Finite Group Databasebeta

← C37×#9489 #22630742

Subgroups — C37×#9489 #22630742

Order 9472.

602 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2975C211yesmaximal, characteristic, complemented
2C37×#2535C211yesmaximal, characteristic
3C37×#1800C211yesmaximal, characteristic, complemented
4C37×#1486C212yesmaximal, complemented
5C37×#1286C212yesmaximal, complemented
6C2×#121×C37—21no—
7C2×C4×D4×C37C2211yescharacteristic
8C2×C4×D4×C37C2211yescharacteristic
9C37×#436—24no—
10C37×#431C2212yes—
11C37×#423C2212yes—
12C2×#100×C37—21no—
13C37×#407—22no—
14C37×#397C412yes—
15C37×#392C412yes—
16C37×#386—22no—
17C37×#382C2211yescharacteristic
18C37×#380—21no—
19C37×#343—21no—
20C37×D4⋊C8—24no—
21C22×D4×C37—22no—
22C22×D4×C37C2×C411yescharacteristic
23C22×D4×C37D411yescharacteristic
24C23×C4×C37—21no—
25C23×C4×C37D412yes—
26C2×M16×C37—24no—
27C2×M16×C37—22no—
28#121×C37—44no—
29C4×D4×C37—22no—
30C4×D4×C37—22no—
31C4×D4×C37—22no—
32C4×D4×C37—22no—
33C2×C4⋊C4×C37—21no—
34C2×C4⋊C4×C37C2×C411yescharacteristic
35C2×C4⋊C4×C37D411yescharacteristic
36C2×C22⋊C4×C37—22no—
37C2×C22⋊C4×C37—21no—
38C2×C22⋊C4×C37—22no—
39C2×C22⋊C4×C37C2×C412yes—
40C2×C42×C37C2311yescharacteristic
41C4⋊C8×C37—22no—
42C4⋊C8×C37—22no—
43C4⋊C8×C37—22no—
44#100×C37—42no—
45C22⋊C8×C37—24no—
46C22⋊C8×C37—22no—
47C4×C8×C37D414yescomplemented
48#95×C37—22no—
49#95×C37—21no—
50#95×C37C2×C412yes—
51C24×C37—21no—
52C24×C37C22⋊C412yes—
53C2×D4×C37—22no—
54C2×D4×C37—22no—
55C2×D4×C37—21no—
56C2×D4×C37—22no—
57C2×D4×C37—21no—
58C2×D4×C37—42no—
59C2×D4×C37—44no—
60C2×D4×C37—44no—
61C2×D4×C37—82no—
62C22×C4×C37—22no—
63C22×C4×C37—22no—
64C22×C4×C37—22no—
65C22×C4×C37—21no—
66C22×C4×C37—42no—
67C22×C4×C37—42no—
68C22×C4×C37—41no—
69C22×C4×C37—41no—
70C22×C4×C37—82no—
71C22×C4×C37C22⋊C412yes—
72C22×C4×C37C22×C411yescharacteristic
73C22×C4×C37C2×D411yescharacteristic
74C22×C4×C37C2×D411yescharacteristic
75M16×C37—42no—
76M16×C37—42no—
77M16×C37—84no—
78C2×C8×C37—24no—
79C2×C8×C37—42no—
80C4⋊C4×C37—22no—
81C4⋊C4×C37—22no—
82C4⋊C4×C37—42no—
83C22⋊C4×C37—24no—
84C22⋊C4×C37—44no—
85C22⋊C4×C37—41no—
86C22⋊C4×C37—41no—
87C22⋊C4×C37—82no—
88C42×C37C2×D412yes—
89C42×C37#4112yes—
90C23×C37—22no—
91C23×C37—22no—
92C23×C37—22no—
93C23×C37—22no—
94C23×C37—42no—
95C23×C37—42no—
96C23×C37—41no—
97C23×C37—41no—
98C23×C37—41no—
99C23×C37—41no—
100C23×C37—41no—
101C23×C37—41no—
102C23×C37C2×C22⋊C411yescharacteristic
103D4×C37—24no—
104D4×C37—42no—
105D4×C37—42no—
106D4×C37—42no—
107D4×C37—88no—
108C2×C4×C37—22no—
109C2×C4×C37—41no—
110C2×C4×C37—41no—
111C2×C4×C37—44no—
112C2×C4×C37—42no—
113C2×C4×C37—42no—
114C2×C4×C37—42no—
115C2×C4×C37—41no—
116C2×C4×C37—41no—
117C2×C4×C37—41no—
118C2×C4×C37—42no—
119C2×C4×C37—82no—
120C2×C4×C37—82no—
121C2×C4×C37—82no—
122C2×C4×C37C4×D412yes—
123C2×C4×C37#12011yescharacteristic
124C2×C4×C37#12112yes—
125C2×C4×C37#12311yescharacteristic
126C2×C4×C37AGL(1,ℤ/8)12yes—
127C2×C4×C37AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C37#13711yescharacteristic
129C8×C37—44no—
130C8×C37—82no—
131#9489C3711yesmaximal, characteristic, direct product factor, Sylow
132C22×C37—21no—
133C22×C37—21no—
134C22×C37—42no—
135C22×C37—44no—
136C22×C37—42no—
137C22×C37—42no—
138C22×C37—42no—
139C22×C37—42no—
140C22×C37—42no—
141C22×C37—82no—
142C22×C37—81no—
143C22×C37—81no—
144C22×C37—81no—
145C22×C37—81no—
146C22×C37#38611yescharacteristic
147C22×C37#41711yescharacteristic
148C22×C37#41811yescharacteristic
149C4×C37—22no—
150C4×C37—21no—
151C4×C37—21no—
152C4×C37—42no—
153C4×C37—82no—
154C4×C37—81no—
155C4×C37#46812yes—
156C4×C37#46912yes—
157#2975C2×C3711yescharacteristic, complemented
158#2535C2×C3711yescharacteristic
159#1800C2×C3711yescharacteristic, complemented
160#1486C2×C3712yescomplemented
161#1286C2×C3712yescomplemented
162C2×C37—21no—
163C2×C37—21no—
164C2×C37—82no—
165C2×C37—82no—
166C2×C37#189111yescharacteristic
167C2×C37#189511yescharacteristic
168C2×C37#191111yescharacteristic
169C2×#121—21no—
170C2×C4×D4C22×C3711yescharacteristic
171C2×C4×D4C22×C3711yescharacteristic
172#436—24no—
173#431C22×C3712yes—
174#423C22×C3712yes—
175C2×#100—21no—
176#407—22no—
177#397C4×C3712yes—
178#392C4×C3712yes—
179#386—22no—
180#382C22×C3711yescharacteristic
181#380—21no—
182#343—21no—
183D4⋊C8—24no—
184C37#948911yescharacteristic, direct product factor, Sylow
185C22×D4—22no—
186C22×D4C2×C4×C3711yescharacteristic
187C22×D4D4×C3711yescharacteristic
188C23×C4—21no—
189C23×C4D4×C3712yes—
190C2×M16—24no—
191C2×M16—22no—
192#121—44no—
193C4×D4—22no—
194C4×D4—22no—
195C4×D4—22no—
196C4×D4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×C4×C3711yescharacteristic
199C2×C4⋊C4D4×C3711yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4C2×C4×C3712yes—
204C2×C42C23×C3711yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8—22no—
208#100—42no—
209C22⋊C8—24no—
210C22⋊C8—22no—
211C4×C8D4×C3714yescomplemented
212#95—22no—
213#95—21no—
214#95C2×C4×C3712yes—
215C24—21no—
216C24C22⋊C4×C3712yes—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—21no—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—42no—
223C2×D4—44no—
224C2×D4—44no—
225C2×D4—82no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—82no—
235C22×C4C22⋊C4×C3712yes—
236C22×C4C22×C4×C3711yescharacteristic
237C22×C4C2×D4×C3711yescharacteristic
238C22×C4C2×D4×C3711yescharacteristic
239M16—42no—
240M16—42no—
241M16—84no—
242C2×C8—24no—
243C2×C8—42no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C22⋊C4—24no—
248C22⋊C4—44no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—82no—
252C42C2×D4×C3712yes—
253C42#41×C3712yes—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊C4×C3711yescharacteristic
267D4—24no—
268D4—42no—
269D4—42no—
270D4—42no—
271D4—88no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4C4×D4×C3712yes—
287C2×C4#120×C3711yescharacteristic
288C2×C4#121×C3712yes—
289C2×C4#123×C3711yescharacteristic
290C2×C4AGL(1,ℤ/8)×C3712yes—
291C2×C4AGL(1,ℤ/8)×C3711yescharacteristic
292C2×C4#137×C3711yescharacteristic
293C8—44no—
294C8—82no—
295C22—21no—
296C22—21no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22C37×#38611yescharacteristic
310C22C37×#41711yescharacteristic
311C22C37×#41811yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4C37×#46812yes—
319C4C37×#46912yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—82no—
324C2C37×#189111yescharacteristic
325C2C37×#189511yescharacteristic
326C2C37×#191111yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC37×#2535C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#2975C2semidirect
3. C37×#1800C2semidirect
4. C37×#1486C2semidirect
5. C37×#1286C2semidirect
47. C4×C8×C37D4semidirect
131. #9489C37direct (N × H)
157. #2975C2×C37semidirect
159. #1800C2×C37semidirect
160. #1486C2×C37semidirect
161. #1286C2×C37semidirect
184. C37#9489direct (N × H)
211. C4×C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#29752
C37×#25352
C37×#18002
C37×#14862
C37×#12862
#948937