Finite Group Databasebeta

← #18005274

Subgroups — #18005274

Order 4736.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558156C211yesmaximal, characteristic, complemented
2#14558136C211yesmaximal, characteristic, complemented
3#14557940C211yesmaximal, characteristic, complemented
4#14557919C211yesmaximal, characteristic, complemented
5#14557889C211yesmaximal, characteristic, complemented
6#14557878C211yesmaximal, characteristic, complemented
7#14557784C211yesmaximal, characteristic, complemented
8#14557781C211yesmaximal, characteristic, complemented
9#14557769C211yesmaximal, characteristic, complemented
10#14557644C211yesmaximal, characteristic, complemented
11#14557634C211yesmaximal, characteristic, complemented
12#14557618C211yesmaximal, characteristic, complemented
13#14557613C211yesmaximal, characteristic, complemented
14#14557488C211yesmaximal, characteristic, complemented
15C37×#465C211yesmaximal, characteristic, complemented
16C2×#10596941C2211yescharacteristic
17C2×D296C2211yescharacteristic
18C2×#10596939C2211yescharacteristic
19C2×#10596934C2211yescharacteristic
20#11924535C2211yescharacteristic
21#11924532C2211yescharacteristic
22#11924531—21no—
23#11924527C2211yescharacteristic
24#11924525C2211yescharacteristic
25#11924522—21no—
26#11924520—21no—
27#11924518—21no—
28#11924518—21no—
29#11924516—21no—
30#11924510C2211yescharacteristic
31#11924510C2211yescharacteristic
32#11924508—21no—
33#11924507—21no—
34Q8×Dic37C2211yescharacteristic
35D4×Dic37C2211yescharacteristic
36#11924498C2211yescharacteristic
37#11924498C2211yescharacteristic
38#11924495C2211yescharacteristic
39#11924470C2211yescharacteristic
40#11924469C2211yescharacteristic
41#11924467C2211yescharacteristic
42#11924460C2211yescharacteristic
43#11924458C2211yescharacteristic
44#11924458C2211yescharacteristic
45#11924457C2211yescharacteristic
46#11924456C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924446C2211yescharacteristic
49#11924446C2211yescharacteristic
50C8×Dic37C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C2×SD16×C37C2211yescharacteristic
53C22×C8×C37C2211yescharacteristic
54C22⋊Q8×C37C2211yescharacteristic
55#121×C37C2211yescharacteristic
56#106×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58#102×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C2×D4×C37—21no—
61C2×D4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C2×C22⋊D37—21no—
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68C2×D148C2311yescharacteristic
69C2×D148C2311yescharacteristic
70C2×C4×D37—21no—
71C2×C4×D37—21no—
72C2×Dic74—21no—
73SD16×C37—22no—
74C2×C8×C37—22no—
75C2×C8×C37C2311yescharacteristic
76C2×C8×C37C2311yescharacteristic
77C4⋊C4×C37—21no—
78C4⋊C4×C37C2311yescharacteristic
79C4⋊C4×C37C2311yescharacteristic
80C22⋊C4×C37—21no—
81C22⋊C4×C37—21no—
82C22⋊Dic37—21no—
83C22⋊Dic37D411yescharacteristic
84C22⋊Dic37D411yescharacteristic
85#10596941—22no—
86#10596939—22no—
87#10596938—21no—
88#10596938—21no—
89#10596938—21no—
90#10596938—21no—
91#10596938—21no—
92#10596938—21no—
93C4⋊Dic37—21no—
94C4⋊Dic37—21no—
95C4⋊Dic37D411yescharacteristic
96C4⋊Dic37D411yescharacteristic
97C4⋊Dic37C2311yescharacteristic
98C4⋊Dic37C2311yescharacteristic
99#10596936—21no—
100#10596936—21no—
101C4×Dic37—21no—
102C4×Dic37C2311yescharacteristic
103C4×Dic37C2311yescharacteristic
104#10596934—22no—
105C2×#64436C2311yescharacteristic
106C2×#64436C2311yescharacteristic
107D296—22no—
108C23×C37—21no—
109C23×C37C2×D411yescharacteristic
110C22×D37—21no—
111C22×D37—21no—
112Q8×C37—21no—
113Q8×C37—21no—
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×C37C2×D411yescharacteristic
123C2×C4×C37C2411yescharacteristic
124C22⋊D37—81no—
125C22⋊D37—81no—
126C22⋊D37—81no—
127C22⋊D37—81no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—81no—
131C2×Dic37C2×D411yescharacteristic
132C2×Dic37C2×D411yescharacteristic
133C2×Dic37C2×D411yescharacteristic
134C2×Dic37C2×D411yescharacteristic
135D148—21no—
136D148—21no—
137D148—21no—
138D148—21no—
139C4×D37—81no—
140C4×D37—81no—
141Dic74—81no—
142C8×C37—21no—
143C8×C37#4112yes—
144#64436—21no—
145#64436#4112yes—
146C22×C37—21no—
147C22×C37—21no—
148C22×C37—21no—
149C22×C37—41no—
150C22×C37—41no—
151C22×C37—41no—
152C22×C37C22×D411yescharacteristic
153C2×D37—41no—
154C2×D37—41no—
155C2×D37—41no—
156C2×D37—41no—
157C2×D37—41no—
158C2×D37—41no—
159C4×C37—21no—
160C4×C37—41no—
161C4×C37—41no—
162C4×C37—41no—
163C4×C37C2×#4111yescharacteristic
164C4×C37C2×#4111yescharacteristic
165Dic37—21no—
166Dic37—21no—
167Dic37—21no—
168Dic37—21no—
169Dic37—41no—
170Dic37—41no—
171#3179—371nomaximal, Sylow
172C2×C37—41no—
173C2×C37—81no—
174C2×C37#53211yescharacteristic
175C2×C37#57611yescharacteristic
176C2×C37#57711yescharacteristic
177D37—81no—
178D37—81no—
179#542—371no—
180#540—371no—
181#501—371no—
182#496—371no—
183#488—371no—
184#486—371no—
185#469—371no—
186#468—371no—
187#466—371no—
188#465D3711yescharacteristic, complemented
189#442—371no—
190#440—371no—
191C4×SD16—371no—
192C4×D8—371no—
193#405—371no—
194C37#317911yescharacteristic, complemented, Sylow
195C2×SD16—371no—
196C2×SD16C2×D3711yescharacteristic
197C2×D8—371no—
198C2×D8—371no—
199C2×M16—371no—
200C22×C8C2×D3711yescharacteristic
201C4⋊Q8—371no—
202#127—371no—
203#126—741no—
204#125—371no—
205#124—371no—
206#124—741no—
207#123—741no—
208#123—741no—
209#123—741no—
210C22⋊Q8—741no—
211C22⋊Q8C2×D3711yescharacteristic
212#121—371no—
213#121—371no—
214#121—741no—
215#121—741no—
216#121C2×D3711yescharacteristic
217C4×Q8—371no—
218C4×D4—371no—
219C4×D4—371no—
220C4×D4—371no—
221#117—371no—
222#107—371no—
223#107—371no—
224#106—371no—
225#106C2×D3711yescharacteristic
226#103—371no—
227#103C2×D3711yescharacteristic
228#102—371no—
229#102—371no—
230#102—371no—
231#102—371no—
232#102—371no—
233#102C2×D3711yescharacteristic
234#97—371no—
235#97—371no—
236C4×C8—371no—
237C4×C8—371no—
238C2×Q8—741no—
239C2×Q8C22×D3711yescharacteristic
240C2×D4—21no—
241C2×D4—371no—
242C2×D4—371no—
243C2×D4—741no—
244C2×D4—741no—
245C2×D4—741no—
246C2×D4—741no—
247C2×D4C22×D3711yescharacteristic
248C22×C4—741no—
249C22×C4—741no—
250C22×C4—741no—
251C22×C4C22×D3711yescharacteristic
252SD16—22no—
253SD16—742no—
254D8—742no—
255D8—742no—
256M16—742no—
257C2×C8—22no—
258C2×C8—371no—
259C2×C8—371no—
260C2×C8C22×D3711yescharacteristic
261C2×C8C22×D3711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—371no—
264C4⋊C4—371no—
265C4⋊C4—371no—
266C4⋊C4—371no—
267C4⋊C4—741no—
268C4⋊C4—741no—
269C4⋊C4—741no—
270C4⋊C4—741no—
271C4⋊C4C22×D3711yescharacteristic
272C4⋊C4C22×D3711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—371no—
276C22⋊C4—371no—
277C22⋊C4—741no—
278C22⋊C4—741no—
279C22⋊C4—741no—
280C22⋊C4—741no—
281C22⋊C4—741no—
282C22⋊C4—741no—
283C22⋊C4—741no—
284C42—371no—
285C42—371no—
286C42—741no—
287C23—21no—
288C23—741no—
289C23—741no—
290C23D4×D3711yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—2961no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—2961no—
298D4—2961no—
299D4—2961no—
300D4—2961no—
301D4—741no—
302D4—741no—
303D4—741no—
304D4—741no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—371no—
311C2×C4—371no—
312C2×C4—371no—
313C2×C4—371no—
314C2×C4—2961no—
315C2×C4—2961no—
316C2×C4—2961no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4D4×D3711yescharacteristic
320C2×C4C23×D3711yescharacteristic
321C8—21no—
322C8—372no—
323C8—741no—
324C8#1059696412yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1481no—
332C22—1481no—
333C22—1481no—
334C22—1481no—
335C22—1481no—
336C22—1481no—
337C22C2×D4×D3711yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—741no—
343C4—741no—
344C4—741no—
345C4—741no—
346C4—1481no—
347C4—1481no—
348C4#41×D3711yescharacteristic
349C4C2×#1059696411yescharacteristic
350C2—41no—
351C2—81no—
352C2—2961no—
353C2—2961no—
354C2#1455807811yescharacteristic
355C2#1455833511yescharacteristic
356C2#1455833911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#465C2
socleC22×C37C22×D4
hypercenter#465D37
hypocenterC37#3179
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14558156C2semidirect
2. #14558136C2semidirect
3. #14557940C2semidirect
4. #14557919C2semidirect
5. #14557889C2semidirect
6. #14557878C2semidirect
7. #14557784C2semidirect
8. #14557781C2semidirect
9. #14557769C2semidirect
10. #14557644C2semidirect
11. #14557634C2semidirect
12. #14557618C2semidirect
13. #14557613C2semidirect
14. #14557488C2semidirect
15. C37×#465C2semidirect
188. #465D37semidirect
194. C37#3179semidirect

Maximal subgroups

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

subgroupindex
#145581562
#145581362
#145579402
#145579192
#145578892
#145578782
#145577842
#145577812
#145577692
#145576442
#145576342
#145576182
#145576132
#145574882
C37×#4652
#317937