Finite Group Databasebeta

← #15683651

Subgroups — #15683651

Order 2944.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093030C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic
3#13092761C211yesmaximal, characteristic, complemented
4#13092760C211yesmaximal, characteristic, complemented
5#13092714C211yesmaximal, characteristic, complemented
6#13092623C211yesmaximal, characteristic, complemented
7#13092622C211yesmaximal, characteristic, complemented
8#13092569C211yesmaximal, characteristic
9#13092569C211yesmaximal, characteristic
10#13092516C211yesmaximal, characteristic, complemented
11#13092514C211yesmaximal, characteristic, complemented
12#13092508C211yesmaximal, characteristic, complemented
13#13092504C211yesmaximal, characteristic, complemented
14#13092477C211yesmaximal, characteristic, complemented
15C23×#478C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C23×#125C2211yescharacteristic, complemented
18C4×D4×C23C2211yescharacteristic
19D4×Dic23C2211yescharacteristic
20C2×#67273C2211yescharacteristic
21C2×#67273C2211yescharacteristic
22C4×C22⋊D23—21no—
23C2×(C2×D23)⋊C4—21no—
24C2×#67263C2211yescharacteristic
25C2×#67263C2211yescharacteristic
26#10625069—21no—
27#10625069—21no—
28#10625068C2211yescharacteristic
29#10625068C2211yescharacteristic
30#10625064C2211yescharacteristic
31#10625063C2211yescharacteristic
32#10625061—21no—
33#10625061—21no—
34#10625058C2211yescharacteristic, complemented
35#10625058C2211yescharacteristic, complemented
36(C22⋊D23)⋊C4—21no—
37C22⋊C4×D23—21no—
38C4×D92C2211yescharacteristic
39#10625043C2211yescharacteristic
40#10625040C2211yescharacteristic, complemented
41C23×#107C2211yescharacteristic, complemented
42C23×#106C2211yescharacteristic, complemented
43C23×C4⋊C8C2211yescharacteristic, complemented
44C23×#102C2211yescharacteristic
45C23×#102C2211yescharacteristic
46(C2×D23)⋊C8C2211yescharacteristic
47(C2×D23)⋊C8C2211yescharacteristic
48#10624998C2211yescharacteristic, complemented
49#10624998C2211yescharacteristic, complemented
50#10624997C2211yescharacteristic, complemented
51C8×Dic23C2211yescharacteristic, complemented
52#10624992C2211yescharacteristic, complemented
53#10624992C2211yescharacteristic, complemented
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58C4⋊(C23⋊C8)C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63C22×Dic23—21no—
64D4×D23—22no—
65D4×D23—22no—
66C2×D92C2311yescharacteristic
67C2×C4×D23—21no—
68C2×C4×D23—21no—
69C2×C4×D23C2311yescharacteristic
70C2×Dic46C2311yescharacteristic
71C2×Dic46C2311yescharacteristic
72C2×C8×C23C2311yescharacteristic
73C2×C8×C23C2311yescharacteristic
74C4⋊C4×C23—21no—
75C4⋊C4×C23—21no—
76C4⋊C4×C23C2311yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C4⋊C4×C23C2311yescharacteristic
79C22⋊C4×C23—21no—
80C42×C23C2311yescharacteristic
81C22⋊Dic23—21no—
82#67273—22no—
83#67273—22no—
84(C2×D23)⋊C4—21no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4D411yescharacteristic
90(C2×D23)⋊C4D411yescharacteristic
91C4⋊Dic23—21no—
92C4⋊Dic23—21no—
93C4⋊Dic23—21no—
94C4⋊Dic23—21no—
95C4⋊Dic23C2311yescharacteristic
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4D411yescharacteristic
99Dic23⋊C4D411yescharacteristic
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23C2311yescharacteristic
104C2×C23⋊C8C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106#67263—22no—
107#67263—22no—
108C23×C23—21no—
109C22×D23—21no—
110C22×D23—24no—
111C22×D23—81no—
112C22×D23—81no—
113C22×D23C2×D411yescharacteristic
114D4×C23—21no—
115D4×C23#4112yes—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23—81no—
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2×D411yescharacteristic
122C2×C4×C23C2411yescharacteristic
123C22⋊D23—24no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23—21no—
127C2×Dic23—81no—
128C2×Dic23C2×D411yescharacteristic
129C2×Dic23C2×D411yescharacteristic
130C2×Dic23C2×D411yescharacteristic
131D92—21no—
132D92#4112yes—
133C4×D23—21no—
134C4×D23—21no—
135C4×D23—81no—
136C4×D23—81no—
137Dic46—21no—
138Dic46—21no—
139Dic46—21no—
140Dic46—21no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3123—231nomaximal, Sylow
146C22×C23—22no—
147C22×C23—41no—
148C22×C23—41no—
149C22×C23C22×D411yescharacteristic
150C2×D23—21no—
151C2×D23—22no—
152C2×D23—21no—
153C2×D23—21no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—84no—
157C4×C23—21no—
158C4×C23—21no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23—41no—
162C4×C23C2×#4111yescharacteristic
163C4×C23C2×#4111yescharacteristic
164Dic23—21no—
165Dic23—21no—
166Dic23—21no—
167Dic23—41no—
168Dic23—41no—
169Dic23—41no—
170#541—231no—
171#518—231no—
172#485—231no—
173#485—231no—
174#478—231no—
175#478D2311yescharacteristic, complemented
176#461—231no—
177#461—231no—
178#450—231no—
179#450—231no—
180#440—231no—
181#440—231no—
182C4×SD16—231no—
183C4×SD16—231no—
184#433—231no—
185C2×C23—42no—
186C2×C23#52511yescharacteristic
187C2×C23#57711yescharacteristic
188C2×C23#57711yescharacteristic
189D23—41no—
190D23—42no—
191C22×D4—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×SD16—231no—
195C2×SD16—231no—
196C4⋊Q8—231no—
197#126—461no—
198#126—461no—
199#125—461no—
200#125—461no—
201#125C2×D2311yescharacteristic, complemented
202C22⋊Q8—231no—
203C22⋊Q8—231no—
204C4×Q8—231no—
205C4×Q8—231no—
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—231no—
209C4×D4—461no—
210C4×D4—461no—
211C4×D4C2×D2311yescharacteristic
212#117—231no—
213#117—231no—
214C2×C22⋊C4—461no—
215C2×C22⋊C4—461no—
216#107—231no—
217#107C2×D2311yescharacteristic, complemented
218#106—231no—
219#106C2×D2311yescharacteristic, complemented
220C4⋊C8—231no—
221C4⋊C8C2×D2311yescharacteristic, complemented
222#103—231no—
223#103—231no—
224#103—231no—
225#103—231no—
226#102—231no—
227#102—231no—
228#102C2×D2311yescharacteristic
229#102C2×D2311yescharacteristic
230C22⋊C8—231no—
231C22⋊C8—231no—
232#97—231no—
233C4×C8—231no—
234C23#312311yescharacteristic, complemented, Sylow
235C24—461no—
236C2×Q8—231no—
237C2×Q8—231no—
238C2×D4—231no—
239C2×D4—461no—
240C2×D4—462no—
241C2×D4—462no—
242C2×D4C22×D2311yescharacteristic
243C22×C4—21no—
244C22×C4—231no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248SD16—462no—
249SD16—462no—
250SD16—462no—
251SD16—462no—
252C2×C8—231no—
253C2×C8—231no—
254C2×C8C22×D2311yescharacteristic
255C2×C8C22×D2311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—231no—
259C4⋊C4—231no—
260C4⋊C4—231no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4C22×D2311yescharacteristic
268C4⋊C4C22×D2311yescharacteristic
269C4⋊C4C22×D2311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—231no—
272C22⋊C4—231no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C22⋊C4—461no—
279C42—231no—
280C42—461no—
281C42—461no—
282C42—461no—
283C42C22×D2311yescharacteristic
284C23—21no—
285C23—231no—
286C23—464no—
287C23—461no—
288C23—1841no—
289C23—1841no—
290Q8—461no—
291Q8—461no—
292Q8—461no—
293Q8—461no—
294D4—21no—
295D4—232no—
296D4—464no—
297D4—461no—
298D4#6729212yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—231no—
304C2×C4—231no—
305C2×C4—231no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4—1841no—
314C2×C4D4×D2311yescharacteristic
315C2×C4D4×D2311yescharacteristic
316C2×C4C23×D2311yescharacteristic
317C8—21no—
318C8—21no—
319C8—461no—
320C8—461no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—461no—
325C22—462no—
326C22—461no—
327C22—461no—
328C22—921no—
329C22—921no—
330C22—1844no—
331C22C2×D4×D2311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—461no—
338C4—461no—
339C4—461no—
340C4—921no—
341C4—921no—
342C4—921no—
343C4C2×#6729211yescharacteristic
344C4#41×D2311yescharacteristic
345C2—42no—
346C2—921no—
347C2—922no—
348C2#1309293011yescharacteristic
349C2#1309322411yescharacteristic
350C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#478C2
socleC22×C23C22×D4
prime radicalC2×D4×D23C22
hypercenter#478D23
hypocenterC23#3123
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #13093030C2semidirect
3. #13092761C2semidirect
4. #13092760C2semidirect
5. #13092714C2semidirect
6. #13092623C2semidirect
7. #13092622C2semidirect
10. #13092516C2semidirect
11. #13092514C2semidirect
12. #13092508C2semidirect
13. #13092504C2semidirect
14. #13092477C2semidirect
15. C23×#478C2semidirect
17. C23×#125C22semidirect
34. #10625058C22semidirect
35. #10625058C22semidirect
40. #10625040C22semidirect
41. C23×#107C22semidirect
42. C23×#106C22semidirect
43. C23×C4⋊C8C22semidirect
48. #10624998C22semidirect
49. #10624998C22semidirect
50. #10624997C22semidirect
51. C8×Dic23C22semidirect
52. #10624992C22semidirect
53. #10624992C22semidirect
56. #10624990C22semidirect
57. #10624989C22semidirect
58. C4⋊(C23⋊C8)C22semidirect
175. #478D23semidirect
201. #125C2×D23semidirect
217. #107C2×D23semidirect
219. #106C2×D23semidirect
221. C4⋊C8C2×D23semidirect
234. C23#3123semidirect

Maximal subgroups

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

subgroupindex
#130930302
#130928892
#130927612
#130927602
#130927142
#130926232
#130926222
#130925692
#130925162
#130925142
#130925082
#130925042
#130924772
C23×#4782
#312323