Finite Group Databasebeta

← C37×#33556 #22654809

Subgroups — C37×#33556 #22654809

Order 9472.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3540C211yesmaximal, characteristic, complemented
2C37×#3028C211yesmaximal, characteristic, complemented
3C37×#3025C211yesmaximal, characteristic, complemented
4C37×#3021C211yesmaximal, characteristic, complemented
5C37×#2200C214yesmaximal, complemented
6C37×#2198C214yesmaximal, complemented
7C37×#2128C211yesmaximal, characteristic, complemented
8C37×#2123C211yesmaximal, characteristic, complemented
9C37×#2120C211yesmaximal, characteristic, complemented
10C37×#585C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C37—21no—
12C37×H(3,𝔽4)—21no—
13C37×#560C2212yescomplemented
14C37×#559C2212yescomplemented
15C37×#556—21no—
16C37×#555—21no—
17C37×#551—21no—
18C37×#548—21no—
19C37×#546—21no—
20C37×#542—22no—
21C37×#542—21no—
22C37×#538—22no—
23C37×#536—21no—
24C37×#536C2211yescharacteristic
25C37×#535C2211yescharacteristic
26C37×#525—21no—
27C37×#525—21no—
28C37×#525C2211yescharacteristic
29C37×#458—21no—
30C37×#458—22no—
31C37×#458C2212yescomplemented
32C37×#458C2214yescomplemented
33C37×B(4,𝔽2)—21no—
34C37×B(4,𝔽2)C2212yescomplemented
35C37×#454—22no—
36C37×#453C2214yes—
37C37×#421—21no—
38C37×#413C2211yescharacteristic
39C37×#410—21no—
40C37×#410—21no—
41C37×#410C2211yescharacteristic
42C37×#410C2211yescharacteristic
43C37×#353C2214yescomplemented
44C37×#352C2212yescomplemented
45C37×#352C2214yescomplemented
46C37×AΣL(1,𝔽16)C2212yescomplemented
472−1+4×C37—21no—
482−1+4×C37—41no—
49H(5,𝔽2)×C37—21no—
50H(5,𝔽2)×C37—21no—
51H(5,𝔽2)×C37—41no—
52H(5,𝔽2)×C37C2312yes—
53C2×#41×C37—21no—
54C2×#41×C37—21no—
55C2×#41×C37—21no—
56C2×#41×C37—21no—
57C2×#41×C37—42no—
58C2×#41×C37C2311yescharacteristic
59C22×Q8×C37D411yescharacteristic, complemented
60C22×D4×C37D411yescharacteristic, complemented
61C23×C4×C37D411yescharacteristic
62AGL(1,ℤ/8)×C37—24no—
63AGL(1,ℤ/8)×C37—42no—
64C2×SD16×C37—41no—
65C2×D8×C37—41no—
66C2×M16×C37—21no—
67C4⋊Q8×C37—21no—
68C4⋊Q8×C37—21no—
69C4⋊Q8×C37—41no—
70#127×C37C2312yes—
71#126×C37—22no—
72#126×C37—22no—
73#126×C37—22no—
74#124×C37—22no—
75#124×C37—21no—
76#124×C37—22no—
77#124×C37—22no—
78#124×C37—21no—
79#124×C37—22no—
80#124×C37—22no—
81#124×C37—41no—
82#124×C37D412yescomplemented
83#123×C37—22no—
84#123×C37—22no—
85#123×C37—22no—
86#123×C37—22no—
87#123×C37—24no—
88#123×C37D411yescharacteristic
89#123×C37D412yescomplemented
90#123×C37C2311yescharacteristic
91#123×C37C2312yes—
92C22⋊Q8×C37—21no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—22no—
95C22⋊Q8×C37—21no—
96C22⋊Q8×C37—21no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—42no—
99C22⋊Q8×C37—41no—
100#121×C37—21no—
101#121×C37—21no—
102#121×C37—22no—
103#121×C37—21no—
104#121×C37—21no—
105#121×C37—22no—
106#121×C37—22no—
107#121×C37—41no—
108#120×C37—22no—
109#120×C37—22no—
110#120×C37—21no—
111#120×C37—21no—
112#120×C37—22no—
113#120×C37D411yescharacteristic
114#120×C37C2311yescharacteristic
115C4×Q8×C37—21no—
116C4×Q8×C37—22no—
117C4×D4×C37—22no—
118C4×D4×C37—21no—
119C4×D4×C37—22no—
120C4×D4×C37—21no—
121C4×D4×C37—21no—
122C4×D4×C37—22no—
123C4×D4×C37—42no—
124#117×C37—21no—
125#117×C37—22no—
126#117×C37—21no—
127#117×C37—21no—
128#117×C37D411yescharacteristic
129#117×C37D411yescharacteristic, complemented
130#117×C37D411yescharacteristic, complemented
131C2×C22⋊C4×C37—22no—
132#104×C37—24no—
133#101×C37—21no—
134#100×C37C2312yes—
135#99×C37—21no—
136#99×C37—21no—
137#99×C37—22no—
138#99×C37—22no—
139#99×C37—24no—
140#99×C37C2312yes—
141#99×C37C2312yes—
142C24×C37—21no—
143C24×C37C2×D411yescharacteristic
144#41×C37—22no—
145#41×C37—22no—
146#41×C37—41no—
147#41×C37—41no—
148#41×C37—42no—
149#41×C37—41no—
150#41×C37—41no—
151#41×C37—41no—
152#41×C37—41no—
153#41×C37—41no—
154#41×C37—42no—
155#41×C37—42no—
156#41×C37—42no—
157#41×C37—41no—
158#41×C37—41no—
159#41×C37—41no—
160#41×C37—81no—
161#41×C37—81no—
162C2×Q8×C37—21no—
163C2×Q8×C37—21no—
164C2×Q8×C37—22no—
165C2×Q8×C37—21no—
166C2×Q8×C37—21no—
167C2×Q8×C37—21no—
168C2×Q8×C37—41no—
169C2×Q8×C37—41no—
170C2×Q8×C37—42no—
171C2×Q8×C37C2×D411yescharacteristic
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—22no—
176C2×D4×C37—22no—
177C2×D4×C37—22no—
178C2×D4×C37—22no—
179C2×D4×C37—21no—
180C2×D4×C37—22no—
181C2×D4×C37—22no—
182C2×D4×C37—21no—
183C2×D4×C37—21no—
184C2×D4×C37—41no—
185C2×D4×C37—41no—
186C2×D4×C37—42no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—41no—
190C2×D4×C37—42no—
191C2×D4×C37C2×D411yescharacteristic
192C2×D4×C37C2×D411yescharacteristic
193C2×D4×C37C2×D412yes—
194C2×D4×C37C2411yescharacteristic
195C22×C4×C37—22no—
196C22×C4×C37—22no—
197C22×C4×C37—22no—
198C22×C4×C37—22no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—41no—
202C22×C4×C37—41no—
203C22×C4×C37—41no—
204C22×C4×C37C2×D411yescharacteristic
205C22×C4×C37C2×D411yescharacteristic
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D412yes—
209SD16×C37—44no—
210D8×C37—44no—
211M16×C37—22no—
212M16×C37—41no—
213C2×C8×C37—41no—
214C4⋊C4×C37—22no—
215C4⋊C4×C37—22no—
216C4⋊C4×C37—22no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—22no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—22no—
224C4⋊C4×C37—41no—
225C4⋊C4×C37—41no—
226C4⋊C4×C37—42no—
227C4⋊C4×C37—44no—
228C22⋊C4×C37—22no—
229C22⋊C4×C37—22no—
230C22⋊C4×C37—22no—
231C22⋊C4×C37—22no—
232C22⋊C4×C37—22no—
233C22⋊C4×C37—22no—
234C22⋊C4×C37—21no—
235C22⋊C4×C37—22no—
236C22⋊C4×C37—21no—
237C22⋊C4×C37—21no—
238C22⋊C4×C37—22no—
239C22⋊C4×C37—22no—
240C22⋊C4×C37—22no—
241C22⋊C4×C37—21no—
242C22⋊C4×C37—21no—
243C22⋊C4×C37—22no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—42no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—44no—
248C22⋊C4×C37C2×D411yescharacteristic
249C22⋊C4×C37C2×D411yescharacteristic
250C22⋊C4×C37C2×D412yes—
251C42×C37—22no—
252C42×C37—22no—
253C42×C37—21no—
254C42×C37—21no—
255C42×C37—41no—
256C42×C37—41no—
257C42×C37C2×D412yes—
258C23×C37—22no—
259C23×C37—22no—
260C23×C37—21no—
261C23×C37—22no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—81no—
265C23×C37—81no—
266C23×C37—82no—
267C23×C37#12011yescharacteristic
268C23×C37C22×D411yescharacteristic
269C23×C37C22×D411yescharacteristic
270Q8×C37—22no—
271Q8×C37—41no—
272Q8×C37—41no—
273Q8×C37—41no—
274Q8×C37—41no—
275Q8×C37—41no—
276Q8×C37—41no—
277Q8×C37—81no—
278Q8×C37—82no—
279D4×C37—22no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—42no—
284D4×C37—41no—
285D4×C37—41no—
286D4×C37—42no—
287D4×C37—42no—
288D4×C37—42no—
289D4×C37—42no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—81no—
294D4×C37—82no—
295D4×C37—82no—
296D4×C37—82no—
297D4×C37—81no—
298D4×C37—82no—
299D4×C37—84no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—21no—
305C2×C4×C37—21no—
306C2×C4×C37—22no—
307C2×C4×C37—22no—
308C2×C4×C37—21no—
309C2×C4×C37—22no—
310C2×C4×C37—22no—
311C2×C4×C37—21no—
312C2×C4×C37—22no—
313C2×C4×C37—21no—
314C2×C4×C37—42no—
315C2×C4×C37—42no—
316C2×C4×C37—42no—
317C2×C4×C37—41no—
318C2×C4×C37—42no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—42no—
323C2×C4×C37—42no—
324C2×C4×C37—42no—
325C2×C4×C37—81no—
326C2×C4×C37—82no—
327C2×C4×C37—82no—
328C2×C4×C37#12011yescharacteristic
329C2×C4×C37#12011yescharacteristic
330C2×C4×C37#12011yescharacteristic
331C2×C4×C37C22×D411yescharacteristic
332C8×C37—42no—
333#33556C3711yesmaximal, characteristic, direct product factor, Sylow
334C22×C37—21no—
335C22×C37—21no—
336C22×C37—21no—
337C22×C37—41no—
338C22×C37—41no—
339C22×C37—41no—
340C22×C37—42no—
341C22×C37—41no—
342C22×C37—41no—
343C22×C37—42no—
344C22×C37—42no—
345C22×C37—42no—
346C22×C37—41no—
347C22×C37—42no—
348C22×C37—82no—
349C22×C37—82no—
350C22×C37—81no—
351C22×C37—161no—
352C22×C37—162no—
353C22×C37C2×#12011yescharacteristic
354C4×C37—21no—
355C4×C37—21no—
356C4×C37—21no—
357C4×C37—41no—
358C4×C37—42no—
359C4×C37—42no—
360C4×C37—41no—
361C4×C37—42no—
362C4×C37—41no—
363C4×C37—42no—
364C4×C37—82no—
365C4×C37—82no—
366C4×C37B(4,𝔽2)11yescharacteristic
367C4×C37B(4,𝔽2)11yescharacteristic
368#3540C2×C3711yescharacteristic, complemented
369#3028C2×C3711yescharacteristic, complemented
370#3025C2×C3711yescharacteristic, complemented
371#3021C2×C3711yescharacteristic, complemented
372#2200C2×C3714yescomplemented
373#2198C2×C3714yescomplemented
374#2128C2×C3711yescharacteristic, complemented
375#2123C2×C3711yescharacteristic, complemented
376#2120C2×C3711yescharacteristic, complemented
377C2×C37—21no—
378C2×C37—41no—
379C2×C37—41no—
380C2×C37—41no—
381C2×C37—81no—
382C2×C37—82no—
383C2×C37—82no—
384C2×C37C2×B(4,𝔽2)11yescharacteristic
385#585C22×C3711yescharacteristic
386C2×AGL(1,ℤ/8)—21no—
387H(3,𝔽4)—21no—
388#560C22×C3712yescomplemented
389#559C22×C3712yescomplemented
390#556—21no—
391#555—21no—
392#551—21no—
393#548—21no—
394#546—21no—
395#542—22no—
396#542—21no—
397#538—22no—
398#536—21no—
399#536C22×C3711yescharacteristic
400#535C22×C3711yescharacteristic
401#525—21no—
402#525—21no—
403#525C22×C3711yescharacteristic
404#458—21no—
405#458—22no—
406#458C22×C3712yescomplemented
407#458C22×C3714yescomplemented
408B(4,𝔽2)—21no—
409B(4,𝔽2)C22×C3712yescomplemented
410#454—22no—
411#453C22×C3714yes—
412#421—21no—
413#413C22×C3711yescharacteristic
414#410—21no—
415#410—21no—
416#410C22×C3711yescharacteristic
417#410C22×C3711yescharacteristic
418#353C22×C3714yescomplemented
419#352C22×C3712yescomplemented
420#352C22×C3714yescomplemented
421AΣL(1,𝔽16)C22×C3712yescomplemented
422C37#3355611yescharacteristic, direct product factor, Sylow
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C3712yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C3711yescharacteristic
435C22×Q8D4×C3711yescharacteristic, complemented
436C22×D4D4×C3711yescharacteristic, complemented
437C23×C4D4×C3711yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C3712yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C3712yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C3711yescharacteristic
465#123D4×C3712yescomplemented
466#123C23×C3711yescharacteristic
467#123C23×C3712yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C3711yescharacteristic
490#120C23×C3711yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C3711yescharacteristic
505#117D4×C3711yescharacteristic, complemented
506#117D4×C3711yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C3712yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C3712yes—
517#99C23×C3712yes—
518C24—21no—
519C24C2×D4×C3711yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C3711yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C3711yescharacteristic
568C2×D4C2×D4×C3711yescharacteristic
569C2×D4C2×D4×C3712yes—
570C2×D4C24×C3711yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C3711yescharacteristic
581C22×C4C2×D4×C3711yescharacteristic
582C22×C4C2×D4×C3711yescharacteristic
583C22×C4C2×D4×C3711yescharacteristic
584C22×C4C2×D4×C3712yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C3711yescharacteristic
625C22⋊C4C2×D4×C3711yescharacteristic
626C22⋊C4C2×D4×C3712yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C3712yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C3711yescharacteristic
644C23C22×D4×C3711yescharacteristic
645C23C22×D4×C3711yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C3711yescharacteristic
705C2×C4#120×C3711yescharacteristic
706C2×C4#120×C3711yescharacteristic
707C2×C4C22×D4×C3711yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C3711yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C37×B(4,𝔽2)11yescharacteristic
742C4C37×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×C37×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C37C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C37
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3540C2semidirect
2. C37×#3028C2semidirect
3. C37×#3025C2semidirect
4. C37×#3021C2semidirect
5. C37×#2200C2semidirect
6. C37×#2198C2semidirect
7. C37×#2128C2semidirect
8. C37×#2123C2semidirect
9. C37×#2120C2semidirect
13. C37×#560C22semidirect
14. C37×#559C22semidirect
31. C37×#458C22semidirect
32. C37×#458C22semidirect
34. C37×B(4,𝔽2)C22semidirect
43. C37×#353C22semidirect
44. C37×#352C22semidirect
45. C37×#352C22semidirect
46. C37×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C37D4semidirect
60. C22×D4×C37D4semidirect
82. #124×C37D4semidirect
89. #123×C37D4semidirect
129. #117×C37D4semidirect
130. #117×C37D4semidirect
333. #33556C37direct (N × H)
368. #3540C2×C37semidirect
369. #3028C2×C37semidirect
370. #3025C2×C37semidirect
371. #3021C2×C37semidirect
372. #2200C2×C37semidirect
373. #2198C2×C37semidirect
374. #2128C2×C37semidirect
375. #2123C2×C37semidirect
376. #2120C2×C37semidirect
388. #560C22×C37semidirect
389. #559C22×C37semidirect
406. #458C22×C37semidirect
407. #458C22×C37semidirect
409. B(4,𝔽2)C22×C37semidirect
418. #353C22×C37semidirect
419. #352C22×C37semidirect
420. #352C22×C37semidirect
421. AΣL(1,𝔽16)C22×C37semidirect
422. C37#33556direct (N × H)
435. C22×Q8D4×C37semidirect
436. C22×D4D4×C37semidirect
458. #124D4×C37semidirect
465. #123D4×C37semidirect
505. #117D4×C37semidirect
506. #117D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35402
C37×#30282
C37×#30252
C37×#30212
C37×#22002
C37×#21982
C37×#21282
C37×#21232
C37×#21202
#3355637