Finite Group Databasebeta

← #15673362

Subgroups — #15673362

Order 2944.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#13093253C211yesmaximal, characteristic
2#13092435C211yesmaximal, characteristic, complemented
3#13092434C211yesmaximal, characteristic, complemented
4#13092414C211yesmaximal, characteristic, complemented
5#13092390C211yesmaximal, characteristic, complemented
6#13092383C211yesmaximal, characteristic, complemented
7C23×#416C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9#10625161—21no—
10#10625161C412yescomplemented
11#10625160—21no—
12#10625160C412yescomplemented
13#41×D23—22no—
14#41×D23—22no—
15#10625158—21no—
16#10625155—21no—
17#10625155—22no—
18C2×#67288—22no—
19C2×#67288C2211yescharacteristic
20C2×#67288C2211yescharacteristic
21C22×C8×C23C2211yescharacteristic, complemented
22C23×#117C2211yescharacteristic, complemented
23#10625097C2211yescharacteristic, complemented
24C2×#67267C2211yescharacteristic, complemented
25C23×#103—21no—
26C23×#102—21no—
27#10625019—22no—
28#10625003—21no—
29(C2×D23)⋊C8—22no—
30#10624998—21no—
31#10624988—22no—
32#10624987—22no—
33#41×C23—21no—
34#41×C23—21no—
35#41×C23C2×C412yes—
36#41×C23D412yes—
37C2×Q8×C23D411yescharacteristic
38C2×D4×C23—21no—
39C2×D4×C23D411yescharacteristic
40C22×C4×C23—21no—
41C22×C4×C23C2311yescharacteristic
42C2×C22⋊D23—24no—
43C2×C22⋊D23—21no—
44C2×C22⋊D23D412yes—
45#67292—22no—
46#67292—22no—
47Q8×D23—22no—
48Q8×D23—22no—
49#67290—24no—
50#67290—22no—
51#67290—22no—
52#67290—24no—
53D4×D23—24no—
54D4×D23—22no—
55D4×D23—24no—
56D4×D23—22no—
57#67288—24no—
58#67288—24no—
59#67288—21no—
60#67288—21no—
61#67288—21no—
62#67288—21no—
63#67288—21no—
64#67288—21no—
65#67288—22no—
66#67288—22no—
67#67288C2×C412yes—
68#67288D412yes—
69C2×D92—22no—
70C2×D92C2×C411yescharacteristic
71C2×D92D411yescharacteristic
72C2×C4×D23—24no—
73C2×C4×D23—21no—
74C2×C4×D23D412yes—
75C2×Dic46—22no—
76C2×Dic46C2×C411yescharacteristic
77C2×Dic46D411yescharacteristic
78C2×C8×C23—21no—
79C2×C8×C23—21no—
80C2×C8×C23—21no—
81C4⋊C4×C23—21no—
82C22⋊C4×C23—21no—
83C42×C23—21no—
84C22⋊Dic23—21no—
85C4⋊Dic23—21no—
86C4×Dic23—21no—
87#67267—21no—
88#67267—21no—
89C2×C23⋊C8—21no—
90C23×C23—21no—
91C23×C23C2×D411yescharacteristic
92C22×D23—24no—
93C22×D23—21no—
94C22×D23C22⋊C412yes—
95Q8×C23—21no—
96Q8×C23C22⋊C412yes—
97D4×C23—22no—
98D4×C23—22no—
99D4×C23—21no—
100D4×C23C22⋊C412yes—
101C2×C4×C23—21no—
102C2×C4×C23—22no—
103C2×C4×C23—22no—
104C2×C4×C23—41no—
105C2×C4×C23C22×C411yescharacteristic
106C2×C4×C23C2×D411yescharacteristic
107C2×C4×C23C2×D411yescharacteristic
108C2×C4×C23C2×D411yescharacteristic
109C2×C4×C23C2×D411yescharacteristic
110C2×C4×C23C2×D411yescharacteristic
111C22⋊D23—24no—
112C22⋊D23—24no—
113C22⋊D23—22no—
114C22⋊D23—22no—
115C22⋊D23—22no—
116C22⋊D23—22no—
117C2×Dic23—24no—
118C2×Dic23—21no—
119C2×Dic23—41no—
120C2×Dic23C22⋊C412yes—
121D92—24no—
122D92—21no—
123D92—21no—
124D92—21no—
125D92C22⋊C412yes—
126C4×D23—24no—
127C4×D23—24no—
128C4×D23—22no—
129C4×D23—22no—
130C4×D23—22no—
131C4×D23—22no—
132Dic46—24no—
133Dic46—21no—
134Dic46—21no—
135Dic46—21no—
136Dic46C22⋊C412yes—
137C8×C23—41no—
138C23⋊C8—41no—
139#1794—231nomaximal, Sylow
140C22×C23—22no—
141C22×C23—41no—
142C22×C23—81no—
143C22×C23C2×C22⋊C411yescharacteristic
144C22×C23#12011yescharacteristic
145C22×C23#12011yescharacteristic
146C2×D23—22no—
147C2×D23—22no—
148C2×D23—42no—
149C2×D23—81no—
150C2×D23—84no—
151C4×C23—22no—
152C4×C23—81no—
153C4×C23C2×C22⋊C411yescharacteristic
154C4×C23C2×C22⋊C411yescharacteristic
155C4×C23#12011yescharacteristic
156C4×C23#12011yescharacteristic
157Dic23—22no—
158Dic23—22no—
159Dic23—81no—
160#585—231no—
161#421—231no—
162#421—231no—
163#416—231no—
164#416D2311yescharacteristic, complemented
165#410—231no—
166#408—231no—
167C2×C23—21no—
168C2×C23—21no—
169C2×C23—21no—
170C2×C23—42no—
171C2×C23#37911yescharacteristic
172D23—42no—
173D23—42no—
1742−1+4—232no—
1752−1+4—461no—
1762−1+4—461no—
177H(5,𝔽2)—232no—
178H(5,𝔽2)—462no—
179H(5,𝔽2)—461no—
180H(5,𝔽2)—461no—
181C2×#41—231no—
182C2×#41—231no—
183C2×#41—462no—
184C2×#41—462no—
185C2×#41—462no—
186C2×#41C2×D2311yescharacteristic
187C2×M16—231no—
188C22×C8C2×D2311yescharacteristic, complemented
189#117—231no—
190#117C2×D2311yescharacteristic, complemented
191#104—462no—
192#104—462no—
193#103—21no—
194#103—461no—
195#102—21no—
196#102—461no—
197#99—462no—
198C22⋊C8—462no—
199C23#179411yescharacteristic, complemented, Sylow
200#41—21no—
201#41—21no—
202#41—232no—
203#41—232no—
204#41—462no—
205#41—462no—
206#41—464no—
207#41—464no—
208#41—464no—
209#41—464no—
210#41—462no—
211#41—462no—
212#41—462no—
213#41—462no—
214#41—461no—
215#41—461no—
216#41—461no—
217#41—461no—
218#41—461no—
219#41—461no—
220#41C4×D2312yes—
221#41D9212yes—
222C2×Q8—231no—
223C2×Q8—231no—
224C2×Q8—462no—
225C2×Q8—462no—
226C2×Q8—462no—
227C2×Q8C22⋊D2311yescharacteristic
228C2×D4—21no—
229C2×D4—232no—
230C2×D4—231no—
231C2×D4—231no—
232C2×D4—462no—
233C2×D4—464no—
234C2×D4—464no—
235C2×D4—462no—
236C2×D4—464no—
237C2×D4—461no—
238C2×D4—462no—
239C2×D4C22⋊D2311yescharacteristic
240C22×C4—21no—
241C22×C4—232no—
242C22×C4—464no—
243C22×C4—461no—
244C22×C4C22×D2311yescharacteristic
245M16—461no—
246M16—461no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—461no—
251C4⋊C4—21no—
252C4⋊C4—461no—
253C22⋊C4—21no—
254C22⋊C4—461no—
255C42—21no—
256C42—461no—
257C23—21no—
258C23—232no—
259C23—464no—
260C23—461no—
261C23D4×D2311yescharacteristic
262Q8—21no—
263Q8—232no—
264Q8—464no—
265Q8—461no—
266Q8—461no—
267Q8—461no—
268Q8(C2×D23)⋊C412yes—
269D4—22no—
270D4—22no—
271D4—21no—
272D4—232no—
273D4—464no—
274D4—464no—
275D4—464no—
276D4—462no—
277D4—462no—
278D4—462no—
279D4—462no—
280D4—461no—
281D4—461no—
282D4—461no—
283D4(C2×D23)⋊C412yes—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—232no—
289C2×C4—464no—
290C2×C4—464no—
291C2×C4—464no—
292C2×C4—461no—
293C2×C4—462no—
294C2×C4—462no—
295C2×C4—462no—
296C2×C4—462no—
297C2×C4—921no—
298C2×C4C2×C4×D2311yescharacteristic
299C2×C4C2×D9211yescharacteristic
300C2×C4D4×D2311yescharacteristic
301C2×C4D4×D2311yescharacteristic
302C2×C4D4×D2311yescharacteristic
303C2×C4C2×C22⋊D2311yescharacteristic
304C8—41no—
305C8—921no—
306C22—22no—
307C22—41no—
308C22—81no—
309C22—462no—
310C22—462no—
311C22—922no—
312C22—1841no—
313C22—1844no—
314C22C22⋊C4×D2311yescharacteristic
315C22#1062505311yescharacteristic
316C22#1062510811yescharacteristic
317C4—22no—
318C4—81no—
319C4—462no—
320C4—462no—
321C4—1841no—
322C4C22⋊C4×D2311yescharacteristic
323C4#1062505311yescharacteristic
324C4C2×(C2×D23)⋊C411yescharacteristic
325C4#1062510811yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—42no—
330C2—922no—
331C2—922no—
332C2#1309227211yescharacteristic
subgroupG/H
centerC4#10625053
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#416C2
socleC2×C23#379
prime radical#13093253C2
cosocleC22×C4×C23C23
hypercenter#416D23
hypocenterC23#1794
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #13092435C2semidirect
3. #13092434C2semidirect
4. #13092414C2semidirect
5. #13092390C2semidirect
6. #13092383C2semidirect
7. C23×#416C2semidirect
10. #10625161C4semidirect
12. #10625160C4semidirect
21. C22×C8×C23C22semidirect
22. C23×#117C22semidirect
23. #10625097C22semidirect
24. C2×#67267C22semidirect
164. #416D23semidirect
188. C22×C8C2×D23semidirect
190. #117C2×D23semidirect
199. C23#1794semidirect

Maximal subgroups

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

subgroupindex
#130932532
#130924352
#130924342
#130924142
#130923902
#130923832
C23×#4162
#179423