Finite Group Databasebeta

← C37×#26634 #22647887

Subgroups — C37×#26634 #22647887

Order 9472.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#482C211yesmaximal, characteristic, complemented
2C2×C37×#442C211yesmaximal, characteristic, complemented
3C37×#2428C211yesmaximal, characteristic, complemented
4C37×#2363C211yesmaximal, characteristic, complemented
5C37×#2067C211yesmaximal, characteristic, complemented
6C37×#2011C211yesmaximal, characteristic, complemented
7C37×#1999C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1982C211yesmaximal, characteristic, complemented
10C37×#1936C211yesmaximal, characteristic, complemented
11C37×#1924C211yesmaximal, characteristic, complemented
12C37×#1919C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1875C211yesmaximal, characteristic, complemented
15C37×#1862C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C22×D8×C37C2211yescharacteristic
18C2×#127×C37C2211yescharacteristic
19C2×#121×C37—21no—
20C2×#121×C37C2211yescharacteristic
21C2×#121×C37C2211yescharacteristic
22C2×#121×C37C2211yescharacteristic
23C2×C4×D4×C37C2211yescharacteristic
24C2×C4×D4×C37C2211yescharacteristic
25C2×#117×C37C2211yescharacteristic
26C37×#482—24no—
27C37×#442—24no—
28C2×#107×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#102×C37C2211yescharacteristic
32C2×#102×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C2×C22⋊C8×C37C2211yescharacteristic
41C2×#97×C37C2211yescharacteristic
42C37×#394—21no—
43C37×#392—21no—
44C37×#390—21no—
45C37×#390C2211yescharacteristic
46C37×#390C2211yescharacteristic
47C37×#389C2211yescharacteristic
48C37×#389C2211yescharacteristic
49C37×#388—21no—
50C37×#386—21no—
51C37×#386—21no—
52C4×C4⋊C4×C37C2211yescharacteristic
53C4×C22⋊C4×C37—21no—
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×D4×C37—21no—
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37C2311yescharacteristic
67C22×D4×C37C2311yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C23×C4×C37—21no—
70C23×C4×C37—21no—
71C23×C4×C37C2311yescharacteristic
72C2×D8×C37—22no—
73C2×D8×C37—22no—
74C2×D8×C37—22no—
75C2×D8×C37—22no—
76C2×D8×C37—41no—
77C2×D8×C37—41no—
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82#127×C37—22no—
83#127×C37—41no—
84#121×C37—22no—
85#121×C37—22no—
86#121×C37—22no—
87#121×C37—22no—
88#121×C37—44no—
89#121×C37—41no—
90#121×C37—41no—
91C4×D4×C37—22no—
92C4×D4×C37—22no—
93C4×D4×C37—41no—
94C4×D4×C37—41no—
95#117×C37—22no—
96#117×C37—41no—
97C2×C4⋊C4×C37—21no—
98C2×C4⋊C4×C37—21no—
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
102C2×C4⋊C4×C37C2311yescharacteristic
103C2×C4⋊C4×C37C2311yescharacteristic
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—21no—
114C2×C22⋊C4×C37D411yescharacteristic
115C2×C22⋊C4×C37D411yescharacteristic
116C2×C42×C37—21no—
117C2×C42×C37—21no—
118C2×C42×C37C2311yescharacteristic
119C2×C42×C37C2311yescharacteristic
120#107×C37—22no—
121#106×C37D414yescomplemented
122C4⋊C8×C37—41no—
123#102×C37—22no—
124#102×C37—22no—
125#102×C37—22no—
126#102×C37—22no—
127#102×C37—22no—
128#102×C37—22no—
129#102×C37—41no—
130#102×C37—41no—
131C22⋊C8×C37—22no—
132C22⋊C8×C37—41no—
133#97×C37—22no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37D411yescharacteristic
138#95×C37D411yescharacteristic
139C24×C37—21no—
140C24×C37—21no—
141C24×C37—21no—
142C24×C37C2×D411yescharacteristic
143C2×D4×C37—24no—
144C2×D4×C37—21no—
145C2×D4×C37—21no—
146C2×D4×C37—21no—
147C2×D4×C37—21no—
148C2×D4×C37—21no—
149C2×D4×C37—21no—
150C2×D4×C37—21no—
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—42no—
161C2×D4×C37—42no—
162C2×D4×C37—42no—
163C2×D4×C37—42no—
164C2×D4×C37—42no—
165C2×D4×C37—42no—
166C2×D4×C37—42no—
167C2×D4×C37—42no—
168C2×D4×C37—81no—
169C2×D4×C37—81no—
170C2×D4×C37—81no—
171C2×D4×C37—81no—
172C2×D4×C37—81no—
173C2×D4×C37—81no—
174C2×D4×C37#4112yes—
175C2×D4×C37#4112yes—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
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—42no—
188C22×C4×C37—42no—
189C22×C4×C37—42no—
190C22×C4×C37—42no—
191C22×C4×C37—81no—
192C22×C4×C37—81no—
193C22×C4×C37C2×D411yescharacteristic
194C22×C4×C37C2×D411yescharacteristic
195C22×C4×C37C2×D411yescharacteristic
196C22×C4×C37C2×D411yescharacteristic
197C22×C4×C37C2×D411yescharacteristic
198C22×C4×C37C2411yescharacteristic
199D8×C37—28no—
200D8×C37—44no—
201C2×C8×C37—21no—
202C2×C8×C37—21no—
203C2×C8×C37—21no—
204C2×C8×C37—21no—
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×C37C2×D412yes—
213C4⋊C4×C37—21no—
214C4⋊C4×C37—21no—
215C4⋊C4×C37—21no—
216C4⋊C4×C37—21no—
217C4⋊C4×C37—21no—
218C4⋊C4×C37—21no—
219C4⋊C4×C37—21no—
220C4⋊C4×C37—42no—
221C4⋊C4×C37—81no—
222C4⋊C4×C37C2×D412yes—
223C4⋊C4×C37C2×D412yes—
224C4⋊C4×C37#4112yes—
225C22⋊C4×C37—24no—
226C22⋊C4×C37—22no—
227C22⋊C4×C37—41no—
228C22⋊C4×C37—42no—
229C22⋊C4×C37—42no—
230C22⋊C4×C37—42no—
231C22⋊C4×C37—42no—
232C22⋊C4×C37—42no—
233C22⋊C4×C37—42no—
234C22⋊C4×C37—42no—
235C22⋊C4×C37—81no—
236C22⋊C4×C37—81no—
237C42×C37—21no—
238C42×C37—21no—
239C42×C37—21no—
240C42×C37—21no—
241C42×C37—42no—
242C42×C37—81no—
243C23×C37—22no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—22no—
247C23×C37—21no—
248C23×C37—21no—
249C23×C37—21no—
250C23×C37—21no—
251C23×C37—21no—
252C23×C37—41no—
253C23×C37—41no—
254C23×C37—41no—
255C23×C37—41no—
256C23×C37—41no—
257C23×C37—41no—
258C23×C37—41no—
259C23×C37—41no—
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×C37C22×D411yescharacteristic
272D4×C37—22no—
273D4×C37—22no—
274D4×C37—22no—
275D4×C37—22no—
276D4×C37—41no—
277D4×C37—41no—
278D4×C37—41no—
279D4×C37—41no—
280D4×C37—41no—
281D4×C37—41no—
282D4×C37—41no—
283D4×C37—41no—
284D4×C37—84no—
285D4×C37—84no—
286D4×C37—84no—
287D4×C37—84no—
288D4×C37—84no—
289C2×C4×C37—21no—
290C2×C4×C37—21no—
291C2×C4×C37—21no—
292C2×C4×C37—22no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—21no—
296C2×C4×C37—22no—
297C2×C4×C37—22no—
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—41no—
307C2×C4×C37—41no—
308C2×C4×C37—41no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
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—84no—
323C2×C4×C37—84no—
324C2×C4×C37AGL(1,ℤ/8)12yes—
325C2×C4×C37C22×D411yescharacteristic
326C2×C4×C37C2×#4111yescharacteristic
327C2×C4×C37C2×#4111yescharacteristic
328C2×C4×C37C2×#4111yescharacteristic
329C2×C4×C37H(5,𝔽2)11yescharacteristic
330C2×C4×C37H(5,𝔽2)11yescharacteristic
331C8×C37—22no—
332C8×C37—41no—
333C8×C37—41no—
334C8×C37—41no—
335#26634C3711yesmaximal, characteristic, direct product factor, Sylow
336C22×C37—41no—
337C22×C37—42no—
338C22×C37—41no—
339C22×C37—42no—
340C22×C37—41no—
341C22×C37—42no—
342C22×C37—42no—
343C22×C37—41no—
344C22×C37—41no—
345C22×C37—41no—
346C22×C37—42no—
347C22×C37—42no—
348C22×C37—41no—
349C22×C37—81no—
350C22×C37—81no—
351C22×C37—81no—
352C22×C37—81no—
353C22×C37—81no—
354C22×C37—81no—
355C22×C37—81no—
356C22×C37—81no—
357C22×C37—81no—
358C22×C37—81no—
359C22×C37—81no—
360C22×C37—81no—
361C22×C37—81no—
362C22×C37—81no—
363C22×C37—81no—
364C22×C37#52511yescharacteristic
365C22×C37D4211yescharacteristic
366C22×C37#54611yescharacteristic
367C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C37#57511yescharacteristic
369C22×C37#57611yescharacteristic
370C22×C37#57611yescharacteristic
371C4×C37—22no—
372C4×C37—42no—
373C4×C37—41no—
374C4×C37—41no—
375C4×C37—42no—
376C4×C37—41no—
377C4×C37—42no—
378C4×C37—41no—
379C4×C37—81no—
380C4×C37—81no—
381C4×C37#52511yescharacteristic
382C4×C37#53811yescharacteristic
383C4×C37#55011yescharacteristic
384C4×C37#55311yescharacteristic
385C2×#482C2×C3711yescharacteristic, complemented
386C2×#442C2×C3711yescharacteristic, complemented
387#2428C2×C3711yescharacteristic, complemented
388#2363C2×C3711yescharacteristic, complemented
389#2067C2×C3711yescharacteristic, complemented
390#2011C2×C3711yescharacteristic, complemented
391#1999C2×C3711yescharacteristic, complemented
392#1999C2×C3711yescharacteristic, complemented
393#1982C2×C3711yescharacteristic, complemented
394#1936C2×C3711yescharacteristic, complemented
395#1924C2×C3711yescharacteristic, complemented
396#1919C2×C3711yescharacteristic, complemented
397#1879C2×C3711yescharacteristic, complemented
398#1875C2×C3711yescharacteristic, complemented
399#1862C2×C3711yescharacteristic, complemented
400C2×C37—81no—
401C2×C37—82no—
402C2×C37—82no—
403C2×C37—161no—
404C2×C37#245611yescharacteristic
405C2×C37#311511yescharacteristic
406C2×C37#312211yescharacteristic
407C2×C37#326811yescharacteristic
408C2×C37#327411yescharacteristic
409C2×C37#331811yescharacteristic
410C2×C37#331911yescharacteristic
411C22×D8C22×C3711yescharacteristic
412C22×D8C22×C3711yescharacteristic
413C2×#127C22×C3711yescharacteristic
414C2×#121—21no—
415C2×#121C22×C3711yescharacteristic
416C2×#121C22×C3711yescharacteristic
417C2×#121C22×C3711yescharacteristic
418C2×C4×D4C22×C3711yescharacteristic
419C2×C4×D4C22×C3711yescharacteristic
420C2×#117C22×C3711yescharacteristic
421#482—24no—
422#442—24no—
423C2×#107C22×C3711yescharacteristic
424C2×#106C22×C3711yescharacteristic
425C2×C4⋊C8C22×C3711yescharacteristic
426C2×#102C22×C3711yescharacteristic
427C2×#102C22×C3711yescharacteristic
428C2×#102C22×C3711yescharacteristic
429C2×#102C22×C3711yescharacteristic
430C2×#102C22×C3711yescharacteristic
431C2×#102C22×C3711yescharacteristic
432C2×#102C22×C3711yescharacteristic
433C2×#102C22×C3711yescharacteristic
434C2×C22⋊C8C22×C3711yescharacteristic
435C2×C22⋊C8C22×C3711yescharacteristic
436C2×#97C22×C3711yescharacteristic
437#394—21no—
438#392—21no—
439#390—21no—
440#390C22×C3711yescharacteristic
441#390C22×C3711yescharacteristic
442#389C22×C3711yescharacteristic
443#389C22×C3711yescharacteristic
444#388—21no—
445#386—21no—
446#386—21no—
447C4×C4⋊C4C22×C3711yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4C22×C3711yescharacteristic
450#340C22×C3711yescharacteristic
451#340C22×C3711yescharacteristic
452#340C22×C3711yescharacteristic
453#340C22×C3711yescharacteristic
454#336C22×C3711yescharacteristic
455#336C22×C3711yescharacteristic
456C37#2663411yescharacteristic, direct product factor, Sylow
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C3711yescharacteristic
463C22×D4C23×C3711yescharacteristic
464C22×D4C23×C3711yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C3711yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C3711yescharacteristic
475C22×C8C23×C3711yescharacteristic
476C22×C8C23×C3711yescharacteristic
477C22×C8C23×C3711yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C3711yescharacteristic
496C2×C4⋊C4C23×C3711yescharacteristic
497C2×C4⋊C4C23×C3711yescharacteristic
498C2×C4⋊C4C23×C3711yescharacteristic
499C2×C4⋊C4C23×C3711yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C3711yescharacteristic
511C2×C22⋊C4D4×C3711yescharacteristic
512C2×C42—21no—
513C2×C42—21no—
514C2×C42C23×C3711yescharacteristic
515C2×C42C23×C3711yescharacteristic
516#107—22no—
517#106D4×C3714yescomplemented
518C4⋊C8—41no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—41no—
529#97—22no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C3711yescharacteristic
534#95D4×C3711yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C3711yescharacteristic
539C2×D4—24no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4#41×C3712yes—
571C2×D4#41×C3712yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C3711yescharacteristic
590C22×C4C2×D4×C3711yescharacteristic
591C22×C4C2×D4×C3711yescharacteristic
592C22×C4C2×D4×C3711yescharacteristic
593C22×C4C2×D4×C3711yescharacteristic
594C22×C4C24×C3711yescharacteristic
595D8—28no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8C2×D4×C3712yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C3712yes—
619C4⋊C4C2×D4×C3712yes—
620C4⋊C4#41×C3712yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C22×D4×C3711yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4AGL(1,ℤ/8)×C3712yes—
721C2×C4C22×D4×C3711yescharacteristic
722C2×C4C2×#41×C3711yescharacteristic
723C2×C4C2×#41×C3711yescharacteristic
724C2×C4C2×#41×C3711yescharacteristic
725C2×C4H(5,𝔽2)×C3711yescharacteristic
726C2×C4H(5,𝔽2)×C3711yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—42no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C37×#52511yescharacteristic
760C22D42×C3711yescharacteristic
761C22C37×#54611yescharacteristic
762C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
763C22C37×#57511yescharacteristic
764C22C37×#57611yescharacteristic
765C22C37×#57611yescharacteristic
766C4—22no—
767C4—42no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—42no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4C37×#52511yescharacteristic
777C4C37×#53811yescharacteristic
778C4C37×#55011yescharacteristic
779C4C37×#55311yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C37×#245611yescharacteristic
785C2C37×#311511yescharacteristic
786C2C37×#312211yescharacteristic
787C2C37×#326811yescharacteristic
788C2C37×#327411yescharacteristic
789C2C37×#331811yescharacteristic
790C2C37×#331911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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
1. C2×C37×#482C2semidirect
2. C2×C37×#442C2semidirect
3. C37×#2428C2semidirect
4. C37×#2363C2semidirect
5. C37×#2067C2semidirect
6. C37×#2011C2semidirect
7. C37×#1999C2semidirect
8. C37×#1999C2semidirect
9. C37×#1982C2semidirect
10. C37×#1936C2semidirect
11. C37×#1924C2semidirect
12. C37×#1919C2semidirect
13. C37×#1879C2semidirect
14. C37×#1875C2semidirect
15. C37×#1862C2semidirect
121. #106×C37D4semidirect
335. #26634C37direct (N × H)
385. C2×#482C2×C37semidirect
386. C2×#442C2×C37semidirect
387. #2428C2×C37semidirect
388. #2363C2×C37semidirect
389. #2067C2×C37semidirect
390. #2011C2×C37semidirect
391. #1999C2×C37semidirect
392. #1999C2×C37semidirect
393. #1982C2×C37semidirect
394. #1936C2×C37semidirect
395. #1924C2×C37semidirect
396. #1919C2×C37semidirect
397. #1879C2×C37semidirect
398. #1875C2×C37semidirect
399. #1862C2×C37semidirect
456. C37#26634direct (N × H)
517. #106D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4822
C2×C37×#4422
C37×#24282
C37×#23632
C37×#20672
C37×#20112
C37×#19992
C37×#19822
C37×#19362
C37×#19242
C37×#19192
C37×#18792
C37×#18752
C37×#18622
#2663437