461no—
198#135—468no—
199C2×Q16—232no—
200C2×SD16—232no—
201C2×SD16C2×D2312yescomplemented
202C2×D8—232no—
203C22×C8—232no—
204#123—461no—
205C22⋊Q8—231no—
206C22⋊Q8C2×D2311yescharacteristic
207#121—231no—
208#121—231no—
209#120—461no—
210C4×D4—461no—
211C4×D4—461no—
212#117—231no—
213#103—232no—
214#103—232no—
215#102—232no—
216#102C2×D2312yescomplemented
217C22⋊C8—231no—
218C22⋊C8—232no—
219C22⋊C8C2×D2311yescharacteristic
220C23#300211yescharacteristic, complemented, Sylow
221C24—21no—
222C24—231no—
223#41—238no—
224#41—464no—
225#41—464no—
226#41—464no—
227#41—468no—
228#41—468no—
229#41—464no—
230C2×Q8—232no—
231C2×Q8—464no—
232C2×Q8—461no—
233C2×Q8C22×D2311yescharacteristic
234C2×D4—24no—
235C2×D4—21no—
236C2×D4—231no—
237C2×D4—461no—
238C2×D4—461no—
239C2×D4—462no—
240C2×D4—462no—
241C2×D4—468no—
242C2×D4—461no—
243C2×D4C22×D2312yes—
244C22×C4—231no—
245C22×C4—231no—
246C22×C4—231no—
247C22×C4—231no—
248C22×C4—231no—
249C22×C4—464no—
250C22×C4—461no—
251C22×C4—462no—
252C22×C4—462no—
253C22×C4—468no—
254C22×C4—461no—
255C22×C4C22×D2311yescharacteristic
256Q16—464no—
257SD16—24no—
258SD16—464no—
259D8—464no—
260C2×C8—232no—
261C2×C8—464no—
262C2×C8C22×D2312yes—
263C4⋊C4—21no—
264C4⋊C4—231no—
265C4⋊C4—461no—
266C4⋊C4C22×D2311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—461no—
269C22⋊C4—461no—
270C22⋊C4—461no—
271C22⋊C4—461no—
272C42—461no—
273C23—24no—
274C23—22no—
275C23—42no—
276C23—42no—
277C23—231no—
278C23—231no—
279C23—462no—
280C23—462no—
281C23—461no—
282C23—921no—
283C23D4×D2311yescharacteristic
284Q8—22no—
285Q8—234no—
286Q8—464no—
287Q8—462no—
288D4—24no—
289D4—22no—
290D4—468no—
291D4—468no—
292D4—462no—
293D4—922no—
294D4—922no—
295D4—922no—
296D4D4×D2314yes—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—231no—
301C2×C4—234no—
302C2×C4—231no—
303C2×C4—462no—
304C2×C4—462no—
305C2×C4—462no—
306C2×C4—468no—
307C2×C4—464no—
308C2×C4—468no—
309C2×C4—462no—
310C2×C4—462no—
311C2×C4—461no—
312C2×C4—922no—
313C2×C4D4×D2311yescharacteristic
314C2×C4C23×D2311yescharacteristic
315C8—22no—
316C8—462no—
317C22—21no—
318C22—21no—
319C22—24no—
320C22—48no—
321C22—42no—
322C22—42no—
323C22—232no—
324C22—461no—
325C22—461no—
326C22—461no—
327C22—461no—
328C22—461no—
329C22—924no—
330C22—921no—
331C22—921no—
332C22—921no—
333C22#1062508712yescomplemented
334C22C2×D4×D2311yescharacteristic
335C4—21no—
336C4—41no—
337C4—41no—
338C4—232no—
339C4—461no—
340C4—464no—
341C4—921no—
342C4C2×D4×D2312yes—
343C2—22no—
344C2—44no—
345C2—462no—
346C2—921no—
347C2—1841no—
348C2#120×D2311yescharacteristic
349C2C2×#1062508711yescharacteristic
350C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#450C2
socleC22×C23C22×D4
hypercenter#450D23
hypocenterC23#3002
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×#67290C2semidirect
2. C2×#10625087C2semidirect
3. #13092930C2semidirect
4. #13092576C2semidirect
5. #13092572C2semidirect
6. #13092563C2semidirect
7. #13092558C2semidirect
8. #13092551C2semidirect
9. #13092410C2semidirect
10. C22⋊C8×D23C2semidirect
11. C23×#450C2semidirect
15. C2×#67292C22semidirect
23. C2×SD16×C23C22semidirect
25. #10625117C22semidirect
26. C2×#67275C22semidirect
27. C2×#67272C22semidirect
30. C2×#67263C22semidirect
31. C2×C8×D23C22semidirect
32. #10625066C22semidirect
35. #10625063C22semidirect
38. C23×#102C22semidirect
40. #10625014C22semidirect
42. (C2×D23)⋊C8C22semidirect
43. #10624998C22semidirect
44. #10624992C22semidirect
67. #67290D4semidirect
148. C22×C23#135semidirect
173. #450D23semidirect
201. C2×SD16C2×D23semidirect
216. #102C2×D23semidirect
220. C23#3002semidirect
333. C22#10625087semidirect

Maximal subgroups

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

subgroupindex
C22×#672902
C2×#106250872
#130929302
#130925762
#130925722
#130925632
#130925582
#130925512
#130924102
C22⋊C8×D232
C23×#4502
#300223