Finite Group Databasebeta

← #17994551

Subgroups — #17994551

Order 4736.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924582C211yesmaximal, characteristic
2C2×#11924464C211yesmaximal, characteristic, complemented
3#14557535C211yesmaximal, characteristic, complemented
4#14557534C211yesmaximal, characteristic, complemented
5C2×#11924452C211yesmaximal, characteristic, complemented
6#14557435C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8#11924582—22no—
9#11924582—22no—
10#11924582—22no—
11#11924582C414yescomplemented
12C2×#10596966—21no—
13C2×#10596962—21no—
14C2×#10596962C2211yescharacteristic
15C22×D148—21no—
16C22×D148C2211yescharacteristic
17C2×D4×D37—22no—
18C2×D4×D37—21no—
19C2×#10596934C2211yescharacteristic, complemented
20C2×C4⋊Dic37C2211yescharacteristic, complemented
21C2×#10596938—22no—
22#11924464—22no—
23#11924461—21no—
24#11924460—21no—
25#11924458—21no—
26#11924457—21no—
27#11924452—22no—
28C2×#41×C37C2211yescharacteristic
29C2×M16×C37C2211yescharacteristic, complemented
30C2×C42×C37C2211yescharacteristic, complemented
31#104×C37—22no—
32C23×D37—22no—
33C23×D37D412yes—
34#41×C37—21no—
35#41×C37—21no—
36#41×C37C2×C412yes—
37#41×C37D412yes—
38C2×Q8×C37D411yescharacteristic
39C2×D4×C37—21no—
40C2×D4×C37D411yescharacteristic
41C22×C4×C37—21no—
42C22×C4×C37—21no—
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—22no—
45C2×C22⋊D37—21no—
46C22×Dic37—21no—
47#10596966—24no—
48#10596966—24no—
49D4×D37—28no—
50D4×D37—24no—
51D4×D37—28no—
52D4×D37—24no—
53#10596962—24no—
54#10596962—21no—
55#10596962—21no—
56#10596962—24no—
57#10596962C2×C412yes—
58#10596962D412yes—
59C2×D148—22no—
60C2×D148—24no—
61C2×D148—21no—
62C2×D148—21no—
63C2×D148—21no—
64C2×D148—21no—
65C2×D148—24no—
66C2×D148C2×C412yes—
67C2×D148D412yes—
68C2×D148D411yescharacteristic
69C2×C4×D37—22no—
70C2×C4×D37—21no—
71C2×Dic74D411yescharacteristic
72M16×C37—21no—
73M16×C37—21no—
74C2×C8×C37—21no—
75C42×C37—21no—
76C42×C37—21no—
77#10596938—44no—
78C4⋊Dic37—21no—
79C4⋊Dic37—21no—
80#10596934—21no—
81#10596934—21no—
82C2×#64436—21no—
83C23×C37—21no—
84C23×C37C2×D411yescharacteristic
85C22×D37—22no—
86C22×D37—21no—
87C22×D37—28no—
88C22×D37—22no—
89C22×D37—42no—
90C22×D37—42no—
91C22×D37—82no—
92C22×D37—82no—
93C22×D37C22⋊C414yes—
94Q8×C37—21no—
95Q8×C37C22⋊C412yescomplemented
96D4×C37—22no—
97D4×C37—22no—
98D4×C37—21no—
99D4×C37C22⋊C412yescomplemented
100C2×C4×C37—21no—
101C2×C4×C37—22no—
102C2×C4×C37—22no—
103C2×C4×C37—22no—
104C2×C4×C37—41no—
105C2×C4×C37—41no—
106C2×C4×C37C22×C411yescharacteristic
107C2×C4×C37C2×D411yescharacteristic
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37C2×D411yescharacteristic
110C2×C4×C37C2×D411yescharacteristic
111C2×C4×C37C2×D411yescharacteristic
112C22⋊D37—28no—
113C22⋊D37—22no—
114C22⋊D37—22no—
115C2×Dic37—21no—
116C2×Dic37—42no—
117C2×Dic37—41no—
118D148—28no—
119D148—22no—
120D148—22no—
121D148—22no—
122D148—21no—
123D148—22no—
124D148C22⋊C412yescomplemented
125C4×D37—28no—
126C4×D37—22no—
127C4×D37—22no—
128Dic74—21no—
129Dic74C22⋊C412yescomplemented
130C8×C37—41no—
131#64436—41no—
132C22×C37—21no—
133C22×C37—21no—
134C22×C37—22no—
135C22×C37—41no—
136C22×C37—41no—
137C22×C37C2×C22⋊C411yescharacteristic
138C22×C37#12011yescharacteristic
139C22×C37#12011yescharacteristic
140C2×D37—24no—
141C2×D37—22no—
142C2×D37—42no—
143C2×D37—41no—
144C2×D37—42no—
145C2×D37—41no—
146C2×D37—44no—
147C2×D37—82no—
148C2×D37—88no—
149C4×C37—22no—
150C4×C37—42no—
151C4×C37C2×C22⋊C411yescharacteristic
152C4×C37C2×C22⋊C411yescharacteristic
153C4×C37#12011yescharacteristic
154C4×C37#12011yescharacteristic
155Dic37—22no—
156Dic37—81no—
157#1792—371nomaximal, Sylow
158C2×C37—21no—
159C2×C37—21no—
160C2×C37—42no—
161C2×C37#37911yescharacteristic
162C2×C37#45311yescharacteristic
163C2×C37#45511yescharacteristic
164D37—44no—
165D37—42no—
166C2×H(5,𝔽2)—371no—
167C2×#104—371no—
168C2×#104D3711yescharacteristic, complemented
169#417—371no—
170#417—371no—
171C2×#100—371no—
172#390—371no—
173C37#179211yescharacteristic, complemented, Sylow
174H(5,𝔽2)—374no—
175H(5,𝔽2)—742no—
176H(5,𝔽2)—742no—
177H(5,𝔽2)—742no—
178C2×#41—371no—
179C2×#41—741no—
180C2×#41—741no—
181C2×#41C2×D3711yescharacteristic
182C22×D4—371no—
183C22×D4—741no—
184C22×D4—742no—
185C22×D4—741no—
186C2×M16—371no—
187C2×M16C2×D3711yescharacteristic, complemented
188C2×C4⋊C4—371no—
189C2×C22⋊C4—742no—
190C2×C42C2×D3711yescharacteristic, complemented
191#104—22no—
192#104—742no—
193#103—741no—
194#103—741no—
195#102—741no—
196#102—741no—
197#100—742no—
198C24—372no—
199C24—742no—
200#41—21no—
201#41—21no—
202#41—372no—
203#41—372no—
204#41—744no—
205#41—744no—
206#41—744no—
207#41—744no—
208#41—741no—
209#41—741no—
210#41C4×D3712yes—
211#41C22⋊D3712yes—
212C2×Q8—371no—
213C2×Q8D14811yescharacteristic
214C2×D4—21no—
215C2×D4—372no—
216C2×D4—371no—
217C2×D4—372no—
218C2×D4—744no—
219C2×D4—742no—
220C2×D4—744no—
221C2×D4—748no—
222C2×D4—748no—
223C2×D4—744no—
224C2×D4—742no—
225C2×D4—741no—
226C2×D4—744no—
227C2×D4—741no—
228C2×D4—741no—
229C2×D4—741no—
230C2×D4—741no—
231C2×D4D14811yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—742no—
235C22×C4—741no—
236C22×C4—741no—
237C22×C4C22×D3711yescharacteristic
238M16—21no—
239M16—21no—
240M16—741no—
241M16—741no—
242C2×C8—21no—
243C2×C8—741no—
244C4⋊C4—741no—
245C4⋊C4—741no—
246C22⋊C4—1484no—
247C42—21no—
248C42—21no—
249C23—21no—
250C23—374no—
251C23—2962no—
252C23—2962no—
253C23—748no—
254C23—742no—
255C23—741no—
256C23—742no—
257C23—1482no—
258C23—1482no—
259C23D4×D3711yescharacteristic
260Q8—21no—
261Q8—372no—
262Q8—741no—
263Q8#1059693812yescomplemented
264D4—22no—
265D4—22no—
266D4—21no—
267D4—372no—
268D4—748no—
269D4—748no—
270D4—742no—
271D4—742no—
272D4—742no—
273D4—742no—
274D4—741no—
275D4—742no—
276D4—742no—
277D4#1059693812yescomplemented
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—748no—
285C2×C4—741no—
286C2×C4—742no—
287C2×C4—742no—
288C2×C4—1482no—
289C2×C4—1481no—
290C2×C4C2×C4×D3711yescharacteristic
291C2×C4C2×D14811yescharacteristic
292C2×C4D4×D3711yescharacteristic
293C2×C4D4×D3711yescharacteristic
294C2×C4D4×D3711yescharacteristic
295C2×C4C2×C22⋊D3711yescharacteristic
296C8—41no—
297C8—1481no—
298C22—21no—
299C22—21no—
300C22—22no—
301C22—41no—
302C22—41no—
303C22—2962no—
304C22—2968no—
305C22—742no—
306C22—744no—
307C22—1484no—
308C22—1481no—
309C22—1482no—
310C22—1481no—
311C22—1482no—
312C22C22⋊C4×D3711yescharacteristic
313C22#1192450411yescharacteristic
314C22#1192450611yescharacteristic
315C4—22no—
316C4—42no—
317C4—2961no—
318C4—742no—
319C4C22⋊C4×D3711yescharacteristic
320C4C2×#1059693811yescharacteristic
321C4#1192450411yescharacteristic
322C4#1192450611yescharacteristic
323C2—21no—
324C2—21no—
325C2—42no—
326C2—1482no—
327C2—1484no—
328C2#1455738811yescharacteristic
329C2#1455770211yescharacteristic
330C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37#120
prime radicalC2×#11924582C2
cosocleC22×C4×C37C23
hypercenterC2×#104D37
hypocenterC37#1792
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#11924464C2semidirect
3. #14557535C2semidirect
4. #14557534C2semidirect
5. C2×#11924452C2semidirect
6. #14557435C2semidirect
7. C2×#104×C37C2semidirect
11. #11924582C4semidirect
19. C2×#10596934C22semidirect
20. C2×C4⋊Dic37C22semidirect
29. C2×M16×C37C22semidirect
30. C2×C42×C37C22semidirect
95. Q8×C37C22⋊C4semidirect
99. D4×C37C22⋊C4semidirect
124. D148C22⋊C4semidirect
129. Dic74C22⋊C4semidirect
168. C2×#104D37semidirect
173. C37#1792semidirect
187. C2×M16C2×D37semidirect
190. C2×C42C2×D37semidirect
263. Q8#10596938semidirect
277. D4#10596938semidirect

Maximal subgroups

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

subgroupindex
C2×#119245822
C2×#119244642
#145575352
#145575342
C2×#119244522
#145574352
C2×#104×C372
#179237