Finite Group Databasebeta

← #15683573

Subgroups — #15683573

Order 2944.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13092952C211yesmaximal, characteristic
2C4×Q8×D23C211yesmaximal, characteristic, complemented
3#13092754C211yesmaximal, characteristic, complemented
4#13092737C211yesmaximal, characteristic
5#13092721C211yesmaximal, characteristic, complemented
6#13092640C211yesmaximal, characteristic, complemented
7#13092639C211yesmaximal, characteristic, complemented
8#13092574C211yesmaximal, characteristic, complemented
9#13092557C211yesmaximal, characteristic
10#13092523C211yesmaximal, characteristic, complemented
11#13092521C211yesmaximal, characteristic, complemented
12#13092520C211yesmaximal, characteristic, complemented
13#13092516C211yesmaximal, characteristic, complemented
14#13092473C211yesmaximal, characteristic, complemented
15C23×#479C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C23×#125C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19Q8×Dic23C2211yescharacteristic
20C2×#67275C2211yescharacteristic
21C2×#67274C2211yescharacteristic
22C2×Dic92C2211yescharacteristic
23C2×#67263C2211yescharacteristic
24#10625069—21no—
25#10625068C2211yescharacteristic
26#10625066C2211yescharacteristic
27#10625065—21no—
28#10625064—21no—
29#10625064C2211yescharacteristic
30#10625063—21no—
31C4⋊C4×D23—21no—
32C4⋊C4×D23C2211yescharacteristic
33#10625058—21no—
34#10625058C2211yescharacteristic
35#10625058C2211yescharacteristic
36#10625046C2211yescharacteristic
37C42×D23—21no—
38C42×D23C2211yescharacteristic
39C4×Dic46—21no—
40C4×Dic46C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#106C2211yescharacteristic
43C23×C4⋊C8C2211yescharacteristic
44C23×#103C2211yescharacteristic
45C23×#103C2211yescharacteristic
46#10625003C2211yescharacteristic
47(C2×D23)⋊C8C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10624998C2211yescharacteristic
50#10624997C2211yescharacteristic
51#10624997C2211yescharacteristic
52#10624992C2211yescharacteristic
53#10624992C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58C4⋊(C23⋊C8)C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60Q8×D23—22no—
61Q8×D23—22no—
62C2×D92—21no—
63C2×D92C2311yescharacteristic
64C2×C4×D23—21no—
65C2×C4×D23—21no—
66C2×C4×D23—21no—
67C2×C4×D23D411yescharacteristic
68C2×C4×D23D411yescharacteristic
69C2×C4×D23C2311yescharacteristic
70C2×Dic46—21no—
71C2×Dic46C2311yescharacteristic
72C2×Dic46C2311yescharacteristic
73C2×C8×C23C2311yescharacteristic
74C2×C8×C23C2311yescharacteristic
75C4⋊C4×C23—21no—
76C4⋊C4×C23—21no—
77C4⋊C4×C23—21no—
78C4⋊C4×C23C2311yescharacteristic
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C42×C23—21no—
82C42×C23C2311yescharacteristic
83#67275—22no—
84#67274—22no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90C4⋊Dic23—21no—
91C4⋊Dic23—21no—
92C4⋊Dic23C2311yescharacteristic
93Dic23⋊C4—21no—
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97C4×Dic23—21no—
98C4×Dic23—21no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23D411yescharacteristic
102C4×Dic23D411yescharacteristic
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106Dic92—22no—
107#67263—22no—
108C22×D23—21no—
109C22×D23C2×D411yescharacteristic
110Q8×C23—21no—
111Q8×C23#4112yes—
112C2×C4×C23—21no—
113C2×C4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23C2×D411yescharacteristic
117C2×C4×C23C2×D411yescharacteristic
118C2×C4×C23C2411yescharacteristic
119C2×Dic23—21no—
120C2×Dic23—21no—
121C2×Dic23—21no—
122C2×Dic23C2×D411yescharacteristic
123C2×Dic23C2×D411yescharacteristic
124C2×Dic23C2×D411yescharacteristic
125D92—21no—
126D92—21no—
127D92—42no—
128C4×D23—24no—
129C4×D23—22no—
130C4×D23—21no—
131C4×D23—21no—
132C4×D23—41no—
133C4×D23—42no—
134C4×D23—42no—
135Dic46—24no—
136Dic46—21no—
137Dic46—21no—
138Dic46—21no—
139Dic46#4112yes—
140C8×C23—21no—
141C8×C23—21no—
142C23⋊C8—21no—
143C23⋊C8—21no—
144#3117—231nomaximal, Sylow
145C22×C23C22×D411yescharacteristic
146C2×D23—21no—
147C2×D23—21no—
148C2×D23—41no—
149C2×D23—41no—
150C2×D23—41no—
151C2×D23#13712yes—
152C4×C23—22no—
153C4×C23—21no—
154C4×C23—21no—
155C4×C23—41no—
156C4×C23—41no—
157C4×C23—41no—
158C4×C23C2×#4111yescharacteristic
159C4×C23C2×#4111yescharacteristic
160Dic23—21no—
161Dic23—22no—
162Dic23—21no—
163Dic23—21no—
164Dic23—41no—
165Dic23—41no—
166#529—231no—
167C2×C4×Q8—231no—
168#484—231no—
169#481—231no—
170#479—231no—
171#479D2311yescharacteristic, complemented
172#464—231no—
173#464—231no—
174#451—231no—
175#448—231no—
176#441—231no—
177#441—231no—
178#440—231no—
179#440—231no—
180#432—231no—
181C2×C23#52511yescharacteristic
182C2×C23C2×#13711yescharacteristic
183C2×C23#57511yescharacteristic
184D23—22no—
185D23—81no—
186C22×Q8—231no—
187C2×Q16—231no—
188C2×Q16—231no—
189C2×SD16—231no—
190C2×SD16—231no—
191#126—461no—
192#125C2×D2311yescharacteristic
193#124—231no—
194#123—461no—
195C22⋊Q8—231no—
196#121—231no—
197C4×Q8—231no—
198C4×Q8—231no—
199C4×Q8—231no—
200C4×Q8—231no—
201C4×Q8—461no—
202C4×Q8—461no—
203C4×Q8C2×D2311yescharacteristic
204C4×D4—231no—
205C4×D4—461no—
206#117—461no—
207C2×C4⋊C4—231no—
208C2×C4⋊C4—461no—
209C2×C42—231no—
210C2×C42—461no—
211#107—231no—
212#107C2×D2311yescharacteristic
213#106—231no—
214#106C2×D2311yescharacteristic
215C4⋊C8—231no—
216C4⋊C8C2×D2311yescharacteristic
217#103—231no—
218#103—231no—
219#103—231no—
220#103—231no—
221#103C2×D2311yescharacteristic
222#103C2×D2311yescharacteristic
223#102—231no—
224#102—231no—
225C22⋊C8—231no—
226C22⋊C8—231no—
227#97—231no—
228#97—231no—
229C23#311711yescharacteristic, complemented, Sylow
230C2×Q8—231no—
231C2×Q8—231no—
232C2×Q8—461no—
233C2×Q8—462no—
234C2×Q8—462no—
235C2×Q8C22×D2311yescharacteristic
236C2×D4—231no—
237C2×D4—461no—
238C22×C4—231no—
239C22×C4—231no—
240C22×C4—231no—
241C22×C4—461no—
242C22×C4—461no—
243C22×C4—461no—
244Q16—462no—
245Q16—462no—
246SD16—462no—
247SD16—462no—
248C2×C8—231no—
249C2×C8—231no—
250C2×C8C22×D2311yescharacteristic
251C2×C8C22×D2311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—231no—
256C4⋊C4—461no—
257C4⋊C4—461no—
258C4⋊C4—461no—
259C4⋊C4—461no—
260C4⋊C4—461no—
261C4⋊C4—461no—
262C4⋊C4C22×D2311yescharacteristic
263C4⋊C4C22×D2311yescharacteristic
264C4⋊C4C22×D2311yescharacteristic
265C22⋊C4—461no—
266C22⋊C4—461no—
267C22⋊C4—461no—
268C22⋊C4—461no—
269C22⋊C4—461no—
270C42—21no—
271C42—231no—
272C42—231no—
273C42—231no—
274C42—461no—
275C42—461no—
276C42—461no—
277C42—461no—
278C42C22×D2311yescharacteristic
279C23—231no—
280C23—461no—
281Q8—21no—
282Q8—232no—
283Q8—464no—
284Q8—461no—
285Q8—461no—
286Q8—461no—
287Q8#6729212yes—
288D4—461no—
289D4—461no—
290D4—922no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—231no—
296C2×C4—231no—
297C2×C4—231no—
298C2×C4—462no—
299C2×C4—464no—
300C2×C4—461no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4—461no—
305C2×C4—921no—
306C2×C4—922no—
307C2×C4—922no—
308C2×C4D4×D2311yescharacteristic
309C2×C4D4×D2311yescharacteristic
310C2×C4C23×D2311yescharacteristic
311C8—21no—
312C8—21no—
313C8—461no—
314C8—461no—
315C22—232no—
316C22—461no—
317C22—461no—
318C22—921no—
319C22—921no—
320C22—921no—
321C22C2×D4×D2311yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—461no—
329C4—462no—
330C4—461no—
331C4—461no—
332C4—921no—
333C4—921no—
334C4C2×#6729211yescharacteristic
335C4#41×D2311yescharacteristic
336C2—462no—
337C2—1841no—
338C2#1309293011yescharacteristic
339C2#137×D2311yescharacteristic
340C2#1309321411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#479C2
socleC22×C23C22×D4
prime radical#10625066C22
hypercenter#479D23
hypocenterC23#3117
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D23C2semidirect
3. #13092754C2semidirect
5. #13092721C2semidirect
6. #13092640C2semidirect
7. #13092639C2semidirect
8. #13092574C2semidirect
10. #13092523C2semidirect
11. #13092521C2semidirect
12. #13092520C2semidirect
13. #13092516C2semidirect
14. #13092473C2semidirect
15. C23×#479C2semidirect
171. #479D23semidirect
229. C23#3117semidirect

Maximal subgroups

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

subgroupindex
#130929522
C4×Q8×D232
#130927542
#130927372
#130927212
#130926402
#130926392
#130925742
#130925572
#130925232
#130925212
#130925202
#130925162
#130924732
C23×#4792
#311723