Finite Group Databasebeta

← C37×#24475 #22645728

Subgroups — C37×#24475 #22645728

Order 9472.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3585C211yesmaximal, characteristic
2C37×#3069C211yesmaximal, characteristic, complemented
3C37×#3040C211yesmaximal, characteristic, complemented
4C37×#3022C211yesmaximal, characteristic, complemented
5C2×C37×#455C211yesmaximal, characteristic, complemented
6C37×#2901C211yesmaximal, characteristic, complemented
7C37×#2050C211yesmaximal, characteristic, complemented
8C37×#2048C211yesmaximal, characteristic, complemented
9C37×#2009C211yesmaximal, characteristic, complemented
10C37×#2003C211yesmaximal, characteristic, complemented
11C37×#1906C211yesmaximal, characteristic, complemented
12C37×#1903C211yesmaximal, characteristic, complemented
13C37×#1902C211yesmaximal, characteristic, complemented
14C37×#1861C211yesmaximal, characteristic, complemented
15C37×#1795C211yesmaximal, characteristic, complemented
16C37×#585C2211yescharacteristic
17C2×H(5,𝔽2)×C37C2211yescharacteristic
18C37×#577—22no—
19C37×#577—22no—
20C37×#576—22no—
21C37×#576—22no—
22C37×#575—22no—
23C37×#575C2211yescharacteristic
24C37×#575C2211yescharacteristic
25C2×#137×C37C2211yescharacteristic
26C2×#137×C37C2211yescharacteristic, complemented
27C2×#137×C37C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C37—22no—
29C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
31C37×#568C2211yescharacteristic
32C37×#568C2211yescharacteristic, complemented
33C37×#536C2211yescharacteristic, complemented
34C2×#124×C37C2211yescharacteristic, complemented
35C4×#41×C37C2211yescharacteristic, complemented
36C37×#473—22no—
37C37×#471—22no—
38C37×#464—22no—
39C37×#463—22no—
40C37×#456—22no—
41C37×#455—22no—
42C37×#455—22no—
43C37×#455—22no—
44C37×#430C2211yescharacteristic, complemented
45C37×#423C2211yescharacteristic, complemented
46C37×#421—22no—
47C37×#421C2211yescharacteristic
48C37×#421C2211yescharacteristic
49C37×#421C2211yescharacteristic, complemented
50C37×#421C2211yescharacteristic, complemented
51C2×#104×C37—22no—
52C2×#104×C37C2211yescharacteristic
53C2×#104×C37C2211yescharacteristic, complemented
54C2×#104×C37C2211yescharacteristic, complemented
55C37×#419C2211yescharacteristic, complemented
56C37×#418C2211yescharacteristic, complemented
57C37×#418C2211yescharacteristic, complemented
58C37×#413C2211yescharacteristic, complemented
59C37×#413C2211yescharacteristic, complemented
60C2×#101×C37C2211yescharacteristic, complemented
61C2×#100×C37C2211yescharacteristic, complemented
62C37×#410C2211yescharacteristic, complemented
63C37×#344C2211yescharacteristic, complemented
64C37×#344C2211yescharacteristic, complemented
65C37×#339C2211yescharacteristic, complemented
66C37×#338C2211yescharacteristic, complemented
672−1+4×C37—21no—
682−1+4×C37—21no—
692−1+4×C37D412yes—
70H(5,𝔽2)×C37—22no—
71H(5,𝔽2)×C37—21no—
72H(5,𝔽2)×C37—22no—
73H(5,𝔽2)×C37—21no—
74H(5,𝔽2)×C37—22no—
75H(5,𝔽2)×C37—41no—
76H(5,𝔽2)×C37—41no—
77H(5,𝔽2)×C37D412yes—
78C2×#41×C37—22no—
79C2×#41×C37—22no—
80C2×#41×C37—21no—
81C2×#41×C37—21no—
82C2×#41×C37—41no—
83C2×#41×C37C2311yescharacteristic
84C2×#41×C37C2311yescharacteristic
85C2×#41×C37C2311yescharacteristic
86C2×#41×C37C2311yescharacteristic
87C22×Q8×C37C2311yescharacteristic
88C22×D4×C37—21no—
89C22×D4×C37—21no—
90C22×D4×C37—41no—
91C22×D4×C37C2311yescharacteristic
92#137×C37—24no—
93#137×C37—21no—
94#137×C37—21no—
95#137×C37—21no—
96#137×C37—22no—
97#137×C37—22no—
98#137×C37—22no—
99#137×C37—22no—
100#137×C37—22no—
101#137×C37—41no—
102#137×C37D412yes—
103AGL(1,ℤ/8)×C37—24no—
104AGL(1,ℤ/8)×C37—24no—
105AGL(1,ℤ/8)×C37—24no—
106AGL(1,ℤ/8)×C37—22no—
107AGL(1,ℤ/8)×C37—22no—
108AGL(1,ℤ/8)×C37—21no—
109AGL(1,ℤ/8)×C37—22no—
110AGL(1,ℤ/8)×C37—21no—
111AGL(1,ℤ/8)×C37—21no—
112AGL(1,ℤ/8)×C37—22no—
113AGL(1,ℤ/8)×C37D412yes—
114#135×C37—24no—
115#135×C37—24no—
116#135×C37—22no—
117#135×C37—22no—
118C2×Q16×C37—21no—
119C2×Q16×C37—21no—
120C2×Q16×C37—21no—
121C2×SD16×C37—24no—
122C2×SD16×C37—21no—
123C2×SD16×C37—21no—
124C2×SD16×C37—21no—
125C2×SD16×C37—21no—
126C2×SD16×C37D412yes—
127C2×D8×C37—24no—
128C2×D8×C37—21no—
129C2×D8×C37D412yes—
130#131×C37—22no—
131#131×C37—22no—
132#131×C37—22no—
133#131×C37—41no—
134C2×M16×C37—22no—
135C2×M16×C37—22no—
136C2×M16×C37C2311yescharacteristic
137C2×M16×C37C2311yescharacteristic
138C2×M16×C37C2311yescharacteristic
139C2×M16×C37C2311yescharacteristic
140C2×M16×C37C2311yescharacteristic
141C2×M16×C37C2311yescharacteristic
142C4⋊Q8×C37—21no—
143#124×C37—22no—
144#124×C37—21no—
145#124×C37—21no—
146#124×C37—21no—
147#123×C37—41no—
148C22⋊Q8×C37—41no—
149C4×Q8×C37—21no—
150C4×D4×C37—21no—
151C4×D4×C37—41no—
152#117×C37—21no—
153#117×C37C2311yescharacteristic
154#117×C37C2311yescharacteristic
155C2×C22⋊C4×C37—41no—
156C2×C42×C37—21no—
157C2×C42×C37C2311yescharacteristic
158#108×C37—22no—
159C4⋊C8×C37—22no—
160#104×C37—22no—
161#104×C37—22no—
162#104×C37—22no—
163#104×C37—22no—
164#104×C37—21no—
165#104×C37—21no—
166#104×C37—21no—
167#104×C37—21no—
168#104×C37D412yes—
169#104×C37D412yes—
170#103×C37—22no—
171#102×C37—22no—
172#102×C37—41no—
173#101×C37—21no—
174#101×C37—21no—
175#101×C37—22no—
176#100×C37—21no—
177#100×C37—21no—
178#100×C37—22no—
179#99×C37—41no—
180C24×C37—21no—
181C24×C37—41no—
182#41×C37—21no—
183#41×C37—21no—
184#41×C37—21no—
185#41×C37—21no—
186#41×C37—24no—
187#41×C37—22no—
188#41×C37—22no—
189#41×C37—22no—
190#41×C37—22no—
191#41×C37—21no—
192#41×C37—21no—
193#41×C37—21no—
194#41×C37—21no—
195#41×C37—21no—
196#41×C37—21no—
197#41×C37—21no—
198#41×C37—21no—
199#41×C37—42no—
200#41×C37—42no—
201#41×C37—42no—
202#41×C37—42no—
203#41×C37—42no—
204#41×C37—42no—
205#41×C37—41no—
206#41×C37—41no—
207#41×C37—42no—
208#41×C37C2×D412yes—
209#41×C37C2×D412yes—
210#41×C37C2×D412yes—
211#41×C37C2×D412yes—
212C2×Q8×C37—22no—
213C2×Q8×C37—22no—
214C2×Q8×C37—21no—
215C2×Q8×C37—21no—
216C2×Q8×C37—21no—
217C2×Q8×C37—21no—
218C2×Q8×C37—21no—
219C2×Q8×C37—21no—
220C2×Q8×C37—41no—
221C2×Q8×C37C2×D411yescharacteristic
222C2×Q8×C37C2×D411yescharacteristic
223C2×Q8×C37C2×D411yescharacteristic
224C2×Q8×C37#4111yescharacteristic
225C2×D4×C37—21no—
226C2×D4×C37—21no—
227C2×D4×C37—24no—
228C2×D4×C37—22no—
229C2×D4×C37—22no—
230C2×D4×C37—21no—
231C2×D4×C37—21no—
232C2×D4×C37—21no—
233C2×D4×C37—21no—
234C2×D4×C37—21no—
235C2×D4×C37—21no—
236C2×D4×C37—21no—
237C2×D4×C37—42no—
238C2×D4×C37—41no—
239C2×D4×C37—41no—
240C2×D4×C37—42no—
241C2×D4×C37—42no—
242C2×D4×C37—41no—
243C2×D4×C37—44no—
244C2×D4×C37—42no—
245C2×D4×C37—42no—
246C2×D4×C37—44no—
247C2×D4×C37—42no—
248C2×D4×C37C2×D411yescharacteristic
249C2×D4×C37C2×D411yescharacteristic
250C2×D4×C37C2×D412yes—
251C2×D4×C37C2×D411yescharacteristic
252C2×D4×C37#4111yescharacteristic
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—21no—
259C22×C4×C37—41no—
260C22×C4×C37—42no—
261C22×C4×C37—41no—
262C22×C4×C37C2411yescharacteristic
263Q16×C37—22no—
264Q16×C37—22no—
265Q16×C37—42no—
266Q16×C37—42no—
267Q16×C37—42no—
268SD16×C37—24no—
269SD16×C37—22no—
270SD16×C37—22no—
271SD16×C37—22no—
272SD16×C37—24no—
273SD16×C37—22no—
274SD16×C37—42no—
275SD16×C37—42no—
276SD16×C37—42no—
277D8×C37—24no—
278D8×C37—22no—
279D8×C37—22no—
280D8×C37—24no—
281M16×C37—24no—
282M16×C37—21no—
283M16×C37—21no—
284M16×C37—21no—
285M16×C37—21no—
286M16×C37—21no—
287M16×C37—21no—
288M16×C37—21no—
289M16×C37—21no—
290M16×C37—21no—
291M16×C37—21no—
292M16×C37—42no—
293M16×C37C2×D412yes—
294M16×C37C2×D412yes—
295C2×C8×C37—24no—
296C2×C8×C37—21no—
297C2×C8×C37—21no—
298C2×C8×C37—21no—
299C2×C8×C37—21no—
300C2×C8×C37—21no—
301C2×C8×C37—42no—
302C2×C8×C37C2×D412yes—
303C4⋊C4×C37—21no—
304C4⋊C4×C37—21no—
305C4⋊C4×C37—41no—
306C4⋊C4×C37—42no—
307C22⋊C4×C37—21no—
308C22⋊C4×C37—21no—
309C22⋊C4×C37—42no—
310C22⋊C4×C37—42no—
311C22⋊C4×C37—41no—
312C22⋊C4×C37—42no—
313C42×C37—21no—
314C42×C37—21no—
315C42×C37—21no—
316C42×C37—41no—
317C42×C37C2×D411yescharacteristic
318C42×C37C2×D411yescharacteristic
319C23×C37—21no—
320C23×C37—21no—
321C23×C37—21no—
322C23×C37—22no—
323C23×C37—21no—
324C23×C37—42no—
325C23×C37—44no—
326C23×C37—41no—
327C23×C37—41no—
328C23×C37—82no—
329C23×C37—162no—
330C23×C37H(5,𝔽2)11yescharacteristic
331Q8×C37—21no—
332Q8×C37—21no—
333Q8×C37—21no—
334Q8×C37—21no—
335Q8×C37—21no—
336Q8×C37—21no—
337Q8×C37—42no—
338Q8×C37—41no—
339Q8×C37—41no—
340Q8×C37—41no—
341Q8×C37—41no—
342Q8×C37#12012yes—
343Q8×C37#12112yes—
344D4×C37—22no—
345D4×C37—22no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—21no—
349D4×C37—21no—
350D4×C37—22no—
351D4×C37—21no—
352D4×C37—21no—
353D4×C37—21no—
354D4×C37—21no—
355D4×C37—22no—
356D4×C37—42no—
357D4×C37—42no—
358D4×C37—44no—
359D4×C37—42no—
360D4×C37—44no—
361D4×C37—41no—
362D4×C37—41no—
363D4×C37—41no—
364D4×C37—41no—
365D4×C37—41no—
366D4×C37—41no—
367D4×C37#12012yes—
368D4×C37#12112yes—
369C2×C4×C37—21no—
370C2×C4×C37—21no—
371C2×C4×C37—22no—
372C2×C4×C37—22no—
373C2×C4×C37—22no—
374C2×C4×C37—22no—
375C2×C4×C37—21no—
376C2×C4×C37—21no—
377C2×C4×C37—21no—
378C2×C4×C37—21no—
379C2×C4×C37—42no—
380C2×C4×C37—42no—
381C2×C4×C37—42no—
382C2×C4×C37—44no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—81no—
393C2×C4×C37—82no—
394C2×C4×C37C22×D411yescharacteristic
395C2×C4×C37C22×D411yescharacteristic
396C2×C4×C37C22×D411yescharacteristic
397C2×C4×C37C22×D411yescharacteristic
398C2×C4×C37C2×#4111yescharacteristic
399C2×C4×C37H(5,𝔽2)11yescharacteristic
400C8×C37—22no—
401C8×C37—22no—
402C8×C37—22no—
403C8×C37—41no—
404C8×C37—41no—
405C8×C37—41no—
406#24475C3711yesmaximal, characteristic, direct product factor, Sylow
407C22×C37—22no—
408C22×C37—22no—
409C22×C37—41no—
410C22×C37—41no—
411C22×C37—42no—
412C22×C37—41no—
413C22×C37—81no—
414C22×C37—81no—
415C22×C37—81no—
416C22×C37—82no—
417C22×C37—81no—
418C22×C37—82no—
419C22×C37—161no—
420C22×C37—162no—
421C22×C37—164no—
422C22×C37#53411yescharacteristic
423C22×C37D4211yescharacteristic
424C22×C37#54611yescharacteristic
425C4×C37—22no—
426C4×C37—22no—
427C4×C37—41no—
428C4×C37—41no—
429C4×C37—41no—
430C4×C37—41no—
431C4×C37—81no—
432C4×C37—81no—
433C4×C37—81no—
434C4×C37C2×#12011yescharacteristic
435C4×C37C2×#12111yescharacteristic
436C4×C37D4211yescharacteristic
437C4×C37#54611yescharacteristic
438#3585C2×C3711yescharacteristic
439#3069C2×C3711yescharacteristic, complemented
440#3040C2×C3711yescharacteristic, complemented
441#3022C2×C3711yescharacteristic, complemented
442C2×#455C2×C3711yescharacteristic, complemented
443#2901C2×C3711yescharacteristic, complemented
444#2050C2×C3711yescharacteristic, complemented
445#2048C2×C3711yescharacteristic, complemented
446#2009C2×C3711yescharacteristic, complemented
447#2003C2×C3711yescharacteristic, complemented
448#1906C2×C3711yescharacteristic, complemented
449#1903C2×C3711yescharacteristic, complemented
450#1902C2×C3711yescharacteristic, complemented
451#1861C2×C3711yescharacteristic, complemented
452#1795C2×C3711yescharacteristic, complemented
453C2×C37—21no—
454C2×C37—21no—
455C2×C37—21no—
456C2×C37—42no—
457C2×C37—42no—
458C2×C37—82no—
459C2×C37—81no—
460C2×C37—81no—
461C2×C37#241011yescharacteristic
462#585C22×C3711yescharacteristic
463C2×H(5,𝔽2)C22×C3711yescharacteristic
464#577—22no—
465#577—22no—
466#576—22no—
467#576—22no—
468#575—22no—
469#575C22×C3711yescharacteristic
470#575C22×C3711yescharacteristic
471C2×#137C22×C3711yescharacteristic
472C2×#137C22×C3711yescharacteristic, complemented
473C2×#137C22×C3711yescharacteristic, complemented
474C2×AGL(1,ℤ/8)—22no—
475C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
476C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
477#568C22×C3711yescharacteristic
478#568C22×C3711yescharacteristic, complemented
479#536C22×C3711yescharacteristic, complemented
480C2×#124C22×C3711yescharacteristic, complemented
481C4×#41C22×C3711yescharacteristic, complemented
482#473—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#456—22no—
487#455—22no—
488#455—22no—
489#455—22no—
490#430C22×C3711yescharacteristic, complemented
491#423C22×C3711yescharacteristic, complemented
492#421—22no—
493#421C22×C3711yescharacteristic
494#421C22×C3711yescharacteristic
495#421C22×C3711yescharacteristic, complemented
496#421C22×C3711yescharacteristic, complemented
497C2×#104—22no—
498C2×#104C22×C3711yescharacteristic
499C2×#104C22×C3711yescharacteristic, complemented
500C2×#104C22×C3711yescharacteristic, complemented
501#419C22×C3711yescharacteristic, complemented
502#418C22×C3711yescharacteristic, complemented
503#418C22×C3711yescharacteristic, complemented
504#413C22×C3711yescharacteristic, complemented
505#413C22×C3711yescharacteristic, complemented
506C2×#101C22×C3711yescharacteristic, complemented
507C2×#100C22×C3711yescharacteristic, complemented
508#410C22×C3711yescharacteristic, complemented
509#344C22×C3711yescharacteristic, complemented
510#344C22×C3711yescharacteristic, complemented
511#339C22×C3711yescharacteristic, complemented
512#338C22×C3711yescharacteristic, complemented
513C37#2447511yescharacteristic, direct product factor, Sylow
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C3712yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C3712yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C3711yescharacteristic
531C2×#41C23×C3711yescharacteristic
532C2×#41C23×C3711yescharacteristic
533C2×#41C23×C3711yescharacteristic
534C22×Q8C23×C3711yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C3711yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C3712yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C3712yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C3712yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C3712yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C3711yescharacteristic
584C2×M16C23×C3711yescharacteristic
585C2×M16C23×C3711yescharacteristic
586C2×M16C23×C3711yescharacteristic
587C2×M16C23×C3711yescharacteristic
588C2×M16C23×C3711yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C3711yescharacteristic
601#117C23×C3711yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C3711yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C3712yes—
616#104D4×C3712yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C3712yes—
656#41C2×D4×C3712yes—
657#41C2×D4×C3712yes—
658#41C2×D4×C3712yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C3711yescharacteristic
669C2×Q8C2×D4×C3711yescharacteristic
670C2×Q8C2×D4×C3711yescharacteristic
671C2×Q8#41×C3711yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C3711yescharacteristic
696C2×D4C2×D4×C3711yescharacteristic
697C2×D4C2×D4×C3712yes—
698C2×D4C2×D4×C3711yescharacteristic
699C2×D4#41×C3711yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C3711yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C3712yes—
741M16C2×D4×C3712yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C3712yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C3711yescharacteristic
765C42C2×D4×C3711yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C3711yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C3712yes—
790Q8#121×C3712yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C3712yes—
815D4#121×C3712yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C3711yescharacteristic
842C2×C4C22×D4×C3711yescharacteristic
843C2×C4C22×D4×C3711yescharacteristic
844C2×C4C22×D4×C3711yescharacteristic
845C2×C4C2×#41×C3711yescharacteristic
846C2×C4H(5,𝔽2)×C3711yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22C37×#53411yescharacteristic
869C22D42×C3711yescharacteristic
870C22C37×#54611yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C3711yescharacteristic
881C4C2×#121×C3711yescharacteristic
882C4D42×C3711yescharacteristic
883C4C37×#54611yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C37×#241011yescharacteristic
subgroupG/H
center, socleC2×C37#2410
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3585C2
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
2. C37×#3069C2semidirect
3. C37×#3040C2semidirect
4. C37×#3022C2semidirect
5. C2×C37×#455C2semidirect
6. C37×#2901C2semidirect
7. C37×#2050C2semidirect
8. C37×#2048C2semidirect
9. C37×#2009C2semidirect
10. C37×#2003C2semidirect
11. C37×#1906C2semidirect
12. C37×#1903C2semidirect
13. C37×#1902C2semidirect
14. C37×#1861C2semidirect
15. C37×#1795C2semidirect
26. C2×#137×C37C22semidirect
27. C2×#137×C37C22semidirect
32. C37×#568C22semidirect
33. C37×#536C22semidirect
34. C2×#124×C37C22semidirect
35. C4×#41×C37C22semidirect
44. C37×#430C22semidirect
45. C37×#423C22semidirect
49. C37×#421C22semidirect
50. C37×#421C22semidirect
53. C2×#104×C37C22semidirect
54. C2×#104×C37C22semidirect
55. C37×#419C22semidirect
56. C37×#418C22semidirect
57. C37×#418C22semidirect
58. C37×#413C22semidirect
59. C37×#413C22semidirect
60. C2×#101×C37C22semidirect
61. C2×#100×C37C22semidirect
62. C37×#410C22semidirect
63. C37×#344C22semidirect
64. C37×#344C22semidirect
65. C37×#339C22semidirect
66. C37×#338C22semidirect
406. #24475C37direct (N × H)
439. #3069C2×C37semidirect
440. #3040C2×C37semidirect
441. #3022C2×C37semidirect
442. C2×#455C2×C37semidirect
443. #2901C2×C37semidirect
444. #2050C2×C37semidirect
445. #2048C2×C37semidirect
446. #2009C2×C37semidirect
447. #2003C2×C37semidirect
448. #1906C2×C37semidirect
449. #1903C2×C37semidirect
450. #1902C2×C37semidirect
451. #1861C2×C37semidirect
452. #1795C2×C37semidirect
472. C2×#137C22×C37semidirect
473. C2×#137C22×C37semidirect
478. #568C22×C37semidirect
479. #536C22×C37semidirect
480. C2×#124C22×C37semidirect
481. C4×#41C22×C37semidirect
490. #430C22×C37semidirect
491. #423C22×C37semidirect
495. #421C22×C37semidirect
496. #421C22×C37semidirect
499. C2×#104C22×C37semidirect
500. C2×#104C22×C37semidirect
501. #419C22×C37semidirect
502. #418C22×C37semidirect
503. #418C22×C37semidirect
504. #413C22×C37semidirect
505. #413C22×C37semidirect
506. C2×#101C22×C37semidirect
507. C2×#100C22×C37semidirect
508. #410C22×C37semidirect
509. #344C22×C37semidirect
510. #344C22×C37semidirect
511. #339C22×C37semidirect
512. #338C22×C37semidirect
513. C37#24475direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35852
C37×#30692
C37×#30402
C37×#30222
C2×C37×#4552
C37×#29012
C37×#20502
C37×#20482
C37×#20092
C37×#20032
C37×#19062
C37×#19032
C37×#19022
C37×#18612
C37×#17952
#2447537