Finite Group Databasebeta

← C37×#10397 #22631650

Subgroups — C37×#10397 #22631650

Order 9472.

632 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2618C211yesmaximal, characteristic
2C37×#1874C211yesmaximal, characteristic
3C37×#1852C211yesmaximal, characteristic, complemented
4C2×C37×#327C211yesmaximal, characteristic
5C2×C37×#324C211yesmaximal, characteristic, complemented
6C37×#1441C211yesmaximal, characteristic, complemented
7C37×#1294C211yesmaximal, characteristic, complemented
8C2×#123×C37—21no—
9C2×#121×C37C2211yescharacteristic
10C22×C4⋊C4×C37C2211yescharacteristic
11C22×C4⋊C4×C37C2211yescharacteristic
12C2×#107×C37—21no—
13C2×#102×C37—21no—
14C2×C22⋊C8×C37C2211yescharacteristic
15C2×C22⋊C8×C37C2211yescharacteristic
16C37×#398—21no—
17C37×#396—21no—
18C37×#396—21no—
19C37×#394—21no—
20C37×#386—21no—
21C37×#380C2211yescharacteristic
22C2×#95×C37—21no—
23C2×#95×C37—21no—
24C2×#95×C37C2211yescharacteristic
25C37×#340—21no—
26C37×#340—21no—
27C37×#327—22no—
28C37×#324—22no—
29C22×D4×C37—21no—
30C22×D4×C37D411yescharacteristic
31C23×C4×C37—21no—
32C23×C4×C37—21no—
33C23×C4×C37D411yescharacteristic
34C23×C4×C37D411yescharacteristic
35C23×C4×C37C2311yescharacteristic
36C22×C8×C37—21no—
37C22×C8×C37—21no—
38#123×C37—42no—
39#123×C37—42no—
40#121×C37—21no—
41#121×C37—21no—
42#121×C37—21no—
43#121×C37—21no—
44C2×C4⋊C4×C37—21no—
45C2×C4⋊C4×C37—21no—
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×C37—21no—
53C2×C4⋊C4×C37—21no—
54C2×C4⋊C4×C37—42no—
55C2×C4⋊C4×C37D411yescharacteristic
56C2×C4⋊C4×C37D411yescharacteristic
57C2×C4⋊C4×C37D411yescharacteristic
58C2×C22⋊C4×C37—21no—
59C2×C22⋊C4×C37—21no—
60C2×C22⋊C4×C37—21no—
61C2×C22⋊C4×C37—21no—
62C2×C22⋊C4×C37—21no—
63C2×C22⋊C4×C37—21no—
64#107×C37—42no—
65#102×C37—42no—
66C22⋊C8×C37—21no—
67C22⋊C8×C37—21no—
68C22⋊C8×C37—21no—
69C22⋊C8×C37D412yes—
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—21no—
80C2×D4×C37—21no—
81C2×D4×C37—41no—
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×C37—41no—
89C22×C4×C37—21no—
90C22×C4×C37—21no—
91C22×C4×C37—21no—
92C22×C4×C37—21no—
93C22×C4×C37—21no—
94C22×C4×C37—21no—
95C22×C4×C37—22no—
96C22×C4×C37—22no—
97C22×C4×C37—21no—
98C22×C4×C37—21no—
99C22×C4×C37—21no—
100C22×C4×C37—21no—
101C22×C4×C37—21no—
102C22×C4×C37—21no—
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—41no—
119C22×C4×C37D812yes—
120C22×C4×C37C2×D411yescharacteristic
121C22×C4×C37C2×D411yescharacteristic
122C22×C4×C37C2×D411yescharacteristic
123C22×C4×C37#4111yescharacteristic
124C22×C4×C37#4111yescharacteristic
125C22×C4×C37#4111yescharacteristic
126C2×C8×C37—22no—
127C2×C8×C37—41no—
128C2×C8×C37—41no—
129C2×C8×C37—41no—
130C2×C8×C37—41no—
131C2×C8×C37—41no—
132C4⋊C4×C37—22no—
133C4⋊C4×C37—22no—
134C4⋊C4×C37—21no—
135C4⋊C4×C37—21no—
136C4⋊C4×C37—41no—
137C4⋊C4×C37—41no—
138C4⋊C4×C37—41no—
139C4⋊C4×C37—41no—
140C4⋊C4×C37—42no—
141C4⋊C4×C37—42no—
142C4⋊C4×C37—41no—
143C4⋊C4×C37—41no—
144C4⋊C4×C37—41no—
145C4⋊C4×C37—41no—
146C22⋊C4×C37—42no—
147C22⋊C4×C37—42no—
148C22⋊C4×C37—41no—
149C22⋊C4×C37—41no—
150C22⋊C4×C37—41no—
151C22⋊C4×C37—41no—
152C22⋊C4×C37—81no—
153C22⋊C4×C37—81no—
154C23×C37—21no—
155C23×C37—21no—
156C23×C37—21no—
157C23×C37—21no—
158C23×C37—41no—
159C23×C37—41no—
160C23×C37—41no—
161C23×C37—41no—
162C23×C37—41no—
163C23×C37—41no—
164C23×C37—41no—
165C23×C37#12011yescharacteristic
166C23×C37#12111yescharacteristic
167C23×C37#12311yescharacteristic
168C23×C37C2×D811yescharacteristic
169C23×C37#13511yescharacteristic
170C23×C37AGL(1,ℤ/8)11yescharacteristic
171C23×C37#13711yescharacteristic
172D4×C37—42no—
173D4×C37—81no—
174D4×C37—81no—
175D4×C37—81no—
176D4×C37—81no—
177D4×C37—81no—
178C2×C4×C37—21no—
179C2×C4×C37—21no—
180C2×C4×C37—21no—
181C2×C4×C37—21no—
182C2×C4×C37—22no—
183C2×C4×C37—22no—
184C2×C4×C37—22no—
185C2×C4×C37—41no—
186C2×C4×C37—41no—
187C2×C4×C37—41no—
188C2×C4×C37—41no—
189C2×C4×C37—41no—
190C2×C4×C37—41no—
191C2×C4×C37—41no—
192C2×C4×C37—41no—
193C2×C4×C37—42no—
194C2×C4×C37—42no—
195C2×C4×C37—42no—
196C2×C4×C37—42no—
197C2×C4×C37—42no—
198C2×C4×C37—42no—
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—41no—
206C2×C4×C37—41no—
207C2×C4×C37—41no—
208C2×C4×C37—41no—
209C2×C4×C37—42no—
210C2×C4×C37—41no—
211C2×C4×C37—41no—
212C2×C4×C37—81no—
213C2×C4×C37—81no—
214C2×C4×C37—81no—
215C2×C4×C37—81no—
216C2×C4×C37—81no—
217C2×C4×C37—81no—
218C2×C4×C37—81no—
219C2×C4×C37—81no—
220C2×C4×C37—81no—
221C2×C4×C37#12111yescharacteristic
222C2×C4×C37#12111yescharacteristic
223C2×C4×C37#12311yescharacteristic
224C2×C4×C37#12411yescharacteristic
225C8×C37—42no—
226C8×C37—81no—
227#10397C3711yesmaximal, characteristic, direct product factor, Sylow
228C22×C37—21no—
229C22×C37—21no—
230C22×C37—21no—
231C22×C37—21no—
232C22×C37—21no—
233C22×C37—21no—
234C22×C37—21no—
235C22×C37—21no—
236C22×C37—21no—
237C22×C37—21no—
238C22×C37—21no—
239C22×C37—21no—
240C22×C37—81no—
241C22×C37—81no—
242C22×C37—81no—
243C22×C37—81no—
244C22×C37—81no—
245C22×C37—81no—
246C22×C37—81no—
247C22×C37#39411yescharacteristic
248C22×C37#44711yescharacteristic
249C22×C37#45211yescharacteristic
250C22×C37#45411yescharacteristic
251C22×C37#45611yescharacteristic
252C22×C37B(4,𝔽2)11yescharacteristic
253C22×C37#45811yescharacteristic
254C22×C37#46611yescharacteristic
255C22×C37#46811yescharacteristic
256C22×C37#48011yescharacteristic
257C22×C37#48211yescharacteristic
258C4×C37—21no—
259C4×C37—21no—
260C4×C37—21no—
261C4×C37—21no—
262C4×C37—42no—
263C4×C37—82no—
264C4×C37—81no—
265C4×C37—82no—
266C4×C37—81no—
267C4×C37—81no—
268C4×C37—81no—
269#2618C2×C3711yescharacteristic
270#1874C2×C3711yescharacteristic
271#1852C2×C3711yescharacteristic, complemented
272C2×#327C2×C3711yescharacteristic
273C2×#324C2×C3711yescharacteristic, complemented
274#1441C2×C3711yescharacteristic, complemented
275#1294C2×C3711yescharacteristic, complemented
276C2×C37—21no—
277C2×C37—21no—
278C2×C37—21no—
279C2×C37—21no—
280C2×C37—161no—
281C2×C37#159811yescharacteristic
282C2×C37#160311yescharacteristic
283C2×C37#161011yescharacteristic
284C2×C37#161511yescharacteristic
285C2×C37#203311yescharacteristic
286C2×C37#203811yescharacteristic
287C2×C37#204411yescharacteristic
288C2×#123—21no—
289C2×#121C22×C3711yescharacteristic
290C22×C4⋊C4C22×C3711yescharacteristic
291C22×C4⋊C4C22×C3711yescharacteristic
292C2×#107—21no—
293C2×#102—21no—
294C2×C22⋊C8C22×C3711yescharacteristic
295C2×C22⋊C8C22×C3711yescharacteristic
296#398—21no—
297#396—21no—
298#396—21no—
299#394—21no—
300#386—21no—
301#380C22×C3711yescharacteristic
302C2×#95—21no—
303C2×#95—21no—
304C2×#95C22×C3711yescharacteristic
305#340—21no—
306#340—21no—
307#327—22no—
308#324—22no—
309C37#1039711yescharacteristic, direct product factor, Sylow
310C22×D4—21no—
311C22×D4D4×C3711yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4D4×C3711yescharacteristic
315C23×C4D4×C3711yescharacteristic
316C23×C4C23×C3711yescharacteristic
317C22×C8—21no—
318C22×C8—21no—
319#123—42no—
320#123—42no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4D4×C3711yescharacteristic
337C2×C4⋊C4D4×C3711yescharacteristic
338C2×C4⋊C4D4×C3711yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345#107—42no—
346#102—42no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8D4×C3712yes—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—42no—
357#95—42no—
358C24—21no—
359C24C2×D4×C3711yescharacteristic
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
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—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4D8×C3712yes—
401C22×C4C2×D4×C3711yescharacteristic
402C22×C4C2×D4×C3711yescharacteristic
403C22×C4C2×D4×C3711yescharacteristic
404C22×C4#41×C3711yescharacteristic
405C22×C4#41×C3711yescharacteristic
406C22×C4#41×C3711yescharacteristic
407C2×C8—22no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—42no—
422C4⋊C4—42no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—81no—
434C22⋊C4—81no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23#120×C3711yescharacteristic
447C23#121×C3711yescharacteristic
448C23#123×C3711yescharacteristic
449C23C2×D8×C3711yescharacteristic
450C23#135×C3711yescharacteristic
451C23AGL(1,ℤ/8)×C3711yescharacteristic
452C23#137×C3711yescharacteristic
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—81no—
501C2×C4—81no—
502C2×C4#121×C3711yescharacteristic
503C2×C4#121×C3711yescharacteristic
504C2×C4#123×C3711yescharacteristic
505C2×C4#124×C3711yescharacteristic
506C8—42no—
507C8—81no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22C37×#39411yescharacteristic
528C22C37×#44711yescharacteristic
529C22C37×#45211yescharacteristic
530C22C37×#45411yescharacteristic
531C22C37×#45611yescharacteristic
532C22C37×B(4,𝔽2)11yescharacteristic
533C22C37×#45811yescharacteristic
534C22C37×#46611yescharacteristic
535C22C37×#46811yescharacteristic
536C22C37×#48011yescharacteristic
537C22C37×#48211yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—82no—
544C4—82no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—81no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—161no—
554C2C37×#159811yescharacteristic
555C2C37×#160311yescharacteristic
556C2C37×#161011yescharacteristic
557C2C37×#161511yescharacteristic
558C2C37×#203311yescharacteristic
559C2C37×#203811yescharacteristic
560C2C37×#204411yescharacteristic
subgroupG/H
center, socleC23×C37#120
commutator, Frattini, cosocleC23×C4C23×C37
prime radicalC2×#121×C37C22
LCSG ▷ C23×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×#1852C2semidirect
5. C2×C37×#324C2semidirect
6. C37×#1441C2semidirect
7. C37×#1294C2semidirect
227. #10397C37direct (N × H)
271. #1852C2×C37semidirect
273. C2×#324C2×C37semidirect
274. #1441C2×C37semidirect
275. #1294C2×C37semidirect
309. C37#10397direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#26182
C37×#18742
C37×#18522
C2×C37×#3272
C2×C37×#3242
C37×#14412
C37×#12942
#1039737