Finite Group Databasebeta

← C37×#18414 #22639667

Subgroups — C37×#18414 #22639667

Order 9472.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3534C211yesmaximal, characteristic, complemented
2C37×#3194C211yesmaximal, characteristic, complemented
3C37×#3186C211yesmaximal, characteristic, complemented
4C37×#2661C211yesmaximal, characteristic, complemented
5C37×#1612C211yesmaximal, characteristic, complemented
6C37×#1610C211yesmaximal, characteristic, complemented
7C37×#1609C211yesmaximal, characteristic, complemented
8C37×#1607C211yesmaximal, characteristic, complemented
9C37×#1600C211yesmaximal, characteristic, complemented
10C37×#1598C211yesmaximal, characteristic, complemented
11C37×#1597C211yesmaximal, characteristic, complemented
12C37×#1595C211yesmaximal, characteristic, complemented
13C37×#1507C211yesmaximal, characteristic, complemented
14C37×#1501C211yesmaximal, characteristic, complemented
15C37×#1468C211yesmaximal, characteristic, complemented
16C37×#562—21no—
17C37×#560—21no—
18C37×#553—21no—
19C37×#551—21no—
20C37×#546—21no—
21C37×#546—21no—
22C37×#546—21no—
23D42×C37—21no—
24C37×#540—21no—
25C37×#539—21no—
26C37×#539C2211yescharacteristic
27C37×#538—21no—
28C37×#538C2211yescharacteristic
29C37×#537C2211yescharacteristic
30C37×#534—21no—
31C37×#534C2211yescharacteristic
32C37×#525C2211yescharacteristic
33C2×#123×C37C2211yescharacteristic
34C2×#121×C37C2211yescharacteristic
35C2×#121×C37C2211yescharacteristic, complemented
36C37×#483C2211yescharacteristic, complemented
37C37×#482—21no—
38C37×#480—21no—
39C37×#480C2211yescharacteristic
40C37×#480C2211yescharacteristic, complemented
41C37×#480C2211yescharacteristic, complemented
42C37×#469—21no—
43C37×#468—21no—
44C37×#466—21no—
45C37×#466—21no—
46C37×#450C2211yescharacteristic, complemented
47C37×#449—21no—
48C37×#447—21no—
49C37×#447C2211yescharacteristic
50C37×#447C2211yescharacteristic, complemented
51C37×#447C2211yescharacteristic, complemented
52C37×#407C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#398C2211yescharacteristic, complemented
55C37×#397C2211yescharacteristic, complemented
56C37×#394—21no—
57C37×#394C2211yescharacteristic, complemented
58C37×#392—21no—
59C37×#392C2211yescharacteristic, complemented
60C37×#390—21no—
61C37×#388—21no—
62C4×C22⋊C4×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×C37D411yescharacteristic, complemented
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37D411yescharacteristic
83C22×D4×C37D411yescharacteristic, complemented
84C22×D4×C37C2311yescharacteristic
85C23×C4×C37C2311yescharacteristic
86C2×SD16×C37—21no—
87C2×D8×C37—21no—
88C2×D8×C37—21no—
89C2×D8×C37—21no—
90C2×M16×C37—21no—
91C22×C8×C37—21no—
92#127×C37—21no—
93#126×C37—21no—
94#126×C37—21no—
95#126×C37—21no—
96#126×C37—21no—
97#125×C37—21no—
98#125×C37—21no—
99#124×C37—21no—
100#124×C37—21no—
101#124×C37—21no—
102#123×C37—21no—
103#123×C37—21no—
104#123×C37—21no—
105#123×C37—21no—
106#123×C37—21no—
107#123×C37—21no—
108#123×C37—21no—
109#123×C37—21no—
110#123×C37—21no—
111#123×C37—21no—
112#123×C37—21no—
113#123×C37—21no—
114#123×C37—21no—
115#123×C37—21no—
116C22⋊Q8×C37—21no—
117C22⋊Q8×C37—21no—
118C22⋊Q8×C37—21no—
119C22⋊Q8×C37—21no—
120C22⋊Q8×C37—21no—
121C22⋊Q8×C37D411yescharacteristic, complemented
122C22⋊Q8×C37C2311yescharacteristic
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—21no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37—21no—
133#121×C37—21no—
134#121×C37—21no—
135#121×C37—21no—
136#121×C37—21no—
137#121×C37—21no—
138#121×C37—21no—
139#121×C37—21no—
140#121×C37—21no—
141#121×C37—21no—
142#121×C37D411yescharacteristic, complemented
143#121×C37D411yescharacteristic, complemented
144#121×C37D411yescharacteristic, complemented
145#121×C37C2311yescharacteristic
146#121×C37C2311yescharacteristic
147#121×C37C2311yescharacteristic
148#120×C37—21no—
149#120×C37—21no—
150#120×C37—21no—
151#120×C37—21no—
152#120×C37—21no—
153#120×C37—21no—
154#120×C37—21no—
155#120×C37—21no—
156C4×D4×C37—21no—
157C4×D4×C37—21no—
158C4×D4×C37—21no—
159C4×D4×C37—21no—
160C4×D4×C37—21no—
161C4×D4×C37—21no—
162C4×D4×C37—21no—
163C4×D4×C37—21no—
164#117×C37—21no—
165#117×C37D411yescharacteristic, complemented
166C2×C4⋊C4×C37—21no—
167C2×C4⋊C4×C37D411yescharacteristic
168C2×C4⋊C4×C37D411yescharacteristic, complemented
169C2×C4⋊C4×C37C2311yescharacteristic
170C2×C4⋊C4×C37C2311yescharacteristic
171C2×C22⋊C4×C37—21no—
172C2×C22⋊C4×C37—21no—
173C2×C22⋊C4×C37—21no—
174C2×C22⋊C4×C37—21no—
175C2×C22⋊C4×C37—21no—
176C2×C22⋊C4×C37—21no—
177C2×C22⋊C4×C37—21no—
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—21no—
180C2×C22⋊C4×C37D411yescharacteristic
181C2×C22⋊C4×C37D411yescharacteristic
182C2×C22⋊C4×C37C2311yescharacteristic
183C2×C42×C37—21no—
184#107×C37—21no—
185#107×C37—21no—
186#107×C37—21no—
187#106×C37—21no—
188#103×C37—21no—
189#102×C37—21no—
190#102×C37—21no—
191#102×C37—21no—
192#102×C37—21no—
193#102×C37—21no—
194#102×C37—21no—
195#102×C37—21no—
196C22⋊C8×C37—21no—
197C22⋊C8×C37—21no—
198C22⋊C8×C37C2311yescharacteristic
199C22⋊C8×C37C2311yescharacteristic
200C22⋊C8×C37C2311yescharacteristic
201C22⋊C8×C37C2311yescharacteristic
202#95×C37—21no—
203#95×C37—21no—
204#95×C37C2311yescharacteristic
205#95×C37C2311yescharacteristic
206C24×C37—21no—
207C24×C37—21no—
208C24×C37—21no—
209C24×C37C2×D411yescharacteristic
210C24×C37C2×D411yescharacteristic
211#41×C37—81no—
212#41×C37—81no—
213#41×C37—81no—
214C2×Q8×C37—21no—
215C2×Q8×C37C2×D411yescharacteristic
216C2×D4×C37—21no—
217C2×D4×C37—21no—
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—21no—
228C2×D4×C37—21no—
229C2×D4×C37—21no—
230C2×D4×C37—21no—
231C2×D4×C37—21no—
232C2×D4×C37—21no—
233C2×D4×C37—21no—
234C2×D4×C37—21no—
235C2×D4×C37—42no—
236C2×D4×C37—41no—
237C2×D4×C37—41no—
238C2×D4×C37—81no—
239C2×D4×C37—81no—
240C2×D4×C37—81no—
241C2×D4×C37—81no—
242C2×D4×C37—81no—
243C2×D4×C37—81no—
244C2×D4×C37—81no—
245C2×D4×C37—81no—
246C2×D4×C37—81no—
247C2×D4×C37—81no—
248C2×D4×C37—81no—
249C2×D4×C37—82no—
250C2×D4×C37C2×D411yescharacteristic
251C2×D4×C37C2×D411yescharacteristic
252C2×D4×C37C2×D411yescharacteristic
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—21no—
259C22×C4×C37—21no—
260C22×C4×C37—21no—
261C22×C4×C37—21no—
262C22×C4×C37—21no—
263C22×C4×C37—81no—
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2×D411yescharacteristic
266C22×C4×C37C2×D411yescharacteristic
267C22×C4×C37C2×D411yescharacteristic
268C22×C4×C37C2×D411yescharacteristic
269C22×C4×C37C2×D411yescharacteristic
270C22×C4×C37C2×D411yescharacteristic
271C22×C4×C37C2×D411yescharacteristic
272C22×C4×C37C2411yescharacteristic
273SD16×C37—81no—
274D8×C37—81no—
275D8×C37—81no—
276D8×C37—81no—
277M16×C37—81no—
278C2×C8×C37—21no—
279C2×C8×C37—21no—
280C2×C8×C37—21no—
281C2×C8×C37—21no—
282C2×C8×C37—81no—
283C4⋊C4×C37—21no—
284C4⋊C4×C37—21no—
285C4⋊C4×C37—21no—
286C4⋊C4×C37—21no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—21no—
291C4⋊C4×C37—21no—
292C4⋊C4×C37—21no—
293C4⋊C4×C37—21no—
294C4⋊C4×C37—21no—
295C4⋊C4×C37—21no—
296C4⋊C4×C37—21no—
297C4⋊C4×C37—21no—
298C4⋊C4×C37—81no—
299C4⋊C4×C37C2×D411yescharacteristic
300C4⋊C4×C37C2×D411yescharacteristic
301C4⋊C4×C37C2×D411yescharacteristic
302C4⋊C4×C37C2×D411yescharacteristic
303C22⋊C4×C37—21no—
304C22⋊C4×C37—21no—
305C22⋊C4×C37—21no—
306C22⋊C4×C37—21no—
307C22⋊C4×C37—21no—
308C22⋊C4×C37—21no—
309C22⋊C4×C37—21no—
310C22⋊C4×C37—21no—
311C22⋊C4×C37—21no—
312C22⋊C4×C37—21no—
313C22⋊C4×C37—21no—
314C22⋊C4×C37—21no—
315C22⋊C4×C37—21no—
316C22⋊C4×C37—21no—
317C22⋊C4×C37—21no—
318C22⋊C4×C37—21no—
319C22⋊C4×C37—21no—
320C22⋊C4×C37—21no—
321C22⋊C4×C37—21no—
322C22⋊C4×C37—21no—
323C22⋊C4×C37—21no—
324C22⋊C4×C37—21no—
325C22⋊C4×C37—21no—
326C22⋊C4×C37—21no—
327C22⋊C4×C37—21no—
328C22⋊C4×C37—42no—
329C22⋊C4×C37—42no—
330C22⋊C4×C37—41no—
331C22⋊C4×C37—41no—
332C22⋊C4×C37—81no—
333C22⋊C4×C37—81no—
334C22⋊C4×C37—81no—
335C42×C37—21no—
336C42×C37—21no—
337C42×C37—21no—
338C42×C37—81no—
339C23×C37—21no—
340C23×C37—21no—
341C23×C37—21no—
342C23×C37—21no—
343C23×C37—21no—
344C23×C37—21no—
345C23×C37—21no—
346C23×C37—21no—
347C23×C37—41no—
348C23×C37—41no—
349C23×C37—42no—
350C23×C37—41no—
351C23×C37—41no—
352C23×C37—41no—
353C23×C37—41no—
354C23×C37—41no—
355C23×C37—41no—
356C23×C37—41no—
357C23×C37—41no—
358C23×C37—41no—
359C23×C37—81no—
360C23×C37—81no—
361C23×C37—81no—
362C23×C37—81no—
363C23×C37—81no—
364C23×C37#12011yescharacteristic
365C23×C37#12011yescharacteristic
366C23×C37C22×D411yescharacteristic
367Q8×C37—41no—
368Q8×C37—81no—
369D4×C37—41no—
370D4×C37—41no—
371D4×C37—41no—
372D4×C37—41no—
373D4×C37—41no—
374D4×C37—41no—
375D4×C37—41no—
376D4×C37—42no—
377D4×C37—42no—
378D4×C37—41no—
379D4×C37—41no—
380D4×C37—41no—
381D4×C37—41no—
382D4×C37—41no—
383D4×C37—41no—
384D4×C37—81no—
385D4×C37—81no—
386D4×C37—81no—
387D4×C37—81no—
388D4×C37—81no—
389D4×C37—81no—
390D4×C37—81no—
391D4×C37—81no—
392D4×C37—81no—
393D4×C37—81no—
394D4×C37—81no—
395D4×C37—81no—
396D4×C37—84no—
397D4×C37—82no—
398D4×C37—82no—
399C2×C4×C37—22no—
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—21no—
409C2×C4×C37—21no—
410C2×C4×C37—41no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37—41no—
414C2×C4×C37—41no—
415C2×C4×C37—41no—
416C2×C4×C37—41no—
417C2×C4×C37—41no—
418C2×C4×C37—41no—
419C2×C4×C37—41no—
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—81no—
427C2×C4×C37—81no—
428C2×C4×C37—81no—
429C2×C4×C37—81no—
430C2×C4×C37—81no—
431C2×C4×C37—81no—
432C2×C4×C37—81no—
433C2×C4×C37#12011yescharacteristic
434C2×C4×C37#12011yescharacteristic
435C2×C4×C37C22×D411yescharacteristic
436C2×C4×C37C22×D411yescharacteristic
437C8×C37—41no—
438C8×C37—41no—
439C8×C37—41no—
440C8×C37—41no—
441#18414C3711yesmaximal, characteristic, direct product factor, Sylow
442C22×C37—21no—
443C22×C37—21no—
444C22×C37—21no—
445C22×C37—21no—
446C22×C37—21no—
447C22×C37—21no—
448C22×C37—21no—
449C22×C37—21no—
450C22×C37—41no—
451C22×C37—41no—
452C22×C37—41no—
453C22×C37—41no—
454C22×C37—41no—
455C22×C37—41no—
456C22×C37—41no—
457C22×C37—41no—
458C22×C37—41no—
459C22×C37—41no—
460C22×C37—41no—
461C22×C37—41no—
462C22×C37—81no—
463C22×C37—81no—
464C22×C37—81no—
465C22×C37—81no—
466C22×C37—81no—
467C22×C37—81no—
468C22×C37—81no—
469C22×C37—81no—
470C22×C37—81no—
471C22×C37—81no—
472C22×C37—81no—
473C22×C37—162no—
474C22×C37—162no—
475C22×C37C2×#12011yescharacteristic
476C22×C37#57611yescharacteristic
477C22×C37#57611yescharacteristic
478C4×C37—21no—
479C4×C37—21no—
480C4×C37—21no—
481C4×C37—21no—
482C4×C37—42no—
483C4×C37—41no—
484C4×C37—41no—
485C4×C37—41no—
486C4×C37—41no—
487C4×C37—41no—
488C4×C37—41no—
489C4×C37—41no—
490C4×C37—41no—
491C4×C37—81no—
492C4×C37—81no—
493#3534C2×C3711yescharacteristic, complemented
494#3194C2×C3711yescharacteristic, complemented
495#3186C2×C3711yescharacteristic, complemented
496#2661C2×C3711yescharacteristic, complemented
497#1612C2×C3711yescharacteristic, complemented
498#1610C2×C3711yescharacteristic, complemented
499#1609C2×C3711yescharacteristic, complemented
500#1607C2×C3711yescharacteristic, complemented
501#1600C2×C3711yescharacteristic, complemented
502#1598C2×C3711yescharacteristic, complemented
503#1597C2×C3711yescharacteristic, complemented
504#1595C2×C3711yescharacteristic, complemented
505#1507C2×C3711yescharacteristic, complemented
506#1501C2×C3711yescharacteristic, complemented
507#1468C2×C3711yescharacteristic, complemented
508C2×C37—21no—
509C2×C37—21no—
510C2×C37—41no—
511C2×C37—41no—
512C2×C37—81no—
513C2×C37—81no—
514C2×C37—81no—
515C2×C37—81no—
516C2×C37—161no—
517C2×C37#300811yescharacteristic
518C2×C37#301811yescharacteristic
519C2×C37#302611yescharacteristic
520#562—21no—
521#560—21no—
522#553—21no—
523#551—21no—
524#546—21no—
525#546—21no—
526#546—21no—
527D42—21no—
528#540—21no—
529#539—21no—
530#539C22×C3711yescharacteristic
531#538—21no—
532#538C22×C3711yescharacteristic
533#537C22×C3711yescharacteristic
534#534—21no—
535#534C22×C3711yescharacteristic
536#525C22×C3711yescharacteristic
537C2×#123C22×C3711yescharacteristic
538C2×#121C22×C3711yescharacteristic
539C2×#121C22×C3711yescharacteristic, complemented
540#483C22×C3711yescharacteristic, complemented
541#482—21no—
542#480—21no—
543#480C22×C3711yescharacteristic
544#480C22×C3711yescharacteristic, complemented
545#480C22×C3711yescharacteristic, complemented
546#469—21no—
547#468—21no—
548#466—21no—
549#466—21no—
550#450C22×C3711yescharacteristic, complemented
551#449—21no—
552#447—21no—
553#447C22×C3711yescharacteristic
554#447C22×C3711yescharacteristic, complemented
555#447C22×C3711yescharacteristic, complemented
556#407C22×C3711yescharacteristic, complemented
557C2×C22⋊C8C22×C3711yescharacteristic, complemented
558#398C22×C3711yescharacteristic, complemented
559#397C22×C3711yescharacteristic, complemented
560#394—21no—
561#394C22×C3711yescharacteristic, complemented
562#392—21no—
563#392C22×C3711yescharacteristic, complemented
564#390—21no—
565#388—21no—
566C4×C22⋊C4C22×C3711yescharacteristic, complemented
567#328C22×C3711yescharacteristic, complemented
568#328C22×C3711yescharacteristic, complemented
569#327C22×C3711yescharacteristic
570#327C22×C3711yescharacteristic
571#327C22×C3711yescharacteristic, complemented
572#327C22×C3711yescharacteristic, complemented
573#327C22×C3711yescharacteristic, complemented
574#327C22×C3711yescharacteristic, complemented
575#324C22×C3711yescharacteristic, complemented
576#324C22×C3711yescharacteristic, complemented
577#323C22×C3711yescharacteristic, complemented
578#323C22×C3711yescharacteristic, complemented
579C37#1841411yescharacteristic, direct product factor, Sylow
580C2×#41—21no—
581C2×#41D4×C3711yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C3711yescharacteristic
588C22×D4D4×C3711yescharacteristic, complemented
589C22×D4C23×C3711yescharacteristic
590C23×C4C23×C3711yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C3711yescharacteristic, complemented
627C22⋊Q8C23×C3711yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C3711yescharacteristic, complemented
648#121D4×C3711yescharacteristic, complemented
649#121D4×C3711yescharacteristic, complemented
650#121C23×C3711yescharacteristic
651#121C23×C3711yescharacteristic
652#121C23×C3711yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C3711yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C3711yescharacteristic
673C2×C4⋊C4D4×C3711yescharacteristic, complemented
674C2×C4⋊C4C23×C3711yescharacteristic
675C2×C4⋊C4C23×C3711yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C3711yescharacteristic
686C2×C22⋊C4D4×C3711yescharacteristic
687C2×C22⋊C4C23×C3711yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C3711yescharacteristic
704C22⋊C8C23×C3711yescharacteristic
705C22⋊C8C23×C3711yescharacteristic
706C22⋊C8C23×C3711yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C3711yescharacteristic
710#95C23×C3711yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C3711yescharacteristic
715C24C2×D4×C3711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C3711yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C3711yescharacteristic
756C2×D4C2×D4×C3711yescharacteristic
757C2×D4C2×D4×C3711yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C3711yescharacteristic
770C22×C4C2×D4×C3711yescharacteristic
771C22×C4C2×D4×C3711yescharacteristic
772C22×C4C2×D4×C3711yescharacteristic
773C22×C4C2×D4×C3711yescharacteristic
774C22×C4C2×D4×C3711yescharacteristic
775C22×C4C2×D4×C3711yescharacteristic
776C22×C4C2×D4×C3711yescharacteristic
777C22×C4C24×C3711yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C3711yescharacteristic
805C4⋊C4C2×D4×C3711yescharacteristic
806C4⋊C4C2×D4×C3711yescharacteristic
807C4⋊C4C2×D4×C3711yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C3711yescharacteristic
870C23#120×C3711yescharacteristic
871C23C22×D4×C3711yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C3711yescharacteristic
939C2×C4#120×C3711yescharacteristic
940C2×C4C22×D4×C3711yescharacteristic
941C2×C4C22×D4×C3711yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C3711yescharacteristic
980C22C37×#57611yescharacteristic
981C22C37×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C37×#300811yescharacteristic
1007C2C37×#301811yescharacteristic
1008C2C37×#302611yescharacteristic
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×#3194C2semidirect
3. C37×#3186C2semidirect
4. C37×#2661C2semidirect
5. C37×#1612C2semidirect
6. C37×#1610C2semidirect
7. C37×#1609C2semidirect
8. C37×#1607C2semidirect
9. C37×#1600C2semidirect
10. C37×#1598C2semidirect
11. C37×#1597C2semidirect
12. C37×#1595C2semidirect
13. C37×#1507C2semidirect
14. C37×#1501C2semidirect
15. C37×#1468C2semidirect
35. C2×#121×C37C22semidirect
36. C37×#483C22semidirect
40. C37×#480C22semidirect
41. C37×#480C22semidirect
46. C37×#450C22semidirect
50. C37×#447C22semidirect
51. C37×#447C22semidirect
52. C37×#407C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C37×#398C22semidirect
55. C37×#397C22semidirect
57. C37×#394C22semidirect
59. C37×#392C22semidirect
62. C4×C22⋊C4×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
76. C2×#41×C37D4semidirect
83. C22×D4×C37D4semidirect
121. C22⋊Q8×C37D4semidirect
142. #121×C37D4semidirect
143. #121×C37D4semidirect
144. #121×C37D4semidirect
165. #117×C37D4semidirect
168. C2×C4⋊C4×C37D4semidirect
441. #18414C37direct (N × H)
493. #3534C2×C37semidirect
494. #3194C2×C37semidirect
495. #3186C2×C37semidirect
496. #2661C2×C37semidirect
497. #1612C2×C37semidirect
498. #1610C2×C37semidirect
499. #1609C2×C37semidirect
500. #1607C2×C37semidirect
501. #1600C2×C37semidirect
502. #1598C2×C37semidirect
503. #1597C2×C37semidirect
504. #1595C2×C37semidirect
505. #1507C2×C37semidirect
506. #1501C2×C37semidirect
507. #1468C2×C37semidirect
539. C2×#121C22×C37semidirect
540. #483C22×C37semidirect
544. #480C22×C37semidirect
545. #480C22×C37semidirect
550. #450C22×C37semidirect
554. #447C22×C37semidirect
555. #447C22×C37semidirect
556. #407C22×C37semidirect
557. C2×C22⋊C8C22×C37semidirect
558. #398C22×C37semidirect
559. #397C22×C37semidirect
561. #394C22×C37semidirect
563. #392C22×C37semidirect
566. C4×C22⋊C4C22×C37semidirect
567. #328C22×C37semidirect
568. #328C22×C37semidirect
571. #327C22×C37semidirect
572. #327C22×C37semidirect
573. #327C22×C37semidirect
574. #327C22×C37semidirect
575. #324C22×C37semidirect
576. #324C22×C37semidirect
577. #323C22×C37semidirect
578. #323C22×C37semidirect
579. C37#18414direct (N × H)
581. C2×#41D4×C37semidirect
588. C22×D4D4×C37semidirect
626. C22⋊Q8D4×C37semidirect
647. #121D4×C37semidirect
648. #121D4×C37semidirect
649. #121D4×C37semidirect
670. #117D4×C37semidirect
673. 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×#31942
C37×#31862
C37×#26612
C37×#16122
C37×#16102
C37×#16092
C37×#16072
C37×#16002
C37×#15982
C37×#15972
C37×#15952
C37×#15072
C37×#15012
C37×#14682
#1841437