Finite Group Databasebeta

← C37×#9016 #22630269

Subgroups — C37×#9016 #22630269

Order 9472.

836 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 150 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×#393C211yesmaximal, characteristic
2C37×#2312C211yesmaximal, characteristic
3C37×#1787C212yesmaximal, complemented
4C2×C37×#323C211yesmaximal, characteristic
5C37×#1294C212yesmaximal, complemented
6C23×Q8×C37C2211yescharacteristic
7C22×C22⋊C4×C37—21no—
8C22×C22⋊C4×C37C2211yescharacteristic
9C2×#103×C37—24no—
10C2×C22⋊C8×C37C2212yes—
11C37×#393—22no—
12C37×#393C414yescomplemented
13C37×#388—24no—
14C37×#380C2212yes—
15C37×#379—21no—
16C4×C22⋊C4×C37—21no—
17C2×#95×C37—21no—
18C2×#95×C37C2211yescharacteristic
19C37×#323—22no—
20C25×C37D411yescharacteristic
21C22×Q8×C37—21no—
22C22×Q8×C37—22no—
23C22×Q8×C37—22no—
24C22×Q8×C37—44no—
25C22×Q8×C37C2×C412yes—
26C23×C4×C37—21no—
27C23×C4×C37—21no—
28C23×C4×C37D411yescharacteristic
29C23×C4×C37C2311yescharacteristic
30C22×C8×C37—22no—
31C2×C4⋊C4×C37D414yes—
32C2×C22⋊C4×C37—22no—
33C2×C22⋊C4×C37—22no—
34C2×C22⋊C4×C37—24no—
35C2×C22⋊C4×C37—22no—
36C2×C22⋊C4×C37—22no—
37C2×C22⋊C4×C37—22no—
38C2×C22⋊C4×C37—44no—
39C2×C22⋊C4×C37C2×C412yes—
40C2×C22⋊C4×C37D412yes—
41C2×C42×C37—22no—
42#103×C37—48no—
43C22⋊C8×C37—22no—
44C22⋊C8×C37—22no—
45#95×C37—22no—
46#95×C37—24no—
47#95×C37—21no—
48#95×C37—22no—
49#95×C37C2×C412yes—
50C24×C37—21no—
51C24×C37—22no—
52C24×C37—21no—
53C24×C37—22no—
54C24×C37—42no—
55C24×C37—42no—
56C24×C37C22⋊C412yes—
57C24×C37C2×D411yescharacteristic
58C2×Q8×C37—28no—
59C2×Q8×C37—24no—
60C2×Q8×C37—44no—
61C2×Q8×C37—44no—
62C2×Q8×C37—44no—
63C2×Q8×C37—48no—
64C2×Q8×C37—42no—
65C22×C4×C37—24no—
66C22×C4×C37—22no—
67C22×C4×C37—21no—
68C22×C4×C37—21no—
69C22×C4×C37—22no—
70C22×C4×C37—24no—
71C22×C4×C37—42no—
72C22×C4×C37—42no—
73C22×C4×C37—41no—
74C22×C4×C37—41no—
75C22×C4×C37—42no—
76C22×C4×C37—42no—
77C22×C4×C37—42no—
78C22×C4×C37—42no—
79C22×C4×C37C22⋊C412yes—
80C22×C4×C37C22×C411yescharacteristic
81C22×C4×C37C2×D412yes—
82C22×C4×C37C2×D411yescharacteristic
83C22×C4×C37#4112yes—
84C2×C8×C37—44no—
85C2×C8×C37—42no—
86C4⋊C4×C37—44no—
87C22⋊C4×C37—24no—
88C22⋊C4×C37—24no—
89C22⋊C4×C37—48no—
90C22⋊C4×C37—42no—
91C22⋊C4×C37—42no—
92C22⋊C4×C37—82no—
93C22⋊C4×C37—82no—
94C42×C37—82no—
95C23×C37—22no—
96C23×C37—22no—
97C23×C37—22no—
98C23×C37—22no—
99C23×C37—22no—
100C23×C37—42no—
101C23×C37—42no—
102C23×C37—48no—
103C23×C37—42no—
104C23×C37—42no—
105C23×C37—42no—
106C23×C37—42no—
107C23×C37—81no—
108C23×C37—81no—
109C23×C37—84no—
110C23×C37C2×C22⋊C411yescharacteristic
111C23×C37#12011yescharacteristic
112C23×C37#12311yescharacteristic
113C23×C37#13512yes—
114C23×C37#13712yes—
115Q8×C37—28no—
116Q8×C37—48no—
117Q8×C37—44no—
118C2×C4×C37—24no—
119C2×C4×C37—24no—
120C2×C4×C37—22no—
121C2×C4×C37—41no—
122C2×C4×C37—41no—
123C2×C4×C37—42no—
124C2×C4×C37—42no—
125C2×C4×C37—44no—
126C2×C4×C37—42no—
127C2×C4×C37—42no—
128C2×C4×C37—44no—
129C2×C4×C37—42no—
130C2×C4×C37—42no—
131C2×C4×C37—42no—
132C2×C4×C37—42no—
133C2×C4×C37—44no—
134C2×C4×C37—44no—
135C2×C4×C37—44no—
136C2×C4×C37—81no—
137C2×C4×C37—84no—
138C2×C4×C37C4×D412yes—
139C2×C4×C37#12112yes—
140C8×C37—82no—
141#9016C3711yesmaximal, characteristic, direct product factor, Sylow
142C22×C37—24no—
143C22×C37—24no—
144C22×C37—21no—
145C22×C37—21no—
146C22×C37—21no—
147C22×C37—21no—
148C22×C37—44no—
149C22×C37—42no—
150C22×C37—42no—
151C22×C37—42no—
152C22×C37—82no—
153C22×C37—84no—
154C22×C37—84no—
155C22×C37#38611yescharacteristic
156C22×C37#41611yescharacteristic
157C22×C37#41911yescharacteristic
158C22×C37#45212yes—
159C22×C37#45512yes—
160C22×C37B(4,𝔽2)12yes—
161C22×C37#48512yes—
162C4×C37—22no—
163C4×C37—22no—
164C4×C37—42no—
165C4×C37—44no—
166C4×C37—82no—
167C4×C37—84no—
168C2×#393C2×C3711yescharacteristic
169#2312C2×C3711yescharacteristic
170#1787C2×C3712yescomplemented
171C2×#323C2×C3711yescharacteristic
172#1294C2×C3712yescomplemented
173C2×C37—21no—
174C2×C37—21no—
175C2×C37—22no—
176C2×C37—82no—
177C2×C37#160614yes—
178C2×C37#187311yescharacteristic
179C2×C37#188511yescharacteristic
180C2×C37#188911yescharacteristic
181C23×Q8C22×C3711yescharacteristic
182C22×C22⋊C4—21no—
183C22×C22⋊C4C22×C3711yescharacteristic
184C2×#103—24no—
185C2×C22⋊C8C22×C3712yes—
186#393—22no—
187#393C4×C3714yescomplemented
188#388—24no—
189#380C22×C3712yes—
190#379—21no—
191C4×C22⋊C4—21no—
192C2×#95—21no—
193C2×#95C22×C3711yescharacteristic
194#323—22no—
195C37#901611yescharacteristic, direct product factor, Sylow
196C25D4×C3711yescharacteristic
197C22×Q8—21no—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—44no—
201C22×Q8C2×C4×C3712yes—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4D4×C3711yescharacteristic
205C23×C4C23×C3711yescharacteristic
206C22×C8—22no—
207C2×C4⋊C4D4×C3714yes—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—24no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—44no—
215C2×C22⋊C4C2×C4×C3712yes—
216C2×C22⋊C4D4×C3712yes—
217C2×C42—22no—
218#103—48no—
219C22⋊C8—22no—
220C22⋊C8—22no—
221#95—22no—
222#95—24no—
223#95—21no—
224#95—22no—
225#95C2×C4×C3712yes—
226C24—21no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24C22⋊C4×C3712yes—
233C24C2×D4×C3711yescharacteristic
234C2×Q8—28no—
235C2×Q8—24no—
236C2×Q8—44no—
237C2×Q8—44no—
238C2×Q8—44no—
239C2×Q8—48no—
240C2×Q8—42no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—24no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4C22⋊C4×C3712yes—
256C22×C4C22×C4×C3711yescharacteristic
257C22×C4C2×D4×C3712yes—
258C22×C4C2×D4×C3711yescharacteristic
259C22×C4#41×C3712yes—
260C2×C8—44no—
261C2×C8—42no—
262C4⋊C4—44no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—48no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—82no—
269C22⋊C4—82no—
270C42—82no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—42no—
277C23—42no—
278C23—48no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—81no—
284C23—81no—
285C23—84no—
286C23C2×C22⋊C4×C3711yescharacteristic
287C23#120×C3711yescharacteristic
288C23#123×C3711yescharacteristic
289C23#135×C3712yes—
290C23#137×C3712yes—
291Q8—28no—
292Q8—48no—
293Q8—44no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—81no—
313C2×C4—84no—
314C2×C4C4×D4×C3712yes—
315C2×C4#121×C3712yes—
316C8—82no—
317C22—24no—
318C22—24no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—44no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—82no—
328C22—84no—
329C22—84no—
330C22C37×#38611yescharacteristic
331C22C37×#41611yescharacteristic
332C22C37×#41911yescharacteristic
333C22C37×#45212yes—
334C22C37×#45512yes—
335C22C37×B(4,𝔽2)12yes—
336C22C37×#48512yes—
337C4—22no—
338C4—22no—
339C4—42no—
340C4—44no—
341C4—82no—
342C4—84no—
343C2—21no—
344C2—21no—
345C2—22no—
346C2—82no—
347C2C37×#160614yes—
348C2C37×#187311yescharacteristic
349C2C37×#188511yescharacteristic
350C2C37×#188911yescharacteristic
subgroupG/H
center, socleC23×C37#120
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC25×C37D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1787C2semidirect
5. C37×#1294C2semidirect
12. C37×#393C4semidirect
141. #9016C37direct (N × H)
170. #1787C2×C37semidirect
172. #1294C2×C37semidirect
187. #393C4×C37semidirect
195. C37#9016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#3932
C37×#23122
C37×#17872
C2×C37×#3232
C37×#12942
#901637