Finite Group Databasebeta

← C37×#24295 #22645548

Subgroups — C37×#24295 #22645548

Order 9472.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#577C211yesmaximal, characteristic, complemented
2C37×#3067C211yesmaximal, characteristic, complemented
3C37×#3057C211yesmaximal, characteristic, complemented
4C37×#3020C211yesmaximal, characteristic, complemented
5C37×#3019C211yesmaximal, characteristic, complemented
6C37×#2955C211yesmaximal, characteristic, complemented
7C37×#2049C211yesmaximal, characteristic, complemented
8C37×#2048C211yesmaximal, characteristic, complemented
9C37×#2009C211yesmaximal, characteristic, complemented
10C37×#2008C211yesmaximal, characteristic, complemented
11C37×#1977C211yesmaximal, characteristic, complemented
12C37×#1976C211yesmaximal, characteristic, complemented
13C37×#1814C211yesmaximal, characteristic, complemented
14C37×#1796C211yesmaximal, characteristic, complemented
15C37×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C37C2211yescharacteristic
17C2×H(5,𝔽2)×C37C2211yescharacteristic
18C37×#577—22no—
19C37×#577—22no—
20C37×#577—22no—
21C37×#577—22no—
22C37×#575C2211yescharacteristic
23C37×#575C2211yescharacteristic
24C37×#575C2211yescharacteristic, complemented
25C2×#137×C37—21no—
26C2×#137×C37C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C37—21no—
28C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
29C2×#135×C37—21no—
30C2×#135×C37C2211yescharacteristic
31C22×SD16×C37—21no—
32C22×SD16×C37C2211yescharacteristic
33C2×#131×C37C2211yescharacteristic
34C2×#131×C37C2211yescharacteristic, complemented
35C37×#536C2211yescharacteristic, complemented
36C37×#535C2211yescharacteristic
37C37×#473—21no—
38C37×#472—21no—
39C37×#471—21no—
40C37×#471—21no—
41C37×#468—22no—
42C37×#465—22no—
43C37×#456—22no—
44C37×#455—22no—
45C37×#454—22no—
46C37×#453—22no—
47C37×#444—22no—
48C37×#443—22no—
49C37×#430C2211yescharacteristic, complemented
50C2×#108×C37C2211yescharacteristic, complemented
51C37×#427C2211yescharacteristic, complemented
52C37×#421C2211yescharacteristic
53C37×#421C2211yescharacteristic
54C37×#421C2211yescharacteristic
55C37×#421C2211yescharacteristic
56C37×#421C2211yescharacteristic, complemented
57C37×#421C2211yescharacteristic, complemented
58C37×#419C2211yescharacteristic, complemented
59C37×#419C2211yescharacteristic, complemented
60C37×#418C2211yescharacteristic
61C37×#418C2211yescharacteristic
62C37×#413C2211yescharacteristic
63C37×#413C2211yescharacteristic, complemented
64C2×#101×C37C2211yescharacteristic, complemented
65C2×#100×C37C2211yescharacteristic
66C37×#410C2211yescharacteristic
67C37×#410C2211yescharacteristic, complemented
68C37×#405C2211yescharacteristic, complemented
69C37×#344C2211yescharacteristic, complemented
70C37×#344C2211yescharacteristic, complemented
712−1+4×C37—22no—
722−1+4×C37—22no—
732−1+4×C37—22no—
742−1+4×C37—41no—
75H(5,𝔽2)×C37—22no—
76H(5,𝔽2)×C37—22no—
77H(5,𝔽2)×C37—22no—
78H(5,𝔽2)×C37—41no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—21no—
82C2×#41×C37—21no—
83C2×#41×C37—41no—
84C2×#41×C37C2311yescharacteristic
85C2×#41×C37C2311yescharacteristic
86C2×#41×C37C2311yescharacteristic
87C2×#41×C37C2311yescharacteristic
88C22×Q8×C37—21no—
89C22×Q8×C37—21no—
90C22×Q8×C37C2311yescharacteristic
91C22×D4×C37—21no—
92C22×D4×C37—21no—
93C22×D4×C37—41no—
94C22×D4×C37C2311yescharacteristic
95#137×C37—24no—
96#137×C37—24no—
97#137×C37—22no—
98#137×C37—21no—
99#137×C37—21no—
100#137×C37—21no—
101#137×C37—21no—
102#137×C37—21no—
103#137×C37—22no—
104#137×C37D412yes—
105AGL(1,ℤ/8)×C37—24no—
106AGL(1,ℤ/8)×C37—24no—
107AGL(1,ℤ/8)×C37—22no—
108AGL(1,ℤ/8)×C37—21no—
109AGL(1,ℤ/8)×C37—21no—
110AGL(1,ℤ/8)×C37—21no—
111AGL(1,ℤ/8)×C37—21no—
112AGL(1,ℤ/8)×C37—21no—
113AGL(1,ℤ/8)×C37—22no—
114AGL(1,ℤ/8)×C37D412yes—
115#135×C37—24no—
116#135×C37—24no—
117#135×C37—22no—
118#135×C37—21no—
119#135×C37—21no—
120#135×C37—21no—
121#135×C37—21no—
122#135×C37—41no—
123#135×C37—41no—
124C2×Q16×C37—21no—
125C2×Q16×C37D411yescharacteristic, complemented
126C2×SD16×C37—24no—
127C2×SD16×C37—24no—
128C2×SD16×C37—21no—
129C2×SD16×C37—21no—
130C2×SD16×C37—21no—
131C2×SD16×C37—21no—
132C2×SD16×C37—21no—
133C2×SD16×C37—21no—
134C2×SD16×C37D412yes—
135C2×SD16×C37D412yes—
136C2×SD16×C37D411yescharacteristic, complemented
137C2×SD16×C37D411yescharacteristic, complemented
138C2×D8×C37—21no—
139C2×D8×C37D411yescharacteristic, complemented
140#131×C37—21no—
141#131×C37—21no—
142#131×C37—21no—
143#131×C37—21no—
144#131×C37—21no—
145#131×C37—21no—
146#131×C37D412yescomplemented
147#131×C37D412yescomplemented
148C2×M16×C37—21no—
149C2×M16×C37—21no—
150C2×M16×C37C2311yescharacteristic
151C2×M16×C37C2311yescharacteristic
152C2×M16×C37C2311yescharacteristic
153C2×M16×C37C2311yescharacteristic
154C2×M16×C37C2311yescharacteristic
155C22×C8×C37—21no—
156C22×C8×C37—21no—
157C22×C8×C37C2311yescharacteristic
158C4⋊Q8×C37—21no—
159#127×C37—21no—
160#124×C37—21no—
161#124×C37—21no—
162#123×C37—41no—
163C22⋊Q8×C37—22no—
164#121×C37—22no—
165#120×C37—41no—
166#117×C37C2311yescharacteristic
167#117×C37C2311yescharacteristic
168#117×C37C2311yescharacteristic
169#108×C37—22no—
170#108×C37—21no—
171#108×C37—21no—
172#107×C37—21no—
173#106×C37—21no—
174#104×C37—22no—
175#104×C37—22no—
176#104×C37—22no—
177#104×C37—22no—
178#104×C37—22no—
179#104×C37—22no—
180#103×C37—22no—
181#103×C37—41no—
182#102×C37—22no—
183#102×C37—41no—
184#101×C37—21no—
185#101×C37—21no—
186#101×C37—22no—
187#100×C37—21no—
188#100×C37—21no—
189#100×C37—22no—
190#99×C37—41no—
191#99×C37—41no—
192#97×C37—21no—
193C4×C8×C37—21no—
194C24×C37—21no—
195C24×C37—41no—
196#41×C37—21no—
197#41×C37—21no—
198#41×C37—24no—
199#41×C37—24no—
200#41×C37—21no—
201#41×C37—21no—
202#41×C37—21no—
203#41×C37—21no—
204#41×C37—21no—
205#41×C37—21no—
206#41×C37—21no—
207#41×C37—21no—
208#41×C37—21no—
209#41×C37—21no—
210#41×C37—21no—
211#41×C37—21no—
212#41×C37—42no—
213#41×C37—44no—
214#41×C37—42no—
215#41×C37—42no—
216#41×C37—42no—
217#41×C37—44no—
218#41×C37—42no—
219#41×C37—42no—
220#41×C37C2×D412yes—
221#41×C37C2×D412yes—
222C2×Q8×C37—21no—
223C2×Q8×C37—24no—
224C2×Q8×C37—21no—
225C2×Q8×C37—21no—
226C2×Q8×C37—21no—
227C2×Q8×C37—21no—
228C2×Q8×C37—41no—
229C2×Q8×C37—42no—
230C2×Q8×C37—42no—
231C2×Q8×C37—42no—
232C2×Q8×C37C2×D411yescharacteristic
233C2×Q8×C37C2×D411yescharacteristic
234C2×Q8×C37C2×D412yes—
235C2×Q8×C37C2×D411yescharacteristic
236C2×Q8×C37#4111yescharacteristic
237C2×D4×C37—21no—
238C2×D4×C37—24no—
239C2×D4×C37—21no—
240C2×D4×C37—21no—
241C2×D4×C37—21no—
242C2×D4×C37—21no—
243C2×D4×C37—21no—
244C2×D4×C37—21no—
245C2×D4×C37—21no—
246C2×D4×C37—21no—
247C2×D4×C37—42no—
248C2×D4×C37—41no—
249C2×D4×C37—41no—
250C2×D4×C37—42no—
251C2×D4×C37—44no—
252C2×D4×C37—44no—
253C2×D4×C37—41no—
254C2×D4×C37—42no—
255C2×D4×C37—42no—
256C2×D4×C37C2×D411yescharacteristic
257C2×D4×C37C2×D411yescharacteristic
258C2×D4×C37C2×D412yes—
259C2×D4×C37C2×D411yescharacteristic
260C2×D4×C37#4111yescharacteristic
261C22×C4×C37—21no—
262C22×C4×C37—21no—
263C22×C4×C37—21no—
264C22×C4×C37—21no—
265C22×C4×C37—21no—
266C22×C4×C37—41no—
267C22×C4×C37—41no—
268C22×C4×C37—41no—
269C22×C4×C37C2411yescharacteristic
270Q16×C37—24no—
271Q16×C37—22no—
272Q16×C37—21no—
273Q16×C37—21no—
274Q16×C37—41no—
275Q16×C37—41no—
276SD16×C37—24no—
277SD16×C37—24no—
278SD16×C37—22no—
279SD16×C37—22no—
280SD16×C37—22no—
281SD16×C37—22no—
282SD16×C37—21no—
283SD16×C37—21no—
284SD16×C37—22no—
285SD16×C37—22no—
286SD16×C37—21no—
287SD16×C37—21no—
288SD16×C37—41no—
289SD16×C37—41no—
290SD16×C37—41no—
291SD16×C37—41no—
292D8×C37—24no—
293D8×C37—22no—
294D8×C37—21no—
295D8×C37—21no—
296D8×C37—41no—
297D8×C37—41no—
298M16×C37—21no—
299M16×C37—21no—
300M16×C37—22no—
301M16×C37—22no—
302M16×C37—21no—
303M16×C37—21no—
304M16×C37—21no—
305M16×C37—21no—
306M16×C37—21no—
307M16×C37—21no—
308M16×C37—41no—
309M16×C37—41no—
310M16×C37C2×D412yes—
311M16×C37C2×D412yes—
312C2×C8×C37—21no—
313C2×C8×C37—21no—
314C2×C8×C37—22no—
315C2×C8×C37—22no—
316C2×C8×C37—21no—
317C2×C8×C37—21no—
318C2×C8×C37—21no—
319C2×C8×C37—41no—
320C2×C8×C37—41no—
321C2×C8×C37C2×D411yescharacteristic
322C2×C8×C37C2×D411yescharacteristic
323C2×C8×C37C2×D411yescharacteristic
324C2×C8×C37C2×D411yescharacteristic
325C2×C8×C37C2×D411yescharacteristic
326C2×C8×C37C2×D411yescharacteristic
327C4⋊C4×C37—21no—
328C4⋊C4×C37—21no—
329C4⋊C4×C37—21no—
330C4⋊C4×C37—42no—
331C22⋊C4×C37—21no—
332C22⋊C4×C37—21no—
333C22⋊C4×C37—21no—
334C22⋊C4×C37—42no—
335C22⋊C4×C37—42no—
336C42×C37—21no—
337C42×C37—21no—
338C42×C37—21no—
339C23×C37—21no—
340C23×C37—21no—
341C23×C37—22no—
342C23×C37—21no—
343C23×C37—21no—
344C23×C37—44no—
345C23×C37—41no—
346C23×C37—41no—
347C23×C37—161no—
348C23×C37—162no—
349C23×C37H(5,𝔽2)11yescharacteristic
350Q8×C37—21no—
351Q8×C37—21no—
352Q8×C37—22no—
353Q8×C37—21no—
354Q8×C37—21no—
355Q8×C37—21no—
356Q8×C37—21no—
357Q8×C37—21no—
358Q8×C37—22no—
359Q8×C37—44no—
360Q8×C37—41no—
361Q8×C37—41no—
362Q8×C37#12112yes—
363D4×C37—22no—
364D4×C37—22no—
365D4×C37—21no—
366D4×C37—22no—
367D4×C37—21no—
368D4×C37—21no—
369D4×C37—21no—
370D4×C37—21no—
371D4×C37—21no—
372D4×C37—21no—
373D4×C37—22no—
374D4×C37—44no—
375D4×C37—44no—
376D4×C37—44no—
377D4×C37—41no—
378D4×C37—41no—
379D4×C37—41no—
380D4×C37—41no—
381D4×C37—41no—
382D4×C37—41no—
383D4×C37—41no—
384D4×C37—41no—
385D4×C37—162no—
386D4×C37#12112yes—
387C2×C4×C37—21no—
388C2×C4×C37—22no—
389C2×C4×C37—22no—
390C2×C4×C37—21no—
391C2×C4×C37—22no—
392C2×C4×C37—21no—
393C2×C4×C37—21no—
394C2×C4×C37—44no—
395C2×C4×C37—44no—
396C2×C4×C37—44no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37C22×D411yescharacteristic
409C2×C4×C37C22×D411yescharacteristic
410C2×C4×C37C22×D411yescharacteristic
411C2×C4×C37C22×D411yescharacteristic
412C2×C4×C37C2×#4111yescharacteristic
413C2×C4×C37H(5,𝔽2)11yescharacteristic
414C8×C37—22no—
415C8×C37—22no—
416C8×C37—41no—
417C8×C37—41no—
418C8×C37—41no—
419C8×C37#12011yescharacteristic
420C8×C37#12011yescharacteristic
421C8×C37#12011yescharacteristic
422C8×C37#12011yescharacteristic
423#24295C3711yesmaximal, characteristic, direct product factor, Sylow
424C22×C37—22no—
425C22×C37—41no—
426C22×C37—42no—
427C22×C37—42no—
428C22×C37—41no—
429C22×C37—42no—
430C22×C37—41no—
431C22×C37—41no—
432C22×C37—82no—
433C22×C37—81no—
434C22×C37—81no—
435C22×C37—82no—
436C22×C37—161no—
437C22×C37—164no—
438C22×C37#53511yescharacteristic
439C22×C37D4211yescharacteristic
440C22×C37#54611yescharacteristic
441C4×C37—22no—
442C4×C37—41no—
443C4×C37—42no—
444C4×C37—41no—
445C4×C37—41no—
446C4×C37—81no—
447C4×C37—81no—
448C4×C37—81no—
449C4×C37C2×#12011yescharacteristic
450C4×C37C2×#12111yescharacteristic
451C4×C37D4211yescharacteristic
452C4×C37#54611yescharacteristic
453C2×#577C2×C3711yescharacteristic, complemented
454#3067C2×C3711yescharacteristic, complemented
455#3057C2×C3711yescharacteristic, complemented
456#3020C2×C3711yescharacteristic, complemented
457#3019C2×C3711yescharacteristic, complemented
458#2955C2×C3711yescharacteristic, complemented
459#2049C2×C3711yescharacteristic, complemented
460#2048C2×C3711yescharacteristic, complemented
461#2009C2×C3711yescharacteristic, complemented
462#2008C2×C3711yescharacteristic, complemented
463#1977C2×C3711yescharacteristic, complemented
464#1976C2×C3711yescharacteristic, complemented
465#1814C2×C3711yescharacteristic, complemented
466#1796C2×C3711yescharacteristic, complemented
467#1795C2×C3711yescharacteristic, complemented
468C2×C37—21no—
469C2×C37—21no—
470C2×C37—21no—
471C2×C37—42no—
472C2×C37—81no—
473C2×C37—81no—
474C2×C37—82no—
475C2×C37—81no—
476C2×C37#240811yescharacteristic
477C2×2−1+4C22×C3711yescharacteristic
478C2×H(5,𝔽2)C22×C3711yescharacteristic
479#577—22no—
480#577—22no—
481#577—22no—
482#577—22no—
483#575C22×C3711yescharacteristic
484#575C22×C3711yescharacteristic
485#575C22×C3711yescharacteristic, complemented
486C2×#137—21no—
487C2×#137C22×C3711yescharacteristic
488C2×AGL(1,ℤ/8)—21no—
489C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
490C2×#135—21no—
491C2×#135C22×C3711yescharacteristic
492C22×SD16—21no—
493C22×SD16C22×C3711yescharacteristic
494C2×#131C22×C3711yescharacteristic
495C2×#131C22×C3711yescharacteristic, complemented
496#536C22×C3711yescharacteristic, complemented
497#535C22×C3711yescharacteristic
498#473—21no—
499#472—21no—
500#471—21no—
501#471—21no—
502#468—22no—
503#465—22no—
504#456—22no—
505#455—22no—
506#454—22no—
507#453—22no—
508#444—22no—
509#443—22no—
510#430C22×C3711yescharacteristic, complemented
511C2×#108C22×C3711yescharacteristic, complemented
512#427C22×C3711yescharacteristic, complemented
513#421C22×C3711yescharacteristic
514#421C22×C3711yescharacteristic
515#421C22×C3711yescharacteristic
516#421C22×C3711yescharacteristic
517#421C22×C3711yescharacteristic, complemented
518#421C22×C3711yescharacteristic, complemented
519#419C22×C3711yescharacteristic, complemented
520#419C22×C3711yescharacteristic, complemented
521#418C22×C3711yescharacteristic
522#418C22×C3711yescharacteristic
523#413C22×C3711yescharacteristic
524#413C22×C3711yescharacteristic, complemented
525C2×#101C22×C3711yescharacteristic, complemented
526C2×#100C22×C3711yescharacteristic
527#410C22×C3711yescharacteristic
528#410C22×C3711yescharacteristic, complemented
529#405C22×C3711yescharacteristic, complemented
530#344C22×C3711yescharacteristic, complemented
531#344C22×C3711yescharacteristic, complemented
532C37#2429511yescharacteristic, direct product factor, Sylow
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C3711yescharacteristic
547C2×#41C23×C3711yescharacteristic
548C2×#41C23×C3711yescharacteristic
549C2×#41C23×C3711yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C3711yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C3711yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C3712yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C3712yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C3711yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C3712yes—
597C2×SD16D4×C3712yes—
598C2×SD16D4×C3711yescharacteristic, complemented
599C2×SD16D4×C3711yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C3711yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C3712yescomplemented
609#131D4×C3712yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C3711yescharacteristic
613C2×M16C23×C3711yescharacteristic
614C2×M16C23×C3711yescharacteristic
615C2×M16C23×C3711yescharacteristic
616C2×M16C23×C3711yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C3711yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C3711yescharacteristic
629#117C23×C3711yescharacteristic
630#117C23×C3711yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C3712yes—
683#41C2×D4×C3712yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C3711yescharacteristic
695C2×Q8C2×D4×C3711yescharacteristic
696C2×Q8C2×D4×C3712yes—
697C2×Q8C2×D4×C3711yescharacteristic
698C2×Q8#41×C3711yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C3711yescharacteristic
719C2×D4C2×D4×C3711yescharacteristic
720C2×D4C2×D4×C3712yes—
721C2×D4C2×D4×C3711yescharacteristic
722C2×D4#41×C3711yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C3711yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C3712yes—
773M16C2×D4×C3712yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C3711yescharacteristic
784C2×C8C2×D4×C3711yescharacteristic
785C2×C8C2×D4×C3711yescharacteristic
786C2×C8C2×D4×C3711yescharacteristic
787C2×C8C2×D4×C3711yescharacteristic
788C2×C8C2×D4×C3711yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C3711yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—21no—
816Q8—21no—
817Q8—21no—
818Q8—21no—
819Q8—21no—
820Q8—22no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C3712yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—22no—
829D4—21no—
830D4—21no—
831D4—21no—
832D4—21no—
833D4—21no—
834D4—21no—
835D4—22no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C3712yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C3711yescharacteristic
871C2×C4C22×D4×C3711yescharacteristic
872C2×C4C22×D4×C3711yescharacteristic
873C2×C4C22×D4×C3711yescharacteristic
874C2×C4C2×#41×C3711yescharacteristic
875C2×C4H(5,𝔽2)×C3711yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C3711yescharacteristic
882C8#120×C3711yescharacteristic
883C8#120×C3711yescharacteristic
884C8#120×C3711yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22C37×#53511yescharacteristic
900C22D42×C3711yescharacteristic
901C22C37×#54611yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C3711yescharacteristic
911C4C2×#121×C3711yescharacteristic
912C4D42×C3711yescharacteristic
913C4C37×#54611yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C37×#240811yescharacteristic
subgroupG/H
center, socleC2×C37#2408
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C22×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#577C2semidirect
2. C37×#3067C2semidirect
3. C37×#3057C2semidirect
4. C37×#3020C2semidirect
5. C37×#3019C2semidirect
6. C37×#2955C2semidirect
7. C37×#2049C2semidirect
8. C37×#2048C2semidirect
9. C37×#2009C2semidirect
10. C37×#2008C2semidirect
11. C37×#1977C2semidirect
12. C37×#1976C2semidirect
13. C37×#1814C2semidirect
14. C37×#1796C2semidirect
15. C37×#1795C2semidirect
24. C37×#575C22semidirect
34. C2×#131×C37C22semidirect
35. C37×#536C22semidirect
49. C37×#430C22semidirect
50. C2×#108×C37C22semidirect
51. C37×#427C22semidirect
56. C37×#421C22semidirect
57. C37×#421C22semidirect
58. C37×#419C22semidirect
59. C37×#419C22semidirect
63. C37×#413C22semidirect
64. C2×#101×C37C22semidirect
67. C37×#410C22semidirect
68. C37×#405C22semidirect
69. C37×#344C22semidirect
70. C37×#344C22semidirect
125. C2×Q16×C37D4semidirect
136. C2×SD16×C37D4semidirect
137. C2×SD16×C37D4semidirect
139. C2×D8×C37D4semidirect
146. #131×C37D4semidirect
147. #131×C37D4semidirect
423. #24295C37direct (N × H)
453. C2×#577C2×C37semidirect
454. #3067C2×C37semidirect
455. #3057C2×C37semidirect
456. #3020C2×C37semidirect
457. #3019C2×C37semidirect
458. #2955C2×C37semidirect
459. #2049C2×C37semidirect
460. #2048C2×C37semidirect
461. #2009C2×C37semidirect
462. #2008C2×C37semidirect
463. #1977C2×C37semidirect
464. #1976C2×C37semidirect
465. #1814C2×C37semidirect
466. #1796C2×C37semidirect
467. #1795C2×C37semidirect
485. #575C22×C37semidirect
495. C2×#131C22×C37semidirect
496. #536C22×C37semidirect
510. #430C22×C37semidirect
511. C2×#108C22×C37semidirect
512. #427C22×C37semidirect
517. #421C22×C37semidirect
518. #421C22×C37semidirect
519. #419C22×C37semidirect
520. #419C22×C37semidirect
524. #413C22×C37semidirect
525. C2×#101C22×C37semidirect
528. #410C22×C37semidirect
529. #405C22×C37semidirect
530. #344C22×C37semidirect
531. #344C22×C37semidirect
532. C37#24295direct (N × H)
587. C2×Q16D4×C37semidirect
598. C2×SD16D4×C37semidirect
599. C2×SD16D4×C37semidirect
601. C2×D8D4×C37semidirect
608. #131D4×C37semidirect
609. #131D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5772
C37×#30672
C37×#30572
C37×#30202
C37×#30192
C37×#29552
C37×#20492
C37×#20482
C37×#20092
C37×#20082
C37×#19772
C37×#19762
C37×#18142
C37×#17962
C37×#17952
#2429537