Finite Group Databasebeta

← #15684901

Subgroups — #15684901

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×SD16×D23C211yesmaximal, characteristic, complemented
2Q8×C22⋊D23C211yesmaximal, characteristic, complemented
3#13093055C211yesmaximal, characteristic
4#13092810C211yesmaximal, characteristic, complemented
5#13092663C211yesmaximal, characteristic, complemented
6#13092655C211yesmaximal, characteristic, complemented
7#13092641C211yesmaximal, characteristic, complemented
8#13092620C211yesmaximal, characteristic, complemented
9#13092579C211yesmaximal, characteristic, complemented
10#13092571C211yesmaximal, characteristic, complemented
11#13092566C211yesmaximal, characteristic, complemented
12#13092556C211yesmaximal, characteristic, complemented
13#13092518C211yesmaximal, characteristic, complemented
14#13092486C211yesmaximal, characteristic, complemented
15C2×C23×#137C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C22×Q8×C23C2211yescharacteristic, complemented
18C2×Q8×D23C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C23×#137—24no—
21C2×Q16×C23C2211yescharacteristic, complemented
22C2×Q16×C23C2211yescharacteristic, complemented
23C2×SD16×C23C2211yescharacteristic
24C2×SD16×C23C2211yescharacteristic
25C2×M16×C23C2211yescharacteristic, complemented
26#10625118C2211yescharacteristic
27#10625117—21no—
28#10625117C2211yescharacteristic
29#10625117C2211yescharacteristic
30Q8×Dic23C2211yescharacteristic, complemented
31#10625115—21no—
32#10625115C2211yescharacteristic, complemented
33C2×#67275C2211yescharacteristic, complemented
34C2×#67274C2211yescharacteristic
35C2×#67274C2211yescharacteristic
36#10625110—21no—
37#10625108—21no—
38D4×Dic23C2211yescharacteristic
39C2×#67273C2211yescharacteristic
40#10625101C2211yescharacteristic
41#10625100—21no—
42C4×C22⋊D23—21no—
43C4×C22⋊D23C2211yescharacteristic
44C2×(C2×D23)⋊C4—21no—
45#10625095—21no—
46#10625095C2211yescharacteristic, complemented
47SD16×D23—24no—
48C2×#67263C2211yescharacteristic
49C2×C8×D23C2211yescharacteristic
50#10625017C2211yescharacteristic, complemented
51#10625017C2211yescharacteristic, complemented
52#10625017C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10625003C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic
57#10625000C2211yescharacteristic, complemented
58#10624998C2211yescharacteristic, complemented
59#10624997C2211yescharacteristic, complemented
60Dic23⋊C8C2211yescharacteristic, complemented
61C23×D23—21no—
62#41×C23—22no—
63#41×C23—41no—
64C2×Q8×C23—21no—
65C2×Q8×C23—22no—
66C2×Q8×C23—41no—
67C2×Q8×C23C2311yescharacteristic
68C2×Q8×C23C2311yescharacteristic
69C2×Q8×C23C2311yescharacteristic
70C2×D4×C23—21no—
71C2×D4×C23C2311yescharacteristic
72C22×C4×C23—21no—
73C22×C4×C23—21no—
74C22×C4×C23C2311yescharacteristic
75C2×C22⋊D23—21no—
76C2×C22⋊D23—21no—
77C2×C22⋊D23D411yescharacteristic
78C22×Dic23—21no—
79Q8×D23—22no—
80Q8×D23—41no—
81D4×D23—22no—
82D4×D23—41no—
83C2×D92C2311yescharacteristic
84C2×C4×D23—21no—
85C2×C4×D23C2311yescharacteristic
86C2×Dic46—21no—
87C2×Dic46C2311yescharacteristic
88Q16×C23—22no—
89Q16×C23—22no—
90SD16×C23—22no—
91SD16×C23D414yescomplemented
92M16×C23—22no—
93C2×C8×C23C2311yescharacteristic
94C2×C8×C23C2311yescharacteristic
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23D411yescharacteristic
98#67275—41no—
99#67274—22no—
100#67274—41no—
101#67273—22no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4D411yescharacteristic
108C4⋊Dic23—21no—
109C4⋊Dic23C2311yescharacteristic
110C4⋊Dic23C2311yescharacteristic
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic23⋊C4—21no—
115Dic23⋊C4—21no—
116Dic23⋊C4D411yescharacteristic
117C4×Dic23—21no—
118C4×Dic23C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121#67263—22no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—42no—
127C22×D23—42no—
128C22×D23—81no—
129C22×D23C2×D411yescharacteristic
130Q8×C23—21no—
131Q8×C23—21no—
132Q8×C23—21no—
133Q8×C23—21no—
134Q8×C23—21no—
135Q8×C23—42no—
136Q8×C23C2×D412yes—
137D4×C23—21no—
138D4×C23—42no—
139D4×C23C2×D412yes—
140C2×C4×C23—21no—
141C2×C4×C23—21no—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—42no—
146C2×C4×C23—42no—
147C2×C4×C23C2×D411yescharacteristic
148C2×C4×C23C2411yescharacteristic
149C22⋊D23—22no—
150C22⋊D23—42no—
151C22⋊D23—81no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—21no—
155C2×Dic23—81no—
156C2×Dic23C2×D411yescharacteristic
157C2×Dic23C2×D411yescharacteristic
158C2×Dic23C2×D411yescharacteristic
159D92—21no—
160D92—21no—
161C4×D23—21no—
162C4×D23—21no—
163C4×D23—42no—
164Dic46—21no—
165Dic46—21no—
166Dic46—42no—
167C8×C23—21no—
168C8×C23C2×D412yes—
169C23⋊C8—21no—
170C23⋊C8—21no—
171#3266—231nomaximal, Sylow
172C22×C23—22no—
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—21no—
176C22×C23—41no—
177C22×C23—41no—
178C22×C23C22×D411yescharacteristic
179C2×D23—21no—
180C2×D23—21no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23—41no—
184C2×D23—84no—
185C2×D23#13712yescomplemented
186C4×C23—22no—
187C4×C23—21no—
188C4×C23—41no—
189C4×C23—41no—
190C4×C23C22×D411yescharacteristic
191C4×C23H(5,𝔽2)11yescharacteristic
192Dic23—21no—
193Dic23—21no—
194Dic23—21no—
195Dic23—41no—
196Dic23—41no—
197Dic23—41no—
198C2×#137D2311yescharacteristic, complemented
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#435—231no—
213C2×C23—42no—
214C2×C23—41no—
215C2×C23D4211yescharacteristic
216C2×C23C2×#13711yescharacteristic
217C2×C23#57711yescharacteristic
218D23—22no—
219D23—81no—
220C2×#41C2×D2311yescharacteristic
221C22×Q8—231no—
222C22×Q8C2×D2311yescharacteristic, complemented
223C22×D4—231no—
224#137—24no—
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×M16C2×D2311yescharacteristic, complemented
236C22×C8—231no—
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—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#97—231no—
265C23#326611yescharacteristic, complemented, Sylow
266C24—461no—
267#41—22no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—231no—
273C2×Q8—461no—
274C2×Q8—462no—
275C2×Q8—921no—
276C2×Q8C22×D2311yescharacteristic
277C2×Q8C22×D2311yescharacteristic
278C2×Q8C22×D2311yescharacteristic
279C2×D4—21no—
280C2×D4—231no—
281C2×D4—231no—
282C2×D4—461no—
283C2×D4—462no—
284C2×D4—461no—
285C2×D4—921no—
286C2×D4C22×D2311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—231no—
290C22×C4—461no—
291C22×C4—461no—
292C22×C4C22×D2311yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—921no—
296SD16—22no—
297SD16—462no—
298SD16—462no—
299SD16—462no—
300SD16—921no—
301SD16C22⋊D2314yescomplemented
302M16—22no—
303C2×C8—231no—
304C2×C8—231no—
305C2×C8—462no—
306C2×C8C22×D2311yescharacteristic
307C2×C8C22×D2311yescharacteristic
308C4⋊C4—231no—
309C4⋊C4—231no—
310C4⋊C4—231no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4—461no—
316C4⋊C4—461no—
317C22⋊C4—231no—
318C22⋊C4—231no—
319C22⋊C4—461no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C42—231no—
327C42—461no—
328C23—21no—
329C23—231no—
330C23—461no—
331C23—922no—
332C23—922no—
333C23—1841no—
334C23D4×D2311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—461no—
342Q8—461no—
343Q8—922no—
344Q8C2×C22⋊D2312yes—
345D4—21no—
346D4—42no—
347D4—462no—
348D4—461no—
349D4—461no—
350D4—922no—
351D4—1841no—
352D4C2×C22⋊D2312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—231no—
361C2×C4—231no—
362C2×C4—231no—
363C2×C4—461no—
364C2×C4—461no—
365C2×C4—461no—
366C2×C4—461no—
367C2×C4—461no—
368C2×C4—922no—
369C2×C4—1841no—
370C2×C4D4×D2311yescharacteristic
371C2×C4C23×D2311yescharacteristic
372C8—21no—
373C8—461no—
374C8—461no—
375C8C2×C22⋊D2312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—232no—
383C22—461no—
384C22—461no—
385C22—921no—
386C22—921no—
387C22—921no—
388C22—1844no—
389C22C2×D4×D2311yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—461no—
395C4—461no—
396C4—461no—
397C4—921no—
398C4—921no—
399C4—921no—
400C4#1062515511yescharacteristic
401C4C22×C22⋊D2311yescharacteristic
402C2—41no—
403C2—42no—
404C2—462no—
405C2—1841no—
406C2D4×C22⋊D2311yescharacteristic
407C2#137×D2311yescharacteristic
408C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#137C2
socleC22×C23C22×D4
prime radical#13093055C2
hypercenterC2×#137D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D23C2semidirect
2. Q8×C22⋊D23C2semidirect
4. #13092810C2semidirect
5. #13092663C2semidirect
6. #13092655C2semidirect
7. #13092641C2semidirect
8. #13092620C2semidirect
9. #13092579C2semidirect
10. #13092571C2semidirect
11. #13092566C2semidirect
12. #13092556C2semidirect
13. #13092518C2semidirect
14. #13092486C2semidirect
15. C2×C23×#137C2semidirect
17. C22×Q8×C23C22semidirect
21. C2×Q16×C23C22semidirect
22. C2×Q16×C23C22semidirect
25. C2×M16×C23C22semidirect
30. Q8×Dic23C22semidirect
32. #10625115C22semidirect
33. C2×#67275C22semidirect
46. #10625095C22semidirect
50. #10625017C22semidirect
51. #10625017C22semidirect
52. #10625017C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
57. #10625000C22semidirect
58. #10624998C22semidirect
59. #10624997C22semidirect
60. Dic23⋊C8C22semidirect
91. SD16×C23D4semidirect
185. C2×D23#137semidirect
198. C2×#137D23semidirect
222. C22×Q8C2×D23semidirect
226. C2×Q16C2×D23semidirect
227. C2×Q16C2×D23semidirect
235. C2×M16C2×D23semidirect
265. C23#3266semidirect
301. SD16C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D232
Q8×C22⋊D232
#130930552
#130928102
#130926632
#130926552
#130926412
#130926202
#130925792
#130925712
#130925662
#130925562
#130925182
#130924862
C2×C23×#1372
#326623