Finite Group Databasebeta

← C37×#16398 #22637651

Subgroups — C37×#16398 #22637651

Order 9472.

1758 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#399C211yesmaximal, characteristic, complemented
2C2×C37×#386C211yesmaximal, characteristic
3C2×C37×#380C211yesmaximal, characteristic, complemented
4C2×C37×#380C211yesmaximal, characteristic, complemented
5C37×#1445C211yesmaximal, characteristic, complemented
6C37×#1442C211yesmaximal, characteristic, complemented
7C37×#1441C212yesmaximal, complemented
8C37×#1439C212yesmaximal, complemented
9C37×#1439C211yesmaximal, characteristic, complemented
10C37×#1439C212yesmaximal, complemented
11C37×#1438C212yesmaximal
12C23×D4×C37C2211yescharacteristic
13C24×C4×C37C2211yescharacteristic
14C22×C4⋊C4×C37C2211yescharacteristic
15C22×C4⋊C4×C37C2212yes—
16C22×C4⋊C4×C37C2212yes—
17C22×C4⋊C4×C37C2211yescharacteristic
18C22×C22⋊C4×C37C2211yescharacteristic
19C22×C22⋊C4×C37C2211yescharacteristic
20C22×C22⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2212yes—
22C22×C22⋊C4×C37C2212yes—
23C22×C22⋊C4×C37C2211yescharacteristic
24C22×C22⋊C4×C37C2212yes—
25C37×#399—24no—
26C37×#386—24no—
27C37×#380—24no—
28C37×#380—24no—
29C2×#95×C37C2212yes—
30C2×#95×C37C2211yescharacteristic
31C2×#95×C37C2211yescharacteristic
32C2×#95×C37C2211yescharacteristic
33C2×#95×C37C2212yes—
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2212yes—
37C2×#95×C37C2212yes—
38C2×#95×C37C2211yescharacteristic
39C25×C37C2311yescharacteristic
40C25×C37C2311yescharacteristic
41C22×D4×C37—22no—
42C22×D4×C37—22no—
43C22×D4×C37—42no—
44C22×D4×C37—42no—
45C22×D4×C37Q814yes—
46C23×C4×C37—22no—
47C23×C4×C37—22no—
48C23×C4×C37—24no—
49C23×C4×C37—42no—
50C23×C4×C37D414yes—
51C23×C4×C37C2311yescharacteristic
52C23×C4×C37C2312yes—
53C23×C4×C37C2312yes—
54C23×C4×C37C2311yescharacteristic
55C23×C4×C37C2312yes—
56C23×C4×C37C2312yes—
57C23×C4×C37C2311yescharacteristic
58C23×C4×C37C2311yescharacteristic
59C23×C4×C37C2311yescharacteristic
60C2×C4⋊C4×C37—24no—
61C2×C4⋊C4×C37—22no—
62C2×C4⋊C4×C37—22no—
63C2×C4⋊C4×C37—24no—
64C2×C4⋊C4×C37—22no—
65C2×C4⋊C4×C37—24no—
66C2×C4⋊C4×C37—22no—
67C2×C4⋊C4×C37—42no—
68C2×C4⋊C4×C37—42no—
69C2×C4⋊C4×C37—42no—
70C2×C4⋊C4×C37—42no—
71C2×C22⋊C4×C37—24no—
72C2×C22⋊C4×C37—22no—
73C2×C22⋊C4×C37—24no—
74C2×C22⋊C4×C37—24no—
75C2×C22⋊C4×C37—22no—
76C2×C22⋊C4×C37—22no—
77C2×C22⋊C4×C37—24no—
78C2×C22⋊C4×C37—22no—
79C2×C22⋊C4×C37—22no—
80C2×C22⋊C4×C37—24no—
81C2×C22⋊C4×C37—42no—
82C2×C22⋊C4×C37—42no—
83C2×C22⋊C4×C37—42no—
84C2×C22⋊C4×C37—42no—
85C2×C22⋊C4×C37—42no—
86C2×C22⋊C4×C37—42no—
87C2×C22⋊C4×C37—42no—
88C2×C22⋊C4×C37—42no—
89C2×C22⋊C4×C37—42no—
90#95×C37—22no—
91#95×C37—24no—
92#95×C37—22no—
93#95×C37—22no—
94#95×C37—42no—
95#95×C37—42no—
96#95×C37—42no—
97#95×C37—42no—
98#95×C37—42no—
99#95×C37D414yescomplemented
100C24×C37—21no—
101C24×C37—21no—
102C24×C37—22no—
103C24×C37—22no—
104C24×C37—21no—
105C24×C37—22no—
106C24×C37—22no—
107C24×C37—21no—
108C24×C37—21no—
109C24×C37—21no—
110C24×C37—21no—
111C24×C37—22no—
112C24×C37—21no—
113C24×C37—22no—
114C24×C37—21no—
115C24×C37—22no—
116C24×C37—22no—
117C24×C37—21no—
118C24×C37C2×D412yes—
119C24×C37C2×Q812yes—
120C24×C37C2×Q812yes—
121C24×C37#4112yes—
122C24×C37C2411yescharacteristic
123C2×D4×C37—28no—
124C2×D4×C37—48no—
125C2×D4×C37—44no—
126C2×D4×C37—44no—
127C2×D4×C37—48no—
128C22×C4×C37—21no—
129C22×C4×C37—21no—
130C22×C4×C37—22no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—21no—
134C22×C4×C37—22no—
135C22×C4×C37—22no—
136C22×C4×C37—21no—
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—22no—
140C22×C4×C37—22no—
141C22×C4×C37—22no—
142C22×C4×C37—22no—
143C22×C4×C37—28no—
144C22×C4×C37—28no—
145C22×C4×C37—21no—
146C22×C4×C37—21no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—21no—
151C22×C4×C37—22no—
152C22×C4×C37—21no—
153C22×C4×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—22no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—21no—
159C22×C4×C37—22no—
160C22×C4×C37—22no—
161C22×C4×C37—22no—
162C22×C4×C37—22no—
163C22×C4×C37—22no—
164C22×C4×C37—22no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—22no—
171C22×C4×C37—22no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—21no—
175C22×C4×C37—22no—
176C22×C4×C37—44no—
177C22×C4×C37—48no—
178C22×C4×C37—48no—
179C22×C4×C37C2×D414yes—
180C22×C4×C37C2×D412yes—
181C22×C4×C37C2×D412yes—
182C22×C4×C37C2×D412yes—
183C22×C4×C37C2×Q812yes—
184C22×C4×C37#4112yes—
185C22×C4×C37#4114yes—
186C4⋊C4×C37—48no—
187C4⋊C4×C37—44no—
188C4⋊C4×C37—48no—
189C4⋊C4×C37—44no—
190C22⋊C4×C37—48no—
191C22⋊C4×C37—48no—
192C22⋊C4×C37—48no—
193C22⋊C4×C37—44no—
194C22⋊C4×C37—48no—
195C22⋊C4×C37—44no—
196C22⋊C4×C37—44no—
197C23×C37—22no—
198C23×C37—22no—
199C23×C37—22no—
200C23×C37—22no—
201C23×C37—22no—
202C23×C37—22no—
203C23×C37—24no—
204C23×C37—24no—
205C23×C37—22no—
206C23×C37—22no—
207C23×C37—22no—
208C23×C37—24no—
209C23×C37—22no—
210C23×C37—24no—
211C23×C37—22no—
212C23×C37—24no—
213C23×C37—22no—
214C23×C37—22no—
215C23×C37—24no—
216C23×C37—42no—
217C23×C37—42no—
218C23×C37—42no—
219C23×C37—42no—
220C23×C37—42no—
221C23×C37—42no—
222C23×C37—42no—
223C23×C37—42no—
224C23×C37—41no—
225C23×C37—41no—
226C23×C37—41no—
227C23×C37—42no—
228C23×C37—41no—
229C23×C37—41no—
230C23×C37—41no—
231C23×C37—42no—
232C23×C37—42no—
233C23×C37—42no—
234C23×C37—42no—
235C23×C37—41no—
236C23×C37—42no—
237C23×C37—42no—
238C23×C37—41no—
239C23×C37—42no—
240C23×C37—42no—
241C23×C37—42no—
242C23×C37C22⋊Q814yes—
243C23×C37C22×D411yescharacteristic
244C23×C37C22×D411yescharacteristic
245C23×C37C22×Q811yescharacteristic
246C23×C37C2×#4111yescharacteristic
247C23×C37C2×#4111yescharacteristic
248C23×C37C2×#4112yes—
249C23×C37H(5,𝔽2)12yes—
250C23×C37H(5,𝔽2)12yes—
251C23×C37H(5,𝔽2)12yes—
252C23×C37H(5,𝔽2)11yescharacteristic
253C23×C372−1+411yescharacteristic
254D4×C37—416no—
255C2×C4×C37—22no—
256C2×C4×C37—22no—
257C2×C4×C37—22no—
258C2×C4×C37—22no—
259C2×C4×C37—24no—
260C2×C4×C37—24no—
261C2×C4×C37—24no—
262C2×C4×C37—24no—
263C2×C4×C37—22no—
264C2×C4×C37—24no—
265C2×C4×C37—24no—
266C2×C4×C37—24no—
267C2×C4×C37—24no—
268C2×C4×C37—416no—
269C2×C4×C37—41no—
270C2×C4×C37—41no—
271C2×C4×C37—42no—
272C2×C4×C37—42no—
273C2×C4×C37—42no—
274C2×C4×C37—42no—
275C2×C4×C37—42no—
276C2×C4×C37—41no—
277C2×C4×C37—42no—
278C2×C4×C37—41no—
279C2×C4×C37—42no—
280C2×C4×C37—41no—
281C2×C4×C37—42no—
282C2×C4×C37—42no—
283C2×C4×C37—41no—
284C2×C4×C37—42no—
285C2×C4×C37—42no—
286C2×C4×C37—42no—
287C2×C4×C37—42no—
288C2×C4×C37—41no—
289C2×C4×C37—42no—
290C2×C4×C37—41no—
291C2×C4×C37—42no—
292C2×C4×C37—42no—
293C2×C4×C37—42no—
294C2×C4×C37—42no—
295C2×C4×C37—42no—
296C2×C4×C37—42no—
297C2×C4×C37—42no—
298C2×C4×C37—42no—
299C2×C4×C37—42no—
300C2×C4×C37—42no—
301C2×C4×C37—42no—
302C2×C4×C37—42no—
303C2×C4×C37—42no—
304C2×C4×C37—42no—
305C2×C4×C37—42no—
306C2×C4×C37—42no—
307C2×C4×C37#12114yes—
308C2×C4×C37#12314yes—
309#16398C3711yesmaximal, characteristic, direct product factor, Sylow
310C22×C37—24no—
311C22×C37—24no—
312C22×C37—24no—
313C22×C37—42no—
314C22×C37—42no—
315C22×C37—42no—
316C22×C37—44no—
317C22×C37—44no—
318C22×C37—44no—
319C22×C37—44no—
320C22×C37—42no—
321C22×C37—42no—
322C22×C37—42no—
323C22×C37—44no—
324C22×C37—42no—
325C22×C37—44no—
326C22×C37—81no—
327C22×C37—81no—
328C22×C37—81no—
329C22×C37—82no—
330C22×C37—82no—
331C22×C37—81no—
332C22×C37C2×#12111yescharacteristic
333C22×C37C2×C22⋊Q811yescharacteristic
334C22×C37C2×#12311yescharacteristic
335C22×C37#53411yescharacteristic
336C22×C37#53511yescharacteristic
337C22×C37#53512yes—
338C22×C37#53511yescharacteristic
339C22×C37#53711yescharacteristic
340C22×C37#53812yes—
341C22×C37#54012yes—
342C22×C37#54012yes—
343C22×C37#54212yes—
344C22×C37#54312yes—
345C22×C37#54612yes—
346C22×C37#54611yescharacteristic
347C22×C37D4×Q811yescharacteristic
348C22×C37#55112yes—
349C22×C37#55211yescharacteristic
350C22×C37#55312yes—
351C22×C37#55411yescharacteristic
352C22×C37#55412yes—
353C22×C37#56012yes—
354C22×C37#56212yes—
355C4×C37—24no—
356C4×C37—24no—
357C4×C37—42no—
358C4×C37—44no—
359C4×C37—81no—
360C4×C37—82no—
361C4×C37—81no—
362C4×C37—82no—
363C4×C37—82no—
364C2×#399C2×C3711yescharacteristic, complemented
365C2×#386C2×C3711yescharacteristic
366C2×#380C2×C3711yescharacteristic, complemented
367C2×#380C2×C3711yescharacteristic, complemented
368#1445C2×C3711yescharacteristic, complemented
369#1442C2×C3711yescharacteristic, complemented
370#1441C2×C3712yescomplemented
371#1439C2×C3711yescharacteristic, complemented
372#1439C2×C3712yescomplemented
373#1439C2×C3712yescomplemented
374#1438C2×C3712yes—
375C2×C37—44no—
376C2×C37—82no—
377C2×C37#241211yescharacteristic
378C2×C37#241711yescharacteristic
379C2×C37#248711yescharacteristic
380C2×C37#261911yescharacteristic
381C2×C37#262411yescharacteristic
382C2×C37#262611yescharacteristic
383C2×C37#269212yes—
384C2×C37#270312yes—
385C2×C37#274112yes—
386C2×C37#274812yes—
387C2×C37#281311yescharacteristic
388C23×D4C22×C3711yescharacteristic
389C24×C4C22×C3711yescharacteristic
390C22×C4⋊C4C22×C3711yescharacteristic
391C22×C4⋊C4C22×C3712yes—
392C22×C4⋊C4C22×C3712yes—
393C22×C4⋊C4C22×C3711yescharacteristic
394C22×C22⋊C4C22×C3711yescharacteristic
395C22×C22⋊C4C22×C3711yescharacteristic
396C22×C22⋊C4C22×C3712yes—
397C22×C22⋊C4C22×C3712yes—
398C22×C22⋊C4C22×C3712yes—
399C22×C22⋊C4C22×C3711yescharacteristic
400C22×C22⋊C4C22×C3712yes—
401#399—24no—
402#386—24no—
403#380—24no—
404#380—24no—
405C2×#95C22×C3712yes—
406C2×#95C22×C3711yescharacteristic
407C2×#95C22×C3711yescharacteristic
408C2×#95C22×C3711yescharacteristic
409C2×#95C22×C3712yes—
410C2×#95C22×C3712yes—
411C2×#95C22×C3712yes—
412C2×#95C22×C3712yes—
413C2×#95C22×C3712yes—
414C2×#95C22×C3711yescharacteristic
415C37#1639811yescharacteristic, direct product factor, Sylow
416C25C23×C3711yescharacteristic
417C25C23×C3711yescharacteristic
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—42no—
421C22×D4—42no—
422C22×D4Q8×C3714yes—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—24no—
426C23×C4—42no—
427C23×C4D4×C3714yes—
428C23×C4C23×C3711yescharacteristic
429C23×C4C23×C3712yes—
430C23×C4C23×C3712yes—
431C23×C4C23×C3712yes—
432C23×C4C23×C3711yescharacteristic
433C23×C4C23×C3712yes—
434C23×C4C23×C3711yescharacteristic
435C23×C4C23×C3711yescharacteristic
436C23×C4C23×C3711yescharacteristic
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467#95—22no—
468#95—24no—
469#95—22no—
470#95—22no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95D4×C3714yescomplemented
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—22no—
489C24—21no—
490C24—22no—
491C24—21no—
492C24—22no—
493C24—22no—
494C24—21no—
495C24C2×D4×C3712yes—
496C24C2×Q8×C3712yes—
497C24C2×Q8×C3712yes—
498C24#41×C3712yes—
499C24C24×C3711yescharacteristic
500C2×D4—28no—
501C2×D4—48no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—48no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4C2×D4×C3714yes—
557C22×C4C2×D4×C3712yes—
558C22×C4C2×D4×C3712yes—
559C22×C4C2×D4×C3712yes—
560C22×C4C2×Q8×C3712yes—
561C22×C4#41×C3712yes—
562C22×C4#41×C3714yes—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—48no—
566C4⋊C4—44no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—44no—
571C22⋊C4—48no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—24no—
586C23—22no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C22⋊Q8×C3714yes—
620C23C22×D4×C3711yescharacteristic
621C23C22×D4×C3711yescharacteristic
622C23C22×Q8×C3711yescharacteristic
623C23C2×#41×C3711yescharacteristic
624C23C2×#41×C3711yescharacteristic
625C23C2×#41×C3712yes—
626C23H(5,𝔽2)×C3712yes—
627C23H(5,𝔽2)×C3712yes—
628C23H(5,𝔽2)×C3712yes—
629C23H(5,𝔽2)×C3711yescharacteristic
630C232−1+4×C3711yescharacteristic
631D4—416no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—416no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4#121×C3714yes—
685C2×C4#123×C3714yes—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—44no—
700C22—42no—
701C22—44no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—82no—
706C22—82no—
707C22—81no—
708C22C2×#121×C3711yescharacteristic
709C22C2×C22⋊Q8×C3711yescharacteristic
710C22C2×#123×C3711yescharacteristic
711C22C37×#53411yescharacteristic
712C22C37×#53511yescharacteristic
713C22C37×#53512yes—
714C22C37×#53511yescharacteristic
715C22C37×#53711yescharacteristic
716C22C37×#53812yes—
717C22C37×#54012yes—
718C22C37×#54012yes—
719C22C37×#54212yes—
720C22C37×#54312yes—
721C22C37×#54612yes—
722C22C37×#54611yescharacteristic
723C22D4×Q8×C3711yescharacteristic
724C22C37×#55112yes—
725C22C37×#55211yescharacteristic
726C22C37×#55312yes—
727C22C37×#55411yescharacteristic
728C22C37×#55412yes—
729C22C37×#56012yes—
730C22C37×#56212yes—
731C4—24no—
732C4—24no—
733C4—42no—
734C4—44no—
735C4—81no—
736C4—82no—
737C4—81no—
738C4—82no—
739C4—82no—
740C2—44no—
741C2—82no—
742C2C37×#241211yescharacteristic
743C2C37×#241711yescharacteristic
744C2C37×#248711yescharacteristic
745C2C37×#261911yescharacteristic
746C2C37×#262411yescharacteristic
747C2C37×#262611yescharacteristic
748C2C37×#269212yes—
749C2C37×#270312yes—
750C2C37×#274112yes—
751C2C37×#274812yes—
752C2C37×#281311yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutator, Frattini, cosocleC24C24×C37
prime radicalC23×D4×C37C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#399C2semidirect
3. C2×C37×#380C2semidirect
4. C2×C37×#380C2semidirect
5. C37×#1445C2semidirect
6. C37×#1442C2semidirect
7. C37×#1441C2semidirect
8. C37×#1439C2semidirect
9. C37×#1439C2semidirect
10. C37×#1439C2semidirect
99. #95×C37D4semidirect
309. #16398C37direct (N × H)
364. C2×#399C2×C37semidirect
366. C2×#380C2×C37semidirect
367. C2×#380C2×C37semidirect
368. #1445C2×C37semidirect
369. #1442C2×C37semidirect
370. #1441C2×C37semidirect
371. #1439C2×C37semidirect
372. #1439C2×C37semidirect
373. #1439C2×C37semidirect
415. C37#16398direct (N × H)
476. #95D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#3992
C2×C37×#3862
C2×C37×#3802
C37×#14452
C37×#14422
C37×#14412
C37×#14392
C37×#14382
#1639837