Finite Group Databasebeta

← #18006470

Subgroups — #18006470

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#14558238C211yesmaximal, characteristic
2#14558196C211yesmaximal, characteristic
3#14557882C211yesmaximal, characteristic, complemented
4#14557870C211yesmaximal, characteristic, complemented
5#14557827C211yesmaximal, characteristic, complemented
6#14557775C211yesmaximal, characteristic, complemented
7#14557772C211yesmaximal, characteristic, complemented
8#14557742C211yesmaximal, characteristic, complemented
9#14557691C211yesmaximal, characteristic, complemented
10#14557690C211yesmaximal, characteristic, complemented
11#14557627C211yesmaximal, characteristic, complemented
12#14557596C211yesmaximal, characteristic
13C2×#11924459C211yesmaximal, characteristic, complemented
14#103×D37C211yesmaximal, characteristic, complemented
15C37×#484C211yesmaximal, characteristic, complemented
16C22×Dic74C2211yescharacteristic
17C2×Q8×D37C2211yescharacteristic
18C2×Dic148C2211yescharacteristic
19C2×Dic148C2211yescharacteristic
20C2×#10596942C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22C2×C8×D37C2211yescharacteristic
23#11924535—21no—
24#11924535C2211yescharacteristic
25#11924534C2211yescharacteristic
26#11924526—21no—
27#11924516C2211yescharacteristic
28#11924516C2211yescharacteristic
29#11924515—21no—
30#11924515C2211yescharacteristic
31#11924514—21no—
32#11924514—21no—
33#11924513—21no—
34#11924501C2211yescharacteristic
35#11924501C2211yescharacteristic
36C4×C22⋊D37—21no—
37C4×C22⋊D37C2211yescharacteristic
38#11924496—21no—
39C4⋊C4×D37C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924461C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924460C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924459C2211yescharacteristic
48#11924459C2211yescharacteristic
49#11924459C2211yescharacteristic
50#11924448C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C22⋊Q8×C37C2211yescharacteristic
53C2×C4⋊C4×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#107×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C22×C4×C37—21no—
61C22×C4×C37C2311yescharacteristic
62C2×C22⋊D37D411yescharacteristic
63C22×Dic37—21no—
64Q8×D37—22no—
65Q8×D37—41no—
66C2×C4×D37—21no—
67C2×C4×D37—21no—
68C2×C4×D37C2311yescharacteristic
69C2×Dic74—22no—
70C2×Dic74—21no—
71C2×Dic74—21no—
72C2×Dic74—21no—
73C2×Dic74—41no—
74C2×Dic74C2311yescharacteristic
75C2×Dic74C2311yescharacteristic
76C2×Dic74C2311yescharacteristic
77C2×C8×C37C2311yescharacteristic
78C2×C8×C37C2311yescharacteristic
79C4⋊C4×C37—21no—
80C4⋊C4×C37—21no—
81C4⋊C4×C37C2311yescharacteristic
82C4⋊C4×C37C2311yescharacteristic
83C4⋊C4×C37C2311yescharacteristic
84C22⋊C4×C37—21no—
85C22⋊Dic37—21no—
86C22⋊Dic37D411yescharacteristic
87#10596942—41no—
88#10596938—21no—
89#10596938—21no—
90#10596938D411yescharacteristic
91C4⋊Dic37—21no—
92C4⋊Dic37—21no—
93C4⋊Dic37C2311yescharacteristic
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97#10596936—21no—
98#10596936—21no—
99#10596936—21no—
100#10596936—21no—
101#10596936D411yescharacteristic
102C4×Dic37—21no—
103C4×Dic37—21no—
104C4×Dic37C2311yescharacteristic
105C2×#64436—41no—
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108Dic148—22no—
109Dic148—41no—
110C8×D37—41no—
111C23×C37C2×D411yescharacteristic
112C22×D37C2×D411yescharacteristic
113Q8×C37—21no—
114Q8×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—81no—
122C2×C4×C37C2×D411yescharacteristic
123C2×C4×C37C2411yescharacteristic
124C22⋊D37Q1614yescomplemented
125C2×Dic37—21no—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—42no—
130C2×Dic37C2×D411yescharacteristic
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133C4×D37—21no—
134C4×D37—21no—
135C4×D37—42no—
136C4×D37—81no—
137Dic74—21no—
138Dic74—21no—
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#484D3711yescharacteristic, complemented
182#477—371no—
183#467—371no—
184#467—371no—
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×Q16—371no—
198C22×C8—371no—
199C22×C8—371no—
200C4⋊Q8—371no—
201C4⋊Q8—371no—
202C4⋊Q8—741no—
203#125—741no—
204C22⋊Q8—371no—
205C22⋊Q8—371no—
206C22⋊Q8—371no—
207C22⋊Q8—741no—
208C22⋊Q8—741no—
209C22⋊Q8—741no—
210C22⋊Q8—741no—
211C22⋊Q8C2×D3711yescharacteristic
212C4×Q8—371no—
213C4×Q8—371no—
214C4×D4—371no—
215C4×D4—741no—
216C4×D4—741no—
217C2×C4⋊C4—371no—
218C2×C4⋊C4C2×D3711yescharacteristic
219#107—371no—
220#107C2×D3711yescharacteristic
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⋊C8C2×D3711yescharacteristic
235C4×C8—371no—
236C2×Q8—371no—
237C2×Q8—371no—
238C2×Q8—371no—
239C2×Q8—741no—
240C2×Q8—741no—
241C2×Q8—742no—
242C2×Q8—741no—
243C2×Q8—742no—
244C2×Q8—1481no—
245C2×Q8—1481no—
246C2×Q8C22×D3711yescharacteristic
247C2×D4—371no—
248C22×C4—21no—
249C22×C4—371no—
250C22×C4—741no—
251C22×C4—741no—
252C22×C4—741no—
253C22×C4C22×D3711yescharacteristic
254Q16—742no—
255Q16—1481no—
256Q16—1481no—
257C2×C8—371no—
258C2×C8—371no—
259C2×C8—1481no—
260C2×C8—1481no—
261C2×C8C22×D3711yescharacteristic
262C2×C8C22×D3711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—741no—
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⋊C4C22×D3711yescharacteristic
277C4⋊C4C22×D3711yescharacteristic
278C4⋊C4C22×D3711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—371no—
281C22⋊C4—371no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C22⋊C4—741no—
285C42—371no—
286C42—741no—
287C42—741no—
288C23—371no—
289C23D4×D3711yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—372no—
293Q8—2961no—
294Q8—741no—
295Q8—741no—
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—81no—
309C2×C4—371no—
310C2×C4—371no—
311C2×C4—371no—
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#1192458211yescharacteristic
348C2—22no—
349C2—742no—
350C2#1455817511yescharacteristic
351C2C2×Q16×D3711yescharacteristic
352C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#484C2
socleC22×C37C22×D4
prime radicalC2×C22⋊D37D4
hypercenter#484D37
hypocenterC37#3299
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #14557882C2semidirect
4. #14557870C2semidirect
5. #14557827C2semidirect
6. #14557775C2semidirect
7. #14557772C2semidirect
8. #14557742C2semidirect
9. #14557691C2semidirect
10. #14557690C2semidirect
11. #14557627C2semidirect
13. C2×#11924459C2semidirect
14. #103×D37C2semidirect
15. C37×#484C2semidirect
124. C22⋊D37Q16semidirect
181. #484D37semidirect
192. C37#3299semidirect

Maximal subgroups

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

subgroupindex
#145582382
#145581962
#145578822
#145578702
#145578272
#145577752
#145577722
#145577422
#145576912
#145576902
#145576272
#145575962
C2×#119244592
#103×D372
C37×#4842
#329937