Finite Group Databasebeta

← #18006061

Subgroups — #18006061

Order 4736.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558154C211yesmaximal, characteristic, complemented
2#14557823C211yesmaximal, characteristic, complemented
3#14557820C211yesmaximal, characteristic, complemented
4#14557818C211yesmaximal, characteristic, complemented
5#14557815C211yesmaximal, characteristic, complemented
6#14557789C211yesmaximal, characteristic, complemented
7#14557784C211yesmaximal, characteristic
8#14557764C211yesmaximal, characteristic, complemented
9#14557760C211yesmaximal, characteristic, complemented
10#14557755C211yesmaximal, characteristic, complemented
11#14557752C211yesmaximal, characteristic, complemented
12#14557748C211yesmaximal, characteristic, complemented
13#14557745C211yesmaximal, characteristic, complemented
14#14557560C211yesmaximal, characteristic, complemented
15C37×#542C211yesmaximal, characteristic, complemented
16C2×#10596942C2211yescharacteristic
17C2×#10596940C2211yescharacteristic
18C2×#10596941C2211yescharacteristic
19C2×#10596939C2211yescharacteristic
20C2×#10596934C2211yescharacteristic
21C22×#64436C2211yescharacteristic
22#11924536C2211yescharacteristic
23#11924531—21no—
24#11924524C2211yescharacteristic
25#11924522—21no—
26#11924518—21no—
27#11924515C2211yescharacteristic
28#11924514—21no—
29#11924510C2211yescharacteristic
30C4×Dic74C2211yescharacteristic
31C4×D148C2211yescharacteristic
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34#11924467C2211yescharacteristic
35#11924467C2211yescharacteristic
36C4⋊#64436C2211yescharacteristic
37C4⋊#64436C2211yescharacteristic
38C4⋊#64436C2211yescharacteristic
39C4⋊#64436C2211yescharacteristic
40#11924460C2211yescharacteristic
41#11924460C2211yescharacteristic
42#11924459C2211yescharacteristic
43#11924459C2211yescharacteristic
44#11924457C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48C4⋊Q8×C37C2211yescharacteristic
49#126×C37—21no—
50#124×C37—21no—
51#124×C37C2211yescharacteristic
52#123×C37—21no—
53C22⋊Q8×C37—21no—
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56C4×Q8×C37C2211yescharacteristic
57C4×D4×C37C2211yescharacteristic
58#117×C37C2211yescharacteristic
59C2×Q8×C37—21no—
60C2×Q8×C37C2311yescharacteristic
61C2×D4×C37—21no—
62C2×D4×C37C2311yescharacteristic
63C22×C4×C37—21no—
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×Dic74—21no—
69C2×Dic74C2311yescharacteristic
70C4⋊C4×C37—21no—
71C4⋊C4×C37—21no—
72C4⋊C4×C37—21no—
73C4⋊C4×C37D411yescharacteristic
74C4⋊C4×C37D411yescharacteristic
75C4⋊C4×C37C2311yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C22⋊C4×C37—21no—
78C22⋊C4×C37—21no—
79C22⋊C4×C37—21no—
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊C4×C37D411yescharacteristic
83C22⋊C4×C37D411yescharacteristic
84C42×C37—21no—
85C42×C37C2311yescharacteristic
86C42×C37C2311yescharacteristic
87C22⋊Dic37—21no—
88#10596942—41no—
89#10596941—41no—
90#10596940—41no—
91#10596939—41no—
92#10596938—21no—
93#10596938—21no—
94#10596938—21no—
95#10596938—21no—
96C4⋊Dic37—21no—
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102#10596934—41no—
103C2×#64436—41no—
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107C2×#64436C2311yescharacteristic
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111Q8×C37—21no—
112Q8×C37—21no—
113Q8×C37—81no—
114D4×C37—21no—
115D4×C37—21no—
116D4×C37—81no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—81no—
123C2×C4×C37C2×D411yescharacteristic
124C2×C4×C37C2×D411yescharacteristic
125C2×C4×C37C2×D411yescharacteristic
126C2×C4×C37C2×D411yescharacteristic
127C2×C4×C37C2×D411yescharacteristic
128C2×C4×C37C2411yescharacteristic
129C22⋊D37—81no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133D148—21no—
134D148—21no—
135C4×D37—81no—
136Dic74—21no—
137Dic74—21no—
138Dic74—81no—
139#64436—21no—
140#64436—21no—
141#64436—21no—
142#64436—21no—
143C22×C37—21no—
144C22×C37—21no—
145C22×C37—21no—
146C22×C37—41no—
147C22×C37—41no—
148C22×C37—41no—
149C22×C37C22×D411yescharacteristic
150C2×D37—41no—
151C2×D37—41no—
152C2×D37—41no—
153C4×C37—21no—
154C4×C37—21no—
155C4×C37—21no—
156C4×C37—21no—
157C4×C37—21no—
158C4×C37—41no—
159C4×C37—41no—
160C4×C37—41no—
161C4×C37H(5,𝔽2)11yescharacteristic
162C4×C372−1+411yescharacteristic
163Dic37—41no—
164Dic37—41no—
165Dic37—41no—
166#3263—371nomaximal, Sylow
167C2×C37—41no—
168C2×C37—81no—
169C2×C37#53711yescharacteristic
170C2×C37#57711yescharacteristic
171C2×C37#57711yescharacteristic
172D37—81no—
173#542—371no—
174#542D3711yescharacteristic, complemented
175#476—371no—
176#476—371no—
177#475—371no—
178#475—371no—
179#470—371no—
180#469—371no—
181#465—371no—
182#465—371no—
183#464—371no—
184#464—371no—
185#463—371no—
186#463—371no—
187#424—371no—
188C37#326311yescharacteristic, complemented, Sylow
189C2×Q16—371no—
190C2×SD16—371no—
191C2×SD16—371no—
192C2×D8—371no—
193C2×M16—371no—
194C22×C8—371no—
195C4⋊Q8—371no—
196C4⋊Q8C2×D3711yescharacteristic
197#126—21no—
198#126—741no—
199#124—21no—
200#124—371no—
201#124—741no—
202#124C2×D3711yescharacteristic
203#123—21no—
204#123—741no—
205C22⋊Q8—21no—
206C22⋊Q8—371no—
207C22⋊Q8—741no—
208C22⋊Q8C2×D3711yescharacteristic
209#121—371no—
210#121C2×D3711yescharacteristic
211C4×Q8—371no—
212C4×Q8C2×D3711yescharacteristic
213C4×D4—371no—
214C4×D4C2×D3711yescharacteristic
215#117C2×D3711yescharacteristic
216#106—371no—
217#106—371no—
218#106—371no—
219#106—371no—
220C4⋊C8—371no—
221C4⋊C8—371no—
222C4⋊C8—371no—
223C4⋊C8—371no—
224#103—371no—
225#103—371no—
226#103—371no—
227#103—371no—
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232C2×Q8—21no—
233C2×Q8—371no—
234C2×Q8—741no—
235C2×Q8C22×D3711yescharacteristic
236C2×D4—21no—
237C2×D4—371no—
238C2×D4—741no—
239C2×D4C22×D3711yescharacteristic
240C22×C4—21no—
241C22×C4—741no—
242C22×C4C22×D3711yescharacteristic
243Q16—1481no—
244SD16—1481no—
245SD16—1481no—
246D8—1481no—
247M16—1481no—
248C2×C8—371no—
249C2×C8—371no—
250C2×C8—371no—
251C2×C8—371no—
252C2×C8—1481no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—371no—
257C4⋊C4—371no—
258C4⋊C4—741no—
259C4⋊C4—741no—
260C4⋊C4—741no—
261C4⋊C4C22⋊D3711yescharacteristic
262C4⋊C4C22⋊D3711yescharacteristic
263C4⋊C4C22×D3711yescharacteristic
264C4⋊C4C22×D3711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—741no—
271C22⋊C4—741no—
272C22⋊C4—741no—
273C22⋊C4—741no—
274C22⋊C4—741no—
275C22⋊C4C22⋊D3711yescharacteristic
276C22⋊C4C22⋊D3711yescharacteristic
277C42—21no—
278C42—741no—
279C42C22×D3711yescharacteristic
280C42C22×D3711yescharacteristic
281C23—21no—
282C23—741no—
283C23C2×C22⋊D3711yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—2961no—
288Q8—741no—
289Q8—741no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—2961no—
294D4—741no—
295D4—741no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—2961no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4—741no—
306C2×C4C2×C22⋊D3711yescharacteristic
307C2×C4C2×C22⋊D3711yescharacteristic
308C2×C4C2×C22⋊D3711yescharacteristic
309C2×C4C2×C22⋊D3711yescharacteristic
310C2×C4C2×C22⋊D3711yescharacteristic
311C2×C4C23×D3711yescharacteristic
312C8—741no—
313C8—741no—
314C8—741no—
315C8—741no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—1481no—
323C22—1481no—
324C22—1481no—
325C22C22×C22⋊D3711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—1481no—
335C4—1481no—
336C4—1481no—
337C4#1192458211yescharacteristic
338C4#1192458311yescharacteristic
339C2—41no—
340C2—81no—
341C2—2961no—
342C2#1455811111yescharacteristic
343C2#1455834111yescharacteristic
344C2#1455834411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#542C2
socleC22×C37C22×D4
prime radical#14557784C2
hypercenter#542D37
hypocenterC37#3263
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #14558154C2semidirect
2. #14557823C2semidirect
3. #14557820C2semidirect
4. #14557818C2semidirect
5. #14557815C2semidirect
6. #14557789C2semidirect
8. #14557764C2semidirect
9. #14557760C2semidirect
10. #14557755C2semidirect
11. #14557752C2semidirect
12. #14557748C2semidirect
13. #14557745C2semidirect
14. #14557560C2semidirect
15. C37×#542C2semidirect
174. #542D37semidirect
188. C37#3263semidirect

Maximal subgroups

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

subgroupindex
#145581542
#145578232
#145578202
#145578182
#145578152
#145577892
#145577842
#145577642
#145577602
#145577552
#145577522
#145577482
#145577452
#145575602
C37×#5422
#326337