Finite Group Databasebeta

← C37×#24142 #22645395

Subgroups — C37×#24142 #22645395

Order 9472.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3505C211yesmaximal, characteristic, complemented
2C37×#2626C211yesmaximal, characteristic, complemented
3C37×#2617C211yesmaximal, characteristic, complemented
4C37×#2321C211yesmaximal, characteristic, complemented
5C37×#2044C212yesmaximal, complemented
6C37×#2021C212yesmaximal, complemented
7C37×#1996C211yesmaximal, characteristic, complemented
8C37×#1964C211yesmaximal, characteristic, complemented
9C37×#1889C212yesmaximal, complemented
10C37×#1867C212yesmaximal, complemented
11C37×#1799C211yesmaximal, characteristic, complemented
12C37×#553—22no—
13C37×#553—21no—
14C37×#552—21no—
15C37×#551—22no—
16C37×#548—21no—
17C37×#546—21no—
18C37×#539—21no—
19C37×#538—21no—
20C37×#534C2212yes—
21C37×#529—21no—
22C37×#525—21no—
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#120×C37C2211yescharacteristic
26C2×#120×C37C2212yes—
27C37×#518C2212yes—
28C2×C4×D4×C37C2211yescharacteristic
29C22×C22⋊C4×C37C2211yescharacteristic
30C2×#99×C37C2212yes—
31C2×#99×C37C2212yes—
32C2×#99×C37C2212yes—
33C37×#399—21no—
34C37×#397—21no—
35C37×#396—22no—
36C37×#394—22no—
37C37×#393—21no—
38C37×#392—21no—
39C37×#390—21no—
40C37×#388—21no—
41C37×#388—21no—
42C37×#386—21no—
43C37×#386C2212yes—
44C37×#386C2211yescharacteristic
45C37×#385C2212yes—
46C37×#385C2211yescharacteristic
47C37×#380C2211yescharacteristic
48C37×#380C2211yescharacteristic
49C37×#379C2212yes—
50C37×#379C2211yescharacteristic
51C4×C22⋊C4×C37C2211yescharacteristic
52C37×#342C2212yes—
53C37×#342C2212yes—
54C37×#342C2212yes—
55C25×C37C2311yescharacteristic
56C2×#41×C37—21no—
57C22×Q8×C37D411yescharacteristic, complemented
58C22×D4×C37—21no—
59C22×D4×C37—22no—
60C22×D4×C37D411yescharacteristic, complemented
61C22×D4×C37C2312yes—
62C22×D4×C37C2311yescharacteristic
63C23×C4×C37D411yescharacteristic, complemented
64C23×C4×C37C2311yescharacteristic
65C23×C4×C37C2311yescharacteristic
66#126×C37—22no—
67#126×C37—22no—
68#126×C37—22no—
69#125×C37—21no—
70#125×C37—22no—
71#124×C37—21no—
72#124×C37—22no—
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#120×C37—22no—
93#120×C37—22no—
94#120×C37—22no—
95#120×C37—22no—
96#120×C37—24no—
97#120×C37—42no—
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×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—22no—
116C2×C4⋊C4×C37D411yescharacteristic, complemented
117C2×C4⋊C4×C37D412yescomplemented
118C2×C4⋊C4×C37D411yescharacteristic, complemented
119C2×C4⋊C4×C37D411yescharacteristic, complemented
120C2×C22⋊C4×C37—22no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—22no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37—21no—
133C2×C22⋊C4×C37—22no—
134C2×C22⋊C4×C37—22no—
135C2×C22⋊C4×C37D412yescomplemented
136C2×C22⋊C4×C37D411yescharacteristic, complemented
137C2×C22⋊C4×C37C2312yes—
138C2×C22⋊C4×C37C2311yescharacteristic
139C2×C22⋊C4×C37C2312yes—
140C2×C22⋊C4×C37C2312yes—
141C2×C22⋊C4×C37C2311yescharacteristic
142C2×C22⋊C4×C37C2311yescharacteristic
143C2×C42×C37—21no—
144C2×C42×C37D411yescharacteristic, complemented
145#99×C37—24no—
146#99×C37—42no—
147#99×C37—42no—
148#95×C37—21no—
149#95×C37—21no—
150#95×C37—21no—
151#95×C37—21no—
152#95×C37—22no—
153#95×C37—21no—
154#95×C37—22no—
155C24×C37—21no—
156C24×C37—21no—
157C24×C37—21no—
158C24×C37—21no—
159C24×C37—21no—
160C24×C37—21no—
161C24×C37—81no—
162C24×C37—81no—
163C24×C37C2×D412yes—
164C24×C37C2×D411yescharacteristic
165C24×C37#4112yescomplemented
166C24×C37C2411yescharacteristic
167#41×C37—82no—
168C2×Q8×C37—21no—
169C2×Q8×C37—21no—
170C2×Q8×C37—81no—
171C2×D4×C37—21no—
172C2×D4×C37—22no—
173C2×D4×C37—21no—
174C2×D4×C37—22no—
175C2×D4×C37—22no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—22no—
179C2×D4×C37—21no—
180C2×D4×C37—22no—
181C2×D4×C37—21no—
182C2×D4×C37—22no—
183C2×D4×C37—22no—
184C2×D4×C37—22no—
185C2×D4×C37—24no—
186C2×D4×C37—21no—
187C2×D4×C37—21no—
188C2×D4×C37—44no—
189C2×D4×C37—81no—
190C2×D4×C37—81no—
191C2×D4×C37—81no—
192C2×D4×C37—82no—
193C2×D4×C37—82no—
194C22×C4×C37—21no—
195C22×C4×C37—22no—
196C22×C4×C37—22no—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—22no—
203C22×C4×C37—22no—
204C22×C4×C37—21no—
205C22×C4×C37—81no—
206C22×C4×C37—81no—
207C22×C4×C37—81no—
208C22×C4×C37C2×D411yescharacteristic
209C22×C4×C37C2×D412yes—
210C22×C4×C37C2×D411yescharacteristic
211C22×C4×C37C2×D412yes—
212C22×C4×C37C2×D411yescharacteristic
213C22×C4×C37C2×D412yes—
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D411yescharacteristic
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37C2×D411yescharacteristic
219C22×C4×C37C2×D411yescharacteristic
220C4⋊C4×C37—22no—
221C4⋊C4×C37—22no—
222C4⋊C4×C37—22no—
223C4⋊C4×C37—22no—
224C4⋊C4×C37—21no—
225C4⋊C4×C37—22no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—22no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—81no—
233C4⋊C4×C37—81no—
234C4⋊C4×C37—81no—
235C4⋊C4×C37—82no—
236C22⋊C4×C37—22no—
237C22⋊C4×C37—22no—
238C22⋊C4×C37—24no—
239C22⋊C4×C37—22no—
240C22⋊C4×C37—22no—
241C22⋊C4×C37—22no—
242C22⋊C4×C37—22no—
243C22⋊C4×C37—21no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—21no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—21no—
248C22⋊C4×C37—22no—
249C22⋊C4×C37—21no—
250C22⋊C4×C37—21no—
251C22⋊C4×C37—22no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—22no—
254C22⋊C4×C37—21no—
255C22⋊C4×C37—22no—
256C22⋊C4×C37—22no—
257C22⋊C4×C37—21no—
258C22⋊C4×C37—44no—
259C22⋊C4×C37—41no—
260C22⋊C4×C37—41no—
261C22⋊C4×C37—41no—
262C22⋊C4×C37—41no—
263C22⋊C4×C37—81no—
264C22⋊C4×C37—82no—
265C22⋊C4×C37—81no—
266C22⋊C4×C37—82no—
267C22⋊C4×C37—81no—
268C22⋊C4×C37—82no—
269C22⋊C4×C37#4112yescomplemented
270C42×C37—22no—
271C42×C37—22no—
272C42×C37—21no—
273C42×C37—21no—
274C42×C37—81no—
275C23×C37—21no—
276C23×C37—22no—
277C23×C37—22no—
278C23×C37—21no—
279C23×C37—22no—
280C23×C37—22no—
281C23×C37—21no—
282C23×C37—22no—
283C23×C37—22no—
284C23×C37—41no—
285C23×C37—41no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—42no—
289C23×C37—41no—
290C23×C37—42no—
291C23×C37—41no—
292C23×C37—41no—
293C23×C37—42no—
294C23×C37—41no—
295C23×C37—42no—
296C23×C37—42no—
297C23×C37—42no—
298C23×C37—41no—
299C23×C37—41no—
300C23×C37—41no—
301C23×C37—41no—
302C23×C37—82no—
303C23×C37—82no—
304C23×C37—82no—
305C23×C37—82no—
306C23×C37C22×D411yescharacteristic
307C23×C37C22×D411yescharacteristic
308C23×C37C22×D411yescharacteristic
309C23×C37C2×#4111yescharacteristic
310C23×C37C2×#4111yescharacteristic
311C23×C37H(5,𝔽2)11yescharacteristic
312C23×C372−1+411yescharacteristic
313Q8×C37—42no—
314Q8×C37—81no—
315D4×C37—42no—
316D4×C37—42no—
317D4×C37—42no—
318D4×C37—41no—
319D4×C37—41no—
320D4×C37—41no—
321D4×C37—42no—
322D4×C37—42no—
323D4×C37—41no—
324D4×C37—81no—
325D4×C37—82no—
326D4×C37—84no—
327D4×C37—82no—
328D4×C37—88no—
329C2×C4×C37—21no—
330C2×C4×C37—22no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—22no—
334C2×C4×C37—22no—
335C2×C4×C37—21no—
336C2×C4×C37—22no—
337C2×C4×C37—21no—
338C2×C4×C37—22no—
339C2×C4×C37—22no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
346C2×C4×C37—42no—
347C2×C4×C37—41no—
348C2×C4×C37—41no—
349C2×C4×C37—41no—
350C2×C4×C37—42no—
351C2×C4×C37—41no—
352C2×C4×C37—42no—
353C2×C4×C37—41no—
354C2×C4×C37—41no—
355C2×C4×C37—42no—
356C2×C4×C37—42no—
357C2×C4×C37—41no—
358C2×C4×C37—42no—
359C2×C4×C37—42no—
360C2×C4×C37—42no—
361C2×C4×C37—41no—
362C2×C4×C37—42no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—42no—
366C2×C4×C37—42no—
367C2×C4×C37—81no—
368C2×C4×C37—82no—
369C2×C4×C37—82no—
370C2×C4×C37#12011yescharacteristic
371C2×C4×C37#12011yescharacteristic
372C2×C4×C37#12011yescharacteristic
373C2×C4×C37#12011yescharacteristic
374#24142C3711yesmaximal, characteristic, direct product factor, Sylow
375C22×C37—21no—
376C22×C37—21no—
377C22×C37—21no—
378C22×C37—21no—
379C22×C37—21no—
380C22×C37—21no—
381C22×C37—41no—
382C22×C37—41no—
383C22×C37—41no—
384C22×C37—41no—
385C22×C37—42no—
386C22×C37—42no—
387C22×C37—44no—
388C22×C37—42no—
389C22×C37—44no—
390C22×C37—41no—
391C22×C37—42no—
392C22×C37—42no—
393C22×C37—41no—
394C22×C37—42no—
395C22×C37—42no—
396C22×C37—41no—
397C22×C37—82no—
398C22×C37—81no—
399C22×C37—82no—
400C22×C37—82no—
401C22×C37—81no—
402C22×C37—81no—
403C22×C37—82no—
404C22×C37—81no—
405C22×C37—81no—
406C22×C37C2×#12011yescharacteristic
407C22×C37#52511yescharacteristic
408C22×C37#53711yescharacteristic
409C22×C37#54611yescharacteristic
410C22×C37#54711yescharacteristic
411C22×C37#54811yescharacteristic
412C22×C37#55011yescharacteristic
413C4×C37—21no—
414C4×C37—21no—
415C4×C37—21no—
416C4×C37—21no—
417C4×C37—42no—
418C4×C37—41no—
419C4×C37—42no—
420C4×C37—41no—
421C4×C37—42no—
422C4×C37—41no—
423C4×C37—42no—
424C4×C37—82no—
425C4×C37—81no—
426C4×C37—82no—
427C4×C37—81no—
428#3505C2×C3711yescharacteristic, complemented
429#2626C2×C3711yescharacteristic, complemented
430#2617C2×C3711yescharacteristic, complemented
431#2321C2×C3711yescharacteristic, complemented
432#2044C2×C3712yescomplemented
433#2021C2×C3712yescomplemented
434#1996C2×C3711yescharacteristic, complemented
435#1964C2×C3711yescharacteristic, complemented
436#1889C2×C3712yescomplemented
437#1867C2×C3712yescomplemented
438#1799C2×C3711yescharacteristic, complemented
439C2×C37—21no—
440C2×C37—21no—
441C2×C37—21no—
442C2×C37—21no—
443C2×C37—21no—
444C2×C37—21no—
445C2×C37—82no—
446C2×C37—81no—
447C2×C37—82no—
448C2×C37#240711yescharacteristic
449C2×C37#302611yescharacteristic
450C2×C37#302711yescharacteristic
451#553—22no—
452#553—21no—
453#552—21no—
454#551—22no—
455#548—21no—
456#546—21no—
457#539—21no—
458#538—21no—
459#534C22×C3712yes—
460#529—21no—
461#525—21no—
462C2×C22⋊Q8C22×C3711yescharacteristic
463C2×#121C22×C3711yescharacteristic
464C2×#120C22×C3711yescharacteristic
465C2×#120C22×C3712yes—
466#518C22×C3712yes—
467C2×C4×D4C22×C3711yescharacteristic
468C22×C22⋊C4C22×C3711yescharacteristic
469C2×#99C22×C3712yes—
470C2×#99C22×C3712yes—
471C2×#99C22×C3712yes—
472#399—21no—
473#397—21no—
474#396—22no—
475#394—22no—
476#393—21no—
477#392—21no—
478#390—21no—
479#388—21no—
480#388—21no—
481#386—21no—
482#386C22×C3711yescharacteristic
483#386C22×C3712yes—
484#385C22×C3711yescharacteristic
485#385C22×C3712yes—
486#380C22×C3711yescharacteristic
487#380C22×C3711yescharacteristic
488#379C22×C3711yescharacteristic
489#379C22×C3712yes—
490C4×C22⋊C4C22×C3711yescharacteristic
491#342C22×C3712yes—
492#342C22×C3712yes—
493#342C22×C3712yes—
494C37#2414211yescharacteristic, direct product factor, Sylow
495C25C23×C3711yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C3711yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C3711yescharacteristic, complemented
501C22×D4C23×C3711yescharacteristic
502C22×D4C23×C3712yes—
503C23×C4D4×C3711yescharacteristic, complemented
504C23×C4C23×C3711yescharacteristic
505C23×C4C23×C3711yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C3711yescharacteristic, complemented
557C2×C4⋊C4D4×C3711yescharacteristic, complemented
558C2×C4⋊C4D4×C3712yescomplemented
559C2×C4⋊C4D4×C3711yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C3711yescharacteristic, complemented
576C2×C22⋊C4D4×C3712yescomplemented
577C2×C22⋊C4C23×C3712yes—
578C2×C22⋊C4C23×C3711yescharacteristic
579C2×C22⋊C4C23×C3712yes—
580C2×C22⋊C4C23×C3711yescharacteristic
581C2×C22⋊C4C23×C3712yes—
582C2×C22⋊C4C23×C3711yescharacteristic
583C2×C42—21no—
584C2×C42D4×C3711yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C3712yes—
604C24C2×D4×C3711yescharacteristic
605C24#41×C3712yescomplemented
606C24C24×C3711yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C3711yescharacteristic
649C22×C4C2×D4×C3712yes—
650C22×C4C2×D4×C3711yescharacteristic
651C22×C4C2×D4×C3712yes—
652C22×C4C2×D4×C3711yescharacteristic
653C22×C4C2×D4×C3712yes—
654C22×C4C2×D4×C3711yescharacteristic
655C22×C4C2×D4×C3711yescharacteristic
656C22×C4C2×D4×C3711yescharacteristic
657C22×C4C2×D4×C3711yescharacteristic
658C22×C4C2×D4×C3711yescharacteristic
659C22×C4C2×D4×C3711yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C3712yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C3711yescharacteristic
747C23C22×D4×C3711yescharacteristic
748C23C22×D4×C3711yescharacteristic
749C23C2×#41×C3711yescharacteristic
750C23C2×#41×C3711yescharacteristic
751C23H(5,𝔽2)×C3711yescharacteristic
752C232−1+4×C3711yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C3711yescharacteristic
811C2×C4#120×C3711yescharacteristic
812C2×C4#120×C3711yescharacteristic
813C2×C4#120×C3711yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C3711yescharacteristic
846C22C37×#52511yescharacteristic
847C22C37×#53711yescharacteristic
848C22C37×#54611yescharacteristic
849C22C37×#54711yescharacteristic
850C22C37×#54811yescharacteristic
851C22C37×#55011yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2C37×#240711yescharacteristic
877C2C37×#302611yescharacteristic
878C2C37×#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×#2626C2semidirect
3. C37×#2617C2semidirect
4. C37×#2321C2semidirect
5. C37×#2044C2semidirect
6. C37×#2021C2semidirect
7. C37×#1996C2semidirect
8. C37×#1964C2semidirect
9. C37×#1889C2semidirect
10. C37×#1867C2semidirect
11. C37×#1799C2semidirect
57. C22×Q8×C37D4semidirect
60. C22×D4×C37D4semidirect
63. C23×C4×C37D4semidirect
116. C2×C4⋊C4×C37D4semidirect
117. C2×C4⋊C4×C37D4semidirect
118. C2×C4⋊C4×C37D4semidirect
119. C2×C4⋊C4×C37D4semidirect
135. C2×C22⋊C4×C37D4semidirect
136. C2×C22⋊C4×C37D4semidirect
144. C2×C42×C37D4semidirect
165. C24×C37#41semidirect
269. C22⋊C4×C37#41semidirect
374. #24142C37direct (N × H)
428. #3505C2×C37semidirect
429. #2626C2×C37semidirect
430. #2617C2×C37semidirect
431. #2321C2×C37semidirect
432. #2044C2×C37semidirect
433. #2021C2×C37semidirect
434. #1996C2×C37semidirect
435. #1964C2×C37semidirect
436. #1889C2×C37semidirect
437. #1867C2×C37semidirect
438. #1799C2×C37semidirect
494. C37#24142direct (N × H)
497. C22×Q8D4×C37semidirect
500. C22×D4D4×C37semidirect
503. C23×C4D4×C37semidirect
556. C2×C4⋊C4D4×C37semidirect
557. C2×C4⋊C4D4×C37semidirect
558. C2×C4⋊C4D4×C37semidirect
559. C2×C4⋊C4D4×C37semidirect
575. C2×C22⋊C4D4×C37semidirect
576. C2×C22⋊C4D4×C37semidirect
584. C2×C42D4×C37semidirect
605. C24#41×C37semidirect
709. 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×#26262
C37×#26172
C37×#23212
C37×#20442
C37×#20212
C37×#19962
C37×#19642
C37×#18892
C37×#18672
C37×#17992
#2414237