Finite Group Databasebeta

← C37×#13586 #22634839

Subgroups — C37×#13586 #22634839

Order 9472.

406 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3152C211yesmaximal, characteristic
2C37×#2126C212yesmaximal
3C37×#1409C214yesmaximal, complemented
4C2×#137×C37—22no—
5C37×#532C2211yescharacteristic
6C2×C4⋊Q8×C37C411yescharacteristic, complemented
7C37×#497—22no—
8C37×#494C412yescomplemented
9C37×#492C2212yes—
10C37×#410—22no—
11C4×M16×C37C411yescharacteristic, complemented
12C37×#354—22no—
13C37×#353C2214yes—
14C2×#41×C37D412yes—
15C22×Q8×C37—21no—
16#137×C37—44no—
17#137×C37—44no—
18C2×Q16×C37—24no—
19C2×SD16×C37—24no—
20C2×M16×C37—21no—
21C4⋊Q8×C37—21no—
22C4⋊Q8×C37—41no—
23C4⋊Q8×C37C2×C412yes—
24C4⋊Q8×C37C2×C411yescharacteristic
25#127×C37C2311yescharacteristic
26#124×C37D412yes—
27#121×C37—41no—
28C4×D4×C37—41no—
29#117×C37—42no—
30C2×C4⋊C4×C37—41no—
31C2×C42×C37C2×C411yescharacteristic
32#99×C37—24no—
33#99×C37—42no—
34#97×C37—21no—
35C4×C8×C37C2×C412yes—
36#41×C37—42no—
37#41×C37—42no—
38C2×Q8×C37—22no—
39C2×Q8×C37—42no—
40C2×Q8×C37—42no—
41C2×Q8×C37—41no—
42C2×Q8×C37C22⋊C412yes—
43C2×D4×C37—22no—
44C2×D4×C37—41no—
45C2×D4×C37C2×D412yes—
46C22×C4×C37—21no—
47C22×C4×C37—22no—
48C22×C4×C37—41no—
49C22×C4×C37C22⋊C411yescharacteristic
50Q16×C37—48no—
51SD16×C37—48no—
52M16×C37—24no—
53C2×C8×C37—22no—
54C4⋊C4×C37—41no—
55C4⋊C4×C37—42no—
56C4⋊C4×C37—42no—
57C4⋊C4×C37—82no—
58C22⋊C4×C37—42no—
59C22⋊C4×C37—44no—
60C42×C37—21no—
61C42×C37—82no—
62C42×C37C22⋊C411yescharacteristic
63C42×C37C22×C411yescharacteristic
64C23×C37—22no—
65C23×C37#9911yescharacteristic
66Q8×C37—42no—
67Q8×C37—44no—
68Q8×C37—82no—
69D4×C37—42no—
70D4×C37—82no—
71D4×C37—82no—
72C2×C4×C37—21no—
73C2×C4×C37—22no—
74C2×C4×C37—21no—
75C2×C4×C37—22no—
76C2×C4×C37—42no—
77C2×C4×C37—42no—
78C2×C4×C37—42no—
79C2×C4×C37—42no—
80C2×C4×C37—81no—
81C2×C4×C37—81no—
82C2×C4×C37—84no—
83C2×C4×C37#9911yescharacteristic
84C2×C4×C37C2×C22⋊C411yescharacteristic
85C8×C37—24no—
86#13586C3711yesmaximal, characteristic, direct product factor, Sylow
87C22×C37—21no—
88C22×C37—41no—
89C22×C37—42no—
90C22×C37—82no—
91C22×C37C2×#9911yescharacteristic
92C4×C37—22no—
93C4×C37—21no—
94C4×C37—41no—
95C4×C37—42no—
96C4×C37—82no—
97C4×C37—164no—
98C4×C37#35312yes—
99#3152C2×C3711yescharacteristic
100#2126C2×C3712yes—
101#1409C2×C3714yescomplemented
102C2×C37—21no—
103C2×C37—41no—
104C2×C37—82no—
105C2×C37C2×#35311yescharacteristic
106C2×#137—22no—
107#532C22×C3711yescharacteristic
108C2×C4⋊Q8C4×C3711yescharacteristic, complemented
109#497—22no—
110#494C4×C3712yescomplemented
111#492C22×C3712yes—
112#410—22no—
113C4×M16C4×C3711yescharacteristic, complemented
114#354—22no—
115#353C22×C3714yes—
116C37#1358611yescharacteristic, direct product factor, Sylow
117C2×#41D4×C3712yes—
118C22×Q8—21no—
119#137—44no—
120#137—44no—
121C2×Q16—24no—
122C2×SD16—24no—
123C2×M16—21no—
124C4⋊Q8—21no—
125C4⋊Q8—41no—
126C4⋊Q8C2×C4×C3712yes—
127C4⋊Q8C2×C4×C3711yescharacteristic
128#127C23×C3711yescharacteristic
129#124D4×C3712yes—
130#121—41no—
131C4×D4—41no—
132#117—42no—
133C2×C4⋊C4—41no—
134C2×C42C2×C4×C3711yescharacteristic
135#99—24no—
136#99—42no—
137#97—21no—
138C4×C8C2×C4×C3712yes—
139#41—42no—
140#41—42no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8C22⋊C4×C3712yes—
146C2×D4—22no—
147C2×D4—41no—
148C2×D4C2×D4×C3712yes—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C22⋊C4×C3711yescharacteristic
153Q16—48no—
154SD16—48no—
155M16—24no—
156C2×C8—22no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—82no—
161C22⋊C4—42no—
162C22⋊C4—44no—
163C42—21no—
164C42—82no—
165C42C22⋊C4×C3711yescharacteristic
166C42C22×C4×C3711yescharacteristic
167C23—22no—
168C23#99×C3711yescharacteristic
169Q8—42no—
170Q8—44no—
171Q8—82no—
172D4—42no—
173D4—82no—
174D4—82no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—84no—
186C2×C4#99×C3711yescharacteristic
187C2×C4C2×C22⋊C4×C3711yescharacteristic
188C8—24no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—82no—
193C22C2×#99×C3711yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—42no—
198C4—82no—
199C4—164no—
200C4C37×#35312yes—
201C2—21no—
202C2—41no—
203C2—82no—
204C2C2×C37×#35311yescharacteristic
subgroupG/H
center, socleC2×C37C2×#353
commutatorC42C22×C4×C37
Frattini, cosocle#127C23×C37
prime radicalC37×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C22×C4×C37 ◁ C37×#532 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1409C2semidirect
6. C2×C4⋊Q8×C37C4semidirect
8. C37×#494C4semidirect
11. C4×M16×C37C4semidirect
86. #13586C37direct (N × H)
101. #1409C2×C37semidirect
108. C2×C4⋊Q8C4×C37semidirect
110. #494C4×C37semidirect
113. C4×M16C4×C37semidirect
116. C37#13586direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31522
C37×#21262
C37×#14092
#1358637