Finite Group Databasebeta

← C37×#24909 #22646162

Subgroups — C37×#24909 #22646162

Order 9472.

1198 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×#447C211yesmaximal, characteristic
2C2×C37×#442C211yesmaximal, characteristic, complemented
3C37×#2420C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C37C211yesmaximal, characteristic, complemented
5C37×#2092C211yesmaximal, characteristic, complemented
6C37×#2077C211yesmaximal, characteristic, complemented
7C37×#2054C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#1936C211yesmaximal, characteristic, complemented
10C37×#1924C211yesmaximal, characteristic, complemented
11C37×#1879C211yesmaximal, characteristic, complemented
12C37×#1879C211yesmaximal, characteristic, complemented
13C37×#1862C211yesmaximal, characteristic, complemented
14C37×#1804C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×C4×D4×C37C2211yescharacteristic
21C2×C4×D4×C37C2211yescharacteristic
22C2×C4×D4×C37C2211yescharacteristic, complemented
23C22×C22⋊C4×C37—21no—
24C37×#447—24no—
25C37×#442—24no—
26C2×#107×C37C2211yescharacteristic, complemented
27C2×#106×C37C2211yescharacteristic, complemented
28C2×C4⋊C8×C37C2211yescharacteristic, complemented
29C2×#102×C37C2211yescharacteristic
30C2×#102×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic, complemented
36C2×#102×C37C2211yescharacteristic, complemented
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×C22⋊C8×C37C2211yescharacteristic
39C2×#97×C37C2211yescharacteristic, complemented
40C37×#397—21no—
41C37×#394—21no—
42C37×#390C2211yescharacteristic
43C37×#390C2211yescharacteristic
44C37×#390C2211yescharacteristic, complemented
45C37×#389C2211yescharacteristic, complemented
46C37×#386—21no—
47C37×#386—21no—
48C37×#386—21no—
49C37×#382C2211yescharacteristic, complemented
50C37×#381—21no—
51C37×#380C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C37×#379—21no—
54C4×C22⋊C4×C37C2211yescharacteristic
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—22no—
65C22×D4×C37—22no—
66C22×D4×C37—21no—
67C22×D4×C37—21no—
68C22×D4×C37—41no—
69C22×D4×C37—41no—
70C22×D4×C37C2311yescharacteristic
71C22×D4×C37C2311yescharacteristic
72C22×D4×C37C2311yescharacteristic
73C23×C4×C37—21no—
74C23×C4×C37—21no—
75C23×C4×C37—21no—
76C23×C4×C37C2311yescharacteristic
77C2×D8×C37—22no—
78C2×D8×C37—22no—
79C2×D8×C37—22no—
80C2×D8×C37—22no—
81C2×D8×C37—41no—
82C2×D8×C37D414yes—
83C22×C8×C37C2311yescharacteristic
84C22×C8×C37C2311yescharacteristic
85C22×C8×C37C2311yescharacteristic
86C22×C8×C37C2311yescharacteristic
87#121×C37—22no—
88#121×C37—41no—
89C4×D4×C37—22no—
90C4×D4×C37—22no—
91C4×D4×C37—22no—
92C4×D4×C37—41no—
93C4×D4×C37—41no—
94C4×D4×C37—41no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C22⋊C4×C37—21no—
102C2×C22⋊C4×C37—21no—
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×C37—44no—
114C2×C22⋊C4×C37D411yescharacteristic
115C2×C22⋊C4×C37D411yescharacteristic
116C2×C42×C37C2311yescharacteristic
117C2×C42×C37C2311yescharacteristic
118#107×C37—41no—
119#106×C37—22no—
120C4⋊C8×C37—41no—
121#102×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—
129C22⋊C8×C37—22no—
130C22⋊C8×C37—41no—
131#97×C37—22no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37D411yescharacteristic
138#95×C37D411yescharacteristic
139C24×C37—21no—
140C24×C37—24no—
141C24×C37—21no—
142C24×C37—21no—
143C24×C37—42no—
144C24×C37—42no—
145C24×C37—42no—
146C24×C37—42no—
147C24×C37—81no—
148C24×C37—81no—
149C24×C37C2×D411yescharacteristic
150C2×D4×C37—24no—
151C2×D4×C37—21no—
152C2×D4×C37—21no—
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—21no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—44no—
167C2×D4×C37—44no—
168C2×D4×C37—44no—
169C2×D4×C37—44no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
172C2×D4×C37—81no—
173C2×D4×C37C2×D412yes—
174C2×D4×C37C2×D412yes—
175C2×D4×C37#4112yes—
176C2×D4×C37#4112yes—
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—42no—
190C22×C4×C37—42no—
191C22×C4×C37—42no—
192C22×C4×C37—42no—
193C22×C4×C37—42no—
194C22×C4×C37—42no—
195C22×C4×C37—81no—
196C22×C4×C37—81no—
197C22×C4×C37—81no—
198C22×C4×C37C2×D411yescharacteristic
199C22×C4×C37C2×D411yescharacteristic
200C22×C4×C37C2×D411yescharacteristic
201C22×C4×C37C2×D411yescharacteristic
202C22×C4×C37C2×D411yescharacteristic
203C22×C4×C37C2411yescharacteristic
204D8×C37—28no—
205D8×C37—44no—
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×C37—21no—
217C2×C8×C37C2×D412yes—
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—81no—
229C22⋊C4×C37—22no—
230C22⋊C4×C37—41no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—42no—
235C22⋊C4×C37—42no—
236C22⋊C4×C37—42no—
237C22⋊C4×C37—42no—
238C22⋊C4×C37—81no—
239C22⋊C4×C37—81no—
240C22⋊C4×C37—81no—
241C22⋊C4×C37—81no—
242C22⋊C4×C37—81no—
243C42×C37—21no—
244C42×C37—21no—
245C42×C37—21no—
246C42×C37—21no—
247C23×C37—21no—
248C23×C37—22no—
249C23×C37—22no—
250C23×C37—21no—
251C23×C37—22no—
252C23×C37—21no—
253C23×C37—21no—
254C23×C37—21no—
255C23×C37—21no—
256C23×C37—22no—
257C23×C37—22no—
258C23×C37—48no—
259C23×C37—48no—
260C23×C37—41no—
261C23×C37—41no—
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—41no—
275C23×C37—41no—
276C23×C37—84no—
277C23×C37—84no—
278C23×C37—84no—
279C23×C37—84no—
280C23×C37—84no—
281C23×C37AGL(1,ℤ/8)12yes—
282C23×C37C22×D411yescharacteristic
283D4×C37—22no—
284D4×C37—22no—
285D4×C37—22no—
286D4×C37—22no—
287D4×C37—22no—
288D4×C37—22no—
289D4×C37—22no—
290D4×C37—48no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—41no—
294D4×C37—41no—
295D4×C37—84no—
296D4×C37#12314yes—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
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—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
310C2×C4×C37—21no—
311C2×C4×C37—21no—
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—84no—
332C2×C4×C37—84no—
333C2×C4×C37—84no—
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#24909C3711yesmaximal, characteristic, direct product factor, Sylow
345C22×C37—22no—
346C22×C37—24no—
347C22×C37—22no—
348C22×C37—22no—
349C22×C37—42no—
350C22×C37—41no—
351C22×C37—42no—
352C22×C37—41no—
353C22×C37—42no—
354C22×C37—41no—
355C22×C37—42no—
356C22×C37—42no—
357C22×C37—41no—
358C22×C37—42no—
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×C37#52511yescharacteristic
375C22×C37D4211yescharacteristic
376C22×C37#54611yescharacteristic
377C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C37#57511yescharacteristic
379C22×C37#57611yescharacteristic
380C22×C37#57611yescharacteristic
381C4×C37—41no—
382C4×C37—41no—
383C4×C37—41no—
384C4×C37—41no—
385C4×C37—41no—
386C4×C37—81no—
387C4×C37—81no—
388C4×C37—81no—
389C4×C37—81no—
390C4×C37—81no—
391C4×C37C2×#12311yescharacteristic
392C4×C37#53811yescharacteristic
393C4×C37#54611yescharacteristic
394C4×C37#55111yescharacteristic
395C2×#447C2×C3711yescharacteristic
396C2×#442C2×C3711yescharacteristic, complemented
397#2420C2×C3711yescharacteristic, complemented
398D4×C22⋊C4C2×C3711yescharacteristic, complemented
399#2092C2×C3711yescharacteristic, complemented
400#2077C2×C3711yescharacteristic, complemented
401#2054C2×C3711yescharacteristic, complemented
402#2033C2×C3711yescharacteristic, complemented
403#1936C2×C3711yescharacteristic, complemented
404#1924C2×C3711yescharacteristic, complemented
405#1879C2×C3711yescharacteristic, complemented
406#1879C2×C3711yescharacteristic, complemented
407#1862C2×C3711yescharacteristic, complemented
408#1804C2×C3711yescharacteristic, complemented
409#1786C2×C3711yescharacteristic, complemented
410C2×C37—42no—
411C2×C37—44no—
412C2×C37—82no—
413C2×C37—82no—
414C2×C37#241811yescharacteristic
415C2×C37#311411yescharacteristic
416C2×C37#312211yescharacteristic
417C2×C37#326411yescharacteristic
418C2×C37#327311yescharacteristic
419C2×C37#331811yescharacteristic
420C2×C37#331911yescharacteristic
421C23×D4C22×C3711yescharacteristic
422C22×D8C22×C3711yescharacteristic
423C22×D8C22×C3711yescharacteristic
424C2×#121C22×C3711yescharacteristic
425C2×C4×D4C22×C3711yescharacteristic
426C2×C4×D4C22×C3711yescharacteristic
427C2×C4×D4C22×C3711yescharacteristic, complemented
428C22×C22⋊C4—21no—
429#447—24no—
430#442—24no—
431C2×#107C22×C3711yescharacteristic, complemented
432C2×#106C22×C3711yescharacteristic, complemented
433C2×C4⋊C8C22×C3711yescharacteristic, complemented
434C2×#102C22×C3711yescharacteristic
435C2×#102C22×C3711yescharacteristic
436C2×#102C22×C3711yescharacteristic
437C2×#102C22×C3711yescharacteristic
438C2×#102C22×C3711yescharacteristic
439C2×#102C22×C3711yescharacteristic
440C2×#102C22×C3711yescharacteristic, complemented
441C2×#102C22×C3711yescharacteristic, complemented
442C2×C22⋊C8C22×C3711yescharacteristic
443C2×C22⋊C8C22×C3711yescharacteristic
444C2×#97C22×C3711yescharacteristic, complemented
445#397—21no—
446#394—21no—
447#390C22×C3711yescharacteristic
448#390C22×C3711yescharacteristic
449#390C22×C3711yescharacteristic, complemented
450#389C22×C3711yescharacteristic, complemented
451#386—21no—
452#386—21no—
453#386—21no—
454#382C22×C3711yescharacteristic, complemented
455#381—21no—
456#380C22×C3711yescharacteristic
457#380C22×C3711yescharacteristic
458#379—21no—
459C4×C22⋊C4C22×C3711yescharacteristic
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#2490911yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C3711yescharacteristic
477C22×D4C23×C3711yescharacteristic
478C22×D4C23×C3711yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C3711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C3714yes—
489C22×C8C23×C3711yescharacteristic
490C22×C8C23×C3711yescharacteristic
491C22×C8C23×C3711yescharacteristic
492C22×C8C23×C3711yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C3711yescharacteristic
503C2×C4⋊C4C23×C3711yescharacteristic
504C2×C4⋊C4C23×C3711yescharacteristic
505C2×C4⋊C4C23×C3711yescharacteristic
506C2×C4⋊C4C23×C3711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
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⋊C4—44no—
520C2×C22⋊C4D4×C3711yescharacteristic
521C2×C22⋊C4D4×C3711yescharacteristic
522C2×C42C23×C3711yescharacteristic
523C2×C42C23×C3711yescharacteristic
524#107—41no—
525#106—22no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537#97—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C3711yescharacteristic
544#95D4×C3711yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C3711yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
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—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C3712yes—
580C2×D4C2×D4×C3712yes—
581C2×D4#41×C3712yes—
582C2×D4#41×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—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C3711yescharacteristic
605C22×C4C2×D4×C3711yescharacteristic
606C22×C4C2×D4×C3711yescharacteristic
607C22×C4C2×D4×C3711yescharacteristic
608C22×C4C2×D4×C3711yescharacteristic
609C22×C4C24×C3711yescharacteristic
610D8—28no—
611D8—44no—
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×C8—21no—
623C2×C8C2×D4×C3712yes—
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—81no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
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—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23AGL(1,ℤ/8)×C3712yes—
688C23C22×D4×C3711yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C3714yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
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—84no—
738C2×C4—84no—
739C2×C4—84no—
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—24no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—42no—
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—
779C22C37×#52511yescharacteristic
780C22D42×C3711yescharacteristic
781C22C37×#54611yescharacteristic
782C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
783C22C37×#57511yescharacteristic
784C22C37×#57611yescharacteristic
785C22C37×#57611yescharacteristic
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C3711yescharacteristic
797C4C37×#53811yescharacteristic
798C4C37×#54611yescharacteristic
799C4C37×#55111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2C37×#241811yescharacteristic
805C2C37×#311411yescharacteristic
806C2C37×#312211yescharacteristic
807C2C37×#326411yescharacteristic
808C2C37×#327311yescharacteristic
809C2C37×#331811yescharacteristic
810C2C37×#331911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C4×C22⋊C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#442C2semidirect
3. C37×#2420C2semidirect
4. D4×C22⋊C4×C37C2semidirect
5. C37×#2092C2semidirect
6. C37×#2077C2semidirect
7. C37×#2054C2semidirect
8. C37×#2033C2semidirect
9. C37×#1936C2semidirect
10. C37×#1924C2semidirect
11. C37×#1879C2semidirect
12. C37×#1879C2semidirect
13. C37×#1862C2semidirect
14. C37×#1804C2semidirect
15. C37×#1786C2semidirect
22. C2×C4×D4×C37C22semidirect
26. C2×#107×C37C22semidirect
27. C2×#106×C37C22semidirect
28. C2×C4⋊C8×C37C22semidirect
35. C2×#102×C37C22semidirect
36. C2×#102×C37C22semidirect
39. C2×#97×C37C22semidirect
44. C37×#390C22semidirect
45. C37×#389C22semidirect
49. C37×#382C22semidirect
55. C37×#340C22semidirect
56. C37×#340C22semidirect
57. C37×#340C22semidirect
58. C37×#340C22semidirect
59. C37×#336C22semidirect
60. C37×#336C22semidirect
344. #24909C37direct (N × H)
396. C2×#442C2×C37semidirect
397. #2420C2×C37semidirect
398. D4×C22⋊C4C2×C37semidirect
399. #2092C2×C37semidirect
400. #2077C2×C37semidirect
401. #2054C2×C37semidirect
402. #2033C2×C37semidirect
403. #1936C2×C37semidirect
404. #1924C2×C37semidirect
405. #1879C2×C37semidirect
406. #1879C2×C37semidirect
407. #1862C2×C37semidirect
408. #1804C2×C37semidirect
409. #1786C2×C37semidirect
427. C2×C4×D4C22×C37semidirect
431. C2×#107C22×C37semidirect
432. C2×#106C22×C37semidirect
433. C2×C4⋊C8C22×C37semidirect
440. C2×#102C22×C37semidirect
441. C2×#102C22×C37semidirect
444. C2×#97C22×C37semidirect
449. #390C22×C37semidirect
450. #389C22×C37semidirect
454. #382C22×C37semidirect
460. #340C22×C37semidirect
461. #340C22×C37semidirect
462. #340C22×C37semidirect
463. #340C22×C37semidirect
464. #336C22×C37semidirect
465. #336C22×C37semidirect
466. C37#24909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4472
C2×C37×#4422
C37×#24202
D4×C22⋊C4×C372
C37×#20922
C37×#20772
C37×#20542
C37×#20332
C37×#19362
C37×#19242
C37×#18792
C37×#18622
C37×#18042
C37×#17862
#2490937