Finite Group Databasebeta

← C37×#24390 #22645643

Subgroups — C37×#24390 #22645643

Order 9472.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#535C211yesmaximal, characteristic, complemented
2C2×C37×#469C211yesmaximal, characteristic, complemented
3C2×C37×#466C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C2×C37×#408C211yesmaximal, characteristic, complemented
6C37×#2615C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#1999C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1893C211yesmaximal, characteristic, complemented
13C37×#1875C211yesmaximal, characteristic, complemented
14C37×#1854C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic, complemented
21C23×C8×C37C2211yescharacteristic, complemented
22C37×#535—24no—
23C37×#535—24no—
24C2×#127×C37—21no—
25C2×#124×C37—21no—
26C2×#121×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×#121×C37C2211yescharacteristic, complemented
32C2×#121×C37C2211yescharacteristic, complemented
33C2×#120×C37—21no—
34C2×#120×C37—21no—
35C2×#117×C37C2211yescharacteristic
36C37×#469—24no—
37C37×#466—24no—
38C37×#447—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C2×#106×C37C2211yescharacteristic, complemented
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic, complemented
48C2×#102×C37C2211yescharacteristic, complemented
49C37×#408—24no—
50C2×C22⋊C8×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#393—21no—
55C37×#392—21no—
56C37×#392—21no—
57C37×#392—21no—
58C37×#380C2211yescharacteristic
59C37×#380C2211yescharacteristic, complemented
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C37×#340C2211yescharacteristic, complemented
65C25×C37—21no—
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C22×Q8×C37D411yescharacteristic
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—22no—
78C22×D4×C37—22no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37—21no—
83C22×D4×C37—22no—
84C22×D4×C37—22no—
85C22×D4×C37—41no—
86C22×D4×C37—41no—
87C22×D4×C37D411yescharacteristic
88C22×D4×C37D411yescharacteristic
89C22×D4×C37D411yescharacteristic
90C22×D4×C37C2311yescharacteristic
91C22×D4×C37C2311yescharacteristic
92C22×D4×C37C2311yescharacteristic
93C23×C4×C37C2311yescharacteristic
94C23×C4×C37C2311yescharacteristic
95C23×C4×C37C2311yescharacteristic
96C2×D8×C37—22no—
97C2×D8×C37—22no—
98C2×D8×C37—22no—
99C2×D8×C37—22no—
100C2×D8×C37—41no—
101C2×D8×C37—41no—
102C2×M16×C37—22no—
103C2×M16×C37—22no—
104C2×M16×C37—41no—
105C22×C8×C37—22no—
106C22×C8×C37—22no—
107C22×C8×C37—41no—
108C22×C8×C37C2311yescharacteristic
109C22×C8×C37C2311yescharacteristic
110C22×C8×C37C2311yescharacteristic
111C22×C8×C37C2311yescharacteristic
112#127×C37—28no—
113#124×C37—28no—
114#121×C37—22no—
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—22no—
123#121×C37—22no—
124#121×C37—41no—
125#121×C37—41no—
126#121×C37D414yescomplemented
127#121×C37D414yescomplemented
128#120×C37—28no—
129#120×C37—28no—
130#117×C37—22no—
131#117×C37—22no—
132C2×C4⋊C4×C37C2311yescharacteristic
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C4⋊C4×C37C2311yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C22⋊C4×C37—21no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37—21no—
142C2×C22⋊C4×C37—21no—
143C2×C22⋊C4×C37—21no—
144C2×C22⋊C4×C37—21no—
145C2×C22⋊C4×C37—21no—
146C2×C22⋊C4×C37—21no—
147C2×C22⋊C4×C37—21no—
148C2×C42×C37—21no—
149#107×C37—22no—
150#106×C37—22no—
151#102×C37—22no—
152#102×C37—22no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—41no—
158#102×C37—41no—
159C22⋊C8×C37—22no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—22no—
162C22⋊C8×C37D414yescomplemented
163#95×C37—21no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—24no—
167C24×C37—21no—
168C24×C37—21no—
169C24×C37—21no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—81no—
173C24×C37—81no—
174C24×C37—81no—
175C24×C37—81no—
176C24×C37C2×D411yescharacteristic
177C24×C37C2×D411yescharacteristic
178C24×C37C2×D411yescharacteristic
179#41×C37—44no—
180#41×C37—44no—
181#41×C37—44no—
182#41×C37—44no—
183C2×Q8×C37—22no—
184C2×Q8×C37—22no—
185C2×Q8×C37—41no—
186C2×D4×C37—24no—
187C2×D4×C37—22no—
188C2×D4×C37—22no—
189C2×D4×C37—22no—
190C2×D4×C37—22no—
191C2×D4×C37—24no—
192C2×D4×C37—24no—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—22no—
196C2×D4×C37—22no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—21no—
213C2×D4×C37—44no—
214C2×D4×C37—44no—
215C2×D4×C37—44no—
216C2×D4×C37—44no—
217C2×D4×C37—41no—
218C2×D4×C37—41no—
219C2×D4×C37—41no—
220C2×D4×C37—42no—
221C2×D4×C37—42no—
222C2×D4×C37—42no—
223C2×D4×C37—42no—
224C2×D4×C37—42no—
225C2×D4×C37—81no—
226C2×D4×C37—81no—
227C2×D4×C37—81no—
228C2×D4×C37—81no—
229C2×D4×C37—81no—
230C2×D4×C37—81no—
231C2×D4×C37—81no—
232C2×D4×C37—81no—
233C2×D4×C37—81no—
234C2×D4×C37—81no—
235C2×D4×C37—81no—
236C2×D4×C37—81no—
237C2×D4×C37—81no—
238C2×D4×C37—81no—
239C2×D4×C37C2×D412yes—
240C2×D4×C37C2×D412yes—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
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×C37C2×D411yescharacteristic
261C22×C4×C37C2×D411yescharacteristic
262C22×C4×C37C2×D412yes—
263C22×C4×C37C2×D412yes—
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2×D412yes—
266C22×C4×C37#4112yes—
267C22×C4×C37C2411yescharacteristic
268D8×C37—44no—
269D8×C37—44no—
270M16×C37—44no—
271C2×C8×C37—21no—
272C2×C8×C37—21no—
273C2×C8×C37—21no—
274C2×C8×C37—21no—
275C2×C8×C37—21no—
276C2×C8×C37—21no—
277C2×C8×C37—21no—
278C2×C8×C37—21no—
279C2×C8×C37—21no—
280C2×C8×C37—21no—
281C2×C8×C37—44no—
282C2×C8×C37C2×D412yes—
283C2×C8×C37C2×D412yes—
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×C37C2×D412yes—
293C4⋊C4×C37C2×D412yes—
294C22⋊C4×C37—24no—
295C22⋊C4×C37—24no—
296C22⋊C4×C37—24no—
297C22⋊C4×C37—24no—
298C22⋊C4×C37—24no—
299C22⋊C4×C37—42no—
300C22⋊C4×C37—42no—
301C22⋊C4×C37—42no—
302C22⋊C4×C37—81no—
303C22⋊C4×C37—81no—
304C22⋊C4×C37—81no—
305C42×C37—24no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37—22no—
319C23×C37—22no—
320C23×C37—21no—
321C23×C37—21no—
322C23×C37—21no—
323C23×C37—21no—
324C23×C37—21no—
325C23×C37—21no—
326C23×C37—21no—
327C23×C37—48no—
328C23×C37—41no—
329C23×C37—41no—
330C23×C37—41no—
331C23×C37—41no—
332C23×C37—41no—
333C23×C37—41no—
334C23×C37—41no—
335C23×C37—41no—
336C23×C37—41no—
337C23×C37—41no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—84no—
348C23×C37—84no—
349C23×C37—84no—
350C23×C37—84no—
351C23×C37—84no—
352C23×C37—84no—
353C23×C37#12012yes—
354C23×C37#12112yes—
355C23×C37C22×D411yescharacteristic
356Q8×C37—44no—
357D4×C37—22no—
358D4×C37—22no—
359D4×C37—22no—
360D4×C37—22no—
361D4×C37—44no—
362D4×C37—44no—
363D4×C37—48no—
364D4×C37—44no—
365D4×C37—41no—
366D4×C37—41no—
367D4×C37—41no—
368D4×C37—41no—
369D4×C37—41no—
370D4×C37—41no—
371D4×C37—41no—
372D4×C37—41no—
373D4×C37—84no—
374D4×C37—84no—
375D4×C37—84no—
376D4×C37—84no—
377D4×C37—84no—
378D4×C37—84no—
379D4×C37—84no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—21no—
384C2×C4×C37—22no—
385C2×C4×C37—22no—
386C2×C4×C37—22no—
387C2×C4×C37—22no—
388C2×C4×C37—22no—
389C2×C4×C37—22no—
390C2×C4×C37—22no—
391C2×C4×C37—22no—
392C2×C4×C37—22no—
393C2×C4×C37—22no—
394C2×C4×C37—21no—
395C2×C4×C37—21no—
396C2×C4×C37—21no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37—41no—
409C2×C4×C37—41no—
410C2×C4×C37—41no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37—41no—
414C2×C4×C37#12012yes—
415C2×C4×C37#12112yes—
416C2×C4×C37C22×D411yescharacteristic
417C2×C4×C37C22×D411yescharacteristic
418C2×C4×C37C22×D411yescharacteristic
419C2×C4×C37C2×#4111yescharacteristic
420C2×C4×C37H(5,𝔽2)11yescharacteristic
421C2×C4×C37H(5,𝔽2)11yescharacteristic
422C8×C37—22no—
423C8×C37—22no—
424C8×C37—41no—
425C8×C37—41no—
426#24390C3711yesmaximal, characteristic, direct product factor, Sylow
427C22×C37—22no—
428C22×C37—22no—
429C22×C37—22no—
430C22×C37—22no—
431C22×C37—22no—
432C22×C37—22no—
433C22×C37—41no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—41no—
437C22×C37—41no—
438C22×C37—41no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—42no—
443C22×C37—42no—
444C22×C37—41no—
445C22×C37—41no—
446C22×C37—41no—
447C22×C37—42no—
448C22×C37—42no—
449C22×C37—41no—
450C22×C37—42no—
451C22×C37—42no—
452C22×C37—41no—
453C22×C37—41no—
454C22×C37—816no—
455C22×C37—81no—
456C22×C37—81no—
457C22×C37—81no—
458C22×C37—81no—
459C22×C37—81no—
460C22×C37—81no—
461C22×C37—81no—
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×C37C2×#12011yescharacteristic
471C22×C37C2×#12111yescharacteristic
472C22×C37#53411yescharacteristic
473C22×C37#57611yescharacteristic
474C22×C37#57611yescharacteristic
475C22×C37#57611yescharacteristic
476C22×C37#57711yescharacteristic
477C4×C37—22no—
478C4×C37—22no—
479C4×C37—41no—
480C4×C37—42no—
481C4×C37—42no—
482C4×C37—81no—
483C4×C37—81no—
484C4×C37—81no—
485C4×C37D4211yescharacteristic
486C4×C37D4211yescharacteristic
487C4×C37#54611yescharacteristic
488C4×C37#54611yescharacteristic
489C2×#535C2×C3711yescharacteristic, complemented
490C2×#469C2×C3711yescharacteristic, complemented
491C2×#466C2×C3711yescharacteristic, complemented
492C2×#447C2×C3711yescharacteristic, complemented
493C2×#408C2×C3711yescharacteristic, complemented
494#2615C2×C3711yescharacteristic, complemented
495#2034C2×C3711yescharacteristic, complemented
496#2033C2×C3711yescharacteristic, complemented
497#1999C2×C3711yescharacteristic, complemented
498#1999C2×C3711yescharacteristic, complemented
499#1895C2×C3711yescharacteristic, complemented
500#1893C2×C3711yescharacteristic, complemented
501#1875C2×C3711yescharacteristic, complemented
502#1854C2×C3711yescharacteristic, complemented
503#1786C2×C3711yescharacteristic, complemented
504C2×C37—42no—
505C2×C37—42no—
506C2×C37—81no—
507C2×C37—82no—
508C2×C37—82no—
509C2×C37—161no—
510C2×C37#241011yescharacteristic
511C2×C37#300811yescharacteristic
512C2×C37#301211yescharacteristic
513C2×C37#305811yescharacteristic
514C2×C37#306211yescharacteristic
515C2×C37#319811yescharacteristic
516C2×C37#319911yescharacteristic
517C22×#41C22×C3711yescharacteristic
518C23×D4C22×C3711yescharacteristic
519C22×D8C22×C3711yescharacteristic
520C22×D8C22×C3711yescharacteristic
521C22×M16C22×C3711yescharacteristic, complemented
522C23×C8C22×C3711yescharacteristic, complemented
523#535—24no—
524#535—24no—
525C2×#127—21no—
526C2×#124—21no—
527C2×#121C22×C3711yescharacteristic
528C2×#121C22×C3711yescharacteristic
529C2×#121C22×C3711yescharacteristic
530C2×#121C22×C3711yescharacteristic
531C2×#121C22×C3711yescharacteristic
532C2×#121C22×C3711yescharacteristic, complemented
533C2×#121C22×C3711yescharacteristic, complemented
534C2×#120—21no—
535C2×#120—21no—
536C2×#117C22×C3711yescharacteristic
537#469—24no—
538#466—24no—
539#447—24no—
540C2×#107C22×C3711yescharacteristic, complemented
541C2×#106C22×C3711yescharacteristic, complemented
542C2×#102C22×C3711yescharacteristic
543C2×#102C22×C3711yescharacteristic
544C2×#102C22×C3711yescharacteristic
545C2×#102C22×C3711yescharacteristic
546C2×#102C22×C3711yescharacteristic
547C2×#102C22×C3711yescharacteristic
548C2×#102C22×C3711yescharacteristic, complemented
549C2×#102C22×C3711yescharacteristic, complemented
550#408—24no—
551C2×C22⋊C8C22×C3711yescharacteristic
552C2×C22⋊C8C22×C3711yescharacteristic
553C2×C22⋊C8C22×C3711yescharacteristic, complemented
554C2×C22⋊C8C22×C3711yescharacteristic, complemented
555#393—21no—
556#392—21no—
557#392—21no—
558#392—21no—
559#380C22×C3711yescharacteristic
560#380C22×C3711yescharacteristic, complemented
561#380C22×C3711yescharacteristic, complemented
562#340C22×C3711yescharacteristic, complemented
563#340C22×C3711yescharacteristic, complemented
564#340C22×C3711yescharacteristic, complemented
565#340C22×C3711yescharacteristic, complemented
566C37#2439011yescharacteristic, direct product factor, Sylow
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C3711yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C3711yescharacteristic
590C22×D4D4×C3711yescharacteristic
591C22×D4D4×C3711yescharacteristic
592C22×D4C23×C3711yescharacteristic
593C22×D4C23×C3711yescharacteristic
594C22×D4C23×C3711yescharacteristic
595C23×C4C23×C3711yescharacteristic
596C23×C4C23×C3711yescharacteristic
597C23×C4C23×C3711yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C3711yescharacteristic
611C22×C8C23×C3711yescharacteristic
612C22×C8C23×C3711yescharacteristic
613C22×C8C23×C3711yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C3714yescomplemented
629#121D4×C3714yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C3711yescharacteristic
635C2×C4⋊C4C23×C3711yescharacteristic
636C2×C4⋊C4C23×C3711yescharacteristic
637C2×C4⋊C4C23×C3711yescharacteristic
638C2×C4⋊C4C23×C3711yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C3714yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C3711yescharacteristic
679C24C2×D4×C3711yescharacteristic
680C24C2×D4×C3711yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C3712yes—
742C2×D4C2×D4×C3712yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C3711yescharacteristic
763C22×C4C2×D4×C3711yescharacteristic
764C22×C4C2×D4×C3712yes—
765C22×C4C2×D4×C3712yes—
766C22×C4C2×D4×C3711yescharacteristic
767C22×C4C2×D4×C3712yes—
768C22×C4#41×C3712yes—
769C22×C4C24×C3711yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C3712yes—
785C2×C8C2×D4×C3712yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C3712yes—
795C4⋊C4C2×D4×C3712yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C3712yes—
856C23#121×C3712yes—
857C23C22×D4×C3711yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C3712yes—
917C2×C4#121×C3712yes—
918C2×C4C22×D4×C3711yescharacteristic
919C2×C4C22×D4×C3711yescharacteristic
920C2×C4C22×D4×C3711yescharacteristic
921C2×C4C2×#41×C3711yescharacteristic
922C2×C4H(5,𝔽2)×C3711yescharacteristic
923C2×C4H(5,𝔽2)×C3711yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C3711yescharacteristic
972C22C2×#121×C3711yescharacteristic
973C22C37×#53411yescharacteristic
974C22C37×#57611yescharacteristic
975C22C37×#57611yescharacteristic
976C22C37×#57611yescharacteristic
977C22C37×#57711yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C3711yescharacteristic
987C4D42×C3711yescharacteristic
988C4C37×#54611yescharacteristic
989C4C37×#54611yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C37×#241011yescharacteristic
997C2C37×#300811yescharacteristic
998C2C37×#301211yescharacteristic
999C2C37×#305811yescharacteristic
1000C2C37×#306211yescharacteristic
1001C2C37×#319811yescharacteristic
1002C2C37×#319911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#535C2semidirect
2. C2×C37×#469C2semidirect
3. C2×C37×#466C2semidirect
4. C2×C37×#447C2semidirect
5. C2×C37×#408C2semidirect
6. C37×#2615C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#1999C2semidirect
10. C37×#1999C2semidirect
11. C37×#1895C2semidirect
12. C37×#1893C2semidirect
13. C37×#1875C2semidirect
14. C37×#1854C2semidirect
15. C37×#1786C2semidirect
20. C22×M16×C37C22semidirect
21. C23×C8×C37C22semidirect
31. C2×#121×C37C22semidirect
32. C2×#121×C37C22semidirect
39. C2×#107×C37C22semidirect
40. C2×#106×C37C22semidirect
47. C2×#102×C37C22semidirect
48. C2×#102×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
59. C37×#380C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
126. #121×C37D4semidirect
127. #121×C37D4semidirect
162. C22⋊C8×C37D4semidirect
426. #24390C37direct (N × H)
489. C2×#535C2×C37semidirect
490. C2×#469C2×C37semidirect
491. C2×#466C2×C37semidirect
492. C2×#447C2×C37semidirect
493. C2×#408C2×C37semidirect
494. #2615C2×C37semidirect
495. #2034C2×C37semidirect
496. #2033C2×C37semidirect
497. #1999C2×C37semidirect
498. #1999C2×C37semidirect
499. #1895C2×C37semidirect
500. #1893C2×C37semidirect
501. #1875C2×C37semidirect
502. #1854C2×C37semidirect
503. #1786C2×C37semidirect
521. C22×M16C22×C37semidirect
522. C23×C8C22×C37semidirect
532. C2×#121C22×C37semidirect
533. C2×#121C22×C37semidirect
540. C2×#107C22×C37semidirect
541. C2×#106C22×C37semidirect
548. C2×#102C22×C37semidirect
549. C2×#102C22×C37semidirect
553. C2×C22⋊C8C22×C37semidirect
554. C2×C22⋊C8C22×C37semidirect
560. #380C22×C37semidirect
561. #380C22×C37semidirect
562. #340C22×C37semidirect
563. #340C22×C37semidirect
564. #340C22×C37semidirect
565. #340C22×C37semidirect
566. C37#24390direct (N × H)
628. #121D4×C37semidirect
629. #121D4×C37semidirect
664. C22⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5352
C2×C37×#4692
C2×C37×#4662
C2×C37×#4472
C2×C37×#4082
C37×#26152
C37×#20342
C37×#20332
C37×#19992
C37×#18952
C37×#18932
C37×#18752
C37×#18542
C37×#17862
#2439037