Finite Group Databasebeta

← C37×#35119 #22656372

Subgroups — C37×#35119 #22656372

Order 9472.

2262 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#529C212yesmaximal, complemented
2C37×#2854C214yesmaximal, complemented
3C37×#2659C211yesmaximal, characteristic, complemented
4C37×#2656C211yesmaximal, characteristic
5C37×#2639C212yesmaximal, complemented
6C37×#2611C214yesmaximal, complemented
7C37×#2610C214yesmaximal, complemented
8C37×#2604C214yesmaximal, complemented
9C37×#2603C214yesmaximal, complemented
10C37×#2325C214yesmaximal, complemented
11C2×C37×#376C211yesmaximal, characteristic, complemented
12C37×#529—216no—
13C2×#126×C37C2214yes—
14C2×#125×C37C2212yes—
15C2×#124×C37C2212yes—
16C2×#123×C37C2214yes—
17C2×C22⋊Q8×C37C2212yes—
18C2×#121×C37C2212yes—
19C2×#121×C37C2214yes—
20C2×C4×Q8×C37C2212yes—
21C2×C4×D4×C37C2214yes—
22C2×C4×D4×C37C2212yes—
23C2×#117×C37C2214yes—
24C22×C42×C37C2212yes—
25C22×C42×C37C2211yescharacteristic
26C37×#400C2214yes—
27C37×#399C2214yes—
28C37×#398C2214yes—
29C37×#397C2214yes—
30C37×#395C2214yes—
31C37×#394C2214yes—
32C37×#393C2214yes—
33C37×#392C2214yes—
34C37×#390C2214yes—
35C37×#390C2214yes—
36C37×#389C2214yes—
37C37×#389C2214yes—
38C37×#388C2218yes—
39C37×#388C2218yes—
40C37×#388C2218yes—
41C37×#387C2218yes—
42C37×#386C2218yes—
43C37×#386C2218yes—
44C37×#385C2218yes—
45C37×#380C2214yes—
46C37×#376C2214yes—
47C37×#376C2214yes—
48C2×#95×C37C2211yescharacteristic
49C2×#95×C37C2211yescharacteristic
50C2×#95×C37C2212yes—
51C22×Q8×C37C2312yes—
52C22×D4×C37C2314yes—
53C22×D4×C37C2312yes—
54C22×D4×C37C2314yes—
55C23×C4×C37C2311yescharacteristic
56C23×C4×C37C2312yes—
57C23×C4×C37C2314yes—
58C23×C4×C37C2311yescharacteristic
59C23×C4×C37C2311yescharacteristic
60C23×C4×C37C2312yes—
61#126×C37—216no—
62#125×C37—28no—
63#124×C37—28no—
64#123×C37—216no—
65C22⋊Q8×C37—28no—
66#121×C37—28no—
67#121×C37—216no—
68C4×Q8×C37—28no—
69C4×D4×C37—216no—
70C4×D4×C37—28no—
71#117×C37—216no—
72C2×C4⋊C4×C37C2312yes—
73C2×C4⋊C4×C37C2314yes—
74C2×C4⋊C4×C37C2312yes—
75C2×C4⋊C4×C37C2314yes—
76C2×C4⋊C4×C37C2314yes—
77C2×C4⋊C4×C37C2314yes—
78C2×C4⋊C4×C37C2314yes—
79C2×C4⋊C4×C37C2314yes—
80C2×C4⋊C4×C37C2314yes—
81C2×C22⋊C4×C37C2314yes—
82C2×C22⋊C4×C37C2318yes—
83C2×C22⋊C4×C37C2314yes—
84C2×C22⋊C4×C37C2314yes—
85C2×C22⋊C4×C37C2314yes—
86C2×C22⋊C4×C37C2314yes—
87C2×C22⋊C4×C37C2318yes—
88C2×C22⋊C4×C37C2318yes—
89C2×C42×C37—28no—
90C2×C42×C37D418yescomplemented
91C2×C42×C37C2314yes—
92C2×C42×C37C2314yes—
93C2×C42×C37C2314yes—
94C2×C42×C37C2312yes—
95C2×C42×C37C2312yes—
96#95×C37C2318yes—
97#95×C37C2314yes—
98#95×C37C2314yes—
99#95×C37C2318yes—
100#95×C37C2318yes—
101#95×C37C2318yes—
102C24×C37C2414yes—
103C24×C37C2411yescharacteristic
104C2×Q8×C37—24no—
105C2×Q8×C37—44no—
106C2×D4×C37—28no—
107C2×D4×C37—216no—
108C2×D4×C37—24no—
109C2×D4×C37—28no—
110C2×D4×C37—44no—
111C2×D4×C37—44no—
112C2×D4×C37—44no—
113C22×C4×C37—24no—
114C22×C4×C37—24no—
115C22×C4×C37—28no—
116C22×C4×C37—42no—
117C22×C4×C37—42no—
118C22×C4×C37—41no—
119C22×C4×C37—41no—
120C22×C4×C37—44no—
121C22×C4×C37—44no—
122C22×C4×C37—42no—
123C22×C4×C37—42no—
124C22×C4×C37—42no—
125C22×C4×C37C2×D414yes—
126C22×C4×C37C2×D414yes—
127C22×C4×C37C2×D414yes—
128C22×C4×C37#4118yes—
129C22×C4×C37C2414yes—
130C22×C4×C37C2414yes—
131C22×C4×C37C2414yes—
132C22×C4×C37C2414yes—
133C22×C4×C37C2412yes—
134C22×C4×C37C2412yes—
135C22×C4×C37C2411yescharacteristic
136C22×C4×C37C2411yescharacteristic
137C22×C4×C37C2414yes—
138C4⋊C4×C37—28no—
139C4⋊C4×C37—28no—
140C4⋊C4×C37—24no—
141C4⋊C4×C37—28no—
142C4⋊C4×C37—24no—
143C4⋊C4×C37—28no—
144C4⋊C4×C37—28no—
145C4⋊C4×C37—44no—
146C4⋊C4×C37—44no—
147C22⋊C4×C37—28no—
148C22⋊C4×C37—28no—
149C22⋊C4×C37—28no—
150C22⋊C4×C37—28no—
151C22⋊C4×C37—28no—
152C22⋊C4×C37—216no—
153C22⋊C4×C37—48no—
154C22⋊C4×C37—48no—
155C42×C37—28no—
156C42×C37—28no—
157C42×C37—28no—
158C42×C37C2×D418yes—
159C42×C37C2×D418yes—
160C23×C37—21no—
161C23×C37—22no—
162C23×C37—21no—
163C23×C37—24no—
164C23×C37—28no—
165C23×C37—24no—
166C23×C37—28no—
167C23×C37—24no—
168C23×C37C22×D412yes—
169C23×C37C2×#4114yes—
170C23×C37C2511yescharacteristic
171Q8×C37—48no—
172D4×C37—48no—
173D4×C37—416no—
174D4×C37—88no—
175C2×C4×C37—28no—
176C2×C4×C37—22no—
177C2×C4×C37—22no—
178C2×C4×C37—24no—
179C2×C4×C37—24no—
180C2×C4×C37—22no—
181C2×C4×C37—22no—
182C2×C4×C37—24no—
183C2×C4×C37—24no—
184C2×C4×C37—24no—
185C2×C4×C37—24no—
186C2×C4×C37—24no—
187C2×C4×C37—28no—
188C2×C4×C37—24no—
189C2×C4×C37—24no—
190C2×C4×C37—24no—
191C2×C4×C37—28no—
192C2×C4×C37—24no—
193C2×C4×C37—44no—
194C2×C4×C37—44no—
195C2×C4×C37—48no—
196C2×C4×C37—416no—
197C2×C4×C37—48no—
198C2×C4×C37C22×D414yes—
199C2×C4×C37C22×D412yes—
200C2×C4×C37C22×D412yes—
201C2×C4×C37C22×D414yes—
202C2×C4×C37C2×#4118yes—
203#35119C3711yesmaximal, characteristic, direct product factor, Sylow
204C22×C37—22no—
205C22×C37—22no—
206C22×C37—24no—
207C22×C37—24no—
208C22×C37—44no—
209C22×C37—44no—
210C22×C37—44no—
211C22×C37—48no—
212C22×C37—48no—
213C22×C37#53214yes—
214C22×C37C23×D411yescharacteristic
215C22×C37C22×#4112yes—
216C22×C37#58511yescharacteristic
217C22×C37#58512yes—
218C22×C37#58511yescharacteristic
219C4×C37—22no—
220C4×C37—22no—
221C4×C37—24no—
222C4×C37—24no—
223C4×C37—28no—
224C4×C37—44no—
225C4×C37—44no—
226C4×C37—44no—
227C4×C37—44no—
228C2×#529C2×C3712yescomplemented
229#2854C2×C3714yescomplemented
230#2659C2×C3711yescharacteristic, complemented
231#2656C2×C3711yescharacteristic
232#2639C2×C3712yescomplemented
233#2611C2×C3714yescomplemented
234#2610C2×C3714yescomplemented
235#2604C2×C3714yescomplemented
236#2603C2×C3714yescomplemented
237#2325C2×C3714yescomplemented
238C2×#376C2×C3711yescharacteristic, complemented
239C2×C37—24no—
240C2×C37—84no—
241C2×C37C2×#53211yescharacteristic
242C2×C37#344911yescharacteristic
243C2×C37#344911yescharacteristic
244C2×C37#349112yes—
245C2×C37#349312yes—
246#529—216no—
247C2×#126C22×C3714yes—
248C2×#125C22×C3712yes—
249C2×#124C22×C3712yes—
250C2×#123C22×C3714yes—
251C2×C22⋊Q8C22×C3712yes—
252C2×#121C22×C3714yes—
253C2×#121C22×C3712yes—
254C2×C4×Q8C22×C3712yes—
255C2×C4×D4C22×C3714yes—
256C2×C4×D4C22×C3712yes—
257C2×#117C22×C3714yes—
258C22×C42C22×C3712yes—
259C22×C42C22×C3711yescharacteristic
260#400C22×C3714yes—
261#399C22×C3714yes—
262#398C22×C3714yes—
263#397C22×C3714yes—
264#395C22×C3714yes—
265#394C22×C3714yes—
266#393C22×C3714yes—
267#392C22×C3714yes—
268#390C22×C3714yes—
269#390C22×C3714yes—
270#389C22×C3714yes—
271#389C22×C3714yes—
272#388C22×C3718yes—
273#388C22×C3718yes—
274#388C22×C3718yes—
275#387C22×C3718yes—
276#386C22×C3718yes—
277#386C22×C3718yes—
278#385C22×C3718yes—
279#380C22×C3714yes—
280#376C22×C3714yes—
281#376C22×C3714yes—
282C2×#95C22×C3712yes—
283C2×#95C22×C3711yescharacteristic
284C2×#95C22×C3711yescharacteristic
285C37#3511911yescharacteristic, direct product factor, Sylow
286C22×Q8C23×C3712yes—
287C22×D4C23×C3714yes—
288C22×D4C23×C3712yes—
289C22×D4C23×C3714yes—
290C23×C4C23×C3711yescharacteristic
291C23×C4C23×C3714yes—
292C23×C4C23×C3712yes—
293C23×C4C23×C3711yescharacteristic
294C23×C4C23×C3711yescharacteristic
295C23×C4C23×C3712yes—
296#126—216no—
297#125—28no—
298#124—28no—
299#123—216no—
300C22⋊Q8—28no—
301#121—28no—
302#121—216no—
303C4×Q8—28no—
304C4×D4—216no—
305C4×D4—28no—
306#117—216no—
307C2×C4⋊C4C23×C3714yes—
308C2×C4⋊C4C23×C3714yes—
309C2×C4⋊C4C23×C3712yes—
310C2×C4⋊C4C23×C3714yes—
311C2×C4⋊C4C23×C3712yes—
312C2×C4⋊C4C23×C3714yes—
313C2×C4⋊C4C23×C3714yes—
314C2×C4⋊C4C23×C3714yes—
315C2×C4⋊C4C23×C3714yes—
316C2×C22⋊C4C23×C3714yes—
317C2×C22⋊C4C23×C3714yes—
318C2×C22⋊C4C23×C3714yes—
319C2×C22⋊C4C23×C3714yes—
320C2×C22⋊C4C23×C3714yes—
321C2×C22⋊C4C23×C3718yes—
322C2×C22⋊C4C23×C3718yes—
323C2×C22⋊C4C23×C3718yes—
324C2×C42—28no—
325C2×C42D4×C3718yescomplemented
326C2×C42C23×C3714yes—
327C2×C42C23×C3714yes—
328C2×C42C23×C3714yes—
329C2×C42C23×C3712yes—
330C2×C42C23×C3712yes—
331#95C23×C3718yes—
332#95C23×C3714yes—
333#95C23×C3714yes—
334#95C23×C3718yes—
335#95C23×C3718yes—
336#95C23×C3718yes—
337C24C24×C3714yes—
338C24C24×C3711yescharacteristic
339C2×Q8—24no—
340C2×Q8—44no—
341C2×D4—28no—
342C2×D4—216no—
343C2×D4—24no—
344C2×D4—28no—
345C2×D4—44no—
346C2×D4—44no—
347C2×D4—44no—
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—28no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—44no—
356C22×C4—44no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4C2×D4×C3714yes—
361C22×C4C2×D4×C3714yes—
362C22×C4C2×D4×C3714yes—
363C22×C4#41×C3718yes—
364C22×C4C24×C3714yes—
365C22×C4C24×C3714yes—
366C22×C4C24×C3714yes—
367C22×C4C24×C3714yes—
368C22×C4C24×C3712yes—
369C22×C4C24×C3712yes—
370C22×C4C24×C3711yescharacteristic
371C22×C4C24×C3711yescharacteristic
372C22×C4C24×C3714yes—
373C4⋊C4—28no—
374C4⋊C4—28no—
375C4⋊C4—24no—
376C4⋊C4—28no—
377C4⋊C4—24no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C22⋊C4—28no—
383C22⋊C4—28no—
384C22⋊C4—28no—
385C22⋊C4—28no—
386C22⋊C4—28no—
387C22⋊C4—216no—
388C22⋊C4—48no—
389C22⋊C4—48no—
390C42—28no—
391C42—28no—
392C42—28no—
393C42C2×D4×C3718yes—
394C42C2×D4×C3718yes—
395C23—21no—
396C23—22no—
397C23—21no—
398C23—24no—
399C23—28no—
400C23—24no—
401C23—28no—
402C23—24no—
403C23C22×D4×C3712yes—
404C23C2×#41×C3714yes—
405C23C25×C3711yescharacteristic
406Q8—48no—
407D4—48no—
408D4—416no—
409D4—88no—
410C2×C4—28no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—28no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—28no—
427C2×C4—24no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—48no—
431C2×C4—416no—
432C2×C4—48no—
433C2×C4C22×D4×C3714yes—
434C2×C4C22×D4×C3712yes—
435C2×C4C22×D4×C3712yes—
436C2×C4C22×D4×C3714yes—
437C2×C4C2×#41×C3718yes—
438C22—22no—
439C22—22no—
440C22—24no—
441C22—24no—
442C22—44no—
443C22—44no—
444C22—44no—
445C22—48no—
446C22—48no—
447C22C37×#53214yes—
448C22C23×D4×C3711yescharacteristic
449C22C22×#41×C3712yes—
450C22C37×#58511yescharacteristic
451C22C37×#58512yes—
452C22C37×#58511yescharacteristic
453C4—22no—
454C4—22no—
455C4—24no—
456C4—24no—
457C4—28no—
458C4—44no—
459C4—44no—
460C4—44no—
461C4—44no—
462C2—24no—
463C2—84no—
464C2C2×C37×#53211yescharacteristic
465C2C37×#344911yescharacteristic
466C2C37×#344911yescharacteristic
467C2C37×#349112yes—
468C2C37×#349312yes—
subgroupG/H
center, socleC23×C37C25
commutator, Frattini, cosocleC23C25×C37
prime radicalC37×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#529C2semidirect
2. C37×#2854C2semidirect
3. C37×#2659C2semidirect
5. C37×#2639C2semidirect
6. C37×#2611C2semidirect
7. C37×#2610C2semidirect
8. C37×#2604C2semidirect
9. C37×#2603C2semidirect
10. C37×#2325C2semidirect
11. C2×C37×#376C2semidirect
90. C2×C42×C37D4semidirect
203. #35119C37direct (N × H)
228. C2×#529C2×C37semidirect
229. #2854C2×C37semidirect
230. #2659C2×C37semidirect
232. #2639C2×C37semidirect
233. #2611C2×C37semidirect
234. #2610C2×C37semidirect
235. #2604C2×C37semidirect
236. #2603C2×C37semidirect
237. #2325C2×C37semidirect
238. C2×#376C2×C37semidirect
285. C37#35119direct (N × H)
325. C2×C42D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5292
C37×#28542
C37×#26592
C37×#26562
C37×#26392
C37×#26112
C37×#26102
C37×#26042
C37×#26032
C37×#23252
C2×C37×#3762
#3511937