Finite Group Databasebeta

← C37×#29656 #22650909

Subgroups — C37×#29656 #22650909

Order 9472.

1428 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1428 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, complemented
2C37×#2405C213yesmaximal
3C37×#2062C214yesmaximal, complemented
4C37×#2029C214yesmaximal, complemented
5C37×#1819C213yesmaximal, complemented
6C23×D4×C37C2211yescharacteristic
7C37×#543—26no—
8C37×#543C2214yes—
9C2×#123×C37—23no—
10C2×C22⋊Q8×C37—23no—
11C2×C22⋊Q8×C37—23no—
12C22×C22⋊C4×C37C2213yes—
13C37×#394—26no—
14C37×#386—23no—
15C37×#385C2216yes—
16C37×#379C2216yes—
17C37×#379C2213yes—
18C37×#342C22112yes—
19C25×C37C2311yescharacteristic
20C25×C37C2311yescharacteristic
21C22×Q8×C37—21no—
22C22×Q8×C37—21no—
23C22×D4×C37—23no—
24C22×D4×C37—23no—
25C22×D4×C37—44no—
26C23×C4×C37D413yes—
27C23×C4×C37D413yes—
28C23×C4×C37C2311yescharacteristic
29#123×C37—412no—
30C22⋊Q8×C37—212no—
31C22⋊Q8×C37—212no—
32C22⋊Q8×C37—212no—
33C22⋊Q8×C37—212no—
34C2×C4⋊C4×C37—23no—
35C2×C4⋊C4×C37—23no—
36C2×C4⋊C4×C37—26no—
37C2×C22⋊C4×C37—26no—
38C2×C22⋊C4×C37—26no—
39C2×C22⋊C4×C37—23no—
40C2×C22⋊C4×C37—26no—
41C2×C22⋊C4×C37—23no—
42C2×C22⋊C4×C37—26no—
43C2×C22⋊C4×C37D416yes—
44C2×C22⋊C4×C37C2316yes—
45C2×C22⋊C4×C37C2316yes—
46#95×C37—26no—
47C24×C37—24no—
48C24×C37—23no—
49C24×C37—24no—
50C24×C37—42no—
51C24×C37—42no—
52C24×C37—81no—
53C24×C37—81no—
54C24×C37C2×D413yes—
55C24×C37C2×D413yes—
56C24×C37C2411yescharacteristic
57C2×Q8×C37—24no—
58C2×Q8×C37—24no—
59C2×Q8×C37—82no—
60C2×Q8×C37—82no—
61C2×D4×C37—212no—
62C2×D4×C37—46no—
63C2×D4×C37—46no—
64C2×D4×C37—46no—
65C2×D4×C37—43no—
66C2×D4×C37—41no—
67C22×C4×C37—23no—
68C22×C4×C37—23no—
69C22×C4×C37—23no—
70C22×C4×C37—23no—
71C22×C4×C37—23no—
72C22×C4×C37—26no—
73C22×C4×C37—42no—
74C22×C4×C37—46no—
75C22×C4×C37—83no—
76C22×C4×C37C2×D416yes—
77C22×C4×C37C2×D416yes—
78C4⋊C4×C37—212no—
79C4⋊C4×C37—212no—
80C4⋊C4×C37—412no—
81C22⋊C4×C37—212no—
82C22⋊C4×C37—212no—
83C22⋊C4×C37—212no—
84C22⋊C4×C37—412no—
85C22⋊C4×C37—46no—
86C22⋊C4×C37—86no—
87C22⋊C4×C37—83no—
88C23×C37—26no—
89C23×C37—26no—
90C23×C37—26no—
91C23×C37—26no—
92C23×C37—41no—
93C23×C37—43no—
94C23×C37—41no—
95C23×C37—43no—
96C23×C37—43no—
97C23×C37—46no—
98C23×C37—43no—
99C23×C37—41no—
100C23×C37—46no—
101C23×C37—88no—
102C23×C37—88no—
103C23×C37#12013yes—
104C23×C37#12011yescharacteristic
105C23×C37C22×D413yes—
106C23×C372−1+414yes—
107Q8×C37—84no—
108Q8×C37—84no—
109D4×C37—412no—
110D4×C37—44no—
111C2×C4×C37—26no—
112C2×C4×C37—26no—
113C2×C4×C37—26no—
114C2×C4×C37—43no—
115C2×C4×C37—46no—
116C2×C4×C37—41no—
117C2×C4×C37—46no—
118C2×C4×C37—46no—
119C2×C4×C37—46no—
120C2×C4×C37—46no—
121C2×C4×C37—46no—
122C2×C4×C37—46no—
123C2×C4×C37—83no—
124C2×C4×C37—83no—
125#29656C3711yesmaximal, characteristic, direct product factor, Sylow
126C22×C37—21no—
127C22×C37—23no—
128C22×C37—21no—
129C22×C37—23no—
130C22×C37—23no—
131C22×C37—23no—
132C22×C37—23no—
133C22×C37—44no—
134C22×C37—412no—
135C22×C37—412no—
136C22×C37—42no—
137C22×C37—86no—
138C22×C37—86no—
139C22×C37—81no—
140C22×C37—81no—
141C22×C37B(4,𝔽2)12yes—
142C22×C37C2×#12011yescharacteristic
143C22×C37#53616yes—
144C4×C37—42no—
145C4×C37—46no—
146C4×C37—46no—
147C4×C37—86no—
148C2×#543C2×C3711yescharacteristic, complemented
149#2405C2×C3713yes—
150#2062C2×C3714yescomplemented
151#2029C2×C3714yescomplemented
152#1819C2×C3713yescomplemented
153C2×C37—26no—
154C2×C37—22no—
155C2×C37—43no—
156C2×C37—82no—
157C2×C37#261411yescharacteristic
158C2×C37C2×B(4,𝔽2)11yescharacteristic
159C2×C37#302611yescharacteristic
160C23×D4C22×C3711yescharacteristic
161#543—26no—
162#543C22×C3714yes—
163C2×#123—23no—
164C2×C22⋊Q8—23no—
165C2×C22⋊Q8—23no—
166C22×C22⋊C4C22×C3713yes—
167#394—26no—
168#386—23no—
169#385C22×C3716yes—
170#379C22×C3713yes—
171#379C22×C3716yes—
172#342C22×C37112yes—
173C37#2965611yescharacteristic, direct product factor, Sylow
174C25C23×C3711yescharacteristic
175C25C23×C3711yescharacteristic
176C22×Q8—21no—
177C22×Q8—21no—
178C22×D4—23no—
179C22×D4—23no—
180C22×D4—44no—
181C23×C4D4×C3713yes—
182C23×C4D4×C3713yes—
183C23×C4C23×C3711yescharacteristic
184#123—412no—
185C22⋊Q8—212no—
186C22⋊Q8—212no—
187C22⋊Q8—212no—
188C22⋊Q8—212no—
189C2×C4⋊C4—23no—
190C2×C4⋊C4—23no—
191C2×C4⋊C4—26no—
192C2×C22⋊C4—26no—
193C2×C22⋊C4—26no—
194C2×C22⋊C4—23no—
195C2×C22⋊C4—26no—
196C2×C22⋊C4—23no—
197C2×C22⋊C4—26no—
198C2×C22⋊C4D4×C3716yes—
199C2×C22⋊C4C23×C3716yes—
200C2×C22⋊C4C23×C3716yes—
201#95—26no—
202C24—24no—
203C24—23no—
204C24—24no—
205C24—42no—
206C24—42no—
207C24—81no—
208C24—81no—
209C24C2×D4×C3713yes—
210C24C2×D4×C3713yes—
211C24C24×C3711yescharacteristic
212C2×Q8—24no—
213C2×Q8—24no—
214C2×Q8—82no—
215C2×Q8—82no—
216C2×D4—212no—
217C2×D4—46no—
218C2×D4—46no—
219C2×D4—46no—
220C2×D4—43no—
221C2×D4—41no—
222C22×C4—23no—
223C22×C4—23no—
224C22×C4—23no—
225C22×C4—23no—
226C22×C4—23no—
227C22×C4—26no—
228C22×C4—42no—
229C22×C4—46no—
230C22×C4—83no—
231C22×C4C2×D4×C3716yes—
232C22×C4C2×D4×C3716yes—
233C4⋊C4—212no—
234C4⋊C4—212no—
235C4⋊C4—412no—
236C22⋊C4—212no—
237C22⋊C4—212no—
238C22⋊C4—212no—
239C22⋊C4—412no—
240C22⋊C4—46no—
241C22⋊C4—86no—
242C22⋊C4—83no—
243C23—26no—
244C23—26no—
245C23—26no—
246C23—26no—
247C23—41no—
248C23—43no—
249C23—41no—
250C23—43no—
251C23—43no—
252C23—46no—
253C23—43no—
254C23—41no—
255C23—46no—
256C23—88no—
257C23—88no—
258C23#120×C3713yes—
259C23#120×C3711yescharacteristic
260C23C22×D4×C3713yes—
261C232−1+4×C3714yes—
262Q8—84no—
263Q8—84no—
264D4—412no—
265D4—44no—
266C2×C4—26no—
267C2×C4—26no—
268C2×C4—26no—
269C2×C4—43no—
270C2×C4—46no—
271C2×C4—41no—
272C2×C4—46no—
273C2×C4—46no—
274C2×C4—46no—
275C2×C4—46no—
276C2×C4—46no—
277C2×C4—46no—
278C2×C4—83no—
279C2×C4—83no—
280C22—21no—
281C22—23no—
282C22—21no—
283C22—23no—
284C22—23no—
285C22—23no—
286C22—23no—
287C22—44no—
288C22—412no—
289C22—412no—
290C22—42no—
291C22—86no—
292C22—86no—
293C22—81no—
294C22—81no—
295C22C37×B(4,𝔽2)12yes—
296C22C2×#120×C3711yescharacteristic
297C22C37×#53616yes—
298C4—42no—
299C4—46no—
300C4—46no—
301C4—86no—
302C2—26no—
303C2—22no—
304C2—43no—
305C2—82no—
306C2C37×#261411yescharacteristic
307C2C2×C37×B(4,𝔽2)11yescharacteristic
308C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC23×D4×C37C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#543C2semidirect
3. C37×#2062C2semidirect
4. C37×#2029C2semidirect
5. C37×#1819C2semidirect
125. #29656C37direct (N × H)
148. C2×#543C2×C37semidirect
150. #2062C2×C37semidirect
151. #2029C2×C37semidirect
152. #1819C2×C37semidirect
173. C37#29656direct (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×#24052
C37×#20622
C37×#20292
C37×#18192
#2965637