Finite Group Databasebeta

← #15674314

Subgroups — #15674314

Order 2944.

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

normal subgroups only

This group has 336 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
1#13092963C211yesmaximal, characteristic
2C2×#10624987C211yesmaximal, characteristic, complemented
3C2×#10625019C211yesmaximal, characteristic, complemented
4C2×#10625007C211yesmaximal, characteristic, complemented
5M16×Dic23C211yesmaximal, characteristic, complemented
6C4×Dic23⋊C4C211yesmaximal, characteristic, complemented
7C2×C23×#104C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9C2×#67288C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C2×C42×C23C2211yescharacteristic
12#10625118C411yescharacteristic, complemented
13#10625115C411yescharacteristic, complemented
14#10625111C411yescharacteristic, complemented
15#10625110—21no—
16#10625110—21no—
17#10625107C411yescharacteristic, complemented
18C4×C22⋊D23—21no—
19C4×C22⋊D23—21no—
20C2×Dic23⋊C4—21no—
21C2×C4×Dic23C2211yescharacteristic
22C2×C4×Dic23C2211yescharacteristic
23C2×#67267C2211yescharacteristic
24C23×#104—22no—
25#10625019—22no—
26C23⋊#95—21no—
27#10625007—22no—
28#10624997—21no—
29C8×Dic23—21no—
30#10624987—22no—
31#41×C23—21no—
32#41×C23—21no—
33#41×C23—21no—
34#41×C23—21no—
35C2×Q8×C23C2×C411yescharacteristic
36C2×D4×C23—21no—
37C2×D4×C23C2×C411yescharacteristic
38C22×C4×C23—21no—
39C22×C4×C23—21no—
40C22×C4×C23C2311yescharacteristic
41C2×C22⋊D23—21no—
42C2×C22⋊D23—21no—
43C2×C22⋊D23—21no—
44C22×Dic23—21no—
45C22×Dic23D411yescharacteristic
46C22×Dic23D411yescharacteristic
47#67288—21no—
48#67288—21no—
49#67288—21no—
50#67288—21no—
51C2×D92C2×C411yescharacteristic
52C2×C4×D23—21no—
53C2×Dic46C2×C411yescharacteristic
54M16×C23—21no—
55M16×C23D412yescomplemented
56C2×C8×C23—21no—
57C42×C23—21no—
58C42×C23—21no—
59C22⋊Dic23—21no—
60C22⋊Dic23—21no—
61(C2×D23)⋊C4—21no—
62(C2×D23)⋊C4—21no—
63Dic23⋊C4—24no—
64Dic23⋊C4—21no—
65Dic23⋊C4—21no—
66C4×Dic23—21no—
67C4×Dic23—21no—
68C4×Dic23C2×C411yescharacteristic
69C4×Dic23C2×C411yescharacteristic
70C4×Dic23D411yescharacteristic
71C4×Dic23D411yescharacteristic
72#67267—21no—
73#67267D412yescomplemented
74C2×C23⋊C8—21no—
75C23×C23—21no—
76C23×C23C2×D411yescharacteristic
77C22×D23—21no—
78Q8×C23—21no—
79Q8×C23—21no—
80D4×C23—21no—
81D4×C23—21no—
82D4×C23—41no—
83D4×C23—41no—
84C2×C4×C23—22no—
85C2×C4×C23—21no—
86C2×C4×C23—41no—
87C2×C4×C23—41no—
88C2×C4×C23—41no—
89C2×C4×C23—41no—
90C2×C4×C23C22×C411yescharacteristic
91C2×C4×C23C2×D411yescharacteristic
92C2×C4×C23C2×D411yescharacteristic
93C2×C4×C23C2×D411yescharacteristic
94C2×C4×C23#4111yescharacteristic
95C2×C4×C23#4111yescharacteristic
96C22⋊D23—42no—
97C22⋊D23—41no—
98C22⋊D23—41no—
99C22⋊D23—42no—
100C2×Dic23—22no—
101C2×Dic23—22no—
102C2×Dic23—21no—
103C2×Dic23—41no—
104C2×Dic23—41no—
105C2×Dic23—41no—
106C2×Dic23C22⋊C411yescharacteristic
107C2×Dic23C22⋊C411yescharacteristic
108C2×Dic23C22⋊C411yescharacteristic
109C2×Dic23C22⋊C411yescharacteristic
110D92—21no—
111D92—21no—
112C4×D23—41no—
113C4×D23—41no—
114Dic46—21no—
115Dic46—21no—
116C8×C23—22no—
117C23⋊C8—22no—
118#1980—231nomaximal, Sylow
119C22×C23—21no—
120C22×C23—21no—
121C22×C23—41no—
122C22×C23—41no—
123C22×C23—41no—
124C22×C23C2×C22⋊C411yescharacteristic
125C22×C23#12411yescharacteristic
126C22×C23#12711yescharacteristic
127C2×D23—41no—
128C2×D23—41no—
129C2×D23—41no—
130C4×C23—42no—
131C4×C23—41no—
132C4×C23C4×D411yescharacteristic
133C4×C23C4×D411yescharacteristic
134C4×C23#12111yescharacteristic
135C4×C23#12111yescharacteristic
136Dic23—21no—
137Dic23—21no—
138Dic23—21no—
139Dic23—42no—
140Dic23—41no—
141Dic23#10412yescomplemented
142#532—231no—
143C2×#104—231no—
144C2×#104—231no—
145C2×#104—231no—
146C2×#104D2311yescharacteristic, complemented
147C4×M16—231no—
148C4×C4⋊C4—231no—
149C2×C23—21no—
150C2×C23—21no—
151C2×C23—81no—
152C2×C23#39011yescharacteristic
153C2×C23C2×#10411yescharacteristic
154C2×C23#42111yescharacteristic
155D23—81no—
156C2×#41—231no—
157C2×#41C2×D2311yescharacteristic
158C2×M16—231no—
159C2×M16C2×D2311yescharacteristic
160C4⋊Q8—231no—
161#127—231no—
162#124—231no—
163#124—231no—
164#121—461no—
165#121—461no—
166C4×D4—461no—
167C4×D4—461no—
168C2×C4⋊C4—461no—
169C2×C42—231no—
170C2×C42—231no—
171C2×C42C2×D2311yescharacteristic
172#104—22no—
173#104—462no—
174#104—462no—
175#104—462no—
176#97—461no—
177C4×C8—461no—
178#95—461no—
179C23#198011yescharacteristic, complemented, Sylow
180#41—21no—
181#41—21no—
182#41—21no—
183#41—21no—
184#41—461no—
185#41—461no—
186#41—461no—
187#41—461no—
188C2×Q8—231no—
189C2×Q8C4×D2311yescharacteristic
190C2×D4—21no—
191C2×D4—231no—
192C2×D4—461no—
193C2×D4—461no—
194C2×D4—461no—
195C2×D4C4×D2311yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—231no—
199C22×C4—231no—
200C22×C4—461no—
201C22×C4—461no—
202C22×C4C22×D2311yescharacteristic
203M16—21no—
204M16—232no—
205M16—461no—
206M16C22⋊D2312yescomplemented
207C2×C8—21no—
208C2×C8—461no—
209C4⋊C4—461no—
210C4⋊C4—461no—
211C4⋊C4—464no—
212C22⋊C4—461no—
213C22⋊C4—461no—
214C22⋊C4—461no—
215C22⋊C4—461no—
216C42—21no—
217C42—21no—
218C42—231no—
219C42—231no—
220C42—231no—
221C42—231no—
222C42—461no—
223C42—461no—
224C23—21no—
225C23—461no—
226C23D4×D2311yescharacteristic
227Q8—21no—
228Q8—21no—
229Q8—461no—
230Q8—461no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—461no—
236D4—461no—
237D4—922no—
238D4—922no—
239D4—921no—
240D4—921no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—231no—
248C2×C4—231no—
249C2×C4—231no—
250C2×C4—231no—
251C2×C4—462no—
252C2×C4—462no—
253C2×C4—461no—
254C2×C4—921no—
255C2×C4—921no—
256C2×C4—921no—
257C2×C4—921no—
258C2×C4—921no—
259C2×C4C2×C4×D2311yescharacteristic
260C2×C4#6728811yescharacteristic
261C2×C4D4×D2311yescharacteristic
262C2×C4D4×D2311yescharacteristic
263C2×C4#6729011yescharacteristic
264C2×C4C2×C22⋊D2311yescharacteristic
265C8—22no—
266C8—462no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22—921no—
273C22—921no—
274C22—921no—
275C22C22⋊C4×D2311yescharacteristic
276C22#1062505611yescharacteristic
277C22#1062511111yescharacteristic
278C4—42no—
279C4—41no—
280C4—232no—
281C4—461no—
282C4—461no—
283C4—461no—
284C4—922no—
285C4—921no—
286C4(C22⋊D23)⋊C411yescharacteristic
287C4#1062505511yescharacteristic
288C4C4×C22⋊D2311yescharacteristic
289C4#1062511011yescharacteristic
290C2—21no—
291C2—21no—
292C2—81no—
293C2—1841no—
294C2#1309231711yescharacteristic
295C2#104×D2311yescharacteristic
296C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#104C2
socleC22×C23C2×C22⋊C4
prime radical#13092963C2
cosocleC22×C4×C23C23
hypercenterC2×#104D23
hypocenterC23#1980
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
2. C2×#10624987C2semidirect
3. C2×#10625019C2semidirect
4. C2×#10625007C2semidirect
5. M16×Dic23C2semidirect
6. C4×Dic23⋊C4C2semidirect
7. C2×C23×#104C2semidirect
12. #10625118C4semidirect
13. #10625115C4semidirect
14. #10625111C4semidirect
17. #10625107C4semidirect
55. M16×C23D4semidirect
73. #67267D4semidirect
141. Dic23#104semidirect
146. C2×#104D23semidirect
179. C23#1980semidirect
206. M16C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130929632
C2×#106249872
C2×#106250192
C2×#106250072
M16×Dic232
C4×Dic23⋊C42
C2×C23×#1042
#198023