Finite Group Databasebeta

← C37×#23876 #22645129

Subgroups — C37×#23876 #22645129

Order 9472.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
2C37×#3488C211yesmaximal, characteristic, complemented
3C2×C37×#453C212yesmaximal, complemented
4C37×#3003C211yesmaximal, characteristic, complemented
5C37×#2433C211yesmaximal, characteristic, complemented
6C37×#2006C212yesmaximal, complemented
7C37×#2002C212yesmaximal, complemented
8C37×#1900C211yesmaximal, characteristic, complemented
9C37×#1883C212yesmaximal, complemented
10C37×#1871C211yesmaximal, characteristic, complemented
11C37×#1789C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C37C2211yescharacteristic, complemented
13C22×#41×C37C2211yescharacteristic
14C23×D4×C37C2211yescharacteristic, complemented
15C2×AGL(1,ℤ/8)×C37—21no—
16C2×AGL(1,ℤ/8)×C37—21no—
17C2×AGL(1,ℤ/8)×C37—28no—
18C2×AGL(1,ℤ/8)×C37C2212yes—
19C2×AGL(1,ℤ/8)×C37C2212yescomplemented
20C2×AGL(1,ℤ/8)×C37C2212yescomplemented
21C22×SD16×C37—21no—
22C22×D8×C37—21no—
23C22×M16×C37C2211yescharacteristic, complemented
24C37×#550—21no—
25C37×#548—21no—
26C37×#546—21no—
27C37×#546—22no—
28D42×C37—22no—
29D42×C37—21no—
30C37×#537—21no—
31C37×#537C2211yescharacteristic, complemented
32C37×#535—21no—
33C37×#535C2211yescharacteristic, complemented
34C2×#127×C37C2212yescomplemented
35C37×#525—21no—
36C37×#525C2211yescharacteristic
37C2×#121×C37—21no—
38C2×#121×C37C2211yescharacteristic
39C2×#120×C37—22no—
40C37×#520C2211yescharacteristic, complemented
41C37×#453—28no—
42C37×#450—21no—
43C37×#450—21no—
44C37×#447—21no—
45C37×#447—21no—
46C2×#104×C37C2212yescomplemented
47C2×#104×C37C2212yescomplemented
48C2×#104×C37C2212yescomplemented
49C37×#418C2212yescomplemented
50C2×#100×C37C2212yescomplemented
51C37×#407C2211yescharacteristic, complemented
52C37×#392—22no—
53C37×#390C2212yescomplemented
54C4×C22⋊C4×C37C2211yescharacteristic, complemented
55C37×#343C2212yescomplemented
56C37×#339C2212yescomplemented
57C25×C37—21no—
58H(5,𝔽2)×C37—24no—
59H(5,𝔽2)×C37—42no—
60C2×#41×C37—21no—
61C2×#41×C37—21no—
62C2×#41×C37—21no—
63C2×#41×C37—21no—
64C2×#41×C37—24no—
65C2×#41×C37—42no—
66C2×#41×C37D411yescharacteristic, complemented
67C2×#41×C37D411yescharacteristic, complemented
68C2×#41×C37C2311yescharacteristic
69C2×#41×C37C2311yescharacteristic
70C2×#41×C37C2311yescharacteristic
71C22×Q8×C37D411yescharacteristic, complemented
72C22×D4×C37—24no—
73C22×D4×C37—21no—
74C22×D4×C37—22no—
75C22×D4×C37—22no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—24no—
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37—21no—
83C22×D4×C37—21no—
84C22×D4×C37—42no—
85C22×D4×C37D412yes—
86C22×D4×C37D411yescharacteristic, complemented
87C22×D4×C37C2311yescharacteristic
88C22×D4×C37C2312yes—
89C23×C4×C37—21no—
90C23×C4×C37C2311yescharacteristic
91AGL(1,ℤ/8)×C37—28no—
92AGL(1,ℤ/8)×C37—28no—
93AGL(1,ℤ/8)×C37—24no—
94AGL(1,ℤ/8)×C37—24no—
95AGL(1,ℤ/8)×C37—24no—
96AGL(1,ℤ/8)×C37—24no—
97AGL(1,ℤ/8)×C37—42no—
98AGL(1,ℤ/8)×C37D418yescomplemented
99C2×SD16×C37—28no—
100C2×SD16×C37—22no—
101C2×SD16×C37—22no—
102C2×SD16×C37—22no—
103C2×D8×C37—28no—
104C2×D8×C37—22no—
105C2×D8×C37—22no—
106C2×D8×C37—22no—
107C2×M16×C37—21no—
108C2×M16×C37—24no—
109C2×M16×C37C2312yes—
110C2×M16×C37C2312yes—
111C22×C8×C37—21no—
112#127×C37—22no—
113#127×C37—21no—
114#127×C37—24no—
115#127×C37—42no—
116#124×C37—22no—
117#124×C37—21no—
118#123×C37—22no—
119#123×C37—21no—
120C22⋊Q8×C37—22no—
121C22⋊Q8×C37—21no—
122C22⋊Q8×C37—21no—
123C22⋊Q8×C37D411yescharacteristic, complemented
124C22⋊Q8×C37D411yescharacteristic, complemented
125#121×C37—22no—
126#121×C37—22no—
127#121×C37—22no—
128#121×C37—22no—
129#121×C37—22no—
130#121×C37—21no—
131#121×C37—21no—
132#121×C37—21no—
133#121×C37—21no—
134#121×C37—21no—
135#121×C37—21no—
136#121×C37—22no—
137#121×C37—21no—
138#121×C37—21no—
139#121×C37D411yescharacteristic, complemented
140#121×C37D411yescharacteristic, complemented
141#120×C37—22no—
142#120×C37—22no—
143#120×C37—22no—
144#120×C37—21no—
145#120×C37—22no—
146#120×C37—48no—
147C4×Q8×C37—21no—
148C4×D4×C37—22no—
149C4×D4×C37—22no—
150C4×D4×C37—21no—
151C4×D4×C37—22no—
152C4×D4×C37—21no—
153C4×D4×C37—21no—
154#117×C37—21no—
155#117×C37C2311yescharacteristic
156C2×C4⋊C4×C37—21no—
157C2×C4⋊C4×C37C2311yescharacteristic
158C2×C22⋊C4×C37—22no—
159C2×C22⋊C4×C37—21no—
160C2×C22⋊C4×C37—24no—
161C2×C22⋊C4×C37D412yes—
162C2×C42×C37C2312yes—
163#104×C37—24no—
164#104×C37—24no—
165#104×C37—42no—
166#102×C37—22no—
167#102×C37—22no—
168#100×C37—24no—
169C22⋊C8×C37—21no—
170C22⋊C8×C37—21no—
171#95×C37—21no—
172C24×C37—22no—
173C24×C37—22no—
174C24×C37—21no—
175C24×C37—44no—
176C24×C37—44no—
177C24×C37—41no—
178C24×C37—41no—
179C24×C37—82no—
180C24×C37C2×D411yescharacteristic
181C24×C37C2×D412yes—
182#41×C37—22no—
183#41×C37—22no—
184#41×C37—22no—
185#41×C37—22no—
186#41×C37—22no—
187#41×C37—22no—
188#41×C37—22no—
189#41×C37—44no—
190#41×C37—41no—
191#41×C37—41no—
192#41×C37—44no—
193#41×C37—44no—
194#41×C37—42no—
195#41×C37—42no—
196#41×C37C2×D414yes—
197C2×Q8×C37—21no—
198C2×Q8×C37—22no—
199C2×Q8×C37—41no—
200C2×Q8×C37C2×D411yescharacteristic
201C2×Q8×C37C2×D411yescharacteristic
202C2×Q8×C37C2×D411yescharacteristic
203C2×D4×C37—21no—
204C2×D4×C37—24no—
205C2×D4×C37—24no—
206C2×D4×C37—22no—
207C2×D4×C37—22no—
208C2×D4×C37—22no—
209C2×D4×C37—22no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—21no—
213C2×D4×C37—21no—
214C2×D4×C37—21no—
215C2×D4×C37—22no—
216C2×D4×C37—22no—
217C2×D4×C37—22no—
218C2×D4×C37—21no—
219C2×D4×C37—22no—
220C2×D4×C37—21no—
221C2×D4×C37—22no—
222C2×D4×C37—22no—
223C2×D4×C37—22no—
224C2×D4×C37—22no—
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—22no—
228C2×D4×C37—22no—
229C2×D4×C37—22no—
230C2×D4×C37—41no—
231C2×D4×C37—44no—
232C2×D4×C37—44no—
233C2×D4×C37—44no—
234C2×D4×C37—44no—
235C2×D4×C37—42no—
236C2×D4×C37—42no—
237C2×D4×C37—48no—
238C2×D4×C37—44no—
239C2×D4×C37—48no—
240C2×D4×C37—42no—
241C2×D4×C37—42no—
242C2×D4×C37—44no—
243C2×D4×C37—48no—
244C2×D4×C37—41no—
245C2×D4×C37—41no—
246C2×D4×C37—84no—
247C2×D4×C37—84no—
248C2×D4×C37C2×D411yescharacteristic
249C2×D4×C37C2×D411yescharacteristic
250C2×D4×C37C2×D411yescharacteristic
251C2×D4×C37C2×D414yescomplemented
252C22×C4×C37—21no—
253C22×C4×C37—22no—
254C22×C4×C37—22no—
255C22×C4×C37—22no—
256C22×C4×C37—21no—
257C22×C4×C37—22no—
258C22×C4×C37—22no—
259C22×C4×C37—21no—
260C22×C4×C37—21no—
261C22×C4×C37—21no—
262C22×C4×C37—21no—
263C22×C4×C37—44no—
264C22×C4×C37C2×D411yescharacteristic
265C22×C4×C37C2×D411yescharacteristic
266C22×C4×C37C2×D411yescharacteristic
267C22×C4×C37C2×D411yescharacteristic
268C22×C4×C37C2×D411yescharacteristic
269C22×C4×C37C2×D412yes—
270C22×C4×C37C2411yescharacteristic
271SD16×C37—28no—
272SD16×C37—28no—
273SD16×C37—44no—
274D8×C37—28no—
275D8×C37—28no—
276D8×C37—44no—
277M16×C37—24no—
278M16×C37—22no—
279M16×C37—22no—
280M16×C37—22no—
281M16×C37C2×D414yescomplemented
282C2×C8×C37—24no—
283C2×C8×C37—22no—
284C2×C8×C37—22no—
285C4⋊C4×C37—22no—
286C4⋊C4×C37—22no—
287C4⋊C4×C37—21no—
288C4⋊C4×C37—21no—
289C4⋊C4×C37—21no—
290C4⋊C4×C37—21no—
291C4⋊C4×C37C2×D411yescharacteristic
292C4⋊C4×C37C2×D411yescharacteristic
293C22⋊C4×C37—22no—
294C22⋊C4×C37—22no—
295C22⋊C4×C37—24no—
296C22⋊C4×C37—22no—
297C22⋊C4×C37—22no—
298C22⋊C4×C37—22no—
299C22⋊C4×C37—21no—
300C22⋊C4×C37—21no—
301C22⋊C4×C37—21no—
302C22⋊C4×C37—21no—
303C22⋊C4×C37—22no—
304C22⋊C4×C37—22no—
305C22⋊C4×C37—21no—
306C22⋊C4×C37—48no—
307C42×C37—22no—
308C42×C37—21no—
309C42×C37—22no—
310C42×C37—22no—
311C23×C37—21no—
312C23×C37—22no—
313C23×C37—22no—
314C23×C37—22no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—24no—
318C23×C37—24no—
319C23×C37—41no—
320C23×C37—42no—
321C23×C37—44no—
322C23×C37—44no—
323C23×C37—44no—
324C23×C37—44no—
325C23×C37—44no—
326C23×C37—42no—
327C23×C37—42no—
328C23×C37—42no—
329C23×C37—42no—
330C23×C37—42no—
331C23×C37—81no—
332C23×C37—82no—
333C23×C37—82no—
334C23×C37—82no—
335C23×C37—82no—
336C23×C37—82no—
337C23×C37—816no—
338C23×C37—82no—
339C23×C37#12011yescharacteristic
340C23×C37#12011yescharacteristic
341C23×C37C22×D411yescharacteristic
342Q8×C37—21no—
343Q8×C37—21no—
344Q8×C37—21no—
345Q8×C37—22no—
346Q8×C37—42no—
347Q8×C37#12012yescomplemented
348D4×C37—24no—
349D4×C37—21no—
350D4×C37—24no—
351D4×C37—21no—
352D4×C37—21no—
353D4×C37—22no—
354D4×C37—24no—
355D4×C37—42no—
356D4×C37—42no—
357D4×C37—44no—
358D4×C37—44no—
359D4×C37—44no—
360D4×C37—42no—
361D4×C37—44no—
362D4×C37—42no—
363D4×C37—42no—
364D4×C37—44no—
365D4×C37—42no—
366D4×C37—41no—
367D4×C37—42no—
368D4×C37—41no—
369D4×C37—42no—
370D4×C37—42no—
371D4×C37—81no—
372D4×C37—82no—
373D4×C37—82no—
374D4×C37—82no—
375D4×C37—82no—
376D4×C37—816no—
377D4×C37#12012yescomplemented
378C2×C4×C37—21no—
379C2×C4×C37—22no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—21no—
383C2×C4×C37—21no—
384C2×C4×C37—22no—
385C2×C4×C37—22no—
386C2×C4×C37—24no—
387C2×C4×C37—24no—
388C2×C4×C37—21no—
389C2×C4×C37—22no—
390C2×C4×C37—21no—
391C2×C4×C37—21no—
392C2×C4×C37—21no—
393C2×C4×C37—42no—
394C2×C4×C37—42no—
395C2×C4×C37—42no—
396C2×C4×C37—44no—
397C2×C4×C37—42no—
398C2×C4×C37—42no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—42no—
402C2×C4×C37—42no—
403C2×C4×C37—82no—
404C2×C4×C37#12011yescharacteristic
405C2×C4×C37#12011yescharacteristic
406C2×C4×C37C22×D411yescharacteristic
407C2×C4×C37C22×D412yes—
408C2×C4×C37C22×D411yescharacteristic
409C2×C4×C37H(5,𝔽2)12yes—
410C8×C37—24no—
411C8×C37—42no—
412#23876C3711yesmaximal, characteristic, direct product factor, Sylow
413C22×C37—21no—
414C22×C37—21no—
415C22×C37—21no—
416C22×C37—21no—
417C22×C37—21no—
418C22×C37—22no—
419C22×C37—21no—
420C22×C37—21no—
421C22×C37—44no—
422C22×C37—48no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—41no—
426C22×C37—41no—
427C22×C37—42no—
428C22×C37—44no—
429C22×C37—42no—
430C22×C37—41no—
431C22×C37—41no—
432C22×C37—41no—
433C22×C37—42no—
434C22×C37—41no—
435C22×C37—84no—
436C22×C37—84no—
437C22×C37—84no—
438C22×C37—88no—
439C22×C37—88no—
440C22×C37—82no—
441C22×C37—82no—
442C22×C37—164no—
443C22×C37#45312yescomplemented
444C22×C37C2×#12011yescharacteristic
445C22×C37D4212yes—
446C4×C37—21no—
447C4×C37—21no—
448C4×C37—22no—
449C4×C37—44no—
450C4×C37—41no—
451C4×C37—41no—
452C4×C37—42no—
453C4×C37—41no—
454C4×C37—41no—
455C4×C37C2×#12011yescharacteristic
456C4×C37#53411yescharacteristic
457C4×C37D4212yes—
458C22×AGL(1,ℤ/8)C2×C3711yescharacteristic, complemented
459#3488C2×C3711yescharacteristic, complemented
460C2×#453C2×C3712yescomplemented
461#3003C2×C3711yescharacteristic, complemented
462#2433C2×C3711yescharacteristic, complemented
463#2006C2×C3712yescomplemented
464#2002C2×C3712yescomplemented
465#1900C2×C3711yescharacteristic, complemented
466#1883C2×C3712yescomplemented
467#1871C2×C3711yescharacteristic, complemented
468#1789C2×C3711yescharacteristic, complemented
469C2×C37—22no—
470C2×C37—22no—
471C2×C37—41no—
472C2×C37—42no—
473C2×C37—81no—
474C2×C37—84no—
475C2×C37—82no—
476C2×C37—81no—
477C2×C37#240311yescharacteristic
478C2×C37C2×#45311yescharacteristic
479C2×C37#302111yescharacteristic
480C2×H(5,𝔽2)C22×C3711yescharacteristic, complemented
481C22×#41C22×C3711yescharacteristic
482C23×D4C22×C3711yescharacteristic, complemented
483C2×AGL(1,ℤ/8)—21no—
484C2×AGL(1,ℤ/8)—21no—
485C2×AGL(1,ℤ/8)—28no—
486C2×AGL(1,ℤ/8)C22×C3712yes—
487C2×AGL(1,ℤ/8)C22×C3712yescomplemented
488C2×AGL(1,ℤ/8)C22×C3712yescomplemented
489C22×SD16—21no—
490C22×D8—21no—
491C22×M16C22×C3711yescharacteristic, complemented
492#550—21no—
493#548—21no—
494#546—21no—
495#546—22no—
496D42—22no—
497D42—21no—
498#537—21no—
499#537C22×C3711yescharacteristic, complemented
500#535—21no—
501#535C22×C3711yescharacteristic, complemented
502C2×#127C22×C3712yescomplemented
503#525—21no—
504#525C22×C3711yescharacteristic
505C2×#121—21no—
506C2×#121C22×C3711yescharacteristic
507C2×#120—22no—
508#520C22×C3711yescharacteristic, complemented
509#453—28no—
510#450—21no—
511#450—21no—
512#447—21no—
513#447—21no—
514C2×#104C22×C3712yescomplemented
515C2×#104C22×C3712yescomplemented
516C2×#104C22×C3712yescomplemented
517#418C22×C3712yescomplemented
518C2×#100C22×C3712yescomplemented
519#407C22×C3711yescharacteristic, complemented
520#392—22no—
521#390C22×C3712yescomplemented
522C4×C22⋊C4C22×C3711yescharacteristic, complemented
523#343C22×C3712yescomplemented
524#339C22×C3712yescomplemented
525C37#2387611yescharacteristic, direct product factor, Sylow
526C25—21no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41D4×C3711yescharacteristic, complemented
536C2×#41D4×C3711yescharacteristic, complemented
537C2×#41C23×C3711yescharacteristic
538C2×#41C23×C3711yescharacteristic
539C2×#41C23×C3711yescharacteristic
540C22×Q8D4×C3711yescharacteristic, complemented
541C22×D4—24no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—24no—
548C22×D4—21no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—42no—
554C22×D4D4×C3712yes—
555C22×D4D4×C3711yescharacteristic, complemented
556C22×D4C23×C3711yescharacteristic
557C22×D4C23×C3712yes—
558C23×C4—21no—
559C23×C4C23×C3711yescharacteristic
560AGL(1,ℤ/8)—28no—
561AGL(1,ℤ/8)—28no—
562AGL(1,ℤ/8)—24no—
563AGL(1,ℤ/8)—24no—
564AGL(1,ℤ/8)—24no—
565AGL(1,ℤ/8)—24no—
566AGL(1,ℤ/8)—42no—
567AGL(1,ℤ/8)D4×C3718yescomplemented
568C2×SD16—28no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—28no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×M16—21no—
577C2×M16—24no—
578C2×M16C23×C3712yes—
579C2×M16C23×C3712yes—
580C22×C8—21no—
581#127—22no—
582#127—21no—
583#127—24no—
584#127—42no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C3711yescharacteristic, complemented
593C22⋊Q8D4×C3711yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121D4×C3711yescharacteristic, complemented
609#121D4×C3711yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—48no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C23×C3711yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C23×C3711yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4D4×C3712yes—
631C2×C42C23×C3712yes—
632#104—24no—
633#104—24no—
634#104—42no—
635#102—22no—
636#102—22no—
637#100—24no—
638C22⋊C8—21no—
639C22⋊C8—21no—
640#95—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—44no—
645C24—44no—
646C24—41no—
647C24—41no—
648C24—82no—
649C24C2×D4×C3711yescharacteristic
650C24C2×D4×C3712yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41C2×D4×C3714yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×D4×C3711yescharacteristic
670C2×Q8C2×D4×C3711yescharacteristic
671C2×Q8C2×D4×C3711yescharacteristic
672C2×D4—21no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—22no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—41no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—48no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—48no—
713C2×D4—41no—
714C2×D4—41no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4C2×D4×C3711yescharacteristic
718C2×D4C2×D4×C3711yescharacteristic
719C2×D4C2×D4×C3711yescharacteristic
720C2×D4C2×D4×C3714yescomplemented
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—44no—
733C22×C4C2×D4×C3711yescharacteristic
734C22×C4C2×D4×C3711yescharacteristic
735C22×C4C2×D4×C3711yescharacteristic
736C22×C4C2×D4×C3711yescharacteristic
737C22×C4C2×D4×C3711yescharacteristic
738C22×C4C2×D4×C3712yes—
739C22×C4C24×C3711yescharacteristic
740SD16—28no—
741SD16—28no—
742SD16—44no—
743D8—28no—
744D8—28no—
745D8—44no—
746M16—24no—
747M16—22no—
748M16—22no—
749M16—22no—
750M16C2×D4×C3714yescomplemented
751C2×C8—24no—
752C2×C8—22no—
753C2×C8—22no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×D4×C3711yescharacteristic
761C4⋊C4C2×D4×C3711yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—24no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—48no—
776C42—22no—
777C42—21no—
778C42—22no—
779C42—22no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—24no—
788C23—41no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—81no—
801C23—82no—
802C23—82no—
803C23—82no—
804C23—82no—
805C23—82no—
806C23—816no—
807C23—82no—
808C23#120×C3711yescharacteristic
809C23#120×C3711yescharacteristic
810C23C22×D4×C3711yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#120×C3712yescomplemented
817D4—24no—
818D4—21no—
819D4—24no—
820D4—21no—
821D4—21no—
822D4—22no—
823D4—24no—
824D4—42no—
825D4—42no—
826D4—44no—
827D4—44no—
828D4—44no—
829D4—42no—
830D4—44no—
831D4—42no—
832D4—42no—
833D4—44no—
834D4—42no—
835D4—41no—
836D4—42no—
837D4—41no—
838D4—42no—
839D4—42no—
840D4—82no—
841D4—81no—
842D4—82no—
843D4—82no—
844D4—82no—
845D4—816no—
846D4#120×C3712yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—44no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—82no—
873C2×C4#120×C3711yescharacteristic
874C2×C4#120×C3711yescharacteristic
875C2×C4C22×D4×C3711yescharacteristic
876C2×C4C22×D4×C3712yes—
877C2×C4C22×D4×C3711yescharacteristic
878C2×C4H(5,𝔽2)×C3712yes—
879C8—24no—
880C8—42no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—22no—
887C22—21no—
888C22—21no—
889C22—44no—
890C22—48no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—44no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—88no—
907C22—88no—
908C22—82no—
909C22—82no—
910C22—164no—
911C22C37×#45312yescomplemented
912C22C2×#120×C3711yescharacteristic
913C22D42×C3712yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—44no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—41no—
923C4C2×#120×C3711yescharacteristic
924C4C37×#53411yescharacteristic
925C4D42×C3712yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—84no—
931C2—81no—
932C2—82no—
933C2—81no—
934C2C37×#240311yescharacteristic
935C2C2×C37×#45311yescharacteristic
936C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×AGL(1,ℤ/8)×C37C2semidirect
2. C37×#3488C2semidirect
3. C2×C37×#453C2semidirect
4. C37×#3003C2semidirect
5. C37×#2433C2semidirect
6. C37×#2006C2semidirect
7. C37×#2002C2semidirect
8. C37×#1900C2semidirect
9. C37×#1883C2semidirect
10. C37×#1871C2semidirect
11. C37×#1789C2semidirect
12. C2×H(5,𝔽2)×C37C22semidirect
14. C23×D4×C37C22semidirect
19. C2×AGL(1,ℤ/8)×C37C22semidirect
20. C2×AGL(1,ℤ/8)×C37C22semidirect
23. C22×M16×C37C22semidirect
31. C37×#537C22semidirect
33. C37×#535C22semidirect
34. C2×#127×C37C22semidirect
40. C37×#520C22semidirect
46. C2×#104×C37C22semidirect
47. C2×#104×C37C22semidirect
48. C2×#104×C37C22semidirect
49. C37×#418C22semidirect
50. C2×#100×C37C22semidirect
51. C37×#407C22semidirect
53. C37×#390C22semidirect
54. C4×C22⋊C4×C37C22semidirect
55. C37×#343C22semidirect
56. C37×#339C22semidirect
66. C2×#41×C37D4semidirect
67. C2×#41×C37D4semidirect
71. C22×Q8×C37D4semidirect
86. C22×D4×C37D4semidirect
98. AGL(1,ℤ/8)×C37D4semidirect
123. C22⋊Q8×C37D4semidirect
124. C22⋊Q8×C37D4semidirect
139. #121×C37D4semidirect
140. #121×C37D4semidirect
251. C2×D4×C37C2×D4semidirect
281. M16×C37C2×D4semidirect
347. Q8×C37#120semidirect
377. D4×C37#120semidirect
412. #23876C37direct (N × H)
443. C22×C37#453semidirect
458. C22×AGL(1,ℤ/8)C2×C37semidirect
459. #3488C2×C37semidirect
460. C2×#453C2×C37semidirect
461. #3003C2×C37semidirect
462. #2433C2×C37semidirect
463. #2006C2×C37semidirect
464. #2002C2×C37semidirect
465. #1900C2×C37semidirect
466. #1883C2×C37semidirect
467. #1871C2×C37semidirect
468. #1789C2×C37semidirect
480. C2×H(5,𝔽2)C22×C37semidirect
482. C23×D4C22×C37semidirect
487. C2×AGL(1,ℤ/8)C22×C37semidirect
488. C2×AGL(1,ℤ/8)C22×C37semidirect
491. C22×M16C22×C37semidirect
499. #537C22×C37semidirect
501. #535C22×C37semidirect
502. C2×#127C22×C37semidirect
508. #520C22×C37semidirect
514. C2×#104C22×C37semidirect
515. C2×#104C22×C37semidirect
516. C2×#104C22×C37semidirect
517. #418C22×C37semidirect
518. C2×#100C22×C37semidirect
519. #407C22×C37semidirect
521. #390C22×C37semidirect
522. C4×C22⋊C4C22×C37semidirect
523. #343C22×C37semidirect
524. #339C22×C37semidirect
525. C37#23876direct (N × H)
535. C2×#41D4×C37semidirect
536. C2×#41D4×C37semidirect
540. C22×Q8D4×C37semidirect
555. C22×D4D4×C37semidirect
567. AGL(1,ℤ/8)D4×C37semidirect
592. C22⋊Q8D4×C37semidirect
593. C22⋊Q8D4×C37semidirect
608. #121D4×C37semidirect
609. #121D4×C37semidirect
720. C2×D4C2×D4×C37semidirect
750. M16C2×D4×C37semidirect
816. Q8#120×C37semidirect
846. D4#120×C37semidirect
911. C22C37×#453semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C372
C37×#34882
C2×C37×#4532
C37×#30032
C37×#24332
C37×#20062
C37×#20022
C37×#19002
C37×#18832
C37×#18712
C37×#17892
#2387637