Finite Group Databasebeta

← #15683017

Subgroups — #15683017

Order 2944.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#10625079C211yesmaximal, characteristic, complemented
2C2×M16×D23C211yesmaximal, characteristic, complemented
3#13092929C211yesmaximal, characteristic, complemented
4C2×#10625066C211yesmaximal, characteristic, complemented
5#13092671C212yesmaximal, complemented
6#13092664C212yesmaximal, complemented
7#13092654C212yesmaximal, complemented
8#13092647C212yesmaximal, complemented
9#13092421C211yesmaximal, characteristic, complemented
10#13092416C211yesmaximal, characteristic, complemented
11C23×#428C211yesmaximal, characteristic, complemented
12C2×#67288C2211yescharacteristic
13C22×D92—21no—
14C22×D92C2211yescharacteristic
15C22×C4×D23C2211yescharacteristic
16C2×M16×C23C2211yescharacteristic
17C23×#117C2211yescharacteristic
18C2×C4⋊C4×C23C2211yescharacteristic
19C2×(C2×D23)⋊C4—21no—
20C2×#67267C2211yescharacteristic
21#10625079—24no—
22M16×D23—24no—
23C2×D184C2212yescomplemented
24C2×#67263C2212yescomplemented
25C2×#67262C2212yescomplemented
26C2×C8×D23C2212yescomplemented
27#10625068C2211yescharacteristic, complemented
28#10625068C2211yescharacteristic, complemented
29#10625066—21no—
30#10625066—21no—
31#10625066C2212yes—
32#10625066C2212yes—
33#10625066C2211yescharacteristic, complemented
34#10625066C2211yescharacteristic, complemented
35#10625057—21no—
36#10625053—21no—
37C4×D92—21no—
38C4×D92—21no—
39C23×#107C2212yescomplemented
40C23×#106C2212yescomplemented
41#10624992C2212yescomplemented
42#10624991C2212yescomplemented
43#10624991C2212yescomplemented
44#10624991C2212yescomplemented
45C23×D23—21no—
46C23×D23D411yescharacteristic
47C22×C4×C23—21no—
48C22×C4×C23C2311yescharacteristic
49C2×C22⋊D23—21no—
50C22×Dic23D411yescharacteristic
51#67288—22no—
52#67288—22no—
53C2×D92—22no—
54C2×D92—22no—
55C2×D92—21no—
56C2×D92—21no—
57C2×D92—22no—
58C2×D92—22no—
59C2×D92—21no—
60C2×D92—44no—
61C2×D92C2312yes—
62C2×D92C2311yescharacteristic
63C2×C4×D23—22no—
64C2×C4×D23—22no—
65C2×C4×D23—21no—
66C2×C4×D23D411yescharacteristic
67C2×C4×D23D411yescharacteristic
68C2×C4×D23C2311yescharacteristic
69C2×C4×D23C2311yescharacteristic
70C2×Dic46C2311yescharacteristic
71M16×C23D414yescomplemented
72C2×C8×C23C2312yes—
73C4⋊C4×C23—21no—
74C4⋊C4×C23C2311yescharacteristic
75C4⋊C4×C23C2312yes—
76C4⋊C4×C23C2311yescharacteristic
77C22⋊C4×C23—21no—
78C42×C23—21no—
79(C2×D23)⋊C4—21no—
80(C2×D23)⋊C4—21no—
81(C2×D23)⋊C4—21no—
82(C2×D23)⋊C4—21no—
83(C2×D23)⋊C4—22no—
84(C2×D23)⋊C4—22no—
85C4⋊Dic23—21no—
86C4⋊Dic23—21no—
87#67267—22no—
88C2×C23⋊C8C2312yes—
89D184—24no—
90#67263—24no—
91#67262—24no—
92C8×D23—24no—
93C23×C23C2×D411yescharacteristic
94C22×D23—22no—
95C22×D23—22no—
96C22×D23—21no—
97C22×D23—22no—
98C22×D23—41no—
99C22×D23—42no—
100C22×D23—42no—
101C22×D23—42no—
102C22×D23C2×D411yescharacteristic
103C22×D23C2×D411yescharacteristic
104C2×C4×C23—21no—
105C2×C4×C23—21no—
106C2×C4×C23—22no—
107C2×C4×C23—42no—
108C2×C4×C23C2×D412yes—
109C2×C4×C23C2×D411yescharacteristic
110C2×C4×C23#4112yes—
111C2×C4×C23C2411yescharacteristic
112C22⋊D23—42no—
113C2×Dic23—22no—
114C2×Dic23—21no—
115C2×Dic23C2×D411yescharacteristic
116C2×Dic23C2×D411yescharacteristic
117D92—22no—
118D92—21no—
119D92—22no—
120D92—21no—
121D92—42no—
122D92—44no—
123D92—42no—
124D92—44no—
125D92—42no—
126C4×D23—22no—
127C4×D23—22no—
128C4×D23—21no—
129C4×D23—21no—
130C4×D23—21no—
131C4×D23—21no—
132C4×D23—42no—
133Dic46—21no—
134Dic46—21no—
135C8×C23C2×D414yescomplemented
136C23⋊C8—22no—
137#3055—231nomaximal, Sylow
138C22×C23—21no—
139C22×C23—21no—
140C22×C23#12112yes—
141C22×C23C22×D411yescharacteristic
142C2×D23—21no—
143C2×D23—21no—
144C2×D23—21no—
145C2×D23—21no—
146C2×D23—21no—
147C2×D23—44no—
148C2×D23—41no—
149C2×D23—42no—
150C2×D23—42no—
151C2×D23—41no—
152C2×D23—41no—
153C2×D23—42no—
154C2×D23—84no—
155C2×D23AGL(1,ℤ/8)12yescomplemented
156C4×C23—42no—
157C4×C23—41no—
158C4×C23—41no—
159C4×C23#12112yes—
160C4×C23C22×D411yescharacteristic
161C4×C23C2×#4111yescharacteristic
162Dic23—21no—
163Dic23—21no—
164Dic23—41no—
165C2×AGL(1,ℤ/8)—231no—
166C22×M16—231no—
167#525—231no—
168C2×#121—231no—
169#469—232no—
170#468—232no—
171#466—232no—
172#465—232no—
173#428D2311yescharacteristic, complemented
174#418—231no—
175#417—231no—
176C2×C23—22no—
177C2×C23C2×#12111yescharacteristic
178C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C23#57511yescharacteristic
180D23—22no—
181D23—41no—
182D23—81no—
183D23—82no—
184C2×#41—231no—
185C22×D4—231no—
186C22×D4—461no—
187C23×C4—231no—
188AGL(1,ℤ/8)—464no—
189C2×SD16—232no—
190C2×D8—232no—
191C2×M16—231no—
192C2×M16—232no—
193C2×M16—464no—
194C2×M16C2×D2311yescharacteristic
195C22×C8—232no—
196#123—461no—
197C22⋊Q8—231no—
198C22⋊Q8—231no—
199#121—232no—
200#121—232no—
201#121—231no—
202#121—231no—
203#121—461no—
204#121—461no—
205#120—461no—
206C4×D4—461no—
207C4×D4—461no—
208#117C2×D2311yescharacteristic
209C2×C4⋊C4C2×D2311yescharacteristic
210C2×C22⋊C4—461no—
211#107C2×D2312yescomplemented
212#106C2×D2312yescomplemented
213#103—232no—
214#102—232no—
215#102—232no—
216#102—232no—
217C23#305511yescharacteristic, complemented, Sylow
218C24—231no—
219C24—461no—
220#41—462no—
221#41—462no—
222C2×Q8—231no—
223C2×D4—231no—
224C2×D4—232no—
225C2×D4—461no—
226C2×D4—461no—
227C2×D4—462no—
228C2×D4—462no—
229C2×D4—461no—
230C2×D4—462no—
231C2×D4—461no—
232C2×D4—462no—
233C2×D4—924no—
234C22×C4—21no—
235C22×C4—231no—
236C22×C4—231no—
237C22×C4—231no—
238C22×C4—231no—
239C22×C4—231no—
240C22×C4—462no—
241C22×C4—462no—
242C22×C4—461no—
243C22×C4C22×D2311yescharacteristic
244SD16—464no—
245D8—464no—
246M16—462no—
247M16—464no—
248M16D9214yescomplemented
249C2×C8—232no—
250C2×C8—464no—
251C2×C8C22×D2312yes—
252C4⋊C4—21no—
253C4⋊C4—461no—
254C4⋊C4—461no—
255C4⋊C4C22×D2311yescharacteristic
256C4⋊C4C22×D2311yescharacteristic
257C4⋊C4C22×D2312yes—
258C22⋊C4—21no—
259C22⋊C4—462no—
260C22⋊C4—462no—
261C22⋊C4—461no—
262C22⋊C4—461no—
263C22⋊C4—461no—
264C22⋊C4—461no—
265C42—21no—
266C23—231no—
267C23—231no—
268C23—462no—
269C23—462no—
270C23—461no—
271C23—462no—
272C23—921no—
273C23—922no—
274C23—922no—
275C23—922no—
276C23D4×D2311yescharacteristic
277Q8—461no—
278Q8—461no—
279D4—461no—
280D4—462no—
281D4—462no—
282D4—461no—
283D4—924no—
284D4—922no—
285D4—924no—
286D4—922no—
287D4—922no—
288D4—922no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—231no—
294C2×C4—231no—
295C2×C4—462no—
296C2×C4—462no—
297C2×C4—462no—
298C2×C4—461no—
299C2×C4—461no—
300C2×C4—461no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—922no—
304C2×C4C2×D9212yes—
305C2×C4D4×D2311yescharacteristic
306C2×C4#6729212yes—
307C2×C4C23×D2311yescharacteristic
308C8—462no—
309C8C2×D9214yescomplemented
310C22—21no—
311C22—21no—
312C22—232no—
313C22—461no—
314C22—461no—
315C22—461no—
316C22—461no—
317C22—461no—
318C22—924no—
319C22—921no—
320C22—922no—
321C22—922no—
322C22—921no—
323C22—921no—
324C22—922no—
325C22—1844no—
326C22#1062506612yes—
327C22C2×D4×D2311yescharacteristic
328C4—42no—
329C4—41no—
330C4—41no—
331C4—461no—
332C4—461no—
333C4—921no—
334C4#1062506612yes—
335C4C22×D9211yescharacteristic
336C4C2×#6729211yescharacteristic
337C2—22no—
338C2—462no—
339C2—921no—
340C2—1842no—
341C2—1841no—
342C2C2×#1062506611yescharacteristic
343C2AGL(1,ℤ/8)×D2311yescharacteristic
344C2#1309321611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#428C2
socleC22×C23C22×D4
hypercenter#428D23
hypocenterC23#3055
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C2×M16×D23C2semidirect
3. #13092929C2semidirect
4. C2×#10625066C2semidirect
5. #13092671C2semidirect
6. #13092664C2semidirect
7. #13092654C2semidirect
8. #13092647C2semidirect
9. #13092421C2semidirect
10. #13092416C2semidirect
11. C23×#428C2semidirect
23. C2×D184C22semidirect
24. C2×#67263C22semidirect
25. C2×#67262C22semidirect
26. C2×C8×D23C22semidirect
27. #10625068C22semidirect
28. #10625068C22semidirect
33. #10625066C22semidirect
34. #10625066C22semidirect
39. C23×#107C22semidirect
40. C23×#106C22semidirect
41. #10624992C22semidirect
42. #10624991C22semidirect
43. #10624991C22semidirect
44. #10624991C22semidirect
71. M16×C23D4semidirect
135. C8×C23C2×D4semidirect
155. C2×D23AGL(1,ℤ/8)semidirect
173. #428D23semidirect
211. #107C2×D23semidirect
212. #106C2×D23semidirect
217. C23#3055semidirect
248. M16D92semidirect
309. C8C2×D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
C2×M16×D232
#130929292
C2×#106250662
#130926712
#130926642
#130926542
#130926472
#130924212
#130924162
C23×#4282
#305523