Finite Group Databasebeta

← #18004809

Subgroups — #18004809

Order 4736.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558144C211yesmaximal, characteristic, complemented
2#14558015C211yesmaximal, characteristic
3#14557867C211yesmaximal, characteristic, complemented
4#14557862C211yesmaximal, characteristic, complemented
5#14557840C211yesmaximal, characteristic, complemented
6#14557834C211yesmaximal, characteristic, complemented
7#14557735C211yesmaximal, characteristic, complemented
8#14557694C211yesmaximal, characteristic
9#14557694C211yesmaximal, characteristic
10#14557640C211yesmaximal, characteristic, complemented
11#14557636C211yesmaximal, characteristic, complemented
12Q16×Dic37C211yesmaximal, characteristic, complemented
13#14557618C211yesmaximal, characteristic, complemented
14#14557593C211yesmaximal, characteristic, complemented
15C37×#462C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596941C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19#11924531—21no—
20#11924531—21no—
21#11924528C2211yescharacteristic
22#11924526—21no—
23#11924526—21no—
24#11924512C2211yescharacteristic
25#11924512C2211yescharacteristic
26Q8×Dic37C2211yescharacteristic
27Q8×Dic37C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic
29C4×D148—21no—
30C4×D148C2211yescharacteristic
31#11924498—21no—
32#11924498C2211yescharacteristic
33#11924493—21no—
34#11924493C2211yescharacteristic
35C4⋊C4×D37—21no—
36C4⋊C4×D37C2211yescharacteristic
37#11924470C2211yescharacteristic
38#11924469C2211yescharacteristic
39#11924468C2211yescharacteristic
40#11924467C2211yescharacteristic
41C4⋊#64436C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924460C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924458C2211yescharacteristic
47#11924458C2211yescharacteristic
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×Q16×C37C2211yescharacteristic
53C2×Q16×C37C2211yescharacteristic
54C4⋊Q8×C37C2211yescharacteristic
55C4×Q8×C37C2211yescharacteristic
56C4⋊C8×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62#10596966—22no—
63#10596966—22no—
64C2×D148—21no—
65C2×D148C2311yescharacteristic
66C2×C4×D37—21no—
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37—21no—
70C2×C4×D37C2311yescharacteristic
71Q16×C37—22no—
72Q16×C37—22no—
73C2×C8×C37C2311yescharacteristic
74C2×C8×C37C2311yescharacteristic
75C4⋊C4×C37—21no—
76C4⋊C4×C37—21no—
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C42×C37—21no—
80C42×C37C2311yescharacteristic
81#10596941—22no—
82#10596941—22no—
83#10596938—21no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938D411yescharacteristic
88#10596938D411yescharacteristic
89C4⋊Dic37—21no—
90C4⋊Dic37—21no—
91C4⋊Dic37—21no—
92C4⋊Dic37C2311yescharacteristic
93C4⋊Dic37C2311yescharacteristic
94C4⋊Dic37C2311yescharacteristic
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936D411yescharacteristic
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37—21no—
105C4×Dic37C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C22×D37—21no—
109C22×D37C2×D411yescharacteristic
110Q8×C37—21no—
111Q8×C37—21no—
112Q8×C37—21no—
113Q8×C37—21no—
114Q8×C37—21no—
115Q8×C37#4112yes—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37C2×D411yescharacteristic
121C2×C4×C37C2×D411yescharacteristic
122C2×C4×C37C2411yescharacteristic
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37—21no—
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129D148—24no—
130D148—21no—
131D148#4112yes—
132C4×D37—24no—
133C4×D37—21no—
134C4×D37—21no—
135C4×D37—81no—
136C4×D37—81no—
137C4×D37—81no—
138C8×C37—21no—
139C8×C37—21no—
140#64436—21no—
141#64436—21no—
142C22×C37C22×D411yescharacteristic
143C2×D37—21no—
144C2×D37—22no—
145C2×D37—21no—
146C2×D37—21no—
147C2×D37—41no—
148C2×D37—41no—
149C4×C37—22no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37—41no—
155C4×C37C2×#4111yescharacteristic
156C4×C37C2×#4111yescharacteristic
157Dic37—21no—
158Dic37—21no—
159Dic37—21no—
160Dic37—41no—
161Dic37—41no—
162Dic37—41no—
163#3120—371nomaximal, Sylow
164C2×C37#52511yescharacteristic
165C2×C37#57711yescharacteristic
166C2×C37#57811yescharacteristic
167D37—41no—
168D37—42no—
169#541—371no—
170#520—371no—
171#484—371no—
172#483—371no—
173#479—371no—
174#478—371no—
175#462D3711yescharacteristic, complemented
176#461—371no—
177#452—371no—
178#452—371no—
179#441—371no—
180#440—371no—
181C4×Q16—371no—
182C4×SD16—371no—
183#433—371no—
184C37#312011yescharacteristic, complemented, Sylow
185C2×#41—371no—
186C2×Q16C2×D3711yescharacteristic
187C2×Q16C2×D3711yescharacteristic
188C2×SD16—371no—
189C2×SD16—371no—
190C4⋊Q8C2×D3711yescharacteristic
191#126—741no—
192#126—741no—
193#125—371no—
194#125—741no—
195#125—741no—
196C22⋊Q8—371no—
197C22⋊Q8—371no—
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8—371no—
201C4×Q8C2×D3711yescharacteristic
202C4×D4—371no—
203C4×D4—371no—
204C4×D4—741no—
205C4×D4—741no—
206#117—371no—
207#117—741no—
208C2×C4⋊C4—371no—
209C2×C4⋊C4—741no—
210#107—371no—
211#107—371no—
212#106—371no—
213#106—371no—
214C4⋊C8—371no—
215C4⋊C8C2×D3711yescharacteristic
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103C2×D3711yescharacteristic
221#103C2×D3711yescharacteristic
222#102—371no—
223#102—371no—
224C22⋊C8—371no—
225C22⋊C8—371no—
226#97—371no—
227C4×C8—371no—
228#41—742no—
229#41—742no—
230C2×Q8C22×D3711yescharacteristic
231C2×Q8C22×D3711yescharacteristic
232C2×Q8C22×D3711yescharacteristic
233C2×D4—371no—
234C2×D4—741no—
235C22×C4—371no—
236C22×C4—741no—
237C22×C4—741no—
238C22×C4—741no—
239C22×C4—741no—
240Q16—22no—
241Q16—22no—
242SD16—742no—
243SD16—742no—
244C2×C8—371no—
245C2×C8—371no—
246C2×C8C22×D3711yescharacteristic
247C2×C8C22×D3711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—371no—
252C4⋊C4—371no—
253C4⋊C4—371no—
254C4⋊C4—371no—
255C4⋊C4—371no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4—741no—
262C4⋊C4—741no—
263C4⋊C4—741no—
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—371no—
266C22⋊C4—371no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C22⋊C4—741no—
270C22⋊C4—741no—
271C42—21no—
272C42—371no—
273C42—741no—
274C42—741no—
275C42—741no—
276C42C22×D3711yescharacteristic
277C23—371no—
278C23—741no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8#1059696412yes—
285D4—372no—
286D4—744no—
287D4—741no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—371no—
293C2×C4—371no—
294C2×C4—371no—
295C2×C4—2961no—
296C2×C4—2961no—
297C2×C4—2961no—
298C2×C4—744no—
299C2×C4—741no—
300C2×C4—741no—
301C2×C4—741no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4D4×D3711yescharacteristic
305C2×C4D4×D3711yescharacteristic
306C2×C4C23×D3711yescharacteristic
307C8—21no—
308C8—21no—
309C8—741no—
310C8—741no—
311C22—742no—
312C22—741no—
313C22—741no—
314C22—741no—
315C22—1481no—
316C22—1481no—
317C22C2×D4×D3711yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—741no—
325C4—741no—
326C4—741no—
327C4—1481no—
328C4—1481no—
329C4—1481no—
330C4#41×D3711yescharacteristic
331C4C2×#1059696411yescharacteristic
332C2—1481no—
333C2—1482no—
334C2#1455804311yescharacteristic
335C2#1455834211yescharacteristic
336C2#1455834611yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#462C2
socleC22×C37C22×D4
prime radicalC2×#10596966C22
hypercenter#462D37
hypocenterC37#3120
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #14558144C2semidirect
3. #14557867C2semidirect
4. #14557862C2semidirect
5. #14557840C2semidirect
6. #14557834C2semidirect
7. #14557735C2semidirect
10. #14557640C2semidirect
11. #14557636C2semidirect
12. Q16×Dic37C2semidirect
13. #14557618C2semidirect
14. #14557593C2semidirect
15. C37×#462C2semidirect
175. #462D37semidirect
184. C37#3120semidirect

Maximal subgroups

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

subgroupindex
#145581442
#145580152
#145578672
#145578622
#145578402
#145578342
#145577352
#145576942
#145576402
#145576362
Q16×Dic372
#145576182
#145575932
C37×#4622
#312037