Finite Group Databasebeta

← C37×#18252 #22639505

Subgroups — C37×#18252 #22639505

Order 9472.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3534C211yesmaximal, characteristic, complemented
2C37×#3006C211yesmaximal, characteristic, complemented
3C37×#3002C211yesmaximal, characteristic, complemented
4C37×#2430C211yesmaximal, characteristic, complemented
5C37×#1606C211yesmaximal, characteristic, complemented
6C37×#1604C211yesmaximal, characteristic, complemented
7C37×#1603C211yesmaximal, characteristic, complemented
8C37×#1601C211yesmaximal, characteristic, complemented
9C37×#1600C211yesmaximal, characteristic, complemented
10C37×#1598C211yesmaximal, characteristic, complemented
11C37×#1597C211yesmaximal, characteristic, complemented
12C37×#1595C211yesmaximal, characteristic, complemented
13C37×#1504C211yesmaximal, characteristic, complemented
14C2×C37×#327C211yesmaximal, characteristic, complemented
15C37×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C37—21no—
18C2×#135×C37—21no—
19C37×#562—21no—
20C37×#560—21no—
21C37×#553—21no—
22C37×#551—21no—
23C37×#546—21no—
24C37×#546—21no—
25C37×#546—21no—
26D42×C37—21no—
27C37×#540—21no—
28C37×#539—21no—
29C37×#539C2211yescharacteristic
30C37×#538—21no—
31C37×#538C2211yescharacteristic
32C37×#537C2211yescharacteristic
33C37×#534—21no—
34C37×#534C2211yescharacteristic
35C37×#525C2211yescharacteristic
36C2×#123×C37C2211yescharacteristic
37C2×#121×C37—21no—
38C2×#121×C37C2211yescharacteristic
39C37×#452—21no—
40C37×#451C2211yescharacteristic, complemented
41C37×#450C2211yescharacteristic, complemented
42C37×#449—21no—
43C37×#449—21no—
44C37×#449—21no—
45C37×#448C2211yescharacteristic
46C37×#448C2211yescharacteristic, complemented
47C37×#448C2211yescharacteristic, complemented
48C37×#447C2211yescharacteristic
49C37×#447C2211yescharacteristic, complemented
50C37×#447C2211yescharacteristic, complemented
51C37×#417—21no—
52C37×#416—21no—
53C37×#407C2211yescharacteristic, complemented
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C37×#395C2211yescharacteristic, complemented
56C37×#394C2211yescharacteristic, complemented
57C37×#393C2211yescharacteristic, complemented
58C37×#392C2211yescharacteristic, complemented
59C37×#386—21no—
60C37×#386—21no—
61C37×#385—21no—
62C2×#95×C37C2211yescharacteristic, complemented
63C37×#328C2211yescharacteristic, complemented
64C37×#328C2211yescharacteristic, complemented
65C37×#327C2211yescharacteristic
66C37×#327C2211yescharacteristic
67C37×#327C2211yescharacteristic, complemented
68C37×#327C2211yescharacteristic, complemented
69C37×#327C2211yescharacteristic, complemented
70C37×#327C2211yescharacteristic, complemented
71C37×#324C2211yescharacteristic, complemented
72C37×#324C2211yescharacteristic, complemented
73C37×#323C2211yescharacteristic, complemented
74C37×#323C2211yescharacteristic, complemented
75C2×#41×C37—21no—
76C2×#41×C37—21no—
77C2×#41×C37—21no—
78C2×#41×C37—21no—
79C2×#41×C37—21no—
80C2×#41×C37—44no—
81C2×#41×C37D411yescharacteristic, complemented
82C22×Q8×C37C2311yescharacteristic
83C22×D4×C37—21no—
84C22×D4×C37—21no—
85C22×D4×C37—21no—
86C22×D4×C37—21no—
87C22×D4×C37—21no—
88C22×D4×C37D411yescharacteristic
89C22×D4×C37D411yescharacteristic, complemented
90C22×D4×C37C2311yescharacteristic
91C23×C4×C37—21no—
92C23×C4×C37—21no—
93C23×C4×C37C2311yescharacteristic
94AGL(1,ℤ/8)×C37—44no—
95#135×C37—44no—
96C2×Q16×C37—21no—
97C2×SD16×C37—21no—
98C2×SD16×C37—21no—
99C2×SD16×C37—21no—
100C2×SD16×C37—21no—
101C2×D8×C37—21no—
102C2×D8×C37—21no—
103C2×D8×C37—21no—
104C2×M16×C37—21no—
105C22×C8×C37—21no—
106#127×C37—21no—
107#126×C37—21no—
108#126×C37—21no—
109#126×C37—21no—
110#126×C37—21no—
111#125×C37—21no—
112#125×C37—21no—
113#124×C37—21no—
114#124×C37—21no—
115#124×C37—21no—
116#123×C37—21no—
117#123×C37—21no—
118#123×C37—21no—
119#123×C37—21no—
120#123×C37—21no—
121#123×C37—21no—
122#123×C37—21no—
123#123×C37—21no—
124#123×C37—21no—
125#123×C37—21no—
126#123×C37—21no—
127#123×C37—21no—
128#123×C37—21no—
129#123×C37—21no—
130C22⋊Q8×C37—21no—
131C22⋊Q8×C37—21no—
132C22⋊Q8×C37—21no—
133C22⋊Q8×C37—21no—
134C22⋊Q8×C37—21no—
135C22⋊Q8×C37D411yescharacteristic, complemented
136C22⋊Q8×C37C2311yescharacteristic
137#121×C37—21no—
138#121×C37—21no—
139#121×C37—21no—
140#121×C37—21no—
141#121×C37—21no—
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—21no—
149#121×C37—21no—
150#121×C37—21no—
151#121×C37—21no—
152#121×C37—44no—
153#121×C37D411yescharacteristic, complemented
154#121×C37D411yescharacteristic, complemented
155#121×C37D411yescharacteristic, complemented
156#121×C37C2311yescharacteristic
157#121×C37C2311yescharacteristic
158#121×C37C2311yescharacteristic
159#120×C37—21no—
160#120×C37—21no—
161#120×C37—21no—
162#120×C37—21no—
163#120×C37—21no—
164#120×C37—21no—
165#120×C37—21no—
166#120×C37—21no—
167C4×D4×C37—21no—
168C4×D4×C37—21no—
169C4×D4×C37—21no—
170C4×D4×C37—21no—
171C4×D4×C37—21no—
172C4×D4×C37—21no—
173C4×D4×C37—21no—
174C4×D4×C37—21no—
175#117×C37—21no—
176#117×C37D411yescharacteristic, complemented
177C2×C4⋊C4×C37—21no—
178C2×C4⋊C4×C37D411yescharacteristic
179C2×C4⋊C4×C37D411yescharacteristic, complemented
180C2×C4⋊C4×C37C2311yescharacteristic
181C2×C22⋊C4×C37—21no—
182C2×C22⋊C4×C37—21no—
183C2×C22⋊C4×C37—21no—
184C2×C22⋊C4×C37—21no—
185C2×C22⋊C4×C37—21no—
186C2×C22⋊C4×C37—21no—
187C2×C22⋊C4×C37—21no—
188C2×C22⋊C4×C37D411yescharacteristic
189C2×C22⋊C4×C37D411yescharacteristic
190C2×C22⋊C4×C37C2311yescharacteristic
191#103×C37—21no—
192#103×C37—21no—
193#103×C37—21no—
194#103×C37—21no—
195#102×C37—21no—
196#102×C37—21no—
197#102×C37—21no—
198#102×C37—21no—
199C22⋊C8×C37—21no—
200C22⋊C8×C37—21no—
201C22⋊C8×C37C2311yescharacteristic
202C22⋊C8×C37C2311yescharacteristic
203C22⋊C8×C37C2311yescharacteristic
204C22⋊C8×C37C2311yescharacteristic
205#95×C37—21no—
206#95×C37—21no—
207#95×C37—21no—
208#95×C37C2311yescharacteristic
209#95×C37C2311yescharacteristic
210C24×C37—21no—
211C24×C37—21no—
212C24×C37—21no—
213C24×C37C2×D411yescharacteristic
214C24×C37C2×D411yescharacteristic
215#41×C37—24no—
216#41×C37—24no—
217#41×C37—42no—
218#41×C37—42no—
219#41×C37—42no—
220#41×C37—42no—
221#41×C37—42no—
222#41×C37—42no—
223#41×C37—42no—
224#41×C37—81no—
225#41×C37—81no—
226C2×Q8×C37—21no—
227C2×Q8×C37—21no—
228C2×Q8×C37—21no—
229C2×Q8×C37—42no—
230C2×Q8×C37C2×D411yescharacteristic
231C2×D4×C37—24no—
232C2×D4×C37—21no—
233C2×D4×C37—21no—
234C2×D4×C37—21no—
235C2×D4×C37—21no—
236C2×D4×C37—21no—
237C2×D4×C37—21no—
238C2×D4×C37—21no—
239C2×D4×C37—21no—
240C2×D4×C37—21no—
241C2×D4×C37—21no—
242C2×D4×C37—21no—
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—21no—
251C2×D4×C37—42no—
252C2×D4×C37—42no—
253C2×D4×C37—42no—
254C2×D4×C37—42no—
255C2×D4×C37—41no—
256C2×D4×C37—41no—
257C2×D4×C37—42no—
258C2×D4×C37—42no—
259C2×D4×C37—81no—
260C2×D4×C37—81no—
261C2×D4×C37—81no—
262C2×D4×C37—81no—
263C2×D4×C37—81no—
264C2×D4×C37—82no—
265C2×D4×C37C2×D411yescharacteristic
266C2×D4×C37C2×D411yescharacteristic
267C2×D4×C37C2×D411yescharacteristic
268C22×C4×C37—21no—
269C22×C4×C37—21no—
270C22×C4×C37—21no—
271C22×C4×C37—21no—
272C22×C4×C37—21no—
273C22×C4×C37—21no—
274C22×C4×C37—21no—
275C22×C4×C37—21no—
276C22×C4×C37—21no—
277C22×C4×C37—21no—
278C22×C4×C37—42no—
279C22×C4×C37—42no—
280C22×C4×C37—42no—
281C22×C4×C37—42no—
282C22×C4×C37—41no—
283C22×C4×C37—41no—
284C22×C4×C37—42no—
285C22×C4×C37—81no—
286C22×C4×C37C2×D411yescharacteristic
287C22×C4×C37C2×D411yescharacteristic
288C22×C4×C37C2×D411yescharacteristic
289C22×C4×C37C2×D411yescharacteristic
290C22×C4×C37C2×D411yescharacteristic
291C22×C4×C37C2×D411yescharacteristic
292C22×C4×C37C2×D411yescharacteristic
293C22×C4×C37C2×D411yescharacteristic
294C22×C4×C37C2411yescharacteristic
295Q16×C37—42no—
296SD16×C37—42no—
297SD16×C37—42no—
298SD16×C37—42no—
299SD16×C37—42no—
300D8×C37—42no—
301D8×C37—42no—
302D8×C37—42no—
303M16×C37—42no—
304C2×C8×C37—21no—
305C2×C8×C37—21no—
306C2×C8×C37—21no—
307C2×C8×C37—21no—
308C2×C8×C37—42no—
309C4⋊C4×C37—21no—
310C4⋊C4×C37—21no—
311C4⋊C4×C37—21no—
312C4⋊C4×C37—21no—
313C4⋊C4×C37—21no—
314C4⋊C4×C37—21no—
315C4⋊C4×C37—21no—
316C4⋊C4×C37—21no—
317C4⋊C4×C37—21no—
318C4⋊C4×C37—21no—
319C4⋊C4×C37—21no—
320C4⋊C4×C37—21no—
321C4⋊C4×C37—21no—
322C4⋊C4×C37—42no—
323C4⋊C4×C37C2×D411yescharacteristic
324C4⋊C4×C37C2×D411yescharacteristic
325C4⋊C4×C37C2×D411yescharacteristic
326C4⋊C4×C37C2×D411yescharacteristic
327C22⋊C4×C37—21no—
328C22⋊C4×C37—21no—
329C22⋊C4×C37—21no—
330C22⋊C4×C37—21no—
331C22⋊C4×C37—21no—
332C22⋊C4×C37—21no—
333C22⋊C4×C37—21no—
334C22⋊C4×C37—21no—
335C22⋊C4×C37—21no—
336C22⋊C4×C37—21no—
337C22⋊C4×C37—21no—
338C22⋊C4×C37—21no—
339C22⋊C4×C37—21no—
340C22⋊C4×C37—21no—
341C22⋊C4×C37—21no—
342C22⋊C4×C37—21no—
343C22⋊C4×C37—21no—
344C22⋊C4×C37—21no—
345C22⋊C4×C37—21no—
346C22⋊C4×C37—21no—
347C22⋊C4×C37—21no—
348C22⋊C4×C37—21no—
349C22⋊C4×C37—21no—
350C22⋊C4×C37—21no—
351C22⋊C4×C37—21no—
352C22⋊C4×C37—42no—
353C22⋊C4×C37—42no—
354C22⋊C4×C37—42no—
355C22⋊C4×C37—81no—
356C42×C37—21no—
357C42×C37—21no—
358C42×C37—21no—
359C23×C37—21no—
360C23×C37—21no—
361C23×C37—22no—
362C23×C37—22no—
363C23×C37—21no—
364C23×C37—21no—
365C23×C37—21no—
366C23×C37—21no—
367C23×C37—21no—
368C23×C37—21no—
369C23×C37—41no—
370C23×C37—41no—
371C23×C37—41no—
372C23×C37—41no—
373C23×C37—41no—
374C23×C37—41no—
375C23×C37—41no—
376C23×C37—41no—
377C23×C37—41no—
378C23×C37—42no—
379C23×C37—81no—
380C23×C37—81no—
381C23×C37—81no—
382C23×C37—81no—
383C23×C37—81no—
384C23×C37#12011yescharacteristic
385C23×C37#12011yescharacteristic
386C23×C37C22×D411yescharacteristic
387Q8×C37—22no—
388Q8×C37—22no—
389Q8×C37—41no—
390Q8×C37—41no—
391Q8×C37—41no—
392Q8×C37—81no—
393D4×C37—22no—
394D4×C37—22no—
395D4×C37—41no—
396D4×C37—41no—
397D4×C37—41no—
398D4×C37—41no—
399D4×C37—41no—
400D4×C37—44no—
401D4×C37—41no—
402D4×C37—41no—
403D4×C37—41no—
404D4×C37—41no—
405D4×C37—41no—
406D4×C37—41no—
407D4×C37—44no—
408D4×C37—42no—
409D4×C37—42no—
410D4×C37—81no—
411D4×C37—81no—
412D4×C37—81no—
413D4×C37—81no—
414D4×C37—81no—
415D4×C37—81no—
416D4×C37—81no—
417D4×C37—81no—
418D4×C37—81no—
419D4×C37—81no—
420D4×C37—81no—
421D4×C37—81no—
422D4×C37—84no—
423C2×C4×C37—22no—
424C2×C4×C37—22no—
425C2×C4×C37—22no—
426C2×C4×C37—22no—
427C2×C4×C37—21no—
428C2×C4×C37—21no—
429C2×C4×C37—21no—
430C2×C4×C37—21no—
431C2×C4×C37—21no—
432C2×C4×C37—21no—
433C2×C4×C37—21no—
434C2×C4×C37—21no—
435C2×C4×C37—21no—
436C2×C4×C37—21no—
437C2×C4×C37—41no—
438C2×C4×C37—41no—
439C2×C4×C37—41no—
440C2×C4×C37—41no—
441C2×C4×C37—44no—
442C2×C4×C37—44no—
443C2×C4×C37—41no—
444C2×C4×C37—41no—
445C2×C4×C37—41no—
446C2×C4×C37—41no—
447C2×C4×C37—41no—
448C2×C4×C37—41no—
449C2×C4×C37—41no—
450C2×C4×C37—41no—
451C2×C4×C37—41no—
452C2×C4×C37—81no—
453C2×C4×C37—81no—
454C2×C4×C37—81no—
455C2×C4×C37—81no—
456C2×C4×C37—81no—
457C2×C4×C37—81no—
458C2×C4×C37—81no—
459C2×C4×C37—84no—
460C2×C4×C37#12011yescharacteristic
461C2×C4×C37#12011yescharacteristic
462C2×C4×C37C22×D411yescharacteristic
463C2×C4×C37C22×D411yescharacteristic
464C8×C37—41no—
465C8×C37—41no—
466C8×C37—41no—
467C8×C37—41no—
468#18252C3711yesmaximal, characteristic, direct product factor, Sylow
469C22×C37—21no—
470C22×C37—21no—
471C22×C37—21no—
472C22×C37—21no—
473C22×C37—21no—
474C22×C37—21no—
475C22×C37—21no—
476C22×C37—42no—
477C22×C37—42no—
478C22×C37—42no—
479C22×C37—42no—
480C22×C37—41no—
481C22×C37—41no—
482C22×C37—41no—
483C22×C37—41no—
484C22×C37—41no—
485C22×C37—41no—
486C22×C37—41no—
487C22×C37—41no—
488C22×C37—42no—
489C22×C37—41no—
490C22×C37—41no—
491C22×C37—41no—
492C22×C37—41no—
493C22×C37—81no—
494C22×C37—81no—
495C22×C37—81no—
496C22×C37—81no—
497C22×C37—81no—
498C22×C37—81no—
499C22×C37—162no—
500C22×C37—162no—
501C22×C37B(4,𝔽2)12yes—
502C22×C37C2×#12011yescharacteristic
503C22×C37#57611yescharacteristic
504C22×C37#57711yescharacteristic
505C4×C37—21no—
506C4×C37—21no—
507C4×C37—21no—
508C4×C37—21no—
509C4×C37—42no—
510C4×C37—41no—
511C4×C37—41no—
512C4×C37—41no—
513C4×C37—41no—
514C4×C37—41no—
515C4×C37—41no—
516C4×C37—42no—
517C4×C37—41no—
518C4×C37—41no—
519C4×C37—81no—
520#3534C2×C3711yescharacteristic, complemented
521#3006C2×C3711yescharacteristic, complemented
522#3002C2×C3711yescharacteristic, complemented
523#2430C2×C3711yescharacteristic, complemented
524#1606C2×C3711yescharacteristic, complemented
525#1604C2×C3711yescharacteristic, complemented
526#1603C2×C3711yescharacteristic, complemented
527#1601C2×C3711yescharacteristic, complemented
528#1600C2×C3711yescharacteristic, complemented
529#1598C2×C3711yescharacteristic, complemented
530#1597C2×C3711yescharacteristic, complemented
531#1595C2×C3711yescharacteristic, complemented
532#1504C2×C3711yescharacteristic, complemented
533C2×#327C2×C3711yescharacteristic, complemented
534#1468C2×C3711yescharacteristic, complemented
535C2×C37—21no—
536C2×C37—21no—
537C2×C37—22no—
538C2×C37—41no—
539C2×C37—82no—
540C2×C37—81no—
541C2×C37—81no—
542C2×C37—81no—
543C2×C37—81no—
544C2×C37#301211yescharacteristic
545C2×C37#301811yescharacteristic
546C2×C37C2×B(4,𝔽2)11yescharacteristic
547C22×#41C22×C3711yescharacteristic, complemented
548C2×AGL(1,ℤ/8)—21no—
549C2×#135—21no—
550#562—21no—
551#560—21no—
552#553—21no—
553#551—21no—
554#546—21no—
555#546—21no—
556#546—21no—
557D42—21no—
558#540—21no—
559#539—21no—
560#539C22×C3711yescharacteristic
561#538—21no—
562#538C22×C3711yescharacteristic
563#537C22×C3711yescharacteristic
564#534—21no—
565#534C22×C3711yescharacteristic
566#525C22×C3711yescharacteristic
567C2×#123C22×C3711yescharacteristic
568C2×#121—21no—
569C2×#121C22×C3711yescharacteristic
570#452—21no—
571#451C22×C3711yescharacteristic, complemented
572#450C22×C3711yescharacteristic, complemented
573#449—21no—
574#449—21no—
575#449—21no—
576#448C22×C3711yescharacteristic
577#448C22×C3711yescharacteristic, complemented
578#448C22×C3711yescharacteristic, complemented
579#447C22×C3711yescharacteristic
580#447C22×C3711yescharacteristic, complemented
581#447C22×C3711yescharacteristic, complemented
582#417—21no—
583#416—21no—
584#407C22×C3711yescharacteristic, complemented
585C2×C22⋊C8C22×C3711yescharacteristic, complemented
586#395C22×C3711yescharacteristic, complemented
587#394C22×C3711yescharacteristic, complemented
588#393C22×C3711yescharacteristic, complemented
589#392C22×C3711yescharacteristic, complemented
590#386—21no—
591#386—21no—
592#385—21no—
593C2×#95C22×C3711yescharacteristic, complemented
594#328C22×C3711yescharacteristic, complemented
595#328C22×C3711yescharacteristic, complemented
596#327C22×C3711yescharacteristic
597#327C22×C3711yescharacteristic
598#327C22×C3711yescharacteristic, complemented
599#327C22×C3711yescharacteristic, complemented
600#327C22×C3711yescharacteristic, complemented
601#327C22×C3711yescharacteristic, complemented
602#324C22×C3711yescharacteristic, complemented
603#324C22×C3711yescharacteristic, complemented
604#323C22×C3711yescharacteristic, complemented
605#323C22×C3711yescharacteristic, complemented
606C37#1825211yescharacteristic, direct product factor, Sylow
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C3711yescharacteristic, complemented
614C22×Q8C23×C3711yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C3711yescharacteristic
621C22×D4D4×C3711yescharacteristic, complemented
622C22×D4C23×C3711yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C3711yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C3711yescharacteristic, complemented
668C22⋊Q8C23×C3711yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C3711yescharacteristic, complemented
686#121D4×C3711yescharacteristic, complemented
687#121D4×C3711yescharacteristic, complemented
688#121C23×C3711yescharacteristic
689#121C23×C3711yescharacteristic
690#121C23×C3711yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C3711yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C3711yescharacteristic
711C2×C4⋊C4D4×C3711yescharacteristic, complemented
712C2×C4⋊C4C23×C3711yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C3711yescharacteristic
721C2×C22⋊C4D4×C3711yescharacteristic
722C2×C22⋊C4C23×C3711yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C3711yescharacteristic
734C22⋊C8C23×C3711yescharacteristic
735C22⋊C8C23×C3711yescharacteristic
736C22⋊C8C23×C3711yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C3711yescharacteristic
741#95C23×C3711yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C3711yescharacteristic
746C24C2×D4×C3711yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C3711yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C3711yescharacteristic
798C2×D4C2×D4×C3711yescharacteristic
799C2×D4C2×D4×C3711yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C3711yescharacteristic
819C22×C4C2×D4×C3711yescharacteristic
820C22×C4C2×D4×C3711yescharacteristic
821C22×C4C2×D4×C3711yescharacteristic
822C22×C4C2×D4×C3711yescharacteristic
823C22×C4C2×D4×C3711yescharacteristic
824C22×C4C2×D4×C3711yescharacteristic
825C22×C4C2×D4×C3711yescharacteristic
826C22×C4C24×C3711yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C3711yescharacteristic
856C4⋊C4C2×D4×C3711yescharacteristic
857C4⋊C4C2×D4×C3711yescharacteristic
858C4⋊C4C2×D4×C3711yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C3711yescharacteristic
917C23#120×C3711yescharacteristic
918C23C22×D4×C3711yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C3711yescharacteristic
993C2×C4#120×C3711yescharacteristic
994C2×C4C22×D4×C3711yescharacteristic
995C2×C4C22×D4×C3711yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C37×B(4,𝔽2)12yes—
1033C22C2×#120×C3711yescharacteristic
1034C22C37×#57611yescharacteristic
1035C22C37×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C37×#301211yescharacteristic
1061C2C37×#301811yescharacteristic
1062C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×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×#3534C2semidirect
2. C37×#3006C2semidirect
3. C37×#3002C2semidirect
4. C37×#2430C2semidirect
5. C37×#1606C2semidirect
6. C37×#1604C2semidirect
7. C37×#1603C2semidirect
8. C37×#1601C2semidirect
9. C37×#1600C2semidirect
10. C37×#1598C2semidirect
11. C37×#1597C2semidirect
12. C37×#1595C2semidirect
13. C37×#1504C2semidirect
14. C2×C37×#327C2semidirect
15. C37×#1468C2semidirect
16. C22×#41×C37C22semidirect
40. C37×#451C22semidirect
41. C37×#450C22semidirect
46. C37×#448C22semidirect
47. C37×#448C22semidirect
49. C37×#447C22semidirect
50. C37×#447C22semidirect
53. C37×#407C22semidirect
54. C2×C22⋊C8×C37C22semidirect
55. C37×#395C22semidirect
56. C37×#394C22semidirect
57. C37×#393C22semidirect
58. C37×#392C22semidirect
62. C2×#95×C37C22semidirect
63. C37×#328C22semidirect
64. C37×#328C22semidirect
67. C37×#327C22semidirect
68. C37×#327C22semidirect
69. C37×#327C22semidirect
70. C37×#327C22semidirect
71. C37×#324C22semidirect
72. C37×#324C22semidirect
73. C37×#323C22semidirect
74. C37×#323C22semidirect
81. C2×#41×C37D4semidirect
89. C22×D4×C37D4semidirect
135. C22⋊Q8×C37D4semidirect
153. #121×C37D4semidirect
154. #121×C37D4semidirect
155. #121×C37D4semidirect
176. #117×C37D4semidirect
179. C2×C4⋊C4×C37D4semidirect
468. #18252C37direct (N × H)
520. #3534C2×C37semidirect
521. #3006C2×C37semidirect
522. #3002C2×C37semidirect
523. #2430C2×C37semidirect
524. #1606C2×C37semidirect
525. #1604C2×C37semidirect
526. #1603C2×C37semidirect
527. #1601C2×C37semidirect
528. #1600C2×C37semidirect
529. #1598C2×C37semidirect
530. #1597C2×C37semidirect
531. #1595C2×C37semidirect
532. #1504C2×C37semidirect
533. C2×#327C2×C37semidirect
534. #1468C2×C37semidirect
547. C22×#41C22×C37semidirect
571. #451C22×C37semidirect
572. #450C22×C37semidirect
577. #448C22×C37semidirect
578. #448C22×C37semidirect
580. #447C22×C37semidirect
581. #447C22×C37semidirect
584. #407C22×C37semidirect
585. C2×C22⋊C8C22×C37semidirect
586. #395C22×C37semidirect
587. #394C22×C37semidirect
588. #393C22×C37semidirect
589. #392C22×C37semidirect
593. C2×#95C22×C37semidirect
594. #328C22×C37semidirect
595. #328C22×C37semidirect
598. #327C22×C37semidirect
599. #327C22×C37semidirect
600. #327C22×C37semidirect
601. #327C22×C37semidirect
602. #324C22×C37semidirect
603. #324C22×C37semidirect
604. #323C22×C37semidirect
605. #323C22×C37semidirect
606. C37#18252direct (N × H)
613. C2×#41D4×C37semidirect
621. C22×D4D4×C37semidirect
667. C22⋊Q8D4×C37semidirect
685. #121D4×C37semidirect
686. #121D4×C37semidirect
687. #121D4×C37semidirect
708. #117D4×C37semidirect
711. C2×C4⋊C4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35342
C37×#30062
C37×#30022
C37×#24302
C37×#16062
C37×#16042
C37×#16032
C37×#16012
C37×#16002
C37×#15982
C37×#15972
C37×#15952
C37×#15042
C2×C37×#3272
C37×#14682
#1825237