Finite Group Databasebeta

← C37×#24031 #22645284

Subgroups — C37×#24031 #22645284

Order 9472.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3488C211yesmaximal, characteristic
2C37×#3093C211yesmaximal, characteristic, complemented
3C37×#2896C211yesmaximal, characteristic, complemented
4C37×#2500C211yesmaximal, characteristic, complemented
5C37×#2040C211yesmaximal, characteristic, complemented
6C37×#2039C211yesmaximal, characteristic, complemented
7C37×#2037C211yesmaximal, characteristic, complemented
8C37×#2037C211yesmaximal, characteristic, complemented
9C37×#1900C211yesmaximal, characteristic, complemented
10C37×#1871C211yesmaximal, characteristic, complemented
11C37×#1860C211yesmaximal, characteristic, complemented
12C37×#1859C211yesmaximal, characteristic, complemented
13C37×#1792C211yesmaximal, characteristic, complemented
14C37×#1792C211yesmaximal, characteristic, complemented
15C37×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic, complemented
19C37×#550—21no—
20C37×#548—21no—
21C37×#546—21no—
22C37×#546—22no—
23D42×C37—22no—
24D42×C37—21no—
25C37×#537—21no—
26C37×#537C2211yescharacteristic
27C37×#535—21no—
28C37×#535C2211yescharacteristic
29C37×#525—21no—
30C37×#525C2211yescharacteristic
31C2×#121×C37—21no—
32C2×#121×C37C2211yescharacteristic
33C37×#520C2211yescharacteristic
34C2×#117×C37C2211yescharacteristic, complemented
35C37×#485—21no—
36C37×#485—21no—
37C37×#482—21no—
38C37×#482—21no—
39C37×#428C2211yescharacteristic, complemented
40C37×#428C2211yescharacteristic, complemented
41C2×#104×C37C2211yescharacteristic
42C2×#104×C37C2211yescharacteristic
43C2×#104×C37C2211yescharacteristic, complemented
44C2×#104×C37C2211yescharacteristic, complemented
45C2×#104×C37C2211yescharacteristic, complemented
46C2×#104×C37C2211yescharacteristic, complemented
47C37×#419—21no—
48C37×#418—21no—
49C37×#417C2211yescharacteristic
50C37×#417C2211yescharacteristic
51C37×#417C2211yescharacteristic, complemented
52C37×#417C2211yescharacteristic, complemented
53C37×#417C2211yescharacteristic, complemented
54C37×#417C2211yescharacteristic, complemented
55C37×#416—21no—
56C37×#416—21no—
57C2×#100×C37C2211yescharacteristic, complemented
58C2×#100×C37C2211yescharacteristic, complemented
59C37×#407C2211yescharacteristic, complemented
60C37×#394—22no—
61C37×#390C2211yescharacteristic, complemented
62C37×#390C2211yescharacteristic, complemented
63C37×#388—22no—
64C37×#384C2211yescharacteristic, complemented
65C37×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C37C2211yescharacteristic, complemented
67C37×#343C2211yescharacteristic, complemented
68C37×#343C2211yescharacteristic, complemented
69C37×#339C2211yescharacteristic, complemented
70C37×#339C2211yescharacteristic, complemented
71H(5,𝔽2)×C37—22no—
72H(5,𝔽2)×C37—22no—
73H(5,𝔽2)×C37—41no—
74H(5,𝔽2)×C37—41no—
75C2×#41×C37—21no—
76C2×#41×C37—21no—
77C2×#41×C37—21no—
78C2×#41×C37—21no—
79C2×#41×C37—22no—
80C2×#41×C37—22no—
81C2×#41×C37—41no—
82C2×#41×C37—41no—
83C2×#41×C37D411yescharacteristic
84C2×#41×C37D411yescharacteristic
85C2×#41×C37C2311yescharacteristic
86C2×#41×C37C2311yescharacteristic
87C2×#41×C37C2311yescharacteristic
88C22×Q8×C37D411yescharacteristic
89C22×D4×C37—21no—
90C22×D4×C37—22no—
91C22×D4×C37—22no—
92C22×D4×C37—21no—
93C22×D4×C37—21no—
94C22×D4×C37D411yescharacteristic
95C22×D4×C37D412yes—
96C22×D4×C37C2311yescharacteristic
97C23×C4×C37—21no—
98C23×C4×C37C2311yescharacteristic
99C2×M16×C37—21no—
100C2×M16×C37—41no—
101C2×M16×C37—41no—
102C2×M16×C37C2311yescharacteristic
103C2×M16×C37C2311yescharacteristic
104C2×M16×C37C2311yescharacteristic
105C2×M16×C37C2311yescharacteristic
106C22×C8×C37—21no—
107#127×C37—22no—
108#127×C37—21no—
109#124×C37—22no—
110#124×C37—21no—
111#123×C37—22no—
112#123×C37—21no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37—21no—
115C22⋊Q8×C37—21no—
116C22⋊Q8×C37D411yescharacteristic
117C22⋊Q8×C37D411yescharacteristic
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—22no—
123#121×C37—21no—
124#121×C37—21no—
125#121×C37—21no—
126#121×C37—21no—
127#121×C37—21no—
128#121×C37—21no—
129#121×C37—22no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37D411yescharacteristic
133#121×C37D411yescharacteristic
134#120×C37—22no—
135#120×C37—22no—
136#120×C37—22no—
137#120×C37—21no—
138#120×C37—22no—
139C4×Q8×C37—21no—
140C4×D4×C37—22no—
141C4×D4×C37—22no—
142C4×D4×C37—21no—
143C4×D4×C37—22no—
144C4×D4×C37—21no—
145C4×D4×C37—21no—
146#117×C37—21no—
147#117×C37—21no—
148#117×C37—21no—
149#117×C37—21no—
150#117×C37—21no—
151#117×C37C2311yescharacteristic
152C2×C4⋊C4×C37—21no—
153C2×C4⋊C4×C37—22no—
154C2×C4⋊C4×C37C2311yescharacteristic
155C2×C4⋊C4×C37C2311yescharacteristic
156C2×C4⋊C4×C37C2311yescharacteristic
157C2×C22⋊C4×C37—22no—
158C2×C22⋊C4×C37—21no—
159C2×C22⋊C4×C37—22no—
160C2×C22⋊C4×C37—21no—
161C2×C22⋊C4×C37—22no—
162C2×C22⋊C4×C37D412yes—
163C2×C42×C37—21no—
164C2×C42×C37C2311yescharacteristic
165C2×C42×C37C2311yescharacteristic
166#107×C37—21no—
167#107×C37—21no—
168#106×C37—21no—
169#106×C37—21no—
170#104×C37—22no—
171#104×C37—22no—
172#104×C37—41no—
173#104×C37—41no—
174#104×C37—41no—
175#104×C37—41no—
176#103×C37—21no—
177#103×C37—21no—
178#103×C37—21no—
179#103×C37—21no—
180#103×C37—21no—
181#103×C37—21no—
182#102×C37—21no—
183#102×C37—21no—
184#102×C37—21no—
185#102×C37—21no—
186#102×C37—21no—
187#102×C37—21no—
188#100×C37—41no—
189#100×C37—41no—
190C22⋊C8×C37—21no—
191C22⋊C8×C37—21no—
192#95×C37—21no—
193#95×C37—22no—
194C24×C37—22no—
195C24×C37—21no—
196C24×C37C2×D412yes—
197C24×C37C2×D411yescharacteristic
198#41×C37—21no—
199#41×C37—21no—
200#41×C37—22no—
201#41×C37—22no—
202#41×C37—21no—
203#41×C37—21no—
204#41×C37—21no—
205#41×C37—21no—
206#41×C37—21no—
207#41×C37—21no—
208#41×C37—21no—
209#41×C37—21no—
210#41×C37—42no—
211#41×C37—42no—
212#41×C37—41no—
213#41×C37—41no—
214#41×C37—42no—
215#41×C37—42no—
216#41×C37—42no—
217#41×C37—42no—
218#41×C37—42no—
219#41×C37—42no—
220#41×C37#4112yes—
221#41×C37#4112yes—
222C2×Q8×C37—21no—
223C2×Q8×C37—22no—
224C2×Q8×C37—41no—
225C2×Q8×C37C2×D411yescharacteristic
226C2×Q8×C37C2×D411yescharacteristic
227C2×Q8×C37C2×D411yescharacteristic
228C2×D4×C37—21no—
229C2×D4×C37—22no—
230C2×D4×C37—22no—
231C2×D4×C37—22no—
232C2×D4×C37—22no—
233C2×D4×C37—21no—
234C2×D4×C37—21no—
235C2×D4×C37—21no—
236C2×D4×C37—21no—
237C2×D4×C37—21no—
238C2×D4×C37—22no—
239C2×D4×C37—22no—
240C2×D4×C37—22no—
241C2×D4×C37—21no—
242C2×D4×C37—22no—
243C2×D4×C37—21no—
244C2×D4×C37—21no—
245C2×D4×C37—21no—
246C2×D4×C37—21no—
247C2×D4×C37—21no—
248C2×D4×C37—21no—
249C2×D4×C37—21no—
250C2×D4×C37—41no—
251C2×D4×C37—42no—
252C2×D4×C37—42no—
253C2×D4×C37—42no—
254C2×D4×C37—42no—
255C2×D4×C37—44no—
256C2×D4×C37—44no—
257C2×D4×C37—42no—
258C2×D4×C37—42no—
259C2×D4×C37—82no—
260C2×D4×C37—84no—
261C2×D4×C37C2×D411yescharacteristic
262C2×D4×C37C2×D411yescharacteristic
263C2×D4×C37C2×D411yescharacteristic
264C22×C4×C37—21no—
265C22×C4×C37—21no—
266C22×C4×C37—21no—
267C22×C4×C37—21no—
268C22×C4×C37—21no—
269C22×C4×C37—22no—
270C22×C4×C37—21no—
271C22×C4×C37—21no—
272C22×C4×C37—22no—
273C22×C4×C37—21no—
274C22×C4×C37—21no—
275C22×C4×C37—21no—
276C22×C4×C37—21no—
277C22×C4×C37—21no—
278C22×C4×C37—21no—
279C22×C4×C37—21no—
280C22×C4×C37—42no—
281C22×C4×C37—42no—
282C22×C4×C37C2×D411yescharacteristic
283C22×C4×C37C2×D411yescharacteristic
284C22×C4×C37C2×D411yescharacteristic
285C22×C4×C37C2×D411yescharacteristic
286C22×C4×C37C2×D411yescharacteristic
287C22×C4×C37C2×D412yes—
288C22×C4×C37C2411yescharacteristic
289M16×C37—21no—
290M16×C37—21no—
291M16×C37—21no—
292M16×C37—21no—
293M16×C37—21no—
294M16×C37—21no—
295M16×C37—21no—
296M16×C37—21no—
297M16×C37—42no—
298C2×C8×C37—21no—
299C2×C8×C37—21no—
300C2×C8×C37—21no—
301C2×C8×C37—21no—
302C2×C8×C37—42no—
303C4⋊C4×C37—22no—
304C4⋊C4×C37—22no—
305C4⋊C4×C37—21no—
306C4⋊C4×C37—21no—
307C4⋊C4×C37—21no—
308C4⋊C4×C37—21no—
309C4⋊C4×C37—21no—
310C4⋊C4×C37—21no—
311C4⋊C4×C37—21no—
312C4⋊C4×C37—21no—
313C4⋊C4×C37—82no—
314C4⋊C4×C37C2×D411yescharacteristic
315C4⋊C4×C37C2×D411yescharacteristic
316C22⋊C4×C37—22no—
317C22⋊C4×C37—22no—
318C22⋊C4×C37—22no—
319C22⋊C4×C37—22no—
320C22⋊C4×C37—22no—
321C22⋊C4×C37—21no—
322C22⋊C4×C37—21no—
323C22⋊C4×C37—21no—
324C22⋊C4×C37—21no—
325C22⋊C4×C37—22no—
326C22⋊C4×C37—22no—
327C22⋊C4×C37—21no—
328C22⋊C4×C37—42no—
329C22⋊C4×C37—44no—
330C22⋊C4×C37—41no—
331C22⋊C4×C37—41no—
332C22⋊C4×C37—82no—
333C42×C37—22no—
334C42×C37—21no—
335C42×C37—21no—
336C42×C37—21no—
337C42×C37—21no—
338C42×C37—21no—
339C42×C37—41no—
340C42×C37—41no—
341C23×C37—21no—
342C23×C37—21no—
343C23×C37—21no—
344C23×C37—22no—
345C23×C37—21no—
346C23×C37—21no—
347C23×C37—22no—
348C23×C37—22no—
349C23×C37—41no—
350C23×C37—41no—
351C23×C37—42no—
352C23×C37—42no—
353C23×C37—44no—
354C23×C37—42no—
355C23×C37—42no—
356C23×C37—81no—
357C23×C37—82no—
358C23×C37—82no—
359C23×C37#12011yescharacteristic
360C23×C37#12011yescharacteristic
361C23×C37C22×D411yescharacteristic
362Q8×C37—21no—
363Q8×C37—21no—
364Q8×C37—21no—
365Q8×C37—21no—
366Q8×C37—21no—
367Q8×C37—42no—
368Q8×C37#12312yes—
369D4×C37—22no—
370D4×C37—22no—
371D4×C37—21no—
372D4×C37—21no—
373D4×C37—21no—
374D4×C37—21no—
375D4×C37—21no—
376D4×C37—42no—
377D4×C37—42no—
378D4×C37—44no—
379D4×C37—42no—
380D4×C37—44no—
381D4×C37—44no—
382D4×C37—42no—
383D4×C37—41no—
384D4×C37—41no—
385D4×C37—41no—
386D4×C37—41no—
387D4×C37—41no—
388D4×C37—41no—
389D4×C37—41no—
390D4×C37—41no—
391D4×C37—81no—
392D4×C37—82no—
393D4×C37—82no—
394D4×C37—82no—
395D4×C37—82no—
396D4×C37#12312yes—
397C2×C4×C37—21no—
398C2×C4×C37—21no—
399C2×C4×C37—21no—
400C2×C4×C37—21no—
401C2×C4×C37—21no—
402C2×C4×C37—21no—
403C2×C4×C37—21no—
404C2×C4×C37—21no—
405C2×C4×C37—21no—
406C2×C4×C37—21no—
407C2×C4×C37—21no—
408C2×C4×C37—22no—
409C2×C4×C37—22no—
410C2×C4×C37—22no—
411C2×C4×C37—21no—
412C2×C4×C37—22no—
413C2×C4×C37—21no—
414C2×C4×C37—21no—
415C2×C4×C37—21no—
416C2×C4×C37—42no—
417C2×C4×C37—42no—
418C2×C4×C37—42no—
419C2×C4×C37—44no—
420C2×C4×C37—41no—
421C2×C4×C37—41no—
422C2×C4×C37—41no—
423C2×C4×C37—41no—
424C2×C4×C37—41no—
425C2×C4×C37—41no—
426C2×C4×C37—42no—
427C2×C4×C37—41no—
428C2×C4×C37—42no—
429C2×C4×C37—41no—
430C2×C4×C37—42no—
431C2×C4×C37—41no—
432C2×C4×C37—41no—
433C2×C4×C37—41no—
434C2×C4×C37—82no—
435C2×C4×C37#12011yescharacteristic
436C2×C4×C37#12011yescharacteristic
437C2×C4×C37C22×D411yescharacteristic
438C2×C4×C37C22×D411yescharacteristic
439C2×C4×C37C2×#4111yescharacteristic
440C2×C4×C37C2×#4111yescharacteristic
441C2×C4×C37H(5,𝔽2)11yescharacteristic
442C2×C4×C37H(5,𝔽2)11yescharacteristic
443C8×C37—41no—
444C8×C37—41no—
445C8×C37—41no—
446C8×C37—41no—
447#24031C3711yesmaximal, characteristic, direct product factor, Sylow
448C22×C37—21no—
449C22×C37—21no—
450C22×C37—21no—
451C22×C37—21no—
452C22×C37—22no—
453C22×C37—21no—
454C22×C37—21no—
455C22×C37—21no—
456C22×C37—21no—
457C22×C37—41no—
458C22×C37—41no—
459C22×C37—41no—
460C22×C37—41no—
461C22×C37—42no—
462C22×C37—41no—
463C22×C37—42no—
464C22×C37—41no—
465C22×C37—42no—
466C22×C37—41no—
467C22×C37—41no—
468C22×C37—81no—
469C22×C37—81no—
470C22×C37—82no—
471C22×C37—82no—
472C22×C37—84no—
473C22×C37—164no—
474C22×C37C2×#12011yescharacteristic
475C22×C37#54611yescharacteristic
476C22×C37#54611yescharacteristic
477C4×C37—21no—
478C4×C37—21no—
479C4×C37—22no—
480C4×C37—42no—
481C4×C37—41no—
482C4×C37—41no—
483C4×C37—41no—
484C4×C37—42no—
485C4×C37—41no—
486C4×C37—81no—
487C4×C37—81no—
488C4×C37—81no—
489C4×C37C2×#12311yescharacteristic
490C4×C37#53411yescharacteristic
491C4×C37#54611yescharacteristic
492C4×C37#54611yescharacteristic
493#3488C2×C3711yescharacteristic
494#3093C2×C3711yescharacteristic, complemented
495#2896C2×C3711yescharacteristic, complemented
496#2500C2×C3711yescharacteristic, complemented
497#2040C2×C3711yescharacteristic, complemented
498#2039C2×C3711yescharacteristic, complemented
499#2037C2×C3711yescharacteristic, complemented
500#2037C2×C3711yescharacteristic, complemented
501#1900C2×C3711yescharacteristic, complemented
502#1871C2×C3711yescharacteristic, complemented
503#1860C2×C3711yescharacteristic, complemented
504#1859C2×C3711yescharacteristic, complemented
505#1792C2×C3711yescharacteristic, complemented
506#1792C2×C3711yescharacteristic, complemented
507#1789C2×C3711yescharacteristic, complemented
508C2×C37—21no—
509C2×C37—21no—
510C2×C37—41no—
511C2×C37—41no—
512C2×C37—42no—
513C2×C37—81no—
514C2×C37—82no—
515C2×C37—81no—
516C2×C37#240511yescharacteristic
517C2×C37#301811yescharacteristic
518C2×C37#301911yescharacteristic
519C2×H(5,𝔽2)C22×C3711yescharacteristic
520C22×#41C22×C3711yescharacteristic
521C22×M16C22×C3711yescharacteristic, complemented
522#550—21no—
523#548—21no—
524#546—21no—
525#546—22no—
526D42—22no—
527D42—21no—
528#537—21no—
529#537C22×C3711yescharacteristic
530#535—21no—
531#535C22×C3711yescharacteristic
532#525—21no—
533#525C22×C3711yescharacteristic
534C2×#121—21no—
535C2×#121C22×C3711yescharacteristic
536#520C22×C3711yescharacteristic
537C2×#117C22×C3711yescharacteristic, complemented
538#485—21no—
539#485—21no—
540#482—21no—
541#482—21no—
542#428C22×C3711yescharacteristic, complemented
543#428C22×C3711yescharacteristic, complemented
544C2×#104C22×C3711yescharacteristic
545C2×#104C22×C3711yescharacteristic
546C2×#104C22×C3711yescharacteristic, complemented
547C2×#104C22×C3711yescharacteristic, complemented
548C2×#104C22×C3711yescharacteristic, complemented
549C2×#104C22×C3711yescharacteristic, complemented
550#419—21no—
551#418—21no—
552#417C22×C3711yescharacteristic
553#417C22×C3711yescharacteristic
554#417C22×C3711yescharacteristic, complemented
555#417C22×C3711yescharacteristic, complemented
556#417C22×C3711yescharacteristic, complemented
557#417C22×C3711yescharacteristic, complemented
558#416—21no—
559#416—21no—
560C2×#100C22×C3711yescharacteristic, complemented
561C2×#100C22×C3711yescharacteristic, complemented
562#407C22×C3711yescharacteristic, complemented
563#394—22no—
564#390C22×C3711yescharacteristic, complemented
565#390C22×C3711yescharacteristic, complemented
566#388—22no—
567#384C22×C3711yescharacteristic, complemented
568#382C22×C3711yescharacteristic, complemented
569C4×C22⋊C4C22×C3711yescharacteristic, complemented
570#343C22×C3711yescharacteristic, complemented
571#343C22×C3711yescharacteristic, complemented
572#339C22×C3711yescharacteristic, complemented
573#339C22×C3711yescharacteristic, complemented
574C37#2403111yescharacteristic, direct product factor, Sylow
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C3711yescharacteristic
588C2×#41D4×C3711yescharacteristic
589C2×#41C23×C3711yescharacteristic
590C2×#41C23×C3711yescharacteristic
591C2×#41C23×C3711yescharacteristic
592C22×Q8D4×C3711yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C3711yescharacteristic
599C22×D4D4×C3712yes—
600C22×D4C23×C3711yescharacteristic
601C23×C4—21no—
602C23×C4C23×C3711yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C3711yescharacteristic
607C2×M16C23×C3711yescharacteristic
608C2×M16C23×C3711yescharacteristic
609C2×M16C23×C3711yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C3711yescharacteristic
621C22⋊Q8D4×C3711yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C3711yescharacteristic
637#121D4×C3711yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C3711yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C3711yescharacteristic
659C2×C4⋊C4C23×C3711yescharacteristic
660C2×C4⋊C4C23×C3711yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C3712yes—
667C2×C42—21no—
668C2×C42C23×C3711yescharacteristic
669C2×C42C23×C3711yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C3712yes—
701C24C2×D4×C3711yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C3712yes—
725#41#41×C3712yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C3711yescharacteristic
730C2×Q8C2×D4×C3711yescharacteristic
731C2×Q8C2×D4×C3711yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C3711yescharacteristic
766C2×D4C2×D4×C3711yescharacteristic
767C2×D4C2×D4×C3711yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C3711yescharacteristic
787C22×C4C2×D4×C3711yescharacteristic
788C22×C4C2×D4×C3711yescharacteristic
789C22×C4C2×D4×C3711yescharacteristic
790C22×C4C2×D4×C3711yescharacteristic
791C22×C4C2×D4×C3712yes—
792C22×C4C24×C3711yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C3711yescharacteristic
819C4⋊C4C2×D4×C3711yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C3711yescharacteristic
864C23#120×C3711yescharacteristic
865C23C22×D4×C3711yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C3712yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C3712yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C3711yescharacteristic
940C2×C4#120×C3711yescharacteristic
941C2×C4C22×D4×C3711yescharacteristic
942C2×C4C22×D4×C3711yescharacteristic
943C2×C4C2×#41×C3711yescharacteristic
944C2×C4C2×#41×C3711yescharacteristic
945C2×C4H(5,𝔽2)×C3711yescharacteristic
946C2×C4H(5,𝔽2)×C3711yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C3711yescharacteristic
978C22C37×#54611yescharacteristic
979C22C37×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C3711yescharacteristic
993C4C37×#53411yescharacteristic
994C4C37×#54611yescharacteristic
995C4C37×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C37×#240511yescharacteristic
1005C2C37×#301811yescharacteristic
1006C2C37×#301911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3488C2
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
2. C37×#3093C2semidirect
3. C37×#2896C2semidirect
4. C37×#2500C2semidirect
5. C37×#2040C2semidirect
6. C37×#2039C2semidirect
7. C37×#2037C2semidirect
8. C37×#2037C2semidirect
9. C37×#1900C2semidirect
10. C37×#1871C2semidirect
11. C37×#1860C2semidirect
12. C37×#1859C2semidirect
13. C37×#1792C2semidirect
14. C37×#1792C2semidirect
15. C37×#1789C2semidirect
18. C22×M16×C37C22semidirect
34. C2×#117×C37C22semidirect
39. C37×#428C22semidirect
40. C37×#428C22semidirect
43. C2×#104×C37C22semidirect
44. C2×#104×C37C22semidirect
45. C2×#104×C37C22semidirect
46. C2×#104×C37C22semidirect
51. C37×#417C22semidirect
52. C37×#417C22semidirect
53. C37×#417C22semidirect
54. C37×#417C22semidirect
57. C2×#100×C37C22semidirect
58. C2×#100×C37C22semidirect
59. C37×#407C22semidirect
61. C37×#390C22semidirect
62. C37×#390C22semidirect
64. C37×#384C22semidirect
65. C37×#382C22semidirect
66. C4×C22⋊C4×C37C22semidirect
67. C37×#343C22semidirect
68. C37×#343C22semidirect
69. C37×#339C22semidirect
70. C37×#339C22semidirect
447. #24031C37direct (N × H)
494. #3093C2×C37semidirect
495. #2896C2×C37semidirect
496. #2500C2×C37semidirect
497. #2040C2×C37semidirect
498. #2039C2×C37semidirect
499. #2037C2×C37semidirect
500. #2037C2×C37semidirect
501. #1900C2×C37semidirect
502. #1871C2×C37semidirect
503. #1860C2×C37semidirect
504. #1859C2×C37semidirect
505. #1792C2×C37semidirect
506. #1792C2×C37semidirect
507. #1789C2×C37semidirect
521. C22×M16C22×C37semidirect
537. C2×#117C22×C37semidirect
542. #428C22×C37semidirect
543. #428C22×C37semidirect
546. C2×#104C22×C37semidirect
547. C2×#104C22×C37semidirect
548. C2×#104C22×C37semidirect
549. C2×#104C22×C37semidirect
554. #417C22×C37semidirect
555. #417C22×C37semidirect
556. #417C22×C37semidirect
557. #417C22×C37semidirect
560. C2×#100C22×C37semidirect
561. C2×#100C22×C37semidirect
562. #407C22×C37semidirect
564. #390C22×C37semidirect
565. #390C22×C37semidirect
567. #384C22×C37semidirect
568. #382C22×C37semidirect
569. C4×C22⋊C4C22×C37semidirect
570. #343C22×C37semidirect
571. #343C22×C37semidirect
572. #339C22×C37semidirect
573. #339C22×C37semidirect
574. C37#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34882
C37×#30932
C37×#28962
C37×#25002
C37×#20402
C37×#20392
C37×#20372
C37×#19002
C37×#18712
C37×#18602
C37×#18592
C37×#17922
C37×#17892
#2403137