Finite Group Databasebeta

← #15683566

Subgroups — #15683566

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#13092949C211yesmaximal, characteristic
2C4×Q8×D23C211yesmaximal, characteristic, complemented
3#13092754C211yesmaximal, characteristic, complemented
4#13092734C211yesmaximal, characteristic
5#13092723C211yesmaximal, characteristic, complemented
6#13092722C211yesmaximal, characteristic, complemented
7#13092638C211yesmaximal, characteristic, complemented
8#13092637C211yesmaximal, characteristic, complemented
9#13092574C211yesmaximal, characteristic, complemented
10#13092554C211yesmaximal, characteristic
11#13092525C211yesmaximal, characteristic, complemented
12#13092522C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092472C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21C2×#67275C2211yescharacteristic
22#10625109C2211yescharacteristic
23#10625107C2211yescharacteristic
24C2×#67273C2211yescharacteristic
25C4×C22⋊D23—21no—
26#10625097—21no—
27C2×Dic92C2211yescharacteristic
28#10625068C2211yescharacteristic
29C4⋊C4×D23—21no—
30C4⋊C4×D23C2211yescharacteristic
31#10625061C2211yescharacteristic
32#10625058—21no—
33#10625058C2211yescharacteristic
34#10625054—21no—
35#10625050—21no—
36C42×D23—21no—
37C42×D23C2211yescharacteristic
38C4×Dic46—21no—
39C4×Dic46C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C23×#97C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625014C2211yescharacteristic
47(C2×D23)⋊C8C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10624999C2211yescharacteristic
50#10624998C2211yescharacteristic
51#10624998C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63Q8×D23—22no—
64Q8×D23—22no—
65C2×C4×D23—21no—
66C2×C4×D23—21no—
67C2×C4×D23D411yescharacteristic
68C2×C4×D23D411yescharacteristic
69C2×C4×D23C2311yescharacteristic
70C2×Dic46—21no—
71C2×Dic46C2311yescharacteristic
72C2×Dic46C2311yescharacteristic
73SD16×C23—22no—
74C2×C8×C23C2311yescharacteristic
75C2×C8×C23C2311yescharacteristic
76C4⋊C4×C23—21no—
77C4⋊C4×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C42×C23—21no—
81C42×C23C2311yescharacteristic
82C22⋊Dic23—21no—
83C22⋊Dic23—21no—
84C22⋊Dic23—21no—
85#67275—22no—
86#67273—22no—
87(C2×D23)⋊C4—21no—
88C4⋊Dic23—21no—
89C4⋊Dic23—21no—
90C4⋊Dic23—21no—
91C4⋊Dic23C2311yescharacteristic
92C4⋊Dic23C2311yescharacteristic
93Dic23⋊C4—21no—
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98C4×Dic23—21no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23D411yescharacteristic
103C4×Dic23D411yescharacteristic
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107Dic92—22no—
108C23×C23—21no—
109C22×D23C2×D411yescharacteristic
110Q8×C23—21no—
111Q8×C23#4112yes—
112D4×C23—21no—
113D4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—42no—
118C2×C4×C23C2×D411yescharacteristic
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2411yescharacteristic
121C22⋊D23—42no—
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23C2×D411yescharacteristic
127C2×Dic23C2×D411yescharacteristic
128C2×Dic23C2×D411yescharacteristic
129C4×D23—24no—
130C4×D23—22no—
131C4×D23—21no—
132C4×D23—21no—
133C4×D23—41no—
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×C23—41no—
146C22×C23—41no—
147C22×C23—41no—
148C22×C23C22×D411yescharacteristic
149C2×D23—21no—
150C2×D23—21no—
151C2×D23#13712yes—
152C4×C23—22no—
153C4×C23—21no—
154C4×C23—21no—
155C4×C23—41no—
156C4×C23—41no—
157C4×C23C2×#4111yescharacteristic
158C4×C23C2×#4111yescharacteristic
159Dic23—21no—
160Dic23—22no—
161Dic23—21no—
162Dic23—21no—
163Dic23—41no—
164Dic23—41no—
165Dic23—41no—
166#529—231no—
167C2×C4×Q8—231no—
168#484—231no—
169#481—231no—
170#479—231no—
171#479—231no—
172#464—231no—
173#464—231no—
174#451—231no—
175#448—231no—
176#441—231no—
177#441—231no—
178#440—231no—
179#440D2311yescharacteristic, complemented
180#432—231no—
181C2×C23—81no—
182C2×C23#52511yescharacteristic
183C2×C23C2×#13711yescharacteristic
184C2×C23#57511yescharacteristic
185D23—22no—
186C22×Q8—231no—
187C2×Q16—231no—
188C2×Q16—231no—
189C2×SD16—231no—
190C2×SD16C2×D2311yescharacteristic
191#126—461no—
192#125—231no—
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—461no—
205C4×D4C2×D2311yescharacteristic
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#106—231no—
215C4⋊C8—231no—
216C4⋊C8—231no—
217#103—231no—
218#103—231no—
219#103—231no—
220#103—231no—
221#103—231no—
222#103C2×D2311yescharacteristic
223#102—231no—
224#102C2×D2311yescharacteristic
225C22⋊C8—231no—
226C22⋊C8—231no—
227#97—231no—
228#97C2×D2311yescharacteristic
229C23#311711yescharacteristic, complemented, Sylow
230C2×Q8—231no—
231C2×Q8—231no—
232C2×Q8—461no—
233C2×Q8—462no—
234C2×Q8—462no—
235C2×Q8C22×D2311yescharacteristic
236C2×D4—461no—
237C2×D4C22×D2311yescharacteristic
238C22×C4—21no—
239C22×C4—231no—
240C22×C4—231no—
241C22×C4—231no—
242C22×C4—461no—
243C22×C4—461no—
244Q16—462no—
245Q16—462no—
246SD16—22no—
247SD16—462no—
248C2×C8—231no—
249C2×C8—231no—
250C2×C8C22×D2311yescharacteristic
251C2×C8C22×D2311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—231no—
254C4⋊C4—231no—
255C4⋊C4—461no—
256C4⋊C4—461no—
257C4⋊C4—461no—
258C4⋊C4—461no—
259C4⋊C4—461no—
260C4⋊C4—461no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4C22×D2311yescharacteristic
264C4⋊C4C22×D2311yescharacteristic
265C22⋊C4—21no—
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—21no—
280C23—231no—
281Q8—21no—
282Q8—232no—
283Q8—464no—
284Q8—461no—
285Q8—461no—
286Q8—461no—
287Q8#6728812yes—
288D4—21no—
289D4—21no—
290D4—922no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
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—461no—
306C2×C4—921no—
307C2×C4—922no—
308C2×C4D4×D2311yescharacteristic
309C2×C4D4×D2311yescharacteristic
310C2×C4C23×D2311yescharacteristic
311C8—21no—
312C8—21no—
313C8—461no—
314C8—461no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—232no—
319C22—461no—
320C22—461no—
321C22C2×D4×D2311yescharacteristic
322C4—22no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—461no—
328C4—462no—
329C4—461no—
330C4—461no—
331C4—921no—
332C4—921no—
333C4—921no—
334C4C2×#6728811yescharacteristic
335C4#41×D2311yescharacteristic
336C2—81no—
337C2—462no—
338C2#1309292611yescharacteristic
339C2#137×D2311yescharacteristic
340C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
prime radical#10625109C22
hypercenter#440D23
hypocenterC23#3117
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D23C2semidirect
3. #13092754C2semidirect
5. #13092723C2semidirect
6. #13092722C2semidirect
7. #13092638C2semidirect
8. #13092637C2semidirect
9. #13092574C2semidirect
11. #13092525C2semidirect
12. #13092522C2semidirect
13. #13092517C2semidirect
14. #13092472C2semidirect
15. C23×#440C2semidirect
179. #440D23semidirect
229. C23#3117semidirect

Maximal subgroups

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

subgroupindex
#130929492
C4×Q8×D232
#130927542
#130927342
#130927232
#130927222
#130926382
#130926372
#130925742
#130925542
#130925252
#130925222
#130925172
#130924722
C23×#4402
#311723