Finite Group Databasebeta

← C37×#28584 #22649837

Subgroups — C37×#28584 #22649837

Order 9472.

992 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#469C211yesmaximal, characteristic, complemented
2C2×C37×#466C211yesmaximal, characteristic, complemented
3C37×#2619C211yesmaximal, characteristic, complemented
4C37×#2324C211yesmaximal, characteristic, complemented
5C37×#2085C211yesmaximal, characteristic, complemented
6C37×#2073C211yesmaximal, characteristic, complemented
7C37×#2041C211yesmaximal, characteristic, complemented
8C37×#2011C211yesmaximal, characteristic, complemented
9C37×#1926C211yesmaximal, characteristic, complemented
10C37×#1925C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1893C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1879C211yesmaximal, characteristic, complemented
15C37×#1729C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C23×C8×C37C2211yescharacteristic
20C2×#127×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×C4×D4×C37C2211yescharacteristic
25C2×#117×C37C2211yescharacteristic
26C37×#469—24no—
27C37×#466—24no—
28C2×#107×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×#102×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C37×#394—21no—
39C37×#394—21no—
40C37×#392—21no—
41C37×#392—21no—
42C37×#390—21no—
43C37×#390C2211yescharacteristic
44C37×#390C2211yescharacteristic
45C37×#390C2211yescharacteristic
46C37×#389C2211yescharacteristic
47C37×#388—21no—
48C37×#386—21no—
49C37×#385—21no—
50C37×#382C2211yescharacteristic
51C37×#380C2211yescharacteristic
52C4×C4⋊C4×C37C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37C2311yescharacteristic
67C22×D4×C37C2311yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C23×C4×C37—21no—
70C23×C4×C37C2311yescharacteristic
71C2×D8×C37—22no—
72C2×D8×C37—22no—
73C2×D8×C37—22no—
74C2×D8×C37—22no—
75C2×D8×C37—41no—
76C2×D8×C37—41no—
77C2×M16×C37—22no—
78C2×M16×C37—22no—
79C2×M16×C37—41no—
80C22×C8×C37—22no—
81C22×C8×C37—22no—
82C22×C8×C37—41no—
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85C22×C8×C37C2311yescharacteristic
86C22×C8×C37C2311yescharacteristic
87#127×C37—41no—
88#127×C37—41no—
89#121×C37—22no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—22no—
93#121×C37—22no—
94#121×C37D414yescomplemented
95C4×D4×C37—41no—
96C4×D4×C37—41no—
97#117×C37—41no—
98#117×C37—41no—
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×C4⋊C4×C37C2311yescharacteristic
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×C22⋊C4×C37—21no—
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37D411yescharacteristic
119C2×C22⋊C4×C37D411yescharacteristic
120C2×C42×C37—21no—
121C2×C42×C37C2311yescharacteristic
122C2×C42×C37C2311yescharacteristic
123#107×C37—22no—
124#106×C37—22no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—22no—
129#102×C37—22no—
130#102×C37—22no—
131#102×C37—41no—
132#102×C37—41no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138C24×C37—21no—
139C24×C37—21no—
140C24×C37—21no—
141C24×C37C2×D411yescharacteristic
142C2×D4×C37—24no—
143C2×D4×C37—21no—
144C2×D4×C37—21no—
145C2×D4×C37—21no—
146C2×D4×C37—21no—
147C2×D4×C37—21no—
148C2×D4×C37—21no—
149C2×D4×C37—21no—
150C2×D4×C37—21no—
151C2×D4×C37—21no—
152C2×D4×C37—21no—
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—42no—
161C2×D4×C37—42no—
162C2×D4×C37—42no—
163C2×D4×C37—42no—
164C2×D4×C37—81no—
165C2×D4×C37—81no—
166C2×D4×C37—81no—
167C2×D4×C37—81no—
168C2×D4×C37—81no—
169C2×D4×C37—81no—
170C2×D4×C37—81no—
171C2×D4×C37—81no—
172C2×D4×C37—81no—
173C2×D4×C37—81no—
174C2×D4×C37C2×D412yes—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—42no—
185C22×C4×C37—81no—
186C22×C4×C37—81no—
187C22×C4×C37C2×D411yescharacteristic
188C22×C4×C37C2×D411yescharacteristic
189C22×C4×C37C2×D411yescharacteristic
190C22×C4×C37C2×D411yescharacteristic
191C22×C4×C37C2×D411yescharacteristic
192C22×C4×C37C2×D412yes—
193C22×C4×C37#4112yes—
194C22×C4×C37C2411yescharacteristic
195D8×C37—44no—
196D8×C37—44no—
197M16×C37—44no—
198C2×C8×C37—21no—
199C2×C8×C37—21no—
200C2×C8×C37—21no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—44no—
209C2×C8×C37#4112yes—
210C2×C8×C37#4112yes—
211C4⋊C4×C37—21no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—41no—
221C4⋊C4×C37—41no—
222C4⋊C4×C37—81no—
223C4⋊C4×C37C2×D412yes—
224C22⋊C4×C37—24no—
225C22⋊C4×C37—41no—
226C22⋊C4×C37—41no—
227C22⋊C4×C37—42no—
228C22⋊C4×C37—42no—
229C22⋊C4×C37—42no—
230C22⋊C4×C37—81no—
231C22⋊C4×C37—81no—
232C22⋊C4×C37—81no—
233C22⋊C4×C37—81no—
234C22⋊C4×C37—81no—
235C22⋊C4×C37—81no—
236C22⋊C4×C37—81no—
237C42×C37—21no—
238C42×C37—21no—
239C42×C37—21no—
240C42×C37—21no—
241C42×C37—81no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—21no—
247C23×C37—21no—
248C23×C37—22no—
249C23×C37—41no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37—41no—
256C23×C37—41no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37#12112yes—
270C23×C37C22×D411yescharacteristic
271D4×C37—22no—
272D4×C37—22no—
273D4×C37—41no—
274D4×C37—41no—
275D4×C37—41no—
276D4×C37—41no—
277D4×C37—41no—
278D4×C37—41no—
279D4×C37—41no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—84no—
284D4×C37—84no—
285D4×C37—84no—
286D4×C37—84no—
287D4×C37—84no—
288C2×C4×C37—21no—
289C2×C4×C37—21no—
290C2×C4×C37—22no—
291C2×C4×C37—22no—
292C2×C4×C37—22no—
293C2×C4×C37—22no—
294C2×C4×C37—22no—
295C2×C4×C37—21no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—41no—
308C2×C4×C37—41no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—84no—
322C2×C4×C37#12112yes—
323C2×C4×C37C22×D411yescharacteristic
324C2×C4×C37C2×#4111yescharacteristic
325C2×C4×C37C2×#4111yescharacteristic
326C2×C4×C37C2×#4111yescharacteristic
327C2×C4×C37H(5,𝔽2)11yescharacteristic
328C2×C4×C37H(5,𝔽2)11yescharacteristic
329C8×C37—22no—
330C8×C37—22no—
331C8×C37—41no—
332C8×C37—41no—
333#28584C3711yesmaximal, characteristic, direct product factor, Sylow
334C22×C37—22no—
335C22×C37—22no—
336C22×C37—22no—
337C22×C37—41no—
338C22×C37—41no—
339C22×C37—41no—
340C22×C37—41no—
341C22×C37—42no—
342C22×C37—42no—
343C22×C37—42no—
344C22×C37—81no—
345C22×C37—81no—
346C22×C37—81no—
347C22×C37—81no—
348C22×C37—81no—
349C22×C37—81no—
350C22×C37—81no—
351C22×C37—81no—
352C22×C37—81no—
353C22×C37—81no—
354C22×C37—81no—
355C22×C37—81no—
356C22×C37—81no—
357C22×C37—81no—
358C22×C37—81no—
359C22×C37—81no—
360C22×C37—81no—
361C22×C37—81no—
362C22×C37C2×#12111yescharacteristic
363C22×C37#53211yescharacteristic
364C22×C37#53411yescharacteristic
365C22×C37#57611yescharacteristic
366C22×C37#57611yescharacteristic
367C22×C37#57611yescharacteristic
368C22×C37#57711yescharacteristic
369C4×C37—22no—
370C4×C37—41no—
371C4×C37—41no—
372C4×C37—41no—
373C4×C37—41no—
374C4×C37—42no—
375C4×C37—81no—
376C4×C37—81no—
377C4×C37—81no—
378C4×C37—81no—
379C4×C37#54611yescharacteristic
380C4×C37#54611yescharacteristic
381C4×C37#55311yescharacteristic
382C4×C37#55311yescharacteristic
383C2×#469C2×C3711yescharacteristic, complemented
384C2×#466C2×C3711yescharacteristic, complemented
385#2619C2×C3711yescharacteristic, complemented
386#2324C2×C3711yescharacteristic, complemented
387#2085C2×C3711yescharacteristic, complemented
388#2073C2×C3711yescharacteristic, complemented
389#2041C2×C3711yescharacteristic, complemented
390#2011C2×C3711yescharacteristic, complemented
391#1926C2×C3711yescharacteristic, complemented
392#1925C2×C3711yescharacteristic, complemented
393#1895C2×C3711yescharacteristic, complemented
394#1893C2×C3711yescharacteristic, complemented
395#1879C2×C3711yescharacteristic, complemented
396#1879C2×C3711yescharacteristic, complemented
397#1729C2×C3711yescharacteristic, complemented
398C2×C37—42no—
399C2×C37—82no—
400C2×C37—161no—
401C2×C37—161no—
402C2×C37#254311yescharacteristic
403C2×C37#304111yescharacteristic
404C2×C37#304511yescharacteristic
405C2×C37#317611yescharacteristic
406C2×C37#317911yescharacteristic
407C2×C37#319811yescharacteristic
408C2×C37#319911yescharacteristic
409C22×D8C22×C3711yescharacteristic
410C22×D8C22×C3711yescharacteristic
411C22×M16C22×C3711yescharacteristic
412C23×C8C22×C3711yescharacteristic
413C2×#127C22×C3711yescharacteristic
414C2×#121C22×C3711yescharacteristic
415C2×#121C22×C3711yescharacteristic
416C2×#121C22×C3711yescharacteristic
417C2×C4×D4C22×C3711yescharacteristic
418C2×#117C22×C3711yescharacteristic
419#469—24no—
420#466—24no—
421C2×#107C22×C3711yescharacteristic
422C2×#106C22×C3711yescharacteristic
423C2×#102C22×C3711yescharacteristic
424C2×#102C22×C3711yescharacteristic
425C2×#102C22×C3711yescharacteristic
426C2×#102C22×C3711yescharacteristic
427C2×#102C22×C3711yescharacteristic
428C2×#102C22×C3711yescharacteristic
429C2×#102C22×C3711yescharacteristic
430C2×#102C22×C3711yescharacteristic
431#394—21no—
432#394—21no—
433#392—21no—
434#392—21no—
435#390—21no—
436#390C22×C3711yescharacteristic
437#390C22×C3711yescharacteristic
438#390C22×C3711yescharacteristic
439#389C22×C3711yescharacteristic
440#388—21no—
441#386—21no—
442#385—21no—
443#382C22×C3711yescharacteristic
444#380C22×C3711yescharacteristic
445C4×C4⋊C4C22×C3711yescharacteristic
446#340C22×C3711yescharacteristic
447#340C22×C3711yescharacteristic
448#340C22×C3711yescharacteristic
449#340C22×C3711yescharacteristic
450#336C22×C3711yescharacteristic
451#336C22×C3711yescharacteristic
452#336C22×C3711yescharacteristic
453#336C22×C3711yescharacteristic
454C37#2858411yescharacteristic, direct product factor, Sylow
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C3711yescharacteristic
461C22×D4C23×C3711yescharacteristic
462C22×D4C23×C3711yescharacteristic
463C23×C4—21no—
464C23×C4C23×C3711yescharacteristic
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—41no—
470C2×D8—41no—
471C2×M16—22no—
472C2×M16—22no—
473C2×M16—41no—
474C22×C8—22no—
475C22×C8—22no—
476C22×C8—41no—
477C22×C8C23×C3711yescharacteristic
478C22×C8C23×C3711yescharacteristic
479C22×C8C23×C3711yescharacteristic
480C22×C8C23×C3711yescharacteristic
481#127—41no—
482#127—41no—
483#121—22no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121D4×C3714yescomplemented
489C4×D4—41no—
490C4×D4—41no—
491#117—41no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4D4×C3711yescharacteristic
495C2×C4⋊C4D4×C3711yescharacteristic
496C2×C4⋊C4C23×C3711yescharacteristic
497C2×C4⋊C4C23×C3711yescharacteristic
498C2×C4⋊C4C23×C3711yescharacteristic
499C2×C4⋊C4C23×C3711yescharacteristic
500C2×C4⋊C4C23×C3711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4D4×C3711yescharacteristic
513C2×C22⋊C4D4×C3711yescharacteristic
514C2×C42—21no—
515C2×C42C23×C3711yescharacteristic
516C2×C42C23×C3711yescharacteristic
517#107—22no—
518#106—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24C2×D4×C3711yescharacteristic
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4—81no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4C2×D4×C3712yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C3711yescharacteristic
582C22×C4C2×D4×C3711yescharacteristic
583C22×C4C2×D4×C3711yescharacteristic
584C22×C4C2×D4×C3711yescharacteristic
585C22×C4C2×D4×C3711yescharacteristic
586C22×C4C2×D4×C3712yes—
587C22×C4#41×C3712yes—
588C22×C4C24×C3711yescharacteristic
589D8—44no—
590D8—44no—
591M16—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—44no—
603C2×C8#41×C3712yes—
604C2×C8#41×C3712yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—41no—
615C4⋊C4—41no—
616C4⋊C4—81no—
617C4⋊C4C2×D4×C3712yes—
618C22⋊C4—24no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—81no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23#121×C3712yes—
664C23C22×D4×C3711yescharacteristic
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4#121×C3712yes—
717C2×C4C22×D4×C3711yescharacteristic
718C2×C4C2×#41×C3711yescharacteristic
719C2×C4C2×#41×C3711yescharacteristic
720C2×C4C2×#41×C3711yescharacteristic
721C2×C4H(5,𝔽2)×C3711yescharacteristic
722C2×C4H(5,𝔽2)×C3711yescharacteristic
723C8—22no—
724C8—22no—
725C8—41no—
726C8—41no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#121×C3711yescharacteristic
756C22C37×#53211yescharacteristic
757C22C37×#53411yescharacteristic
758C22C37×#57611yescharacteristic
759C22C37×#57611yescharacteristic
760C22C37×#57611yescharacteristic
761C22C37×#57711yescharacteristic
762C4—22no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C37×#54611yescharacteristic
773C4C37×#54611yescharacteristic
774C4C37×#55311yescharacteristic
775C4C37×#55311yescharacteristic
776C2—42no—
777C2—82no—
778C2—161no—
779C2—161no—
780C2C37×#254311yescharacteristic
781C2C37×#304111yescharacteristic
782C2C37×#304511yescharacteristic
783C2C37×#317611yescharacteristic
784C2C37×#317911yescharacteristic
785C2C37×#319811yescharacteristic
786C2C37×#319911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×#117×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#469C2semidirect
2. C2×C37×#466C2semidirect
3. C37×#2619C2semidirect
4. C37×#2324C2semidirect
5. C37×#2085C2semidirect
6. C37×#2073C2semidirect
7. C37×#2041C2semidirect
8. C37×#2011C2semidirect
9. C37×#1926C2semidirect
10. C37×#1925C2semidirect
11. C37×#1895C2semidirect
12. C37×#1893C2semidirect
13. C37×#1879C2semidirect
14. C37×#1879C2semidirect
15. C37×#1729C2semidirect
94. #121×C37D4semidirect
333. #28584C37direct (N × H)
383. C2×#469C2×C37semidirect
384. C2×#466C2×C37semidirect
385. #2619C2×C37semidirect
386. #2324C2×C37semidirect
387. #2085C2×C37semidirect
388. #2073C2×C37semidirect
389. #2041C2×C37semidirect
390. #2011C2×C37semidirect
391. #1926C2×C37semidirect
392. #1925C2×C37semidirect
393. #1895C2×C37semidirect
394. #1893C2×C37semidirect
395. #1879C2×C37semidirect
396. #1879C2×C37semidirect
397. #1729C2×C37semidirect
454. C37#28584direct (N × H)
488. #121D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4692
C2×C37×#4662
C37×#26192
C37×#23242
C37×#20852
C37×#20732
C37×#20412
C37×#20112
C37×#19262
C37×#19252
C37×#18952
C37×#18932
C37×#18792
C37×#17292
#2858437