Finite Group Databasebeta

← C37×#19415 #22640668

Subgroups — C37×#19415 #22640668

Order 9472.

640 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3229C211yesmaximal, characteristic, complemented
2C37×#3076C211yesmaximal, characteristic
3C37×#3039C211yesmaximal, characteristic
4C37×#2988C211yesmaximal, characteristic
5C37×#1680C212yesmaximal, complemented
6C37×#1679C212yesmaximal, complemented
7C37×#1672C212yesmaximal, complemented
8C37×#1671C212yesmaximal, complemented
9C37×#1570C211yesmaximal, characteristic, complemented
10C37×#1550C211yesmaximal, characteristic, complemented
11C2×C37×#332C211yesmaximal, characteristic, complemented
12C2×#137×C37—21no—
13C37×#533C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C4×#41×C37C2211yescharacteristic
16C37×#498C2212yes—
17C37×#487C2212yes—
18C37×#483—22no—
19C37×#479—21no—
20C37×#478—21no—
21C37×#477C2211yescharacteristic
22C37×#476C2211yescharacteristic
23C37×#475—21no—
24C37×#475—21no—
25C37×#475C2211yescharacteristic
26C37×#474C2211yescharacteristic
27C37×#462—21no—
28C37×#462C2212yes—
29C37×#461—21no—
30C37×#461C2212yes—
31C8×Q8×C37C2212yes—
32C8×D4×C37—22no—
33C8×D4×C37C2212yes—
34C37×#431—21no—
35C37×#431C2211yescharacteristic
36C37×#427—21no—
37C37×#423C2211yescharacteristic
38C2×C4⋊C8×C37—21no—
39C2×C4⋊C8×C37C2211yescharacteristic
40C2×C4⋊C8×C37C2211yescharacteristic
41C37×#419—21no—
42C37×#416—21no—
43C37×#334C2212yes—
44C37×#334C2212yes—
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#332C2212yes—
49C2×#41×C37D411yescharacteristic
50C22×Q8×C37—21no—
51#137×C37—44no—
52C2×Q16×C37—22no—
53C2×SD16×C37—22no—
54C2×M16×C37—21no—
55C22×C8×C37—21no—
56C22×C8×C37—21no—
57C22×C8×C37—22no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37—21no—
61C4⋊Q8×C37C2312yes—
62C4⋊Q8×C37C2311yescharacteristic
63C4⋊Q8×C37C2311yescharacteristic
64#125×C37—21no—
65C22⋊Q8×C37—21no—
66C22⋊Q8×C37—21no—
67C4×Q8×C37—21no—
68C4×Q8×C37—21no—
69C4×Q8×C37D411yescharacteristic
70C4×Q8×C37C2311yescharacteristic
71C4×D4×C37—21no—
72C4×D4×C37—21no—
73C4×D4×C37D411yescharacteristic
74C4×D4×C37C2311yescharacteristic
75#117×C37—21no—
76#117×C37—21no—
77#117×C37D411yescharacteristic
78C2×C4⋊C4×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C42×C37—21no—
81C2×C42×C37C2311yescharacteristic
82#107×C37—21no—
83#107×C37—21no—
84#106×C37—22no—
85#106×C37—22no—
86#106×C37—21no—
87#106×C37—21no—
88C4⋊C8×C37—22no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91C4⋊C8×C37—21no—
92C4⋊C8×C37D411yescharacteristic
93C4⋊C8×C37D411yescharacteristic
94C4⋊C8×C37C2312yes—
95C4⋊C8×C37C2311yescharacteristic
96C4⋊C8×C37C2311yescharacteristic
97C4⋊C8×C37C2312yes—
98#103×C37—21no—
99#103×C37—21no—
100#103×C37—22no—
101#103×C37—22no—
102#103×C37—22no—
103#103×C37—22no—
104#102×C37—21no—
105#102×C37—21no—
106C22⋊C8×C37—22no—
107C22⋊C8×C37D412yes—
108C4×C8×C37—22no—
109C4×C8×C37C2312yes—
110#41×C37—22no—
111#41×C37SD1614yes—
112C2×Q8×C37—21no—
113C2×Q8×C37—22no—
114C2×Q8×C37—21no—
115C2×Q8×C37—41no—
116C2×Q8×C37—42no—
117C2×Q8×C37—42no—
118C2×Q8×C37C2×D411yescharacteristic
119C2×D4×C37—21no—
120C2×D4×C37C2×D411yescharacteristic
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—41no—
125C22×C4×C37C2×D411yescharacteristic
126C22×C4×C37C2×D411yescharacteristic
127C22×C4×C37#4111yescharacteristic
128Q16×C37—44no—
129SD16×C37—44no—
130M16×C37—42no—
131C2×C8×C37—22no—
132C2×C8×C37—21no—
133C2×C8×C37—21no—
134C2×C8×C37—22no—
135C2×C8×C37—42no—
136C2×C8×C37—82no—
137C2×C8×C37—81no—
138C2×C8×C37C2×D412yes—
139C2×C8×C37C2×D412yes—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—21no—
142C4⋊C4×C37—21no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—22no—
145C4⋊C4×C37—21no—
146C4⋊C4×C37—22no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—41no—
149C4⋊C4×C37—41no—
150C4⋊C4×C37—41no—
151C4⋊C4×C37—41no—
152C4⋊C4×C37C2×D411yescharacteristic
153C4⋊C4×C37C2×D411yescharacteristic
154C22⋊C4×C37—21no—
155C22⋊C4×C37—21no—
156C22⋊C4×C37—21no—
157C22⋊C4×C37—41no—
158C42×C37—21no—
159C42×C37—21no—
160C42×C37—21no—
161C42×C37—41no—
162C42×C37C2×D411yescharacteristic
163C42×C37C2×D411yescharacteristic
164C42×C37#4111yescharacteristic
165C42×C37C2411yescharacteristic
166C23×C37—21no—
167C23×C37#12111yescharacteristic
168Q8×C37—21no—
169Q8×C37—42no—
170Q8×C37—42no—
171Q8×C37—41no—
172Q8×C37—41no—
173Q8×C37—81no—
174Q8×C37—82no—
175Q8×C37C2×SD1612yes—
176D4×C37—24no—
177D4×C37—21no—
178D4×C37C2×SD1612yes—
179C2×C4×C37—21no—
180C2×C4×C37—21no—
181C2×C4×C37—21no—
182C2×C4×C37—24no—
183C2×C4×C37—21no—
184C2×C4×C37—21no—
185C2×C4×C37—41no—
186C2×C4×C37—41no—
187C2×C4×C37—41no—
188C2×C4×C37—41no—
189C2×C4×C37—41no—
190C2×C4×C37—42no—
191C2×C4×C37—81no—
192C2×C4×C37—82no—
193C2×C4×C37#12111yescharacteristic
194C2×C4×C37#12111yescharacteristic
195C2×C4×C37#12111yescharacteristic
196C2×C4×C37C2×SD1612yes—
197C2×C4×C37#13512yes—
198C2×C4×C37C22×D411yescharacteristic
199C2×C4×C37C22×D411yescharacteristic
200C2×C4×C37C2×#4111yescharacteristic
201C8×C37—22no—
202C8×C37—22no—
203C8×C37—42no—
204C8×C37—41no—
205C8×C37—41no—
206C8×C37—42no—
207#19415C3711yesmaximal, characteristic, direct product factor, Sylow
208C22×C37—21no—
209C22×C37—21no—
210C22×C37—22no—
211C22×C37—41no—
212C22×C37—41no—
213C22×C37#46512yes—
214C22×C37C2×#12111yescharacteristic
215C4×C37—21no—
216C4×C37—22no—
217C4×C37—21no—
218C4×C37—21no—
219C4×C37—41no—
220C4×C37—41no—
221C4×C37—81no—
222C4×C37—82no—
223C4×C37—81no—
224C4×C37#46512yes—
225C4×C37C22×SD1611yescharacteristic
226C4×C37C2×#13511yescharacteristic
227C4×C37#57711yescharacteristic
228C4×C37#57811yescharacteristic
229#3229C2×C3711yescharacteristic, complemented
230#3076C2×C3711yescharacteristic
231#3039C2×C3711yescharacteristic
232#2988C2×C3711yescharacteristic
233#1680C2×C3712yescomplemented
234#1679C2×C3712yescomplemented
235#1672C2×C3712yescomplemented
236#1671C2×C3712yescomplemented
237#1570C2×C3711yescharacteristic, complemented
238#1550C2×C3711yescharacteristic, complemented
239C2×#332C2×C3711yescharacteristic, complemented
240C2×C37—22no—
241C2×C37—42no—
242C2×C37#304611yescharacteristic
243C2×C37C2×#46511yescharacteristic
244C2×C37#306911yescharacteristic
245C2×#137—21no—
246#533C22×C3711yescharacteristic
247C2×C4⋊Q8C22×C3711yescharacteristic
248C4×#41C22×C3711yescharacteristic
249#498C22×C3712yes—
250#487C22×C3712yes—
251#483—22no—
252#479—21no—
253#478—21no—
254#477C22×C3711yescharacteristic
255#476C22×C3711yescharacteristic
256#475—21no—
257#475—21no—
258#475C22×C3711yescharacteristic
259#474C22×C3711yescharacteristic
260#462—21no—
261#462C22×C3712yes—
262#461—21no—
263#461C22×C3712yes—
264C8×Q8C22×C3712yes—
265C8×D4—22no—
266C8×D4C22×C3712yes—
267#431—21no—
268#431C22×C3711yescharacteristic
269#427—21no—
270#423C22×C3711yescharacteristic
271C2×C4⋊C8—21no—
272C2×C4⋊C8C22×C3711yescharacteristic
273C2×C4⋊C8C22×C3711yescharacteristic
274#419—21no—
275#416—21no—
276#334C22×C3712yes—
277#334C22×C3712yes—
278#333C22×C3712yes—
279#332C22×C3712yes—
280#332C22×C3712yes—
281#332C22×C3712yes—
282C37#1941511yescharacteristic, direct product factor, Sylow
283C2×#41D4×C3711yescharacteristic
284C22×Q8—21no—
285#137—44no—
286C2×Q16—22no—
287C2×SD16—22no—
288C2×M16—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—22no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C23×C3712yes—
296C4⋊Q8C23×C3711yescharacteristic
297C4⋊Q8C23×C3711yescharacteristic
298#125—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8D4×C3711yescharacteristic
304C4×Q8C23×C3711yescharacteristic
305C4×D4—21no—
306C4×D4—21no—
307C4×D4D4×C3711yescharacteristic
308C4×D4C23×C3711yescharacteristic
309#117—21no—
310#117—21no—
311#117D4×C3711yescharacteristic
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C42—21no—
315C2×C42C23×C3711yescharacteristic
316#107—21no—
317#107—21no—
318#106—22no—
319#106—22no—
320#106—21no—
321#106—21no—
322C4⋊C8—22no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8D4×C3711yescharacteristic
327C4⋊C8D4×C3711yescharacteristic
328C4⋊C8C23×C3712yes—
329C4⋊C8C23×C3711yescharacteristic
330C4⋊C8C23×C3711yescharacteristic
331C4⋊C8C23×C3712yes—
332#103—21no—
333#103—21no—
334#103—22no—
335#103—22no—
336#103—22no—
337#103—22no—
338#102—21no—
339#102—21no—
340C22⋊C8—22no—
341C22⋊C8D4×C3712yes—
342C4×C8—22no—
343C4×C8C23×C3712yes—
344#41—22no—
345#41SD16×C3714yes—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8C2×D4×C3711yescharacteristic
353C2×D4—21no—
354C2×D4C2×D4×C3711yescharacteristic
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—41no—
359C22×C4C2×D4×C3711yescharacteristic
360C22×C4C2×D4×C3711yescharacteristic
361C22×C4#41×C3711yescharacteristic
362Q16—44no—
363SD16—44no—
364M16—42no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—82no—
371C2×C8—81no—
372C2×C8C2×D4×C3712yes—
373C2×C8C2×D4×C3712yes—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4C2×D4×C3711yescharacteristic
387C4⋊C4C2×D4×C3711yescharacteristic
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—41no—
392C42—21no—
393C42—21no—
394C42—21no—
395C42—41no—
396C42C2×D4×C3711yescharacteristic
397C42C2×D4×C3711yescharacteristic
398C42#41×C3711yescharacteristic
399C42C24×C3711yescharacteristic
400C23—21no—
401C23#121×C3711yescharacteristic
402Q8—21no—
403Q8—42no—
404Q8—42no—
405Q8—41no—
406Q8—41no—
407Q8—81no—
408Q8—82no—
409Q8C2×SD16×C3712yes—
410D4—24no—
411D4—21no—
412D4C2×SD16×C3712yes—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—81no—
426C2×C4—82no—
427C2×C4#121×C3711yescharacteristic
428C2×C4#121×C3711yescharacteristic
429C2×C4#121×C3711yescharacteristic
430C2×C4C2×SD16×C3712yes—
431C2×C4#135×C3712yes—
432C2×C4C22×D4×C3711yescharacteristic
433C2×C4C22×D4×C3711yescharacteristic
434C2×C4C2×#41×C3711yescharacteristic
435C8—22no—
436C8—22no—
437C8—42no—
438C8—41no—
439C8—41no—
440C8—42no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22C37×#46512yes—
447C22C2×#121×C3711yescharacteristic
448C4—21no—
449C4—22no—
450C4—21no—
451C4—21no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—82no—
456C4—81no—
457C4C37×#46512yes—
458C4C22×SD16×C3711yescharacteristic
459C4C2×#135×C3711yescharacteristic
460C4C37×#57711yescharacteristic
461C4C37×#57811yescharacteristic
462C2—22no—
463C2—42no—
464C2C37×#304611yescharacteristic
465C2C2×C37×#46511yescharacteristic
466C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×#41×C37D4
LCSG ▷ C42 ▷ 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×#3229C2semidirect
5. C37×#1680C2semidirect
6. C37×#1679C2semidirect
7. C37×#1672C2semidirect
8. C37×#1671C2semidirect
9. C37×#1570C2semidirect
10. C37×#1550C2semidirect
11. C2×C37×#332C2semidirect
207. #19415C37direct (N × H)
229. #3229C2×C37semidirect
233. #1680C2×C37semidirect
234. #1679C2×C37semidirect
235. #1672C2×C37semidirect
236. #1671C2×C37semidirect
237. #1570C2×C37semidirect
238. #1550C2×C37semidirect
239. C2×#332C2×C37semidirect
282. C37#19415direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32292
C37×#30762
C37×#30392
C37×#29882
C37×#16802
C37×#16792
C37×#16722
C37×#16712
C37×#15702
C37×#15502
C2×C37×#3322
#1941537