Finite Group Databasebeta

← #17995063

Subgroups — #17995063

Order 4736.

338 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D37C211yesmaximal, characteristic
2C2×#11924516C211yesmaximal, characteristic
3C2×#11924454C211yesmaximal, characteristic, complemented
4C2×#11924454C211yesmaximal, characteristic, complemented
5#14557496C211yesmaximal, characteristic
6#14557302C211yesmaximal, characteristic, complemented
7C37×#343C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×C4×D37C2211yescharacteristic
10C2×#10596934C2211yescharacteristic
11C2×#10596934C2211yescharacteristic
12C2×#10596929—21no—
13M16×D37—22no—
14M16×D37—22no—
15C2×C8×D37—21no—
16#11924516—21no—
17#11924516—21no—
18#11924516—21no—
19#11924516—21no—
20C2×C4⋊Dic37C412yes—
21C2×#10596938C412yes—
22#11924454—22no—
23#11924454—22no—
24#11924448—21no—
25#11924448—21no—
26C2×M16×C37C2211yescharacteristic
27C2×M16×C37C2211yescharacteristic
28C2×C4⋊C4×C37C2211yescharacteristic
29C23×D37C2×C411yescharacteristic
30C22×C4×C37C2×C412yes—
31C22×C4×C37C2311yescharacteristic
32C22×Dic37C2×C412yes—
33C22×Dic37C2×C411yescharacteristic
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37D411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×Dic74—21no—
43C2×Dic74—21no—
44C2×Dic74—21no—
45C2×Dic74—21no—
46C2×Dic74—21no—
47C2×Dic74—21no—
48M16×C37—21no—
49M16×C37—21no—
50M16×C37—21no—
51M16×C37D412yes—
52C2×C8×C37—21no—
53C2×C8×C37—21no—
54C4⋊C4×C37—21no—
55C4⋊C4×C37—21no—
56#10596938—22no—
57#10596938—22no—
58C4⋊Dic37—22no—
59C4⋊Dic37—22no—
60#10596934—21no—
61#10596934—21no—
62#10596934—21no—
63#10596934D412yes—
64C2×#64436—21no—
65C2×#64436—21no—
66#10596929—24no—
67C8×D37—24no—
68C23×C37C22×C411yescharacteristic
69C22×D37—21no—
70C22×D37—21no—
71C22×D37—22no—
72C22×D37—41no—
73C22×D37C22⋊C411yescharacteristic
74C22×D37C22⋊C411yescharacteristic
75C2×C4×C37—22no—
76C2×C4×C37—42no—
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C2×C4×C37#4111yescharacteristic
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37—22no—
88C2×Dic37C22⋊C411yescharacteristic
89C2×Dic37C22⋊C411yescharacteristic
90C4×D37—21no—
91C4×D37—21no—
92C4×D37—21no—
93C4×D37—21no—
94C4×D37—21no—
95C4×D37—21no—
96C4×D37—21no—
97C4×D37—21no—
98Dic74—41no—
99Dic74—41no—
100Dic74—41no—
101Dic74—41no—
102C8×C37—22no—
103C8×C37—41no—
104#64436—22no—
105#64436—41no—
106C22×C37—21no—
107C22×C37—21no—
108C22×C37C2×C22⋊C411yescharacteristic
109C22×C37C4×D411yescharacteristic
110C22×C37C4×D411yescharacteristic
111C2×D37—21no—
112C2×D37—21no—
113C2×D37—21no—
114C2×D37—21no—
115C2×D37—21no—
116C2×D37—42no—
117C2×D37—42no—
118C2×D37#10112yescomplemented
119C4×C37—42no—
120C4×C37#12011yescharacteristic
121C4×C37#12111yescharacteristic
122C4×C37#12111yescharacteristic
123C4×C37#12311yescharacteristic
124Dic37—21no—
125Dic37—21no—
126Dic37—42no—
127#1901—371nomaximal, Sylow
128C2×C37—21no—
129C2×C37—21no—
130C2×C37#38611yescharacteristic
131C2×C37C2×#10111yescharacteristic
132C2×C37#41311yescharacteristic
133D37—22no—
134D37—41no—
135C22×M16—371no—
136C2×C22⋊Q8—371no—
137C2×#101—371no—
138C2×#101—371no—
139#407—371no—
140#343—371no—
141#343D3711yescharacteristic, complemented
142C37#190111yescharacteristic, complemented, Sylow
143C22×Q8—371no—
144C23×C4—371no—
145C2×M16—371no—
146C2×M16—371no—
147C2×M16—741no—
148C2×M16—742no—
149C2×M16—742no—
150C2×M16C2×D3711yescharacteristic
151C2×M16C2×D3711yescharacteristic
152C22×C8—741no—
153C22⋊Q8—741no—
154C22⋊Q8—741no—
155C22⋊Q8—741no—
156C22⋊Q8—741no—
157C2×C4⋊C4—372no—
158C2×C4⋊C4C2×D3711yescharacteristic
159C2×C22⋊C4—372no—
160#101—742no—
161#101—742no—
162C22⋊C8—741no—
163C22⋊C8—741no—
164C24—371no—
165C2×Q8—741no—
166C2×Q8—741no—
167C2×Q8—741no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C22×C4—371no—
172C22×C4—371no—
173C22×C4—371no—
174C22×C4—371no—
175C22×C4—371no—
176C22×C4—372no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180C22×C4—741no—
181C22×C4C4×D3712yes—
182C22×C4C22×D3711yescharacteristic
183M16—21no—
184M16—21no—
185M16—21no—
186M16—372no—
187M16—744no—
188M16—741no—
189M16—741no—
190M16—741no—
191M16D14812yes—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—744no—
195C2×C8—741no—
196C2×C8—741no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—742no—
200C4⋊C4—742no—
201C22⋊C4—742no—
202C22⋊C4—742no—
203C23—371no—
204C23—371no—
205C23—742no—
206C23—741no—
207C23—741no—
208C23—1481no—
209C23C2×C4×D3711yescharacteristic
210Q8—1481no—
211Q8—1481no—
212Q8—1481no—
213Q8—1481no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—741no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—741no—
227C2×C4—741no—
228C2×C4—742no—
229C2×C4—742no—
230C2×C4—742no—
231C2×C4C2×D14811yescharacteristic
232C2×C4#1059696211yescharacteristic
233C2×C4D4×D3711yescharacteristic
234C2×C4D4×D3711yescharacteristic
235C2×C4D4×D3711yescharacteristic
236C2×C4#1059696611yescharacteristic
237C8—22no—
238C8—41no—
239C8—742no—
240C8—1481no—
241C22—21no—
242C22—21no—
243C22—372no—
244C22—741no—
245C22—741no—
246C22—741no—
247C22—741no—
248C22—741no—
249C22—1482no—
250C22—1482no—
251C22C22⋊C4×D3711yescharacteristic
252C22#1192449811yescharacteristic
253C22C4×D14811yescharacteristic
254C4—42no—
255C4—741no—
256C4—741no—
257C4—1482no—
258C4#1192450611yescharacteristic
259C4#1192450911yescharacteristic
260C4#1192451111yescharacteristic
261C4#1192452111yescharacteristic
262C2—21no—
263C2—21no—
264C2—742no—
265C2—1481no—
266C2#1455741111yescharacteristic
267C2#101×D3711yescharacteristic
268C2#1455751411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#343C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#343D37
hypocenterC37#1901
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. C2×#11924454C2semidirect
4. C2×#11924454C2semidirect
6. #14557302C2semidirect
7. C37×#343C2semidirect
118. C2×D37#101semidirect
141. #343D37semidirect
142. C37#1901semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D372
C2×#119245162
C2×#119244542
#145574962
#145573022
C37×#3432
#190137