Finite Group Databasebeta

← C37×#29657 #22650910

Subgroups — C37×#29657 #22650910

Order 9472.

1148 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 242 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×C37×#543C211yesmaximal, characteristic
2C37×#2483C213yesmaximal
3C37×#2062C214yesmaximal, complemented
4C37×#2030C214yesmaximal, complemented
5C37×#1819C213yesmaximal
6C37×#543—26no—
7C37×#543C2214yes—
8C2×C22⋊Q8×C37—23no—
9C2×C22⋊Q8×C37—23no—
10C22×C22⋊C4×C37C2211yescharacteristic
11C22×C22⋊C4×C37C2213yes—
12C37×#397—26no—
13C37×#385—23no—
14C37×#385C2216yes—
15C37×#381—23no—
16C37×#381C2216yes—
17C37×#379C2213yes—
18C37×#342C22112yes—
19C25×C37C2311yescharacteristic
20C22×Q8×C37—21no—
21C22×Q8×C37—21no—
22C23×C4×C37D413yes—
23C23×C4×C37D413yes—
24C23×C4×C37C2311yescharacteristic
25C23×C4×C37C2311yescharacteristic
26C22⋊Q8×C37—212no—
27C22⋊Q8×C37—212no—
28C22⋊Q8×C37—212no—
29C22⋊Q8×C37—212no—
30C2×C4⋊C4×C37—23no—
31C2×C4⋊C4×C37—23no—
32C2×C4⋊C4×C37—26no—
33C2×C22⋊C4×C37—26no—
34C2×C22⋊C4×C37—26no—
35C2×C22⋊C4×C37—23no—
36C2×C22⋊C4×C37—23no—
37C2×C22⋊C4×C37—23no—
38C2×C22⋊C4×C37—23no—
39C2×C22⋊C4×C37D416yes—
40C2×C22⋊C4×C37C2316yes—
41C2×C22⋊C4×C37C2316yes—
42#95×C37—26no—
43#95×C37—26no—
44#95×C37—26no—
45C24×C37—24no—
46C24×C37—42no—
47C24×C37—81no—
48C24×C37C2×D413yes—
49C24×C37C2×D413yes—
50C24×C37C2411yescharacteristic
51C2×Q8×C37—24no—
52C2×Q8×C37—24no—
53C2×Q8×C37—82no—
54C2×Q8×C37—82no—
55C22×C4×C37—23no—
56C22×C4×C37—23no—
57C22×C4×C37—23no—
58C22×C4×C37—23no—
59C22×C4×C37—23no—
60C22×C4×C37—26no—
61C22×C4×C37—23no—
62C22×C4×C37—24no—
63C22×C4×C37—46no—
64C22×C4×C37—81no—
65C22×C4×C37—83no—
66C22×C4×C37C2×D416yes—
67C22×C4×C37C2×D416yes—
68C4⋊C4×C37—212no—
69C4⋊C4×C37—212no—
70C4⋊C4×C37—86no—
71C22⋊C4×C37—212no—
72C22⋊C4×C37—212no—
73C22⋊C4×C37—212no—
74C22⋊C4×C37—46no—
75C22⋊C4×C37—43no—
76C22⋊C4×C37—41no—
77C22⋊C4×C37—83no—
78C23×C37—26no—
79C23×C37—26no—
80C23×C37—26no—
81C23×C37—43no—
82C23×C37—41no—
83C23×C37—41no—
84C23×C37—43no—
85C23×C37—43no—
86C23×C37—88no—
87C23×C37#12013yes—
88C23×C37#12011yescharacteristic
89C23×C37C22×D413yes—
90C23×C372−1+414yes—
91Q8×C37—84no—
92Q8×C37—84no—
93C2×C4×C37—26no—
94C2×C4×C37—26no—
95C2×C4×C37—46no—
96C2×C4×C37—46no—
97C2×C4×C37—46no—
98C2×C4×C37—46no—
99C2×C4×C37—46no—
100C2×C4×C37—46no—
101C2×C4×C37—46no—
102C2×C4×C37—41no—
103C2×C4×C37—41no—
104C2×C4×C37—46no—
105C2×C4×C37—46no—
106C2×C4×C37—83no—
107C2×C4×C37—83no—
108#29657C3711yesmaximal, characteristic, direct product factor, Sylow
109C22×C37—21no—
110C22×C37—23no—
111C22×C37—21no—
112C22×C37—23no—
113C22×C37—23no—
114C22×C37—23no—
115C22×C37—23no—
116C22×C37—44no—
117C22×C37—412no—
118C22×C37—86no—
119C22×C37#45812yes—
120C22×C37C2×#12011yescharacteristic
121C22×C37#53616yes—
122C4×C37—46no—
123C4×C37—46no—
124C4×C37—86no—
125C4×C37—81no—
126C4×C37—81no—
127C2×#543C2×C3711yescharacteristic
128#2483C2×C3713yes—
129#2062C2×C3714yescomplemented
130#2030C2×C3714yescomplemented
131#1819C2×C3713yes—
132C2×C37—26no—
133C2×C37—22no—
134C2×C37—43no—
135C2×C37#261411yescharacteristic
136C2×C37C2×#45811yescharacteristic
137C2×C37#302611yescharacteristic
138#543—26no—
139#543C22×C3714yes—
140C2×C22⋊Q8—23no—
141C2×C22⋊Q8—23no—
142C22×C22⋊C4C22×C3711yescharacteristic
143C22×C22⋊C4C22×C3713yes—
144#397—26no—
145#385—23no—
146#385C22×C3716yes—
147#381—23no—
148#381C22×C3716yes—
149#379C22×C3713yes—
150#342C22×C37112yes—
151C37#2965711yescharacteristic, direct product factor, Sylow
152C25C23×C3711yescharacteristic
153C22×Q8—21no—
154C22×Q8—21no—
155C23×C4D4×C3713yes—
156C23×C4D4×C3713yes—
157C23×C4C23×C3711yescharacteristic
158C23×C4C23×C3711yescharacteristic
159C22⋊Q8—212no—
160C22⋊Q8—212no—
161C22⋊Q8—212no—
162C22⋊Q8—212no—
163C2×C4⋊C4—23no—
164C2×C4⋊C4—23no—
165C2×C4⋊C4—26no—
166C2×C22⋊C4—26no—
167C2×C22⋊C4—26no—
168C2×C22⋊C4—23no—
169C2×C22⋊C4—23no—
170C2×C22⋊C4—23no—
171C2×C22⋊C4—23no—
172C2×C22⋊C4D4×C3716yes—
173C2×C22⋊C4C23×C3716yes—
174C2×C22⋊C4C23×C3716yes—
175#95—26no—
176#95—26no—
177#95—26no—
178C24—24no—
179C24—42no—
180C24—81no—
181C24C2×D4×C3713yes—
182C24C2×D4×C3713yes—
183C24C24×C3711yescharacteristic
184C2×Q8—24no—
185C2×Q8—24no—
186C2×Q8—82no—
187C2×Q8—82no—
188C22×C4—23no—
189C22×C4—23no—
190C22×C4—23no—
191C22×C4—23no—
192C22×C4—23no—
193C22×C4—26no—
194C22×C4—23no—
195C22×C4—24no—
196C22×C4—46no—
197C22×C4—81no—
198C22×C4—83no—
199C22×C4C2×D4×C3716yes—
200C22×C4C2×D4×C3716yes—
201C4⋊C4—212no—
202C4⋊C4—212no—
203C4⋊C4—86no—
204C22⋊C4—212no—
205C22⋊C4—212no—
206C22⋊C4—212no—
207C22⋊C4—46no—
208C22⋊C4—43no—
209C22⋊C4—41no—
210C22⋊C4—83no—
211C23—26no—
212C23—26no—
213C23—26no—
214C23—43no—
215C23—41no—
216C23—41no—
217C23—43no—
218C23—43no—
219C23—88no—
220C23#120×C3713yes—
221C23#120×C3711yescharacteristic
222C23C22×D4×C3713yes—
223C232−1+4×C3714yes—
224Q8—84no—
225Q8—84no—
226C2×C4—26no—
227C2×C4—26no—
228C2×C4—46no—
229C2×C4—46no—
230C2×C4—46no—
231C2×C4—46no—
232C2×C4—46no—
233C2×C4—46no—
234C2×C4—46no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—46no—
238C2×C4—46no—
239C2×C4—83no—
240C2×C4—83no—
241C22—21no—
242C22—23no—
243C22—21no—
244C22—23no—
245C22—23no—
246C22—23no—
247C22—23no—
248C22—44no—
249C22—412no—
250C22—86no—
251C22C37×#45812yes—
252C22C2×#120×C3711yescharacteristic
253C22C37×#53616yes—
254C4—46no—
255C4—46no—
256C4—86no—
257C4—81no—
258C4—81no—
259C2—26no—
260C2—22no—
261C2—43no—
262C2C37×#261411yescharacteristic
263C2C2×C37×#45811yescharacteristic
264C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC25×C37C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#2062C2semidirect
4. C37×#2030C2semidirect
108. #29657C37direct (N × H)
129. #2062C2×C37semidirect
130. #2030C2×C37semidirect
151. C37#29657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5432
C37×#24832
C37×#20622
C37×#20302
C37×#18192
#2965737