Finite Group Databasebeta

← C37×#23857 #22645110

Subgroups — C37×#23857 #22645110

Order 9472.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C37C211yesmaximal, characteristic, complemented
2C2×C37×#550C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C2×C37×#449C211yesmaximal, characteristic, complemented
5C2×C37×#449C211yesmaximal, characteristic, complemented
6C37×#2407C211yesmaximal, characteristic, complemented
7C37×#2014C211yesmaximal, characteristic, complemented
8C37×#2011C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1893C211yesmaximal, characteristic, complemented
12C37×#1880C211yesmaximal, characteristic, complemented
13C37×#1878C211yesmaximal, characteristic, complemented
14C37×#1869C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C22×#41×C37C2211yescharacteristic
19C2×#135×C37—24no—
20C2×#135×C37—24no—
21C2×#135×C37—24no—
22C22×Q16×C37C2211yescharacteristic
23C22×SD16×C37C2211yescharacteristic
24C22×SD16×C37C2211yescharacteristic
25C22×SD16×C37C2211yescharacteristic
26C22×D8×C37C2211yescharacteristic
27C22×D8×C37C2211yescharacteristic
28C23×C8×C37C2211yescharacteristic
29C37×#550—24no—
30C37×#550—24no—
31C2×#127×C37—21no—
32C2×#127×C37C2211yescharacteristic
33C2×C22⋊Q8×C37C2211yescharacteristic
34C2×#121×C37—21no—
35C2×#121×C37—21no—
36C2×#121×C37C2211yescharacteristic
37C2×#121×C37C2211yescharacteristic
38C2×#121×C37C2211yescharacteristic
39C2×C4×Q8×C37C2211yescharacteristic
40C2×C4×D4×C37—21no—
41C2×C4×D4×C37C2211yescharacteristic
42C37×#452—24no—
43C37×#449—24no—
44C37×#449—24no—
45C2×#103×C37C2211yescharacteristic
46C2×#103×C37C2211yescharacteristic
47C2×#103×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic
51C2×#102×C37C2211yescharacteristic
52C2×#102×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C2×C22⋊C8×C37C2211yescharacteristic
55C2×C22⋊C8×C37C2211yescharacteristic
56C37×#394—21no—
57C37×#392—21no—
58C37×#391C2211yescharacteristic
59C37×#390C2211yescharacteristic
60C37×#386—21no—
61C37×#385—21no—
62C37×#380C2211yescharacteristic
63C37×#340C2211yescharacteristic
64C37×#340C2211yescharacteristic
65C37×#336C2211yescharacteristic
66C37×#336C2211yescharacteristic
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—22no—
71C2×#41×C37—22no—
72C2×#41×C37—22no—
73C2×#41×C37—22no—
74C2×#41×C37—22no—
75C2×#41×C37—22no—
76C2×#41×C37—22no—
77C2×#41×C37—22no—
78C2×#41×C37—41no—
79C2×#41×C37—41no—
80C2×#41×C37—41no—
81C2×#41×C37—41no—
82C2×#41×C37—41no—
83C2×#41×C37—41no—
84C2×#41×C37D414yescomplemented
85C22×Q8×C37C2311yescharacteristic
86C22×Q8×C37C2311yescharacteristic
87C22×D4×C37—21no—
88C22×D4×C37—21no—
89C22×D4×C37—21no—
90C22×D4×C37—21no—
91C22×D4×C37—21no—
92C22×D4×C37—21no—
93C22×D4×C37—21no—
94C22×D4×C37—21no—
95C22×D4×C37D411yescharacteristic
96C22×D4×C37C2311yescharacteristic
97C22×D4×C37C2311yescharacteristic
98C22×D4×C37C2311yescharacteristic
99C23×C4×C37—21no—
100C23×C4×C37—21no—
101C23×C4×C37—21no—
102C23×C4×C37C2311yescharacteristic
103C23×C4×C37C2311yescharacteristic
104#135×C37—232no—
105C2×Q16×C37—22no—
106C2×Q16×C37—22no—
107C2×Q16×C37D414yescomplemented
108C2×SD16×C37—22no—
109C2×SD16×C37—22no—
110C2×SD16×C37—22no—
111C2×SD16×C37—22no—
112C2×SD16×C37—22no—
113C2×SD16×C37—22no—
114C2×SD16×C37—22no—
115C2×SD16×C37—41no—
116C2×SD16×C37D414yescomplemented
117C2×D8×C37—22no—
118C2×D8×C37—22no—
119C2×D8×C37—22no—
120C2×D8×C37—22no—
121C2×D8×C37—22no—
122C2×D8×C37—41no—
123C22×C8×C37—22no—
124C22×C8×C37—22no—
125C22×C8×C37—22no—
126C22×C8×C37C2311yescharacteristic
127C22×C8×C37C2311yescharacteristic
128C22×C8×C37C2311yescharacteristic
129C22×C8×C37C2311yescharacteristic
130#127×C37—28no—
131#127×C37—22no—
132#127×C37—22no—
133C22⋊Q8×C37—22no—
134C22⋊Q8×C37—41no—
135#121×C37—28no—
136#121×C37—28no—
137#121×C37—22no—
138#121×C37—22no—
139#121×C37—22no—
140#121×C37—22no—
141#121×C37—41no—
142#121×C37D414yescomplemented
143C4×Q8×C37—22no—
144C4×Q8×C37—22no—
145C4×D4×C37—28no—
146C4×D4×C37—22no—
147C4×D4×C37—22no—
148C2×C4⋊C4×C37—21no—
149C2×C4⋊C4×C37—21no—
150C2×C4⋊C4×C37D411yescharacteristic
151C2×C4⋊C4×C37C2311yescharacteristic
152C2×C4⋊C4×C37C2311yescharacteristic
153C2×C4⋊C4×C37C2311yescharacteristic
154C2×C22⋊C4×C37—21no—
155C2×C22⋊C4×C37—21no—
156C2×C22⋊C4×C37—21no—
157C2×C22⋊C4×C37—21no—
158C2×C22⋊C4×C37—21no—
159C2×C22⋊C4×C37—21no—
160C2×C22⋊C4×C37—21no—
161C2×C22⋊C4×C37D411yescharacteristic
162C2×C22⋊C4×C37D411yescharacteristic
163C2×C42×C37—21no—
164C2×C42×C37C2311yescharacteristic
165#103×C37—22no—
166#103×C37—22no—
167#103×C37—22no—
168#102×C37—22no—
169#102×C37—22no—
170#102×C37—22no—
171#102×C37—41no—
172#102×C37—41no—
173C22⋊C8×C37—22no—
174C22⋊C8×C37—22no—
175C22⋊C8×C37—22no—
176#95×C37—21no—
177#95×C37—21no—
178#95×C37—21no—
179C24×C37—21no—
180C24×C37—21no—
181C24×C37—21no—
182C24×C37C2×D411yescharacteristic
183C24×C37C2×D411yescharacteristic
184#41×C37—28no—
185#41×C37—28no—
186#41×C37—44no—
187#41×C37—44no—
188#41×C37—44no—
189#41×C37—44no—
190#41×C37—44no—
191#41×C37—44no—
192#41×C37—44no—
193#41×C37—44no—
194#41×C37—44no—
195#41×C37—44no—
196C2×Q8×C37—21no—
197C2×Q8×C37—21no—
198C2×Q8×C37—21no—
199C2×Q8×C37—21no—
200C2×Q8×C37—21no—
201C2×Q8×C37—21no—
202C2×Q8×C37—21no—
203C2×Q8×C37—21no—
204C2×Q8×C37C2×D412yes—
205C2×Q8×C37C2×D412yes—
206C2×Q8×C37C2×D412yes—
207C2×Q8×C37C2×D412yes—
208C2×D4×C37—24no—
209C2×D4×C37—24no—
210C2×D4×C37—22no—
211C2×D4×C37—24no—
212C2×D4×C37—24no—
213C2×D4×C37—24no—
214C2×D4×C37—24no—
215C2×D4×C37—22no—
216C2×D4×C37—21no—
217C2×D4×C37—21no—
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—21no—
228C2×D4×C37—21no—
229C2×D4×C37—21no—
230C2×D4×C37—21no—
231C2×D4×C37—41no—
232C2×D4×C37—42no—
233C2×D4×C37—42no—
234C2×D4×C37—42no—
235C2×D4×C37—42no—
236C2×D4×C37—42no—
237C2×D4×C37—42no—
238C2×D4×C37—42no—
239C2×D4×C37—42no—
240C2×D4×C37—42no—
241C2×D4×C37—42no—
242C2×D4×C37—42no—
243C2×D4×C37—81no—
244C2×D4×C37—81no—
245C2×D4×C37—81no—
246C2×D4×C37—81no—
247C2×D4×C37—81no—
248C2×D4×C37—81no—
249C2×D4×C37—81no—
250C2×D4×C37C2×D412yes—
251C2×D4×C37C2×D412yes—
252C2×D4×C37C2×D412yes—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—24no—
259C22×C4×C37—21no—
260C22×C4×C37—21no—
261C22×C4×C37—24no—
262C22×C4×C37—21no—
263C22×C4×C37—21no—
264C22×C4×C37—21no—
265C22×C4×C37—21no—
266C22×C4×C37—21no—
267C22×C4×C37—21no—
268C22×C4×C37—21no—
269C22×C4×C37—21no—
270C22×C4×C37—42no—
271C22×C4×C37—42no—
272C22×C4×C37—42no—
273C22×C4×C37—42no—
274C22×C4×C37—42no—
275C22×C4×C37—42no—
276C22×C4×C37—42no—
277C22×C4×C37C2×D411yescharacteristic
278C22×C4×C37C2×D411yescharacteristic
279C22×C4×C37C2×D411yescharacteristic
280C22×C4×C37C2×D412yes—
281C22×C4×C37C2×D412yes—
282C22×C4×C37C2×D411yescharacteristic
283C22×C4×C37C2411yescharacteristic
284Q16×C37—28no—
285SD16×C37—28no—
286SD16×C37—28no—
287SD16×C37—44no—
288D8×C37—28no—
289D8×C37—44no—
290C2×C8×C37—28no—
291C2×C8×C37—21no—
292C2×C8×C37—21no—
293C2×C8×C37—21no—
294C2×C8×C37—21no—
295C2×C8×C37—21no—
296C2×C8×C37—21no—
297C2×C8×C37—21no—
298C2×C8×C37—21no—
299C2×C8×C37—21no—
300C2×C8×C37—21no—
301C2×C8×C37C2×D412yes—
302C2×C8×C37C2×D412yes—
303C4⋊C4×C37—24no—
304C4⋊C4×C37—22no—
305C4⋊C4×C37—21no—
306C4⋊C4×C37—21no—
307C4⋊C4×C37—21no—
308C4⋊C4×C37—21no—
309C4⋊C4×C37—21no—
310C4⋊C4×C37—42no—
311C4⋊C4×C37C2×D412yes—
312C22⋊C4×C37—24no—
313C22⋊C4×C37—22no—
314C22⋊C4×C37—24no—
315C22⋊C4×C37—22no—
316C22⋊C4×C37—42no—
317C22⋊C4×C37—42no—
318C22⋊C4×C37—42no—
319C22⋊C4×C37—81no—
320C22⋊C4×C37—81no—
321C42×C37—24no—
322C42×C37—21no—
323C42×C37—21no—
324C23×C37—21no—
325C23×C37—21no—
326C23×C37—21no—
327C23×C37—21no—
328C23×C37—21no—
329C23×C37—21no—
330C23×C37—21no—
331C23×C37—22no—
332C23×C37—22no—
333C23×C37—21no—
334C23×C37—22no—
335C23×C37—21no—
336C23×C37—21no—
337C23×C37—21no—
338C23×C37—21no—
339C23×C37—21no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—41no—
348C23×C37—41no—
349C23×C37—41no—
350C23×C37—41no—
351C23×C37—41no—
352C23×C37—41no—
353C23×C37—41no—
354C23×C37—41no—
355C23×C37—41no—
356C23×C37—41no—
357C23×C37—41no—
358C23×C37#12012yes—
359C23×C37C22×D411yescharacteristic
360Q8×C37—22no—
361Q8×C37—22no—
362Q8×C37—22no—
363Q8×C37—22no—
364Q8×C37—22no—
365Q8×C37—41no—
366Q8×C37—41no—
367Q8×C37#12014yes—
368D4×C37—22no—
369D4×C37—22no—
370D4×C37—22no—
371D4×C37—22no—
372D4×C37—22no—
373D4×C37—22no—
374D4×C37—44no—
375D4×C37—48no—
376D4×C37—48no—
377D4×C37—48no—
378D4×C37—48no—
379D4×C37—41no—
380D4×C37—41no—
381D4×C37—41no—
382D4×C37—41no—
383D4×C37—41no—
384D4×C37—41no—
385D4×C37—84no—
386D4×C37—84no—
387D4×C37—84no—
388D4×C37—84no—
389C2×C4×C37—21no—
390C2×C4×C37—22no—
391C2×C4×C37—21no—
392C2×C4×C37—21no—
393C2×C4×C37—22no—
394C2×C4×C37—22no—
395C2×C4×C37—21no—
396C2×C4×C37—22no—
397C2×C4×C37—22no—
398C2×C4×C37—22no—
399C2×C4×C37—22no—
400C2×C4×C37—21no—
401C2×C4×C37—22no—
402C2×C4×C37—21no—
403C2×C4×C37—21no—
404C2×C4×C37—22no—
405C2×C4×C37—21no—
406C2×C4×C37—21no—
407C2×C4×C37—21no—
408C2×C4×C37—48no—
409C2×C4×C37—48no—
410C2×C4×C37—48no—
411C2×C4×C37—41no—
412C2×C4×C37—41no—
413C2×C4×C37—41no—
414C2×C4×C37—41no—
415C2×C4×C37—41no—
416C2×C4×C37—41no—
417C2×C4×C37—41no—
418C2×C4×C37—41no—
419C2×C4×C37—41no—
420C2×C4×C37—41no—
421C2×C4×C37—41no—
422C2×C4×C37—41no—
423C2×C4×C37—41no—
424C2×C4×C37—41no—
425C2×C4×C37#12012yes—
426C2×C4×C37#13512yescomplemented
427C2×C4×C37C22×D411yescharacteristic
428C2×C4×C37C22×D411yescharacteristic
429C2×C4×C37C22×D411yescharacteristic
430C2×C4×C37C22×D411yescharacteristic
431C2×C4×C37H(5,𝔽2)11yescharacteristic
432C2×C4×C37H(5,𝔽2)11yescharacteristic
433C8×C37—22no—
434C8×C37—22no—
435C8×C37—41no—
436C8×C37—41no—
437#23857C3711yesmaximal, characteristic, direct product factor, Sylow
438C22×C37—22no—
439C22×C37—22no—
440C22×C37—22no—
441C22×C37—41no—
442C22×C37—41no—
443C22×C37—41no—
444C22×C37—41no—
445C22×C37—42no—
446C22×C37—42no—
447C22×C37—42no—
448C22×C37—41no—
449C22×C37—41no—
450C22×C37—42no—
451C22×C37—42no—
452C22×C37—41no—
453C22×C37—42no—
454C22×C37—42no—
455C22×C37—41no—
456C22×C37—42no—
457C22×C37—41no—
458C22×C37—41no—
459C22×C37—42no—
460C22×C37—41no—
461C22×C37—81no—
462C22×C37—81no—
463C22×C37—81no—
464C22×C37—81no—
465C22×C37—81no—
466C22×C37—81no—
467C22×C37—81no—
468C22×C37—81no—
469C22×C37—81no—
470C22×C37—81no—
471C22×C37—81no—
472C22×C37—81no—
473C22×C37C2×#12011yescharacteristic
474C22×C37D4211yescharacteristic
475C22×C37D4211yescharacteristic
476C22×C37C2×#13511yescharacteristic
477C22×C37#57511yescharacteristic
478C22×C37#57611yescharacteristic
479C22×C37#57711yescharacteristic
480C4×C37—22no—
481C4×C37—24no—
482C4×C37—22no—
483C4×C37—41no—
484C4×C37—42no—
485C4×C37—41no—
486C4×C37—42no—
487C4×C37—81no—
488C4×C37—81no—
489C4×C37C2×#12011yescharacteristic
490C4×C37#53411yescharacteristic
491C4×C37D4211yescharacteristic
492C4×C37D4211yescharacteristic
493C22×#135C2×C3711yescharacteristic, complemented
494C2×#550C2×C3711yescharacteristic, complemented
495C2×#452C2×C3711yescharacteristic, complemented
496C2×#449C2×C3711yescharacteristic, complemented
497C2×#449C2×C3711yescharacteristic, complemented
498#2407C2×C3711yescharacteristic, complemented
499#2014C2×C3711yescharacteristic, complemented
500#2011C2×C3711yescharacteristic, complemented
501#2000C2×C3711yescharacteristic, complemented
502#1999C2×C3711yescharacteristic, complemented
503#1893C2×C3711yescharacteristic, complemented
504#1880C2×C3711yescharacteristic, complemented
505#1878C2×C3711yescharacteristic, complemented
506#1869C2×C3711yescharacteristic, complemented
507#1788C2×C3711yescharacteristic, complemented
508C2×C37—42no—
509C2×C37—81no—
510C2×C37—82no—
511C2×C37—82no—
512C2×C37—82no—
513C2×C37#240311yescharacteristic
514C2×C37#300211yescharacteristic
515C2×C37#301211yescharacteristic
516C2×C37#326811yescharacteristic
517C2×C37#327111yescharacteristic
518C2×C37#328411yescharacteristic
519C2×C37#328711yescharacteristic
520C22×#41C22×C3711yescharacteristic
521C22×#41C22×C3711yescharacteristic
522C22×#41C22×C3711yescharacteristic
523C2×#135—24no—
524C2×#135—24no—
525C2×#135—24no—
526C22×Q16C22×C3711yescharacteristic
527C22×SD16C22×C3711yescharacteristic
528C22×SD16C22×C3711yescharacteristic
529C22×SD16C22×C3711yescharacteristic
530C22×D8C22×C3711yescharacteristic
531C22×D8C22×C3711yescharacteristic
532C23×C8C22×C3711yescharacteristic
533#550—24no—
534#550—24no—
535C2×#127—21no—
536C2×#127C22×C3711yescharacteristic
537C2×C22⋊Q8C22×C3711yescharacteristic
538C2×#121—21no—
539C2×#121—21no—
540C2×#121C22×C3711yescharacteristic
541C2×#121C22×C3711yescharacteristic
542C2×#121C22×C3711yescharacteristic
543C2×C4×Q8C22×C3711yescharacteristic
544C2×C4×D4—21no—
545C2×C4×D4C22×C3711yescharacteristic
546#452—24no—
547#449—24no—
548#449—24no—
549C2×#103C22×C3711yescharacteristic
550C2×#103C22×C3711yescharacteristic
551C2×#103C22×C3711yescharacteristic
552C2×#102C22×C3711yescharacteristic
553C2×#102C22×C3711yescharacteristic
554C2×#102C22×C3711yescharacteristic
555C2×#102C22×C3711yescharacteristic
556C2×#102C22×C3711yescharacteristic
557C2×C22⋊C8C22×C3711yescharacteristic
558C2×C22⋊C8C22×C3711yescharacteristic
559C2×C22⋊C8C22×C3711yescharacteristic
560#394—21no—
561#392—21no—
562#391C22×C3711yescharacteristic
563#390C22×C3711yescharacteristic
564#386—21no—
565#385—21no—
566#380C22×C3711yescharacteristic
567#340C22×C3711yescharacteristic
568#340C22×C3711yescharacteristic
569#336C22×C3711yescharacteristic
570#336C22×C3711yescharacteristic
571C37#2385711yescharacteristic, direct product factor, Sylow
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C3714yescomplemented
590C22×Q8C23×C3711yescharacteristic
591C22×Q8C23×C3711yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C3711yescharacteristic
601C22×D4C23×C3711yescharacteristic
602C22×D4C23×C3711yescharacteristic
603C22×D4C23×C3711yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C3711yescharacteristic
608C23×C4C23×C3711yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C3714yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C3714yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C3711yescharacteristic
632C22×C8C23×C3711yescharacteristic
633C22×C8C23×C3711yescharacteristic
634C22×C8C23×C3711yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C3714yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C3711yescharacteristic
656C2×C4⋊C4C23×C3711yescharacteristic
657C2×C4⋊C4C23×C3711yescharacteristic
658C2×C4⋊C4C23×C3711yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C3711yescharacteristic
667C2×C22⋊C4D4×C3711yescharacteristic
668C2×C42—21no—
669C2×C42C23×C3711yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C3711yescharacteristic
688C24C2×D4×C3711yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C3712yes—
710C2×Q8C2×D4×C3712yes—
711C2×Q8C2×D4×C3712yes—
712C2×Q8C2×D4×C3712yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C3712yes—
756C2×D4C2×D4×C3712yes—
757C2×D4C2×D4×C3712yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C3711yescharacteristic
783C22×C4C2×D4×C3711yescharacteristic
784C22×C4C2×D4×C3711yescharacteristic
785C22×C4C2×D4×C3712yes—
786C22×C4C2×D4×C3712yes—
787C22×C4C2×D4×C3711yescharacteristic
788C22×C4C24×C3711yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C3712yes—
807C2×C8C2×D4×C3712yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C3712yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C3712yes—
864C23C22×D4×C3711yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C3714yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C3712yes—
931C2×C4#135×C3712yescomplemented
932C2×C4C22×D4×C3711yescharacteristic
933C2×C4C22×D4×C3711yescharacteristic
934C2×C4C22×D4×C3711yescharacteristic
935C2×C4C22×D4×C3711yescharacteristic
936C2×C4H(5,𝔽2)×C3711yescharacteristic
937C2×C4H(5,𝔽2)×C3711yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C3711yescharacteristic
978C22D42×C3711yescharacteristic
979C22D42×C3711yescharacteristic
980C22C2×#135×C3711yescharacteristic
981C22C37×#57511yescharacteristic
982C22C37×#57611yescharacteristic
983C22C37×#57711yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C3711yescharacteristic
994C4C37×#53411yescharacteristic
995C4D42×C3711yescharacteristic
996C4D42×C3711yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2C37×#240311yescharacteristic
1003C2C37×#300211yescharacteristic
1004C2C37×#301211yescharacteristic
1005C2C37×#326811yescharacteristic
1006C2C37×#327111yescharacteristic
1007C2C37×#328411yescharacteristic
1008C2C37×#328711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C37C2semidirect
2. C2×C37×#550C2semidirect
3. C2×C37×#452C2semidirect
4. C2×C37×#449C2semidirect
5. C2×C37×#449C2semidirect
6. C37×#2407C2semidirect
7. C37×#2014C2semidirect
8. C37×#2011C2semidirect
9. C37×#2000C2semidirect
10. C37×#1999C2semidirect
11. C37×#1893C2semidirect
12. C37×#1880C2semidirect
13. C37×#1878C2semidirect
14. C37×#1869C2semidirect
15. C37×#1788C2semidirect
84. C2×#41×C37D4semidirect
107. C2×Q16×C37D4semidirect
116. C2×SD16×C37D4semidirect
142. #121×C37D4semidirect
426. C2×C4×C37#135semidirect
437. #23857C37direct (N × H)
493. C22×#135C2×C37semidirect
494. C2×#550C2×C37semidirect
495. C2×#452C2×C37semidirect
496. C2×#449C2×C37semidirect
497. C2×#449C2×C37semidirect
498. #2407C2×C37semidirect
499. #2014C2×C37semidirect
500. #2011C2×C37semidirect
501. #2000C2×C37semidirect
502. #1999C2×C37semidirect
503. #1893C2×C37semidirect
504. #1880C2×C37semidirect
505. #1878C2×C37semidirect
506. #1869C2×C37semidirect
507. #1788C2×C37semidirect
571. C37#23857direct (N × H)
589. C2×#41D4×C37semidirect
612. C2×Q16D4×C37semidirect
621. C2×SD16D4×C37semidirect
647. #121D4×C37semidirect
931. C2×C4#135×C37semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C372
C2×C37×#5502
C2×C37×#4522
C2×C37×#4492
C37×#24072
C37×#20142
C37×#20112
C37×#20002
C37×#19992
C37×#18932
C37×#18802
C37×#18782
C37×#18692
C37×#17882
#2385737