Finite Group Databasebeta

← C37×#19411 #22640664

Subgroups — C37×#19411 #22640664

Order 9472.

620 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3209C211yesmaximal, characteristic, complemented
2C37×#3079C211yesmaximal, characteristic
3C37×#3076C211yesmaximal, characteristic
4C37×#2988C211yesmaximal, characteristic
5C37×#1684C212yesmaximal, complemented
6C37×#1683C212yesmaximal, complemented
7C37×#1670C212yesmaximal, complemented
8C37×#1669C212yesmaximal, complemented
9C37×#1571C211yesmaximal, characteristic, complemented
10C37×#1550C211yesmaximal, characteristic, complemented
11C2×C37×#332C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C4×#41×C37C2211yescharacteristic
15C37×#494C2212yes—
16C37×#487C2212yes—
17C37×#479—21no—
18C37×#478—21no—
19C37×#477—21no—
20C37×#477C2211yescharacteristic
21C37×#476—21no—
22C37×#476C2211yescharacteristic
23C37×#475C2211yescharacteristic
24C37×#475C2212yes—
25C37×#474C2211yescharacteristic
26C37×#474C2212yes—
27C37×#462—21no—
28C37×#462—21no—
29C37×#451—22no—
30C8×Q8×C37C2212yes—
31C8×D4×C37—22no—
32C8×D4×C37C2212yes—
33C37×#431—21no—
34C37×#431C2211yescharacteristic
35C37×#428—21no—
36C37×#427—21no—
37C37×#423C2211yescharacteristic
38C2×C4⋊C8×C37—21no—
39C2×C4⋊C8×C37C2211yescharacteristic
40C2×C4⋊C8×C37C2211yescharacteristic
41C37×#417—21no—
42C37×#416—21no—
43C37×#335C2212yes—
44C37×#335C2212yes—
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#332C2212yes—
49C2×#41×C37D411yescharacteristic
50C22×Q8×C37—21no—
51C2×Q16×C37—22no—
52C2×Q16×C37—22no—
53C2×M16×C37—21no—
54C22×C8×C37—21no—
55C22×C8×C37—21no—
56C22×C8×C37—22no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37C2312yes—
61C4⋊Q8×C37C2311yescharacteristic
62C4⋊Q8×C37C2311yescharacteristic
63#125×C37—21no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—21no—
66C4×Q8×C37—21no—
67C4×Q8×C37—21no—
68C4×Q8×C37D411yescharacteristic
69C4×Q8×C37C2311yescharacteristic
70C4×D4×C37—21no—
71C4×D4×C37—21no—
72C4×D4×C37D411yescharacteristic
73C4×D4×C37C2311yescharacteristic
74#117×C37—21no—
75#117×C37—21no—
76#117×C37D411yescharacteristic
77C2×C4⋊C4×C37—21no—
78C2×C4⋊C4×C37—21no—
79C2×C42×C37—21no—
80C2×C42×C37C2311yescharacteristic
81#107×C37—21no—
82#107×C37—21no—
83#107×C37—22no—
84#106×C37—21no—
85#106×C37—21no—
86#106×C37—22no—
87C4⋊C8×C37—22no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37—21no—
91C4⋊C8×C37D411yescharacteristic
92C4⋊C8×C37D411yescharacteristic
93C4⋊C8×C37C2312yes—
94C4⋊C8×C37C2311yescharacteristic
95C4⋊C8×C37C2311yescharacteristic
96C4⋊C8×C37C2312yes—
97#103×C37—21no—
98#103×C37—21no—
99#103×C37—22no—
100#103×C37—22no—
101#103×C37—22no—
102#102×C37—21no—
103#102×C37—21no—
104#102×C37—22no—
105C22⋊C8×C37—22no—
106C22⋊C8×C37D412yes—
107C4×C8×C37—22no—
108C4×C8×C37C2312yes—
109#41×C37—22no—
110#41×C37Q1614yescomplemented
111C2×Q8×C37—22no—
112C2×Q8×C37—21no—
113C2×Q8×C37—21no—
114C2×Q8×C37—41no—
115C2×Q8×C37—81no—
116C2×Q8×C37—81no—
117C2×Q8×C37C2×D411yescharacteristic
118C2×D4×C37—21no—
119C2×D4×C37C2×D411yescharacteristic
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—41no—
124C22×C4×C37C2×D411yescharacteristic
125C22×C4×C37C2×D411yescharacteristic
126C22×C4×C37#4111yescharacteristic
127Q16×C37—82no—
128Q16×C37—82no—
129M16×C37—42no—
130C2×C8×C37—22no—
131C2×C8×C37—21no—
132C2×C8×C37—22no—
133C2×C8×C37—21no—
134C2×C8×C37—42no—
135C2×C8×C37—82no—
136C2×C8×C37—81no—
137C2×C8×C37C2×D412yes—
138C2×C8×C37C2×D412yes—
139C4⋊C4×C37—21no—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—22no—
142C4⋊C4×C37—21no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—21no—
145C4⋊C4×C37—22no—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—41no—
148C4⋊C4×C37—41no—
149C4⋊C4×C37—41no—
150C4⋊C4×C37—41no—
151C4⋊C4×C37C2×D411yescharacteristic
152C4⋊C4×C37C2×D411yescharacteristic
153C22⋊C4×C37—21no—
154C22⋊C4×C37—21no—
155C22⋊C4×C37—21no—
156C22⋊C4×C37—41no—
157C42×C37—21no—
158C42×C37—21no—
159C42×C37—21no—
160C42×C37—41no—
161C42×C37C2×D411yescharacteristic
162C42×C37C2×D411yescharacteristic
163C42×C37#4111yescharacteristic
164C42×C37C2411yescharacteristic
165C23×C37—21no—
166C23×C37#12111yescharacteristic
167Q8×C37—21no—
168Q8×C37—41no—
169Q8×C37—42no—
170Q8×C37—41no—
171Q8×C37—42no—
172Q8×C37—81no—
173Q8×C37—82no—
174Q8×C37C2×Q1612yes—
175D4×C37—24no—
176D4×C37—21no—
177D4×C37C2×Q1612yes—
178C2×C4×C37—21no—
179C2×C4×C37—21no—
180C2×C4×C37—21no—
181C2×C4×C37—24no—
182C2×C4×C37—21no—
183C2×C4×C37—21no—
184C2×C4×C37—41no—
185C2×C4×C37—41no—
186C2×C4×C37—41no—
187C2×C4×C37—41no—
188C2×C4×C37—41no—
189C2×C4×C37—42no—
190C2×C4×C37—81no—
191C2×C4×C37—82no—
192C2×C4×C37#12111yescharacteristic
193C2×C4×C37#12111yescharacteristic
194C2×C4×C37#12111yescharacteristic
195C2×C4×C37C2×Q1612yes—
196C2×C4×C37#13512yes—
197C2×C4×C37C22×D411yescharacteristic
198C2×C4×C37C22×D411yescharacteristic
199C2×C4×C37C2×#4111yescharacteristic
200C8×C37—22no—
201C8×C37—22no—
202C8×C37—41no—
203C8×C37—41no—
204C8×C37—42no—
205C8×C37—42no—
206#19411C3711yesmaximal, characteristic, direct product factor, Sylow
207C22×C37—21no—
208C22×C37—21no—
209C22×C37—22no—
210C22×C37—41no—
211C22×C37—41no—
212C22×C37#46712yes—
213C22×C37C2×#12111yescharacteristic
214C4×C37—21no—
215C4×C37—22no—
216C4×C37—21no—
217C4×C37—21no—
218C4×C37—41no—
219C4×C37—41no—
220C4×C37—82no—
221C4×C37—81no—
222C4×C37—81no—
223C4×C37#46712yes—
224C4×C37C22×Q1611yescharacteristic
225C4×C37C2×#13511yescharacteristic
226C4×C37#57611yescharacteristic
227C4×C37#57711yescharacteristic
228#3209C2×C3711yescharacteristic, complemented
229#3079C2×C3711yescharacteristic
230#3076C2×C3711yescharacteristic
231#2988C2×C3711yescharacteristic
232#1684C2×C3712yescomplemented
233#1683C2×C3712yescomplemented
234#1670C2×C3712yescomplemented
235#1669C2×C3712yescomplemented
236#1571C2×C3711yescharacteristic, complemented
237#1550C2×C3711yescharacteristic, complemented
238C2×#332C2×C3711yescharacteristic, complemented
239C2×C37—22no—
240C2×C37—42no—
241C2×C37#304511yescharacteristic
242C2×C37C2×#46711yescharacteristic
243C2×C37#306911yescharacteristic
244#533C22×C3711yescharacteristic
245C2×C4⋊Q8C22×C3711yescharacteristic
246C4×#41C22×C3711yescharacteristic
247#494C22×C3712yes—
248#487C22×C3712yes—
249#479—21no—
250#478—21no—
251#477—21no—
252#477C22×C3711yescharacteristic
253#476—21no—
254#476C22×C3711yescharacteristic
255#475C22×C3711yescharacteristic
256#475C22×C3712yes—
257#474C22×C3711yescharacteristic
258#474C22×C3712yes—
259#462—21no—
260#462—21no—
261#451—22no—
262C8×Q8C22×C3712yes—
263C8×D4—22no—
264C8×D4C22×C3712yes—
265#431—21no—
266#431C22×C3711yescharacteristic
267#428—21no—
268#427—21no—
269#423C22×C3711yescharacteristic
270C2×C4⋊C8—21no—
271C2×C4⋊C8C22×C3711yescharacteristic
272C2×C4⋊C8C22×C3711yescharacteristic
273#417—21no—
274#416—21no—
275#335C22×C3712yes—
276#335C22×C3712yes—
277#333C22×C3712yes—
278#332C22×C3712yes—
279#332C22×C3712yes—
280#332C22×C3712yes—
281C37#1941111yescharacteristic, direct product factor, Sylow
282C2×#41D4×C3711yescharacteristic
283C22×Q8—21no—
284C2×Q16—22no—
285C2×Q16—22no—
286C2×M16—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C23×C3712yes—
294C4⋊Q8C23×C3711yescharacteristic
295C4⋊Q8C23×C3711yescharacteristic
296#125—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8D4×C3711yescharacteristic
302C4×Q8C23×C3711yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C4×D4D4×C3711yescharacteristic
306C4×D4C23×C3711yescharacteristic
307#117—21no—
308#117—21no—
309#117D4×C3711yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—21no—
313C2×C42C23×C3711yescharacteristic
314#107—21no—
315#107—21no—
316#107—22no—
317#106—21no—
318#106—21no—
319#106—22no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8D4×C3711yescharacteristic
325C4⋊C8D4×C3711yescharacteristic
326C4⋊C8C23×C3712yes—
327C4⋊C8C23×C3711yescharacteristic
328C4⋊C8C23×C3711yescharacteristic
329C4⋊C8C23×C3712yes—
330#103—21no—
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#102—21no—
336#102—21no—
337#102—22no—
338C22⋊C8—22no—
339C22⋊C8D4×C3712yes—
340C4×C8—22no—
341C4×C8C23×C3712yes—
342#41—22no—
343#41Q16×C3714yescomplemented
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—41no—
348C2×Q8—81no—
349C2×Q8—81no—
350C2×Q8C2×D4×C3711yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C3711yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C3711yescharacteristic
358C22×C4C2×D4×C3711yescharacteristic
359C22×C4#41×C3711yescharacteristic
360Q16—82no—
361Q16—82no—
362M16—42no—
363C2×C8—22no—
364C2×C8—21no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—42no—
368C2×C8—82no—
369C2×C8—81no—
370C2×C8C2×D4×C3712yes—
371C2×C8C2×D4×C3712yes—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C3711yescharacteristic
385C4⋊C4C2×D4×C3711yescharacteristic
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—41no—
394C42C2×D4×C3711yescharacteristic
395C42C2×D4×C3711yescharacteristic
396C42#41×C3711yescharacteristic
397C42C24×C3711yescharacteristic
398C23—21no—
399C23#121×C3711yescharacteristic
400Q8—21no—
401Q8—41no—
402Q8—42no—
403Q8—41no—
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8C2×Q16×C3712yes—
408D4—24no—
409D4—21no—
410D4C2×Q16×C3712yes—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4#121×C3711yescharacteristic
426C2×C4#121×C3711yescharacteristic
427C2×C4#121×C3711yescharacteristic
428C2×C4C2×Q16×C3712yes—
429C2×C4#135×C3712yes—
430C2×C4C22×D4×C3711yescharacteristic
431C2×C4C22×D4×C3711yescharacteristic
432C2×C4C2×#41×C3711yescharacteristic
433C8—22no—
434C8—22no—
435C8—41no—
436C8—41no—
437C8—42no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—41no—
443C22—41no—
444C22C37×#46712yes—
445C22C2×#121×C3711yescharacteristic
446C4—21no—
447C4—22no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4C37×#46712yes—
456C4C22×Q16×C3711yescharacteristic
457C4C2×#135×C3711yescharacteristic
458C4C37×#57611yescharacteristic
459C4C37×#57711yescharacteristic
460C2—22no—
461C2—42no—
462C2C37×#304511yescharacteristic
463C2C2×C37×#46711yescharacteristic
464C2C37×#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×#3209C2semidirect
5. C37×#1684C2semidirect
6. C37×#1683C2semidirect
7. C37×#1670C2semidirect
8. C37×#1669C2semidirect
9. C37×#1571C2semidirect
10. C37×#1550C2semidirect
11. C2×C37×#332C2semidirect
110. #41×C37Q16semidirect
206. #19411C37direct (N × H)
228. #3209C2×C37semidirect
232. #1684C2×C37semidirect
233. #1683C2×C37semidirect
234. #1670C2×C37semidirect
235. #1669C2×C37semidirect
236. #1571C2×C37semidirect
237. #1550C2×C37semidirect
238. C2×#332C2×C37semidirect
281. C37#19411direct (N × H)
343. #41Q16×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#32092
C37×#30792
C37×#30762
C37×#29882
C37×#16842
C37×#16832
C37×#16702
C37×#16692
C37×#15712
C37×#15502
C2×C37×#3322
#1941137