Finite Group Databasebeta

← C37×#29635 #22650888

Subgroups — C37×#29635 #22650888

Order 9472.

1596 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#534C211yesmaximal, characteristic
2C37×#2483C211yesmaximal, characteristic, complemented
3C37×#2405C212yesmaximal, complemented
4C37×#2044C214yesmaximal, complemented
5C37×#2022C214yesmaximal, complemented
6C37×#1819C211yesmaximal, characteristic, complemented
7C37×#1781C212yesmaximal, complemented
8C23×D4×C37C2212yes—
9C37×#534—24no—
10C37×#534—22no—
11C37×#534C2214yes—
12C2×#123×C37—22no—
13C2×#123×C37C2214yescomplemented
14C2×#121×C37—21no—
15C2×#121×C37—21no—
16C2×#120×C37—22no—
17C22×C22⋊C4×C37C2211yescharacteristic
18C22×C22⋊C4×C37C2211yescharacteristic
19C2×#99×C37C2218yescomplemented
20C37×#397—22no—
21C37×#394—24no—
22C37×#386C2214yescomplemented
23C37×#385—22no—
24C37×#385—21no—
25C37×#385C2212yescomplemented
26C37×#381—21no—
27C37×#381C2212yescomplemented
28C37×#379—22no—
29C37×#379C2212yes—
30C37×#379C2211yescharacteristic
31C37×#342C2214yescomplemented
32C25×C37D412yes—
33C25×C37C2311yescharacteristic
34C22×D4×C37—22no—
35C22×D4×C37—22no—
36C22×D4×C37—22no—
37C22×D4×C37—22no—
38C22×D4×C37—21no—
39C22×D4×C37—21no—
40C22×D4×C37—48no—
41C22×D4×C37D414yes—
42C22×D4×C37C2314yes—
43C23×C4×C37D411yescharacteristic
44C23×C4×C37D412yes—
45C23×C4×C37D411yescharacteristic
46C23×C4×C37C2311yescharacteristic
47C23×C4×C37C2311yescharacteristic
48#123×C37—28no—
49#123×C37—28no—
50#123×C37—48no—
51#121×C37—24no—
52#121×C37—24no—
53#121×C37—24no—
54#121×C37—24no—
55#120×C37—28no—
56#120×C37—28no—
57C2×C4⋊C4×C37—21no—
58C2×C4⋊C4×C37—21no—
59C2×C4⋊C4×C37—24no—
60C2×C4⋊C4×C37—22no—
61C2×C22⋊C4×C37—22no—
62C2×C22⋊C4×C37—22no—
63C2×C22⋊C4×C37—22no—
64C2×C22⋊C4×C37—22no—
65C2×C22⋊C4×C37—24no—
66C2×C22⋊C4×C37—22no—
67C2×C22⋊C4×C37—22no—
68C2×C22⋊C4×C37—21no—
69C2×C22⋊C4×C37—21no—
70C2×C22⋊C4×C37—22no—
71C2×C22⋊C4×C37—21no—
72C2×C22⋊C4×C37—24no—
73C2×C22⋊C4×C37—22no—
74C2×C22⋊C4×C37—21no—
75C2×C22⋊C4×C37D412yes—
76C2×C22⋊C4×C37C2314yes—
77C2×C22⋊C4×C37C2312yes—
78C2×C22⋊C4×C37C2312yes—
79#99×C37—48no—
80#95×C37—22no—
81#95×C37—22no—
82#95×C37—22no—
83#95×C37—24no—
84C24×C37—24no—
85C24×C37—22no—
86C24×C37—22no—
87C24×C37—44no—
88C24×C37—42no—
89C24×C37—44no—
90C24×C37—81no—
91C24×C37—82no—
92C24×C37C2×D412yes—
93C24×C37C2×D411yescharacteristic
94C24×C37C2×D414yes—
95C24×C37C2×D412yes—
96C24×C37C2×D411yescharacteristic
97C24×C37C2411yescharacteristic
98C2×D4×C37—24no—
99C2×D4×C37—24no—
100C2×D4×C37—24no—
101C2×D4×C37—24no—
102C2×D4×C37—28no—
103C2×D4×C37—28no—
104C2×D4×C37—24no—
105C2×D4×C37—24no—
106C2×D4×C37—44no—
107C2×D4×C37—44no—
108C2×D4×C37—48no—
109C2×D4×C37—48no—
110C2×D4×C37—48no—
111C2×D4×C37—48no—
112C2×D4×C37—82no—
113C2×D4×C37—82no—
114C22×C4×C37—21no—
115C22×C4×C37—21no—
116C22×C4×C37—22no—
117C22×C4×C37—22no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—22no—
122C22×C4×C37—22no—
123C22×C4×C37—21no—
124C22×C4×C37—24no—
125C22×C4×C37—22no—
126C22×C4×C37—24no—
127C22×C4×C37—44no—
128C22×C4×C37—42no—
129C22×C4×C37—81no—
130C22×C4×C37—81no—
131C22×C4×C37C2×D414yes—
132C22×C4×C37C2×D412yes—
133C22×C4×C37C2×D412yes—
134C4⋊C4×C37—24no—
135C4⋊C4×C37—24no—
136C4⋊C4×C37—48no—
137C4⋊C4×C37—82no—
138C22⋊C4×C37—28no—
139C22⋊C4×C37—28no—
140C22⋊C4×C37—24no—
141C22⋊C4×C37—24no—
142C22⋊C4×C37—24no—
143C22⋊C4×C37—28no—
144C22⋊C4×C37—42no—
145C22⋊C4×C37—44no—
146C22⋊C4×C37—48no—
147C22⋊C4×C37—42no—
148C22⋊C4×C37—41no—
149C22⋊C4×C37—41no—
150C22⋊C4×C37—82no—
151C22⋊C4×C37—84no—
152C22⋊C4×C37—81no—
153C23×C37—24no—
154C23×C37—22no—
155C23×C37—22no—
156C23×C37—24no—
157C23×C37—24no—
158C23×C37—22no—
159C23×C37—24no—
160C23×C37—24no—
161C23×C37—24no—
162C23×C37—41no—
163C23×C37—41no—
164C23×C37—41no—
165C23×C37—42no—
166C23×C37—41no—
167C23×C37—42no—
168C23×C37—41no—
169C23×C37—42no—
170C23×C37—44no—
171C23×C37—44no—
172C23×C37—44no—
173C23×C37—44no—
174C23×C37—44no—
175C23×C37—44no—
176C23×C37—82no—
177C23×C37—82no—
178C23×C37—88no—
179C23×C37—816no—
180C23×C37#12012yes—
181C23×C37#12011yescharacteristic
182C23×C37#12011yescharacteristic
183C23×C37C22×D412yes—
184C23×C37C22×D411yescharacteristic
185C23×C37H(5,𝔽2)14yes—
186D4×C37—48no—
187D4×C37—48no—
188D4×C37—48no—
189D4×C37—48no—
190D4×C37—84no—
191D4×C37—84no—
192C2×C4×C37—22no—
193C2×C4×C37—22no—
194C2×C4×C37—24no—
195C2×C4×C37—24no—
196C2×C4×C37—24no—
197C2×C4×C37—44no—
198C2×C4×C37—44no—
199C2×C4×C37—42no—
200C2×C4×C37—42no—
201C2×C4×C37—42no—
202C2×C4×C37—42no—
203C2×C4×C37—42no—
204C2×C4×C37—44no—
205C2×C4×C37—44no—
206C2×C4×C37—42no—
207C2×C4×C37—44no—
208C2×C4×C37—42no—
209C2×C4×C37—41no—
210C2×C4×C37—41no—
211C2×C4×C37—44no—
212C2×C4×C37—44no—
213C2×C4×C37—42no—
214C2×C4×C37—42no—
215C2×C4×C37—81no—
216C2×C4×C37—81no—
217#29635C3711yesmaximal, characteristic, direct product factor, Sylow
218C22×C37—21no—
219C22×C37—21no—
220C22×C37—22no—
221C22×C37—21no—
222C22×C37—22no—
223C22×C37—21no—
224C22×C37—22no—
225C22×C37—21no—
226C22×C37—21no—
227C22×C37—22no—
228C22×C37—21no—
229C22×C37—22no—
230C22×C37—44no—
231C22×C37—44no—
232C22×C37—48no—
233C22×C37—48no—
234C22×C37—44no—
235C22×C37—44no—
236C22×C37—44no—
237C22×C37—84no—
238C22×C37—82no—
239C22×C37—84no—
240C22×C37—88no—
241C22×C37—88no—
242C22×C37#45812yes—
243C22×C37C2×#12011yescharacteristic
244C22×C37#53414yes—
245C22×C37#53512yes—
246C4×C37—44no—
247C4×C37—42no—
248C4×C37—42no—
249C4×C37—84no—
250C4×C37—82no—
251C4×C37—81no—
252C4×C37—81no—
253C2×#534C2×C3711yescharacteristic
254#2483C2×C3711yescharacteristic, complemented
255#2405C2×C3712yescomplemented
256#2044C2×C3714yescomplemented
257#2022C2×C3714yescomplemented
258#1819C2×C3711yescharacteristic, complemented
259#1781C2×C3712yescomplemented
260C2×C37—24no—
261C2×C37—22no—
262C2×C37—22no—
263C2×C37—41no—
264C2×C37—42no—
265C2×C37—84no—
266C2×C37#261311yescharacteristic
267C2×C37C2×#45811yescharacteristic
268C2×C37#302611yescharacteristic
269C23×D4C22×C3712yes—
270#534—24no—
271#534—22no—
272#534C22×C3714yes—
273C2×#123—22no—
274C2×#123C22×C3714yescomplemented
275C2×#121—21no—
276C2×#121—21no—
277C2×#120—22no—
278C22×C22⋊C4C22×C3711yescharacteristic
279C22×C22⋊C4C22×C3711yescharacteristic
280C2×#99C22×C3718yescomplemented
281#397—22no—
282#394—24no—
283#386C22×C3714yescomplemented
284#385—22no—
285#385—21no—
286#385C22×C3712yescomplemented
287#381—21no—
288#381C22×C3712yescomplemented
289#379—22no—
290#379C22×C3712yes—
291#379C22×C3711yescharacteristic
292#342C22×C3714yescomplemented
293C37#2963511yescharacteristic, direct product factor, Sylow
294C25D4×C3712yes—
295C25C23×C3711yescharacteristic
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—48no—
303C22×D4D4×C3714yes—
304C22×D4C23×C3714yes—
305C23×C4D4×C3711yescharacteristic
306C23×C4D4×C3712yes—
307C23×C4D4×C3711yescharacteristic
308C23×C4C23×C3711yescharacteristic
309C23×C4C23×C3711yescharacteristic
310#123—28no—
311#123—28no—
312#123—48no—
313#121—24no—
314#121—24no—
315#121—24no—
316#121—24no—
317#120—28no—
318#120—28no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4D4×C3712yes—
338C2×C22⋊C4C23×C3714yes—
339C2×C22⋊C4C23×C3712yes—
340C2×C22⋊C4C23×C3712yes—
341#99—48no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95—24no—
346C24—24no—
347C24—22no—
348C24—22no—
349C24—44no—
350C24—42no—
351C24—44no—
352C24—81no—
353C24—82no—
354C24C2×D4×C3712yes—
355C24C2×D4×C3711yescharacteristic
356C24C2×D4×C3714yes—
357C24C2×D4×C3712yes—
358C24C2×D4×C3711yescharacteristic
359C24C24×C3711yescharacteristic
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—24no—
367C2×D4—24no—
368C2×D4—44no—
369C2×D4—44no—
370C2×D4—48no—
371C2×D4—48no—
372C2×D4—48no—
373C2×D4—48no—
374C2×D4—82no—
375C2×D4—82no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—24no—
389C22×C4—44no—
390C22×C4—42no—
391C22×C4—81no—
392C22×C4—81no—
393C22×C4C2×D4×C3714yes—
394C22×C4C2×D4×C3712yes—
395C22×C4C2×D4×C3712yes—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—48no—
399C4⋊C4—82no—
400C22⋊C4—28no—
401C22⋊C4—28no—
402C22⋊C4—24no—
403C22⋊C4—24no—
404C22⋊C4—24no—
405C22⋊C4—28no—
406C22⋊C4—42no—
407C22⋊C4—44no—
408C22⋊C4—48no—
409C22⋊C4—42no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—82no—
413C22⋊C4—84no—
414C22⋊C4—81no—
415C23—24no—
416C23—22no—
417C23—22no—
418C23—24no—
419C23—24no—
420C23—22no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—42no—
428C23—41no—
429C23—42no—
430C23—41no—
431C23—42no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—44no—
438C23—82no—
439C23—82no—
440C23—88no—
441C23—816no—
442C23#120×C3712yes—
443C23#120×C3711yescharacteristic
444C23#120×C3711yescharacteristic
445C23C22×D4×C3712yes—
446C23C22×D4×C3711yescharacteristic
447C23H(5,𝔽2)×C3714yes—
448D4—48no—
449D4—48no—
450D4—48no—
451D4—48no—
452D4—84no—
453D4—84no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—81no—
478C2×C4—81no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—21no—
483C22—22no—
484C22—21no—
485C22—22no—
486C22—21no—
487C22—21no—
488C22—22no—
489C22—21no—
490C22—22no—
491C22—44no—
492C22—48no—
493C22—44no—
494C22—48no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22—84no—
499C22—82no—
500C22—84no—
501C22—88no—
502C22—88no—
503C22C37×#45812yes—
504C22C2×#120×C3711yescharacteristic
505C22C37×#53414yes—
506C22C37×#53512yes—
507C4—44no—
508C4—42no—
509C4—42no—
510C4—84no—
511C4—82no—
512C4—81no—
513C4—81no—
514C2—24no—
515C2—22no—
516C2—22no—
517C2—42no—
518C2—41no—
519C2—84no—
520C2C37×#261311yescharacteristic
521C2C2×C37×#45811yescharacteristic
522C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
prime radicalC2×C37×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2483C2semidirect
3. C37×#2405C2semidirect
4. C37×#2044C2semidirect
5. C37×#2022C2semidirect
6. C37×#1819C2semidirect
7. C37×#1781C2semidirect
13. C2×#123×C37C22semidirect
19. C2×#99×C37C22semidirect
22. C37×#386C22semidirect
25. C37×#385C22semidirect
27. C37×#381C22semidirect
31. C37×#342C22semidirect
217. #29635C37direct (N × H)
254. #2483C2×C37semidirect
255. #2405C2×C37semidirect
256. #2044C2×C37semidirect
257. #2022C2×C37semidirect
258. #1819C2×C37semidirect
259. #1781C2×C37semidirect
274. C2×#123C22×C37semidirect
280. C2×#99C22×C37semidirect
283. #386C22×C37semidirect
286. #385C22×C37semidirect
288. #381C22×C37semidirect
292. #342C22×C37semidirect
293. C37#29635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5342
C37×#24832
C37×#24052
C37×#20442
C37×#20222
C37×#18192
C37×#17812
#2963537