Finite Group Databasebeta

← #15684906

Subgroups — #15684906

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×#10625089C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093082C211yesmaximal, characteristic, complemented
4#13093060C211yesmaximal, characteristic
5#13092660C211yesmaximal, characteristic, complemented
6#13092655C211yesmaximal, characteristic, complemented
7#13092636C211yesmaximal, characteristic, complemented
8#13092619C211yesmaximal, characteristic, complemented
9#13092578C211yesmaximal, characteristic, complemented
10#13092571C211yesmaximal, characteristic, complemented
11#13092566C211yesmaximal, characteristic, complemented
12#13092554C211yesmaximal, characteristic, complemented
13#13092519C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#497C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic
18C2×Q8×D23C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic
20C2×Q16×C23C2211yescharacteristic, complemented
21C2×Q16×C23C2211yescharacteristic, complemented
22C2×SD16×C23C2211yescharacteristic
23C2×SD16×C23C2211yescharacteristic
24C23×C4⋊Q8C2211yescharacteristic, complemented
25C23×#124C2211yescharacteristic
26#10625117C2211yescharacteristic
27#10625117C2211yescharacteristic
28#10625117C2211yescharacteristic, complemented
29C2×#67275C2211yescharacteristic, complemented
30C2×#67274C2211yescharacteristic
31C2×#67274C2211yescharacteristic
32#10625109C2211yescharacteristic
33C2×#67273C2211yescharacteristic
34#10625089—24no—
35SD16×D23—24no—
36C2×#67263C2211yescharacteristic
37C2×#67262C2211yescharacteristic, complemented
38C2×C8×D23C2211yescharacteristic
39#10625067—21no—
40#10625067—21no—
41#10625064—21no—
42#10625059—21no—
43#10625055—21no—
44#10625054—21no—
45#10625053—21no—
46C22⋊C4×D23—21no—
47C4×D92C2211yescharacteristic
48C4×D92C2211yescharacteristic
49C4×Dic46C2211yescharacteristic, complemented
50C23×#97C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625017C2211yescharacteristic, complemented
53#10625017C2211yescharacteristic, complemented
54#10625014C2211yescharacteristic
55#10625003C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic
57(C2×D23)⋊C8C2211yescharacteristic, complemented
58#10625000C2211yescharacteristic, complemented
59#10624998C2211yescharacteristic, complemented
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×Q8×C23C2311yescharacteristic
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68#67292—22no—
69#67292—41no—
70Q8×D23—22no—
71Q8×D23—22no—
72Q8×D23—41no—
73Q8×D23—41no—
74D4×D23—22no—
75D4×D23—41no—
76C2×D92—21no—
77C2×D92D411yescharacteristic
78C2×D92C2311yescharacteristic
79C2×C4×D23—21no—
80C2×C4×D23—21no—
81C2×C4×D23—21no—
82C2×C4×D23—21no—
83C2×C4×D23C2311yescharacteristic
84C2×C4×D23C2311yescharacteristic
85C2×Dic46—21no—
86C2×Dic46—21no—
87C2×Dic46C2311yescharacteristic
88Q16×C23—22no—
89Q16×C23—41no—
90SD16×C23—22no—
91SD16×C23—41no—
92C2×C8×C23C2311yescharacteristic
93C2×C8×C23C2311yescharacteristic
94C4⋊C4×C23—21no—
95C4⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C42×C23C2311yescharacteristic
99C22⋊Dic23—21no—
100#67275—22no—
101#67274—22no—
102#67274—22no—
103#67273—22no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4D411yescharacteristic
109(C2×D23)⋊C4D411yescharacteristic
110C4⋊Dic23D411yescharacteristic
111C4⋊Dic23C2311yescharacteristic
112C4⋊Dic23C2311yescharacteristic
113Dic23⋊C4—21no—
114Dic23⋊C4—21no—
115Dic23⋊C4—21no—
116Dic23⋊C4—21no—
117C4×Dic23—21no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120#67263D414yescomplemented
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C22×D23—21no—
125C22×D23—42no—
126C22×D23—42no—
127C22×D23—81no—
128C22×D23C2×D411yescharacteristic
129C22×D23C2×D411yescharacteristic
130Q8×C23—21no—
131Q8×C23—21no—
132Q8×C23—21no—
133Q8×C23—21no—
134Q8×C23—21no—
135Q8×C23—21no—
136D4×C23—21no—
137D4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23C2×D411yescharacteristic
142C2×C4×C23C2×D411yescharacteristic
143C2×C4×C23C2411yescharacteristic
144C22⋊D23—42no—
145C22⋊D23—81no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23C2×D411yescharacteristic
150C2×Dic23C2×D411yescharacteristic
151D92—22no—
152D92—21no—
153D92—42no—
154D92C2×D412yes—
155C4×D23—21no—
156C4×D23—21no—
157C4×D23—21no—
158C4×D23—21no—
159C4×D23—42no—
160C4×D23—42no—
161C4×D23—42no—
162C4×D23—81no—
163Dic46—21no—
164Dic46—42no—
165Dic46—42no—
166Dic46C2×D412yes—
167C8×C23—21no—
168C8×C23C2×D412yes—
169C23⋊C8—21no—
170C23⋊C8—21no—
171#3266—231nomaximal, Sylow
172C22×C23—41no—
173C22×C23—41no—
174C22×C23—41no—
175C22×C23C22×D411yescharacteristic
176C2×D23—21no—
177C2×D23—21no—
178C2×D23—21no—
179C2×D23—22no—
180C2×D23—21no—
181C2×D23—21no—
182C2×D23—41no—
183C2×D23—41no—
184C2×D23—84no—
185C2×D23#13712yescomplemented
186C4×C23—21no—
187C4×C23—21no—
188C4×C23—41no—
189C4×C23—41no—
190C4×C23—41no—
191C4×C23C22×D411yescharacteristic
192C4×C23H(5,𝔽2)11yescharacteristic
193Dic23—22no—
194Dic23—21no—
195Dic23—21no—
196Dic23—41no—
197Dic23—41no—
198C2×#137—231no—
199C22×SD16—231no—
200D4×Q8—231no—
201#546—231no—
202#497D2311yescharacteristic, complemented
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#435—231no—
213C2×C23—81no—
214C2×C23D4211yescharacteristic
215C2×C23C2×#13711yescharacteristic
216C2×C23#57711yescharacteristic
217D23—22no—
218D23—41no—
219D23—42no—
220C2×#41—231no—
221C22×Q8—231no—
222C22×Q8—231no—
223C22×D4—231no—
224#137—464no—
225C2×Q16—231no—
226C2×Q16C2×D2311yescharacteristic, complemented
227C2×Q16C2×D2311yescharacteristic, complemented
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16—231no—
231C2×SD16—231no—
232C2×SD16—464no—
233C2×SD16C2×D2311yescharacteristic
234C2×SD16C2×D2311yescharacteristic
235C2×M16—231no—
236C22×C8—231no—
237C4⋊Q8—461no—
238C4⋊Q8C2×D2311yescharacteristic, complemented
239#124C2×D2311yescharacteristic
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—231no—
252C4×D4—461no—
253C2×C22⋊C4—461no—
254#107—231no—
255C4⋊C8—231no—
256#103—231no—
257#103—231no—
258#103—231no—
259#103—231no—
260#102—231no—
261#102—231no—
262C22⋊C8—231no—
263C22⋊C8—231no—
264#97C2×D2311yescharacteristic, complemented
265C23#326611yescharacteristic, complemented, Sylow
266C24—461no—
267#41—462no—
268#41—921no—
269C2×Q8—231no—
270C2×Q8—461no—
271C2×Q8—461no—
272C2×Q8—462no—
273C2×Q8—462no—
274C2×Q8—921no—
275C2×Q8—921no—
276C2×Q8C22×D2311yescharacteristic
277C2×Q8C22×D2311yescharacteristic
278C2×Q8C22×D2311yescharacteristic
279C2×D4—231no—
280C2×D4—231no—
281C2×D4—461no—
282C2×D4—461no—
283C2×D4—462no—
284C2×D4—461no—
285C2×D4—921no—
286C2×D4C22×D2311yescharacteristic
287C22×C4—231no—
288C22×C4—231no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4—461no—
292C22×C4—461no—
293Q16—22no—
294Q16—41no—
295Q16—462no—
296SD16—22no—
297SD16—41no—
298SD16—234no—
299SD16—462no—
300SD16—462no—
301SD16—462no—
302M16—462no—
303C2×C8—231no—
304C2×C8—231no—
305C2×C8—462no—
306C2×C8C22×D2311yescharacteristic
307C2×C8C22×D2311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—231no—
311C4⋊C4—231no—
312C4⋊C4—231no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4—461no—
316C4⋊C4—461no—
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—231no—
320C22⋊C4—231no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C42—461no—
327C42C22×D2311yescharacteristic
328C23—21no—
329C23—231no—
330C23—231no—
331C23—461no—
332C23—922no—
333C23—922no—
334C23—1841no—
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—21no—
341Q8—232no—
342Q8—461no—
343Q8—922no—
344Q8—922no—
345D4—21no—
346D4—21no—
347D4—232no—
348D4—462no—
349D4—461no—
350D4—922no—
351D4—922no—
352D4—1841no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—231no—
357C2×C4—231no—
358C2×C4—461no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—461no—
364C2×C4—461no—
365C2×C4—922no—
366C2×C4—922no—
367C2×C4—922no—
368C2×C4—1841no—
369C2×C4D4×D2311yescharacteristic
370C2×C4D4×D2311yescharacteristic
371C2×C4C23×D2311yescharacteristic
372C8—21no—
373C8—461no—
374C8—461no—
375C8D4×D2312yes—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—232no—
380C22—461no—
381C22—461no—
382C22—461no—
383C22—461no—
384C22—461no—
385C22—462no—
386C22—921no—
387C22—921no—
388C22—1844no—
389C22C2×D4×D2311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—461no—
396C4—461no—
397C4—462no—
398C4—921no—
399C4—921no—
400C4C2×D4×D2311yescharacteristic
401C4#1062515511yescharacteristic
402C2—81no—
403C2—462no—
404C2—921no—
405C2—922no—
406C2#1309305211yescharacteristic
407C2#137×D2311yescharacteristic
408C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#497C2
socleC22×C23C22×D4
prime radical#13093060C2
hypercenter#497D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#10625089C2semidirect
2. C2×SD16×D23C2semidirect
3. #13093082C2semidirect
5. #13092660C2semidirect
6. #13092655C2semidirect
7. #13092636C2semidirect
8. #13092619C2semidirect
9. #13092578C2semidirect
10. #13092571C2semidirect
11. #13092566C2semidirect
12. #13092554C2semidirect
13. #13092519C2semidirect
14. #13092490C2semidirect
15. C23×#497C2semidirect
18. C2×Q8×D23C22semidirect
20. C2×Q16×C23C22semidirect
21. C2×Q16×C23C22semidirect
24. C23×C4⋊Q8C22semidirect
28. #10625117C22semidirect
29. C2×#67275C22semidirect
37. C2×#67262C22semidirect
49. C4×Dic46C22semidirect
50. C23×#97C22semidirect
51. #10625017C22semidirect
52. #10625017C22semidirect
53. #10625017C22semidirect
57. (C2×D23)⋊C8C22semidirect
58. #10625000C22semidirect
59. #10624998C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
120. #67263D4semidirect
185. C2×D23#137semidirect
202. #497D23semidirect
226. C2×Q16C2×D23semidirect
227. C2×Q16C2×D23semidirect
238. C4⋊Q8C2×D23semidirect
264. #97C2×D23semidirect
265. C23#3266semidirect

Maximal subgroups

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

subgroupindex
C2×#106250892
C2×SD16×D232
#130930822
#130930602
#130926602
#130926552
#130926362
#130926192
#130925782
#130925712
#130925662
#130925542
#130925192
#130924902
C23×#4972
#326623