Finite Group Databasebeta

← C37×#25144 #22646397

Subgroups — C37×#25144 #22646397

Order 9472.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#471C211yesmaximal, characteristic, complemented
2C37×#3056C211yesmaximal, characteristic, complemented
3C37×#3003C211yesmaximal, characteristic
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C37×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C37C211yesmaximal, characteristic, complemented
7C37×#2063C211yesmaximal, characteristic, complemented
8C37×#2051C211yesmaximal, characteristic, complemented
9C37×#2046C211yesmaximal, characteristic, complemented
10C37×#2019C211yesmaximal, characteristic, complemented
11C37×#1977C211yesmaximal, characteristic, complemented
12C37×#1931C211yesmaximal, characteristic, complemented
13C37×#1907C211yesmaximal, characteristic, complemented
14C37×#1901C211yesmaximal, characteristic, complemented
15C37×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C2×#137×C37C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C22×SD16×C37C2211yescharacteristic
22C2×#131×C37C2211yescharacteristic, complemented
23C22×M16×C37C2211yescharacteristic
24C22×M16×C37C2211yescharacteristic
25C37×#525C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C37×#471—24no—
28C37×#470—21no—
29C37×#468—21no—
30C37×#467—21no—
31C37×#465—21no—
32C37×#450—21no—
33C37×#450—21no—
34C37×#450—21no—
35C37×#450—21no—
36C37×#450—21no—
37C37×#450—21no—
38C37×#447—21no—
39C37×#447—21no—
40C37×#436—21no—
41C37×#435—21no—
42C37×#435—21no—
43C8×D4×C37—21no—
44C2×#108×C37C2211yescharacteristic, complemented
45C2×#108×C37C2211yescharacteristic, complemented
46C37×#428C2211yescharacteristic, complemented
47C37×#424C2211yescharacteristic, complemented
48C37×#419C2211yescharacteristic, complemented
49C37×#418C2211yescharacteristic
50C37×#418C2211yescharacteristic
51C37×#417C2211yescharacteristic, complemented
52C2×#102×C37C2211yescharacteristic
53C2×#102×C37C2211yescharacteristic
54C2×#101×C37C2211yescharacteristic, complemented
55C2×#101×C37C2211yescharacteristic, complemented
56C2×#100×C37—24no—
57C2×#100×C37C2211yescharacteristic
58C2×#100×C37C2211yescharacteristic
59C2×#100×C37C2211yescharacteristic
60C2×#100×C37C2211yescharacteristic
61C37×#408C2211yescharacteristic, complemented
62C37×#407C2211yescharacteristic
63C2×C22⋊C8×C37C2211yescharacteristic
64C37×#405C2211yescharacteristic, complemented
65C37×#343C2211yescharacteristic, complemented
66C37×#343C2211yescharacteristic, complemented
67C37×#341C2211yescharacteristic, complemented
68C37×#341C2211yescharacteristic, complemented
69C25×C37—21no—
70C2×#41×C37C2311yescharacteristic
71C22×Q8×C37C2311yescharacteristic
72C22×D4×C37—22no—
73C22×D4×C37—22no—
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—41no—
80C22×D4×C37—41no—
81C22×D4×C37C2311yescharacteristic
82C22×D4×C37C2311yescharacteristic
83C23×C4×C37C2311yescharacteristic
84#137×C37—22no—
85#137×C37—41no—
86AGL(1,ℤ/8)×C37—22no—
87AGL(1,ℤ/8)×C37—22no—
88AGL(1,ℤ/8)×C37—41no—
89AGL(1,ℤ/8)×C37—41no—
90C2×Q16×C37—21no—
91C2×SD16×C37—21no—
92C2×SD16×C37—21no—
93C2×SD16×C37—22no—
94C2×SD16×C37—21no—
95C2×SD16×C37—22no—
96C2×SD16×C37—21no—
97C2×SD16×C37—21no—
98C2×SD16×C37—21no—
99C2×SD16×C37—21no—
100C2×SD16×C37—41no—
101C2×SD16×C37—41no—
102C2×D8×C37—21no—
103C2×D8×C37—21no—
104#131×C37—22no—
105#131×C37—41no—
106C2×M16×C37—21no—
107C2×M16×C37—21no—
108C2×M16×C37—21no—
109C2×M16×C37—22no—
110C2×M16×C37—22no—
111C2×M16×C37—41no—
112C2×M16×C37—41no—
113C2×M16×C37C2311yescharacteristic
114C2×M16×C37C2311yescharacteristic
115C2×M16×C37C2311yescharacteristic
116C2×M16×C37C2311yescharacteristic
117C2×M16×C37C2311yescharacteristic
118C2×M16×C37C2311yescharacteristic
119C22×C8×C37—21no—
120C22×C8×C37—21no—
121C22×C8×C37—21no—
122C22×C8×C37C2311yescharacteristic
123C22×C8×C37C2311yescharacteristic
124#123×C37—21no—
125C22⋊Q8×C37—21no—
126C22⋊Q8×C37—21no—
127C22⋊Q8×C37—21no—
128C22⋊Q8×C37—21no—
129C22⋊Q8×C37D411yescharacteristic
130C22⋊Q8×C37D411yescharacteristic
131#121×C37D411yescharacteristic
132#121×C37D411yescharacteristic
133#120×C37—21no—
134C4×D4×C37—21no—
135C4×D4×C37—21no—
136#117×C37C2311yescharacteristic
137C2×C4⋊C4×C37—21no—
138C2×C4⋊C4×C37C2311yescharacteristic
139C2×C22⋊C4×C37—21no—
140#108×C37—22no—
141#108×C37—41no—
142#107×C37—21no—
143#106×C37—21no—
144C4⋊C8×C37—21no—
145C4⋊C8×C37—21no—
146#103×C37—21no—
147#103×C37—21no—
148#103×C37—21no—
149#102×C37—21no—
150#102×C37—21no—
151#102×C37—21no—
152#102×C37—21no—
153#102×C37—21no—
154#102×C37—21no—
155#102×C37—21no—
156#102×C37—21no—
157#102×C37—21no—
158#101×C37—22no—
159#101×C37—41no—
160#100×C37—22no—
161#100×C37—22no—
162#100×C37—22no—
163#100×C37D414yescomplemented
164C22⋊C8×C37—21no—
165C22⋊C8×C37—21no—
166C22⋊C8×C37—21no—
167C22⋊C8×C37—21no—
168C22⋊C8×C37D411yescharacteristic
169C22⋊C8×C37D411yescharacteristic
170C22⋊C8×C37D411yescharacteristic
171C22⋊C8×C37D411yescharacteristic
172#97×C37—21no—
173C4×C8×C37—21no—
174C24×C37—24no—
175C24×C37—21no—
176C24×C37—21no—
177C24×C37—42no—
178C24×C37—41no—
179C24×C37—41no—
180C24×C37—82no—
181C24×C37—82no—
182C24×C37#4111yescharacteristic
183#41×C37—21no—
184#41×C37—21no—
185#41×C37—21no—
186#41×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37—21no—
189C2×Q8×C37—21no—
190C2×Q8×C37—21no—
191C2×Q8×C37—21no—
192C2×Q8×C37—21no—
193C2×Q8×C37C2×D411yescharacteristic
194C2×D4×C37—24no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—42no—
209C2×D4×C37—42no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—41no—
218C2×D4×C37—41no—
219C2×D4×C37C2×D412yes—
220C2×D4×C37C2×D411yescharacteristic
221C2×D4×C37#4112yes—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37C2×D411yescharacteristic
230C22×C4×C37C2×D411yescharacteristic
231C22×C4×C37C2×D411yescharacteristic
232C22×C4×C37C2×D411yescharacteristic
233C22×C4×C37#4111yescharacteristic
234C22×C4×C37C2411yescharacteristic
235Q16×C37—42no—
236SD16×C37—42no—
237SD16×C37—42no—
238SD16×C37—42no—
239SD16×C37—42no—
240SD16×C37—42no—
241SD16×C37—42no—
242SD16×C37—42no—
243D8×C37—42no—
244D8×C37—42no—
245M16×C37—21no—
246M16×C37—21no—
247M16×C37—21no—
248M16×C37—21no—
249M16×C37—21no—
250M16×C37—21no—
251M16×C37—21no—
252M16×C37—21no—
253M16×C37—21no—
254M16×C37—21no—
255M16×C37—42no—
256M16×C37—42no—
257M16×C37—42no—
258M16×C37C2×D412yes—
259M16×C37C2×D412yes—
260C2×C8×C37—21no—
261C2×C8×C37—21no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—42no—
271C2×C8×C37—42no—
272C2×C8×C37—42no—
273C2×C8×C37C2×D411yescharacteristic
274C2×C8×C37C2×D411yescharacteristic
275C2×C8×C37C2×D411yescharacteristic
276C2×C8×C37C2×D411yescharacteristic
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—41no—
282C4⋊C4×C37—41no—
283C4⋊C4×C37C2×D411yescharacteristic
284C4⋊C4×C37C2×D411yescharacteristic
285C22⋊C4×C37—21no—
286C22⋊C4×C37—21no—
287C22⋊C4×C37—21no—
288C22⋊C4×C37—21no—
289C22⋊C4×C37—21no—
290C22⋊C4×C37—41no—
291C22⋊C4×C37—41no—
292C42×C37—21no—
293C23×C37—21no—
294C23×C37—21no—
295C23×C37—22no—
296C23×C37—21no—
297C23×C37—22no—
298C23×C37—22no—
299C23×C37—41no—
300C23×C37—44no—
301C23×C37—44no—
302C23×C37—41no—
303C23×C37—41no—
304C23×C37—41no—
305C23×C37—41no—
306C23×C37—81no—
307C23×C37—81no—
308C23×C37—81no—
309C23×C37—81no—
310C23×C37—82no—
311C23×C37—82no—
312C23×C37—82no—
313C23×C37—88no—
314C23×C37—88no—
315C23×C37—82no—
316C23×C37#12111yescharacteristic
317C23×C37#12111yescharacteristic
318C23×C37C2×#4111yescharacteristic
319Q8×C37—21no—
320Q8×C37—21no—
321Q8×C37—41no—
322Q8×C37—41no—
323Q8×C37—41no—
324Q8×C37—41no—
325D4×C37—21no—
326D4×C37—22no—
327D4×C37—22no—
328D4×C37—21no—
329D4×C37—22no—
330D4×C37—22no—
331D4×C37—44no—
332D4×C37—44no—
333D4×C37—41no—
334D4×C37—41no—
335D4×C37—42no—
336D4×C37—41no—
337D4×C37—41no—
338D4×C37—41no—
339D4×C37—41no—
340D4×C37—81no—
341C2×C4×C37—21no—
342C2×C4×C37—21no—
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—21no—
354C2×C4×C37—41no—
355C2×C4×C37—41no—
356C2×C4×C37—41no—
357C2×C4×C37—41no—
358C2×C4×C37—41no—
359C2×C4×C37—41no—
360C2×C4×C37—81no—
361C2×C4×C37#12111yescharacteristic
362C2×C4×C37#12111yescharacteristic
363C2×C4×C37C22×D411yescharacteristic
364C2×C4×C37C22×D411yescharacteristic
365C2×C4×C37C22×D411yescharacteristic
366C2×C4×C37C2×#4111yescharacteristic
367C2×C4×C37H(5,𝔽2)11yescharacteristic
368C2×C4×C37H(5,𝔽2)11yescharacteristic
369C8×C37—21no—
370C8×C37—21no—
371C8×C37—22no—
372C8×C37—22no—
373C8×C37—21no—
374C8×C37—21no—
375C8×C37—41no—
376C8×C37—41no—
377C8×C37—41no—
378C8×C37—41no—
379#25144C3711yesmaximal, characteristic, direct product factor, Sylow
380C22×C37—21no—
381C22×C37—21no—
382C22×C37—21no—
383C22×C37—21no—
384C22×C37—21no—
385C22×C37—21no—
386C22×C37—21no—
387C22×C37—42no—
388C22×C37—42no—
389C22×C37—41no—
390C22×C37—42no—
391C22×C37—42no—
392C22×C37—41no—
393C22×C37—41no—
394C22×C37—82no—
395C22×C37—82no—
396C22×C37—88no—
397C22×C37—82no—
398C22×C37—82no—
399C22×C37—88no—
400C22×C37—81no—
401C22×C37—81no—
402C22×C37—81no—
403C22×C37—81no—
404C22×C37#47112yescomplemented
405C22×C37C2×#12111yescharacteristic
406C22×C37#52511yescharacteristic
407C22×C37#53811yescharacteristic
408C4×C37—21no—
409C4×C37—21no—
410C4×C37—41no—
411C4×C37—41no—
412C4×C37—41no—
413C4×C37—81no—
414C4×C37—81no—
415C4×C37D4211yescharacteristic
416C4×C37D4211yescharacteristic
417C4×C37#54611yescharacteristic
418C4×C37#54611yescharacteristic
419C2×#471C2×C3711yescharacteristic, complemented
420#3056C2×C3711yescharacteristic, complemented
421#3003C2×C3711yescharacteristic
422C2×#450C2×C3711yescharacteristic, complemented
423#2933C2×C3711yescharacteristic, complemented
424C22×#100C2×C3711yescharacteristic, complemented
425#2063C2×C3711yescharacteristic, complemented
426#2051C2×C3711yescharacteristic, complemented
427#2046C2×C3711yescharacteristic, complemented
428#2019C2×C3711yescharacteristic, complemented
429#1977C2×C3711yescharacteristic, complemented
430#1931C2×C3711yescharacteristic, complemented
431#1907C2×C3711yescharacteristic, complemented
432#1901C2×C3711yescharacteristic, complemented
433#1855C2×C3711yescharacteristic, complemented
434C2×C37—21no—
435C2×C37—21no—
436C2×C37—22no—
437C2×C37—41no—
438C2×C37—81no—
439C2×C37—82no—
440C2×C37—82no—
441C2×C37#242411yescharacteristic
442C2×C37C2×#47111yescharacteristic
443C2×C37#306811yescharacteristic
444C23×D4C22×C3711yescharacteristic
445C2×#137C22×C3711yescharacteristic, complemented
446C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
447C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
448C22×SD16C22×C3711yescharacteristic
449C22×SD16C22×C3711yescharacteristic
450C2×#131C22×C3711yescharacteristic, complemented
451C22×M16C22×C3711yescharacteristic
452C22×M16C22×C3711yescharacteristic
453#525C22×C3711yescharacteristic
454C2×C22⋊Q8C22×C3711yescharacteristic
455#471—24no—
456#470—21no—
457#468—21no—
458#467—21no—
459#465—21no—
460#450—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#447—21no—
467#447—21no—
468#436—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108C22×C3711yescharacteristic, complemented
473C2×#108C22×C3711yescharacteristic, complemented
474#428C22×C3711yescharacteristic, complemented
475#424C22×C3711yescharacteristic, complemented
476#419C22×C3711yescharacteristic, complemented
477#418C22×C3711yescharacteristic
478#418C22×C3711yescharacteristic
479#417C22×C3711yescharacteristic, complemented
480C2×#102C22×C3711yescharacteristic
481C2×#102C22×C3711yescharacteristic
482C2×#101C22×C3711yescharacteristic, complemented
483C2×#101C22×C3711yescharacteristic, complemented
484C2×#100—24no—
485C2×#100C22×C3711yescharacteristic
486C2×#100C22×C3711yescharacteristic
487C2×#100C22×C3711yescharacteristic
488C2×#100C22×C3711yescharacteristic
489#408C22×C3711yescharacteristic, complemented
490#407C22×C3711yescharacteristic
491C2×C22⋊C8C22×C3711yescharacteristic
492#405C22×C3711yescharacteristic, complemented
493#343C22×C3711yescharacteristic, complemented
494#343C22×C3711yescharacteristic, complemented
495#341C22×C3711yescharacteristic, complemented
496#341C22×C3711yescharacteristic, complemented
497C37#2514411yescharacteristic, direct product factor, Sylow
498C25—21no—
499C2×#41C23×C3711yescharacteristic
500C22×Q8C23×C3711yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C3711yescharacteristic
511C22×D4C23×C3711yescharacteristic
512C23×C4C23×C3711yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C3711yescharacteristic
543C2×M16C23×C3711yescharacteristic
544C2×M16C23×C3711yescharacteristic
545C2×M16C23×C3711yescharacteristic
546C2×M16C23×C3711yescharacteristic
547C2×M16C23×C3711yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C3711yescharacteristic
552C22×C8C23×C3711yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C3711yescharacteristic
559C22⋊Q8D4×C3711yescharacteristic
560#121D4×C3711yescharacteristic
561#121D4×C3711yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C3711yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C3711yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C3714yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C3711yescharacteristic
598C22⋊C8D4×C3711yescharacteristic
599C22⋊C8D4×C3711yescharacteristic
600C22⋊C8D4×C3711yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C3711yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C3711yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C3712yes—
649C2×D4C2×D4×C3711yescharacteristic
650C2×D4#41×C3712yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C3711yescharacteristic
659C22×C4C2×D4×C3711yescharacteristic
660C22×C4C2×D4×C3711yescharacteristic
661C22×C4C2×D4×C3711yescharacteristic
662C22×C4#41×C3711yescharacteristic
663C22×C4C24×C3711yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C3712yes—
688M16C2×D4×C3712yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C3711yescharacteristic
703C2×C8C2×D4×C3711yescharacteristic
704C2×C8C2×D4×C3711yescharacteristic
705C2×C8C2×D4×C3711yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C3711yescharacteristic
713C4⋊C4C2×D4×C3711yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C3711yescharacteristic
746C23#121×C3711yescharacteristic
747C23C2×#41×C3711yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—41no—
763D4—41no—
764D4—42no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C3711yescharacteristic
791C2×C4#121×C3711yescharacteristic
792C2×C4C22×D4×C3711yescharacteristic
793C2×C4C22×D4×C3711yescharacteristic
794C2×C4C22×D4×C3711yescharacteristic
795C2×C4C2×#41×C3711yescharacteristic
796C2×C4H(5,𝔽2)×C3711yescharacteristic
797C2×C4H(5,𝔽2)×C3711yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—88no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22C37×#47112yescomplemented
833C22C2×#121×C3711yescharacteristic
834C22C37×#52511yescharacteristic
835C22C37×#53811yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C3711yescharacteristic
844C4D42×C3711yescharacteristic
845C4C37×#54611yescharacteristic
846C4C37×#54611yescharacteristic
847C2—21no—
848C2—21no—
849C2—22no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2C37×#242411yescharacteristic
855C2C2×C37×#47111yescharacteristic
856C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3003C2
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. C2×C37×#471C2semidirect
2. C37×#3056C2semidirect
4. C2×C37×#450C2semidirect
5. C37×#2933C2semidirect
6. C22×#100×C37C2semidirect
7. C37×#2063C2semidirect
8. C37×#2051C2semidirect
9. C37×#2046C2semidirect
10. C37×#2019C2semidirect
11. C37×#1977C2semidirect
12. C37×#1931C2semidirect
13. C37×#1907C2semidirect
14. C37×#1901C2semidirect
15. C37×#1855C2semidirect
17. C2×#137×C37C22semidirect
22. C2×#131×C37C22semidirect
44. C2×#108×C37C22semidirect
45. C2×#108×C37C22semidirect
46. C37×#428C22semidirect
47. C37×#424C22semidirect
48. C37×#419C22semidirect
51. C37×#417C22semidirect
54. C2×#101×C37C22semidirect
55. C2×#101×C37C22semidirect
61. C37×#408C22semidirect
64. C37×#405C22semidirect
65. C37×#343C22semidirect
66. C37×#343C22semidirect
67. C37×#341C22semidirect
68. C37×#341C22semidirect
163. #100×C37D4semidirect
379. #25144C37direct (N × H)
404. C22×C37#471semidirect
419. C2×#471C2×C37semidirect
420. #3056C2×C37semidirect
422. C2×#450C2×C37semidirect
423. #2933C2×C37semidirect
424. C22×#100C2×C37semidirect
425. #2063C2×C37semidirect
426. #2051C2×C37semidirect
427. #2046C2×C37semidirect
428. #2019C2×C37semidirect
429. #1977C2×C37semidirect
430. #1931C2×C37semidirect
431. #1907C2×C37semidirect
432. #1901C2×C37semidirect
433. #1855C2×C37semidirect
445. C2×#137C22×C37semidirect
450. C2×#131C22×C37semidirect
472. C2×#108C22×C37semidirect
473. C2×#108C22×C37semidirect
474. #428C22×C37semidirect
475. #424C22×C37semidirect
476. #419C22×C37semidirect
479. #417C22×C37semidirect
482. C2×#101C22×C37semidirect
483. C2×#101C22×C37semidirect
489. #408C22×C37semidirect
492. #405C22×C37semidirect
493. #343C22×C37semidirect
494. #343C22×C37semidirect
495. #341C22×C37semidirect
496. #341C22×C37semidirect
497. C37#25144direct (N × H)
592. #100D4×C37semidirect
832. C22C37×#471semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4712
C37×#30562
C37×#30032
C2×C37×#4502
C37×#29332
C22×#100×C372
C37×#20632
C37×#20512
C37×#20462
C37×#20192
C37×#19772
C37×#19312
C37×#19072
C37×#19012
C37×#18552
#2514437