Finite Group Databasebeta

← C37×#26605 #22647858

Subgroups — C37×#26605 #22647858

Order 9472.

944 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#460C211yesmaximal, characteristic
2C2×C37×#440C211yesmaximal, characteristic, complemented
3C37×#2445C211yesmaximal, characteristic
4C37×#2365C211yesmaximal, characteristic, complemented
5C37×#2068C211yesmaximal, characteristic, complemented
6C37×#2014C211yesmaximal, characteristic
7C37×#2013C211yesmaximal, characteristic, complemented
8C37×#2013C211yesmaximal, characteristic, complemented
9C37×#1973C211yesmaximal, characteristic, complemented
10C37×#1925C211yesmaximal, characteristic, complemented
11C37×#1925C211yesmaximal, characteristic, complemented
12C37×#1917C211yesmaximal, characteristic, complemented
13C37×#1880C211yesmaximal, characteristic, complemented
14C37×#1877C211yesmaximal, characteristic, complemented
15C37×#1863C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C2×C4⋊Q8×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#123×C37—21no—
23C2×C4×Q8×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C37×#460—24no—
27C37×#440—24no—
28C2×#107×C37C2211yescharacteristic
29C2×#107×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#97×C37C2211yescharacteristic
40C37×#394—21no—
41C37×#394—21no—
42C37×#391C2211yescharacteristic
43C37×#391C2211yescharacteristic
44C37×#390C2211yescharacteristic
45C37×#390C2211yescharacteristic
46C37×#390C2211yescharacteristic
47C37×#389—21no—
48C37×#389C2211yescharacteristic
49C37×#387—21no—
50C37×#387—21no—
51C37×#386—21no—
52C4×C4⋊C4×C37—21no—
53C4×C4⋊C4×C37C2211yescharacteristic
54C4×C4⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×Q8×C37C2311yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37C2311yescharacteristic
66C22×D4×C37C2311yescharacteristic
67C23×C4×C37—21no—
68C2×SD16×C37—22no—
69C2×SD16×C37—22no—
70C2×SD16×C37—22no—
71C2×SD16×C37—22no—
72C2×SD16×C37—22no—
73C2×SD16×C37—22no—
74C2×SD16×C37—22no—
75C2×SD16×C37—22no—
76C2×SD16×C37—41no—
77C2×SD16×C37—41no—
78C2×SD16×C37—41no—
79C2×SD16×C37—41no—
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84C4⋊Q8×C37—22no—
85C4⋊Q8×C37—22no—
86#127×C37—22no—
87#127×C37—41no—
88#123×C37—44no—
89C4×Q8×C37—22no—
90C4×Q8×C37—22no—
91C4×Q8×C37—41no—
92C4×Q8×C37—41no—
93C4×D4×C37—22no—
94C4×D4×C37—41no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37—21no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37—21no—
100C2×C4⋊C4×C37D411yescharacteristic
101C2×C4⋊C4×C37D411yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C4⋊C4×C37C2311yescharacteristic
104C2×C4⋊C4×C37C2311yescharacteristic
105C2×C4⋊C4×C37C2311yescharacteristic
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C42×C37—21no—
114C2×C42×C37—21no—
115C2×C42×C37—21no—
116C2×C42×C37C2311yescharacteristic
117C2×C42×C37C2311yescharacteristic
118C2×C42×C37C2311yescharacteristic
119#107×C37—22no—
120#107×C37—41no—
121C4⋊C8×C37—22no—
122#103×C37—22no—
123#103×C37—22no—
124#103×C37—41no—
125#103×C37—41no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—41no—
129#102×C37D414yes—
130#97×C37—22no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37D411yescharacteristic
138#95×C37D411yescharacteristic
139C24×C37—21no—
140C24×C37—21no—
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37—21no—
151C2×Q8×C37#4112yes—
152C2×Q8×C37#4112yes—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—21no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—42no—
167C2×D4×C37—42no—
168C2×D4×C37—81no—
169C2×D4×C37—81no—
170C2×D4×C37C2×D412yes—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—42no—
178C22×C4×C37—42no—
179C22×C4×C37—81no—
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183C22×C4×C37C2×D411yescharacteristic
184C22×C4×C37C2×D411yescharacteristic
185C22×C4×C37C2×D411yescharacteristic
186C22×C4×C37C2411yescharacteristic
187SD16×C37—28no—
188SD16×C37—44no—
189SD16×C37—44no—
190SD16×C37—44no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37—21no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37C2×D412yes—
202C2×C8×C37#4112yes—
203C4⋊C4×C37—24no—
204C4⋊C4×C37—24no—
205C4⋊C4×C37—22no—
206C4⋊C4×C37—22no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—42no—
215C4⋊C4×C37—42no—
216C4⋊C4×C37—42no—
217C4⋊C4×C37C2×D412yes—
218C22⋊C4×C37—42no—
219C22⋊C4×C37—42no—
220C22⋊C4×C37—42no—
221C22⋊C4×C37—42no—
222C22⋊C4×C37—81no—
223C22⋊C4×C37—81no—
224C22⋊C4×C37—81no—
225C42×C37—21no—
226C42×C37—21no—
227C42×C37—21no—
228C42×C37—21no—
229C42×C37—21no—
230C42×C37—21no—
231C42×C37—42no—
232C42×C37—42no—
233C42×C37—42no—
234C23×C37—22no—
235C23×C37—41no—
236C23×C37—41no—
237C23×C37—41no—
238C23×C37—41no—
239C23×C37—41no—
240C23×C37—41no—
241C23×C37—41no—
242C23×C37—41no—
243C23×C37—41no—
244C23×C37—41no—
245C23×C37—41no—
246C23×C37—41no—
247C23×C37—41no—
248C23×C37C22×D411yescharacteristic
249Q8×C37—22no—
250Q8×C37—22no—
251Q8×C37—22no—
252Q8×C37—22no—
253Q8×C37—41no—
254Q8×C37—41no—
255Q8×C37—41no—
256Q8×C37—41no—
257D4×C37—22no—
258D4×C37—22no—
259D4×C37—41no—
260D4×C37—41no—
261D4×C37—41no—
262D4×C37—41no—
263D4×C37—41no—
264D4×C37—41no—
265D4×C37—84no—
266D4×C37—84no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
272C2×C4×C37—22no—
273C2×C4×C37—22no—
274C2×C4×C37—21no—
275C2×C4×C37—21no—
276C2×C4×C37—21no—
277C2×C4×C37—22no—
278C2×C4×C37—21no—
279C2×C4×C37—21no—
280C2×C4×C37—21no—
281C2×C4×C37—21no—
282C2×C4×C37—21no—
283C2×C4×C37—21no—
284C2×C4×C37—21no—
285C2×C4×C37—21no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—41no—
295C2×C4×C37—41no—
296C2×C4×C37—41no—
297C2×C4×C37—41no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37—41no—
301C2×C4×C37—84no—
302C2×C4×C37AGL(1,ℤ/8)12yes—
303C2×C4×C37#13712yes—
304C2×C4×C37C22×D411yescharacteristic
305C2×C4×C37C2×#4111yescharacteristic
306C2×C4×C37C2×#4111yescharacteristic
307C2×C4×C37C2×#4111yescharacteristic
308C2×C4×C37H(5,𝔽2)11yescharacteristic
309C2×C4×C37H(5,𝔽2)11yescharacteristic
310C8×C37—22no—
311C8×C37—22no—
312C8×C37—41no—
313C8×C37—41no—
314#26605C3711yesmaximal, characteristic, direct product factor, Sylow
315C22×C37—42no—
316C22×C37—42no—
317C22×C37—42no—
318C22×C37—81no—
319C22×C37—81no—
320C22×C37—81no—
321C22×C37—81no—
322C22×C37—81no—
323C22×C37—81no—
324C22×C37—81no—
325C22×C37—81no—
326C22×C37—81no—
327C22×C37—81no—
328C22×C37—81no—
329C22×C37#52511yescharacteristic
330C22×C37D4211yescharacteristic
331C22×C37#55011yescharacteristic
332C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C37C2×#13711yescharacteristic
334C22×C37#57711yescharacteristic
335C22×C37#57711yescharacteristic
336C4×C37—22no—
337C4×C37—22no—
338C4×C37—41no—
339C4×C37—42no—
340C4×C37—42no—
341C4×C37—41no—
342C4×C37—41no—
343C4×C37—41no—
344C4×C37—42no—
345C4×C37—81no—
346C4×C37—81no—
347C4×C37—81no—
348C4×C37#52511yescharacteristic
349C4×C37#53811yescharacteristic
350C4×C37#54611yescharacteristic
351C4×C37#55311yescharacteristic
352C2×#460C2×C3711yescharacteristic
353C2×#440C2×C3711yescharacteristic, complemented
354#2445C2×C3711yescharacteristic
355#2365C2×C3711yescharacteristic, complemented
356#2068C2×C3711yescharacteristic, complemented
357#2014C2×C3711yescharacteristic
358#2013C2×C3711yescharacteristic, complemented
359#2013C2×C3711yescharacteristic, complemented
360#1973C2×C3711yescharacteristic, complemented
361#1925C2×C3711yescharacteristic, complemented
362#1925C2×C3711yescharacteristic, complemented
363#1917C2×C3711yescharacteristic, complemented
364#1880C2×C3711yescharacteristic, complemented
365#1877C2×C3711yescharacteristic, complemented
366#1863C2×C3711yescharacteristic, complemented
367C2×C37—82no—
368C2×C37—161no—
369C2×C37#245611yescharacteristic
370C2×C37#311211yescharacteristic
371C2×C37#312611yescharacteristic
372C2×C37#326611yescharacteristic
373C2×C37#327211yescharacteristic
374C2×C37#339711yescharacteristic
375C2×C37#340011yescharacteristic
376C22×SD16C22×C3711yescharacteristic
377C22×SD16C22×C3711yescharacteristic
378C22×SD16C22×C3711yescharacteristic
379C22×SD16C22×C3711yescharacteristic
380C2×C4⋊Q8C22×C3711yescharacteristic
381C2×#127C22×C3711yescharacteristic
382C2×#123—21no—
383C2×C4×Q8C22×C3711yescharacteristic
384C2×C4×Q8C22×C3711yescharacteristic
385C2×C4×D4C22×C3711yescharacteristic
386#460—24no—
387#440—24no—
388C2×#107C22×C3711yescharacteristic
389C2×#107C22×C3711yescharacteristic
390C2×C4⋊C8C22×C3711yescharacteristic
391C2×#103C22×C3711yescharacteristic
392C2×#103C22×C3711yescharacteristic
393C2×#103C22×C3711yescharacteristic
394C2×#103C22×C3711yescharacteristic
395C2×#102C22×C3711yescharacteristic
396C2×#102C22×C3711yescharacteristic
397C2×#102C22×C3711yescharacteristic
398C2×#102C22×C3711yescharacteristic
399C2×#97C22×C3711yescharacteristic
400#394—21no—
401#394—21no—
402#391C22×C3711yescharacteristic
403#391C22×C3711yescharacteristic
404#390C22×C3711yescharacteristic
405#390C22×C3711yescharacteristic
406#390C22×C3711yescharacteristic
407#389—21no—
408#389C22×C3711yescharacteristic
409#387—21no—
410#387—21no—
411#386—21no—
412C4×C4⋊C4—21no—
413C4×C4⋊C4C22×C3711yescharacteristic
414C4×C4⋊C4C22×C3711yescharacteristic
415#340C22×C3711yescharacteristic
416#340C22×C3711yescharacteristic
417#336C22×C3711yescharacteristic
418#336C22×C3711yescharacteristic
419#336C22×C3711yescharacteristic
420#336C22×C3711yescharacteristic
421C37#2660511yescharacteristic, direct product factor, Sylow
422C22×Q8C23×C3711yescharacteristic
423C22×Q8C23×C3711yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C23×C3711yescharacteristic
427C22×D4C23×C3711yescharacteristic
428C23×C4—21no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—41no—
438C2×SD16—41no—
439C2×SD16—41no—
440C2×SD16—41no—
441C22×C8C23×C3711yescharacteristic
442C22×C8C23×C3711yescharacteristic
443C22×C8C23×C3711yescharacteristic
444C22×C8C23×C3711yescharacteristic
445C4⋊Q8—22no—
446C4⋊Q8—22no—
447#127—22no—
448#127—41no—
449#123—44no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—41no—
453C4×Q8—41no—
454C4×D4—22no—
455C4×D4—41no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4D4×C3711yescharacteristic
462C2×C4⋊C4D4×C3711yescharacteristic
463C2×C4⋊C4C23×C3711yescharacteristic
464C2×C4⋊C4C23×C3711yescharacteristic
465C2×C4⋊C4C23×C3711yescharacteristic
466C2×C4⋊C4C23×C3711yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42C23×C3711yescharacteristic
478C2×C42C23×C3711yescharacteristic
479C2×C42C23×C3711yescharacteristic
480#107—22no—
481#107—41no—
482C4⋊C8—22no—
483#103—22no—
484#103—22no—
485#103—41no—
486#103—41no—
487#102—22no—
488#102—22no—
489#102—41no—
490#102D4×C3714yes—
491#97—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C3711yescharacteristic
499#95D4×C3711yescharacteristic
500C24—21no—
501C24—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8#41×C3712yes—
513C2×Q8#41×C3712yes—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C2×D4×C3712yes—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4C2×D4×C3711yescharacteristic
542C22×C4C2×D4×C3711yescharacteristic
543C22×C4C2×D4×C3711yescharacteristic
544C22×C4C2×D4×C3711yescharacteristic
545C22×C4C2×D4×C3711yescharacteristic
546C22×C4C2×D4×C3711yescharacteristic
547C22×C4C24×C3711yescharacteristic
548SD16—28no—
549SD16—44no—
550SD16—44no—
551SD16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8C2×D4×C3712yes—
563C2×C8#41×C3712yes—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4C2×D4×C3712yes—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42—42no—
594C42—42no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C22×D4×C3711yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—84no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4AGL(1,ℤ/8)×C3712yes—
664C2×C4#137×C3712yes—
665C2×C4C22×D4×C3711yescharacteristic
666C2×C4C2×#41×C3711yescharacteristic
667C2×C4C2×#41×C3711yescharacteristic
668C2×C4C2×#41×C3711yescharacteristic
669C2×C4H(5,𝔽2)×C3711yescharacteristic
670C2×C4H(5,𝔽2)×C3711yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C37×#52511yescharacteristic
690C22D42×C3711yescharacteristic
691C22C37×#55011yescharacteristic
692C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
693C22C2×#137×C3711yescharacteristic
694C22C37×#57711yescharacteristic
695C22C37×#57711yescharacteristic
696C4—22no—
697C4—22no—
698C4—41no—
699C4—42no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4C37×#52511yescharacteristic
709C4C37×#53811yescharacteristic
710C4C37×#54611yescharacteristic
711C4C37×#55311yescharacteristic
712C2—82no—
713C2—161no—
714C2C37×#245611yescharacteristic
715C2C37×#311211yescharacteristic
716C2C37×#312611yescharacteristic
717C2C37×#326611yescharacteristic
718C2C37×#327211yescharacteristic
719C2C37×#339711yescharacteristic
720C2C37×#340011yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#127×C37C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C4⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#440C2semidirect
4. C37×#2365C2semidirect
5. C37×#2068C2semidirect
7. C37×#2013C2semidirect
8. C37×#2013C2semidirect
9. C37×#1973C2semidirect
10. C37×#1925C2semidirect
11. C37×#1925C2semidirect
12. C37×#1917C2semidirect
13. C37×#1880C2semidirect
14. C37×#1877C2semidirect
15. C37×#1863C2semidirect
314. #26605C37direct (N × H)
353. C2×#440C2×C37semidirect
355. #2365C2×C37semidirect
356. #2068C2×C37semidirect
358. #2013C2×C37semidirect
359. #2013C2×C37semidirect
360. #1973C2×C37semidirect
361. #1925C2×C37semidirect
362. #1925C2×C37semidirect
363. #1917C2×C37semidirect
364. #1880C2×C37semidirect
365. #1877C2×C37semidirect
366. #1863C2×C37semidirect
421. C37#26605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4602
C2×C37×#4402
C37×#24452
C37×#23652
C37×#20682
C37×#20142
C37×#20132
C37×#19732
C37×#19252
C37×#19172
C37×#18802
C37×#18772
C37×#18632
#2660537