Finite Group Databasebeta

← C37×#9383 #22630636

Subgroups — C37×#9383 #22630636

Order 9472.

570 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2972C211yesmaximal, characteristic
2C37×#2564C211yesmaximal, characteristic
3C37×#1799C211yesmaximal, characteristic
4C37×#1520C212yesmaximal, complemented
5C37×#1294C212yesmaximal, complemented
6C2×C22⋊Q8×C37C2211yescharacteristic
7C2×C4×D4×C37C2211yescharacteristic
8C8×D4×C37—24no—
9C37×#431—21no—
10C2×#99×C37—21no—
11C2×C22⋊C8×C37—21no—
12C2×C22⋊C8×C37C2212yes—
13C37×#400C411yescharacteristic, complemented
14C37×#399C411yescharacteristic, complemented
15C37×#395C411yescharacteristic, complemented
16C37×#393C411yescharacteristic, complemented
17C37×#387—21no—
18C37×#386—21no—
19C37×#385—21no—
20C37×#380—21no—
21C37×#380C2212yes—
22C2×#95×C37C2211yescharacteristic
23C37×#342—21no—
24C37×#328—24no—
25C22×Q8×C37C2×C411yescharacteristic
26C22×D4×C37D411yescharacteristic
27C23×C4×C37—21no—
28C23×C4×C37D411yescharacteristic
29C23×C4×C37C2311yescharacteristic
30C22×C8×C37—22no—
31C22×C8×C37—22no—
32C22⋊Q8×C37—22no—
33C22⋊Q8×C37—22no—
34C4×D4×C37—22no—
35C4×D4×C37—22no—
36C2×C4⋊C4×C37—21no—
37C2×C4⋊C4×C37—21no—
38C2×C4⋊C4×C37—21no—
39C2×C4⋊C4×C37—22no—
40C2×C4⋊C4×C37C2×C411yescharacteristic
41C2×C4⋊C4×C37C2×C411yescharacteristic
42C2×C22⋊C4×C37—21no—
43C2×C22⋊C4×C37—21no—
44C2×C22⋊C4×C37—22no—
45C2×C22⋊C4×C37—21no—
46C2×C22⋊C4×C37C2×C411yescharacteristic
47C2×C22⋊C4×C37D411yescharacteristic
48C2×C42×C37D411yescharacteristic
49C4⋊C8×C37—22no—
50#99×C37—42no—
51C22⋊C8×C37—22no—
52C22⋊C8×C37—22no—
53C22⋊C8×C37D414yes—
54C4×C8×C37—22no—
55#95×C37—21no—
56#95×C37—21no—
57#95×C37—21no—
58#95×C37—21no—
59#95×C37—21no—
60#95×C37—22no—
61#95×C37C2×C411yescharacteristic
62#95×C37C2×C411yescharacteristic
63C24×C37C22⋊C411yescharacteristic
64C24×C37C2×D411yescharacteristic
65C2×Q8×C37—22no—
66C2×Q8×C37—81no—
67C2×D4×C37—22no—
68C2×D4×C37—22no—
69C2×D4×C37SD1612yes—
70C2×D4×C37Q1612yes—
71C22×C4×C37—21no—
72C22×C4×C37—21no—
73C22×C4×C37—21no—
74C22×C4×C37—21no—
75C22×C4×C37—21no—
76C22×C4×C37—21no—
77C22×C4×C37—42no—
78C22×C4×C37—42no—
79C22×C4×C37—42no—
80C22×C4×C37—81no—
81C22×C4×C37—81no—
82C22×C4×C37—81no—
83C22×C4×C37C22⋊C411yescharacteristic
84C22×C4×C37C22⋊C411yescharacteristic
85C22×C4×C37C22⋊C411yescharacteristic
86C22×C4×C37C22×C411yescharacteristic
87C22×C4×C37C2×D412yes—
88C22×C4×C37C2×D411yescharacteristic
89C22×C4×C37#4112yes—
90C2×C8×C37—24no—
91C2×C8×C37—82no—
92C2×C8×C37—82no—
93C4⋊C4×C37—22no—
94C4⋊C4×C37—22no—
95C4⋊C4×C37—42no—
96C4⋊C4×C37—41no—
97C4⋊C4×C37—41no—
98C4⋊C4×C37—81no—
99C4⋊C4×C37—82no—
100C22⋊C4×C37—22no—
101C22⋊C4×C37—22no—
102C22⋊C4×C37—42no—
103C22⋊C4×C37—42no—
104C22⋊C4×C37—42no—
105C22⋊C4×C37—42no—
106C22⋊C4×C37—81no—
107C42×C37—21no—
108C42×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—41no—
112C23×C37—41no—
113C23×C37—41no—
114C23×C37—41no—
115C23×C37#10312yes—
116C23×C37C2×C22⋊C411yescharacteristic
117C23×C37#12112yes—
118C23×C37C2×SD1611yescharacteristic
119C23×C37C2×Q1611yescharacteristic
120C23×C37#13512yes—
121Q8×C37—82no—
122D4×C37—24no—
123D4×C37—24no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—22no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37—42no—
130C2×C4×C37—42no—
131C2×C4×C37—41no—
132C2×C4×C37—41no—
133C2×C4×C37—42no—
134C2×C4×C37—41no—
135C2×C4×C37—41no—
136C2×C4×C37—41no—
137C2×C4×C37—41no—
138C2×C4×C37—41no—
139C2×C4×C37—41no—
140C2×C4×C37—41no—
141C2×C4×C37—41no—
142C2×C4×C37—41no—
143C2×C4×C37—41no—
144C2×C4×C37—41no—
145C2×C4×C37—41no—
146C2×C4×C37—41no—
147C2×C4×C37—81no—
148C2×C4×C37—84no—
149C2×C4×C37—82no—
150C2×C4×C37—82no—
151C2×C4×C37—82no—
152C2×C4×C37#10312yes—
153C2×C4×C37C4×D412yes—
154C2×C4×C37#12011yescharacteristic
155C2×C4×C37#12311yescharacteristic
156C8×C37—44no—
157#9383C3711yesmaximal, characteristic, direct product factor, Sylow
158C22×C37—21no—
159C22×C37—22no—
160C22×C37—21no—
161C22×C37—22no—
162C22×C37—22no—
163C22×C37—42no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—42no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—81no—
170C22×C37#38611yescharacteristic
171C22×C37C2×#10311yescharacteristic
172C22×C37#41611yescharacteristic
173C22×C37#46512yes—
174C22×C37#46712yes—
175C4×C37—22no—
176C4×C37—21no—
177C4×C37—21no—
178C4×C37—22no—
179C4×C37—42no—
180C4×C37—41no—
181C4×C37—41no—
182C4×C37—81no—
183C4×C37—81no—
184C4×C37—81no—
185C4×C37—162no—
186#2972C2×C3711yescharacteristic
187#2564C2×C3711yescharacteristic
188#1799C2×C3711yescharacteristic
189#1520C2×C3712yescomplemented
190#1294C2×C3712yescomplemented
191C2×C37—21no—
192C2×C37—22no—
193C2×C37—21no—
194C2×C37—22no—
195C2×C37—42no—
196C2×C37#188411yescharacteristic
197C2×C37#189211yescharacteristic
198C2×C37#191311yescharacteristic
199C2×C22⋊Q8C22×C3711yescharacteristic
200C2×C4×D4C22×C3711yescharacteristic
201C8×D4—24no—
202#431—21no—
203C2×#99—21no—
204C2×C22⋊C8—21no—
205C2×C22⋊C8C22×C3712yes—
206#400C4×C3711yescharacteristic, complemented
207#399C4×C3711yescharacteristic, complemented
208#395C4×C3711yescharacteristic, complemented
209#393C4×C3711yescharacteristic, complemented
210#387—21no—
211#386—21no—
212#385—21no—
213#380—21no—
214#380C22×C3712yes—
215C2×#95C22×C3711yescharacteristic
216#342—21no—
217#328—24no—
218C37#938311yescharacteristic, direct product factor, Sylow
219C22×Q8C2×C4×C3711yescharacteristic
220C22×D4D4×C3711yescharacteristic
221C23×C4—21no—
222C23×C4D4×C3711yescharacteristic
223C23×C4C23×C3711yescharacteristic
224C22×C8—22no—
225C22×C8—22no—
226C22⋊Q8—22no—
227C22⋊Q8—22no—
228C4×D4—22no—
229C4×D4—22no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4C2×C4×C3711yescharacteristic
235C2×C4⋊C4C2×C4×C3711yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4C2×C4×C3711yescharacteristic
241C2×C22⋊C4D4×C3711yescharacteristic
242C2×C42D4×C3711yescharacteristic
243C4⋊C8—22no—
244#99—42no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247C22⋊C8D4×C3714yes—
248C4×C8—22no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—22no—
255#95C2×C4×C3711yescharacteristic
256#95C2×C4×C3711yescharacteristic
257C24C22⋊C4×C3711yescharacteristic
258C24C2×D4×C3711yescharacteristic
259C2×Q8—22no—
260C2×Q8—81no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4SD16×C3712yes—
264C2×D4Q16×C3712yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—81no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4C22⋊C4×C3711yescharacteristic
278C22×C4C22⋊C4×C3711yescharacteristic
279C22×C4C22⋊C4×C3711yescharacteristic
280C22×C4C22×C4×C3711yescharacteristic
281C22×C4C2×D4×C3712yes—
282C22×C4C2×D4×C3711yescharacteristic
283C22×C4#41×C3712yes—
284C2×C8—24no—
285C2×C8—82no—
286C2×C8—82no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—42no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—81no—
293C4⋊C4—82no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—81no—
301C42—21no—
302C42—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#103×C3712yes—
310C23C2×C22⋊C4×C3711yescharacteristic
311C23#121×C3712yes—
312C23C2×SD16×C3711yescharacteristic
313C23C2×Q16×C3711yescharacteristic
314C23#135×C3712yes—
315Q8—82no—
316D4—24no—
317D4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—84no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4#103×C3712yes—
347C2×C4C4×D4×C3712yes—
348C2×C4#120×C3711yescharacteristic
349C2×C4#123×C3711yescharacteristic
350C8—44no—
351C22—21no—
352C22—22no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—41no—
361C22—41no—
362C22—81no—
363C22C37×#38611yescharacteristic
364C22C2×#103×C3711yescharacteristic
365C22C37×#41611yescharacteristic
366C22C37×#46512yes—
367C22C37×#46712yes—
368C4—22no—
369C4—21no—
370C4—21no—
371C4—22no—
372C4—42no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—162no—
379C2—21no—
380C2—22no—
381C2—21no—
382C2—22no—
383C2—42no—
384C2C37×#188411yescharacteristic
385C2C37×#189211yescharacteristic
386C2C37×#191311yescharacteristic
subgroupG/H
center, socleC22×C37#386
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC22×D4×C37D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1520C2semidirect
5. C37×#1294C2semidirect
13. C37×#400C4semidirect
14. C37×#399C4semidirect
15. C37×#395C4semidirect
16. C37×#393C4semidirect
157. #9383C37direct (N × H)
189. #1520C2×C37semidirect
190. #1294C2×C37semidirect
206. #400C4×C37semidirect
207. #399C4×C37semidirect
208. #395C4×C37semidirect
209. #393C4×C37semidirect
218. C37#9383direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#29722
C37×#25642
C37×#17992
C37×#15202
C37×#12942
#938337