Finite Group Databasebeta

← C37×#25563 #22646816

Subgroups — C37×#25563 #22646816

Order 9472.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3490C211yesmaximal, characteristic, complemented
2C37×#2410C212yesmaximal, complemented
3C37×#2405C211yesmaximal, characteristic, complemented
4C37×#2062C211yesmaximal, characteristic, complemented
5C37×#2044C211yesmaximal, characteristic, complemented
6C37×#2029C211yesmaximal, characteristic, complemented
7C37×#2021C211yesmaximal, characteristic, complemented
8C37×#1898C212yesmaximal, complemented
9C37×#1889C212yesmaximal, complemented
10C37×#1867C212yesmaximal, complemented
11C2×C37×#342C211yesmaximal, characteristic, complemented
12C23×D4×C37C2211yescharacteristic
13C37×#551—22no—
14C37×#551—22no—
15C37×#546—22no—
16C37×#546—22no—
17C37×#543C2211yescharacteristic
18C37×#538—21no—
19C37×#538—21no—
20C37×#534C2211yescharacteristic
21C37×#525—21no—
22C37×#525—21no—
23C2×#123×C37—21no—
24C2×#121×C37—22no—
25C2×#120×C37C2212yes—
26C2×#120×C37C2212yes—
27C37×#518C2212yes—
28C22×C22⋊C4×C37C2211yescharacteristic
29C22×C22⋊C4×C37C2212yes—
30C2×#99×C37C2212yes—
31C2×#99×C37C2212yes—
32C37×#394—21no—
33C37×#394—21no—
34C37×#394—22no—
35C37×#392—22no—
36C37×#386—21no—
37C37×#386—22no—
38C37×#386C2212yes—
39C37×#385C2211yescharacteristic
40C37×#385C2212yes—
41C37×#385C2211yescharacteristic
42C37×#379C2211yescharacteristic
43C37×#379C2212yes—
44C37×#379C2211yescharacteristic
45C37×#379C2211yescharacteristic
46C37×#342C2212yes—
47C37×#342C2212yes—
48C37×#342C2212yes—
49C37×#342C2211yescharacteristic
50C37×#342C2211yescharacteristic
51C25×C37C2311yescharacteristic
52C25×C37C2311yescharacteristic
53C2×#41×C37—21no—
54C2×#41×C37—21no—
55C22×D4×C37—22no—
56C22×D4×C37—21no—
57C22×D4×C37—22no—
58C22×D4×C37—21no—
59C22×D4×C37—22no—
60C22×D4×C37—44no—
61C22×D4×C37D412yescomplemented
62C22×D4×C37D412yescomplemented
63C22×D4×C37C2312yes—
64C23×C4×C37—22no—
65C23×C4×C37D411yescharacteristic, complemented
66C23×C4×C37D411yescharacteristic, complemented
67C23×C4×C37C2311yescharacteristic
68#126×C37—22no—
69#126×C37—22no—
70#124×C37—22no—
71#124×C37—22no—
72#123×C37—22no—
73#123×C37—22no—
74#123×C37—22no—
75#123×C37—22no—
76#123×C37—22no—
77#123×C37—44no—
78C22⋊Q8×C37—21no—
79C22⋊Q8×C37—21no—
80C22⋊Q8×C37—21no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84#121×C37—21no—
85#121×C37—21no—
86#121×C37—22no—
87#121×C37—22no—
88#121×C37—21no—
89#121×C37—21no—
90#121×C37—48no—
91#120×C37—22no—
92#120×C37—22no—
93#120×C37—22no—
94#120×C37—22no—
95#120×C37—22no—
96#120×C37—24no—
97#120×C37—42no—
98C4×D4×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103C4×D4×C37—22no—
104#117×C37—21no—
105#117×C37—21no—
106#117×C37—22no—
107C2×C4⋊C4×C37—22no—
108C2×C4⋊C4×C37—21no—
109C2×C4⋊C4×C37—21no—
110C2×C22⋊C4×C37—22no—
111C2×C22⋊C4×C37—22no—
112C2×C22⋊C4×C37—22no—
113C2×C22⋊C4×C37—24no—
114C2×C22⋊C4×C37—22no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—22no—
117C2×C22⋊C4×C37—22no—
118C2×C22⋊C4×C37—22no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—42no—
126C2×C22⋊C4×C37D412yescomplemented
127C2×C22⋊C4×C37D412yescomplemented
128C2×C22⋊C4×C37D411yescharacteristic, complemented
129C2×C22⋊C4×C37D411yescharacteristic, complemented
130C2×C22⋊C4×C37C2312yes—
131C2×C22⋊C4×C37C2311yescharacteristic
132C2×C22⋊C4×C37C2311yescharacteristic
133C2×C22⋊C4×C37C2312yes—
134C2×C22⋊C4×C37C2311yescharacteristic
135C2×C22⋊C4×C37C2311yescharacteristic
136C2×C22⋊C4×C37C2312yes—
137#99×C37—24no—
138#99×C37—42no—
139#95×C37—22no—
140#95×C37—21no—
141#95×C37—21no—
142#95×C37—22no—
143C24×C37—22no—
144C24×C37—21no—
145C24×C37—21no—
146C24×C37—21no—
147C24×C37—22no—
148C24×C37—22no—
149C24×C37—21no—
150C24×C37—21no—
151C24×C37—42no—
152C24×C37—42no—
153C24×C37—81no—
154C24×C37—81no—
155C24×C37C2×D412yes—
156C24×C37C2×D411yescharacteristic
157C24×C37C2×D412yes—
158C24×C37C2×D412yes—
159C24×C37C2×D411yescharacteristic
160C24×C37C2411yescharacteristic
161#41×C37—82no—
162#41×C37—82no—
163C2×Q8×C37—21no—
164C2×Q8×C37—21no—
165C2×D4×C37—28no—
166C2×D4×C37—24no—
167C2×D4×C37—22no—
168C2×D4×C37—22no—
169C2×D4×C37—22no—
170C2×D4×C37—22no—
171C2×D4×C37—22no—
172C2×D4×C37—22no—
173C2×D4×C37—22no—
174C2×D4×C37—22no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—22no—
178C2×D4×C37—22no—
179C2×D4×C37—44no—
180C2×D4×C37—42no—
181C2×D4×C37—44no—
182C2×D4×C37—42no—
183C2×D4×C37—44no—
184C2×D4×C37—42no—
185C2×D4×C37—44no—
186C2×D4×C37—42no—
187C2×D4×C37—41no—
188C2×D4×C37—41no—
189C2×D4×C37—44no—
190C2×D4×C37—44no—
191C2×D4×C37—82no—
192C2×D4×C37—82no—
193C22×C4×C37—21no—
194C22×C4×C37—21no—
195C22×C4×C37—22no—
196C22×C4×C37—21no—
197C22×C4×C37—22no—
198C22×C4×C37—22no—
199C22×C4×C37—22no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—22no—
205C22×C4×C37—42no—
206C22×C4×C37—44no—
207C22×C4×C37—42no—
208C22×C4×C37—44no—
209C22×C4×C37—81no—
210C22×C4×C37—82no—
211C22×C4×C37C2×D412yes—
212C22×C4×C37C2×D411yescharacteristic
213C22×C4×C37C2×D412yes—
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D412yes—
217C22×C4×C37C2×D411yescharacteristic
218C4⋊C4×C37—22no—
219C4⋊C4×C37—22no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—22no—
225C4⋊C4×C37—22no—
226C4⋊C4×C37—44no—
227C4⋊C4×C37—42no—
228C4⋊C4×C37—42no—
229C22⋊C4×C37—22no—
230C22⋊C4×C37—22no—
231C22⋊C4×C37—22no—
232C22⋊C4×C37—22no—
233C22⋊C4×C37—22no—
234C22⋊C4×C37—22no—
235C22⋊C4×C37—22no—
236C22⋊C4×C37—22no—
237C22⋊C4×C37—22no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—22no—
240C22⋊C4×C37—22no—
241C22⋊C4×C37—22no—
242C22⋊C4×C37—22no—
243C22⋊C4×C37—22no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—21no—
247C22⋊C4×C37—22no—
248C22⋊C4×C37—21no—
249C22⋊C4×C37—44no—
250C22⋊C4×C37—44no—
251C22⋊C4×C37—44no—
252C22⋊C4×C37—44no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—42no—
256C22⋊C4×C37—81no—
257C22⋊C4×C37—81no—
258C22⋊C4×C37—82no—
259C22⋊C4×C37—81no—
260C22⋊C4×C37#4114yescomplemented
261C42×C37—22no—
262C42×C37—22no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—22no—
266C23×C37—22no—
267C23×C37—22no—
268C23×C37—24no—
269C23×C37—21no—
270C23×C37—21no—
271C23×C37—22no—
272C23×C37—22no—
273C23×C37—22no—
274C23×C37—24no—
275C23×C37—22no—
276C23×C37—22no—
277C23×C37—22no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—42no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—42no—
285C23×C37—42no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—42no—
289C23×C37—41no—
290C23×C37—42no—
291C23×C37—42no—
292C23×C37—42no—
293C23×C37—42no—
294C23×C37—41no—
295C23×C37—41no—
296C23×C37—41no—
297C23×C37—42no—
298C23×C37—42no—
299C23×C37—84no—
300C23×C37—84no—
301C23×C37—82no—
302C23×C37—82no—
303C23×C37—82no—
304C23×C37—82no—
305C23×C37#12012yes—
306C23×C37#12011yescharacteristic
307C23×C37#12011yescharacteristic
308C23×C37C22×D411yescharacteristic
309C23×C37C22×D412yes—
310C23×C37C2×#4112yes—
311C23×C37H(5,𝔽2)11yescharacteristic
312C23×C372−1+411yescharacteristic
313Q8×C37—81no—
314Q8×C37—81no—
315D4×C37—44no—
316D4×C37—48no—
317D4×C37—44no—
318D4×C37—42no—
319D4×C37—42no—
320D4×C37—42no—
321D4×C37—42no—
322D4×C37—44no—
323D4×C37—44no—
324D4×C37—82no—
325D4×C37—82no—
326D4×C37—81no—
327D4×C37—81no—
328D4×C37—88no—
329C2×C4×C37—24no—
330C2×C4×C37—22no—
331C2×C4×C37—22no—
332C2×C4×C37—21no—
333C2×C4×C37—21no—
334C2×C4×C37—22no—
335C2×C4×C37—22no—
336C2×C4×C37—21no—
337C2×C4×C37—21no—
338C2×C4×C37—24no—
339C2×C4×C37—22no—
340C2×C4×C37—22no—
341C2×C4×C37—42no—
342C2×C4×C37—41no—
343C2×C4×C37—42no—
344C2×C4×C37—42no—
345C2×C4×C37—42no—
346C2×C4×C37—41no—
347C2×C4×C37—42no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—42no—
351C2×C4×C37—41no—
352C2×C4×C37—41no—
353C2×C4×C37—42no—
354C2×C4×C37—41no—
355C2×C4×C37—41no—
356C2×C4×C37—42no—
357C2×C4×C37—41no—
358C2×C4×C37—41no—
359C2×C4×C37—42no—
360C2×C4×C37—41no—
361C2×C4×C37—41no—
362C2×C4×C37—42no—
363C2×C4×C37—81no—
364C2×C4×C37—81no—
365C2×C4×C37—82no—
366C2×C4×C37—82no—
367C2×C4×C37—88no—
368#25563C3711yesmaximal, characteristic, direct product factor, Sylow
369C22×C37—21no—
370C22×C37—21no—
371C22×C37—22no—
372C22×C37—21no—
373C22×C37—22no—
374C22×C37—21no—
375C22×C37—21no—
376C22×C37—22no—
377C22×C37—21no—
378C22×C37—22no—
379C22×C37—21no—
380C22×C37—22no—
381C22×C37—42no—
382C22×C37—41no—
383C22×C37—41no—
384C22×C37—44no—
385C22×C37—42no—
386C22×C37—42no—
387C22×C37—44no—
388C22×C37—44no—
389C22×C37—42no—
390C22×C37—42no—
391C22×C37—44no—
392C22×C37—42no—
393C22×C37—42no—
394C22×C37—42no—
395C22×C37—42no—
396C22×C37—82no—
397C22×C37—81no—
398C22×C37—81no—
399C22×C37—82no—
400C22×C37—82no—
401C22×C37—82no—
402C22×C37—82no—
403C22×C37—81no—
404C22×C37—81no—
405C22×C37—82no—
406C22×C37—81no—
407C22×C37—81no—
408C22×C37B(4,𝔽2)12yes—
409C22×C37C2×#12011yescharacteristic
410C22×C37#53211yescharacteristic
411C22×C37#53711yescharacteristic
412C22×C37#54612yes—
413C22×C37#54712yes—
414C4×C37—44no—
415C4×C37—42no—
416C4×C37—42no—
417C4×C37—41no—
418C4×C37—41no—
419C4×C37—42no—
420C4×C37—41no—
421C4×C37—41no—
422C4×C37—42no—
423C4×C37—81no—
424C4×C37—81no—
425C4×C37—82no—
426#3490C2×C3711yescharacteristic, complemented
427#2410C2×C3712yescomplemented
428#2405C2×C3711yescharacteristic, complemented
429#2062C2×C3711yescharacteristic, complemented
430#2044C2×C3711yescharacteristic, complemented
431#2029C2×C3711yescharacteristic, complemented
432#2021C2×C3711yescharacteristic, complemented
433#1898C2×C3712yescomplemented
434#1889C2×C3712yescomplemented
435#1867C2×C3712yescomplemented
436C2×#342C2×C3711yescharacteristic, complemented
437C2×C37—22no—
438C2×C37—21no—
439C2×C37—21no—
440C2×C37—22no—
441C2×C37—22no—
442C2×C37—41no—
443C2×C37—42no—
444C2×C37—82no—
445C2×C37—82no—
446C2×C37#243011yescharacteristic
447C2×C37C2×B(4,𝔽2)11yescharacteristic
448C2×C37#302611yescharacteristic
449C23×D4C22×C3711yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C3711yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C3711yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C3712yes—
463C2×#120C22×C3712yes—
464#518C22×C3712yes—
465C22×C22⋊C4C22×C3711yescharacteristic
466C22×C22⋊C4C22×C3712yes—
467C2×#99C22×C3712yes—
468C2×#99C22×C3712yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C3712yes—
476#385C22×C3712yes—
477#385C22×C3711yescharacteristic
478#385C22×C3711yescharacteristic
479#379C22×C3711yescharacteristic
480#379C22×C3712yes—
481#379C22×C3711yescharacteristic
482#379C22×C3711yescharacteristic
483#342C22×C3712yes—
484#342C22×C3711yescharacteristic
485#342C22×C3712yes—
486#342C22×C3712yes—
487#342C22×C3711yescharacteristic
488C37#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C3711yescharacteristic
490C25C23×C3711yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C3712yescomplemented
500C22×D4D4×C3712yescomplemented
501C22×D4C23×C3712yes—
502C23×C4—22no—
503C23×C4D4×C3711yescharacteristic, complemented
504C23×C4D4×C3711yescharacteristic, complemented
505C23×C4C23×C3711yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C3711yescharacteristic, complemented
565C2×C22⋊C4D4×C3711yescharacteristic, complemented
566C2×C22⋊C4D4×C3712yescomplemented
567C2×C22⋊C4D4×C3712yescomplemented
568C2×C22⋊C4C23×C3712yes—
569C2×C22⋊C4C23×C3711yescharacteristic
570C2×C22⋊C4C23×C3711yescharacteristic
571C2×C22⋊C4C23×C3711yescharacteristic
572C2×C22⋊C4C23×C3711yescharacteristic
573C2×C22⋊C4C23×C3712yes—
574C2×C22⋊C4C23×C3712yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C3712yes—
594C24C2×D4×C3711yescharacteristic
595C24C2×D4×C3712yes—
596C24C2×D4×C3712yes—
597C24C2×D4×C3711yescharacteristic
598C24C24×C3711yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C3712yes—
650C22×C4C2×D4×C3711yescharacteristic
651C22×C4C2×D4×C3712yes—
652C22×C4C2×D4×C3711yescharacteristic
653C22×C4C2×D4×C3711yescharacteristic
654C22×C4C2×D4×C3712yes—
655C22×C4C2×D4×C3711yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C3714yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C3712yes—
744C23#120×C3711yescharacteristic
745C23#120×C3711yescharacteristic
746C23C22×D4×C3711yescharacteristic
747C23C22×D4×C3712yes—
748C23C2×#41×C3712yes—
749C23H(5,𝔽2)×C3711yescharacteristic
750C232−1+4×C3711yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C37×B(4,𝔽2)12yes—
846C22C2×#120×C3711yescharacteristic
847C22C37×#53211yescharacteristic
848C22C37×#53711yescharacteristic
849C22C37×#54612yes—
850C22C37×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C37×#243011yescharacteristic
873C2C2×C37×B(4,𝔽2)11yescharacteristic
874C2C37×#302611yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3490C2semidirect
2. C37×#2410C2semidirect
3. C37×#2405C2semidirect
4. C37×#2062C2semidirect
5. C37×#2044C2semidirect
6. C37×#2029C2semidirect
7. C37×#2021C2semidirect
8. C37×#1898C2semidirect
9. C37×#1889C2semidirect
10. C37×#1867C2semidirect
11. C2×C37×#342C2semidirect
61. C22×D4×C37D4semidirect
62. C22×D4×C37D4semidirect
65. C23×C4×C37D4semidirect
66. C23×C4×C37D4semidirect
126. C2×C22⋊C4×C37D4semidirect
127. C2×C22⋊C4×C37D4semidirect
128. C2×C22⋊C4×C37D4semidirect
129. C2×C22⋊C4×C37D4semidirect
260. C22⋊C4×C37#41semidirect
368. #25563C37direct (N × H)
426. #3490C2×C37semidirect
427. #2410C2×C37semidirect
428. #2405C2×C37semidirect
429. #2062C2×C37semidirect
430. #2044C2×C37semidirect
431. #2029C2×C37semidirect
432. #2021C2×C37semidirect
433. #1898C2×C37semidirect
434. #1889C2×C37semidirect
435. #1867C2×C37semidirect
436. C2×#342C2×C37semidirect
488. C37#25563direct (N × H)
499. C22×D4D4×C37semidirect
500. C22×D4D4×C37semidirect
503. C23×C4D4×C37semidirect
504. C23×C4D4×C37semidirect
564. C2×C22⋊C4D4×C37semidirect
565. C2×C22⋊C4D4×C37semidirect
566. C2×C22⋊C4D4×C37semidirect
567. C2×C22⋊C4D4×C37semidirect
698. C22⋊C4#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34902
C37×#24102
C37×#24052
C37×#20622
C37×#20442
C37×#20292
C37×#20212
C37×#18982
C37×#18892
C37×#18672
C2×C37×#3422
#2556337