Finite Group Databasebeta

← C37×#25523 #22646776

Subgroups — C37×#25523 #22646776

Order 9472.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3494C211yesmaximal, characteristic
2C37×#3095C211yesmaximal, characteristic, complemented
3C37×#3056C211yesmaximal, characteristic, complemented
4C37×#2850C211yesmaximal, characteristic, complemented
5C37×#2061C211yesmaximal, characteristic, complemented
6C37×#2037C211yesmaximal, characteristic, complemented
7C37×#2028C211yesmaximal, characteristic, complemented
8C37×#2004C211yesmaximal, characteristic, complemented
9C37×#1900C211yesmaximal, characteristic, complemented
10C37×#1896C211yesmaximal, characteristic, complemented
11C37×#1885C211yesmaximal, characteristic, complemented
12C37×#1882C211yesmaximal, characteristic, complemented
13C37×#1860C211yesmaximal, characteristic, complemented
14C37×#1856C211yesmaximal, characteristic, complemented
15C2×C37×#339C211yesmaximal, characteristic, complemented
16C2×#137×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C37×#555—21no—
19C37×#553—21no—
20C37×#553—21no—
21C37×#551—22no—
22C37×#547—21no—
23C37×#546—22no—
24C37×#544C2211yescharacteristic
25C37×#542—21no—
26C37×#540—21no—
27C37×#535C2211yescharacteristic
28C37×#532—21no—
29C37×#529—21no—
30C2×#124×C37C2211yescharacteristic
31C37×#525C2211yescharacteristic
32C2×C22⋊Q8×C37C2211yescharacteristic
33C2×#121×C37C2211yescharacteristic
34C37×#520C2211yescharacteristic
35C37×#518C2211yescharacteristic
36C2×#117×C37C2211yescharacteristic
37C22×C42×C37C2211yescharacteristic
38C37×#485—21no—
39C37×#485—21no—
40C37×#484—21no—
41C37×#483—21no—
42C37×#470—21no—
43C37×#468—21no—
44C37×#467—21no—
45C37×#465—21no—
46C37×#428C2211yescharacteristic
47C37×#428C2211yescharacteristic
48C37×#428C2211yescharacteristic
49C2×#104×C37C2211yescharacteristic
50C2×#104×C37C2211yescharacteristic
51C37×#419C2211yescharacteristic
52C37×#419C2211yescharacteristic
53C37×#419C2211yescharacteristic
54C37×#417C2211yescharacteristic
55C2×#100×C37C2211yescharacteristic
56C2×#100×C37C2211yescharacteristic
57C37×#407C2211yescharacteristic
58C37×#391C2211yescharacteristic
59C37×#390C2211yescharacteristic
60C37×#388—22no—
61C37×#386—22no—
62C37×#382C2211yescharacteristic
63C37×#343C2211yescharacteristic
64C37×#343C2211yescharacteristic
65C37×#339C2211yescharacteristic
66C37×#339C2211yescharacteristic
67C37×#339C2211yescharacteristic
68C37×#339C2211yescharacteristic
69C37×#339C2211yescharacteristic
70C37×#339C2211yescharacteristic
71C2×#41×C37—22no—
72C2×#41×C37C2311yescharacteristic
73C22×Q8×C37C2311yescharacteristic
74C22×D4×C37D412yes—
75C22×D4×C37C2311yescharacteristic
76C23×C4×C37—21no—
77C23×C4×C37C2311yescharacteristic
78#137×C37—22no—
79#137×C37—41no—
80C2×Q16×C37—21no—
81C2×SD16×C37—21no—
82C2×M16×C37—21no—
83C2×M16×C37—22no—
84C2×M16×C37—41no—
85C2×M16×C37C2311yescharacteristic
86C2×M16×C37C2311yescharacteristic
87C2×M16×C37C2311yescharacteristic
88C2×M16×C37C2311yescharacteristic
89C22×C8×C37—21no—
90C4⋊Q8×C37—21no—
91C4⋊Q8×C37—21no—
92#127×C37—21no—
93#126×C37—22no—
94#126×C37—22no—
95#125×C37—21no—
96#125×C37—21no—
97#124×C37—22no—
98#124×C37—22no—
99#124×C37—21no—
100#124×C37—22no—
101#124×C37—41no—
102#123×C37—22no—
103#123×C37—22no—
104#123×C37—22no—
105#123×C37—22no—
106#123×C37—21no—
107C22⋊Q8×C37—22no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—21no—
110C22⋊Q8×C37—21no—
111C22⋊Q8×C37—21no—
112C22⋊Q8×C37—21no—
113C22⋊Q8×C37D411yescharacteristic
114C22⋊Q8×C37D411yescharacteristic
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37—21no—
119#121×C37—21no—
120#121×C37—21no—
121#121×C37—21no—
122#121×C37—21no—
123#121×C37—21no—
124#121×C37D411yescharacteristic
125#121×C37D411yescharacteristic
126#120×C37—21no—
127#120×C37—22no—
128C4×Q8×C37—21no—
129C4×D4×C37—22no—
130C4×D4×C37—22no—
131C4×D4×C37—21no—
132C4×D4×C37—22no—
133C4×D4×C37—21no—
134C4×D4×C37—21no—
135C4×D4×C37—21no—
136C4×D4×C37—21no—
137C4×D4×C37—21no—
138C4×D4×C37—21no—
139#117×C37—22no—
140#117×C37—21no—
141#117×C37—21no—
142#117×C37—21no—
143#117×C37D411yescharacteristic
144#117×C37D411yescharacteristic
145#117×C37C2311yescharacteristic
146#117×C37C2311yescharacteristic
147#117×C37C2311yescharacteristic
148C2×C4⋊C4×C37—21no—
149C2×C4⋊C4×C37—21no—
150C2×C4⋊C4×C37D411yescharacteristic
151C2×C4⋊C4×C37D411yescharacteristic
152C2×C4⋊C4×C37C2311yescharacteristic
153C2×C4⋊C4×C37C2311yescharacteristic
154C2×C22⋊C4×C37—21no—
155C2×C22⋊C4×C37—22no—
156C2×C22⋊C4×C37—21no—
157C2×C22⋊C4×C37—22no—
158C2×C22⋊C4×C37—22no—
159C2×C22⋊C4×C37D412yes—
160C2×C42×C37—21no—
161C2×C42×C37—22no—
162C2×C42×C37—21no—
163C2×C42×C37—41no—
164C2×C42×C37C2311yescharacteristic
165C2×C42×C37C2311yescharacteristic
166#107×C37—21no—
167#107×C37—21no—
168#107×C37—21no—
169#106×C37—21no—
170#106×C37—21no—
171#106×C37—21no—
172#104×C37—22no—
173#104×C37—41no—
174#103×C37—21no—
175#103×C37—21no—
176#103×C37—21no—
177#103×C37—21no—
178#103×C37—21no—
179#103×C37—21no—
180#103×C37—21no—
181#102×C37—21no—
182#100×C37—22no—
183#100×C37—41no—
184C22⋊C8×C37—21no—
185C22⋊C8×C37—21no—
186#95×C37—22no—
187#95×C37—22no—
188C24×C37C2×D411yescharacteristic
189C24×C37C2×D412yes—
190#41×C37—21no—
191#41×C37—21no—
192#41×C37—21no—
193#41×C37—21no—
194#41×C37—84no—
195C2×Q8×C37—22no—
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×C37C2×D411yescharacteristic
203C2×D4×C37—21no—
204C2×D4×C37—22no—
205C2×D4×C37—21no—
206C2×D4×C37—22no—
207C2×D4×C37—22no—
208C2×D4×C37—21no—
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—21no—
216C2×D4×C37—44no—
217C2×D4×C37C2×D411yescharacteristic
218C22×C4×C37—21no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—22no—
226C22×C4×C37—22no—
227C22×C4×C37—22no—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—42no—
233C22×C4×C37—42no—
234C22×C4×C37—42no—
235C22×C4×C37C2×D411yescharacteristic
236C22×C4×C37C2×D411yescharacteristic
237C22×C4×C37C2×D411yescharacteristic
238C22×C4×C37C2×D411yescharacteristic
239C22×C4×C37C2×D411yescharacteristic
240C22×C4×C37C2×D412yes—
241C22×C4×C37C2411yescharacteristic
242Q16×C37—42no—
243SD16×C37—42no—
244M16×C37—21no—
245M16×C37—21no—
246M16×C37—21no—
247M16×C37—21no—
248M16×C37—21no—
249M16×C37—21no—
250M16×C37—21no—
251M16×C37—42no—
252M16×C37#4112yescomplemented
253C2×C8×C37—21no—
254C2×C8×C37—21no—
255C2×C8×C37—21no—
256C2×C8×C37—21no—
257C2×C8×C37—42no—
258C4⋊C4×C37—22no—
259C4⋊C4×C37—22no—
260C4⋊C4×C37—22no—
261C4⋊C4×C37—22no—
262C4⋊C4×C37—21no—
263C4⋊C4×C37—21no—
264C4⋊C4×C37—21no—
265C4⋊C4×C37—21no—
266C4⋊C4×C37—21no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—41no—
271C4⋊C4×C37—41no—
272C4⋊C4×C37C2×D411yescharacteristic
273C4⋊C4×C37C2×D411yescharacteristic
274C4⋊C4×C37C2×D411yescharacteristic
275C4⋊C4×C37C2×D411yescharacteristic
276C4⋊C4×C37C2×D411yescharacteristic
277C4⋊C4×C37C2×D411yescharacteristic
278C22⋊C4×C37—22no—
279C22⋊C4×C37—22no—
280C22⋊C4×C37—22no—
281C22⋊C4×C37—22no—
282C22⋊C4×C37—22no—
283C22⋊C4×C37—21no—
284C22⋊C4×C37—21no—
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—22no—
291C22⋊C4×C37—22no—
292C22⋊C4×C37—21no—
293C22⋊C4×C37—21no—
294C22⋊C4×C37—44no—
295C22⋊C4×C37—44no—
296C22⋊C4×C37—41no—
297C22⋊C4×C37—41no—
298C42×C37—22no—
299C42×C37—21no—
300C42×C37—21no—
301C42×C37—21no—
302C42×C37—21no—
303C42×C37—21no—
304C42×C37—21no—
305C42×C37—21no—
306C42×C37—21no—
307C42×C37—42no—
308C42×C37#4112yescomplemented
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—22no—
312C23×C37—22no—
313C23×C37—21no—
314C23×C37—22no—
315C23×C37—22no—
316C23×C37—41no—
317C23×C37—42no—
318C23×C37—42no—
319C23×C37#12011yescharacteristic
320C23×C37#12011yescharacteristic
321C23×C37C22×D411yescharacteristic
322Q8×C37—21no—
323Q8×C37—21no—
324Q8×C37—41no—
325Q8×C37—41no—
326Q8×C37—41no—
327Q8×C37—41no—
328Q8×C37—82no—
329D4×C37—21no—
330D4×C37—21no—
331D4×C37—41no—
332D4×C37—41no—
333D4×C37—44no—
334D4×C37—42no—
335D4×C37—41no—
336D4×C37—41no—
337D4×C37—41no—
338D4×C37—41no—
339D4×C37—81no—
340D4×C37—82no—
341D4×C37—82no—
342D4×C37—82no—
343C2×C4×C37—21no—
344C2×C4×C37—21no—
345C2×C4×C37—21no—
346C2×C4×C37—21no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—22no—
354C2×C4×C37—21no—
355C2×C4×C37—21no—
356C2×C4×C37—21no—
357C2×C4×C37—21no—
358C2×C4×C37—21no—
359C2×C4×C37—21no—
360C2×C4×C37—21no—
361C2×C4×C37—22no—
362C2×C4×C37—22no—
363C2×C4×C37—41no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—48no—
367C2×C4×C37—41no—
368C2×C4×C37—42no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
371C2×C4×C37—42no—
372C2×C4×C37—42no—
373C2×C4×C37—41no—
374C2×C4×C37—41no—
375C2×C4×C37—41no—
376C2×C4×C37—41no—
377C2×C4×C37—81no—
378C2×C4×C37—82no—
379C2×C4×C37—82no—
380C2×C4×C37—82no—
381C2×C4×C37#12011yescharacteristic
382C2×C4×C37#12011yescharacteristic
383C2×C4×C37C22×D411yescharacteristic
384C2×C4×C37C22×D411yescharacteristic
385C2×C4×C37C2×#4111yescharacteristic
386C2×C4×C37C2×#4111yescharacteristic
387C2×C4×C37H(5,𝔽2)11yescharacteristic
388C2×C4×C372−1+411yescharacteristic
389C8×C37—22no—
390C8×C37—41no—
391C8×C37—41no—
392C8×C37—41no—
393#25523C3711yesmaximal, characteristic, direct product factor, Sylow
394C22×C37—21no—
395C22×C37—21no—
396C22×C37—21no—
397C22×C37—21no—
398C22×C37—21no—
399C22×C37—21no—
400C22×C37—21no—
401C22×C37—42no—
402C22×C37—42no—
403C22×C37—41no—
404C22×C37—42no—
405C22×C37—41no—
406C22×C37—42no—
407C22×C37—42no—
408C22×C37—41no—
409C22×C37—82no—
410C22×C37—82no—
411C22×C37#45512yes—
412C22×C37C2×#12011yescharacteristic
413C22×C37#54611yescharacteristic
414C22×C37#54711yescharacteristic
415C4×C37—21no—
416C4×C37—21no—
417C4×C37—42no—
418C4×C37—42no—
419C4×C37—41no—
420C4×C37—41no—
421C4×C37—41no—
422C4×C37—42no—
423C4×C37—41no—
424C4×C37—41no—
425C4×C37—41no—
426C4×C37—41no—
427C4×C37—81no—
428C4×C37—81no—
429C4×C37#53211yescharacteristic
430C4×C37#53711yescharacteristic
431C4×C37#54611yescharacteristic
432C4×C37#54711yescharacteristic
433#3494C2×C3711yescharacteristic
434#3095C2×C3711yescharacteristic, complemented
435#3056C2×C3711yescharacteristic, complemented
436#2850C2×C3711yescharacteristic, complemented
437#2061C2×C3711yescharacteristic, complemented
438#2037C2×C3711yescharacteristic, complemented
439#2028C2×C3711yescharacteristic, complemented
440#2004C2×C3711yescharacteristic, complemented
441#1900C2×C3711yescharacteristic, complemented
442#1896C2×C3711yescharacteristic, complemented
443#1885C2×C3711yescharacteristic, complemented
444#1882C2×C3711yescharacteristic, complemented
445#1860C2×C3711yescharacteristic, complemented
446#1856C2×C3711yescharacteristic, complemented
447C2×#339C2×C3711yescharacteristic, complemented
448C2×C37—21no—
449C2×C37—21no—
450C2×C37—22no—
451C2×C37—41no—
452C2×C37—81no—
453C2×C37—82no—
454C2×C37#243011yescharacteristic
455C2×C37C2×#45511yescharacteristic
456C2×C37#301811yescharacteristic
457C2×#137C22×C3711yescharacteristic
458C22×M16C22×C3711yescharacteristic
459#555—21no—
460#553—21no—
461#553—21no—
462#551—22no—
463#547—21no—
464#546—22no—
465#544C22×C3711yescharacteristic
466#542—21no—
467#540—21no—
468#535C22×C3711yescharacteristic
469#532—21no—
470#529—21no—
471C2×#124C22×C3711yescharacteristic
472#525C22×C3711yescharacteristic
473C2×C22⋊Q8C22×C3711yescharacteristic
474C2×#121C22×C3711yescharacteristic
475#520C22×C3711yescharacteristic
476#518C22×C3711yescharacteristic
477C2×#117C22×C3711yescharacteristic
478C22×C42C22×C3711yescharacteristic
479#485—21no—
480#485—21no—
481#484—21no—
482#483—21no—
483#470—21no—
484#468—21no—
485#467—21no—
486#465—21no—
487#428C22×C3711yescharacteristic
488#428C22×C3711yescharacteristic
489#428C22×C3711yescharacteristic
490C2×#104C22×C3711yescharacteristic
491C2×#104C22×C3711yescharacteristic
492#419C22×C3711yescharacteristic
493#419C22×C3711yescharacteristic
494#419C22×C3711yescharacteristic
495#417C22×C3711yescharacteristic
496C2×#100C22×C3711yescharacteristic
497C2×#100C22×C3711yescharacteristic
498#407C22×C3711yescharacteristic
499#391C22×C3711yescharacteristic
500#390C22×C3711yescharacteristic
501#388—22no—
502#386—22no—
503#382C22×C3711yescharacteristic
504#343C22×C3711yescharacteristic
505#343C22×C3711yescharacteristic
506#339C22×C3711yescharacteristic
507#339C22×C3711yescharacteristic
508#339C22×C3711yescharacteristic
509#339C22×C3711yescharacteristic
510#339C22×C3711yescharacteristic
511#339C22×C3711yescharacteristic
512C37#2552311yescharacteristic, direct product factor, Sylow
513C2×#41—22no—
514C2×#41C23×C3711yescharacteristic
515C22×Q8C23×C3711yescharacteristic
516C22×D4D4×C3712yes—
517C22×D4C23×C3711yescharacteristic
518C23×C4—21no—
519C23×C4C23×C3711yescharacteristic
520#137—22no—
521#137—41no—
522C2×Q16—21no—
523C2×SD16—21no—
524C2×M16—21no—
525C2×M16—22no—
526C2×M16—41no—
527C2×M16C23×C3711yescharacteristic
528C2×M16C23×C3711yescharacteristic
529C2×M16C23×C3711yescharacteristic
530C2×M16C23×C3711yescharacteristic
531C22×C8—21no—
532C4⋊Q8—21no—
533C4⋊Q8—21no—
534#127—21no—
535#126—22no—
536#126—22no—
537#125—21no—
538#125—21no—
539#124—22no—
540#124—22no—
541#124—21no—
542#124—22no—
543#124—41no—
544#123—22no—
545#123—22no—
546#123—22no—
547#123—22no—
548#123—21no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8D4×C3711yescharacteristic
556C22⋊Q8D4×C3711yescharacteristic
557#121—22no—
558#121—22no—
559#121—22no—
560#121—21no—
561#121—21no—
562#121—21no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121D4×C3711yescharacteristic
567#121D4×C3711yescharacteristic
568#120—21no—
569#120—22no—
570C4×Q8—21no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—21no—
574C4×D4—22no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581#117—22no—
582#117—21no—
583#117—21no—
584#117—21no—
585#117D4×C3711yescharacteristic
586#117D4×C3711yescharacteristic
587#117C23×C3711yescharacteristic
588#117C23×C3711yescharacteristic
589#117C23×C3711yescharacteristic
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4D4×C3711yescharacteristic
593C2×C4⋊C4D4×C3711yescharacteristic
594C2×C4⋊C4C23×C3711yescharacteristic
595C2×C4⋊C4C23×C3711yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4D4×C3712yes—
602C2×C42—21no—
603C2×C42—22no—
604C2×C42—21no—
605C2×C42—41no—
606C2×C42C23×C3711yescharacteristic
607C2×C42C23×C3711yescharacteristic
608#107—21no—
609#107—21no—
610#107—21no—
611#106—21no—
612#106—21no—
613#106—21no—
614#104—22no—
615#104—41no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#103—21no—
623#102—21no—
624#100—22no—
625#100—41no—
626C22⋊C8—21no—
627C22⋊C8—21no—
628#95—22no—
629#95—22no—
630C24C2×D4×C3711yescharacteristic
631C24C2×D4×C3712yes—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—84no—
637C2×Q8—22no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8C2×D4×C3711yescharacteristic
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—44no—
659C2×D4C2×D4×C3711yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4C2×D4×C3711yescharacteristic
678C22×C4C2×D4×C3711yescharacteristic
679C22×C4C2×D4×C3711yescharacteristic
680C22×C4C2×D4×C3711yescharacteristic
681C22×C4C2×D4×C3711yescharacteristic
682C22×C4C2×D4×C3712yes—
683C22×C4C24×C3711yescharacteristic
684Q16—42no—
685SD16—42no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—21no—
690M16—21no—
691M16—21no—
692M16—21no—
693M16—42no—
694M16#41×C3712yescomplemented
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4C2×D4×C3711yescharacteristic
715C4⋊C4C2×D4×C3711yescharacteristic
716C4⋊C4C2×D4×C3711yescharacteristic
717C4⋊C4C2×D4×C3711yescharacteristic
718C4⋊C4C2×D4×C3711yescharacteristic
719C4⋊C4C2×D4×C3711yescharacteristic
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—44no—
737C22⋊C4—44no—
738C22⋊C4—41no—
739C22⋊C4—41no—
740C42—22no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—21no—
749C42—42no—
750C42#41×C3712yescomplemented
751C23—21no—
752C23—21no—
753C23—22no—
754C23—22no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—41no—
759C23—42no—
760C23—42no—
761C23#120×C3711yescharacteristic
762C23#120×C3711yescharacteristic
763C23C22×D4×C3711yescharacteristic
764Q8—21no—
765Q8—21no—
766Q8—41no—
767Q8—41no—
768Q8—41no—
769Q8—41no—
770Q8—82no—
771D4—21no—
772D4—21no—
773D4—41no—
774D4—41no—
775D4—44no—
776D4—42no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—82no—
782D4—81no—
783D4—82no—
784D4—82no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—48no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—81no—
820C2×C4—82no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4#120×C3711yescharacteristic
824C2×C4#120×C3711yescharacteristic
825C2×C4C22×D4×C3711yescharacteristic
826C2×C4C22×D4×C3711yescharacteristic
827C2×C4C2×#41×C3711yescharacteristic
828C2×C4C2×#41×C3711yescharacteristic
829C2×C4H(5,𝔽2)×C3711yescharacteristic
830C2×C42−1+4×C3711yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—42no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—41no—
850C22—82no—
851C22—82no—
852C22C37×#45512yes—
853C22C2×#120×C3711yescharacteristic
854C22C37×#54611yescharacteristic
855C22C37×#54711yescharacteristic
856C4—21no—
857C4—21no—
858C4—42no—
859C4—42no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—42no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4C37×#53211yescharacteristic
871C4C37×#53711yescharacteristic
872C4C37×#54611yescharacteristic
873C4C37×#54711yescharacteristic
874C2—21no—
875C2—21no—
876C2—22no—
877C2—41no—
878C2—82no—
879C2—81no—
880C2C37×#243011yescharacteristic
881C2C2×C37×#45511yescharacteristic
882C2C37×#301811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3494C2
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
2. C37×#3095C2semidirect
3. C37×#3056C2semidirect
4. C37×#2850C2semidirect
5. C37×#2061C2semidirect
6. C37×#2037C2semidirect
7. C37×#2028C2semidirect
8. C37×#2004C2semidirect
9. C37×#1900C2semidirect
10. C37×#1896C2semidirect
11. C37×#1885C2semidirect
12. C37×#1882C2semidirect
13. C37×#1860C2semidirect
14. C37×#1856C2semidirect
15. C2×C37×#339C2semidirect
252. M16×C37#41semidirect
308. C42×C37#41semidirect
393. #25523C37direct (N × H)
434. #3095C2×C37semidirect
435. #3056C2×C37semidirect
436. #2850C2×C37semidirect
437. #2061C2×C37semidirect
438. #2037C2×C37semidirect
439. #2028C2×C37semidirect
440. #2004C2×C37semidirect
441. #1900C2×C37semidirect
442. #1896C2×C37semidirect
443. #1885C2×C37semidirect
444. #1882C2×C37semidirect
445. #1860C2×C37semidirect
446. #1856C2×C37semidirect
447. C2×#339C2×C37semidirect
512. C37#25523direct (N × H)
694. M16#41×C37semidirect
750. C42#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34942
C37×#30952
C37×#30562
C37×#28502
C37×#20612
C37×#20372
C37×#20282
C37×#20042
C37×#19002
C37×#18962
C37×#18852
C37×#18822
C37×#18602
C37×#18562
C2×C37×#3392
#2552337