Finite Group Databasebeta

← C37×#7802 #22629055

Subgroups — C37×#7802 #22629055

Order 9472.

366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2809C211yesmaximal, characteristic
2C37×#2096C211yesmaximal, characteristic
3C37×#2083C212yesmaximal
4C37×#1272C211yesmaximal, characteristic
5C37×#1271C212yesmaximal
6C2×#107×C37—22no—
7C2×#106×C37—21no—
8C2×#103×C37—21no—
9C37×#400—21no—
10C37×#398—22no—
11C37×#391—21no—
12C37×#391C2211yescharacteristic
13C37×#389C2212yes—
14C37×#387—22no—
15C37×#384C2211yescharacteristic
16C37×#340—22no—
17C37×#336C2211yescharacteristic
18C37×#336C2212yes—
19C22×Q8×C37D411yescharacteristic
20C22×C8×C37—22no—
21C22×C8×C37—21no—
22C2×C4⋊C4×C37—22no—
23C2×C4⋊C4×C37—22no—
24C2×C4⋊C4×C37—21no—
25C2×C4⋊C4×C37—21no—
26C2×C4⋊C4×C37—21no—
27C2×C4⋊C4×C37D412yes—
28C2×C4⋊C4×C37D412yes—
29C2×C4⋊C4×C37D411yescharacteristic
30C2×C42×C37—21no—
31C2×C42×C37C2311yescharacteristic
32#107×C37—44no—
33#106×C37—42no—
34#103×C37—42no—
35#95×C37—21no—
36#95×C37—22no—
37#95×C37—22no—
38#95×C37—22no—
39#95×C37—22no—
40C2×Q8×C37—21no—
41C2×Q8×C37—41no—
42C2×Q8×C37—41no—
43C2×Q8×C37Q1612yes—
44C22×C4×C37—21no—
45C22×C4×C37—21no—
46C22×C4×C37—22no—
47C22×C4×C37—22no—
48C22×C4×C37—41no—
49C22×C4×C37C2×D411yescharacteristic
50C22×C4×C37C2×D412yes—
51C2×C8×C37—22no—
52C2×C8×C37—24no—
53C2×C8×C37—42no—
54C2×C8×C37—41no—
55C2×C8×C37—42no—
56C2×C8×C37—41no—
57C4⋊C4×C37—22no—
58C4⋊C4×C37—22no—
59C4⋊C4×C37—41no—
60C4⋊C4×C37—42no—
61C4⋊C4×C37—41no—
62C4⋊C4×C37—41no—
63C4⋊C4×C37—42no—
64C4⋊C4×C37—42no—
65C4⋊C4×C37—42no—
66C4⋊C4×C37—42no—
67C4⋊C4×C37—81no—
68C4⋊C4×C37—81no—
69C42×C37—41no—
70C42×C37—81no—
71C23×C37#12011yescharacteristic
72Q8×C37—42no—
73Q8×C37—81no—
74C2×C4×C37—21no—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—21no—
78C2×C4×C37—22no—
79C2×C4×C37—41no—
80C2×C4×C37—41no—
81C2×C4×C37—42no—
82C2×C4×C37—42no—
83C2×C4×C37—42no—
84C2×C4×C37—41no—
85C2×C4×C37—42no—
86C2×C4×C37—42no—
87C2×C4×C37—42no—
88C2×C4×C37—42no—
89C2×C4×C37—82no—
90C2×C4×C37—81no—
91C2×C4×C37C2×Q1611yescharacteristic
92C2×C4×C37#13512yes—
93C2×C4×C37AGL(1,ℤ/8)12yes—
94C2×C4×C37#13711yescharacteristic
95C8×C37—44no—
96C8×C37—42no—
97#7802C3711yesmaximal, characteristic, direct product factor, Sylow
98C22×C37#44912yes—
99C22×C37#45111yescharacteristic
100C22×C37#45311yescharacteristic
101C22×C37#45612yes—
102C22×C37#45811yescharacteristic
103C4×C37—22no—
104C4×C37—22no—
105C4×C37—21no—
106C4×C37—21no—
107C4×C37—42no—
108C4×C37—82no—
109C4×C37—82no—
110C4×C37—81no—
111C4×C37—161no—
112#2809C2×C3711yescharacteristic
113#2096C2×C3711yescharacteristic
114#2083C2×C3712yes—
115#1272C2×C3711yescharacteristic
116#1271C2×C3712yes—
117C2×C37#160912yes—
118C2×C37#161411yescharacteristic
119C2×C37#162411yescharacteristic
120C2×C37#164812yes—
121C2×C37#166011yescharacteristic
122C2×#107—22no—
123C2×#106—21no—
124C2×#103—21no—
125#400—21no—
126#398—22no—
127#391—21no—
128#391C22×C3711yescharacteristic
129#389C22×C3712yes—
130#387—22no—
131#384C22×C3711yescharacteristic
132#340—22no—
133#336C22×C3712yes—
134#336C22×C3711yescharacteristic
135C37#780211yescharacteristic, direct product factor, Sylow
136C22×Q8D4×C3711yescharacteristic
137C22×C8—22no—
138C22×C8—21no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4D4×C3712yes—
145C2×C4⋊C4D4×C3712yes—
146C2×C4⋊C4D4×C3711yescharacteristic
147C2×C42—21no—
148C2×C42C23×C3711yescharacteristic
149#107—44no—
150#106—42no—
151#103—42no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156#95—22no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8Q16×C3712yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—41no—
166C22×C4C2×D4×C3711yescharacteristic
167C22×C4C2×D4×C3712yes—
168C2×C8—22no—
169C2×C8—24no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—42no—
173C2×C8—41no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—81no—
185C4⋊C4—81no—
186C42—41no—
187C42—81no—
188C23#120×C3711yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—82no—
207C2×C4—81no—
208C2×C4C2×Q16×C3711yescharacteristic
209C2×C4#135×C3712yes—
210C2×C4AGL(1,ℤ/8)×C3712yes—
211C2×C4#137×C3711yescharacteristic
212C8—44no—
213C8—42no—
214C22C37×#44912yes—
215C22C37×#45111yescharacteristic
216C22C37×#45311yescharacteristic
217C22C37×#45612yes—
218C22C37×#45811yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—82no—
225C4—82no—
226C4—81no—
227C4—161no—
228C2C37×#160912yes—
229C2C37×#161411yescharacteristic
230C2C37×#162411yescharacteristic
231C2C37×#164812yes—
232C2C37×#166011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C37#120
commutator, Frattini, cosocleC2×C42C23×C37
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
97. #7802C37direct (N × H)
135. C37#7802direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#28092
C37×#20962
C37×#20832
C37×#12722
C37×#12712
#780237