Finite Group Databasebeta

← #15682226

Subgroups — #15682226

Order 2944.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625082C211yesmaximal, characteristic
2#13092896C211yesmaximal, characteristic, complemented
3#13092889C211yesmaximal, characteristic, complemented
4#13092526C211yesmaximal, characteristic, complemented
5#13092519C211yesmaximal, characteristic, complemented
6#13092514C211yesmaximal, characteristic, complemented
7#13092504C211yesmaximal, characteristic, complemented
8C4×#67273C211yesmaximal, characteristic, complemented
9D8×Dic23C211yesmaximal, characteristic, complemented
10C4×#67272C211yesmaximal, characteristic, complemented
11#13092456C211yesmaximal, characteristic, complemented
12#13092410C211yesmaximal, characteristic, complemented
13#102×D23C211yesmaximal, characteristic, complemented
14#13092374C211yesmaximal, characteristic, complemented
15C23×#442C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×D8×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20C4×D4×C23C2211yescharacteristic, complemented
21D4×Dic23C2211yescharacteristic
22D4×Dic23C2211yescharacteristic, complemented
23C2×#67273C2211yescharacteristic
24C2×#67272C2211yescharacteristic
25C4×C22⋊D23—21no—
26C4×C22⋊D23—21no—
27C2×(C2×D23)⋊C4—21no—
28C2×Dic23⋊C4—21no—
29#10625082C418yescomplemented
30C2×#67263C2211yescharacteristic
31C2×#67262C2211yescharacteristic
32C2×C8×D23C2211yescharacteristic
33#10625064C2211yescharacteristic
34#10625063C2211yescharacteristic
35C4⋊C4×D23C2211yescharacteristic
36#10625058C2211yescharacteristic, complemented
37(C22⋊D23)⋊C4—21no—
38(C22⋊D23)⋊C4—21no—
39C22⋊C4×D23—21no—
40#10625048—21no—
41C4×D92C2211yescharacteristic
42#10625043C2211yescharacteristic
43C4×Dic46C2211yescharacteristic, complemented
44C23×#106C2211yescharacteristic, complemented
45C23×#102C2211yescharacteristic
46C23×#102C2211yescharacteristic, complemented
47C23×#97C2211yescharacteristic, complemented
48#10625014C2211yescharacteristic
49#10625014C2211yescharacteristic, complemented
50#10625003C2211yescharacteristic
51#10625000C2211yescharacteristic, complemented
52#10624998C2211yescharacteristic, complemented
53#10624997C2211yescharacteristic, complemented
54C8×Dic23C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic
57#10624990C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C4×C23⋊C8C2211yescharacteristic, complemented
60C23×D23—21no—
61C2×D4×C23C2311yescharacteristic
62C2×D4×C23C2311yescharacteristic
63C22×C4×C23—21no—
64C22×C4×C23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C22×Dic23—21no—
68C22×Dic23—21no—
69C22×Dic23—21no—
70#67290—22no—
71#67290C2×C414yescomplemented
72D4×D23—22no—
73D4×D23C2×C414yescomplemented
74C2×D92C2311yescharacteristic
75C2×C4×D23—21no—
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×C4×D23C2311yescharacteristic
79C2×Dic46C2311yescharacteristic
80D8×C23C2×C414yescomplemented
81C2×C8×C23C2311yescharacteristic
82C2×C8×C23C2311yescharacteristic
83C4⋊C4×C23C2311yescharacteristic
84C4⋊C4×C23C2311yescharacteristic
85C22⋊C4×C23—21no—
86C22⋊C4×C23—21no—
87C42×C23C2311yescharacteristic
88C22⋊Dic23—21no—
89C22⋊Dic23—21no—
90#67273C2×C414yescomplemented
91#67272C2×C414yescomplemented
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4—21no—
94(C2×D23)⋊C4—21no—
95(C2×D23)⋊C4D411yescharacteristic
96(C2×D23)⋊C4D411yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98C4⋊Dic23C2311yescharacteristic
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4—21no—
102Dic23⋊C4D411yescharacteristic
103Dic23⋊C4D411yescharacteristic
104C4×Dic23—21no—
105C4×Dic23—21no—
106C4×Dic23—21no—
107C4×Dic23C2311yescharacteristic
108C2×C23⋊C8C2311yescharacteristic
109C2×C23⋊C8C2311yescharacteristic
110#67263C2×C414yescomplemented
111#67262C2×C414yescomplemented
112C8×D23—22no—
113C23×C23—21no—
114C23×C23—21no—
115C22×D23—21no—
116C22×D23—24no—
117C22×D23—81no—
118C22×D23—81no—
119C22×D23C2×D411yescharacteristic
120D4×C23—21no—
121D4×C23—21no—
122D4×C23C22×C412yes—
123D4×C23C22×C412yes—
124C2×C4×C23—21no—
125C2×C4×C23—21no—
126C2×C4×C23—81no—
127C2×C4×C23—81no—
128C2×C4×C23C2×D411yescharacteristic
129C2×C4×C23C2×D411yescharacteristic
130C2×C4×C23C2411yescharacteristic
131C22⋊D23—24no—
132C22⋊D23—24no—
133C2×Dic23—21no—
134C2×Dic23—24no—
135C2×Dic23—21no—
136C2×Dic23—21no—
137C2×Dic23—81no—
138C2×Dic23—81no—
139C2×Dic23C2×D411yescharacteristic
140C2×Dic23C2×D411yescharacteristic
141C2×Dic23C2×D411yescharacteristic
142D92—21no—
143D92C22×C412yes—
144C4×D23—81no—
145C4×D23—81no—
146C4×D23—81no—
147C4×D23C22×C412yes—
148C4×D23#4112yes—
149Dic46—21no—
150Dic46C22×C412yes—
151C8×C23—21no—
152C8×C23C22×C412yes—
153C23⋊C8—21no—
154C23⋊C8C22×C412yes—
155#2946—231nomaximal, Sylow
156C22×C23—22no—
157C22×C23—22no—
158C22×C23—41no—
159C22×C23—41no—
160C22×C23—41no—
161C22×C23—41no—
162C22×C23C22×D411yescharacteristic
163C2×D23—21no—
164C2×D23—21no—
165C2×D23—22no—
166C2×D23—41no—
167C2×D23—41no—
168C2×D23—84no—
169C2×D23C4×D412yes—
170C4×C23—21no—
171C4×C23—21no—
172C4×C23—41no—
173C4×C23—41no—
174C4×C23C23×C411yescharacteristic
175C4×C23C2×#4111yescharacteristic
176Dic23—22no—
177Dic23—21no—
178Dic23—21no—
179Dic23—41no—
180Dic23—41no—
181Dic23C4×D412yes—
182C2×AGL(1,ℤ/8)—231no—
183#520—231no—
184#518—231no—
185#442—231no—
186#442D2311yescharacteristic, complemented
187#440—231no—
188#440—231no—
189C4×SD16—231no—
190C4×SD16—231no—
191C4×D8—231no—
192C4×D8—231no—
193#428—231no—
194#416—231no—
195C2×#102—231no—
196#405—231no—
197C2×C23—42no—
198C2×C23—42no—
199C2×C23C2×C4×D411yescharacteristic
200C2×C23#57611yescharacteristic
201C2×C23#57711yescharacteristic
202D23—22no—
203D23—42no—
204C2×#41—231no—
205C22×D4—231no—
206AGL(1,ℤ/8)—238no—
207C2×SD16—231no—
208C2×SD16—231no—
209C2×D8—231no—
210C2×D8C2×D2311yescharacteristic
211C2×M16—231no—
212C22×C8—231no—
213C4×Q8—231no—
214C4×Q8—231no—
215C4×D4—231no—
216C4×D4—231no—
217C4×D4—231no—
218C4×D4—231no—
219C4×D4—461no—
220C4×D4—461no—
221C4×D4—461no—
222C4×D4—461no—
223C4×D4C2×D2311yescharacteristic
224C4×D4C2×D2311yescharacteristic, complemented
225#117—231no—
226#117—231no—
227#117—461no—
228C2×C4⋊C4—231no—
229C2×C4⋊C4—461no—
230C2×C22⋊C4—461no—
231C2×C22⋊C4—461no—
232#107—231no—
233#107—231no—
234#106—231no—
235#106C2×D2311yescharacteristic, complemented
236#103—231no—
237#103—231no—
238#102—231no—
239#102—231no—
240#102—231no—
241#102—231no—
242#102C2×D2311yescharacteristic
243#102C2×D2311yescharacteristic, complemented
244#97—231no—
245#97C2×D2311yescharacteristic, complemented
246C4×C8—231no—
247C4×C8—231no—
248C23#294611yescharacteristic, complemented, Sylow
249C24—461no—
250#41—234no—
251#41—462no—
252C2×Q8—231no—
253C2×D4—234no—
254C2×D4—231no—
255C2×D4—462no—
256C2×D4—461no—
257C2×D4—461no—
258C2×D4C22×D2311yescharacteristic
259C2×D4C22×D2311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—231no—
263C22×C4—461no—
264C22×C4—461no—
265C22×C4—461no—
266C22×C4—461no—
267C22×C4—461no—
268C22×C4—461no—
269SD16—234no—
270SD16—234no—
271D8—234no—
272D8C4×D2314yescomplemented
273M16—234no—
274C2×C8—231no—
275C2×C8—231no—
276C2×C8—462no—
277C2×C8C22×D2311yescharacteristic
278C2×C8C22×D2311yescharacteristic
279C4⋊C4—231no—
280C4⋊C4—231no—
281C4⋊C4—231no—
282C4⋊C4—231no—
283C4⋊C4—461no—
284C4⋊C4—461no—
285C4⋊C4—461no—
286C4⋊C4C22×D2311yescharacteristic
287C4⋊C4C22×D2311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—231no—
291C22⋊C4—231no—
292C22⋊C4—461no—
293C22⋊C4—461no—
294C22⋊C4—461no—
295C22⋊C4—461no—
296C22⋊C4—461no—
297C42—231no—
298C42—461no—
299C42—461no—
300C42—461no—
301C42C22×D2311yescharacteristic
302C23—21no—
303C23—21no—
304C23—231no—
305C23—464no—
306C23—461no—
307C23—1841no—
308C23—1841no—
309Q8—232no—
310Q8—461no—
311D4—21no—
312D4—21no—
313D4—232no—
314D4—464no—
315D4—464no—
316D4—461no—
317D4C2×C4×D2312yes—
318D4C2×C4×D2312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—231no—
324C2×C4—232no—
325C2×C4—232no—
326C2×C4—231no—
327C2×C4—231no—
328C2×C4—464no—
329C2×C4—461no—
330C2×C4—461no—
331C2×C4—461no—
332C2×C4—1841no—
333C2×C4—1841no—
334C2×C4—1841no—
335C2×C4—1841no—
336C2×C4—1841no—
337C2×C4D4×D2311yescharacteristic
338C2×C4D4×D2311yescharacteristic
339C2×C4C23×D2311yescharacteristic
340C8—21no—
341C8—232no—
342C8—461no—
343C8C2×C4×D2312yes—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—232no—
351C22—461no—
352C22—461no—
353C22—462no—
354C22—921no—
355C22—921no—
356C22—1844no—
357C22C2×D4×D2311yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—232no—
363C4—462no—
364C4—461no—
365C4—461no—
366C4—921no—
367C4—921no—
368C4C22×C4×D2311yescharacteristic
369C4#41×D2311yescharacteristic
370C2—42no—
371C2—42no—
372C2—462no—
373C2—922no—
374C2C4×D4×D2311yescharacteristic
375C2#1309322111yescharacteristic
376C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×#442C2
socleC22×C23C22×D4
prime radicalC2×#10625082C2
cosocleC2×C4×C23C24
hypercenter#442D23
hypocenterC23#2946
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #13092896C2semidirect
3. #13092889C2semidirect
4. #13092526C2semidirect
5. #13092519C2semidirect
6. #13092514C2semidirect
7. #13092504C2semidirect
8. C4×#67273C2semidirect
9. D8×Dic23C2semidirect
10. C4×#67272C2semidirect
11. #13092456C2semidirect
12. #13092410C2semidirect
13. #102×D23C2semidirect
14. #13092374C2semidirect
15. C23×#442C2semidirect
20. C4×D4×C23C22semidirect
22. D4×Dic23C22semidirect
29. #10625082C4semidirect
36. #10625058C22semidirect
43. C4×Dic46C22semidirect
44. C23×#106C22semidirect
46. C23×#102C22semidirect
47. C23×#97C22semidirect
49. #10625014C22semidirect
51. #10625000C22semidirect
52. #10624998C22semidirect
53. #10624997C22semidirect
54. C8×Dic23C22semidirect
55. #10624992C22semidirect
57. #10624990C22semidirect
58. #10624989C22semidirect
59. C4×C23⋊C8C22semidirect
71. #67290C2×C4semidirect
73. D4×D23C2×C4semidirect
80. D8×C23C2×C4semidirect
90. #67273C2×C4semidirect
91. #67272C2×C4semidirect
110. #67263C2×C4semidirect
111. #67262C2×C4semidirect
186. #442D23semidirect
224. C4×D4C2×D23semidirect
235. #106C2×D23semidirect
243. #102C2×D23semidirect
245. #97C2×D23semidirect
248. C23#2946semidirect
272. D8C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
#130928962
#130928892
#130925262
#130925192
#130925142
#130925042
C4×#672732
D8×Dic232
C4×#672722
#130924562
#130924102
#102×D232
#130923742
C23×#4422
#294623