Finite Group Databasebeta

← C37×#60492 #22681745

Subgroups — C37×#60492 #22681745

Order 9472.

2038 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3458C211yesmaximal, characteristic, complemented
2C2×C37×#520C211yesmaximal, characteristic
3C37×#3084C218yesmaximal, complemented
4C37×#3083C218yesmaximal, complemented
5C37×#3078C214yesmaximal, complemented
6C37×#3077C214yesmaximal, complemented
7C2×C37×#428C212yesmaximal, complemented
8C37×#2905C211yesmaximal, characteristic, complemented
9C37×#2896C212yesmaximal
10C22×#41×C37C2211yescharacteristic
11C22×M16×C37C2212yes—
12C37×#544—21no—
13C37×#544—21no—
14C37×#544C2214yescomplemented
15C37×#544C2214yescomplemented
16C37×#543—22no—
17C37×#533—24no—
18C37×#533C2214yes—
19C37×#520—24no—
20C37×#520C2218yes—
21C2×C4×Q8×C37C2212yes—
22C2×C4×D4×C37—22no—
23C2×C4×D4×C37C2212yes—
24C2×#117×C37—21no—
25C2×#117×C37C2212yes—
26C2×#117×C37C2211yescharacteristic
27C22×C4⋊C4×C37—21no—
28C22×C4⋊C4×C37C2211yescharacteristic
29C37×#479C22116yescomplemented
30C37×#478C22116yescomplemented
31C37×#477C2218yescomplemented
32C37×#476C2218yescomplemented
33C37×#475C2218yescomplemented
34C37×#474C2218yescomplemented
35C37×#428C2218yes—
36C37×#428C2218yescomplemented
37C2×#107×C37C2214yescomplemented
38C2×#106×C37C2214yescomplemented
39C37×#424C2218yescomplemented
40C37×#423C2214yes—
41C37×#419C2214yes—
42C37×#418C2214yes—
43C37×#417C2214yes—
44C37×#417C2214yes—
45C37×#416C2218yes—
46C2×#41×C37—22no—
47C2×#41×C37—24no—
48C2×#41×C37Q818yescomplemented
49C2×#41×C37C2314yes—
50C22×Q8×C37C2311yescharacteristic
51C22×D4×C37—21no—
52C22×D4×C37C2311yescharacteristic
53C23×C4×C37—21no—
54C23×C4×C37—21no—
55C23×C4×C37—22no—
56C23×C4×C37C2311yescharacteristic
57C2×M16×C37—28no—
58C2×M16×C37C2314yes—
59C2×M16×C37C2314yes—
60C22×C8×C37C2314yes—
61C4⋊Q8×C37—24no—
62C4⋊Q8×C37—24no—
63C4⋊Q8×C37C2314yes—
64C4⋊Q8×C37C2314yes—
65#125×C37—24no—
66#125×C37—24no—
67#125×C37C2318yes—
68C22⋊Q8×C37—24no—
69C22⋊Q8×C37—24no—
70C22⋊Q8×C37—28no—
71C22⋊Q8×C37—28no—
72C4×Q8×C37—24no—
73C4×Q8×C37—24no—
74C4×Q8×C37—24no—
75C4×Q8×C37C2318yes—
76C4×D4×C37—216no—
77C4×D4×C37—24no—
78C4×D4×C37C2318yes—
79#117×C37—22no—
80#117×C37—22no—
81#117×C37—28no—
82#117×C37D414yes—
83#117×C37C2314yes—
84#117×C37C2314yes—
85#117×C37C2314yes—
86C2×C4⋊C4×C37—22no—
87C2×C4⋊C4×C37—21no—
88C2×C4⋊C4×C37—22no—
89C2×C4⋊C4×C37—28no—
90C2×C4⋊C4×C37D411yescharacteristic
91C2×C4⋊C4×C37D411yescharacteristic
92C2×C4⋊C4×C37C2314yes—
93C2×C4⋊C4×C37C2312yes—
94C2×C4⋊C4×C37C2312yes—
95C2×C4⋊C4×C37C2312yes—
96C2×C22⋊C4×C37—22no—
97C2×C22⋊C4×C37—22no—
98C2×C22⋊C4×C37D412yes—
99C2×C42×C37—22no—
100C2×C42×C37—22no—
101C2×C42×C37C2312yes—
102#107×C37C23116yes—
103#106×C37C23116yes—
104C4⋊C8×C37C2318yes—
105C4⋊C8×C37C2318yes—
106#103×C37C2318yes—
107#103×C37C2318yes—
108#102×C37C2318yes—
109#102×C37C2318yes—
110C24×C37—21no—
111C24×C37C2×D411yescharacteristic
112#41×C37—216no—
113#41×C37—28no—
114#41×C37C2×Q8116yes—
115C2×Q8×C37—21no—
116C2×Q8×C37—24no—
117C2×Q8×C37—24no—
118C2×Q8×C37—22no—
119C2×Q8×C37C2×Q814yes—
120C2×Q8×C37C2412yes—
121C2×D4×C37—28no—
122C2×D4×C37—24no—
123C2×D4×C37—21no—
124C2×D4×C37—22no—
125C2×D4×C37C2×Q814yes—
126C2×D4×C37C2412yes—
127C22×C4×C37—21no—
128C22×C4×C37—28no—
129C22×C4×C37—24no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—24no—
134C22×C4×C37—28no—
135C22×C4×C37—84no—
136C22×C4×C37—82no—
137C22×C4×C37C2×D412yes—
138C22×C4×C37C2×D412yes—
139C22×C4×C37C2×D412yes—
140C22×C4×C37C2×D411yescharacteristic
141C22×C4×C37C2×Q814yes—
142C22×C4×C37#4114yes—
143C22×C4×C37C2411yescharacteristic
144C22×C4×C37C2412yes—
145M16×C37—28no—
146M16×C37—28no—
147C2×C8×C37—28no—
148C2×C8×C37C2418yes—
149C4⋊C4×C37—24no—
150C4⋊C4×C37—28no—
151C4⋊C4×C37—22no—
152C4⋊C4×C37—22no—
153C4⋊C4×C37—22no—
154C4⋊C4×C37—24no—
155C4⋊C4×C37—24no—
156C4⋊C4×C37—28no—
157C4⋊C4×C37—28no—
158C4⋊C4×C37C2×D414yes—
159C4⋊C4×C37C2×D414yes—
160C4⋊C4×C37C2414yes—
161C4⋊C4×C37C2414yes—
162C4⋊C4×C37C2414yes—
163C22⋊C4×C37—24no—
164C22⋊C4×C37—24no—
165C22⋊C4×C37—28no—
166C22⋊C4×C37C2×D418yes—
167C42×C37—28no—
168C42×C37—24no—
169C42×C37—24no—
170C42×C37C2×D414yes—
171C42×C37C2414yes—
172C23×C37—24no—
173C23×C37—22no—
174C23×C37—41no—
175C23×C37—41no—
176C23×C37—42no—
177C23×C37—42no—
178C23×C37C22⋊Q814yes—
179C23×C37C22×D411yescharacteristic
180C23×C37C22×D412yes—
181Q8×C37—24no—
182Q8×C37—22no—
183Q8×C37—84no—
184Q8×C37—84no—
185Q8×C37C22×Q814yes—
186D4×C37—216no—
187D4×C37—24no—
188D4×C37—22no—
189D4×C37C22×Q814yes—
190C2×C4×C37—24no—
191C2×C4×C37—22no—
192C2×C4×C37—216no—
193C2×C4×C37—24no—
194C2×C4×C37—24no—
195C2×C4×C37—24no—
196C2×C4×C37—42no—
197C2×C4×C37—42no—
198C2×C4×C37—44no—
199C2×C4×C37—88no—
200C2×C4×C37—82no—
201C2×C4×C37—82no—
202C2×C4×C37—84no—
203C2×C4×C37C22⋊Q814yes—
204C2×C4×C37C22⋊Q818yes—
205C2×C4×C37C22×D414yes—
206C2×C4×C37C22×D414yes—
207C2×C4×C37C22×D411yescharacteristic
208C2×C4×C37C22×D412yes—
209C2×C4×C37C22×Q812yes—
210C2×C4×C37C22×Q814yes—
211C2×C4×C37C2×#4114yes—
212C2×C4×C37C2×#4112yes—
213C2×C4×C37C2511yescharacteristic
214C8×C37—28no—
215#60492C3711yesmaximal, characteristic, direct product factor, Sylow
216C22×C37—21no—
217C22×C37—22no—
218C22×C37—21no—
219C22×C37—22no—
220C22×C37—24no—
221C22×C37—44no—
222C22×C37—48no—
223C22×C37—42no—
224C22×C37—42no—
225C22×C37C2×C22⋊Q812yes—
226C22×C37C2×C22⋊Q814yes—
227C22×C37C23×D411yescharacteristic
228C4×C37—24no—
229C4×C37—24no—
230C4×C37—24no—
231C4×C37—44no—
232C4×C37—44no—
233C4×C37—44no—
234C4×C37C2×C22⋊Q814yes—
235C4×C37C2×C22⋊Q812yes—
236C4×C37C23×Q811yescharacteristic
237C4×C37C22×#4111yescharacteristic
238#3458C2×C3711yescharacteristic, complemented
239C2×#520C2×C3711yescharacteristic
240#3084C2×C3718yescomplemented
241#3083C2×C3718yescomplemented
242#3078C2×C3714yescomplemented
243#3077C2×C3714yescomplemented
244C2×#428C2×C3712yescomplemented
245#2905C2×C3711yescharacteristic, complemented
246#2896C2×C3712yes—
247C2×C37—22no—
248C2×C37—24no—
249C2×C37—44no—
250C2×C37C22×C22⋊Q811yescharacteristic
251C2×C37#358511yescharacteristic
252C2×C37#358611yescharacteristic
253C22×#41C22×C3711yescharacteristic
254C22×M16C22×C3712yes—
255#544—21no—
256#544—21no—
257#544C22×C3714yescomplemented
258#544C22×C3714yescomplemented
259#543—22no—
260#533—24no—
261#533C22×C3714yes—
262#520—24no—
263#520C22×C3718yes—
264C2×C4×Q8C22×C3712yes—
265C2×C4×D4—22no—
266C2×C4×D4C22×C3712yes—
267C2×#117—21no—
268C2×#117C22×C3712yes—
269C2×#117C22×C3711yescharacteristic
270C22×C4⋊C4—21no—
271C22×C4⋊C4C22×C3711yescharacteristic
272#479C22×C37116yescomplemented
273#478C22×C37116yescomplemented
274#477C22×C3718yescomplemented
275#476C22×C3718yescomplemented
276#475C22×C3718yescomplemented
277#474C22×C3718yescomplemented
278#428C22×C3718yes—
279#428C22×C3718yescomplemented
280C2×#107C22×C3714yescomplemented
281C2×#106C22×C3714yescomplemented
282#424C22×C3718yescomplemented
283#423C22×C3714yes—
284#419C22×C3714yes—
285#418C22×C3714yes—
286#417C22×C3714yes—
287#417C22×C3714yes—
288#416C22×C3718yes—
289C37#6049211yescharacteristic, direct product factor, Sylow
290C2×#41—22no—
291C2×#41—24no—
292C2×#41Q8×C3718yescomplemented
293C2×#41C23×C3714yes—
294C22×Q8C23×C3711yescharacteristic
295C22×D4—21no—
296C22×D4C23×C3711yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4—22no—
300C23×C4C23×C3711yescharacteristic
301C2×M16—28no—
302C2×M16C23×C3714yes—
303C2×M16C23×C3714yes—
304C22×C8C23×C3714yes—
305C4⋊Q8—24no—
306C4⋊Q8—24no—
307C4⋊Q8C23×C3714yes—
308C4⋊Q8C23×C3714yes—
309#125—24no—
310#125—24no—
311#125C23×C3718yes—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—28no—
315C22⋊Q8—28no—
316C4×Q8—24no—
317C4×Q8—24no—
318C4×Q8—24no—
319C4×Q8C23×C3718yes—
320C4×D4—216no—
321C4×D4—24no—
322C4×D4C23×C3718yes—
323#117—22no—
324#117—22no—
325#117—28no—
326#117D4×C3714yes—
327#117C23×C3714yes—
328#117C23×C3714yes—
329#117C23×C3714yes—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4D4×C3711yescharacteristic
335C2×C4⋊C4D4×C3711yescharacteristic
336C2×C4⋊C4C23×C3712yes—
337C2×C4⋊C4C23×C3714yes—
338C2×C4⋊C4C23×C3712yes—
339C2×C4⋊C4C23×C3712yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4D4×C3712yes—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42C23×C3712yes—
346#107C23×C37116yes—
347#106C23×C37116yes—
348C4⋊C8C23×C3718yes—
349C4⋊C8C23×C3718yes—
350#103C23×C3718yes—
351#103C23×C3718yes—
352#102C23×C3718yes—
353#102C23×C3718yes—
354C24—21no—
355C24C2×D4×C3711yescharacteristic
356#41—216no—
357#41—28no—
358#41C2×Q8×C37116yes—
359C2×Q8—21no—
360C2×Q8—24no—
361C2×Q8—24no—
362C2×Q8—22no—
363C2×Q8C2×Q8×C3714yes—
364C2×Q8C24×C3712yes—
365C2×D4—28no—
366C2×D4—24no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4C2×Q8×C3714yes—
370C2×D4C24×C3712yes—
371C22×C4—21no—
372C22×C4—28no—
373C22×C4—24no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—24no—
378C22×C4—28no—
379C22×C4—84no—
380C22×C4—82no—
381C22×C4C2×D4×C3712yes—
382C22×C4C2×D4×C3712yes—
383C22×C4C2×D4×C3712yes—
384C22×C4C2×D4×C3711yescharacteristic
385C22×C4C2×Q8×C3714yes—
386C22×C4#41×C3714yes—
387C22×C4C24×C3711yescharacteristic
388C22×C4C24×C3712yes—
389M16—28no—
390M16—28no—
391C2×C8—28no—
392C2×C8C24×C3718yes—
393C4⋊C4—24no—
394C4⋊C4—28no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—28no—
401C4⋊C4—28no—
402C4⋊C4C2×D4×C3714yes—
403C4⋊C4C2×D4×C3714yes—
404C4⋊C4C24×C3714yes—
405C4⋊C4C24×C3714yes—
406C4⋊C4C24×C3714yes—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—28no—
410C22⋊C4C2×D4×C3718yes—
411C42—28no—
412C42—24no—
413C42—24no—
414C42C2×D4×C3714yes—
415C42C24×C3714yes—
416C23—24no—
417C23—22no—
418C23—41no—
419C23—41no—
420C23—42no—
421C23—42no—
422C23C22⋊Q8×C3714yes—
423C23C22×D4×C3711yescharacteristic
424C23C22×D4×C3712yes—
425Q8—24no—
426Q8—22no—
427Q8—84no—
428Q8—84no—
429Q8C22×Q8×C3714yes—
430D4—216no—
431D4—24no—
432D4—22no—
433D4C22×Q8×C3714yes—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—216no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—88no—
444C2×C4—84no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4C22⋊Q8×C3714yes—
448C2×C4C22⋊Q8×C3718yes—
449C2×C4C22×D4×C3714yes—
450C2×C4C22×D4×C3714yes—
451C2×C4C22×D4×C3711yescharacteristic
452C2×C4C22×D4×C3712yes—
453C2×C4C22×Q8×C3712yes—
454C2×C4C22×Q8×C3714yes—
455C2×C4C2×#41×C3714yes—
456C2×C4C2×#41×C3712yes—
457C2×C4C25×C3711yescharacteristic
458C8—28no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—22no—
463C22—24no—
464C22—44no—
465C22—48no—
466C22—42no—
467C22—42no—
468C22C2×C22⋊Q8×C3712yes—
469C22C2×C22⋊Q8×C3714yes—
470C22C23×D4×C3711yescharacteristic
471C4—24no—
472C4—24no—
473C4—24no—
474C4—44no—
475C4—44no—
476C4—44no—
477C4C2×C22⋊Q8×C3714yes—
478C4C2×C22⋊Q8×C3712yes—
479C4C23×Q8×C3711yescharacteristic
480C4C22×#41×C3711yescharacteristic
481C2—22no—
482C2—24no—
483C2—44no—
484C2C22×C22⋊Q8×C3711yescharacteristic
485C2C37×#358511yescharacteristic
486C2C37×#358611yescharacteristic
subgroupG/H
center, socleC22×C37C23×D4
commutator, Frattini, cosocleC2×C4C25×C37
prime radicalC22×#41×C37C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3458C2semidirect
3. C37×#3084C2semidirect
4. C37×#3083C2semidirect
5. C37×#3078C2semidirect
6. C37×#3077C2semidirect
7. C2×C37×#428C2semidirect
8. C37×#2905C2semidirect
14. C37×#544C22semidirect
15. C37×#544C22semidirect
29. C37×#479C22semidirect
30. C37×#478C22semidirect
31. C37×#477C22semidirect
32. C37×#476C22semidirect
33. C37×#475C22semidirect
34. C37×#474C22semidirect
36. C37×#428C22semidirect
37. C2×#107×C37C22semidirect
38. C2×#106×C37C22semidirect
39. C37×#424C22semidirect
48. C2×#41×C37Q8semidirect
215. #60492C37direct (N × H)
238. #3458C2×C37semidirect
240. #3084C2×C37semidirect
241. #3083C2×C37semidirect
242. #3078C2×C37semidirect
243. #3077C2×C37semidirect
244. C2×#428C2×C37semidirect
245. #2905C2×C37semidirect
257. #544C22×C37semidirect
258. #544C22×C37semidirect
272. #479C22×C37semidirect
273. #478C22×C37semidirect
274. #477C22×C37semidirect
275. #476C22×C37semidirect
276. #475C22×C37semidirect
277. #474C22×C37semidirect
279. #428C22×C37semidirect
280. C2×#107C22×C37semidirect
281. C2×#106C22×C37semidirect
282. #424C22×C37semidirect
289. C37#60492direct (N × H)
292. C2×#41Q8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34582
C2×C37×#5202
C37×#30842
C37×#30832
C37×#30782
C37×#30772
C2×C37×#4282
C37×#29052
C37×#28962
#6049237