Finite Group Databasebeta

← C37×#12218 #22633471

Subgroups — C37×#12218 #22633471

Order 9472.

456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C37×#2842C211yesmaximal, characteristic
2C37×#2029C211yesmaximal, characteristic
3C37×#1614C212yesmaximal, complemented
4C37×#1352C212yesmaximal, complemented
5C37×#1316C211yesmaximal, characteristic
6C37×#543C2211yescharacteristic
7C37×#484—22no—
8C37×#399—21no—
9C37×#399C2212yes—
10C37×#396—22no—
11C37×#396—22no—
12C37×#379—21no—
13C37×#379—21no—
14C37×#379C2211yescharacteristic
15C37×#342—21no—
16C37×#342C2211yescharacteristic
17C37×#328—22no—
18C37×#323C2212yes—
19C25×C37D411yescharacteristic
20C22⋊Q8×C37—22no—
21C22⋊Q8×C37—42no—
22C2×C4⋊C4×C37—22no—
23C2×C4⋊C4×C37—21no—
24C2×C4⋊C4×C37—22no—
25C2×C4⋊C4×C37D412yes—
26C2×C22⋊C4×C37—21no—
27C2×C22⋊C4×C37—21no—
28C2×C22⋊C4×C37—21no—
29C2×C22⋊C4×C37—22no—
30C2×C22⋊C4×C37—21no—
31C2×C22⋊C4×C37—22no—
32C2×C22⋊C4×C37—22no—
33C2×C22⋊C4×C37—42no—
34C2×C22⋊C4×C37D411yescharacteristic
35C2×C22⋊C4×C37C2311yescharacteristic
36#107×C37—42no—
37#103×C37—42no—
38C22⋊C8×C37—22no—
39#95×C37—21no—
40#95×C37D412yes—
41C24×C37—21no—
42C24×C37—21no—
43C24×C37—41no—
44C24×C37—41no—
45C24×C37—82no—
46C24×C37Q1612yes—
47C24×C37C2×D411yescharacteristic
48C2×Q8×C37—22no—
49C22×C4×C37—22no—
50C22×C4×C37—21no—
51C22×C4×C37—22no—
52C22×C4×C37—22no—
53C22×C4×C37—41no—
54C22×C4×C37C2×D412yes—
55C2×C8×C37—42no—
56C4⋊C4×C37—22no—
57C4⋊C4×C37—42no—
58C4⋊C4×C37—42no—
59C4⋊C4×C37—82no—
60C4⋊C4×C37—82no—
61C4⋊C4×C37—81no—
62C22⋊C4×C37—41no—
63C22⋊C4×C37—41no—
64C22⋊C4×C37—41no—
65C22⋊C4×C37—41no—
66C22⋊C4×C37—41no—
67C22⋊C4×C37—41no—
68C22⋊C4×C37—82no—
69C22⋊C4×C37—82no—
70C22⋊C4×C37—82no—
71C22⋊C4×C37—81no—
72C22⋊C4×C37—81no—
73C22⋊C4×C37—84no—
74C23×C37—21no—
75C23×C37—21no—
76C23×C37—22no—
77C23×C37—42no—
78C23×C37—42no—
79C23×C37—42no—
80C23×C37—42no—
81C23×C37—44no—
82C23×C37—41no—
83C23×C37—41no—
84C23×C37—81no—
85C23×C37—82no—
86C23×C37—82no—
87C23×C37—82no—
88C23×C37—84no—
89C23×C37#12011yescharacteristic
90C23×C37C2×Q1611yescharacteristic
91C23×C37#13711yescharacteristic
92Q8×C37—82no—
93C2×C4×C37—22no—
94C2×C4×C37—42no—
95C2×C4×C37—42no—
96C2×C4×C37—42no—
97C2×C4×C37—42no—
98C2×C4×C37—42no—
99C2×C4×C37—42no—
100C2×C4×C37—41no—
101C2×C4×C37—42no—
102C2×C4×C37—42no—
103C2×C4×C37—42no—
104C2×C4×C37—82no—
105C2×C4×C37—81no—
106C2×C4×C37—82no—
107C8×C37—82no—
108#12218C3711yesmaximal, characteristic, direct product factor, Sylow
109C22×C37—22no—
110C22×C37—21no—
111C22×C37—21no—
112C22×C37—41no—
113C22×C37—41no—
114C22×C37—42no—
115C22×C37—42no—
116C22×C37—42no—
117C22×C37—44no—
118C22×C37—42no—
119C22×C37—81no—
120C22×C37—82no—
121C22×C37—82no—
122C22×C37—84no—
123C22×C37—82no—
124C22×C37#45111yescharacteristic
125C22×C37#45511yescharacteristic
126C22×C37B(4,𝔽2)11yescharacteristic
127C4×C37—42no—
128C4×C37—81no—
129C4×C37—82no—
130C4×C37—82no—
131C4×C37—82no—
132C4×C37—161no—
133#2842C2×C3711yescharacteristic
134#2029C2×C3711yescharacteristic
135#1614C2×C3712yescomplemented
136#1352C2×C3712yescomplemented
137#1316C2×C3711yescharacteristic
138C2×C37—21no—
139C2×C37—21no—
140C2×C37—41no—
141C2×C37—41no—
142C2×C37—82no—
143C2×C37#160211yescharacteristic
144C2×C37#220012yes—
145#543C22×C3711yescharacteristic
146#484—22no—
147#399—21no—
148#399C22×C3712yes—
149#396—22no—
150#396—22no—
151#379—21no—
152#379—21no—
153#379C22×C3711yescharacteristic
154#342—21no—
155#342C22×C3711yescharacteristic
156#328—22no—
157#323C22×C3712yes—
158C37#1221811yescharacteristic, direct product factor, Sylow
159C25D4×C3711yescharacteristic
160C22⋊Q8—22no—
161C22⋊Q8—42no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4D4×C3712yes—
166C2×C22⋊C4—21no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—42no—
174C2×C22⋊C4D4×C3711yescharacteristic
175C2×C22⋊C4C23×C3711yescharacteristic
176#107—42no—
177#103—42no—
178C22⋊C8—22no—
179#95—21no—
180#95D4×C3712yes—
181C24—21no—
182C24—21no—
183C24—41no—
184C24—41no—
185C24—82no—
186C24Q16×C3712yes—
187C24C2×D4×C3711yescharacteristic
188C2×Q8—22no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4C2×D4×C3712yes—
195C2×C8—42no—
196C4⋊C4—22no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—82no—
200C4⋊C4—82no—
201C4⋊C4—81no—
202C22⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—41no—
206C22⋊C4—41no—
207C22⋊C4—41no—
208C22⋊C4—82no—
209C22⋊C4—82no—
210C22⋊C4—82no—
211C22⋊C4—81no—
212C22⋊C4—81no—
213C22⋊C4—84no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—44no—
222C23—41no—
223C23—41no—
224C23—81no—
225C23—82no—
226C23—82no—
227C23—82no—
228C23—84no—
229C23#120×C3711yescharacteristic
230C23C2×Q16×C3711yescharacteristic
231C23#137×C3711yescharacteristic
232Q8—82no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—82no—
247C8—82no—
248C22—22no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—44no—
257C22—42no—
258C22—81no—
259C22—82no—
260C22—82no—
261C22—84no—
262C22—82no—
263C22C37×#45111yescharacteristic
264C22C37×#45511yescharacteristic
265C22C37×B(4,𝔽2)11yescharacteristic
266C4—42no—
267C4—81no—
268C4—82no—
269C4—82no—
270C4—82no—
271C4—161no—
272C2—21no—
273C2—21no—
274C2—41no—
275C2—41no—
276C2—82no—
277C2C37×#160211yescharacteristic
278C2C37×#220012yes—
subgroupG/H
center, socleC22×C37B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C37
prime radicalC25×C37D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C37 ◁ C2×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1614C2semidirect
4. C37×#1352C2semidirect
108. #12218C37direct (N × H)
135. #1614C2×C37semidirect
136. #1352C2×C37semidirect
158. C37#12218direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#28422
C37×#20292
C37×#16142
C37×#13522
C37×#13162
#1221837