Finite Group Databasebeta

← C37×#24468 #22645721

Subgroups — C37×#24468 #22645721

Order 9472.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3488C211yesmaximal, characteristic, complemented
2C37×#3055C211yesmaximal, characteristic, complemented
3C2×C37×#453C211yesmaximal, characteristic, complemented
4C37×#3006C211yesmaximal, characteristic, complemented
5C2×C37×#421C211yesmaximal, characteristic, complemented
6C37×#2619C211yesmaximal, characteristic, complemented
7C37×#2040C211yesmaximal, characteristic, complemented
8C37×#2037C211yesmaximal, characteristic, complemented
9C37×#2006C211yesmaximal, characteristic, complemented
10C37×#2002C211yesmaximal, characteristic, complemented
11C37×#1900C211yesmaximal, characteristic, complemented
12C37×#1897C211yesmaximal, characteristic, complemented
13C37×#1883C211yesmaximal, characteristic, complemented
14C37×#1860C211yesmaximal, characteristic, complemented
15C37×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
21C22×M16×C37C2211yescharacteristic, complemented
22C37×#550—21no—
23C37×#548—21no—
24C37×#546—21no—
25C37×#546—22no—
26D42×C37—22no—
27D42×C37—21no—
28C37×#537—21no—
29C37×#537C2211yescharacteristic
30C37×#535—21no—
31C37×#535C2211yescharacteristic
32C2×#127×C37C2211yescharacteristic, complemented
33C37×#525—21no—
34C37×#525C2211yescharacteristic
35C2×#121×C37—21no—
36C2×#121×C37C2211yescharacteristic
37C2×#121×C37C2211yescharacteristic, complemented
38C37×#520C2211yescharacteristic
39C2×#117×C37C2211yescharacteristic, complemented
40C37×#469—21no—
41C37×#468—21no—
42C37×#466—21no—
43C37×#465—21no—
44C37×#453—24no—
45C37×#449—21no—
46C37×#449—21no—
47C37×#448—21no—
48C37×#447—21no—
49C37×#428C2211yescharacteristic, complemented
50C37×#421—24no—
51C2×#104×C37C2211yescharacteristic
52C2×#104×C37C2211yescharacteristic
53C2×#104×C37C2211yescharacteristic, complemented
54C2×#104×C37C2211yescharacteristic, complemented
55C2×#104×C37C2211yescharacteristic, complemented
56C2×#104×C37C2211yescharacteristic, complemented
57C37×#418C2211yescharacteristic, complemented
58C37×#417C2211yescharacteristic
59C37×#417C2211yescharacteristic, complemented
60C37×#417C2211yescharacteristic, complemented
61C2×#100×C37C2211yescharacteristic, complemented
62C2×#100×C37C2211yescharacteristic, complemented
63C37×#407C2211yescharacteristic, complemented
64C37×#394—22no—
65C37×#392—22no—
66C37×#390C2211yescharacteristic, complemented
67C37×#390C2211yescharacteristic, complemented
68C37×#382C2211yescharacteristic, complemented
69C37×#343C2211yescharacteristic, complemented
70C37×#343C2211yescharacteristic, complemented
71C37×#339C2211yescharacteristic, complemented
72C37×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C37—22no—
74H(5,𝔽2)×C37—22no—
75H(5,𝔽2)×C37—41no—
76H(5,𝔽2)×C37—41no—
77C2×#41×C37—21no—
78C2×#41×C37—21no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—22no—
82C2×#41×C37—22no—
83C2×#41×C37—41no—
84C2×#41×C37—41no—
85C2×#41×C37D411yescharacteristic, complemented
86C2×#41×C37D411yescharacteristic, complemented
87C2×#41×C37C2311yescharacteristic
88C2×#41×C37C2311yescharacteristic
89C2×#41×C37C2311yescharacteristic
90C22×Q8×C37D411yescharacteristic, complemented
91C22×D4×C37—21no—
92C22×D4×C37—22no—
93C22×D4×C37—22no—
94C22×D4×C37—21no—
95C22×D4×C37—21no—
96C22×D4×C37—21no—
97C22×D4×C37—22no—
98C22×D4×C37D412yes—
99C22×D4×C37D411yescharacteristic, complemented
100C22×D4×C37C2311yescharacteristic
101C22×D4×C37C2311yescharacteristic
102C23×C4×C37—21no—
103C23×C4×C37C2311yescharacteristic
104AGL(1,ℤ/8)×C37—22no—
105AGL(1,ℤ/8)×C37—22no—
106AGL(1,ℤ/8)×C37—22no—
107AGL(1,ℤ/8)×C37—41no—
108AGL(1,ℤ/8)×C37—41no—
109AGL(1,ℤ/8)×C37—41no—
110C2×SD16×C37—21no—
111C2×SD16×C37—21no—
112C2×SD16×C37—21no—
113C2×D8×C37—21no—
114C2×D8×C37—21no—
115C2×D8×C37—21no—
116C2×M16×C37—21no—
117C2×M16×C37—22no—
118C2×M16×C37—41no—
119C2×M16×C37C2311yescharacteristic
120C2×M16×C37C2311yescharacteristic
121C2×M16×C37C2311yescharacteristic
122C2×M16×C37C2311yescharacteristic
123C22×C8×C37—21no—
124#127×C37—22no—
125#127×C37—21no—
126#127×C37—22no—
127#127×C37—41no—
128#124×C37—22no—
129#124×C37—21no—
130#123×C37—22no—
131#123×C37—21no—
132C22⋊Q8×C37—22no—
133C22⋊Q8×C37—21no—
134C22⋊Q8×C37—21no—
135C22⋊Q8×C37D411yescharacteristic, complemented
136C22⋊Q8×C37D411yescharacteristic, complemented
137#121×C37—22no—
138#121×C37—22no—
139#121×C37—22no—
140#121×C37—22no—
141#121×C37—22no—
142#121×C37—21no—
143#121×C37—21no—
144#121×C37—21no—
145#121×C37—21no—
146#121×C37—21no—
147#121×C37—21no—
148#121×C37—22no—
149#121×C37—21no—
150#121×C37—21no—
151#121×C37—21no—
152#121×C37—21no—
153#121×C37—21no—
154#121×C37—21no—
155#121×C37D411yescharacteristic, complemented
156#121×C37D411yescharacteristic, complemented
157#120×C37—22no—
158#120×C37—22no—
159#120×C37—22no—
160#120×C37—21no—
161#120×C37—22no—
162C4×Q8×C37—21no—
163C4×D4×C37—22no—
164C4×D4×C37—22no—
165C4×D4×C37—21no—
166C4×D4×C37—22no—
167C4×D4×C37—21no—
168C4×D4×C37—21no—
169#117×C37—21no—
170#117×C37—22no—
171#117×C37—41no—
172#117×C37C2311yescharacteristic
173C2×C4⋊C4×C37—21no—
174C2×C4⋊C4×C37—21no—
175C2×C4⋊C4×C37C2311yescharacteristic
176C2×C4⋊C4×C37C2311yescharacteristic
177C2×C22⋊C4×C37—22no—
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—21no—
180C2×C22⋊C4×C37—22no—
181C2×C22⋊C4×C37—22no—
182C2×C22⋊C4×C37D412yes—
183C2×C42×C37C2311yescharacteristic
184C2×C42×C37C2311yescharacteristic
185#107×C37—21no—
186#106×C37—21no—
187#104×C37—22no—
188#104×C37—22no—
189#104×C37—22no—
190#104×C37—22no—
191#104×C37—41no—
192#104×C37D414yescomplemented
193#103×C37—21no—
194#103×C37—21no—
195#103×C37—21no—
196#102×C37—21no—
197#102×C37—21no—
198#102×C37—21no—
199#102×C37—21no—
200#102×C37—21no—
201#100×C37—22no—
202#100×C37—41no—
203C22⋊C8×C37—21no—
204C22⋊C8×C37—21no—
205#95×C37—22no—
206C24×C37—22no—
207C24×C37—21no—
208C24×C37—21no—
209C24×C37C2×D412yes—
210C24×C37C2×D411yescharacteristic
211#41×C37—21no—
212#41×C37—21no—
213#41×C37—22no—
214#41×C37—22no—
215#41×C37—21no—
216#41×C37—21no—
217#41×C37—21no—
218#41×C37—21no—
219#41×C37—21no—
220#41×C37—21no—
221#41×C37—21no—
222#41×C37—21no—
223#41×C37—42no—
224#41×C37—42no—
225#41×C37—41no—
226#41×C37—41no—
227#41×C37—42no—
228#41×C37—42no—
229#41×C37—42no—
230#41×C37—42no—
231#41×C37—42no—
232#41×C37—42no—
233#41×C37C2×D412yes—
234#41×C37#4112yes—
235C2×Q8×C37—21no—
236C2×Q8×C37—22no—
237C2×Q8×C37—41no—
238C2×Q8×C37C2×D411yescharacteristic
239C2×Q8×C37C2×D411yescharacteristic
240C2×Q8×C37C2×D411yescharacteristic
241C2×D4×C37—21no—
242C2×D4×C37—22no—
243C2×D4×C37—22no—
244C2×D4×C37—22no—
245C2×D4×C37—22no—
246C2×D4×C37—21no—
247C2×D4×C37—21no—
248C2×D4×C37—21no—
249C2×D4×C37—21no—
250C2×D4×C37—21no—
251C2×D4×C37—22no—
252C2×D4×C37—22no—
253C2×D4×C37—22no—
254C2×D4×C37—21no—
255C2×D4×C37—22no—
256C2×D4×C37—21no—
257C2×D4×C37—21no—
258C2×D4×C37—21no—
259C2×D4×C37—21no—
260C2×D4×C37—21no—
261C2×D4×C37—21no—
262C2×D4×C37—21no—
263C2×D4×C37—21no—
264C2×D4×C37—21no—
265C2×D4×C37—21no—
266C2×D4×C37—21no—
267C2×D4×C37—21no—
268C2×D4×C37—21no—
269C2×D4×C37—41no—
270C2×D4×C37—42no—
271C2×D4×C37—42no—
272C2×D4×C37—44no—
273C2×D4×C37—42no—
274C2×D4×C37—42no—
275C2×D4×C37—44no—
276C2×D4×C37—44no—
277C2×D4×C37—42no—
278C2×D4×C37—42no—
279C2×D4×C37—41no—
280C2×D4×C37—41no—
281C2×D4×C37—82no—
282C2×D4×C37—82no—
283C2×D4×C37—82no—
284C2×D4×C37—82no—
285C2×D4×C37—84no—
286C2×D4×C37C2×D411yescharacteristic
287C2×D4×C37C2×D411yescharacteristic
288C2×D4×C37C2×D411yescharacteristic
289C22×C4×C37—21no—
290C22×C4×C37—21no—
291C22×C4×C37—21no—
292C22×C4×C37—21no—
293C22×C4×C37—21no—
294C22×C4×C37—22no—
295C22×C4×C37—21no—
296C22×C4×C37—21no—
297C22×C4×C37—22no—
298C22×C4×C37—21no—
299C22×C4×C37—21no—
300C22×C4×C37—21no—
301C22×C4×C37—21no—
302C22×C4×C37—21no—
303C22×C4×C37—21no—
304C22×C4×C37—42no—
305C22×C4×C37—42no—
306C22×C4×C37C2×D411yescharacteristic
307C22×C4×C37C2×D411yescharacteristic
308C22×C4×C37C2×D411yescharacteristic
309C22×C4×C37C2×D411yescharacteristic
310C22×C4×C37C2×D411yescharacteristic
311C22×C4×C37C2×D412yes—
312C22×C4×C37C2411yescharacteristic
313SD16×C37—42no—
314SD16×C37—42no—
315SD16×C37—42no—
316D8×C37—42no—
317D8×C37—42no—
318D8×C37—42no—
319M16×C37—21no—
320M16×C37—21no—
321M16×C37—21no—
322M16×C37—21no—
323M16×C37—21no—
324M16×C37—21no—
325M16×C37—21no—
326M16×C37—42no—
327M16×C37C2×D412yescomplemented
328C2×C8×C37—21no—
329C2×C8×C37—21no—
330C2×C8×C37—21no—
331C2×C8×C37—21no—
332C2×C8×C37—42no—
333C4⋊C4×C37—22no—
334C4⋊C4×C37—22no—
335C4⋊C4×C37—21no—
336C4⋊C4×C37—21no—
337C4⋊C4×C37—21no—
338C4⋊C4×C37—21no—
339C4⋊C4×C37—21no—
340C4⋊C4×C37—21no—
341C4⋊C4×C37—42no—
342C4⋊C4×C37C2×D411yescharacteristic
343C4⋊C4×C37C2×D411yescharacteristic
344C22⋊C4×C37—22no—
345C22⋊C4×C37—22no—
346C22⋊C4×C37—22no—
347C22⋊C4×C37—22no—
348C22⋊C4×C37—22no—
349C22⋊C4×C37—21no—
350C22⋊C4×C37—21no—
351C22⋊C4×C37—21no—
352C22⋊C4×C37—21no—
353C22⋊C4×C37—22no—
354C22⋊C4×C37—22no—
355C22⋊C4×C37—21no—
356C22⋊C4×C37—42no—
357C22⋊C4×C37—41no—
358C22⋊C4×C37—41no—
359C22⋊C4×C37—82no—
360C22⋊C4×C37—82no—
361C42×C37—22no—
362C42×C37—21no—
363C42×C37—21no—
364C42×C37—21no—
365C42×C37—21no—
366C42×C37C2×D412yescomplemented
367C23×C37—21no—
368C23×C37—21no—
369C23×C37—21no—
370C23×C37—22no—
371C23×C37—21no—
372C23×C37—21no—
373C23×C37—22no—
374C23×C37—22no—
375C23×C37—41no—
376C23×C37—41no—
377C23×C37—42no—
378C23×C37—42no—
379C23×C37—44no—
380C23×C37—42no—
381C23×C37—42no—
382C23×C37—42no—
383C23×C37—42no—
384C23×C37—41no—
385C23×C37—41no—
386C23×C37—41no—
387C23×C37—81no—
388C23×C37—82no—
389C23×C37—82no—
390C23×C37#12011yescharacteristic
391C23×C37#12011yescharacteristic
392C23×C37C22×D411yescharacteristic
393Q8×C37—21no—
394Q8×C37—21no—
395Q8×C37—21no—
396Q8×C37—21no—
397Q8×C37—21no—
398Q8×C37—42no—
399Q8×C37#12112yes—
400D4×C37—22no—
401D4×C37—22no—
402D4×C37—21no—
403D4×C37—21no—
404D4×C37—21no—
405D4×C37—21no—
406D4×C37—21no—
407D4×C37—42no—
408D4×C37—42no—
409D4×C37—44no—
410D4×C37—42no—
411D4×C37—44no—
412D4×C37—44no—
413D4×C37—42no—
414D4×C37—41no—
415D4×C37—41no—
416D4×C37—41no—
417D4×C37—41no—
418D4×C37—41no—
419D4×C37—41no—
420D4×C37—41no—
421D4×C37—41no—
422D4×C37—41no—
423D4×C37—41no—
424D4×C37—41no—
425D4×C37—41no—
426D4×C37—81no—
427D4×C37—82no—
428D4×C37—82no—
429D4×C37—82no—
430D4×C37—82no—
431D4×C37—88no—
432D4×C37—82no—
433D4×C37—82no—
434D4×C37#12112yes—
435C2×C4×C37—21no—
436C2×C4×C37—21no—
437C2×C4×C37—21no—
438C2×C4×C37—21no—
439C2×C4×C37—21no—
440C2×C4×C37—21no—
441C2×C4×C37—21no—
442C2×C4×C37—21no—
443C2×C4×C37—21no—
444C2×C4×C37—22no—
445C2×C4×C37—21no—
446C2×C4×C37—21no—
447C2×C4×C37—22no—
448C2×C4×C37—21no—
449C2×C4×C37—22no—
450C2×C4×C37—21no—
451C2×C4×C37—21no—
452C2×C4×C37—21no—
453C2×C4×C37—22no—
454C2×C4×C37—42no—
455C2×C4×C37—42no—
456C2×C4×C37—42no—
457C2×C4×C37—44no—
458C2×C4×C37—41no—
459C2×C4×C37—41no—
460C2×C4×C37—41no—
461C2×C4×C37—41no—
462C2×C4×C37—41no—
463C2×C4×C37—41no—
464C2×C4×C37—42no—
465C2×C4×C37—41no—
466C2×C4×C37—41no—
467C2×C4×C37—42no—
468C2×C4×C37—41no—
469C2×C4×C37—41no—
470C2×C4×C37—82no—
471C2×C4×C37#12011yescharacteristic
472C2×C4×C37#12011yescharacteristic
473C2×C4×C37C22×D411yescharacteristic
474C2×C4×C37C22×D411yescharacteristic
475C2×C4×C37C22×D411yescharacteristic
476C2×C4×C37C2×#4111yescharacteristic
477C2×C4×C37H(5,𝔽2)11yescharacteristic
478C2×C4×C37H(5,𝔽2)11yescharacteristic
479C8×C37—22no—
480C8×C37—41no—
481C8×C37—41no—
482C8×C37—41no—
483#24468C3711yesmaximal, characteristic, direct product factor, Sylow
484C22×C37—21no—
485C22×C37—21no—
486C22×C37—21no—
487C22×C37—21no—
488C22×C37—22no—
489C22×C37—21no—
490C22×C37—21no—
491C22×C37—21no—
492C22×C37—21no—
493C22×C37—41no—
494C22×C37—41no—
495C22×C37—41no—
496C22×C37—41no—
497C22×C37—42no—
498C22×C37—42no—
499C22×C37—41no—
500C22×C37—41no—
501C22×C37—41no—
502C22×C37—42no—
503C22×C37—41no—
504C22×C37—81no—
505C22×C37—81no—
506C22×C37—82no—
507C22×C37—82no—
508C22×C37—82no—
509C22×C37—82no—
510C22×C37—84no—
511C22×C37—81no—
512C22×C37—81no—
513C22×C37—81no—
514C22×C37—164no—
515C22×C37C2×#12011yescharacteristic
516C22×C37D4211yescharacteristic
517C22×C37#54611yescharacteristic
518C4×C37—21no—
519C4×C37—21no—
520C4×C37—22no—
521C4×C37—42no—
522C4×C37—41no—
523C4×C37—41no—
524C4×C37—42no—
525C4×C37—41no—
526C4×C37—41no—
527C4×C37—81no—
528C4×C37—81no—
529C4×C37C2×#12111yescharacteristic
530C4×C37#53411yescharacteristic
531C4×C37D4211yescharacteristic
532C4×C37#54611yescharacteristic
533#3488C2×C3711yescharacteristic, complemented
534#3055C2×C3711yescharacteristic, complemented
535C2×#453C2×C3711yescharacteristic, complemented
536#3006C2×C3711yescharacteristic, complemented
537C2×#421C2×C3711yescharacteristic, complemented
538#2619C2×C3711yescharacteristic, complemented
539#2040C2×C3711yescharacteristic, complemented
540#2037C2×C3711yescharacteristic, complemented
541#2006C2×C3711yescharacteristic, complemented
542#2002C2×C3711yescharacteristic, complemented
543#1900C2×C3711yescharacteristic, complemented
544#1897C2×C3711yescharacteristic, complemented
545#1883C2×C3711yescharacteristic, complemented
546#1860C2×C3711yescharacteristic, complemented
547#1792C2×C3711yescharacteristic, complemented
548C2×C37—21no—
549C2×C37—21no—
550C2×C37—41no—
551C2×C37—41no—
552C2×C37—42no—
553C2×C37—81no—
554C2×C37—82no—
555C2×C37—81no—
556C2×C37—161no—
557C2×C37#241011yescharacteristic
558C2×C37#301911yescharacteristic
559C2×C37#302111yescharacteristic
560C2×H(5,𝔽2)C22×C3711yescharacteristic
561C22×#41C22×C3711yescharacteristic
562C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
563C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
564C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
565C22×M16C22×C3711yescharacteristic, complemented
566#550—21no—
567#548—21no—
568#546—21no—
569#546—22no—
570D42—22no—
571D42—21no—
572#537—21no—
573#537C22×C3711yescharacteristic
574#535—21no—
575#535C22×C3711yescharacteristic
576C2×#127C22×C3711yescharacteristic, complemented
577#525—21no—
578#525C22×C3711yescharacteristic
579C2×#121—21no—
580C2×#121C22×C3711yescharacteristic
581C2×#121C22×C3711yescharacteristic, complemented
582#520C22×C3711yescharacteristic
583C2×#117C22×C3711yescharacteristic, complemented
584#469—21no—
585#468—21no—
586#466—21no—
587#465—21no—
588#453—24no—
589#449—21no—
590#449—21no—
591#448—21no—
592#447—21no—
593#428C22×C3711yescharacteristic, complemented
594#421—24no—
595C2×#104C22×C3711yescharacteristic
596C2×#104C22×C3711yescharacteristic
597C2×#104C22×C3711yescharacteristic, complemented
598C2×#104C22×C3711yescharacteristic, complemented
599C2×#104C22×C3711yescharacteristic, complemented
600C2×#104C22×C3711yescharacteristic, complemented
601#418C22×C3711yescharacteristic, complemented
602#417C22×C3711yescharacteristic
603#417C22×C3711yescharacteristic, complemented
604#417C22×C3711yescharacteristic, complemented
605C2×#100C22×C3711yescharacteristic, complemented
606C2×#100C22×C3711yescharacteristic, complemented
607#407C22×C3711yescharacteristic, complemented
608#394—22no—
609#392—22no—
610#390C22×C3711yescharacteristic, complemented
611#390C22×C3711yescharacteristic, complemented
612#382C22×C3711yescharacteristic, complemented
613#343C22×C3711yescharacteristic, complemented
614#343C22×C3711yescharacteristic, complemented
615#339C22×C3711yescharacteristic, complemented
616#339C22×C3711yescharacteristic, complemented
617C37#2446811yescharacteristic, direct product factor, Sylow
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C3711yescharacteristic, complemented
631C2×#41D4×C3711yescharacteristic, complemented
632C2×#41C23×C3711yescharacteristic
633C2×#41C23×C3711yescharacteristic
634C2×#41C23×C3711yescharacteristic
635C22×Q8D4×C3711yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C3712yes—
644C22×D4D4×C3711yescharacteristic, complemented
645C22×D4C23×C3711yescharacteristic
646C22×D4C23×C3711yescharacteristic
647C23×C4—21no—
648C23×C4C23×C3711yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C3711yescharacteristic
665C2×M16C23×C3711yescharacteristic
666C2×M16C23×C3711yescharacteristic
667C2×M16C23×C3711yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C3711yescharacteristic, complemented
681C22⋊Q8D4×C3711yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C3711yescharacteristic, complemented
701#121D4×C3711yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C3711yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C3711yescharacteristic
721C2×C4⋊C4C23×C3711yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C3712yes—
728C2×C42C23×C3711yescharacteristic
729C2×C42C23×C3711yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C3714yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C3712yes—
755C24C2×D4×C3711yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C3712yes—
779#41#41×C3712yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C3711yescharacteristic
784C2×Q8C2×D4×C3711yescharacteristic
785C2×Q8C2×D4×C3711yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C3711yescharacteristic
832C2×D4C2×D4×C3711yescharacteristic
833C2×D4C2×D4×C3711yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C3711yescharacteristic
852C22×C4C2×D4×C3711yescharacteristic
853C22×C4C2×D4×C3711yescharacteristic
854C22×C4C2×D4×C3711yescharacteristic
855C22×C4C2×D4×C3711yescharacteristic
856C22×C4C2×D4×C3712yes—
857C22×C4C24×C3711yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C3712yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C3711yescharacteristic
888C4⋊C4C2×D4×C3711yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C3712yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C3711yescharacteristic
936C23#120×C3711yescharacteristic
937C23C22×D4×C3711yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C3712yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C3712yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C3711yescharacteristic
1017C2×C4#120×C3711yescharacteristic
1018C2×C4C22×D4×C3711yescharacteristic
1019C2×C4C22×D4×C3711yescharacteristic
1020C2×C4C22×D4×C3711yescharacteristic
1021C2×C4C2×#41×C3711yescharacteristic
1022C2×C4H(5,𝔽2)×C3711yescharacteristic
1023C2×C4H(5,𝔽2)×C3711yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C3711yescharacteristic
1060C22D42×C3711yescharacteristic
1061C22C37×#54611yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C3711yescharacteristic
1074C4C37×#53411yescharacteristic
1075C4D42×C3711yescharacteristic
1076C4C37×#54611yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2C37×#241011yescharacteristic
1087C2C37×#301911yescharacteristic
1088C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3488C2semidirect
2. C37×#3055C2semidirect
3. C2×C37×#453C2semidirect
4. C37×#3006C2semidirect
5. C2×C37×#421C2semidirect
6. C37×#2619C2semidirect
7. C37×#2040C2semidirect
8. C37×#2037C2semidirect
9. C37×#2006C2semidirect
10. C37×#2002C2semidirect
11. C37×#1900C2semidirect
12. C37×#1897C2semidirect
13. C37×#1883C2semidirect
14. C37×#1860C2semidirect
15. C37×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C37C22semidirect
20. C2×AGL(1,ℤ/8)×C37C22semidirect
21. C22×M16×C37C22semidirect
32. C2×#127×C37C22semidirect
37. C2×#121×C37C22semidirect
39. C2×#117×C37C22semidirect
49. C37×#428C22semidirect
53. C2×#104×C37C22semidirect
54. C2×#104×C37C22semidirect
55. C2×#104×C37C22semidirect
56. C2×#104×C37C22semidirect
57. C37×#418C22semidirect
59. C37×#417C22semidirect
60. C37×#417C22semidirect
61. C2×#100×C37C22semidirect
62. C2×#100×C37C22semidirect
63. C37×#407C22semidirect
66. C37×#390C22semidirect
67. C37×#390C22semidirect
68. C37×#382C22semidirect
69. C37×#343C22semidirect
70. C37×#343C22semidirect
71. C37×#339C22semidirect
72. C37×#339C22semidirect
85. C2×#41×C37D4semidirect
86. C2×#41×C37D4semidirect
90. C22×Q8×C37D4semidirect
99. C22×D4×C37D4semidirect
135. C22⋊Q8×C37D4semidirect
136. C22⋊Q8×C37D4semidirect
155. #121×C37D4semidirect
156. #121×C37D4semidirect
192. #104×C37D4semidirect
327. M16×C37C2×D4semidirect
366. C42×C37C2×D4semidirect
483. #24468C37direct (N × H)
533. #3488C2×C37semidirect
534. #3055C2×C37semidirect
535. C2×#453C2×C37semidirect
536. #3006C2×C37semidirect
537. C2×#421C2×C37semidirect
538. #2619C2×C37semidirect
539. #2040C2×C37semidirect
540. #2037C2×C37semidirect
541. #2006C2×C37semidirect
542. #2002C2×C37semidirect
543. #1900C2×C37semidirect
544. #1897C2×C37semidirect
545. #1883C2×C37semidirect
546. #1860C2×C37semidirect
547. #1792C2×C37semidirect
563. C2×AGL(1,ℤ/8)C22×C37semidirect
564. C2×AGL(1,ℤ/8)C22×C37semidirect
565. C22×M16C22×C37semidirect
576. C2×#127C22×C37semidirect
581. C2×#121C22×C37semidirect
583. C2×#117C22×C37semidirect
593. #428C22×C37semidirect
597. C2×#104C22×C37semidirect
598. C2×#104C22×C37semidirect
599. C2×#104C22×C37semidirect
600. C2×#104C22×C37semidirect
601. #418C22×C37semidirect
603. #417C22×C37semidirect
604. #417C22×C37semidirect
605. C2×#100C22×C37semidirect
606. C2×#100C22×C37semidirect
607. #407C22×C37semidirect
610. #390C22×C37semidirect
611. #390C22×C37semidirect
612. #382C22×C37semidirect
613. #343C22×C37semidirect
614. #343C22×C37semidirect
615. #339C22×C37semidirect
616. #339C22×C37semidirect
617. C37#24468direct (N × H)
630. C2×#41D4×C37semidirect
631. C2×#41D4×C37semidirect
635. C22×Q8D4×C37semidirect
644. C22×D4D4×C37semidirect
680. C22⋊Q8D4×C37semidirect
681. C22⋊Q8D4×C37semidirect
700. #121D4×C37semidirect
701. #121D4×C37semidirect
737. #104D4×C37semidirect
872. M16C2×D4×C37semidirect
911. C42C2×D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34882
C37×#30552
C2×C37×#4532
C37×#30062
C2×C37×#4212
C37×#26192
C37×#20402
C37×#20372
C37×#20062
C37×#20022
C37×#19002
C37×#18972
C37×#18832
C37×#18602
C37×#17922
#2446837