Finite Group Databasebeta

← #15684912

Subgroups — #15684912

Order 2944.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625080C211yesmaximal, characteristic, complemented
2C22×#67263C211yesmaximal, characteristic, complemented
3D4×Dic46C211yesmaximal, characteristic, complemented
4#13093063C211yesmaximal, characteristic
5#13092811C211yesmaximal, characteristic, complemented
6#13092663C211yesmaximal, characteristic, complemented
7#13092658C211yesmaximal, characteristic, complemented
8#13092640C211yesmaximal, characteristic, complemented
9#13092623C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092575C211yesmaximal, characteristic, complemented
12#13092570C211yesmaximal, characteristic, complemented
13#13092558C211yesmaximal, characteristic, complemented
14#13092519C211yesmaximal, characteristic, complemented
15C23×#435C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C22×D92C2211yescharacteristic
18C22×Dic46C2211yescharacteristic
19C22×Dic46C2211yescharacteristic, complemented
20C2×M16×C23C2211yescharacteristic, complemented
21C22×C8×C23C2211yescharacteristic
22C4×D4×C23C2211yescharacteristic
23#10625108—21no—
24D4×Dic23—21no—
25#10625101C2211yescharacteristic
26#10625095C2211yescharacteristic
27#10625095C2211yescharacteristic
28#10625095C2211yescharacteristic, complemented
29#10625080—24no—
30C2×Dic92C2211yescharacteristic, complemented
31C2×Dic92C2211yescharacteristic, complemented
32C2×Dic92C2211yescharacteristic, complemented
33C2×#67263—24no—
34C2×#67263C2211yescharacteristic
35C2×#67263C2211yescharacteristic
36C2×#67263C2211yescharacteristic
37C2×#67263C2211yescharacteristic
38C2×#67263C2211yescharacteristic
39C2×#67263C2211yescharacteristic
40#10625065—21no—
41#10625059—21no—
42#10625055—21no—
43C22⋊C4×D23—21no—
44#10625049—21no—
45#10625049—21no—
46#10625046C2211yescharacteristic
47C4×D92C2211yescharacteristic
48#10625040C2211yescharacteristic, complemented
49C4×Dic46C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×C22⋊C8C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic, complemented
53C23×#97C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic
55#10625003C2211yescharacteristic
56#10625000C2211yescharacteristic, complemented
57#10624998C2211yescharacteristic, complemented
58#10624998C2211yescharacteristic, complemented
59#10624998C2211yescharacteristic, complemented
60#10624998C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×D4×C23D411yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C22×Dic23—21no—
68C22×Dic23—21no—
69#67288—22no—
70#67288—41no—
71C2×D92—22no—
72C2×D92—21no—
73C2×D92—41no—
74C2×D92C2311yescharacteristic
75C2×D92C2311yescharacteristic
76C2×C4×D23—21no—
77C2×C4×D23—21no—
78C2×Dic46—22no—
79C2×Dic46—22no—
80C2×Dic46—21no—
81C2×Dic46—21no—
82C2×Dic46—41no—
83C2×Dic46—41no—
84C2×Dic46C2311yescharacteristic
85C2×Dic46C2311yescharacteristic
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88M16×C23—22no—
89C2×C8×C23—22no—
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C2×C8×C23C2311yescharacteristic
93C2×C8×C23C2311yescharacteristic
94C4⋊C4×C23D411yescharacteristic
95C22⋊C4×C23D411yescharacteristic
96C22⋊C4×C23D411yescharacteristic
97C42×C23C2311yescharacteristic
98C22⋊Dic23—21no—
99C22⋊Dic23—21no—
100C22⋊Dic23—21no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105C4⋊Dic23—21no—
106C4⋊Dic23—21no—
107C4⋊Dic23C2311yescharacteristic
108C4⋊Dic23C2311yescharacteristic
109Dic23⋊C4—21no—
110Dic23⋊C4—21no—
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113C4×Dic23—21no—
114Dic92—22no—
115Dic92—22no—
116Dic92—41no—
117#67263—22no—
118#67263—22no—
119#67263—22no—
120#67263—22no—
121#67263—41no—
122#67263D414yescomplemented
123C23×C23C2×D411yescharacteristic
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—42no—
128C22×D23—42no—
129C22×D23—81no—
130D4×C23—22no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23C2×D411yescharacteristic
136C2×C4×C23C2×D411yescharacteristic
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2411yescharacteristic
140C22⋊D23—42no—
141C22⋊D23—81no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—42no—
149C2×Dic23—42no—
150D92—21no—
151D92—21no—
152D92—21no—
153D92—42no—
154D92C2×D412yes—
155C4×D23—42no—
156C4×D23—81no—
157Dic46—21no—
158Dic46—21no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46—42no—
165Dic46—42no—
166Dic46C2×D412yes—
167C8×C23—21no—
168C8×C23—21no—
169C8×C23—21no—
170C8×C23C2×D412yes—
171#3266—231nomaximal, Sylow
172C22×C23—21no—
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—21no—
176C22×C23—21no—
177C22×C23#13712yescomplemented
178C22×C23C22×D411yescharacteristic
179C2×D23—22no—
180C2×D23—41no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23—41no—
184C2×D23—41no—
185C2×D23—84no—
186C4×C23—21no—
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—21no—
190C4×C23C22×D411yescharacteristic
191C4×C23H(5,𝔽2)11yescharacteristic
192Dic23—22no—
193Dic23—41no—
194Dic23—41no—
195Dic23—41no—
196Dic23—41no—
197Dic23—41no—
198C2×#137—231no—
199C22×SD16—231no—
200D4×Q8—231no—
201#546—231no—
202#497—231no—
203#468—231no—
204#467—231no—
205#464—231no—
206#461—231no—
207#452—231no—
208#451—231no—
209#450—231no—
210#448—231no—
211#440—231no—
212#435D2311yescharacteristic, complemented
213C2×C23—22no—
214C2×C23—41no—
215C2×C23D4211yescharacteristic
216C2×C23C2×#13711yescharacteristic
217C2×C23#57711yescharacteristic
218D23—42no—
219D23—81no—
220C2×#41—231no—
221C22×Q8—231no—
222C22×Q8—231no—
223C22×D4—231no—
224#137—464no—
225C2×Q16—231no—
226C2×Q16—231no—
227C2×Q16—231no—
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16—231no—
231C2×SD16—231no—
232C2×SD16—231no—
233C2×SD16—231no—
234C2×SD16—464no—
235C2×M16C2×D2311yescharacteristic, complemented
236C22×C8C2×D2311yescharacteristic
237C4⋊Q8—231no—
238C4⋊Q8—461no—
239#124—231no—
240#123—461no—
241C22⋊Q8—231no—
242C22⋊Q8—231no—
243C22⋊Q8—231no—
244C22⋊Q8—461no—
245C22⋊Q8—461no—
246#121—231no—
247#121—461no—
248#120—461no—
249C4×Q8—231no—
250C4×D4—231no—
251C4×D4—461no—
252C4×D4C2×D2311yescharacteristic
253C2×C22⋊C4—461no—
254#107—231no—
255C4⋊C8C2×D2311yescharacteristic, complemented
256#103—231no—
257#103—231no—
258#103—231no—
259#103—231no—
260#102—231no—
261#102—231no—
262C22⋊C8C2×D2311yescharacteristic
263C22⋊C8C2×D2311yescharacteristic, complemented
264#97C2×D2311yescharacteristic, complemented
265C23#326611yescharacteristic, complemented, Sylow
266C24—461no—
267#41—462no—
268#41—921no—
269C2×Q8—231no—
270C2×Q8—231no—
271C2×Q8—231no—
272C2×Q8—231no—
273C2×Q8—462no—
274C2×Q8—462no—
275C2×Q8—461no—
276C2×Q8—461no—
277C2×Q8—921no—
278C2×Q8—921no—
279C2×D4—231no—
280C2×D4—231no—
281C2×D4—462no—
282C2×D4—461no—
283C2×D4—461no—
284C2×D4—461no—
285C2×D4—921no—
286C2×D4D9211yescharacteristic
287C22×C4—461no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4C22×D2311yescharacteristic
292C22×C4C22×D2311yescharacteristic
293Q16—462no—
294Q16—462no—
295Q16—921no—
296SD16—234no—
297SD16—462no—
298SD16—462no—
299SD16—462no—
300SD16—462no—
301SD16—921no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D2311yescharacteristic
305C2×C8C22×D2311yescharacteristic
306C2×C8C22×D2311yescharacteristic
307C2×C8C22×D2311yescharacteristic
308C4⋊C4—231no—
309C4⋊C4—231no—
310C4⋊C4—461no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4—461no—
316C4⋊C4D9211yescharacteristic
317C22⋊C4—461no—
318C22⋊C4—461no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4D9211yescharacteristic
325C22⋊C4D9211yescharacteristic
326C42—461no—
327C42C22×D2311yescharacteristic
328C23—461no—
329C23—461no—
330C23—922no—
331C23—922no—
332C23—1841no—
333C23C2×D9211yescharacteristic
334C23C2×D9211yescharacteristic
335Q8—232no—
336Q8—461no—
337Q8—461no—
338Q8—461no—
339Q8—461no—
340Q8—461no—
341Q8—461no—
342Q8—461no—
343Q8—922no—
344Q8—922no—
345D4—22no—
346D4—232no—
347D4—461no—
348D4—461no—
349D4—461no—
350D4—922no—
351D4—922no—
352D4—1841no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—461no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—922no—
364C2×C4—922no—
365C2×C4—922no—
366C2×C4—1841no—
367C2×C4C2×D9211yescharacteristic
368C2×C4C2×D9211yescharacteristic
369C2×C4C2×D9211yescharacteristic
370C2×C4C2×D9211yescharacteristic
371C2×C4C23×D2311yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D2312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—462no—
382C22—921no—
383C22—921no—
384C22—921no—
385C22—921no—
386C22—921no—
387C22—1844no—
388C22#1062508012yescomplemented
389C22C22×D9211yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—462no—
395C4—921no—
396C4—921no—
397C4—921no—
398C4—921no—
399C4—921no—
400C4C2×D4×D2311yescharacteristic
401C4#1062516011yescharacteristic
402C2—22no—
403C2—41no—
404C2—922no—
405C2—1841no—
406C2D4×D9211yescharacteristic
407C2C2×#1062508011yescharacteristic
408C2#1309322911yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#435C2
socleC22×C23C22×D4
prime radical#13093063C2
hypercenter#435D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#10625080C2semidirect
2. C22×#67263C2semidirect
3. D4×Dic46C2semidirect
5. #13092811C2semidirect
6. #13092663C2semidirect
7. #13092658C2semidirect
8. #13092640C2semidirect
9. #13092623C2semidirect
10. #13092581C2semidirect
11. #13092575C2semidirect
12. #13092570C2semidirect
13. #13092558C2semidirect
14. #13092519C2semidirect
15. C23×#435C2semidirect
19. C22×Dic46C22semidirect
20. C2×M16×C23C22semidirect
28. #10625095C22semidirect
30. C2×Dic92C22semidirect
31. C2×Dic92C22semidirect
32. C2×Dic92C22semidirect
48. #10625040C22semidirect
49. C4×Dic46C22semidirect
50. C23×C4⋊C8C22semidirect
52. C23×C22⋊C8C22semidirect
53. C23×#97C22semidirect
56. #10625000C22semidirect
57. #10624998C22semidirect
58. #10624998C22semidirect
59. #10624998C22semidirect
60. #10624998C22semidirect
122. #67263D4semidirect
177. C22×C23#137semidirect
212. #435D23semidirect
235. C2×M16C2×D23semidirect
255. C4⋊C8C2×D23semidirect
263. C22⋊C8C2×D23semidirect
264. #97C2×D23semidirect
265. C23#3266semidirect
388. C22#10625080semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
C22×#672632
D4×Dic462
#130930632
#130928112
#130926632
#130926582
#130926402
#130926232
#130925812
#130925752
#130925702
#130925582
#130925192
C23×#4352
#326623