Finite Group Databasebeta

← C37×#14401 #22635654

Subgroups — C37×#14401 #22635654

Order 9472.

2118 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×#390C211yesmaximal, characteristic
2C2×C37×#386C211yesmaximal, characteristic
3C2×C37×#386C211yesmaximal, characteristic
4C2×C37×#385C212yesmaximal, complemented
5C2×C37×#380C212yesmaximal, complemented
6C37×#1444C212yesmaximal, complemented
7C37×#1439C212yesmaximal, complemented
8C37×#1439C212yesmaximal, complemented
9C37×#1436C212yesmaximal, complemented
10C23×D4×C37C2211yescharacteristic
11C24×C4×C37C2211yescharacteristic
12C24×C4×C37C2211yescharacteristic
13C22×C4⋊C4×C37C2212yes—
14C22×C4⋊C4×C37C2212yes—
15C22×C4⋊C4×C37C2212yes—
16C22×C4⋊C4×C37C2211yescharacteristic
17C22×C22⋊C4×C37C2212yes—
18C22×C22⋊C4×C37C2212yes—
19C22×C22⋊C4×C37C2212yes—
20C22×C22⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2211yescharacteristic
22C22×C22⋊C4×C37C2211yescharacteristic
23C22×C42×C37C2211yescharacteristic
24C37×#390—24no—
25C37×#386—24no—
26C37×#386C418yescomplemented
27C37×#385—28no—
28C37×#380—28no—
29C2×#95×C37C2212yes—
30C2×#95×C37C2212yes—
31C2×#95×C37C2212yes—
32C2×#95×C37C2212yes—
33C2×#95×C37C2212yes—
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C25×C37C2311yescharacteristic
37C25×C37C2311yescharacteristic
38C22×D4×C37—41no—
39C22×D4×C37—41no—
40C22×D4×C37—41no—
41C22×D4×C37—41no—
42C22×D4×C37C2×C414yes—
43C22×D4×C37D414yes—
44C22×D4×C37Q814yes—
45C23×C4×C37—24no—
46C23×C4×C37—24no—
47C23×C4×C37—22no—
48C23×C4×C37—24no—
49C23×C4×C37—41no—
50C23×C4×C37—41no—
51C23×C4×C37—42no—
52C23×C4×C37—41no—
53C23×C4×C37—41no—
54C23×C4×C37C2×C414yescomplemented
55C23×C4×C37C2312yes—
56C23×C4×C37C2312yes—
57C23×C4×C37C2312yes—
58C23×C4×C37C2312yes—
59C23×C4×C37C2312yes—
60C23×C4×C37C2311yescharacteristic
61C23×C4×C37C2312yes—
62C2×C4⋊C4×C37—24no—
63C2×C4⋊C4×C37—24no—
64C2×C4⋊C4×C37—24no—
65C2×C4⋊C4×C37—24no—
66C2×C4⋊C4×C37—22no—
67C2×C4⋊C4×C37—24no—
68C2×C4⋊C4×C37—42no—
69C2×C4⋊C4×C37—42no—
70C2×C4⋊C4×C37—41no—
71C2×C4⋊C4×C37—41no—
72C2×C4⋊C4×C37—42no—
73C2×C4⋊C4×C37—42no—
74C2×C22⋊C4×C37—24no—
75C2×C22⋊C4×C37—24no—
76C2×C22⋊C4×C37—24no—
77C2×C22⋊C4×C37—22no—
78C2×C22⋊C4×C37—24no—
79C2×C22⋊C4×C37—24no—
80C2×C22⋊C4×C37—24no—
81C2×C22⋊C4×C37—24no—
82C2×C22⋊C4×C37—24no—
83C2×C22⋊C4×C37—41no—
84C2×C22⋊C4×C37—41no—
85C2×C22⋊C4×C37—42no—
86C2×C22⋊C4×C37—42no—
87C2×C22⋊C4×C37—42no—
88C2×C22⋊C4×C37—41no—
89C2×C22⋊C4×C37—41no—
90C2×C22⋊C4×C37C2×C418yes—
91C2×C22⋊C4×C37C2×C414yescomplemented
92C2×C42×C37—22no—
93C2×C42×C37—41no—
94C2×C42×C37—41no—
95#95×C37—24no—
96#95×C37—24no—
97#95×C37—24no—
98#95×C37—42no—
99#95×C37—42no—
100#95×C37C2×C418yescomplemented
101#95×C37D418yescomplemented
102C24×C37—22no—
103C24×C37—22no—
104C24×C37—22no—
105C24×C37—22no—
106C24×C37—22no—
107C24×C37—22no—
108C24×C37—21no—
109C24×C37—21no—
110C24×C37—21no—
111C24×C37—21no—
112C24×C37—21no—
113C24×C37—21no—
114C24×C37—21no—
115C24×C37—21no—
116C24×C37—22no—
117C24×C37—22no—
118C24×C37C22×C412yes—
119C24×C37C22×C412yes—
120C24×C37C2×D412yes—
121C24×C37C2×D412yes—
122C24×C37C2×Q812yes—
123C24×C37C2×Q812yes—
124C24×C37C2411yescharacteristic
125C2×D4×C37—44no—
126C2×D4×C37—44no—
127C2×D4×C37—44no—
128C2×D4×C37—44no—
129C2×D4×C37—44no—
130C2×D4×C37—44no—
131C2×D4×C37C4⋊C4116yescomplemented
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—21no—
135C22×C4×C37—21no—
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—22no—
141C22×C4×C37—22no—
142C22×C4×C37—22no—
143C22×C4×C37—22no—
144C22×C4×C37—22no—
145C22×C4×C37—22no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—22no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—216no—
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—44no—
174C22×C4×C37—44no—
175C22×C4×C37—48no—
176C22×C4×C37—44no—
177C22×C4×C37—44no—
178C22×C4×C37—48no—
179C22×C4×C37—48no—
180C22×C4×C37—44no—
181C22×C4×C37—44no—
182C22×C4×C37C22×C414yes—
183C22×C4×C37C22×C412yes—
184C22×C4×C37C22×C414yes—
185C22×C4×C37C2×D414yes—
186C22×C4×C37C2×D414yes—
187C22×C4×C37C2×D412yes—
188C22×C4×C37C2×D414yes—
189C22×C4×C37C2×Q812yes—
190C22×C4×C37#4114yes—
191C4⋊C4×C37—48no—
192C4⋊C4×C37—48no—
193C4⋊C4×C37—44no—
194C4⋊C4×C37—48no—
195C22⋊C4×C37—216no—
196C22⋊C4×C37—44no—
197C22⋊C4×C37—48no—
198C22⋊C4×C37—48no—
199C22⋊C4×C37—48no—
200C22⋊C4×C37—44no—
201C42×C37—44no—
202C23×C37—24no—
203C23×C37—24no—
204C23×C37—22no—
205C23×C37—22no—
206C23×C37—22no—
207C23×C37—22no—
208C23×C37—24no—
209C23×C37—24no—
210C23×C37—22no—
211C23×C37—22no—
212C23×C37—22no—
213C23×C37—22no—
214C23×C37—22no—
215C23×C37—22no—
216C23×C37—22no—
217C23×C37—22no—
218C23×C37—24no—
219C23×C37—24no—
220C23×C37—24no—
221C23×C37—24no—
222C23×C37—24no—
223C23×C37—24no—
224C23×C37—24no—
225C23×C37—24no—
226C23×C37—42no—
227C23×C37—42no—
228C23×C37—42no—
229C23×C37—42no—
230C23×C37—42no—
231C23×C37—42no—
232C23×C37—42no—
233C23×C37—42no—
234C23×C37—41no—
235C23×C37—41no—
236C23×C37—42no—
237C23×C37—42no—
238C23×C37—41no—
239C23×C37—41no—
240C23×C37—41no—
241C23×C37—41no—
242C23×C37—42no—
243C23×C37—42no—
244C23×C37—41no—
245C23×C37—41no—
246C23×C37C2×C4⋊C414yes—
247C23×C37C2×C4⋊C414yes—
248C23×C37C23×C411yescharacteristic
249C23×C37C22×D411yescharacteristic
250C23×C37C22×D412yes—
251C23×C37C22×Q811yescharacteristic
252C23×C37C2×#4112yes—
253C23×C37H(5,𝔽2)11yescharacteristic
254C23×C37H(5,𝔽2)11yescharacteristic
255C23×C37H(5,𝔽2)11yescharacteristic
256C23×C37H(5,𝔽2)11yescharacteristic
257C23×C37H(5,𝔽2)12yes—
258C23×C372−1+412yes—
259D4×C37—416no—
260C2×C4×C37—24no—
261C2×C4×C37—24no—
262C2×C4×C37—22no—
263C2×C4×C37—22no—
264C2×C4×C37—22no—
265C2×C4×C37—22no—
266C2×C4×C37—22no—
267C2×C4×C37—22no—
268C2×C4×C37—24no—
269C2×C4×C37—24no—
270C2×C4×C37—24no—
271C2×C4×C37—24no—
272C2×C4×C37—24no—
273C2×C4×C37—24no—
274C2×C4×C37—24no—
275C2×C4×C37—24no—
276C2×C4×C37—24no—
277C2×C4×C37—24no—
278C2×C4×C37—24no—
279C2×C4×C37—24no—
280C2×C4×C37—24no—
281C2×C4×C37—416no—
282C2×C4×C37—416no—
283C2×C4×C37—42no—
284C2×C4×C37—42no—
285C2×C4×C37—42no—
286C2×C4×C37—42no—
287C2×C4×C37—42no—
288C2×C4×C37—42no—
289C2×C4×C37—42no—
290C2×C4×C37—42no—
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—42no—
308C2×C4×C37—42no—
309C2×C4×C37C2×C4⋊C414yes—
310C2×C4×C37C4×D418yes—
311#14401C3711yesmaximal, characteristic, direct product factor, Sylow
312C22×C37—24no—
313C22×C37—24no—
314C22×C37—28no—
315C22×C37—28no—
316C22×C37—44no—
317C22×C37—44no—
318C22×C37—42no—
319C22×C37—42no—
320C22×C37—42no—
321C22×C37—42no—
322C22×C37—42no—
323C22×C37—42no—
324C22×C37—44no—
325C22×C37—44no—
326C22×C37—42no—
327C22×C37—42no—
328C22×C37—44no—
329C22×C37—44no—
330C22×C37—42no—
331C22×C37—42no—
332C22×C37—42no—
333C22×C37—42no—
334C22×C37C22×C4⋊C411yescharacteristic
335C22×C37C2×C4×D412yes—
336C22×C37#51811yescharacteristic
337C22×C37#51811yescharacteristic
338C22×C37#52012yes—
339C22×C37#53411yescharacteristic
340C22×C37#53411yescharacteristic
341C22×C37#53512yes—
342C22×C37#53712yes—
343C22×C37#54012yes—
344C22×C37#54212yes—
345C22×C37#54311yescharacteristic
346C22×C37#54311yescharacteristic
347C22×C37D4212yes—
348C22×C37D4211yescharacteristic
349C22×C37#54612yes—
350C22×C37#54712yes—
351C22×C37D4×Q812yes—
352C22×C37#55111yescharacteristic
353C22×C37#55412yes—
354C22×C37#56011yescharacteristic
355C22×C37#56212yes—
356C22×C37#56311yescharacteristic
357C4×C37—24no—
358C4×C37—28no—
359C4×C37—44no—
360C4×C37—44no—
361C4×C37—44no—
362C4×C37—82no—
363C4×C37—82no—
364C2×#390C2×C3711yescharacteristic
365C2×#386C2×C3711yescharacteristic
366C2×#386C2×C3711yescharacteristic
367C2×#385C2×C3712yescomplemented
368C2×#380C2×C3712yescomplemented
369#1444C2×C3712yescomplemented
370#1439C2×C3712yescomplemented
371#1439C2×C3712yescomplemented
372#1436C2×C3712yescomplemented
373C2×C37—44no—
374C2×C37—44no—
375C2×C37#231511yescharacteristic
376C2×C37#232412yes—
377C2×C37D4×C4⋊C412yes—
378C2×C37#235811yescharacteristic
379C2×C37#237611yescharacteristic
380C2×C37#266911yescharacteristic
381C2×C37#267112yes—
382C2×C37#268311yescharacteristic
383C2×C37#269212yes—
384C2×C37#271711yescharacteristic
385C2×C37#274811yescharacteristic
386C23×D4C22×C3711yescharacteristic
387C24×C4C22×C3711yescharacteristic
388C24×C4C22×C3711yescharacteristic
389C22×C4⋊C4C22×C3712yes—
390C22×C4⋊C4C22×C3712yes—
391C22×C4⋊C4C22×C3712yes—
392C22×C4⋊C4C22×C3711yescharacteristic
393C22×C22⋊C4C22×C3712yes—
394C22×C22⋊C4C22×C3712yes—
395C22×C22⋊C4C22×C3712yes—
396C22×C22⋊C4C22×C3712yes—
397C22×C22⋊C4C22×C3711yescharacteristic
398C22×C22⋊C4C22×C3711yescharacteristic
399C22×C42C22×C3711yescharacteristic
400#390—24no—
401#386—24no—
402#386C4×C3718yescomplemented
403#385—28no—
404#380—28no—
405C2×#95C22×C3712yes—
406C2×#95C22×C3712yes—
407C2×#95C22×C3712yes—
408C2×#95C22×C3712yes—
409C2×#95C22×C3712yes—
410C2×#95C22×C3712yes—
411C2×#95C22×C3712yes—
412C37#1440111yescharacteristic, direct product factor, Sylow
413C25C23×C3711yescharacteristic
414C25C23×C3711yescharacteristic
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4—41no—
419C22×D4C2×C4×C3714yes—
420C22×D4D4×C3714yes—
421C22×D4Q8×C3714yes—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—22no—
425C23×C4—24no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—42no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4C2×C4×C3714yescomplemented
432C23×C4C23×C3712yes—
433C23×C4C23×C3712yes—
434C23×C4C23×C3712yes—
435C23×C4C23×C3712yes—
436C23×C4C23×C3712yes—
437C23×C4C23×C3711yescharacteristic
438C23×C4C23×C3712yes—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—41no—
466C2×C22⋊C4—41no—
467C2×C22⋊C4C2×C4×C3718yes—
468C2×C22⋊C4C2×C4×C3714yescomplemented
469C2×C42—22no—
470C2×C42—41no—
471C2×C42—41no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—42no—
476#95—42no—
477#95C2×C4×C3718yescomplemented
478#95D4×C3718yescomplemented
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24C22×C4×C3712yes—
496C24C22×C4×C3712yes—
497C24C2×D4×C3712yes—
498C24C2×D4×C3712yes—
499C24C2×Q8×C3712yes—
500C24C2×Q8×C3712yes—
501C24C24×C3711yescharacteristic
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4C4⋊C4×C37116yescomplemented
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—216no—
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—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4C22×C4×C3714yes—
560C22×C4C22×C4×C3712yes—
561C22×C4C22×C4×C3714yes—
562C22×C4C2×D4×C3714yes—
563C22×C4C2×D4×C3714yes—
564C22×C4C2×D4×C3712yes—
565C22×C4C2×D4×C3714yes—
566C22×C4C2×Q8×C3712yes—
567C22×C4#41×C3714yes—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—44no—
571C4⋊C4—48no—
572C22⋊C4—216no—
573C22⋊C4—44no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—44no—
578C42—44no—
579C23—24no—
580C23—24no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23C2×C4⋊C4×C3714yes—
624C23C2×C4⋊C4×C3714yes—
625C23C23×C4×C3711yescharacteristic
626C23C22×D4×C3711yescharacteristic
627C23C22×D4×C3712yes—
628C23C22×Q8×C3711yescharacteristic
629C23C2×#41×C3712yes—
630C23H(5,𝔽2)×C3712yes—
631C23H(5,𝔽2)×C3711yescharacteristic
632C23H(5,𝔽2)×C3711yescharacteristic
633C23H(5,𝔽2)×C3711yescharacteristic
634C23H(5,𝔽2)×C3711yescharacteristic
635C232−1+4×C3712yes—
636D4—416no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—416no—
659C2×C4—416no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
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—42no—
685C2×C4—42no—
686C2×C4C2×C4⋊C4×C3714yes—
687C2×C4C4×D4×C3718yes—
688C22—24no—
689C22—24no—
690C22—28no—
691C22—28no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—44no—
699C22—44no—
700C22—42no—
701C22—42no—
702C22—44no—
703C22—44no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—44no—
710C22C22×C4⋊C4×C3711yescharacteristic
711C22C2×C4×D4×C3712yes—
712C22C37×#51811yescharacteristic
713C22C37×#51811yescharacteristic
714C22C37×#52012yes—
715C22C37×#53411yescharacteristic
716C22C37×#53411yescharacteristic
717C22C37×#53512yes—
718C22C37×#53712yes—
719C22C37×#54012yes—
720C22C37×#54212yes—
721C22C37×#54311yescharacteristic
722C22C37×#54311yescharacteristic
723C22D42×C3711yescharacteristic
724C22D42×C3712yes—
725C22C37×#54612yes—
726C22C37×#54712yes—
727C22D4×Q8×C3712yes—
728C22C37×#55111yescharacteristic
729C22C37×#55412yes—
730C22C37×#56011yescharacteristic
731C22C37×#56212yes—
732C22C37×#56311yescharacteristic
733C4—28no—
734C4—24no—
735C4—44no—
736C4—44no—
737C4—44no—
738C4—82no—
739C4—82no—
740C2—44no—
741C2—44no—
742C2C37×#231511yescharacteristic
743C2C37×#232412yes—
744C2D4×C4⋊C4×C3712yes—
745C2C37×#235811yescharacteristic
746C2C37×#237611yescharacteristic
747C2C37×#266911yescharacteristic
748C2C37×#267112yes—
749C2C37×#268311yescharacteristic
750C2C37×#269212yes—
751C2C37×#271711yescharacteristic
752C2C37×#274811yescharacteristic
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC23×D4×C37C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C37×#385C2semidirect
5. C2×C37×#380C2semidirect
6. C37×#1444C2semidirect
7. C37×#1439C2semidirect
8. C37×#1439C2semidirect
9. C37×#1436C2semidirect
26. C37×#386C4semidirect
54. C23×C4×C37C2×C4semidirect
91. C2×C22⋊C4×C37C2×C4semidirect
100. #95×C37C2×C4semidirect
101. #95×C37D4semidirect
131. C2×D4×C37C4⋊C4semidirect
311. #14401C37direct (N × H)
367. C2×#385C2×C37semidirect
368. C2×#380C2×C37semidirect
369. #1444C2×C37semidirect
370. #1439C2×C37semidirect
371. #1439C2×C37semidirect
372. #1436C2×C37semidirect
402. #386C4×C37semidirect
412. C37#14401direct (N × H)
431. C23×C4C2×C4×C37semidirect
468. C2×C22⋊C4C2×C4×C37semidirect
477. #95C2×C4×C37semidirect
478. #95D4×C37semidirect
508. C2×D4C4⋊C4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#3902
C2×C37×#3862
C2×C37×#3852
C2×C37×#3802
C37×#14442
C37×#14392
C37×#14362
#1440137