Finite Group Databasebeta

← #18006467

Subgroups — #18006467

Order 4736.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558241C211yesmaximal, characteristic
2#14558196C211yesmaximal, characteristic
3#14557882C211yesmaximal, characteristic, complemented
4#14557870C211yesmaximal, characteristic, complemented
5#14557866C211yesmaximal, characteristic, complemented
6#14557827C211yesmaximal, characteristic, complemented
7#14557773C211yesmaximal, characteristic, complemented
8#14557741C211yesmaximal, characteristic, complemented
9#14557688C211yesmaximal, characteristic, complemented
10#14557687C211yesmaximal, characteristic, complemented
11#14557625C211yesmaximal, characteristic, complemented
12C8×C22⋊D37C211yesmaximal, characteristic
13C2×#11924461C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#467C211yesmaximal, characteristic, complemented
16C22×Dic74C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596942C2211yescharacteristic
20C2×C8×D37C2211yescharacteristic
21#11924535—21no—
22#11924535C2211yescharacteristic
23#11924534C2211yescharacteristic
24#11924526—21no—
25#11924516—21no—
26#11924516C2211yescharacteristic
27#11924514—21no—
28#11924513—21no—
29#11924513—21no—
30#11924512C2211yescharacteristic
31Q8×Dic37C2211yescharacteristic
32#11924501C2211yescharacteristic
33C4×C22⋊D37C2211yescharacteristic
34#11924496—21no—
35#11924496—21no—
36C2×C4⋊Dic37C2211yescharacteristic
37C4⋊C4×D37C2211yescharacteristic
38#11924469C2211yescharacteristic
39#11924469C2211yescharacteristic
40#11924465C2211yescharacteristic
41#11924461C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924460C2211yescharacteristic
46#11924460C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924459C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×Q16×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C22⋊Q8×C37C2211yescharacteristic
55C22⋊Q8×C37C2211yescharacteristic
56#107×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×Q8×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37D411yescharacteristic
63C22×Dic37—21no—
64C22×Dic37—21no—
65Q8×D37—22no—
66Q8×D37—41no—
67C2×C4×D37—21no—
68C2×C4×D37—21no—
69C2×C4×D37C2311yescharacteristic
70C2×Dic74—22no—
71C2×Dic74—21no—
72C2×Dic74—21no—
73C2×Dic74—21no—
74C2×Dic74—41no—
75C2×Dic74C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77Q16×C37—41no—
78C2×C8×C37—41no—
79C2×C8×C37C2311yescharacteristic
80C2×C8×C37C2311yescharacteristic
81C4⋊C4×C37—21no—
82C4⋊C4×C37—21no—
83C4⋊C4×C37C2311yescharacteristic
84C4⋊C4×C37C2311yescharacteristic
85C22⋊C4×C37—21no—
86C22⋊C4×C37—21no—
87C22⋊Dic37D411yescharacteristic
88#10596942—22no—
89#10596942—41no—
90#10596938—21no—
91#10596938—21no—
92#10596938D411yescharacteristic
93C4⋊Dic37—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37—21no—
96C4⋊Dic37C2311yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936—21no—
102#10596936—21no—
103#10596936—21no—
104#10596936D411yescharacteristic
105C4×Dic37—21no—
106C4×Dic37—21no—
107C4×Dic37C2311yescharacteristic
108C2×#64436C2311yescharacteristic
109C2×#64436C2311yescharacteristic
110C8×D37—41no—
111C23×C37C2×D411yescharacteristic
112C22×D37C2×D411yescharacteristic
113Q8×C37—21no—
114Q8×C37—21no—
115Q8×C37—21no—
116Q8×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2411yescharacteristic
125C22⋊D37Q1614yescomplemented
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—42no—
131C2×Dic37—81no—
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135C4×D37—21no—
136C4×D37—21no—
137C4×D37—42no—
138C4×D37—81no—
139Dic74—21no—
140Dic74—21no—
141Dic74—21no—
142Dic74—42no—
143Dic74—42no—
144Dic74—81no—
145Dic74#4112yes—
146C8×C37—21no—
147C8×C37—21no—
148#64436—21no—
149#64436—21no—
150C22×C37—21no—
151C22×C37—21no—
152C22×C37C2×Q1612yes—
153C22×C37C22×D411yescharacteristic
154C2×D37—21no—
155C2×D37—21no—
156C2×D37C2×Q1612yes—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37C2×#4111yescharacteristic
163C4×C37H(5,𝔽2)11yescharacteristic
164Dic37—22no—
165Dic37—21no—
166Dic37—21no—
167Dic37—41no—
168Dic37—41no—
169Dic37—41no—
170Dic37C2×Q1612yes—
171#3299—371nomaximal, Sylow
172C2×C37—22no—
173C2×C37#54611yescharacteristic
174C2×C37C22×Q1611yescharacteristic
175C2×C37#57711yescharacteristic
176D37—22no—
177#554—371no—
178D4×Q8—371no—
179#487—371no—
180#484—371no—
181#484—371no—
182#477—371no—
183#467—371no—
184#467D3711yescharacteristic, complemented
185#462—371no—
186#451—371no—
187#451—371no—
188C4×Q16—371no—
189C8×D4—371no—
190C2×#103—371no—
191C2×#103—371no—
192C37#329911yescharacteristic, complemented, Sylow
193C22×Q8—371no—
194C22×Q8—371no—
195C2×Q16—371no—
196C2×Q16—371no—
197C2×Q16C2×D3711yescharacteristic
198C22×C8—371no—
199C22×C8C2×D3711yescharacteristic
200C4⋊Q8—371no—
201C4⋊Q8—371no—
202C4⋊Q8—741no—
203#125—741no—
204C22⋊Q8—371no—
205C22⋊Q8—371no—
206C22⋊Q8—741no—
207C22⋊Q8—741no—
208C22⋊Q8—741no—
209C22⋊Q8—741no—
210C22⋊Q8C2×D3711yescharacteristic
211C22⋊Q8C2×D3711yescharacteristic
212C4×Q8—371no—
213C4×Q8—371no—
214C4×D4—371no—
215C4×D4—741no—
216C4×D4—741no—
217C2×C4⋊C4—371no—
218C2×C4⋊C4—371no—
219#107—371no—
220#107—371no—
221#107C2×D3711yescharacteristic
222C4⋊C8—371no—
223#103—371no—
224#103—371no—
225#103—371no—
226#103—371no—
227#103—371no—
228#103—371no—
229#103—371no—
230#103—371no—
231#103C2×D3711yescharacteristic
232#103C2×D3711yescharacteristic
233C22⋊C8—371no—
234C22⋊C8—371no—
235C4×C8—371no—
236C2×Q8—371no—
237C2×Q8—371no—
238C2×Q8—741no—
239C2×Q8—741no—
240C2×Q8—742no—
241C2×Q8—741no—
242C2×Q8—742no—
243C2×Q8—1481no—
244C2×Q8—1481no—
245C2×Q8C22×D3711yescharacteristic
246C2×Q8C22×D3711yescharacteristic
247C2×D4—371no—
248C22×C4—371no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4—741no—
252C22×C4—741no—
253C22×C4C22×D3711yescharacteristic
254Q16—41no—
255Q16—742no—
256Q16—1481no—
257C2×C8—41no—
258C2×C8—371no—
259C2×C8—371no—
260C2×C8—1481no—
261C2×C8C22×D3711yescharacteristic
262C2×C8C22×D3711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—371no—
268C4⋊C4—741no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4—741no—
272C4⋊C4—741no—
273C4⋊C4—741no—
274C4⋊C4—741no—
275C4⋊C4—741no—
276C4⋊C4—741no—
277C4⋊C4C22×D3711yescharacteristic
278C4⋊C4C22×D3711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—371no—
282C22⋊C4—371no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C42—371no—
286C42—741no—
287C42—741no—
288C23—371no—
289C23D4×D3711yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—372no—
295Q8—2961no—
296Q8—741no—
297Q8—741no—
298Q8—741no—
299Q8—1482no—
300Q8—1482no—
301D4—374no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—371no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—2961no—
312C2×C4—2961no—
313C2×C4—741no—
314C2×C4—741no—
315C2×C4—741no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—1482no—
320C2×C4—1482no—
321C2×C4D4×D3711yescharacteristic
322C2×C4C23×D3711yescharacteristic
323C8—21no—
324C8—21no—
325C8—741no—
326C8—741no—
327C22—21no—
328C22—21no—
329C22—372no—
330C22—741no—
331C22—741no—
332C22Q16×D3712yes—
333C22C2×D4×D3711yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—372no—
340C4—741no—
341C4—741no—
342C4—742no—
343C4—1481no—
344C4—1481no—
345C4—1481no—
346C4#41×D3711yescharacteristic
347C4#1192458111yescharacteristic
348C2—22no—
349C2—742no—
350C2#1455817211yescharacteristic
351C2C2×Q16×D3711yescharacteristic
352C2#1455834011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#467C2
socleC22×C37C22×D4
prime radicalC2×C22⋊D37D4
hypercenter#467D37
hypocenterC37#3299
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #14557882C2semidirect
4. #14557870C2semidirect
5. #14557866C2semidirect
6. #14557827C2semidirect
7. #14557773C2semidirect
8. #14557741C2semidirect
9. #14557688C2semidirect
10. #14557687C2semidirect
11. #14557625C2semidirect
13. C2×#11924461C2semidirect
14. #103×D37C2semidirect
15. C37×#467C2semidirect
125. C22⋊D37Q16semidirect
184. #467D37semidirect
192. C37#3299semidirect

Maximal subgroups

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

subgroupindex
#145582412
#145581962
#145578822
#145578702
#145578662
#145578272
#145577732
#145577412
#145576882
#145576872
#145576252
C8×C22⋊D372
C2×#119244612
#103×D372
C37×#4672
#329937