Finite Group Databasebeta

← C37×#34967 #22656220

Subgroups — C37×#34967 #22656220

Order 9472.

2164 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2522C214yesmaximal, complemented
2C37×#2516C214yesmaximal, complemented
3C37×#2464C214yesmaximal, complemented
4C37×#2457C214yesmaximal, complemented
5C37×#2402C211yesmaximal, characteristic, complemented
6C37×#2397C211yesmaximal, characteristic, complemented
7C37×#2392C212yesmaximal, complemented
8C4×#123×C37C214yesmaximal, complemented
9C4×#121×C37C214yesmaximal, complemented
10C37×#2298C211yesmaximal, characteristic, complemented
11C42×D4×C37C212yesmaximal, complemented
12C2×#123×C37C2214yes—
13C2×#121×C37C2214yes—
14C2×C4×D4×C37C2212yes—
15C2×C4×D4×C37C2214yes—
16C2×C4×D4×C37C2214yes—
17C2×C4×D4×C37C2214yes—
18C2×#117×C37C2211yescharacteristic
19C22×C42×C37C2214yes—
20C37×#400C2214yes—
21C37×#399C2214yes—
22C37×#398C2212yes—
23C37×#398C2214yes—
24C37×#397C2212yes—
25C37×#396C2214yes—
26C37×#394C2212yes—
27C37×#394C2214yes—
28C37×#392C2212yes—
29C37×#392C2214yes—
30C37×#390C2214yes—
31C37×#389C2214yes—
32C37×#388C2214yes—
33C37×#388C2214yes—
34C37×#388C2214yes—
35C37×#388C2214yes—
36C37×#388C2214yes—
37C37×#387C2214yes—
38C37×#387C2214yes—
39C37×#387C2214yes—
40C37×#386C2214yes—
41C37×#386C2214yes—
42C37×#386C2214yes—
43C37×#385C2214yes—
44C37×#381C2214yes—
45C37×#380C2214yes—
46C4×C4⋊C4×C37C2212yes—
47C4×C4⋊C4×C37C2214yes—
48C4×C4⋊C4×C37C2214yes—
49C4×C4⋊C4×C37C2212yes—
50C4×C22⋊C4×C37C2214yes—
51C4×C22⋊C4×C37C2214yes—
52C4×C22⋊C4×C37C2214yes—
53C4×C22⋊C4×C37C2214yes—
54C4×C22⋊C4×C37C2212yes—
55C37×#376C2211yescharacteristic
56C43×C37C2211yescharacteristic
57C22×D4×C37C2312yes—
58C22×D4×C37C2314yes—
59C22×D4×C37C2314yes—
60C23×C4×C37C2314yes—
61C23×C4×C37C2311yescharacteristic
62C23×C4×C37C2314yes—
63C23×C4×C37C2314yes—
64#123×C37—216no—
65#121×C37—216no—
66C4×D4×C37—216no—
67C4×D4×C37—28no—
68C4×D4×C37—48no—
69C4×D4×C37—48no—
70#117×C37—24no—
71C2×C4⋊C4×C37C2314yes—
72C2×C4⋊C4×C37C2314yes—
73C2×C4⋊C4×C37C2314yes—
74C2×C4⋊C4×C37C2314yes—
75C2×C4⋊C4×C37C2312yes—
76C2×C4⋊C4×C37C2312yes—
77C2×C4⋊C4×C37C2314yes—
78C2×C4⋊C4×C37C2314yes—
79C2×C22⋊C4×C37C2314yes—
80C2×C22⋊C4×C37C2314yes—
81C2×C22⋊C4×C37C2314yes—
82C2×C22⋊C4×C37C2314yes—
83C2×C22⋊C4×C37C2314yes—
84C2×C22⋊C4×C37C2312yes—
85C2×C22⋊C4×C37C2314yes—
86C2×C22⋊C4×C37C2314yes—
87C2×C22⋊C4×C37C2314yes—
88C2×C22⋊C4×C37C2314yes—
89C2×C22⋊C4×C37C2314yes—
90C2×C42×C37—48no—
91C2×C42×C37C2314yes—
92C2×C42×C37C2312yes—
93C2×C42×C37C2312yes—
94C2×C42×C37C2311yescharacteristic
95C2×C42×C37C2314yes—
96C2×C42×C37C2314yes—
97C2×C42×C37C2314yes—
98C2×C42×C37C2311yescharacteristic
99#95×C37C2314yes—
100#95×C37C2314yes—
101#95×C37C2314yes—
102#95×C37C2312yes—
103#95×C37C2312yes—
104#95×C37C2314yes—
105#95×C37C2314yes—
106#95×C37C2314yes—
107#95×C37C2314yes—
108#95×C37C2314yes—
109#95×C37C2314yes—
110C24×C37C2411yescharacteristic
111C24×C37C2414yes—
112C2×D4×C37—28no—
113C2×D4×C37—28no—
114C2×D4×C37—28no—
115C2×D4×C37—28no—
116C2×D4×C37—24no—
117C2×D4×C37—28no—
118C2×D4×C37—44no—
119C2×D4×C37—44no—
120C22×C4×C37—28no—
121C22×C4×C37—22no—
122C22×C4×C37—28no—
123C22×C4×C37—28no—
124C22×C4×C37—28no—
125C22×C4×C37—28no—
126C22×C4×C37—28no—
127C22×C4×C37—28no—
128C22×C4×C37—24no—
129C22×C4×C37—44no—
130C22×C4×C37—44no—
131C22×C4×C37C2414yes—
132C22×C4×C37C2412yes—
133C22×C4×C37C2414yes—
134C22×C4×C37C2414yes—
135C22×C4×C37C2411yescharacteristic
136C22×C4×C37C2414yes—
137C22×C4×C37C2412yes—
138C22×C4×C37C2414yes—
139C22×C4×C37C2411yescharacteristic
140C4⋊C4×C37—24no—
141C4⋊C4×C37—28no—
142C4⋊C4×C37—24no—
143C4⋊C4×C37—28no—
144C4⋊C4×C37—28no—
145C4⋊C4×C37—28no—
146C4⋊C4×C37—44no—
147C4⋊C4×C37—44no—
148C22⋊C4×C37—28no—
149C22⋊C4×C37—24no—
150C22⋊C4×C37—28no—
151C22⋊C4×C37—28no—
152C22⋊C4×C37—28no—
153C22⋊C4×C37—28no—
154C22⋊C4×C37—44no—
155C22⋊C4×C37—44no—
156C22⋊C4×C37—44no—
157C22⋊C4×C37—44no—
158C22⋊C4×C37#41116yes—
159C42×C37—22no—
160C42×C37—28no—
161C42×C37—24no—
162C42×C37—28no—
163C42×C37—24no—
164C42×C37—44no—
165C42×C37—44no—
166C42×C37#4114yes—
167C23×C37—24no—
168C23×C37—24no—
169C23×C37—24no—
170C23×C37—24no—
171C23×C37—24no—
172C23×C37—24no—
173C23×C37—21no—
174C23×C37—24no—
175C23×C37—22no—
176C23×C37C2×#4118yes—
177C23×C37C2511yescharacteristic
178D4×C37—216no—
179D4×C37—416no—
180D4×C37—416no—
181C2×C4×C37—24no—
182C2×C4×C37—24no—
183C2×C4×C37—24no—
184C2×C4×C37—24no—
185C2×C4×C37—24no—
186C2×C4×C37—22no—
187C2×C4×C37—24no—
188C2×C4×C37—24no—
189C2×C4×C37—24no—
190C2×C4×C37—24no—
191C2×C4×C37—24no—
192C2×C4×C37—21no—
193C2×C4×C37—24no—
194C2×C4×C37—24no—
195C2×C4×C37—24no—
196C2×C4×C37—24no—
197C2×C4×C37—24no—
198C2×C4×C37—22no—
199C2×C4×C37—416no—
200C2×C4×C37—416no—
201C2×C4×C37—416no—
202C2×C4×C37—44no—
203C2×C4×C37C2×#4118yes—
204C2×C4×C37C2×#4114yes—
205C2×C4×C37C2×#4118yes—
206C2×C4×C37C2×#4112yes—
207C2×C4×C37H(5,𝔽2)14yes—
208#34967C3711yesmaximal, characteristic, direct product factor, Sylow
209C22×C37—28no—
210C22×C37—28no—
211C22×C37—28no—
212C22×C37—44no—
213C22×C37—44no—
214C22×C37—44no—
215C22×C37—44no—
216C22×C37—42no—
217C22×C37—41no—
218C22×C37—44no—
219C22×C37C22×#4111yescharacteristic
220C22×C37C22×#4114yes—
221C22×C37C2×H(5,𝔽2)12yes—
222C4×C37—24no—
223C4×C37—28no—
224C4×C37—28no—
225C4×C37—42no—
226C4×C37—44no—
227C4×C37—41no—
228C4×C37—44no—
229C4×C37—44no—
230C4×C37#54014yes—
231#2522C2×C3714yescomplemented
232#2516C2×C3714yescomplemented
233#2464C2×C3714yescomplemented
234#2457C2×C3714yescomplemented
235#2402C2×C3711yescharacteristic, complemented
236#2397C2×C3711yescharacteristic, complemented
237#2392C2×C3712yescomplemented
238C4×#123C2×C3714yescomplemented
239C4×#121C2×C3714yescomplemented
240#2298C2×C3711yescharacteristic, complemented
241C42×D4C2×C3712yescomplemented
242C2×C37—48no—
243C2×C37—81no—
244C2×C37#344412yes—
245C2×C37C2×#54011yescharacteristic
246C2×C37#348114yes—
247C2×#123C22×C3714yes—
248C2×#121C22×C3714yes—
249C2×C4×D4C22×C3712yes—
250C2×C4×D4C22×C3714yes—
251C2×C4×D4C22×C3714yes—
252C2×C4×D4C22×C3714yes—
253C2×#117C22×C3711yescharacteristic
254C22×C42C22×C3714yes—
255#400C22×C3714yes—
256#399C22×C3714yes—
257#398C22×C3712yes—
258#398C22×C3714yes—
259#397C22×C3712yes—
260#396C22×C3714yes—
261#394C22×C3712yes—
262#394C22×C3714yes—
263#392C22×C3712yes—
264#392C22×C3714yes—
265#390C22×C3714yes—
266#389C22×C3714yes—
267#388C22×C3714yes—
268#388C22×C3714yes—
269#388C22×C3714yes—
270#388C22×C3714yes—
271#388C22×C3714yes—
272#387C22×C3714yes—
273#387C22×C3714yes—
274#387C22×C3714yes—
275#386C22×C3714yes—
276#386C22×C3714yes—
277#386C22×C3714yes—
278#385C22×C3714yes—
279#381C22×C3714yes—
280#380C22×C3714yes—
281C4×C4⋊C4C22×C3712yes—
282C4×C4⋊C4C22×C3714yes—
283C4×C4⋊C4C22×C3714yes—
284C4×C4⋊C4C22×C3712yes—
285C4×C22⋊C4C22×C3714yes—
286C4×C22⋊C4C22×C3714yes—
287C4×C22⋊C4C22×C3714yes—
288C4×C22⋊C4C22×C3714yes—
289C4×C22⋊C4C22×C3712yes—
290#376C22×C3711yescharacteristic
291C43C22×C3711yescharacteristic
292C37#3496711yescharacteristic, direct product factor, Sylow
293C22×D4C23×C3712yes—
294C22×D4C23×C3714yes—
295C22×D4C23×C3714yes—
296C23×C4C23×C3711yescharacteristic
297C23×C4C23×C3714yes—
298C23×C4C23×C3714yes—
299C23×C4C23×C3714yes—
300#123—216no—
301#121—216no—
302C4×D4—216no—
303C4×D4—28no—
304C4×D4—48no—
305C4×D4—48no—
306#117—24no—
307C2×C4⋊C4C23×C3712yes—
308C2×C4⋊C4C23×C3714yes—
309C2×C4⋊C4C23×C3712yes—
310C2×C4⋊C4C23×C3714yes—
311C2×C4⋊C4C23×C3714yes—
312C2×C4⋊C4C23×C3714yes—
313C2×C4⋊C4C23×C3714yes—
314C2×C4⋊C4C23×C3714yes—
315C2×C22⋊C4C23×C3712yes—
316C2×C22⋊C4C23×C3714yes—
317C2×C22⋊C4C23×C3714yes—
318C2×C22⋊C4C23×C3714yes—
319C2×C22⋊C4C23×C3714yes—
320C2×C22⋊C4C23×C3714yes—
321C2×C22⋊C4C23×C3714yes—
322C2×C22⋊C4C23×C3714yes—
323C2×C22⋊C4C23×C3714yes—
324C2×C22⋊C4C23×C3714yes—
325C2×C22⋊C4C23×C3714yes—
326C2×C42—48no—
327C2×C42C23×C3711yescharacteristic
328C2×C42C23×C3712yes—
329C2×C42C23×C3714yes—
330C2×C42C23×C3714yes—
331C2×C42C23×C3712yes—
332C2×C42C23×C3714yes—
333C2×C42C23×C3714yes—
334C2×C42C23×C3711yescharacteristic
335#95C23×C3714yes—
336#95C23×C3714yes—
337#95C23×C3714yes—
338#95C23×C3712yes—
339#95C23×C3712yes—
340#95C23×C3714yes—
341#95C23×C3714yes—
342#95C23×C3714yes—
343#95C23×C3714yes—
344#95C23×C3714yes—
345#95C23×C3714yes—
346C24C24×C3711yescharacteristic
347C24C24×C3714yes—
348C2×D4—28no—
349C2×D4—28no—
350C2×D4—28no—
351C2×D4—28no—
352C2×D4—24no—
353C2×D4—28no—
354C2×D4—44no—
355C2×D4—44no—
356C22×C4—28no—
357C22×C4—22no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—28no—
363C22×C4—28no—
364C22×C4—24no—
365C22×C4—44no—
366C22×C4—44no—
367C22×C4C24×C3714yes—
368C22×C4C24×C3712yes—
369C22×C4C24×C3714yes—
370C22×C4C24×C3714yes—
371C22×C4C24×C3711yescharacteristic
372C22×C4C24×C3714yes—
373C22×C4C24×C3712yes—
374C22×C4C24×C3714yes—
375C22×C4C24×C3711yescharacteristic
376C4⋊C4—24no—
377C4⋊C4—28no—
378C4⋊C4—24no—
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—28no—
382C4⋊C4—44no—
383C4⋊C4—44no—
384C22⋊C4—28no—
385C22⋊C4—24no—
386C22⋊C4—28no—
387C22⋊C4—28no—
388C22⋊C4—28no—
389C22⋊C4—28no—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4#41×C37116yes—
395C42—22no—
396C42—28no—
397C42—24no—
398C42—28no—
399C42—24no—
400C42—44no—
401C42—44no—
402C42#41×C3714yes—
403C23—24no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—24no—
408C23—24no—
409C23—21no—
410C23—24no—
411C23—22no—
412C23C2×#41×C3718yes—
413C23C25×C3711yescharacteristic
414D4—216no—
415D4—416no—
416D4—416no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—21no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—416no—
436C2×C4—416no—
437C2×C4—416no—
438C2×C4—44no—
439C2×C4C2×#41×C3718yes—
440C2×C4C2×#41×C3714yes—
441C2×C4C2×#41×C3718yes—
442C2×C4C2×#41×C3712yes—
443C2×C4H(5,𝔽2)×C3714yes—
444C22—28no—
445C22—28no—
446C22—28no—
447C22—44no—
448C22—44no—
449C22—44no—
450C22—44no—
451C22—42no—
452C22—41no—
453C22—44no—
454C22C22×#41×C3711yescharacteristic
455C22C22×#41×C3714yes—
456C22C2×H(5,𝔽2)×C3712yes—
457C4—24no—
458C4—28no—
459C4—28no—
460C4—42no—
461C4—44no—
462C4—41no—
463C4—44no—
464C4—44no—
465C4C37×#54014yes—
466C2—48no—
467C2—81no—
468C2C37×#344412yes—
469C2C2×C37×#54011yescharacteristic
470C2C37×#348114yes—
subgroupG/H
centerC22×C4×C37C24
commutator, Frattini, cosocleC23C25×C37
socleC23×C37C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#2522C2semidirect
2. C37×#2516C2semidirect
3. C37×#2464C2semidirect
4. C37×#2457C2semidirect
5. C37×#2402C2semidirect
6. C37×#2397C2semidirect
7. C37×#2392C2semidirect
8. C4×#123×C37C2semidirect
9. C4×#121×C37C2semidirect
10. C37×#2298C2semidirect
11. C42×D4×C37C2semidirect
208. #34967C37direct (N × H)
231. #2522C2×C37semidirect
232. #2516C2×C37semidirect
233. #2464C2×C37semidirect
234. #2457C2×C37semidirect
235. #2402C2×C37semidirect
236. #2397C2×C37semidirect
237. #2392C2×C37semidirect
238. C4×#123C2×C37semidirect
239. C4×#121C2×C37semidirect
240. #2298C2×C37semidirect
241. C42×D4C2×C37semidirect
292. C37#34967direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#25222
C37×#25162
C37×#24642
C37×#24572
C37×#24022
C37×#23972
C37×#23922
C4×#123×C372
C4×#121×C372
C37×#22982
C42×D4×C372
#3496737