Finite Group Databasebeta

← #17995644

Subgroups — #17995644

Order 4736.

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

normal subgroups only

This group has 370 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×#11924569C211yesmaximal, characteristic, complemented
2C2×#11924566C211yesmaximal, characteristic, complemented
3#14558111C211yesmaximal, characteristic
4C2×#11924464C211yesmaximal, characteristic, complemented
5#14557439C211yesmaximal, characteristic, complemented
6#14557301C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924569—22no—
11#11924569—22no—
12#11924566—22no—
13#11924566—22no—
14C2×Dic148—21no—
15C2×#10596942—21no—
16C2×#10596930—21no—
17C2×#10596940—21no—
18C2×#10596934C2211yescharacteristic
19#11924515—21no—
20#11924512—21no—
21#11924510—21no—
22#11924508—22no—
23#11924507—21no—
24C2×C4⋊Dic37C2211yescharacteristic
25#11924464—22no—
26#11924443—22no—
27C2×#41×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29C2×C42×C37C2211yescharacteristic
30#104×C37—22no—
31#41×C37—21no—
32#41×C37—21no—
33#41×C37—21no—
34#41×C37—21no—
35C2×Q8×C37D411yescharacteristic
36C2×D4×C37—21no—
37C2×D4×C37D411yescharacteristic
38C22×C4×C37—21no—
39C22×C4×C37—21no—
40C22×C4×C37C2311yescharacteristic
41C2×C22⋊D37—21no—
42C2×C22⋊D37—22no—
43C22×Dic37—21no—
44C22×Dic37D412yes—
45#10596962—21no—
46#10596962—21no—
47#10596962—21no—
48#10596962—21no—
49C2×D148D411yescharacteristic
50C2×C4×D37—21no—
51C2×Dic74—21no—
52C2×Dic74—21no—
53C2×Dic74—21no—
54C2×Dic74—21no—
55C2×Dic74—21no—
56C2×Dic74D411yescharacteristic
57C2×Dic74D412yescomplemented
58M16×C37—21no—
59M16×C37D412yescomplemented
60C2×C8×C37—21no—
61C42×C37—21no—
62C42×C37—21no—
63C22⋊Dic37—22no—
64#10596942—24no—
65#10596940—24no—
66#10596938—22no—
67C4⋊Dic37—21no—
68C4⋊Dic37—21no—
69#10596936—22no—
70#10596934—21no—
71#10596934D412yescomplemented
72C2×#64436—21no—
73Dic148—24no—
74#10596930—24no—
75C23×C37—21no—
76C23×C37C2×D411yescharacteristic
77C22×D37—21no—
78Q8×C37—21no—
79Q8×C37—21no—
80D4×C37—21no—
81D4×C37—21no—
82D4×C37—41no—
83D4×C37—41no—
84C2×C4×C37—22no—
85C2×C4×C37—21no—
86C2×C4×C37—41no—
87C2×C4×C37—41no—
88C2×C4×C37—41no—
89C2×C4×C37—41no—
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37C2×D411yescharacteristic
93C2×C4×C37C2×D411yescharacteristic
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37#4111yescharacteristic
96C22⋊D37—41no—
97C22⋊D37—41no—
98C22⋊D37—82no—
99C2×Dic37—21no—
100C2×Dic37—22no—
101C2×Dic37—22no—
102C2×Dic37—41no—
103C2×Dic37—41no—
104C2×Dic37—42no—
105D148—21no—
106D148—21no—
107C4×D37—41no—
108C4×D37—41no—
109Dic74—22no—
110Dic74—21no—
111Dic74—22no—
112Dic74—21no—
113Dic74—41no—
114Dic74—41no—
115C8×C37—22no—
116#64436—22no—
117C22×C37—21no—
118C22×C37—21no—
119C22×C37—41no—
120C22×C37—41no—
121C22×C37—41no—
122C22×C37#12011yescharacteristic
123C22×C37#12111yescharacteristic
124C22×C37#12711yescharacteristic
125C2×D37—41no—
126C2×D37—41no—
127C2×D37—41no—
128C4×C37—42no—
129C4×C37—41no—
130C4×C37#12011yescharacteristic
131C4×C37#12011yescharacteristic
132C4×C37#12111yescharacteristic
133C4×C37#12111yescharacteristic
134Dic37—42no—
135Dic37—41no—
136Dic37—42no—
137#2007—371nomaximal, Sylow
138C2×C37—21no—
139C2×C37—21no—
140C2×C37—81no—
141C2×C37#39211yescharacteristic
142C2×C37#45511yescharacteristic
143C2×C37#45611yescharacteristic
144D37—81no—
145C2×#137—371no—
146C2×#137—371no—
147#537—371no—
148C2×#104—371no—
149C2×#104D3711yescharacteristic, complemented
150#391—371no—
151#343—371no—
152C37#200711yescharacteristic, complemented, Sylow
153C2×#41—371no—
154C2×#41C2×D3711yescharacteristic
155C22×Q8—371no—
156#137—742no—
157#137—742no—
158#137—742no—
159#137—742no—
160C2×Q16—741no—
161C2×Q16—741no—
162C2×SD16—741no—
163C2×SD16—741no—
164C2×M16—371no—
165C2×M16C2×D3711yescharacteristic
166C22⋊Q8—741no—
167C22⋊Q8—741no—
168#121—741no—
169#121—742no—
170#121—741no—
171C2×C4⋊C4—371no—
172C2×C42C2×D3711yescharacteristic
173#104—22no—
174#104—742no—
175#95—742no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—741no—
181#41—741no—
182#41—741no—
183#41—741no—
184C2×Q8—371no—
185C2×Q8—372no—
186C2×Q8—741no—
187C2×Q8—741no—
188C2×Q8—741no—
189C2×Q8—741no—
190C2×Q8—741no—
191C2×Q8D14811yescharacteristic
192C2×D4—21no—
193C2×D4—371no—
194C2×D4—742no—
195C2×D4—741no—
196C2×D4D14811yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—372no—
200C22×C4—741no—
201C22×C4—741no—
202C22×C4C22×D3711yescharacteristic
203Q16—744no—
204Q16—744no—
205SD16—744no—
206SD16—744no—
207M16—21no—
208M16—372no—
209M16—741no—
210M16C22⋊D3712yescomplemented
211C2×C8—21no—
212C2×C8—741no—
213C4⋊C4—742no—
214C4⋊C4—741no—
215C4⋊C4—741no—
216C22⋊C4—742no—
217C22⋊C4—742no—
218C42—21no—
219C42—21no—
220C23—21no—
221C23—741no—
222C23D4×D3711yescharacteristic
223Q8—21no—
224Q8—21no—
225Q8—742no—
226Q8—741no—
227Q8—742no—
228Q8—741no—
229Q8—1481no—
230Q8—1481no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—2962no—
236D4—741no—
237D4—741no—
238D4—1481no—
239D4—1481no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—742no—
247C2×C4—741no—
248C2×C4—742no—
249C2×C4—1481no—
250C2×C4—1481no—
251C2×C4—1481no—
252C2×C4—1481no—
253C2×C4—1482no—
254C2×C4C2×D14811yescharacteristic
255C2×C4#1059696211yescharacteristic
256C2×C4D4×D3711yescharacteristic
257C2×C4D4×D3711yescharacteristic
258C2×C4D4×D3711yescharacteristic
259C2×C4C2×C22⋊D3711yescharacteristic
260C8—22no—
261C8—742no—
262C22—21no—
263C22—21no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—1481no—
268C22—1481no—
269C22—1481no—
270C22#1192450611yescharacteristic
271C22#1192450911yescharacteristic
272C22#1192453211yescharacteristic
273C4—42no—
274C4—41no—
275C4—1481no—
276C4—1482no—
277C4—1482no—
278C4#1192450411yescharacteristic
279C4#1192450611yescharacteristic
280C4#1192450911yescharacteristic
281C4#1192451011yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—2961no—
286C2#1455744211yescharacteristic
287C2#1455771211yescharacteristic
288C2#1455771711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37#120
prime radical#14558111C2
hypercenterC2×#104D37
hypocenterC37#2007
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×#11924569C2semidirect
2. C2×#11924566C2semidirect
4. C2×#11924464C2semidirect
5. #14557439C2semidirect
6. #14557301C2semidirect
7. C2×#104×C37C2semidirect
57. C2×Dic74D4semidirect
59. M16×C37D4semidirect
71. #10596934D4semidirect
149. C2×#104D37semidirect
152. C37#2007semidirect
210. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
C2×#119245662
#145581112
C2×#119244642
#145574392
#145573012
C2×#104×C372
#200737