Finite Group Databasebeta

← C37×#24878 #22646131

Subgroups — C37×#24878 #22646131

Order 9472.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#481C211yesmaximal, characteristic, complemented
2C2×C37×#418C211yesmaximal, characteristic, complemented
3C37×#2408C211yesmaximal, characteristic
4C37×#2352C211yesmaximal, characteristic, complemented
5C37×#2092C211yesmaximal, characteristic, complemented
6C37×#2073C211yesmaximal, characteristic, complemented
7C37×#2033C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#1926C211yesmaximal, characteristic, complemented
10C37×#1925C211yesmaximal, characteristic, complemented
11C37×#1874C211yesmaximal, characteristic, complemented
12C37×#1870C211yesmaximal, characteristic, complemented
13C37×#1854C211yesmaximal, characteristic, complemented
14C37×#1809C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×M16×C37C2211yescharacteristic
18C2×#121×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×#120×C37—21no—
21C2×C4×D4×C37C2211yescharacteristic
22C2×#117×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic, complemented
24C37×#481—24no—
25C2×#107×C37C2211yescharacteristic, complemented
26C2×#107×C37C2211yescharacteristic, complemented
27C2×#106×C37C2211yescharacteristic, complemented
28C2×#106×C37C2211yescharacteristic, complemented
29C37×#418—24no—
30C2×#102×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic, complemented
40C2×C22⋊C8×C37C2211yescharacteristic, complemented
41C37×#394—21no—
42C37×#392—21no—
43C37×#390C2211yescharacteristic
44C37×#390C2211yescharacteristic
45C37×#388—21no—
46C37×#387—21no—
47C37×#386—21no—
48C37×#382C2211yescharacteristic, complemented
49C37×#380C2211yescharacteristic
50C37×#380C2211yescharacteristic
51C37×#380C2211yescharacteristic, complemented
52C37×#379—21no—
53C4×C4⋊C4×C37C2211yescharacteristic, complemented
54C4×C22⋊C4×C37—21no—
55C37×#340C2211yescharacteristic, complemented
56C37×#340C2211yescharacteristic, complemented
57C37×#340C2211yescharacteristic, complemented
58C37×#340C2211yescharacteristic, complemented
59C37×#336C2211yescharacteristic, complemented
60C37×#336C2211yescharacteristic, complemented
61C25×C37—21no—
62C22×D4×C37—22no—
63C22×D4×C37—22no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37—22no—
68C22×D4×C37—22no—
69C22×D4×C37—41no—
70C22×D4×C37—41no—
71C22×D4×C37D411yescharacteristic
72C22×D4×C37C2311yescharacteristic
73C22×D4×C37C2311yescharacteristic
74C23×C4×C37—21no—
75C23×C4×C37C2311yescharacteristic
76C23×C4×C37C2311yescharacteristic
77C2×M16×C37—22no—
78C2×M16×C37—22no—
79C2×M16×C37—41no—
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82C22×C8×C37C2311yescharacteristic
83C22×C8×C37C2311yescharacteristic
84#121×C37—22no—
85#121×C37—22no—
86#121×C37—41no—
87#121×C37—41no—
88#120×C37—44no—
89C4×D4×C37—22no—
90C4×D4×C37—22no—
91#117×C37—22no—
92#117×C37—41no—
93C2×C4⋊C4×C37—22no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—41no—
96C2×C4⋊C4×C37D411yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C22⋊C4×C37—21no—
104C2×C22⋊C4×C37—21no—
105C2×C22⋊C4×C37—21no—
106C2×C22⋊C4×C37—21no—
107C2×C22⋊C4×C37—21no—
108C2×C22⋊C4×C37—21no—
109C2×C22⋊C4×C37—21no—
110C2×C22⋊C4×C37—21no—
111C2×C22⋊C4×C37—21no—
112C2×C22⋊C4×C37—21no—
113C2×C22⋊C4×C37D411yescharacteristic
114C2×C22⋊C4×C37D411yescharacteristic
115C2×C42×C37—21no—
116C2×C42×C37—21no—
117C2×C42×C37C2311yescharacteristic
118#107×C37—41no—
119#107×C37—41no—
120#106×C37—22no—
121#106×C37—22no—
122#102×C37—22no—
123#102×C37—22no—
124#102×C37—22no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—41no—
128#102×C37—41no—
129#102×C37D414yescomplemented
130C22⋊C8×C37—22no—
131C22⋊C8×C37—22no—
132C22⋊C8×C37—41no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138#95×C37—21no—
139C24×C37—21no—
140C24×C37—21no—
141C24×C37—42no—
142C24×C37—42no—
143C24×C37—42no—
144C24×C37—42no—
145C24×C37—42no—
146C24×C37—81no—
147C24×C37—81no—
148C24×C37C2×D411yescharacteristic
149C24×C37C2×D411yescharacteristic
150C2×D4×C37—28no—
151C2×D4×C37—22no—
152C2×D4×C37—22no—
153C2×D4×C37—21no—
154C2×D4×C37—21no—
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—44no—
164C2×D4×C37—44no—
165C2×D4×C37—41no—
166C2×D4×C37—42no—
167C2×D4×C37—42no—
168C2×D4×C37—44no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
172C2×D4×C37—42no—
173C2×D4×C37—42no—
174C2×D4×C37—81no—
175C2×D4×C37—81no—
176C2×D4×C37C2×D412yes—
177C2×D4×C37#4112yes—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—21no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
185C22×C4×C37—21no—
186C22×C4×C37—21no—
187C22×C4×C37—21no—
188C22×C4×C37—21no—
189C22×C4×C37—21no—
190C22×C4×C37—21no—
191C22×C4×C37—21no—
192C22×C4×C37—21no—
193C22×C4×C37—21no—
194C22×C4×C37—42no—
195C22×C4×C37—42no—
196C22×C4×C37—81no—
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37C2×D411yescharacteristic
199C22×C4×C37C2×D411yescharacteristic
200C22×C4×C37C2×D411yescharacteristic
201C22×C4×C37#4112yes—
202C22×C4×C37#4112yes—
203C22×C4×C37C2411yescharacteristic
204M16×C37—44no—
205C2×C8×C37—21no—
206C2×C8×C37—21no—
207C2×C8×C37—21no—
208C2×C8×C37—21no—
209C2×C8×C37—21no—
210C2×C8×C37—21no—
211C2×C8×C37—21no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
215C2×C8×C37—21no—
216C2×C8×C37C2×D412yes—
217C4⋊C4×C37—22no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—21no—
221C4⋊C4×C37—21no—
222C4⋊C4×C37—21no—
223C4⋊C4×C37—21no—
224C4⋊C4×C37—21no—
225C4⋊C4×C37—21no—
226C4⋊C4×C37—21no—
227C4⋊C4×C37—21no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—42no—
230C4⋊C4×C37C2×D412yes—
231C22⋊C4×C37—22no—
232C22⋊C4×C37—22no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—42no—
235C22⋊C4×C37—42no—
236C22⋊C4×C37—42no—
237C22⋊C4×C37—42no—
238C22⋊C4×C37—42no—
239C22⋊C4×C37—42no—
240C22⋊C4×C37—81no—
241C22⋊C4×C37—81no—
242C22⋊C4×C37—81no—
243C42×C37—21no—
244C42×C37—21no—
245C42×C37—42no—
246C42×C37—81no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—21no—
253C23×C37—21no—
254C23×C37—21no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—22no—
260C23×C37—22no—
261C23×C37—48no—
262C23×C37—41no—
263C23×C37—41no—
264C23×C37—41no—
265C23×C37—41no—
266C23×C37—41no—
267C23×C37—41no—
268C23×C37—41no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—84no—
275C23×C37—84no—
276C23×C37—84no—
277C23×C37—84no—
278C23×C37—84no—
279C23×C37—84no—
280C23×C37#12312yes—
281C23×C37AGL(1,ℤ/8)12yes—
282C23×C37C22×D411yescharacteristic
283D4×C37—22no—
284D4×C37—22no—
285D4×C37—22no—
286D4×C37—22no—
287D4×C37—48no—
288D4×C37—44no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—84no—
294D4×C37—84no—
295C2×C4×C37—21no—
296C2×C4×C37—21no—
297C2×C4×C37—22no—
298C2×C4×C37—22no—
299C2×C4×C37—22no—
300C2×C4×C37—22no—
301C2×C4×C37—21no—
302C2×C4×C37—21no—
303C2×C4×C37—21no—
304C2×C4×C37—22no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—41no—
312C2×C4×C37—41no—
313C2×C4×C37—41no—
314C2×C4×C37—41no—
315C2×C4×C37—41no—
316C2×C4×C37—41no—
317C2×C4×C37—41no—
318C2×C4×C37—41no—
319C2×C4×C37—41no—
320C2×C4×C37—41no—
321C2×C4×C37—41no—
322C2×C4×C37—41no—
323C2×C4×C37—41no—
324C2×C4×C37—41no—
325C2×C4×C37—41no—
326C2×C4×C37—41no—
327C2×C4×C37—41no—
328C2×C4×C37—41no—
329C2×C4×C37—41no—
330C2×C4×C37—41no—
331C2×C4×C37—41no—
332C2×C4×C37—84no—
333C2×C4×C37#12312yes—
334C2×C4×C37C22×D411yescharacteristic
335C2×C4×C37C2×#4111yescharacteristic
336C2×C4×C37C2×#4111yescharacteristic
337C2×C4×C37C2×#4111yescharacteristic
338C2×C4×C37H(5,𝔽2)11yescharacteristic
339C2×C4×C37H(5,𝔽2)11yescharacteristic
340C8×C37—22no—
341C8×C37—41no—
342C8×C37—41no—
343C8×C37—41no—
344#24878C3711yesmaximal, characteristic, direct product factor, Sylow
345C22×C37—22no—
346C22×C37—22no—
347C22×C37—22no—
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—41no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—41no—
359C22×C37—42no—
360C22×C37—42no—
361C22×C37—42no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—42no—
365C22×C37—816no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37—81no—
369C22×C37—81no—
370C22×C37—81no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37—81no—
374C22×C37C2×#12311yescharacteristic
375C22×C37D4211yescharacteristic
376C22×C37#54611yescharacteristic
377C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C37#57511yescharacteristic
379C22×C37#57611yescharacteristic
380C22×C37#57711yescharacteristic
381C4×C37—22no—
382C4×C37—41no—
383C4×C37—41no—
384C4×C37—41no—
385C4×C37—42no—
386C4×C37—81no—
387C4×C37—81no—
388C4×C37—81no—
389C4×C37—81no—
390C4×C37—81no—
391C4×C37#52511yescharacteristic
392C4×C37#53811yescharacteristic
393C4×C37#54611yescharacteristic
394C4×C37#55111yescharacteristic
395C2×#481C2×C3711yescharacteristic, complemented
396C2×#418C2×C3711yescharacteristic, complemented
397#2408C2×C3711yescharacteristic
398#2352C2×C3711yescharacteristic, complemented
399#2092C2×C3711yescharacteristic, complemented
400#2073C2×C3711yescharacteristic, complemented
401#2033C2×C3711yescharacteristic, complemented
402#2033C2×C3711yescharacteristic, complemented
403#1926C2×C3711yescharacteristic, complemented
404#1925C2×C3711yescharacteristic, complemented
405#1874C2×C3711yescharacteristic, complemented
406#1870C2×C3711yescharacteristic, complemented
407#1854C2×C3711yescharacteristic, complemented
408#1809C2×C3711yescharacteristic, complemented
409#1786C2×C3711yescharacteristic, complemented
410C2×C37—42no—
411C2×C37—42no—
412C2×C37—82no—
413C2×C37—82no—
414C2×C37#241811yescharacteristic
415C2×C37#309411yescharacteristic
416C2×C37#309611yescharacteristic
417C2×C37#326511yescharacteristic
418C2×C37#327311yescharacteristic
419C2×C37#331811yescharacteristic
420C2×C37#332311yescharacteristic
421C23×D4C22×C3711yescharacteristic
422C22×M16C22×C3711yescharacteristic
423C2×#121C22×C3711yescharacteristic
424C2×#121C22×C3711yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C3711yescharacteristic
427C2×#117C22×C3711yescharacteristic
428C22×C4⋊C4C22×C3711yescharacteristic, complemented
429#481—24no—
430C2×#107C22×C3711yescharacteristic, complemented
431C2×#107C22×C3711yescharacteristic, complemented
432C2×#106C22×C3711yescharacteristic, complemented
433C2×#106C22×C3711yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C3711yescharacteristic
436C2×#102C22×C3711yescharacteristic
437C2×#102C22×C3711yescharacteristic
438C2×#102C22×C3711yescharacteristic
439C2×#102C22×C3711yescharacteristic
440C2×#102C22×C3711yescharacteristic
441C2×#102C22×C3711yescharacteristic
442C2×#102C22×C3711yescharacteristic
443C2×C22⋊C8C22×C3711yescharacteristic
444C2×C22⋊C8C22×C3711yescharacteristic, complemented
445C2×C22⋊C8C22×C3711yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390C22×C3711yescharacteristic
449#390C22×C3711yescharacteristic
450#388—21no—
451#387—21no—
452#386—21no—
453#382C22×C3711yescharacteristic, complemented
454#380C22×C3711yescharacteristic
455#380C22×C3711yescharacteristic
456#380C22×C3711yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4C22×C3711yescharacteristic, complemented
459C4×C22⋊C4—21no—
460#340C22×C3711yescharacteristic, complemented
461#340C22×C3711yescharacteristic, complemented
462#340C22×C3711yescharacteristic, complemented
463#340C22×C3711yescharacteristic, complemented
464#336C22×C3711yescharacteristic, complemented
465#336C22×C3711yescharacteristic, complemented
466C37#2487811yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4D4×C3711yescharacteristic
478C22×D4C23×C3711yescharacteristic
479C22×D4C23×C3711yescharacteristic
480C23×C4—21no—
481C23×C4C23×C3711yescharacteristic
482C23×C4C23×C3711yescharacteristic
483C2×M16—22no—
484C2×M16—22no—
485C2×M16—41no—
486C22×C8C23×C3711yescharacteristic
487C22×C8C23×C3711yescharacteristic
488C22×C8C23×C3711yescharacteristic
489C22×C8C23×C3711yescharacteristic
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4D4×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C4⋊C4C23×C3711yescharacteristic
505C2×C4⋊C4C23×C3711yescharacteristic
506C2×C4⋊C4C23×C3711yescharacteristic
507C2×C4⋊C4C23×C3711yescharacteristic
508C2×C4⋊C4C23×C3711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C3711yescharacteristic
520C2×C22⋊C4D4×C3711yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C3711yescharacteristic
524#107—41no—
525#107—41no—
526#106—22no—
527#106—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102D4×C3714yescomplemented
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C3711yescharacteristic
555C24C2×D4×C3711yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C3712yes—
583C2×D4#41×C3712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C3711yescharacteristic
604C22×C4C2×D4×C3711yescharacteristic
605C22×C4C2×D4×C3711yescharacteristic
606C22×C4C2×D4×C3711yescharacteristic
607C22×C4#41×C3712yes—
608C22×C4#41×C3712yes—
609C22×C4C24×C3711yescharacteristic
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8C2×D4×C3712yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C3712yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C3712yes—
687C23AGL(1,ℤ/8)×C3712yes—
688C23C22×D4×C3711yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4#123×C3712yes—
740C2×C4C22×D4×C3711yescharacteristic
741C2×C4C2×#41×C3711yescharacteristic
742C2×C4C2×#41×C3711yescharacteristic
743C2×C4C2×#41×C3711yescharacteristic
744C2×C4H(5,𝔽2)×C3711yescharacteristic
745C2×C4H(5,𝔽2)×C3711yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#123×C3711yescharacteristic
780C22D42×C3711yescharacteristic
781C22C37×#54611yescharacteristic
782C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
783C22C37×#57511yescharacteristic
784C22C37×#57611yescharacteristic
785C22C37×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C37×#52511yescharacteristic
797C4C37×#53811yescharacteristic
798C4C37×#54611yescharacteristic
799C4C37×#55111yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2C37×#241811yescharacteristic
805C2C37×#309411yescharacteristic
806C2C37×#309611yescharacteristic
807C2C37×#326511yescharacteristic
808C2C37×#327311yescharacteristic
809C2C37×#331811yescharacteristic
810C2C37×#332311yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C2×C4×D4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#481C2semidirect
2. C2×C37×#418C2semidirect
4. C37×#2352C2semidirect
5. C37×#2092C2semidirect
6. C37×#2073C2semidirect
7. C37×#2033C2semidirect
8. C37×#2033C2semidirect
9. C37×#1926C2semidirect
10. C37×#1925C2semidirect
11. C37×#1874C2semidirect
12. C37×#1870C2semidirect
13. C37×#1854C2semidirect
14. C37×#1809C2semidirect
15. C37×#1786C2semidirect
23. C22×C4⋊C4×C37C22semidirect
25. C2×#107×C37C22semidirect
26. C2×#107×C37C22semidirect
27. C2×#106×C37C22semidirect
28. C2×#106×C37C22semidirect
39. C2×C22⋊C8×C37C22semidirect
40. C2×C22⋊C8×C37C22semidirect
48. C37×#382C22semidirect
51. C37×#380C22semidirect
53. C4×C4⋊C4×C37C22semidirect
55. C37×#340C22semidirect
56. C37×#340C22semidirect
57. C37×#340C22semidirect
58. C37×#340C22semidirect
59. C37×#336C22semidirect
60. C37×#336C22semidirect
129. #102×C37D4semidirect
344. #24878C37direct (N × H)
395. C2×#481C2×C37semidirect
396. C2×#418C2×C37semidirect
398. #2352C2×C37semidirect
399. #2092C2×C37semidirect
400. #2073C2×C37semidirect
401. #2033C2×C37semidirect
402. #2033C2×C37semidirect
403. #1926C2×C37semidirect
404. #1925C2×C37semidirect
405. #1874C2×C37semidirect
406. #1870C2×C37semidirect
407. #1854C2×C37semidirect
408. #1809C2×C37semidirect
409. #1786C2×C37semidirect
428. C22×C4⋊C4C22×C37semidirect
430. C2×#107C22×C37semidirect
431. C2×#107C22×C37semidirect
432. C2×#106C22×C37semidirect
433. C2×#106C22×C37semidirect
444. C2×C22⋊C8C22×C37semidirect
445. C2×C22⋊C8C22×C37semidirect
453. #382C22×C37semidirect
456. #380C22×C37semidirect
458. C4×C4⋊C4C22×C37semidirect
460. #340C22×C37semidirect
461. #340C22×C37semidirect
462. #340C22×C37semidirect
463. #340C22×C37semidirect
464. #336C22×C37semidirect
465. #336C22×C37semidirect
466. C37#24878direct (N × H)
535. #102D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4812
C2×C37×#4182
C37×#24082
C37×#23522
C37×#20922
C37×#20732
C37×#20332
C37×#19262
C37×#19252
C37×#18742
C37×#18702
C37×#18542
C37×#18092
C37×#17862
#2487837