Finite Group Databasebeta

← C37×#19417 #22640670

Subgroups — C37×#19417 #22640670

Order 9472.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3230C211yesmaximal, characteristic, complemented
2C37×#3079C211yesmaximal, characteristic
3C37×#3076C211yesmaximal, characteristic
4C37×#2988C211yesmaximal, characteristic
5C37×#1684C212yesmaximal, complemented
6C37×#1683C212yesmaximal, complemented
7C37×#1676C212yesmaximal, complemented
8C37×#1675C212yesmaximal, complemented
9C37×#1571C211yesmaximal, characteristic, complemented
10C37×#1550C211yesmaximal, characteristic, complemented
11C2×C37×#333C211yesmaximal, characteristic, complemented
12C37×#533C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C4×#41×C37C2211yescharacteristic
15C37×#500C2212yes—
16C37×#487C2212yes—
17C37×#484—22no—
18C37×#479—21no—
19C37×#478—21no—
20C37×#477—21no—
21C37×#477—21no—
22C37×#477C2211yescharacteristic
23C37×#477C2212yes—
24C37×#476C2211yescharacteristic
25C37×#476C2212yes—
26C37×#475—21no—
27C37×#475C2211yescharacteristic
28C37×#474—21no—
29C37×#474C2211yescharacteristic
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×#333C2212yes—
47C37×#333C2212yes—
48C37×#332C2212yes—
49C2×#41×C37D411yescharacteristic
50C22×Q8×C37—21no—
51C2×M16×C37—21no—
52C22×C8×C37—21no—
53C22×C8×C37—21no—
54C22×C8×C37—22no—
55C4⋊Q8×C37—21no—
56C4⋊Q8×C37—21no—
57C4⋊Q8×C37—21no—
58C4⋊Q8×C37C2312yes—
59C4⋊Q8×C37C2311yescharacteristic
60C4⋊Q8×C37C2311yescharacteristic
61#125×C37—21no—
62C22⋊Q8×C37—21no—
63C22⋊Q8×C37—21no—
64C4×Q8×C37—21no—
65C4×Q8×C37—21no—
66C4×Q8×C37D411yescharacteristic
67C4×Q8×C37C2311yescharacteristic
68C4×D4×C37—21no—
69C4×D4×C37—21no—
70C4×D4×C37D411yescharacteristic
71C4×D4×C37C2311yescharacteristic
72#117×C37—21no—
73#117×C37—21no—
74#117×C37D411yescharacteristic
75C2×C4⋊C4×C37—21no—
76C2×C4⋊C4×C37—21no—
77C2×C42×C37—21no—
78C2×C42×C37C2311yescharacteristic
79#107×C37—22no—
80#107×C37—22no—
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×C37C2312yes—
95C4⋊C8×C37C2311yescharacteristic
96C4⋊C8×C37C2311yescharacteristic
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×C37Q1614yes—
111C2×Q8×C37—21no—
112C2×Q8×C37—21no—
113C2×Q8×C37—22no—
114C2×Q8×C37—41no—
115C2×Q8×C37—82no—
116C2×Q8×C37C2×D411yescharacteristic
117C2×D4×C37—21no—
118C2×D4×C37C2×D411yescharacteristic
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—21no—
122C22×C4×C37—41no—
123C22×C4×C37C2×D411yescharacteristic
124C22×C4×C37C2×D411yescharacteristic
125C22×C4×C37#4111yescharacteristic
126M16×C37—42no—
127C2×C8×C37—22no—
128C2×C8×C37—21no—
129C2×C8×C37—22no—
130C2×C8×C37—21no—
131C2×C8×C37—42no—
132C2×C8×C37—82no—
133C2×C8×C37—81no—
134C2×C8×C37C2×D412yes—
135C2×C8×C37C2×D412yes—
136C4⋊C4×C37—21no—
137C4⋊C4×C37—21no—
138C4⋊C4×C37—22no—
139C4⋊C4×C37—21no—
140C4⋊C4×C37—21no—
141C4⋊C4×C37—22no—
142C4⋊C4×C37—21no—
143C4⋊C4×C37—21no—
144C4⋊C4×C37—41no—
145C4⋊C4×C37—41no—
146C4⋊C4×C37—41no—
147C4⋊C4×C37—41no—
148C4⋊C4×C37C2×D411yescharacteristic
149C4⋊C4×C37C2×D411yescharacteristic
150C22⋊C4×C37—21no—
151C22⋊C4×C37—21no—
152C22⋊C4×C37—21no—
153C22⋊C4×C37—41no—
154C42×C37—21no—
155C42×C37—21no—
156C42×C37—21no—
157C42×C37—41no—
158C42×C37C2×D411yescharacteristic
159C42×C37C2×D411yescharacteristic
160C42×C37#4111yescharacteristic
161C42×C37C2411yescharacteristic
162C23×C37—21no—
163C23×C37#12111yescharacteristic
164Q8×C37—21no—
165Q8×C37—41no—
166Q8×C37—41no—
167Q8×C37—81no—
168Q8×C37—82no—
169Q8×C37—82no—
170Q8×C37C2×Q1612yes—
171D4×C37—24no—
172D4×C37—21no—
173D4×C37C2×Q1612yes—
174C2×C4×C37—21no—
175C2×C4×C37—21no—
176C2×C4×C37—21no—
177C2×C4×C37—24no—
178C2×C4×C37—21no—
179C2×C4×C37—21no—
180C2×C4×C37—41no—
181C2×C4×C37—41no—
182C2×C4×C37—41no—
183C2×C4×C37—41no—
184C2×C4×C37—41no—
185C2×C4×C37—42no—
186C2×C4×C37—81no—
187C2×C4×C37—82no—
188C2×C4×C37#12111yescharacteristic
189C2×C4×C37#12111yescharacteristic
190C2×C4×C37#12111yescharacteristic
191C2×C4×C37C2×Q1612yes—
192C2×C4×C37#13512yes—
193C2×C4×C37C22×D411yescharacteristic
194C2×C4×C37C22×D411yescharacteristic
195C2×C4×C37C2×#4111yescharacteristic
196C8×C37—22no—
197C8×C37—22no—
198C8×C37—41no—
199C8×C37—41no—
200C8×C37—42no—
201C8×C37—42no—
202#19417C3711yesmaximal, characteristic, direct product factor, Sylow
203C22×C37—21no—
204C22×C37—21no—
205C22×C37—22no—
206C22×C37—41no—
207C22×C37—41no—
208C22×C37#46712yes—
209C22×C37C2×#12111yescharacteristic
210C4×C37—21no—
211C4×C37—22no—
212C4×C37—21no—
213C4×C37—21no—
214C4×C37—41no—
215C4×C37—41no—
216C4×C37—81no—
217C4×C37—82no—
218C4×C37—81no—
219C4×C37#46712yes—
220C4×C37C22×Q1611yescharacteristic
221C4×C37C2×#13511yescharacteristic
222C4×C37#57711yescharacteristic
223C4×C37#57811yescharacteristic
224#3230C2×C3711yescharacteristic, complemented
225#3079C2×C3711yescharacteristic
226#3076C2×C3711yescharacteristic
227#2988C2×C3711yescharacteristic
228#1684C2×C3712yescomplemented
229#1683C2×C3712yescomplemented
230#1676C2×C3712yescomplemented
231#1675C2×C3712yescomplemented
232#1571C2×C3711yescharacteristic, complemented
233#1550C2×C3711yescharacteristic, complemented
234C2×#333C2×C3711yescharacteristic, complemented
235C2×C37—22no—
236C2×C37—42no—
237C2×C37#304611yescharacteristic
238C2×C37C2×#46711yescharacteristic
239C2×C37#306811yescharacteristic
240#533C22×C3711yescharacteristic
241C2×C4⋊Q8C22×C3711yescharacteristic
242C4×#41C22×C3711yescharacteristic
243#500C22×C3712yes—
244#487C22×C3712yes—
245#484—22no—
246#479—21no—
247#478—21no—
248#477—21no—
249#477—21no—
250#477C22×C3711yescharacteristic
251#477C22×C3712yes—
252#476C22×C3711yescharacteristic
253#476C22×C3712yes—
254#475—21no—
255#475C22×C3711yescharacteristic
256#474—21no—
257#474C22×C3711yescharacteristic
258C8×Q8C22×C3712yes—
259C8×D4—22no—
260C8×D4C22×C3712yes—
261#431—21no—
262#431C22×C3711yescharacteristic
263#428—21no—
264#427—21no—
265#423C22×C3711yescharacteristic
266C2×C4⋊C8—21no—
267C2×C4⋊C8C22×C3711yescharacteristic
268C2×C4⋊C8C22×C3711yescharacteristic
269#417—21no—
270#416—21no—
271#335C22×C3712yes—
272#335C22×C3712yes—
273#333C22×C3712yes—
274#333C22×C3712yes—
275#333C22×C3712yes—
276#332C22×C3712yes—
277C37#1941711yescharacteristic, direct product factor, Sylow
278C2×#41D4×C3711yescharacteristic
279C22×Q8—21no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—22no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C23×C3712yes—
288C4⋊Q8C23×C3711yescharacteristic
289C4⋊Q8C23×C3711yescharacteristic
290#125—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C3711yescharacteristic
296C4×Q8C23×C3711yescharacteristic
297C4×D4—21no—
298C4×D4—21no—
299C4×D4D4×C3711yescharacteristic
300C4×D4C23×C3711yescharacteristic
301#117—21no—
302#117—21no—
303#117D4×C3711yescharacteristic
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C42—21no—
307C2×C42C23×C3711yescharacteristic
308#107—22no—
309#107—22no—
310#107—21no—
311#107—21no—
312#107—22no—
313#106—21no—
314#106—21no—
315#106—22no—
316C4⋊C8—22no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320C4⋊C8D4×C3711yescharacteristic
321C4⋊C8D4×C3711yescharacteristic
322C4⋊C8C23×C3712yes—
323C4⋊C8C23×C3712yes—
324C4⋊C8C23×C3711yescharacteristic
325C4⋊C8C23×C3711yescharacteristic
326#103—21no—
327#103—21no—
328#103—22no—
329#103—22no—
330#103—22no—
331#102—21no—
332#102—21no—
333#102—22no—
334C22⋊C8—22no—
335C22⋊C8D4×C3712yes—
336C4×C8—22no—
337C4×C8C23×C3712yes—
338#41—22no—
339#41Q16×C3714yes—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×Q8C2×D4×C3711yescharacteristic
346C2×D4—21no—
347C2×D4C2×D4×C3711yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4C2×D4×C3711yescharacteristic
353C22×C4C2×D4×C3711yescharacteristic
354C22×C4#41×C3711yescharacteristic
355M16—42no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8—22no—
359C2×C8—21no—
360C2×C8—42no—
361C2×C8—82no—
362C2×C8—81no—
363C2×C8C2×D4×C3712yes—
364C2×C8C2×D4×C3712yes—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4C2×D4×C3711yescharacteristic
378C4⋊C4C2×D4×C3711yescharacteristic
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—41no—
383C42—21no—
384C42—21no—
385C42—21no—
386C42—41no—
387C42C2×D4×C3711yescharacteristic
388C42C2×D4×C3711yescharacteristic
389C42#41×C3711yescharacteristic
390C42C24×C3711yescharacteristic
391C23—21no—
392C23#121×C3711yescharacteristic
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—82no—
397Q8—81no—
398Q8—82no—
399Q8C2×Q16×C3712yes—
400D4—24no—
401D4—21no—
402D4C2×Q16×C3712yes—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4#121×C3711yescharacteristic
418C2×C4#121×C3711yescharacteristic
419C2×C4#121×C3711yescharacteristic
420C2×C4C2×Q16×C3712yes—
421C2×C4#135×C3712yes—
422C2×C4C22×D4×C3711yescharacteristic
423C2×C4C22×D4×C3711yescharacteristic
424C2×C4C2×#41×C3711yescharacteristic
425C8—22no—
426C8—22no—
427C8—41no—
428C8—41no—
429C8—42no—
430C8—42no—
431C22—21no—
432C22—21no—
433C22—22no—
434C22—41no—
435C22—41no—
436C22C37×#46712yes—
437C22C2×#121×C3711yescharacteristic
438C4—21no—
439C4—22no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—81no—
445C4—82no—
446C4—81no—
447C4C37×#46712yes—
448C4C22×Q16×C3711yescharacteristic
449C4C2×#135×C3711yescharacteristic
450C4C37×#57711yescharacteristic
451C4C37×#57811yescharacteristic
452C2—22no—
453C2—42no—
454C2C37×#304611yescharacteristic
455C2C2×C37×#46711yescharacteristic
456C2C37×#306811yescharacteristic
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×#3230C2semidirect
5. C37×#1684C2semidirect
6. C37×#1683C2semidirect
7. C37×#1676C2semidirect
8. C37×#1675C2semidirect
9. C37×#1571C2semidirect
10. C37×#1550C2semidirect
11. C2×C37×#333C2semidirect
202. #19417C37direct (N × H)
224. #3230C2×C37semidirect
228. #1684C2×C37semidirect
229. #1683C2×C37semidirect
230. #1676C2×C37semidirect
231. #1675C2×C37semidirect
232. #1571C2×C37semidirect
233. #1550C2×C37semidirect
234. C2×#333C2×C37semidirect
277. C37#19417direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32302
C37×#30792
C37×#30762
C37×#29882
C37×#16842
C37×#16832
C37×#16762
C37×#16752
C37×#15712
C37×#15502
C2×C37×#3332
#1941737