Finite Group Databasebeta

← C2×C37×#2905 #22681350

Subgroups — C2×C37×#2905 #22681350

Order 9472.

2830 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C37C212yesmaximal
2C22×#117×C37C211yesmaximal, characteristic
3C37×#2905C2116yesmaximal, direct product factor
4C2×C37×#424C218yesmaximal, complemented
5C2×C37×#423C214yesmaximal, complemented
6C24×C4×C37C2211yescharacteristic
7C22×M16×C37—216no—
8C22×M16×C37C2214yes—
9C22×M16×C37C2214yes—
10C22×M16×C37C22116yes—
11C23×C8×C37C2214yes—
12C2×#117×C37C414yes—
13C2×#117×C37C418yes—
14C2×#117×C37C2214yes—
15C2×#117×C37C2218yes—
16C22×C4⋊C4×C37C412yes—
17C22×C22⋊C4×C37C412yes—
18C22×C42×C37C2212yes—
19C37×#424C22164yescomplemented
20C37×#423C22132yescomplemented
21C2×C4⋊C8×C37C22116yescomplemented
22C25×C37C2×C411yescharacteristic
23C23×C4×C37C2×C414yes—
24C23×C4×C37C2×C411yescharacteristic
25C23×C4×C37C2×C412yes—
26C23×C4×C37C2×C414yes—
27C23×C4×C37D418yes—
28C23×C4×C37Q818yes—
29C23×C4×C37C2314yes—
30C23×C4×C37C2312yes—
31C23×C4×C37C2311yescharacteristic
32C2×M16×C37—216no—
33C2×M16×C37—216no—
34C2×M16×C37—264no—
35C2×M16×C37C23116yes—
36C2×M16×C37C23116yes—
37C22×C8×C37—216no—
38C22×C8×C37C23116yes—
39C22×C8×C37C2318yes—
40#117×C37C2×C4116yes—
41#117×C37C2×C4132yes—
42#117×C37C23116yes—
43C2×C4⋊C4×C37C2×C418yes—
44C2×C4⋊C4×C37C2×C4116yes—
45C2×C22⋊C4×C37C2×C418yes—
46C2×C22⋊C4×C37C2×C4116yes—
47C2×C42×C37C2×C414yes—
48C2×C42×C37C2×C418yes—
49C2×C42×C37C2318yes—
50C2×C42×C37C2314yes—
51C4⋊C8×C37C23164yescomplemented
52C24×C37—44no—
53C24×C37C4⋊C418yes—
54C24×C37C22×C412yes—
55C24×C37C22×C411yescharacteristic
56C24×C37C22×C414yes—
57C22×C4×C37—48no—
58C22×C4×C37C4⋊C418yes—
59C22×C4×C37C4⋊C4116yes—
60C22×C4×C37C4⋊C4132yes—
61C22×C4×C37C22×C418yes—
62C22×C4×C37C22×C4116yes—
63C22×C4×C37C22×C411yescharacteristic
64C22×C4×C37C22×C412yes—
65C22×C4×C37C22×C414yes—
66C22×C4×C37C22×C412yes—
67C22×C4×C37C22×C418yes—
68C22×C4×C37C22×C414yes—
69C22×C4×C37C2×D418yes—
70C22×C4×C37C2×D414yes—
71C22×C4×C37C2×D4116yes—
72C22×C4×C37C2×Q8116yes—
73C22×C4×C37C2×Q818yes—
74C22×C4×C37C2×Q814yes—
75C22×C4×C37C2412yes—
76C22×C4×C37C2414yes—
77C22×C4×C37C2411yescharacteristic
78M16×C37—232no—
79M16×C37—232no—
80C2×C8×C37—216no—
81C2×C8×C37—232no—
82C2×C8×C37C24116yes—
83C4⋊C4×C37C22×C4132yes—
84C22⋊C4×C37C22×C4132yes—
85C42×C37C22×C4116yes—
86C42×C37C22×C418yes—
87C42×C37C2418yes—
88C23×C37—24no—
89C23×C37—28no—
90C23×C37—416no—
91C23×C37—48no—
92C23×C37C2×C4⋊C418yes—
93C23×C37C2×C4⋊C414yes—
94C23×C37C2×C4⋊C4116yes—
95C23×C37C23×C414yes—
96C23×C37C23×C412yes—
97C23×C37C23×C411yescharacteristic
98C2×C4×C37—216no—
99C2×C4×C37—416no—
100C2×C4×C37C2×C4⋊C418yes—
101C2×C4×C37C2×C4⋊C4116yes—
102C2×C4×C37C2×C4⋊C4116yes—
103C2×C4×C37C2×C4⋊C4132yes—
104C2×C4×C37C2×C4⋊C414yes—
105C2×C4×C37C2×C4⋊C418yes—
106C2×C4×C37C23×C4116yes—
107C2×C4×C37C23×C412yes—
108C2×C4×C37C23×C411yescharacteristic
109C2×C4×C37C23×C414yes—
110C2×C4×C37C22×D412yes—
111C2×C4×C37C22×D418yes—
112C2×C4×C37C22×D414yes—
113C2×C4×C37C22×Q814yes—
114C2×C4×C37C22×Q818yes—
115C2×C4×C37C22×Q812yes—
116C2×C4×C37C2511yescharacteristic
117C8×C37—216no—
118C2×#2905C3711yesmaximal, characteristic, direct product factor, Sylow
119C22×C37—28no—
120C22×C37—216no—
121C22×C37—24no—
122C22×C37—28no—
123C22×C37—416no—
124C22×C37C22×C4⋊C418yes—
125C22×C37C22×C4⋊C414yes—
126C22×C37C22×C4⋊C412yes—
127C22×C37#56814yes—
128C22×C37C24×C411yescharacteristic
129C4×C37—216no—
130C4×C37C22×C4⋊C414yes—
131C4×C37C22×C4⋊C412yes—
132C4×C37C22×C4⋊C418yes—
133C4×C37C23×D411yescharacteristic
134C4×C37C23×Q811yescharacteristic
135C23×M16C2×C3712yes—
136C22×#117C2×C3711yescharacteristic
137#2905C2×C37116yesdirect product factor
138C2×#424C2×C3718yescomplemented
139C2×#423C2×C3714yescomplemented
140C2×C37—24no—
141C2×C37—28no—
142C2×C37#290514yesdirect product factor
143C2×C37C23×C4⋊C411yescharacteristic
144C2×C37C2×#56812yes—
145C24×C4C22×C3711yescharacteristic
146C22×M16—216no—
147C22×M16C22×C3714yes—
148C22×M16C22×C3714yes—
149C22×M16C22×C37116yes—
150C23×C8C22×C3714yes—
151C2×#117C4×C3714yes—
152C2×#117C4×C3718yes—
153C2×#117C22×C3714yes—
154C2×#117C22×C3718yes—
155C22×C4⋊C4C4×C3712yes—
156C22×C22⋊C4C4×C3712yes—
157C22×C42C22×C3712yes—
158#424C22×C37164yescomplemented
159#423C22×C37132yescomplemented
160C2×C4⋊C8C22×C37116yescomplemented
161C37C2×#290511yescharacteristic, direct product factor, Sylow
162C25C2×C4×C3711yescharacteristic
163C23×C4C2×C4×C3714yes—
164C23×C4C2×C4×C3711yescharacteristic
165C23×C4C2×C4×C3712yes—
166C23×C4C2×C4×C3714yes—
167C23×C4D4×C3718yes—
168C23×C4Q8×C3718yes—
169C23×C4C23×C3712yes—
170C23×C4C23×C3714yes—
171C23×C4C23×C3711yescharacteristic
172C2×M16—216no—
173C2×M16—216no—
174C2×M16—264no—
175C2×M16C23×C37116yes—
176C2×M16C23×C37116yes—
177C22×C8—216no—
178C22×C8C23×C3718yes—
179C22×C8C23×C37116yes—
180#117C2×C4×C37116yes—
181#117C2×C4×C37132yes—
182#117C23×C37116yes—
183C2×C4⋊C4C2×C4×C3718yes—
184C2×C4⋊C4C2×C4×C37116yes—
185C2×C22⋊C4C2×C4×C3718yes—
186C2×C22⋊C4C2×C4×C37116yes—
187C2×C42C2×C4×C3714yes—
188C2×C42C2×C4×C3718yes—
189C2×C42C23×C3714yes—
190C2×C42C23×C3718yes—
191C4⋊C8C23×C37164yescomplemented
192C24—44no—
193C24C4⋊C4×C3718yes—
194C24C22×C4×C3712yes—
195C24C22×C4×C3711yescharacteristic
196C24C22×C4×C3714yes—
197C22×C4—48no—
198C22×C4C4⋊C4×C3718yes—
199C22×C4C4⋊C4×C37116yes—
200C22×C4C4⋊C4×C37132yes—
201C22×C4C22×C4×C3718yes—
202C22×C4C22×C4×C37116yes—
203C22×C4C22×C4×C3712yes—
204C22×C4C22×C4×C3711yescharacteristic
205C22×C4C22×C4×C3714yes—
206C22×C4C22×C4×C3712yes—
207C22×C4C22×C4×C3714yes—
208C22×C4C22×C4×C3718yes—
209C22×C4C2×D4×C3718yes—
210C22×C4C2×D4×C3714yes—
211C22×C4C2×D4×C37116yes—
212C22×C4C2×Q8×C3718yes—
213C22×C4C2×Q8×C3714yes—
214C22×C4C2×Q8×C37116yes—
215C22×C4C24×C3712yes—
216C22×C4C24×C3714yes—
217C22×C4C24×C3711yescharacteristic
218M16—232no—
219M16—232no—
220C2×C8—216no—
221C2×C8—232no—
222C2×C8C24×C37116yes—
223C4⋊C4C22×C4×C37132yes—
224C22⋊C4C22×C4×C37132yes—
225C42C22×C4×C3718yes—
226C42C22×C4×C37116yes—
227C42C24×C3718yes—
228C23—24no—
229C23—28no—
230C23—416no—
231C23—48no—
232C23C2×C4⋊C4×C3718yes—
233C23C2×C4⋊C4×C3714yes—
234C23C2×C4⋊C4×C37116yes—
235C23C23×C4×C3714yes—
236C23C23×C4×C3712yes—
237C23C23×C4×C3711yescharacteristic
238C2×C4—216no—
239C2×C4—416no—
240C2×C4C2×C4⋊C4×C3718yes—
241C2×C4C2×C4⋊C4×C37116yes—
242C2×C4C2×C4⋊C4×C37116yes—
243C2×C4C2×C4⋊C4×C37132yes—
244C2×C4C2×C4⋊C4×C3714yes—
245C2×C4C2×C4⋊C4×C3718yes—
246C2×C4C23×C4×C37116yes—
247C2×C4C23×C4×C3712yes—
248C2×C4C23×C4×C3711yescharacteristic
249C2×C4C23×C4×C3714yes—
250C2×C4C22×D4×C3712yes—
251C2×C4C22×D4×C3718yes—
252C2×C4C22×D4×C3714yes—
253C2×C4C22×Q8×C3714yes—
254C2×C4C22×Q8×C3718yes—
255C2×C4C22×Q8×C3712yes—
256C2×C4C25×C3711yescharacteristic
257C8—216no—
258C22—28no—
259C22—216no—
260C22—24no—
261C22—28no—
262C22—416no—
263C22C22×C4⋊C4×C3718yes—
264C22C22×C4⋊C4×C3714yes—
265C22C22×C4⋊C4×C3712yes—
266C22C37×#56814yes—
267C22C24×C4×C3711yescharacteristic
268C4—216no—
269C4C22×C4⋊C4×C3712yes—
270C4C22×C4⋊C4×C3714yes—
271C4C22×C4⋊C4×C3718yes—
272C4C23×D4×C3711yescharacteristic
273C4C23×Q8×C3711yescharacteristic
274C2—24no—
275C2—28no—
276C2C37×#290514yesdirect product factor
277C2C23×C4⋊C4×C3711yescharacteristic
278C2C2×C37×#56812yes—
subgroupG/H
centerC22×C4×C37C24
commutatorC22C24×C4×C37
Frattini, cosocleC2×C4C25×C37
socleC23×C37C23×C4
prime radicalC25×C37C2×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#2905C2direct (N × H)
4. C2×C37×#424C2semidirect
5. C2×C37×#423C2semidirect
19. C37×#424C22semidirect
20. C37×#423C22semidirect
21. C2×C4⋊C8×C37C22semidirect
51. C4⋊C8×C37C23semidirect
118. C2×#2905C37direct (N × H)
137. #2905C2×C37direct (N × H)
138. C2×#424C2×C37semidirect
139. C2×#423C2×C37semidirect
142. C2×C37#2905direct (N × H)
158. #424C22×C37semidirect
159. #423C22×C37semidirect
160. C2×C4⋊C8C22×C37semidirect
161. C37C2×#2905direct (N × H)
191. C4⋊C8C23×C37semidirect
276. C2C37×#2905direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C372
C22×#117×C372
C37×#29052
C2×C37×#4242
C2×C37×#4232
C2×#290537