Finite Group Databasebeta

← #17995639

Subgroups — #17995639

Order 4736.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11924564C211yesmaximal, characteristic, complemented
2C2×#11924561C211yesmaximal, characteristic, complemented
3#14558111C211yesmaximal, characteristic, complemented
4C2×#11924464C211yesmaximal, characteristic, complemented
5#14557435C211yesmaximal, characteristic, complemented
6#14557301C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10#11924564—22no—
11#11924564—22no—
12#11924561—22no—
13#11924561—22no—
14C2×#10596930—21no—
15C2×#10596941—21no—
16C2×D296—21no—
17C2×#10596939—21no—
18C2×#10596934C2211yescharacteristic
19#11924515—21no—
20#11924512—21no—
21#11924510—21no—
22#11924508—22no—
23#11924507—21no—
24C2×C4⋊Dic37C2211yescharacteristic
25C2×#10596938—22no—
26#11924464—22no—
27C2×#41×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29C2×C42×C37C2211yescharacteristic
30#104×C37—22no—
31C23×D37—21no—
32#41×C37—21no—
33#41×C37—21no—
34#41×C37—21no—
35#41×C37—21no—
36C2×Q8×C37D411yescharacteristic
37C2×D4×C37—21no—
38C2×D4×C37D411yescharacteristic
39C22×C4×C37—21no—
40C22×C4×C37—21no—
41C22×C4×C37C2311yescharacteristic
42C2×C22⋊D37—21no—
43C2×C22⋊D37—22no—
44C22×Dic37D412yes—
45#10596962—21no—
46#10596962—21no—
47#10596962—21no—
48#10596962—21no—
49C2×D148—21no—
50C2×D148—21no—
51C2×D148—21no—
52C2×D148—21no—
53C2×D148—21no—
54C2×D148D411yescharacteristic
55C2×D148D412yescomplemented
56C2×C4×D37—21no—
57C2×Dic74D411yescharacteristic
58M16×C37—21no—
59M16×C37D412yescomplemented
60C2×C8×C37—21no—
61C42×C37—21no—
62C42×C37—21no—
63C22⋊Dic37—22no—
64#10596941—24no—
65#10596939—24no—
66#10596938—22no—
67#10596938—44no—
68C4⋊Dic37—21no—
69C4⋊Dic37—21no—
70#10596936—22no—
71#10596934—21no—
72#10596934D412yescomplemented
73C2×#64436—21no—
74D296—24no—
75#10596930—24no—
76C23×C37—21no—
77C23×C37C2×D411yescharacteristic
78C22×D37—21no—
79C22×D37—22no—
80C22×D37—42no—
81C22×D37—42no—
82C22×D37—41no—
83C22×D37—41no—
84Q8×C37—21no—
85Q8×C37—21no—
86D4×C37—21no—
87D4×C37—21no—
88D4×C37—41no—
89D4×C37—41no—
90C2×C4×C37—22no—
91C2×C4×C37—21no—
92C2×C4×C37—41no—
93C2×C4×C37—41no—
94C2×C4×C37—41no—
95C2×C4×C37—41no—
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37C2×D411yescharacteristic
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2×D411yescharacteristic
101C2×C4×C37#4111yescharacteristic
102C22⋊D37—41no—
103C22⋊D37—41no—
104C22⋊D37—82no—
105C2×Dic37—21no—
106C2×Dic37—22no—
107C2×Dic37—42no—
108D148—22no—
109D148—21no—
110D148—22no—
111D148—21no—
112D148—41no—
113D148—41no—
114C4×D37—41no—
115C4×D37—41no—
116Dic74—21no—
117Dic74—21no—
118C8×C37—22no—
119#64436—22no—
120C22×C37—21no—
121C22×C37—21no—
122C22×C37—41no—
123C22×C37—41no—
124C22×C37—41no—
125C22×C37#12011yescharacteristic
126C22×C37#12111yescharacteristic
127C22×C37#12711yescharacteristic
128C2×D37—44no—
129C2×D37—41no—
130C2×D37—42no—
131C2×D37—41no—
132C2×D37—41no—
133C2×D37—82no—
134C2×D37—81no—
135C2×D37—81no—
136C4×C37—42no—
137C4×C37—41no—
138C4×C37#12011yescharacteristic
139C4×C37#12011yescharacteristic
140C4×C37#12111yescharacteristic
141C4×C37#12111yescharacteristic
142Dic37—41no—
143Dic37—42no—
144#2006—371nomaximal, Sylow
145C2×C37—21no—
146C2×C37—21no—
147C2×C37—81no—
148C2×C37#39211yescharacteristic
149C2×C37#45311yescharacteristic
150C2×C37#45411yescharacteristic
151D37—81no—
152D37—82no—
153C2×AGL(1,ℤ/8)—371no—
154C2×AGL(1,ℤ/8)—371no—
155#537—371no—
156C2×#104—371no—
157C2×#104D3711yescharacteristic, complemented
158#390—371no—
159#343—371no—
160C37#200611yescharacteristic, complemented, Sylow
161C2×#41—371no—
162C2×#41C2×D3711yescharacteristic
163C22×D4—371no—
164AGL(1,ℤ/8)—742no—
165AGL(1,ℤ/8)—742no—
166AGL(1,ℤ/8)—742no—
167AGL(1,ℤ/8)—742no—
168C2×SD16—741no—
169C2×SD16—741no—
170C2×D8—741no—
171C2×D8—741no—
172C2×M16—371no—
173C2×M16C2×D3711yescharacteristic
174C22⋊Q8—741no—
175C22⋊Q8—741no—
176#121—741no—
177#121—742no—
178#121—741no—
179C2×C4⋊C4—371no—
180C2×C22⋊C4—742no—
181C2×C42C2×D3711yescharacteristic
182#104—22no—
183#104—742no—
184C24—741no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—21no—
189#41—741no—
190#41—741no—
191#41—741no—
192#41—741no—
193C2×Q8—371no—
194C2×Q8D14811yescharacteristic
195C2×D4—21no—
196C2×D4—371no—
197C2×D4—372no—
198C2×D4—742no—
199C2×D4—741no—
200C2×D4—741no—
201C2×D4—741no—
202C2×D4—741no—
203C2×D4—741no—
204C2×D4—741no—
205C2×D4D14811yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—372no—
209C22×C4—741no—
210C22×C4C22×D3711yescharacteristic
211SD16—744no—
212SD16—744no—
213D8—744no—
214D8—744no—
215M16—21no—
216M16—372no—
217M16—741no—
218M16C22⋊D3712yescomplemented
219C2×C8—21no—
220C2×C8—741no—
221C4⋊C4—742no—
222C4⋊C4—741no—
223C4⋊C4—741no—
224C22⋊C4—742no—
225C22⋊C4—742no—
226C22⋊C4—1484no—
227C42—21no—
228C42—21no—
229C23—21no—
230C23—741no—
231C23—742no—
232C23—1482no—
233C23—1482no—
234C23—1481no—
235C23—1481no—
236C23D4×D3711yescharacteristic
237Q8—21no—
238Q8—21no—
239Q8—741no—
240Q8—741no—
241D4—21no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—2962no—
246D4—741no—
247D4—742no—
248D4—742no—
249D4—741no—
250D4—1481no—
251D4—1481no—
252D4—1481no—
253D4—1481no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—742no—
261C2×C4—741no—
262C2×C4—1481no—
263C2×C4—1481no—
264C2×C4—1482no—
265C2×C4C2×D14811yescharacteristic
266C2×C4#1059696211yescharacteristic
267C2×C4D4×D3711yescharacteristic
268C2×C4D4×D3711yescharacteristic
269C2×C4D4×D3711yescharacteristic
270C2×C4C2×C22⋊D3711yescharacteristic
271C8—22no—
272C8—742no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—2962no—
279C22—2961no—
280C22—2961no—
281C22—1484no—
282C22—1481no—
283C22—1482no—
284C22—1481no—
285C22—1481no—
286C22#1192450611yescharacteristic
287C22#1192450911yescharacteristic
288C22#1192453211yescharacteristic
289C4—42no—
290C4—41no—
291C4—1481no—
292C4—1482no—
293C4#1192450411yescharacteristic
294C4#1192450611yescharacteristic
295C4#1192450911yescharacteristic
296C4#1192451011yescharacteristic
297C2—21no—
298C2—21no—
299C2—81no—
300C2—2962no—
301C2—2961no—
302C2#1455744211yescharacteristic
303C2#1455770211yescharacteristic
304C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37#120
hypercenterC2×#104D37
hypocenterC37#2006
LCSG ▷ C22×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
1. C2×#11924564C2semidirect
2. C2×#11924561C2semidirect
3. #14558111C2semidirect
4. C2×#11924464C2semidirect
5. #14557435C2semidirect
6. #14557301C2semidirect
7. C2×#104×C37C2semidirect
55. C2×D148D4semidirect
59. M16×C37D4semidirect
72. #10596934D4semidirect
157. C2×#104D37semidirect
160. C37#2006semidirect
218. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245642
C2×#119245612
#145581112
C2×#119244642
#145574352
#145573012
C2×#104×C372
#200637