Finite Group Databasebeta

← C37×#9043 #22630296

Subgroups — C37×#9043 #22630296

Order 9472.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#480C211yesmaximal, characteristic
2C37×#2325C211yesmaximal, characteristic
3C37×#1823C211yesmaximal, characteristic, complemented
4C2×C37×#327C211yesmaximal, characteristic
5C37×#1445C211yesmaximal, characteristic, complemented
6C37×#1294C211yesmaximal, characteristic, complemented
7C37×#1280C211yesmaximal, characteristic, complemented
8C2×#121×C37C2211yescharacteristic
9C2×C4×D4×C37—21no—
10C22×C4⋊C4×C37C2211yescharacteristic
11C37×#480—22no—
12C37×#480C414yescomplemented
13C2×#107×C37—21no—
14C2×#102×C37—21no—
15C2×C22⋊C8×C37C2211yescharacteristic
16C2×C22⋊C8×C37C2211yescharacteristic
17C37×#388—21no—
18C37×#387—21no—
19C37×#386—21no—
20C37×#386—21no—
21C37×#385—21no—
22C37×#380C2211yescharacteristic
23C2×#95×C37—21no—
24C2×#95×C37—21no—
25C2×#95×C37C2211yescharacteristic
26C2×#95×C37C2211yescharacteristic
27C37×#340—21no—
28C37×#340—21no—
29C37×#327—22no—
30C22×D4×C37—21no—
31C22×D4×C37D411yescharacteristic
32C23×C4×C37—21no—
33C23×C4×C37—21no—
34C23×C4×C37—21no—
35C23×C4×C37D411yescharacteristic
36C23×C4×C37D411yescharacteristic
37C23×C4×C37C2311yescharacteristic
38C22×C8×C37—21no—
39C22×C8×C37—21no—
40#121×C37—21no—
41#121×C37—21no—
42#121×C37C2×C412yes—
43#121×C37D412yes—
44C4×D4×C37—42no—
45C4×D4×C37—42no—
46C2×C4⋊C4×C37—21no—
47C2×C4⋊C4×C37—21no—
48C2×C4⋊C4×C37—21no—
49C2×C4⋊C4×C37—21no—
50C2×C4⋊C4×C37—21no—
51C2×C4⋊C4×C37—21no—
52C2×C4⋊C4×C37C2×C412yescomplemented
53C2×C4⋊C4×C37D411yescharacteristic
54C2×C4⋊C4×C37D411yescharacteristic
55C2×C4⋊C4×C37D411yescharacteristic
56C2×C22⋊C4×C37—21no—
57C2×C22⋊C4×C37—21no—
58C2×C22⋊C4×C37—21no—
59C2×C22⋊C4×C37—21no—
60C2×C22⋊C4×C37—21no—
61C2×C42×C37—21no—
62#107×C37—24no—
63#102×C37—24no—
64C22⋊C8×C37—21no—
65C22⋊C8×C37—21no—
66C22⋊C8×C37—21no—
67C22⋊C8×C37C2×C412yescomplemented
68#95×C37—21no—
69#95×C37—21no—
70#95×C37—21no—
71#95×C37—21no—
72#95×C37—21no—
73#95×C37—21no—
74#95×C37—21no—
75#95×C37—42no—
76#95×C37—42no—
77C24×C37—21no—
78C24×C37C2×D411yescharacteristic
79C2×D4×C37—22no—
80C2×D4×C37—22no—
81C2×D4×C37—21no—
82C2×D4×C37—41no—
83C2×D4×C37—41no—
84C2×D4×C37—41no—
85C2×D4×C37—41no—
86C2×D4×C37—41no—
87C2×D4×C37—41no—
88C2×D4×C37C22⋊C412yes—
89C22×C4×C37—21no—
90C22×C4×C37—21no—
91C22×C4×C37—21no—
92C22×C4×C37—22no—
93C22×C4×C37—22no—
94C22×C4×C37—21no—
95C22×C4×C37—21no—
96C22×C4×C37—21no—
97C22×C4×C37—21no—
98C22×C4×C37—21no—
99C22×C4×C37—41no—
100C22×C4×C37—41no—
101C22×C4×C37—42no—
102C22×C4×C37—41no—
103C22×C4×C37—41no—
104C22×C4×C37—41no—
105C22×C4×C37—41no—
106C22×C4×C37—41no—
107C22×C4×C37—41no—
108C22×C4×C37—41no—
109C22×C4×C37—41no—
110C22×C4×C37—41no—
111C22×C4×C37—41no—
112C22×C4×C37—41no—
113C22×C4×C37—41no—
114C22×C4×C37—41no—
115C22×C4×C37—41no—
116C22×C4×C37—41no—
117C22×C4×C37—41no—
118C22×C4×C37—81no—
119C22×C4×C37—81no—
120C22×C4×C37D812yes—
121C22×C4×C37C22×C411yescharacteristic
122C22×C4×C37C2×D411yescharacteristic
123C22×C4×C37C2×D411yescharacteristic
124C22×C4×C37C2×D411yescharacteristic
125C22×C4×C37#4111yescharacteristic
126C22×C4×C37#4111yescharacteristic
127C2×C8×C37—22no—
128C2×C8×C37—41no—
129C2×C8×C37—41no—
130C2×C8×C37—41no—
131C2×C8×C37—41no—
132C2×C8×C37—41no—
133C4⋊C4×C37—21no—
134C4⋊C4×C37—22no—
135C4⋊C4×C37—22no—
136C4⋊C4×C37—41no—
137C4⋊C4×C37—41no—
138C4⋊C4×C37—42no—
139C4⋊C4×C37—41no—
140C4⋊C4×C37—41no—
141C4⋊C4×C37C22⋊C412yes—
142C22⋊C4×C37—22no—
143C22⋊C4×C37—22no—
144C22⋊C4×C37—42no—
145C22⋊C4×C37—41no—
146C22⋊C4×C37—41no—
147C22⋊C4×C37—81no—
148C22⋊C4×C37—81no—
149C42×C37—42no—
150C23×C37—21no—
151C23×C37—21no—
152C23×C37—21no—
153C23×C37—21no—
154C23×C37—22no—
155C23×C37—41no—
156C23×C37—41no—
157C23×C37—41no—
158C23×C37—41no—
159C23×C37—41no—
160C23×C37—41no—
161C23×C37C4×D411yescharacteristic
162C23×C37#12011yescharacteristic
163C23×C37#12111yescharacteristic
164C23×C37C2×D811yescharacteristic
165C23×C37#13511yescharacteristic
166C23×C37AGL(1,ℤ/8)11yescharacteristic
167C23×C37AGL(1,ℤ/8)11yescharacteristic
168D4×C37—42no—
169D4×C37—42no—
170D4×C37—42no—
171D4×C37—42no—
172D4×C37—42no—
173D4×C37—81no—
174C2×C4×C37—21no—
175C2×C4×C37—21no—
176C2×C4×C37—21no—
177C2×C4×C37—21no—
178C2×C4×C37—22no—
179C2×C4×C37—22no—
180C2×C4×C37—41no—
181C2×C4×C37—41no—
182C2×C4×C37—41no—
183C2×C4×C37—41no—
184C2×C4×C37—41no—
185C2×C4×C37—41no—
186C2×C4×C37—41no—
187C2×C4×C37—41no—
188C2×C4×C37—42no—
189C2×C4×C37—42no—
190C2×C4×C37—42no—
191C2×C4×C37—42no—
192C2×C4×C37—42no—
193C2×C4×C37—42no—
194C2×C4×C37—42no—
195C2×C4×C37—42no—
196C2×C4×C37—41no—
197C2×C4×C37—41no—
198C2×C4×C37—41no—
199C2×C4×C37—41no—
200C2×C4×C37—41no—
201C2×C4×C37—41no—
202C2×C4×C37—41no—
203C2×C4×C37—41no—
204C2×C4×C37—41no—
205C2×C4×C37—81no—
206C2×C4×C37—84no—
207C2×C4×C37—81no—
208C2×C4×C37—81no—
209C2×C4×C37—81no—
210C2×C4×C37—81no—
211C2×C4×C37—81no—
212C2×C4×C37—81no—
213C2×C4×C37—81no—
214C2×C4×C37—81no—
215C2×C4×C37—81no—
216C2×C4×C37C2×C22⋊C411yescharacteristic
217C2×C4×C37C4×D411yescharacteristic
218C2×C4×C37#12111yescharacteristic
219C2×C4×C37#12311yescharacteristic
220C8×C37—42no—
221C8×C37—81no—
222#9043C3711yesmaximal, characteristic, direct product factor, Sylow
223C22×C37—21no—
224C22×C37—21no—
225C22×C37—21no—
226C22×C37—21no—
227C22×C37—21no—
228C22×C37—21no—
229C22×C37—21no—
230C22×C37—21no—
231C22×C37—21no—
232C22×C37—21no—
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—42no—
236C22×C37—42no—
237C22×C37—42no—
238C22×C37—81no—
239C22×C37—81no—
240C22×C37—81no—
241C22×C37—81no—
242C22×C37#38611yescharacteristic
243C22×C37C4×D811yescharacteristic
244C22×C37#44211yescharacteristic
245C22×C37#44711yescharacteristic
246C22×C37#44911yescharacteristic
247C22×C37#45511yescharacteristic
248C22×C37#45611yescharacteristic
249C22×C37#45811yescharacteristic
250C22×C37#45811yescharacteristic
251C22×C37#45911yescharacteristic
252C22×C37#46311yescharacteristic
253C4×C37—21no—
254C4×C37—21no—
255C4×C37—21no—
256C4×C37—21no—
257C4×C37—42no—
258C4×C37—42no—
259C4×C37—82no—
260C4×C37—81no—
261C4×C37—81no—
262C4×C37—81no—
263C4×C37—82no—
264C2×#480C2×C3711yescharacteristic
265#2325C2×C3711yescharacteristic
266#1823C2×C3711yescharacteristic, complemented
267C2×#327C2×C3711yescharacteristic
268#1445C2×C3711yescharacteristic, complemented
269#1294C2×C3711yescharacteristic, complemented
270#1280C2×C3711yescharacteristic, complemented
271C2×C37—21no—
272C2×C37—21no—
273C2×C37—21no—
274C2×C37—21no—
275C2×C37—82no—
276C2×C37#160711yescharacteristic
277C2×C37#160911yescharacteristic
278C2×C37#161011yescharacteristic
279C2×C37#161211yescharacteristic
280C2×C37#187911yescharacteristic
281C2×C37#188211yescharacteristic
282C2×C37#189011yescharacteristic
283C2×#121C22×C3711yescharacteristic
284C2×C4×D4—21no—
285C22×C4⋊C4C22×C3711yescharacteristic
286#480—22no—
287#480C4×C3714yescomplemented
288C2×#107—21no—
289C2×#102—21no—
290C2×C22⋊C8C22×C3711yescharacteristic
291C2×C22⋊C8C22×C3711yescharacteristic
292#388—21no—
293#387—21no—
294#386—21no—
295#386—21no—
296#385—21no—
297#380C22×C3711yescharacteristic
298C2×#95—21no—
299C2×#95—21no—
300C2×#95C22×C3711yescharacteristic
301C2×#95C22×C3711yescharacteristic
302#340—21no—
303#340—21no—
304#327—22no—
305C37#904311yescharacteristic, direct product factor, Sylow
306C22×D4—21no—
307C22×D4D4×C3711yescharacteristic
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—21no—
311C23×C4D4×C3711yescharacteristic
312C23×C4D4×C3711yescharacteristic
313C23×C4C23×C3711yescharacteristic
314C22×C8—21no—
315C22×C8—21no—
316#121—21no—
317#121—21no—
318#121C2×C4×C3712yes—
319#121D4×C3712yes—
320C4×D4—42no—
321C4×D4—42no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C2×C4×C3712yescomplemented
329C2×C4⋊C4D4×C3711yescharacteristic
330C2×C4⋊C4D4×C3711yescharacteristic
331C2×C4⋊C4D4×C3711yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C42—21no—
338#107—24no—
339#102—24no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8C2×C4×C3712yescomplemented
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—42no—
352#95—42no—
353C24—21no—
354C24C2×D4×C3711yescharacteristic
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4C22⋊C4×C3712yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4D8×C3712yes—
397C22×C4C22×C4×C3711yescharacteristic
398C22×C4C2×D4×C3711yescharacteristic
399C22×C4C2×D4×C3711yescharacteristic
400C22×C4C2×D4×C3711yescharacteristic
401C22×C4#41×C3711yescharacteristic
402C22×C4#41×C3711yescharacteristic
403C2×C8—22no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—42no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C22⋊C4×C3712yes—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C42—42no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C4×D4×C3711yescharacteristic
438C23#120×C3711yescharacteristic
439C23#121×C3711yescharacteristic
440C23C2×D8×C3711yescharacteristic
441C23#135×C3711yescharacteristic
442C23AGL(1,ℤ/8)×C3711yescharacteristic
443C23AGL(1,ℤ/8)×C3711yescharacteristic
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—84no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4C2×C22⋊C4×C3711yescharacteristic
493C2×C4C4×D4×C3711yescharacteristic
494C2×C4#121×C3711yescharacteristic
495C2×C4#123×C3711yescharacteristic
496C8—42no—
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C37×#38611yescharacteristic
518C22C4×D8×C3711yescharacteristic
519C22C37×#44211yescharacteristic
520C22C37×#44711yescharacteristic
521C22C37×#44911yescharacteristic
522C22C37×#45511yescharacteristic
523C22C37×#45611yescharacteristic
524C22C37×#45811yescharacteristic
525C22C37×#45811yescharacteristic
526C22C37×#45911yescharacteristic
527C22C37×#46311yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—82no—
544C2C37×#160711yescharacteristic
545C2C37×#160911yescharacteristic
546C2C37×#161011yescharacteristic
547C2C37×#161211yescharacteristic
548C2C37×#187911yescharacteristic
549C2C37×#188211yescharacteristic
550C2C37×#189011yescharacteristic
subgroupG/H
center, socleC23×C37#120
commutatorC22×C4C22×C4×C37
Frattini, cosocleC23×C4C23×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1823C2semidirect
5. C37×#1445C2semidirect
6. C37×#1294C2semidirect
7. C37×#1280C2semidirect
12. C37×#480C4semidirect
52. C2×C4⋊C4×C37C2×C4semidirect
67. C22⋊C8×C37C2×C4semidirect
222. #9043C37direct (N × H)
266. #1823C2×C37semidirect
268. #1445C2×C37semidirect
269. #1294C2×C37semidirect
270. #1280C2×C37semidirect
287. #480C4×C37semidirect
305. C37#9043direct (N × H)
328. C2×C4⋊C4C2×C4×C37semidirect
343. C22⋊C8C2×C4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4802
C37×#23252
C37×#18232
C2×C37×#3272
C37×#14452
C37×#12942
C37×#12802
#904337