Finite Group Databasebeta

← #15673696

Subgroups — #15673696

Order 2944.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D23C211yesmaximal, characteristic, complemented
2#13092924C211yesmaximal, characteristic
3C2×#10625019C211yesmaximal, characteristic, complemented
4C4×(C2×D23)⋊C4C211yesmaximal, characteristic, complemented
5#13092178C211yesmaximal, characteristic, complemented
6#13092177C211yesmaximal, characteristic, complemented
7C2×C23×#104C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9C22×C4×D23C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×C42×C23C2211yescharacteristic
12#10625117C411yescharacteristic, complemented
13#10625117C411yescharacteristic, complemented
14#10625109C411yescharacteristic, complemented
15#10625109C411yescharacteristic, complemented
16#10625108—21no—
17#10625106—21no—
18C4×C22⋊D23—21no—
19C4×C22⋊D23—21no—
20C2×(C2×D23)⋊C4—21no—
21#10625097C2211yescharacteristic
22C2×C4×Dic23C2211yescharacteristic
23C2×#67267C2211yescharacteristic
24M16×D23—22no—
25M16×D23—22no—
26C2×#67262—21no—
27C2×C8×D23—21no—
28C23×#104—22no—
29#10625019—22no—
30C23⋊#95—21no—
31C23×D23D411yescharacteristic
32#41×C23—21no—
33#41×C23—21no—
34#41×C23—21no—
35#41×C23—21no—
36C2×Q8×C23C2×C411yescharacteristic
37C2×D4×C23—21no—
38C2×D4×C23C2×C411yescharacteristic
39C22×C4×C23—21no—
40C22×C4×C23—21no—
41C22×C4×C23C2311yescharacteristic
42C2×C22⋊D23—21no—
43C2×C22⋊D23—21no—
44C22×Dic23—21no—
45C22×Dic23D411yescharacteristic
46C2×C4×D23—21no—
47C2×C4×D23—21no—
48C2×C4×D23—21no—
49C2×C4×D23—21no—
50C2×C4×D23C2×C411yescharacteristic
51C2×C4×D23C2×C411yescharacteristic
52C2×C4×D23D411yescharacteristic
53C2×C4×D23D411yescharacteristic
54M16×C23—21no—
55M16×C23D412yescomplemented
56C2×C8×C23—21no—
57C42×C23—21no—
58C42×C23—21no—
59C22⋊Dic23—21no—
60C22⋊Dic23—21no—
61C22⋊Dic23—21no—
62(C2×D23)⋊C4—24no—
63(C2×D23)⋊C4—21no—
64(C2×D23)⋊C4—21no—
65C4⋊Dic23C2×C411yescharacteristic
66C4⋊Dic23C2×C411yescharacteristic
67Dic23⋊C4—21no—
68Dic23⋊C4—21no—
69C4×Dic23—21no—
70C4×Dic23—21no—
71C4×Dic23—21no—
72#67267—21no—
73#67267D412yescomplemented
74C2×C23⋊C8—21no—
75#67262—24no—
76C8×D23—24no—
77C23×C23—21no—
78C23×C23C2×D411yescharacteristic
79C22×D23—21no—
80C22×D23—21no—
81C22×D23—22no—
82C22×D23—41no—
83C22×D23C22⋊C411yescharacteristic
84C22×D23C22⋊C411yescharacteristic
85Q8×C23—21no—
86Q8×C23—21no—
87D4×C23—21no—
88D4×C23—21no—
89D4×C23—41no—
90D4×C23—41no—
91C2×C4×C23—22no—
92C2×C4×C23—21no—
93C2×C4×C23—41no—
94C2×C4×C23—41no—
95C2×C4×C23—41no—
96C2×C4×C23—41no—
97C2×C4×C23C22×C411yescharacteristic
98C2×C4×C23C2×D411yescharacteristic
99C2×C4×C23C2×D411yescharacteristic
100C2×C4×C23C2×D411yescharacteristic
101C2×C4×C23#4111yescharacteristic
102C2×C4×C23#4111yescharacteristic
103C22⋊D23—42no—
104C22⋊D23—42no—
105C2×Dic23—21no—
106C2×Dic23—21no—
107C2×Dic23—22no—
108C2×Dic23—21no—
109C2×Dic23—21no—
110C2×Dic23—41no—
111C2×Dic23—41no—
112C2×Dic23C22⋊C411yescharacteristic
113C2×Dic23C22⋊C411yescharacteristic
114C4×D23—21no—
115C4×D23—21no—
116C4×D23—21no—
117C4×D23—21no—
118C4×D23—21no—
119C4×D23—21no—
120C4×D23—21no—
121C4×D23—21no—
122C8×C23—22no—
123C23⋊C8—22no—
124#1871—231nomaximal, Sylow
125C22×C23—21no—
126C22×C23—21no—
127C22×C23—41no—
128C22×C23—41no—
129C22×C23—41no—
130C22×C23C2×C22⋊C411yescharacteristic
131C22×C23#12111yescharacteristic
132C22×C23#12111yescharacteristic
133C2×D23—21no—
134C2×D23—21no—
135C2×D23—21no—
136C2×D23—21no—
137C2×D23—21no—
138C2×D23—42no—
139C2×D23—42no—
140C2×D23#10412yescomplemented
141C4×C23—42no—
142C4×C23—41no—
143C4×C23C4×D411yescharacteristic
144C4×C23C4×D411yescharacteristic
145C4×C23#12011yescharacteristic
146C4×C23#12311yescharacteristic
147Dic23—21no—
148Dic23—21no—
149Dic23—42no—
150Dic23—41no—
151Dic23—41no—
152C22×M16—231no—
153#525—231no—
154C2×#104—231no—
155C2×#104D2311yescharacteristic, complemented
156C4×C22⋊C4—231no—
157#339—231no—
158#339—231no—
159C2×C23—21no—
160C2×C23—21no—
161C2×C23—81no—
162C2×C23#38611yescharacteristic
163C2×C23C2×#10411yescharacteristic
164C2×C23#42111yescharacteristic
165D23—22no—
166D23—41no—
167C2×#41C2×D2311yescharacteristic
168C23×C4—231no—
169C2×M16—231no—
170C2×M16—461no—
171C2×M16—462no—
172C2×M16—462no—
173C2×M16C2×D2311yescharacteristic
174C22×C8—461no—
175#123—461no—
176C22⋊Q8—231no—
177C22⋊Q8—231no—
178#121—231no—
179#121—231no—
180#120—461no—
181C4×D4—461no—
182C4×D4—461no—
183#117—231no—
184C2×C22⋊C4—461no—
185C2×C42—231no—
186C2×C42C2×D2311yescharacteristic
187#104—22no—
188#104—462no—
189#95—461no—
190C23#187111yescharacteristic, complemented, Sylow
191C24—231no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196C2×Q8C4×D2311yescharacteristic
197C2×D4—21no—
198C2×D4—461no—
199C2×D4—461no—
200C2×D4C4×D2311yescharacteristic
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—231no—
204C22×C4—231no—
205C22×C4—231no—
206C22×C4—231no—
207C22×C4—231no—
208C22×C4—461no—
209C22×C4—461no—
210C22×C4—461no—
211C22×C4—461no—
212C22×C4—461no—
213C22×C4C22×D2311yescharacteristic
214M16—21no—
215M16—232no—
216M16—464no—
217M16—461no—
218M16C22⋊D2312yescomplemented
219C2×C8—21no—
220C2×C8—464no—
221C2×C8—461no—
222C4⋊C4—231no—
223C4⋊C4—231no—
224C4⋊C4—461no—
225C4⋊C4—461no—
226C22⋊C4—461no—
227C22⋊C4—461no—
228C22⋊C4—464no—
229C22⋊C4—461no—
230C22⋊C4—461no—
231C22⋊C4—461no—
232C42—21no—
233C42—21no—
234C42—461no—
235C42—461no—
236C42—461no—
237C23—21no—
238C23—231no—
239C23—231no—
240C23—462no—
241C23—461no—
242C23—461no—
243C23—921no—
244C23D4×D2311yescharacteristic
245Q8—21no—
246Q8—21no—
247D4—21no—
248D4—21no—
249D4—41no—
250D4—41no—
251D4—922no—
252D4—922no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—231no—
260C2×C4—231no—
261C2×C4—461no—
262C2×C4—461no—
263C2×C4—461no—
264C2×C4—461no—
265C2×C4—461no—
266C2×C4—461no—
267C2×C4—461no—
268C2×C4—461no—
269C2×C4—461no—
270C2×C4—461no—
271C2×C4—462no—
272C2×C4—461no—
273C2×C4—461no—
274C2×C4—921no—
275C2×C4—921no—
276C2×C4C2×C4×D2311yescharacteristic
277C2×C4#6728811yescharacteristic
278C2×C4D4×D2311yescharacteristic
279C2×C4D4×D2311yescharacteristic
280C2×C4#6729011yescharacteristic
281C2×C4C2×C22⋊D2311yescharacteristic
282C8—22no—
283C8—462no—
284C22—21no—
285C22—21no—
286C22—41no—
287C22—41no—
288C22—41no—
289C22—232no—
290C22—461no—
291C22—461no—
292C22—461no—
293C22—461no—
294C22—461no—
295C22—922no—
296C22—922no—
297C22C22⋊C4×D2311yescharacteristic
298C22#1062505511yescharacteristic
299C22#1062510911yescharacteristic
300C4—42no—
301C4—41no—
302C4—461no—
303C4—461no—
304C4—922no—
305C4—921no—
306C4—921no—
307C4(C22⋊D23)⋊C411yescharacteristic
308C4#1062505411yescharacteristic
309C4C4×C22⋊D2311yescharacteristic
310C4#1062510811yescharacteristic
311C2—21no—
312C2—21no—
313C2—81no—
314C2—462no—
315C2—921no—
316C2#1309229311yescharacteristic
317C2#104×D2311yescharacteristic
318C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#104C2
socleC22×C23C2×C22⋊C4
prime radical#13092924C2
cosocleC22×C4×C23C23
hypercenterC2×#104D23
hypocenterC23#1871
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×M16×D23C2semidirect
3. C2×#10625019C2semidirect
4. C4×(C2×D23)⋊C4C2semidirect
5. #13092178C2semidirect
6. #13092177C2semidirect
7. C2×C23×#104C2semidirect
12. #10625117C4semidirect
13. #10625117C4semidirect
14. #10625109C4semidirect
15. #10625109C4semidirect
55. M16×C23D4semidirect
73. #67267D4semidirect
140. C2×D23#104semidirect
155. C2×#104D23semidirect
190. C23#1871semidirect
218. M16C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D232
#130929242
C2×#106250192
C4×(C2×D23)⋊C42
#130921782
#130921772
C2×C23×#1042
#187123