Finite Group Databasebeta

← #15683034

Subgroups — #15683034

Order 2944.

492 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D23C211yesmaximal, characteristic, complemented
2C2×#10625078C211yesmaximal, characteristic, complemented
3#13092990C211yesmaximal, characteristic, complemented
4#13092983C211yesmaximal, characteristic
5#13092664C211yesmaximal, characteristic, complemented
6#13092663C211yesmaximal, characteristic, complemented
7#13092660C211yesmaximal, characteristic, complemented
8#13092649C211yesmaximal, characteristic, complemented
9#13092648C211yesmaximal, characteristic, complemented
10#13092645C211yesmaximal, characteristic, complemented
11#13092644C211yesmaximal, characteristic, complemented
12#13092454C211yesmaximal, characteristic, complemented
13#13092424C211yesmaximal, characteristic, complemented
14#13092420C211yesmaximal, characteristic, complemented
15C23×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic
20C2×M16×C23C2211yescharacteristic, complemented
21C23×C22⋊Q8C2211yescharacteristic, complemented
22C23×#121C2211yescharacteristic
23#10625117C2211yescharacteristic, complemented
24C2×#67274C2211yescharacteristic
25#10625111—21no—
26#10625109C2211yescharacteristic
27#10625108—21no—
28C2×#67273C2211yescharacteristic
29#10625101C2211yescharacteristic
30#10625095C2211yescharacteristic, complemented
31C22×C23⋊C8C2211yescharacteristic, complemented
32SD16×D23—24no—
33#10625078—24no—
34C2×#67263C2211yescharacteristic
35C2×#67262C2211yescharacteristic
36C2×#67262C2211yescharacteristic, complemented
37C2×C8×D23C2211yescharacteristic
38C2×C8×D23C2211yescharacteristic, complemented
39#10625068C2211yescharacteristic, complemented
40#10625066C2211yescharacteristic
41#10625065—21no—
42#10625063C2211yescharacteristic
43#10625063C2211yescharacteristic
44#10625059—21no—
45#10625056—21no—
46#10625056—21no—
47#10625054—21no—
48#10625053—21no—
49C23×#107C2211yescharacteristic, complemented
50C23×#103C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic
52#10625017C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic
55#10625000C2211yescharacteristic, complemented
56#10624998C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624991C2211yescharacteristic
59#10624990C2211yescharacteristic, complemented
60#10624990C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23D411yescharacteristic
70C2×C22⋊D23D411yescharacteristic
71Q8×D23—22no—
72Q8×D23—22no—
73D4×D23—22no—
74D4×D23—22no—
75#67288—22no—
76#67288—22no—
77C2×D92—21no—
78C2×D92D411yescharacteristic
79C2×D92C2311yescharacteristic
80C2×C4×D23—21no—
81C2×C4×D23C2311yescharacteristic
82C2×C4×D23C2311yescharacteristic
83C2×Dic46—21no—
84C2×Dic46D411yescharacteristic
85C2×Dic46C2311yescharacteristic
86SD16×C23—22no—
87M16×C23—22no—
88C2×C8×C23C2311yescharacteristic
89C2×C8×C23C2311yescharacteristic
90C4⋊C4×C23—21no—
91C4⋊C4×C23C2311yescharacteristic
92C4⋊C4×C23C2311yescharacteristic
93C22⋊C4×C23—21no—
94C22⋊C4×C23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97#67274—22no—
98#67273—22no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—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⋊Dic23C2311yescharacteristic
107C4⋊Dic23C2311yescharacteristic
108Dic23⋊C4—21no—
109Dic23⋊C4—21no—
110C4×Dic23—21no—
111C4×Dic23—21no—
112C2×C23⋊C8—22no—
113C2×C23⋊C8C2311yescharacteristic
114C2×C23⋊C8C2311yescharacteristic
115#67263—22no—
116#67262—22no—
117#67262—22no—
118C8×D23—22no—
119C8×D23D414yescomplemented
120C23×C23—21no—
121C23×C23C2×D411yescharacteristic
122C22×D23—21no—
123C22×D23—42no—
124C22×D23—81no—
125C22×D23—81no—
126C22×D23C2×D411yescharacteristic
127C22×D23C2×D411yescharacteristic
128Q8×C23—21no—
129Q8×C23—21no—
130D4×C23—21no—
131D4×C23—21no—
132D4×C23—81no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2411yescharacteristic
140C22⋊D23—22no—
141C22⋊D23—22no—
142C22⋊D23—42no—
143C22⋊D23—81no—
144C22⋊D23—81no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23C2×D411yescharacteristic
149C2×Dic23C2×D411yescharacteristic
150D92—22no—
151D92—21no—
152D92—21no—
153D92—81no—
154C4×D23—21no—
155C4×D23—21no—
156C4×D23—42no—
157C4×D23C2×D412yes—
158C4×D23#4112yes—
159Dic46—22no—
160Dic46—21no—
161Dic46—21no—
162Dic46—42no—
163C8×C23—21no—
164C8×C23C2×D412yes—
165C23⋊C8—21no—
166C23⋊C8C2×D412yes—
167#3057—231nomaximal, Sylow
168C22×C23—21no—
169C22×C23—21no—
170C22×C23—21no—
171C22×C23—41no—
172C22×C23—41no—
173C22×C23—41no—
174C22×C23C22×D411yescharacteristic
175C2×D23—21no—
176C2×D23—21no—
177C2×D23—21no—
178C2×D23—21no—
179C2×D23—21no—
180C2×D23—41no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23—84no—
184C2×D23#12112yes—
185C4×C23—21no—
186C4×C23—41no—
187C4×C23—41no—
188C4×C23—41no—
189C4×C23C22×D411yescharacteristic
190C4×C23C2×#4111yescharacteristic
191Dic23—21no—
192Dic23—41no—
193Dic23—41no—
194Dic23—41no—
195Dic23#12112yes—
196C22×SD16—231no—
197C2×#131—231no—
198#536—231no—
199#535—231no—
200#468—231no—
201#468—231no—
202#468—231no—
203#468D2311yescharacteristic, complemented
204#465—231no—
205#465—231no—
206#465—231no—
207#465—231no—
208#427—231no—
209#419—231no—
210#418—231no—
211C2×C23—41no—
212C2×C23—81no—
213C2×C23C2×#12111yescharacteristic
214C2×C23#57711yescharacteristic
215C2×C23#57711yescharacteristic
216D23—22no—
217D23—41no—
218D23—81no—
219C2×#41—231no—
220C22×Q8—231no—
221C22×D4—231no—
222C2×SD16—231no—
223C2×SD16—231no—
224C2×SD16—231no—
225C2×SD16—464no—
226C2×SD16C2×D2311yescharacteristic
227#131—464no—
228C2×M16—231no—
229C2×M16—231no—
230C2×M16C2×D2311yescharacteristic, complemented
231C22×C8—231no—
232C22×C8—231no—
233C22×C8—231no—
234C4⋊Q8—461no—
235#127—461no—
236#124—461no—
237#124—461no—
238#123—461no—
239#123—461no—
240C22⋊Q8—231no—
241C22⋊Q8—231no—
242C22⋊Q8—231no—
243C22⋊Q8C2×D2311yescharacteristic, complemented
244#121—231no—
245#121—231no—
246#121—231no—
247#121C2×D2311yescharacteristic
248#120—461no—
249#120—461no—
250#117—231no—
251#117—231no—
252#107—231no—
253#107C2×D2311yescharacteristic, complemented
254#106—231no—
255#106—231no—
256#103—231no—
257#103—231no—
258#103—231no—
259#103C2×D2311yescharacteristic, complemented
260#102—231no—
261#102—231no—
262#102—231no—
263#102C2×D2311yescharacteristic
264C23#305711yescharacteristic, complemented, Sylow
265C24—461no—
266#41—462no—
267#41—462no—
268C2×Q8—231no—
269C2×Q8—231no—
270C2×Q8—461no—
271C2×Q8—462no—
272C2×Q8—462no—
273C2×Q8C22×D2311yescharacteristic
274C2×D4—21no—
275C2×D4—231no—
276C2×D4—231no—
277C2×D4—231no—
278C2×D4—231no—
279C2×D4—461no—
280C2×D4—462no—
281C2×D4—462no—
282C2×D4—461no—
283C2×D4—461no—
284C2×D4—461no—
285C2×D4C22×D2311yescharacteristic
286C22×C4—231no—
287C22×C4—231no—
288C22×C4—461no—
289C22×C4C22×D2311yescharacteristic
290SD16—22no—
291SD16—462no—
292SD16—462no—
293SD16—462no—
294M16—22no—
295M16—462no—
296M16—462no—
297C2×C8—231no—
298C2×C8—234no—
299C2×C8—231no—
300C2×C8—462no—
301C2×C8—462no—
302C2×C8C22×D2311yescharacteristic
303C2×C8C22×D2311yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—231no—
306C4⋊C4—231no—
307C4⋊C4—461no—
308C4⋊C4—461no—
309C4⋊C4—461no—
310C4⋊C4C22×D2311yescharacteristic
311C4⋊C4C22×D2311yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—461no—
315C22⋊C4—461no—
316C22⋊C4—461no—
317C22⋊C4—461no—
318C22⋊C4—461no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C42—461no—
323C42—461no—
324C23—21no—
325C23—231no—
326C23—231no—
327C23—461no—
328C23—922no—
329C23—1841no—
330C23—1841no—
331C23D4×D2311yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—462no—
335Q8—461no—
336Q8—461no—
337Q8—922no—
338D4—21no—
339D4—21no—
340D4—81no—
341D4—462no—
342D4—462no—
343D4—462no—
344D4—461no—
345D4—461no—
346D4—922no—
347D4—1841no—
348D4—1841no—
349D4—1841no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—231no—
356C2×C4—232no—
357C2×C4—232no—
358C2×C4—231no—
359C2×C4—461no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—461no—
364C2×C4—922no—
365C2×C4D4×D2311yescharacteristic
366C2×C4C23×D2311yescharacteristic
367C8—21no—
368C8—232no—
369C8—461no—
370C8D4×D2312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—232no—
378C22—461no—
379C22—461no—
380C22—461no—
381C22—461no—
382C22—461no—
383C22—921no—
384C22—921no—
385C22—921no—
386C22—1844no—
387C22C2×D4×D2311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—232no—
393C4—461no—
394C4—921no—
395C4—921no—
396C4—921no—
397C4C2×D4×D2311yescharacteristic
398C4#41×D2311yescharacteristic
399C2—41no—
400C2—81no—
401C2—462no—
402C2—921no—
403C2—1841no—
404C2#121×D2311yescharacteristic
405C2#1309322611yescharacteristic
406C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#468C2
socleC22×C23C22×D4
prime radical#13092983C2
hypercenter#468D23
hypocenterC23#3057
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D23C2semidirect
2. C2×#10625078C2semidirect
3. #13092990C2semidirect
5. #13092664C2semidirect
6. #13092663C2semidirect
7. #13092660C2semidirect
8. #13092649C2semidirect
9. #13092648C2semidirect
10. #13092645C2semidirect
11. #13092644C2semidirect
12. #13092454C2semidirect
13. #13092424C2semidirect
14. #13092420C2semidirect
15. C23×#468C2semidirect
20. C2×M16×C23C22semidirect
21. C23×C22⋊Q8C22semidirect
23. #10625117C22semidirect
30. #10625095C22semidirect
31. C22×C23⋊C8C22semidirect
36. C2×#67262C22semidirect
38. C2×C8×D23C22semidirect
39. #10625068C22semidirect
49. C23×#107C22semidirect
50. C23×#103C22semidirect
52. #10625017C22semidirect
55. #10625000C22semidirect
56. #10624998C22semidirect
57. #10624992C22semidirect
59. #10624990C22semidirect
60. #10624990C22semidirect
119. C8×D23D4semidirect
203. #468D23semidirect
230. C2×M16C2×D23semidirect
243. C22⋊Q8C2×D23semidirect
253. #107C2×D23semidirect
259. #103C2×D23semidirect
264. C23#3057semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D232
C2×#106250782
#130929902
#130929832
#130926642
#130926632
#130926602
#130926492
#130926482
#130926452
#130926442
#130924542
#130924242
#130924202
C23×#4682
#305723