Finite Group Databasebeta

← C37×#25585 #22646838

Subgroups — C37×#25585 #22646838

Order 9472.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3505C211yesmaximal, characteristic, complemented
2C37×#2435C211yesmaximal, characteristic, complemented
3C37×#2433C211yesmaximal, characteristic, complemented
4C37×#2408C211yesmaximal, characteristic, complemented
5C37×#2021C214yesmaximal, complemented
6C37×#1996C211yesmaximal, characteristic, complemented
7C37×#1964C211yesmaximal, characteristic, complemented
8C37×#1889C214yesmaximal, complemented
9C4×#99×C37C211yesmaximal, characteristic, complemented
10C23×D4×C37C2211yescharacteristic
11C37×#553—21no—
12C37×#553—22no—
13C37×#552—21no—
14C37×#551—22no—
15C37×#548—21no—
16C37×#546—21no—
17C37×#539—21no—
18C37×#538—21no—
19C37×#534C2212yes—
20C2×#127×C37—21no—
21C37×#529—21no—
22C2×#124×C37—21no—
23C37×#525—21no—
24C2×C22⋊Q8×C37C2211yescharacteristic
25C2×#121×C37—21no—
26C2×#121×C37C2211yescharacteristic
27C2×#120×C37C2214yes—
28C2×#120×C37C2212yes—
29C37×#518C2212yes—
30C2×C4×D4×C37C2211yescharacteristic
31C2×#99×C37C2212yes—
32C2×#99×C37C2214yes—
33C37×#394—21no—
34C37×#394—22no—
35C37×#392—21no—
36C37×#392—22no—
37C37×#390—21no—
38C37×#390—21no—
39C37×#390—21no—
40C37×#380C2211yescharacteristic
41C37×#379C2212yes—
42C37×#379C2214yes—
43C4×C22⋊C4×C37C2211yescharacteristic
44C4×C22⋊C4×C37C2211yescharacteristic
45C37×#342C2212yes—
46C37×#342C2214yes—
47C25×C37C2312yes—
48C2×#41×C37—21no—
49C22×Q8×C37D411yescharacteristic, complemented
50C22×D4×C37—22no—
51C22×D4×C37—24no—
52C22×D4×C37—21no—
53C22×D4×C37—21no—
54C22×D4×C37—21no—
55C22×D4×C37—21no—
56C22×D4×C37—21no—
57C22×D4×C37—21no—
58C22×D4×C37—44no—
59C22×D4×C37D411yescharacteristic, complemented
60C22×D4×C37C2312yes—
61C22×D4×C37C2311yescharacteristic
62C23×C4×C37D411yescharacteristic, complemented
63C23×C4×C37C2311yescharacteristic
64#127×C37—44no—
65#126×C37—22no—
66#126×C37—22no—
67#126×C37—22no—
68#125×C37—21no—
69#125×C37—22no—
70#124×C37—21no—
71#124×C37—22no—
72#124×C37—44no—
73#123×C37—22no—
74#123×C37—22no—
75#123×C37—22no—
76#123×C37—22no—
77#123×C37—22no—
78C22⋊Q8×C37—21no—
79C22⋊Q8×C37—22no—
80C22⋊Q8×C37—21no—
81C22⋊Q8×C37—21no—
82C22⋊Q8×C37—21no—
83C22⋊Q8×C37—21no—
84#121×C37—21no—
85#121×C37—22no—
86#121×C37—21no—
87#121×C37—21no—
88#121×C37—21no—
89#121×C37—21no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—44no—
93#120×C37—22no—
94#120×C37—22no—
95#120×C37—28no—
96#120×C37—44no—
97#120×C37—44no—
98C4×Q8×C37—21no—
99C4×D4×C37—22no—
100C4×D4×C37—21no—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103C4×D4×C37—21no—
104C4×D4×C37—21no—
105C4×D4×C37—22no—
106C4×D4×C37—21no—
107C4×D4×C37—21no—
108C4×D4×C37—22no—
109#117×C37—21no—
110#117×C37—22no—
111#117×C37—22no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37D411yescharacteristic, complemented
114C2×C4⋊C4×C37D411yescharacteristic, complemented
115C2×C4⋊C4×C37D412yescomplemented
116C2×C4⋊C4×C37D411yescharacteristic, complemented
117C2×C22⋊C4×C37—22no—
118C2×C22⋊C4×C37—24no—
119C2×C22⋊C4×C37—22no—
120C2×C22⋊C4×C37—22no—
121C2×C22⋊C4×C37—24no—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—24no—
124C2×C22⋊C4×C37D412yescomplemented
125C2×C22⋊C4×C37D411yescharacteristic, complemented
126C2×C22⋊C4×C37C2312yes—
127C2×C22⋊C4×C37C2312yes—
128C2×C22⋊C4×C37C2312yes—
129C2×C22⋊C4×C37C2311yescharacteristic
130C2×C22⋊C4×C37C2312yes—
131C2×C42×C37—21no—
132C2×C42×C37—21no—
133C2×C42×C37D411yescharacteristic, complemented
134#99×C37—24no—
135#99×C37—44no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37—21no—
139C24×C37—22no—
140C24×C37—22no—
141C24×C37—22no—
142C24×C37—24no—
143C24×C37—24no—
144C24×C37—44no—
145C24×C37—82no—
146C24×C37C2×D412yes—
147C24×C37C2×D411yescharacteristic
148C24×C37C2411yescharacteristic
149#41×C37—82no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—42no—
153C2×D4×C37—24no—
154C2×D4×C37—24no—
155C2×D4×C37—24no—
156C2×D4×C37—21no—
157C2×D4×C37—22no—
158C2×D4×C37—21no—
159C2×D4×C37—22no—
160C2×D4×C37—22no—
161C2×D4×C37—24no—
162C2×D4×C37—24no—
163C2×D4×C37—22no—
164C2×D4×C37—22no—
165C2×D4×C37—22no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—42no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
172C2×D4×C37—48no—
173C2×D4×C37—44no—
174C2×D4×C37—44no—
175C2×D4×C37—44no—
176C2×D4×C37—44no—
177C2×D4×C37—44no—
178C2×D4×C37—48no—
179C2×D4×C37—41no—
180C2×D4×C37—41no—
181C2×D4×C37—41no—
182C2×D4×C37—41no—
183C2×D4×C37—84no—
184C2×D4×C37—82no—
185C22×C4×C37—22no—
186C22×C4×C37—22no—
187C22×C4×C37—22no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—22no—
191C22×C4×C37—22no—
192C22×C4×C37—42no—
193C22×C4×C37—42no—
194C22×C4×C37C2×D411yescharacteristic
195C22×C4×C37C2×D412yes—
196C22×C4×C37C2×D411yescharacteristic
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37C2×D411yescharacteristic
199C22×C4×C37C2×D411yescharacteristic
200C22×C4×C37C2×D412yes—
201C22×C4×C37C2×D411yescharacteristic
202C22×C4×C37C2×D412yes—
203C22×C4×C37C2×D411yescharacteristic
204C22×C4×C37C2×D411yescharacteristic
205C22×C4×C37C2×D411yescharacteristic
206C4⋊C4×C37—22no—
207C4⋊C4×C37—22no—
208C4⋊C4×C37—22no—
209C4⋊C4×C37—22no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—22no—
212C4⋊C4×C37—21no—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—22no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—42no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—22no—
222C22⋊C4×C37—22no—
223C22⋊C4×C37—22no—
224C22⋊C4×C37—22no—
225C22⋊C4×C37—21no—
226C22⋊C4×C37—22no—
227C22⋊C4×C37—21no—
228C22⋊C4×C37—22no—
229C22⋊C4×C37—22no—
230C22⋊C4×C37—22no—
231C22⋊C4×C37—21no—
232C22⋊C4×C37—21no—
233C22⋊C4×C37—22no—
234C22⋊C4×C37—22no—
235C22⋊C4×C37—22no—
236C22⋊C4×C37—24no—
237C22⋊C4×C37—48no—
238C22⋊C4×C37—44no—
239C22⋊C4×C37—44no—
240C22⋊C4×C37—48no—
241C22⋊C4×C37—84no—
242C22⋊C4×C37—82no—
243C22⋊C4×C37#4114yescomplemented
244C42×C37—22no—
245C42×C37—22no—
246C42×C37—21no—
247C42×C37—21no—
248C42×C37—42no—
249C42×C37—42no—
250C23×C37—24no—
251C23×C37—24no—
252C23×C37—24no—
253C23×C37—21no—
254C23×C37—22no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—24no—
258C23×C37—41no—
259C23×C37—41no—
260C23×C37—41no—
261C23×C37—41no—
262C23×C37—44no—
263C23×C37—42no—
264C23×C37—42no—
265C23×C37—42no—
266C23×C37—42no—
267C23×C37—42no—
268C23×C37—44no—
269C23×C37—42no—
270C23×C37—42no—
271C23×C37—42no—
272C23×C37—42no—
273C23×C37—42no—
274C23×C37—44no—
275C23×C37—44no—
276C23×C37—88no—
277C23×C37—88no—
278C23×C37C22×D411yescharacteristic
279C23×C37C22×D411yescharacteristic
280C23×C37C22×D411yescharacteristic
281C23×C37C2×#4112yes—
282C23×C37H(5,𝔽2)12yes—
283Q8×C37—42no—
284Q8×C37—81no—
285D4×C37—44no—
286D4×C37—44no—
287D4×C37—44no—
288D4×C37—42no—
289D4×C37—42no—
290D4×C37—42no—
291D4×C37—42no—
292D4×C37—44no—
293D4×C37—44no—
294D4×C37—42no—
295D4×C37—81no—
296D4×C37—82no—
297D4×C37—82no—
298D4×C37—816no—
299D4×C37—88no—
300C2×C4×C37—22no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—21no—
304C2×C4×C37—22no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—22no—
308C2×C4×C37—22no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—24no—
312C2×C4×C37—24no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—42no—
317C2×C4×C37—42no—
318C2×C4×C37—42no—
319C2×C4×C37—41no—
320C2×C4×C37—42no—
321C2×C4×C37—41no—
322C2×C4×C37—42no—
323C2×C4×C37—42no—
324C2×C4×C37—42no—
325C2×C4×C37—42no—
326C2×C4×C37—42no—
327C2×C4×C37—42no—
328C2×C4×C37—42no—
329C2×C4×C37—81no—
330C2×C4×C37—82no—
331C2×C4×C37—82no—
332C2×C4×C37#12011yescharacteristic
333C2×C4×C37#12011yescharacteristic
334C2×C4×C37#12011yescharacteristic
335C2×C4×C37#12011yescharacteristic
336#25585C3711yesmaximal, characteristic, direct product factor, Sylow
337C22×C37—21no—
338C22×C37—21no—
339C22×C37—21no—
340C22×C37—21no—
341C22×C37—21no—
342C22×C37—21no—
343C22×C37—42no—
344C22×C37—42no—
345C22×C37—42no—
346C22×C37—48no—
347C22×C37—44no—
348C22×C37—48no—
349C22×C37—44no—
350C22×C37—41no—
351C22×C37—42no—
352C22×C37—41no—
353C22×C37—42no—
354C22×C37—44no—
355C22×C37—42no—
356C22×C37—41no—
357C22×C37—84no—
358C22×C37—81no—
359C22×C37—84no—
360C22×C37—82no—
361C22×C37—84no—
362C22×C37—82no—
363C22×C37—82no—
364C22×C37—82no—
365C22×C37C2×#12011yescharacteristic
366C22×C37#53211yescharacteristic
367C22×C37#53511yescharacteristic
368C22×C37#54612yes—
369C22×C37#55012yes—
370C4×C37—21no—
371C4×C37—21no—
372C4×C37—21no—
373C4×C37—44no—
374C4×C37—41no—
375C4×C37—42no—
376C4×C37—41no—
377C4×C37—42no—
378C4×C37—41no—
379C4×C37—42no—
380C4×C37—82no—
381C4×C37—82no—
382C4×C37B(4,𝔽2)12yes—
383#3505C2×C3711yescharacteristic, complemented
384#2435C2×C3711yescharacteristic, complemented
385#2433C2×C3711yescharacteristic, complemented
386#2408C2×C3711yescharacteristic, complemented
387#2021C2×C3714yescomplemented
388#1996C2×C3711yescharacteristic, complemented
389#1964C2×C3711yescharacteristic, complemented
390#1889C2×C3714yescomplemented
391C4×#99C2×C3711yescharacteristic, complemented
392C2×C37—22no—
393C2×C37—21no—
394C2×C37—22no—
395C2×C37—21no—
396C2×C37—84no—
397C2×C37—81no—
398C2×C37—82no—
399C2×C37#243111yescharacteristic
400C2×C37C2×B(4,𝔽2)11yescharacteristic
401C2×C37#302711yescharacteristic
402C23×D4C22×C3711yescharacteristic
403#553—21no—
404#553—22no—
405#552—21no—
406#551—22no—
407#548—21no—
408#546—21no—
409#539—21no—
410#538—21no—
411#534C22×C3712yes—
412C2×#127—21no—
413#529—21no—
414C2×#124—21no—
415#525—21no—
416C2×C22⋊Q8C22×C3711yescharacteristic
417C2×#121—21no—
418C2×#121C22×C3711yescharacteristic
419C2×#120C22×C3714yes—
420C2×#120C22×C3712yes—
421#518C22×C3712yes—
422C2×C4×D4C22×C3711yescharacteristic
423C2×#99C22×C3712yes—
424C2×#99C22×C3714yes—
425#394—21no—
426#394—22no—
427#392—21no—
428#392—22no—
429#390—21no—
430#390—21no—
431#390—21no—
432#380C22×C3711yescharacteristic
433#379C22×C3712yes—
434#379C22×C3714yes—
435C4×C22⋊C4C22×C3711yescharacteristic
436C4×C22⋊C4C22×C3711yescharacteristic
437#342C22×C3712yes—
438#342C22×C3714yes—
439C37#2558511yescharacteristic, direct product factor, Sylow
440C25C23×C3712yes—
441C2×#41—21no—
442C22×Q8D4×C3711yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C3711yescharacteristic, complemented
453C22×D4C23×C3711yescharacteristic
454C22×D4C23×C3712yes—
455C23×C4D4×C3711yescharacteristic, complemented
456C23×C4C23×C3711yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C3711yescharacteristic, complemented
507C2×C4⋊C4D4×C3711yescharacteristic, complemented
508C2×C4⋊C4D4×C3711yescharacteristic, complemented
509C2×C4⋊C4D4×C3712yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C3711yescharacteristic, complemented
518C2×C22⋊C4D4×C3712yescomplemented
519C2×C22⋊C4C23×C3712yes—
520C2×C22⋊C4C23×C3712yes—
521C2×C22⋊C4C23×C3711yescharacteristic
522C2×C22⋊C4C23×C3712yes—
523C2×C22⋊C4C23×C3712yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C3711yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C3712yes—
540C24C2×D4×C3711yescharacteristic
541C24C24×C3711yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C3711yescharacteristic
588C22×C4C2×D4×C3712yes—
589C22×C4C2×D4×C3711yescharacteristic
590C22×C4C2×D4×C3711yescharacteristic
591C22×C4C2×D4×C3711yescharacteristic
592C22×C4C2×D4×C3711yescharacteristic
593C22×C4C2×D4×C3712yes—
594C22×C4C2×D4×C3711yescharacteristic
595C22×C4C2×D4×C3712yes—
596C22×C4C2×D4×C3711yescharacteristic
597C22×C4C2×D4×C3711yescharacteristic
598C22×C4C2×D4×C3711yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C3714yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C3711yescharacteristic
672C23C22×D4×C3711yescharacteristic
673C23C22×D4×C3711yescharacteristic
674C23C2×#41×C3712yes—
675C23H(5,𝔽2)×C3712yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C3711yescharacteristic
726C2×C4#120×C3711yescharacteristic
727C2×C4#120×C3711yescharacteristic
728C2×C4#120×C3711yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C3711yescharacteristic
758C22C37×#53211yescharacteristic
759C22C37×#53511yescharacteristic
760C22C37×#54612yes—
761C22C37×#55012yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4C37×B(4,𝔽2)12yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C37×#243111yescharacteristic
783C2C2×C37×B(4,𝔽2)11yescharacteristic
784C2C37×#302711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC24C24×C37
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3505C2semidirect
2. C37×#2435C2semidirect
3. C37×#2433C2semidirect
4. C37×#2408C2semidirect
5. C37×#2021C2semidirect
6. C37×#1996C2semidirect
7. C37×#1964C2semidirect
8. C37×#1889C2semidirect
9. C4×#99×C37C2semidirect
49. C22×Q8×C37D4semidirect
59. C22×D4×C37D4semidirect
62. C23×C4×C37D4semidirect
113. C2×C4⋊C4×C37D4semidirect
114. C2×C4⋊C4×C37D4semidirect
115. C2×C4⋊C4×C37D4semidirect
116. C2×C4⋊C4×C37D4semidirect
124. C2×C22⋊C4×C37D4semidirect
125. C2×C22⋊C4×C37D4semidirect
133. C2×C42×C37D4semidirect
243. C22⋊C4×C37#41semidirect
336. #25585C37direct (N × H)
383. #3505C2×C37semidirect
384. #2435C2×C37semidirect
385. #2433C2×C37semidirect
386. #2408C2×C37semidirect
387. #2021C2×C37semidirect
388. #1996C2×C37semidirect
389. #1964C2×C37semidirect
390. #1889C2×C37semidirect
391. C4×#99C2×C37semidirect
439. C37#25585direct (N × H)
442. C22×Q8D4×C37semidirect
452. C22×D4D4×C37semidirect
455. C23×C4D4×C37semidirect
506. C2×C4⋊C4D4×C37semidirect
507. C2×C4⋊C4D4×C37semidirect
508. C2×C4⋊C4D4×C37semidirect
509. C2×C4⋊C4D4×C37semidirect
517. C2×C22⋊C4D4×C37semidirect
518. C2×C22⋊C4D4×C37semidirect
526. C2×C42D4×C37semidirect
636. 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×#35052
C37×#24352
C37×#24332
C37×#24082
C37×#20212
C37×#19962
C37×#19642
C37×#18892
C4×#99×C372
#2558537