Finite Group Databasebeta

← C37×#9938 #22631191

Subgroups — C37×#9938 #22631191

Order 9472.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3006C211yesmaximal, characteristic, complemented
2C37×#2539C211yesmaximal, characteristic, complemented
3C37×#2404C211yesmaximal, characteristic, complemented
4C37×#1789C211yesmaximal, characteristic, complemented
5C37×#1510C211yesmaximal, characteristic, complemented
6C37×#1462C211yesmaximal, characteristic, complemented
7C37×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C37C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C37—21no—
10C2×#123×C37—21no—
11C2×#121×C37C2211yescharacteristic
12C2×#120×C37—21no—
13C2×#120×C37—21no—
14C22×C22⋊C4×C37C2211yescharacteristic
15C37×#449—22no—
16C37×#448—21no—
17C37×#447—21no—
18C2×#104×C37—22no—
19C37×#417—21no—
20C37×#407C2211yescharacteristic
21C37×#407C2211yescharacteristic
22C37×#399—21no—
23C37×#393—21no—
24C37×#392—21no—
25C37×#392—21no—
26C37×#390—22no—
27C37×#386—21no—
28C37×#386—22no—
29C37×#381C2211yescharacteristic
30C4×C22⋊C4×C37C2211yescharacteristic
31C37×#327—22no—
32C37×#323—22no—
33C25×C37D411yescharacteristic
34C2×#41×C37—21no—
35C2×#41×C37—21no—
36C2×#41×C37—21no—
37C2×#41×C37—21no—
38C2×#41×C37—44no—
39C22×Q8×C37D411yescharacteristic, complemented
40C22×D4×C37—21no—
41C22×D4×C37—21no—
42C22×D4×C37—22no—
43C22×D4×C37—22no—
44C22×D4×C37D411yescharacteristic, complemented
45C22×D4×C37D411yescharacteristic, complemented
46C23×C4×C37—21no—
47C23×C4×C37D411yescharacteristic
48C23×C4×C37C2311yescharacteristic
49AGL(1,ℤ/8)×C37—44no—
50C2×SD16×C37—22no—
51C2×D8×C37—22no—
52C2×M16×C37—21no—
53C2×M16×C37—21no—
54#123×C37—44no—
55#121×C37—21no—
56#121×C37—21no—
57#121×C37—21no—
58#121×C37—21no—
59#120×C37—44no—
60#120×C37—44no—
61C2×C4⋊C4×C37—22no—
62C2×C4⋊C4×C37D411yescharacteristic, complemented
63C2×C22⋊C4×C37—21no—
64C2×C22⋊C4×C37—22no—
65C2×C22⋊C4×C37—22no—
66C2×C22⋊C4×C37—22no—
67C2×C22⋊C4×C37—21no—
68C2×C22⋊C4×C37—21no—
69C2×C22⋊C4×C37—21no—
70C2×C22⋊C4×C37—21no—
71C2×C22⋊C4×C37—21no—
72C2×C22⋊C4×C37—21no—
73C2×C22⋊C4×C37—21no—
74C2×C22⋊C4×C37—21no—
75C2×C22⋊C4×C37—22no—
76C2×C42×C37D412yescomplemented
77#104×C37—44no—
78#103×C37—22no—
79#102×C37—22no—
80C22⋊C8×C37—21no—
81C22⋊C8×C37—21no—
82C22⋊C8×C37—21no—
83C22⋊C8×C37D412yescomplemented
84#95×C37—22no—
85#95×C37—21no—
86#95×C37—21no—
87#95×C37D412yescomplemented
88C24×C37—21no—
89C24×C37—21no—
90C24×C37—21no—
91C24×C37—21no—
92C24×C37—21no—
93C24×C37—42no—
94C24×C37—42no—
95C24×C37—42no—
96C24×C37C2×D411yescharacteristic
97#41×C37—24no—
98#41×C37—24no—
99#41×C37—42no—
100#41×C37—42no—
101#41×C37—42no—
102#41×C37—42no—
103#41×C37—42no—
104#41×C37—42no—
105C2×Q8×C37—21no—
106C2×Q8×C37—21no—
107C2×Q8×C37—42no—
108C2×D4×C37—24no—
109C2×D4×C37—21no—
110C2×D4×C37—21no—
111C2×D4×C37—21no—
112C2×D4×C37—21no—
113C2×D4×C37—42no—
114C2×D4×C37—44no—
115C2×D4×C37—42no—
116C2×D4×C37—42no—
117C2×D4×C37—41no—
118C2×D4×C37—41no—
119C2×D4×C37—42no—
120C2×D4×C37—44no—
121C2×D4×C37—42no—
122C2×D4×C37—44no—
123C2×D4×C37—44no—
124C2×D4×C37—41no—
125C2×D4×C37—41no—
126C2×D4×C37—82no—
127C2×D4×C37—82no—
128C22×C4×C37—21no—
129C22×C4×C37—22no—
130C22×C4×C37—22no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—21no—
135C22×C4×C37—42no—
136C22×C4×C37—42no—
137C22×C4×C37—42no—
138C22×C4×C37—41no—
139C22×C4×C37—41no—
140C22×C4×C37—42no—
141C22×C4×C37C2×D411yescharacteristic
142C22×C4×C37C2×D411yescharacteristic
143C22×C4×C37C2×D411yescharacteristic
144C22×C4×C37C2×D411yescharacteristic
145C22×C4×C37C2×D411yescharacteristic
146C22×C4×C37#4111yescharacteristic
147SD16×C37—44no—
148D8×C37—44no—
149M16×C37—42no—
150M16×C37—42no—
151C2×C8×C37—22no—
152C2×C8×C37—41no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—44no—
156C22⋊C4×C37—24no—
157C22⋊C4×C37—44no—
158C22⋊C4×C37—44no—
159C22⋊C4×C37—44no—
160C22⋊C4×C37—42no—
161C22⋊C4×C37—41no—
162C22⋊C4×C37—41no—
163C22⋊C4×C37—41no—
164C22⋊C4×C37—41no—
165C22⋊C4×C37—41no—
166C22⋊C4×C37—41no—
167C22⋊C4×C37—82no—
168C42×C37—42no—
169C23×C37—22no—
170C23×C37—22no—
171C23×C37—22no—
172C23×C37—22no—
173C23×C37—22no—
174C23×C37—22no—
175C23×C37—41no—
176C23×C37—42no—
177C23×C37—42no—
178C23×C37—41no—
179C23×C37—42no—
180C23×C37—41no—
181C23×C37—41no—
182C23×C37—41no—
183C23×C37—41no—
184C23×C37—41no—
185C23×C37—42no—
186C23×C37—41no—
187C23×C37—41no—
188C23×C37—42no—
189C23×C37—42no—
190C23×C37—42no—
191C23×C37—41no—
192C23×C37—42no—
193C23×C37—81no—
194C23×C37—81no—
195C23×C37—88no—
196C23×C37#12011yescharacteristic
197C23×C37#12011yescharacteristic
198C23×C37#12111yescharacteristic
199Q8×C37—22no—
200Q8×C37—22no—
201Q8×C37—41no—
202Q8×C37—41no—
203D4×C37—22no—
204D4×C37—22no—
205D4×C37—41no—
206D4×C37—41no—
207D4×C37—42no—
208D4×C37—44no—
209D4×C37—44no—
210D4×C37—81no—
211D4×C37—88no—
212D4×C37—82no—
213D4×C37—88no—
214D4×C37—82no—
215C2×C4×C37—22no—
216C2×C4×C37—22no—
217C2×C4×C37—24no—
218C2×C4×C37—22no—
219C2×C4×C37—41no—
220C2×C4×C37—41no—
221C2×C4×C37—41no—
222C2×C4×C37—41no—
223C2×C4×C37—44no—
224C2×C4×C37—44no—
225C2×C4×C37—41no—
226C2×C4×C37—42no—
227C2×C4×C37—41no—
228C2×C4×C37—42no—
229C2×C4×C37—42no—
230C2×C4×C37—41no—
231C2×C4×C37—42no—
232C2×C4×C37—41no—
233C2×C4×C37—42no—
234C2×C4×C37—41no—
235C2×C4×C37—41no—
236C2×C4×C37—42no—
237C2×C4×C37—42no—
238C2×C4×C37—81no—
239C2×C4×C37#12011yescharacteristic
240C2×C4×C37#12111yescharacteristic
241C2×C4×C37#12111yescharacteristic
242C2×C4×C37#12711yescharacteristic
243C8×C37—42no—
244C8×C37—81no—
245#9938C3711yesmaximal, characteristic, direct product factor, Sylow
246C22×C37—21no—
247C22×C37—21no—
248C22×C37—21no—
249C22×C37—21no—
250C22×C37—21no—
251C22×C37—21no—
252C22×C37—21no—
253C22×C37—44no—
254C22×C37—44no—
255C22×C37—44no—
256C22×C37—44no—
257C22×C37—42no—
258C22×C37—42no—
259C22×C37—82no—
260C22×C37—82no—
261C22×C37—82no—
262C22×C37—82no—
263C22×C37—82no—
264C22×C37—82no—
265C22×C37—82no—
266C22×C37—81no—
267C22×C37—81no—
268C22×C37—81no—
269C22×C37—81no—
270C22×C37—81no—
271C22×C37—81no—
272C22×C37—81no—
273C22×C37#39211yescharacteristic
274C22×C37#45312yes—
275C22×C37B(4,𝔽2)12yes—
276C4×C37—21no—
277C4×C37—21no—
278C4×C37—21no—
279C4×C37—21no—
280C4×C37—44no—
281C4×C37—42no—
282C4×C37—82no—
283C4×C37—81no—
284C4×C37—81no—
285#3006C2×C3711yescharacteristic, complemented
286#2539C2×C3711yescharacteristic, complemented
287#2404C2×C3711yescharacteristic, complemented
288#1789C2×C3711yescharacteristic, complemented
289#1510C2×C3711yescharacteristic, complemented
290#1462C2×C3711yescharacteristic, complemented
291#1284C2×C3711yescharacteristic, complemented
292C2×C37—22no—
293C2×C37—22no—
294C2×C37—41no—
295C2×C37—82no—
296C2×C37—82no—
297C2×C37—161no—
298C2×C37#200211yescharacteristic
299C2×C37#201011yescharacteristic
300C2×C37#202111yescharacteristic
301C22×#41C22×C3711yescharacteristic
302C2×AGL(1,ℤ/8)—21no—
303C2×#123—21no—
304C2×#121C22×C3711yescharacteristic
305C2×#120—21no—
306C2×#120—21no—
307C22×C22⋊C4C22×C3711yescharacteristic
308#449—22no—
309#448—21no—
310#447—21no—
311C2×#104—22no—
312#417—21no—
313#407C22×C3711yescharacteristic
314#407C22×C3711yescharacteristic
315#399—21no—
316#393—21no—
317#392—21no—
318#392—21no—
319#390—22no—
320#386—21no—
321#386—22no—
322#381C22×C3711yescharacteristic
323C4×C22⋊C4C22×C3711yescharacteristic
324#327—22no—
325#323—22no—
326C37#993811yescharacteristic, direct product factor, Sylow
327C25D4×C3711yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C3711yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C3711yescharacteristic, complemented
339C22×D4D4×C3711yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C3711yescharacteristic
342C23×C4C23×C3711yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C3711yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C3712yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C3712yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C3712yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C3711yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C3711yescharacteristic
436C22×C4C2×D4×C3711yescharacteristic
437C22×C4C2×D4×C3711yescharacteristic
438C22×C4C2×D4×C3711yescharacteristic
439C22×C4C2×D4×C3711yescharacteristic
440C22×C4#41×C3711yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C3711yescharacteristic
491C23#120×C3711yescharacteristic
492C23#121×C3711yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C3711yescharacteristic
534C2×C4#121×C3711yescharacteristic
535C2×C4#121×C3711yescharacteristic
536C2×C4#127×C3711yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C37×#39211yescharacteristic
567C22C37×#45312yes—
568C22C37×B(4,𝔽2)12yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C37×#200211yescharacteristic
585C2C37×#201011yescharacteristic
586C2C37×#202111yescharacteristic
subgroupG/H
center, socleC22×C37#392
commutator, Frattini, cosocleC23×C4C23×C37
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3006C2semidirect
2. C37×#2539C2semidirect
3. C37×#2404C2semidirect
4. C37×#1789C2semidirect
5. C37×#1510C2semidirect
6. C37×#1462C2semidirect
7. C37×#1284C2semidirect
39. C22×Q8×C37D4semidirect
44. C22×D4×C37D4semidirect
45. C22×D4×C37D4semidirect
62. C2×C4⋊C4×C37D4semidirect
76. C2×C42×C37D4semidirect
83. C22⋊C8×C37D4semidirect
87. #95×C37D4semidirect
245. #9938C37direct (N × H)
285. #3006C2×C37semidirect
286. #2539C2×C37semidirect
287. #2404C2×C37semidirect
288. #1789C2×C37semidirect
289. #1510C2×C37semidirect
290. #1462C2×C37semidirect
291. #1284C2×C37semidirect
326. C37#9938direct (N × H)
333. C22×Q8D4×C37semidirect
338. C22×D4D4×C37semidirect
339. C22×D4D4×C37semidirect
356. C2×C4⋊C4D4×C37semidirect
370. C2×C42D4×C37semidirect
377. C22⋊C8D4×C37semidirect
381. #95D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#30062
C37×#25392
C37×#24042
C37×#17892
C37×#15102
C37×#14622
C37×#12842
#993837