Finite Group Databasebeta

← C37×#14142 #22635395

Subgroups — C37×#14142 #22635395

Order 9472.

1490 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#391C211yesmaximal, characteristic
2C2×C37×#391C211yesmaximal, characteristic
3C2×C37×#391C211yesmaximal, characteristic
4C2×C37×#389C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C37C211yesmaximal, characteristic
6C37×#1443C212yesmaximal
7C37×#1442C212yesmaximal
8C37×#1436C212yesmaximal
9C37×C4⋊#95C211yesmaximal, characteristic
10C37×#1434C212yesmaximal
11C4×#95×C37C211yesmaximal, characteristic
12C23×Q8×C37C2211yescharacteristic
13C22×C4⋊C4×C37C2212yes—
14C22×C4⋊C4×C37C2211yescharacteristic
15C22×C4⋊C4×C37C2211yescharacteristic
16C22×C4⋊C4×C37C2211yescharacteristic
17C22×C42×C37C2211yescharacteristic
18C22×C42×C37C2211yescharacteristic
19C22×C42×C37C2212yes—
20C22×C42×C37C2211yescharacteristic
21C37×#391—24no—
22C37×#391—24no—
23C37×#391C418yescomplemented
24C37×#389—24no—
25C4×C4⋊C4×C37—24no—
26C2×#95×C37C2211yescharacteristic
27C2×#95×C37C2211yescharacteristic
28C2×#95×C37C2211yescharacteristic
29C2×#95×C37C2212yes—
30C2×#95×C37C2212yes—
31C2×#95×C37C2212yes—
32C2×#95×C37C2212yes—
33C2×#95×C37C2212yes—
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2212yes—
37C2×#95×C37C2212yes—
38C2×#95×C37C2212yes—
39C2×#95×C37C2211yescharacteristic
40C22×Q8×C37—22no—
41C22×Q8×C37—22no—
42C22×Q8×C37—22no—
43C22×Q8×C37—22no—
44C22×Q8×C37—22no—
45C22×Q8×C37—22no—
46C22×Q8×C37C2×C414yes—
47C23×C4×C37C2312yes—
48C23×C4×C37C2311yescharacteristic
49C23×C4×C37C2312yes—
50C23×C4×C37C2312yes—
51C23×C4×C37C2312yes—
52C23×C4×C37C2311yescharacteristic
53C23×C4×C37C2311yescharacteristic
54C23×C4×C37C2311yescharacteristic
55C23×C4×C37C2311yescharacteristic
56C23×C4×C37C2311yescharacteristic
57C23×C4×C37C2311yescharacteristic
58C2×C4⋊C4×C37—22no—
59C2×C4⋊C4×C37—22no—
60C2×C4⋊C4×C37—22no—
61C2×C4⋊C4×C37—22no—
62C2×C4⋊C4×C37—22no—
63C2×C4⋊C4×C37—22no—
64C2×C4⋊C4×C37—24no—
65C2×C4⋊C4×C37—24no—
66C2×C4⋊C4×C37—42no—
67C2×C4⋊C4×C37C2×C414yes—
68C2×C4⋊C4×C37D414yes—
69C2×C4⋊C4×C37D414yes—
70C2×C42×C37—22no—
71C2×C42×C37—22no—
72C2×C42×C37—24no—
73C2×C42×C37—22no—
74C2×C42×C37—22no—
75C2×C42×C37—22no—
76C2×C42×C37—24no—
77C2×C42×C37—22no—
78C2×C42×C37—22no—
79C2×C42×C37—22no—
80C2×C42×C37—42no—
81C2×C42×C37C2×C414yes—
82#95×C37—24no—
83#95×C37—24no—
84#95×C37—24no—
85#95×C37—24no—
86#95×C37—24no—
87#95×C37—24no—
88#95×C37—22no—
89#95×C37—24no—
90#95×C37—22no—
91#95×C37—22no—
92#95×C37—42no—
93#95×C37C2×C418yes—
94#95×C37C2×C418yes—
95#95×C37Q814yescomplemented
96C24×C37C2411yescharacteristic
97C2×Q8×C37—28no—
98C2×Q8×C37—28no—
99C2×Q8×C37—28no—
100C2×Q8×C37—44no—
101C2×Q8×C37—44no—
102C2×Q8×C37—44no—
103C2×Q8×C37—44no—
104C22×C4×C37—21no—
105C22×C4×C37—21no—
106C22×C4×C37—21no—
107C22×C4×C37—21no—
108C22×C4×C37—21no—
109C22×C4×C37—21no—
110C22×C4×C37—21no—
111C22×C4×C37—21no—
112C22×C4×C37—21no—
113C22×C4×C37—21no—
114C22×C4×C37—22no—
115C22×C4×C37—22no—
116C22×C4×C37—22no—
117C22×C4×C37—22no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—21no—
121C22×C4×C37—22no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—22no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
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—22no—
139C22×C4×C37—22no—
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—21no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—21no—
151C22×C4×C37—21no—
152C22×C4×C37—21no—
153C22×C4×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—22no—
156C22×C4×C37—21no—
157C22×C4×C37—21no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—21no—
162C22×C4×C37C22×C412yes—
163C22×C4×C37C22×C414yes—
164C22×C4×C37C22×C414yes—
165C22×C4×C37C22×C412yes—
166C22×C4×C37C22×C412yes—
167C22×C4×C37C2×D414yes—
168C22×C4×C37C2×D414yes—
169C22×C4×C37C2×D412yes—
170C22×C4×C37C2×D412yes—
171C22×C4×C37C2×Q812yes—
172C22×C4×C37C2×Q812yes—
173C22×C4×C37C2×Q812yes—
174C22×C4×C37#4112yes—
175C22×C4×C37#4112yes—
176C22×C4×C37#4112yes—
177C22×C4×C37#4112yes—
178C22×C4×C37#4112yes—
179C22×C4×C37#4112yes—
180C22×C4×C37#4112yes—
181C4⋊C4×C37—28no—
182C4⋊C4×C37—28no—
183C4⋊C4×C37—28no—
184C4⋊C4×C37—48no—
185C42×C37—28no—
186C42×C37—48no—
187C42×C37—44no—
188C42×C37—44no—
189C23×C37C23×C411yescharacteristic
190C23×C37C22×D411yescharacteristic
191C23×C37C22×D411yescharacteristic
192C23×C37C22×Q811yescharacteristic
193C23×C37C2×#4111yescharacteristic
194C23×C37C2×#4111yescharacteristic
195C23×C37C2×#4111yescharacteristic
196C23×C37C2×#4111yescharacteristic
197C23×C37C2×#4111yescharacteristic
198C23×C37C2×#4111yescharacteristic
199C23×C37C2×#4111yescharacteristic
200C23×C37H(5,𝔽2)11yescharacteristic
201C23×C372−1+411yescharacteristic
202C23×C372−1+411yescharacteristic
203C23×C372−1+411yescharacteristic
204Q8×C37—416no—
205C2×C4×C37—22no—
206C2×C4×C37—22no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—22no—
210C2×C4×C37—22no—
211C2×C4×C37—24no—
212C2×C4×C37—22no—
213C2×C4×C37—24no—
214C2×C4×C37—24no—
215C2×C4×C37—24no—
216C2×C4×C37—22no—
217C2×C4×C37—24no—
218C2×C4×C37—22no—
219C2×C4×C37—24no—
220C2×C4×C37—24no—
221C2×C4×C37—24no—
222C2×C4×C37—22no—
223C2×C4×C37—22no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
226C2×C4×C37—24no—
227C2×C4×C37—22no—
228C2×C4×C37—24no—
229C2×C4×C37—24no—
230C2×C4×C37—24no—
231C2×C4×C37—22no—
232C2×C4×C37—22no—
233C2×C4×C37—22no—
234C2×C4×C37—22no—
235C2×C4×C37—22no—
236C2×C4×C37—22no—
237C2×C4×C37—22no—
238C2×C4×C37—41no—
239C2×C4×C37—41no—
240C2×C4×C37—42no—
241C2×C4×C37—42no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—42no—
245C2×C4×C37—42no—
246C2×C4×C37—42no—
247C2×C4×C37—42no—
248C2×C4×C37—41no—
249C2×C4×C37—41no—
250C2×C4×C37—41no—
251C2×C4×C37—42no—
252C2×C4×C37—42no—
253C2×C4×C37—41no—
254C2×C4×C37—42no—
255C2×C4×C37—42no—
256C2×C4×C37—41no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—41no—
260C2×C4×C37—41no—
261C2×C4×C37—41no—
262C2×C4×C37—41no—
263C2×C4×C37—42no—
264C2×C4×C37—42no—
265C2×C4×C37—41no—
266C2×C4×C37—41no—
267C2×C4×C37—41no—
268C2×C4×C37—41no—
269C2×C4×C37—42no—
270C2×C4×C37—42no—
271C2×C4×C37—41no—
272C2×C4×C37—42no—
273C2×C4×C37—42no—
274C2×C4×C37#11714yes—
275C2×C4×C37C4×D414yes—
276C2×C4×C37C4×D414yes—
277C2×C4×C37C4×Q814yes—
278C2×C4×C37#12114yes—
279C2×C4×C37#12314yes—
280C2×C4×C37#12414yes—
281C2×C4×C37#12614yes—
282#14142C3711yesmaximal, characteristic, direct product factor, Sylow
283C22×C37C2×#11711yescharacteristic
284C22×C37C2×C4×D411yescharacteristic
285C22×C37C2×C4×D411yescharacteristic
286C22×C37C2×C4×Q811yescharacteristic
287C22×C37C4×#4111yescharacteristic
288C22×C37#51911yescharacteristic
289C22×C37#52011yescharacteristic
290C22×C37C2×#12111yescharacteristic
291C22×C37C2×#12311yescharacteristic
292C22×C37C2×#12411yescharacteristic
293C22×C37C2×#12611yescharacteristic
294C22×C37#52911yescharacteristic
295C22×C37#52911yescharacteristic
296C22×C37#53311yescharacteristic
297C22×C37#53311yescharacteristic
298C22×C37#54111yescharacteristic
299C22×C37#54111yescharacteristic
300C22×C37#54211yescharacteristic
301C22×C37#54211yescharacteristic
302C22×C37#54611yescharacteristic
303C22×C37#54611yescharacteristic
304C22×C37#54711yescharacteristic
305C22×C37#54711yescharacteristic
306C22×C37#54811yescharacteristic
307C22×C37#54811yescharacteristic
308C22×C37D4×Q811yescharacteristic
309C22×C37D4×Q811yescharacteristic
310C22×C37#55211yescharacteristic
311C22×C37#55211yescharacteristic
312C22×C37#55411yescharacteristic
313C22×C37#55611yescharacteristic
314C22×C37#55611yescharacteristic
315C22×C37#55611yescharacteristic
316C22×C37#55711yescharacteristic
317C22×C37#55911yescharacteristic
318C4×C37—24no—
319C4×C37—42no—
320C4×C37—44no—
321C4×C37—44no—
322C4×C37—42no—
323C4×C37—42no—
324C4×C37—44no—
325C4×C37—42no—
326C4×C37—42no—
327C4×C37—44no—
328C4×C37#38818yes—
329C2×#391C2×C3711yescharacteristic
330C2×#391C2×C3711yescharacteristic
331C2×#391C2×C3711yescharacteristic
332C2×#389C2×C3711yescharacteristic
333C2×C4×C4⋊C4C2×C3711yescharacteristic
334#1443C2×C3712yes—
335#1442C2×C3712yes—
336#1436C2×C3712yes—
337C4⋊#95C2×C3711yescharacteristic
338#1434C2×C3712yes—
339C4×#95C2×C3711yescharacteristic
340C2×C37C2×#38811yescharacteristic
341C2×C37#229511yescharacteristic
342C2×C37#232011yescharacteristic
343C2×C37#236011yescharacteristic
344C2×C37#236211yescharacteristic
345C2×C37#236511yescharacteristic
346C2×C37#236711yescharacteristic
347C2×C37#242711yescharacteristic
348C2×C37#242911yescharacteristic
349C2×C37#244611yescharacteristic
350C2×C37#244711yescharacteristic
351C2×C37#248911yescharacteristic
352C2×C37#249211yescharacteristic
353C2×C37#251111yescharacteristic
354C2×C37#251411yescharacteristic
355C23×Q8C22×C3711yescharacteristic
356C22×C4⋊C4C22×C3712yes—
357C22×C4⋊C4C22×C3711yescharacteristic
358C22×C4⋊C4C22×C3711yescharacteristic
359C22×C4⋊C4C22×C3711yescharacteristic
360C22×C42C22×C3711yescharacteristic
361C22×C42C22×C3711yescharacteristic
362C22×C42C22×C3712yes—
363C22×C42C22×C3711yescharacteristic
364#391—24no—
365#391—24no—
366#391C4×C3718yescomplemented
367#389—24no—
368C4×C4⋊C4—24no—
369C2×#95C22×C3711yescharacteristic
370C2×#95C22×C3711yescharacteristic
371C2×#95C22×C3711yescharacteristic
372C2×#95C22×C3712yes—
373C2×#95C22×C3712yes—
374C2×#95C22×C3712yes—
375C2×#95C22×C3712yes—
376C2×#95C22×C3712yes—
377C2×#95C22×C3712yes—
378C2×#95C22×C3712yes—
379C2×#95C22×C3712yes—
380C2×#95C22×C3712yes—
381C2×#95C22×C3712yes—
382C2×#95C22×C3711yescharacteristic
383C37#1414211yescharacteristic, direct product factor, Sylow
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8C2×C4×C3714yes—
391C23×C4C23×C3712yes—
392C23×C4C23×C3712yes—
393C23×C4C23×C3711yescharacteristic
394C23×C4C23×C3712yes—
395C23×C4C23×C3712yes—
396C23×C4C23×C3711yescharacteristic
397C23×C4C23×C3711yescharacteristic
398C23×C4C23×C3711yescharacteristic
399C23×C4C23×C3711yescharacteristic
400C23×C4C23×C3711yescharacteristic
401C23×C4C23×C3711yescharacteristic
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4C2×C4×C3714yes—
412C2×C4⋊C4D4×C3714yes—
413C2×C4⋊C4D4×C3714yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—42no—
425C2×C42C2×C4×C3714yes—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—22no—
433#95—24no—
434#95—22no—
435#95—22no—
436#95—42no—
437#95C2×C4×C3718yes—
438#95C2×C4×C3718yes—
439#95Q8×C3714yescomplemented
440C24C24×C3711yescharacteristic
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4C22×C4×C3712yes—
507C22×C4C22×C4×C3714yes—
508C22×C4C22×C4×C3714yes—
509C22×C4C22×C4×C3712yes—
510C22×C4C22×C4×C3712yes—
511C22×C4C2×D4×C3714yes—
512C22×C4C2×D4×C3714yes—
513C22×C4C2×D4×C3712yes—
514C22×C4C2×D4×C3712yes—
515C22×C4C2×Q8×C3712yes—
516C22×C4C2×Q8×C3712yes—
517C22×C4C2×Q8×C3712yes—
518C22×C4#41×C3712yes—
519C22×C4#41×C3712yes—
520C22×C4#41×C3712yes—
521C22×C4#41×C3712yes—
522C22×C4#41×C3712yes—
523C22×C4#41×C3712yes—
524C22×C4#41×C3712yes—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—48no—
529C42—28no—
530C42—48no—
531C42—44no—
532C42—44no—
533C23C23×C4×C3711yescharacteristic
534C23C22×D4×C3711yescharacteristic
535C23C22×D4×C3711yescharacteristic
536C23C22×Q8×C3711yescharacteristic
537C23C2×#41×C3711yescharacteristic
538C23C2×#41×C3711yescharacteristic
539C23C2×#41×C3711yescharacteristic
540C23C2×#41×C3711yescharacteristic
541C23C2×#41×C3711yescharacteristic
542C23C2×#41×C3711yescharacteristic
543C23C2×#41×C3711yescharacteristic
544C23H(5,𝔽2)×C3711yescharacteristic
545C232−1+4×C3711yescharacteristic
546C232−1+4×C3711yescharacteristic
547C232−1+4×C3711yescharacteristic
548Q8—416no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4#117×C3714yes—
619C2×C4C4×D4×C3714yes—
620C2×C4C4×D4×C3714yes—
621C2×C4C4×Q8×C3714yes—
622C2×C4#121×C3714yes—
623C2×C4#123×C3714yes—
624C2×C4#124×C3714yes—
625C2×C4#126×C3714yes—
626C22C2×#117×C3711yescharacteristic
627C22C2×C4×D4×C3711yescharacteristic
628C22C2×C4×D4×C3711yescharacteristic
629C22C2×C4×Q8×C3711yescharacteristic
630C22C4×#41×C3711yescharacteristic
631C22C37×#51911yescharacteristic
632C22C37×#52011yescharacteristic
633C22C2×#121×C3711yescharacteristic
634C22C2×#123×C3711yescharacteristic
635C22C2×#124×C3711yescharacteristic
636C22C2×#126×C3711yescharacteristic
637C22C37×#52911yescharacteristic
638C22C37×#52911yescharacteristic
639C22C37×#53311yescharacteristic
640C22C37×#53311yescharacteristic
641C22C37×#54111yescharacteristic
642C22C37×#54111yescharacteristic
643C22C37×#54211yescharacteristic
644C22C37×#54211yescharacteristic
645C22C37×#54611yescharacteristic
646C22C37×#54611yescharacteristic
647C22C37×#54711yescharacteristic
648C22C37×#54711yescharacteristic
649C22C37×#54811yescharacteristic
650C22C37×#54811yescharacteristic
651C22D4×Q8×C3711yescharacteristic
652C22D4×Q8×C3711yescharacteristic
653C22C37×#55211yescharacteristic
654C22C37×#55211yescharacteristic
655C22C37×#55411yescharacteristic
656C22C37×#55611yescharacteristic
657C22C37×#55611yescharacteristic
658C22C37×#55611yescharacteristic
659C22C37×#55711yescharacteristic
660C22C37×#55911yescharacteristic
661C4—24no—
662C4—42no—
663C4—44no—
664C4—44no—
665C4—42no—
666C4—42no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—44no—
671C4C37×#38818yes—
672C2C2×C37×#38811yescharacteristic
673C2C37×#229511yescharacteristic
674C2C37×#232011yescharacteristic
675C2C37×#236011yescharacteristic
676C2C37×#236211yescharacteristic
677C2C37×#236511yescharacteristic
678C2C37×#236711yescharacteristic
679C2C37×#242711yescharacteristic
680C2C37×#242911yescharacteristic
681C2C37×#244611yescharacteristic
682C2C37×#244711yescharacteristic
683C2C37×#248911yescharacteristic
684C2C37×#249211yescharacteristic
685C2C37×#251111yescharacteristic
686C2C37×#251411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
23. C37×#391C4semidirect
95. #95×C37Q8semidirect
282. #14142C37direct (N × H)
366. #391C4×C37semidirect
383. C37#14142direct (N × H)
439. #95Q8×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#3912
C2×C37×#3892
C2×C4×C4⋊C4×C372
C37×#14432
C37×#14422
C37×#14362
C37×C4⋊#952
C37×#14342
C4×#95×C372
#1414237