Finite Group Databasebeta

← C37×#26204 #22647457

Subgroups — C37×#26204 #22647457

Order 9472.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2417C211yesmaximal, characteristic
2D4×C4⋊C4×C37C211yesmaximal, characteristic
3C37×#2100C211yesmaximal, characteristic, complemented
4C37×#2076C211yesmaximal, characteristic, complemented
5C37×#2072C211yesmaximal, characteristic, complemented
6C37×#2036C211yesmaximal, characteristic, complemented
7C37×#1928C211yesmaximal, characteristic, complemented
8C37×#1921C211yesmaximal, characteristic, complemented
9C37×#1892C211yesmaximal, characteristic, complemented
10C37×#1872C211yesmaximal, characteristic, complemented
11C37×#1872C211yesmaximal, characteristic, complemented
12C37×#1869C211yesmaximal, characteristic
13C37×#1852C211yesmaximal, characteristic, complemented
14C37×#1824C211yesmaximal, characteristic, complemented
15C2×C37×#340C211yesmaximal, characteristic, complemented
16C23×C8×C37C2211yescharacteristic
17C2×C22⋊Q8×C37C2211yescharacteristic
18C2×C22⋊Q8×C37C2211yescharacteristic
19C2×C4×D4×C37—21no—
20C2×C4×D4×C37C2211yescharacteristic
21C22×C4⋊C4×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic
24C2×#107×C37C2211yescharacteristic
25C2×#107×C37C2211yescharacteristic
26C2×#103×C37C2211yescharacteristic
27C2×#103×C37C2211yescharacteristic
28C2×#103×C37C2211yescharacteristic
29C2×#103×C37C2211yescharacteristic
30C2×C22⋊C8×C37C2211yescharacteristic
31C2×C22⋊C8×C37C2211yescharacteristic
32C2×C22⋊C8×C37C2211yescharacteristic
33C37×#398—21no—
34C37×#396—21no—
35C37×#391C2211yescharacteristic
36C37×#389—21no—
37C37×#389C2211yescharacteristic
38C37×#386—21no—
39C37×#385—21no—
40C37×#385—21no—
41C37×#384C2211yescharacteristic
42C37×#380—21no—
43C37×#380C2211yescharacteristic
44C37×#380C2211yescharacteristic
45C37×#380C2211yescharacteristic
46C4×C4⋊C4×C37C2211yescharacteristic
47C37×#340C2211yescharacteristic
48C37×#340C2211yescharacteristic
49C37×#340C2211yescharacteristic
50C37×#340C2211yescharacteristic
51C37×#340C2211yescharacteristic
52C37×#340C2211yescharacteristic
53C37×#340C2211yescharacteristic
54C37×#340C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#336C2211yescharacteristic
58C37×#336C2211yescharacteristic
59C22×Q8×C37C2311yescharacteristic
60C22×D4×C37D411yescharacteristic
61C23×C4×C37—21no—
62C23×C4×C37—21no—
63C23×C4×C37—21no—
64C23×C4×C37C2311yescharacteristic
65C23×C4×C37C2311yescharacteristic
66C22×C8×C37—22no—
67C22×C8×C37—41no—
68C22×C8×C37—41no—
69C22×C8×C37C2311yescharacteristic
70C22×C8×C37C2311yescharacteristic
71C22×C8×C37C2311yescharacteristic
72C22×C8×C37C2311yescharacteristic
73C22⋊Q8×C37—22no—
74C22⋊Q8×C37—22no—
75C22⋊Q8×C37—22no—
76C22⋊Q8×C37—41no—
77C4×D4×C37—22no—
78C4×D4×C37—22no—
79C4×D4×C37—44no—
80C2×C4⋊C4×C37—22no—
81C2×C4⋊C4×C37—22no—
82C2×C4⋊C4×C37—22no—
83C2×C4⋊C4×C37—21no—
84C2×C4⋊C4×C37—21no—
85C2×C4⋊C4×C37—21no—
86C2×C4⋊C4×C37—21no—
87C2×C4⋊C4×C37—21no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—41no—
92C2×C4⋊C4×C37—41no—
93C2×C4⋊C4×C37—41no—
94C2×C4⋊C4×C37D411yescharacteristic
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C4⋊C4×C37C2311yescharacteristic
100C2×C4⋊C4×C37C2311yescharacteristic
101C2×C4⋊C4×C37C2311yescharacteristic
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×C37D411yescharacteristic
108C2×C22⋊C4×C37D411yescharacteristic
109C2×C42×C37—21no—
110C2×C42×C37C2311yescharacteristic
111#107×C37—22no—
112#107×C37—41no—
113#103×C37—22no—
114#103×C37—41no—
115#103×C37—41no—
116#103×C37—41no—
117C22⋊C8×C37—22no—
118C22⋊C8×C37—41no—
119C22⋊C8×C37—41no—
120#95×C37—21no—
121#95×C37—21no—
122#95×C37—21no—
123#95×C37—21no—
124#95×C37—21no—
125#95×C37—21no—
126#95×C37—21no—
127C24×C37C2×D411yescharacteristic
128C24×C37C2×D411yescharacteristic
129C2×Q8×C37—21no—
130C2×Q8×C37—21no—
131C2×Q8×C37—21no—
132C2×Q8×C37—21no—
133C2×Q8×C37—21no—
134C2×Q8×C37—21no—
135C2×D4×C37—22no—
136C2×D4×C37—22no—
137C2×D4×C37Q1614yes—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—21no—
142C22×C4×C37—21no—
143C22×C4×C37—21no—
144C22×C4×C37—21no—
145C22×C4×C37—21no—
146C22×C4×C37—21no—
147C22×C4×C37—21no—
148C22×C4×C37—21no—
149C22×C4×C37—21no—
150C22×C4×C37—21no—
151C22×C4×C37—21no—
152C22×C4×C37—21no—
153C22×C4×C37—21no—
154C22×C4×C37—21no—
155C22×C4×C37—21no—
156C22×C4×C37—42no—
157C22×C4×C37—42no—
158C22×C4×C37—42no—
159C22×C4×C37—42no—
160C22×C4×C37—42no—
161C22×C4×C37—42no—
162C22×C4×C37—81no—
163C22×C4×C37—81no—
164C22×C4×C37—81no—
165C22×C4×C37C2×D411yescharacteristic
166C22×C4×C37C2×D411yescharacteristic
167C22×C4×C37C2×D411yescharacteristic
168C22×C4×C37C2×D411yescharacteristic
169C22×C4×C37#4112yes—
170C22×C4×C37#4112yes—
171C22×C4×C37C2411yescharacteristic
172C2×C8×C37—21no—
173C2×C8×C37—21no—
174C2×C8×C37—21no—
175C2×C8×C37—21no—
176C2×C8×C37—21no—
177C2×C8×C37—21no—
178C2×C8×C37—21no—
179C2×C8×C37—21no—
180C2×C8×C37—21no—
181C2×C8×C37—21no—
182C2×C8×C37—21no—
183C2×C8×C37—21no—
184C2×C8×C37—44no—
185C4⋊C4×C37—22no—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—21no—
192C4⋊C4×C37—21no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—42no—
199C4⋊C4×C37—42no—
200C4⋊C4×C37—42no—
201C4⋊C4×C37—42no—
202C4⋊C4×C37—42no—
203C4⋊C4×C37—42no—
204C4⋊C4×C37—81no—
205C4⋊C4×C37—81no—
206C4⋊C4×C37#4112yes—
207C4⋊C4×C37#4112yes—
208C22⋊C4×C37—22no—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—42no—
211C22⋊C4×C37—42no—
212C22⋊C4×C37—42no—
213C22⋊C4×C37—42no—
214C22⋊C4×C37—81no—
215C42×C37—21no—
216C42×C37—21no—
217C42×C37—42no—
218C23×C37—21no—
219C23×C37—21no—
220C23×C37—21no—
221C23×C37—21no—
222C23×C37—21no—
223C23×C37—21no—
224C23×C37—21no—
225C23×C37—21no—
226C23×C37—21no—
227C23×C37—21no—
228C23×C37#12312yes—
229C23×C37C2×Q1612yes—
230C23×C37C2×Q1612yes—
231C23×C37AGL(1,ℤ/8)12yes—
232C23×C37C22×D411yescharacteristic
233Q8×C37—41no—
234Q8×C37—41no—
235Q8×C37—41no—
236Q8×C37—41no—
237D4×C37—28no—
238C2×C4×C37—21no—
239C2×C4×C37—21no—
240C2×C4×C37—21no—
241C2×C4×C37—21no—
242C2×C4×C37—22no—
243C2×C4×C37—22no—
244C2×C4×C37—22no—
245C2×C4×C37—22no—
246C2×C4×C37—21no—
247C2×C4×C37—21no—
248C2×C4×C37—22no—
249C2×C4×C37—22no—
250C2×C4×C37—21no—
251C2×C4×C37—21no—
252C2×C4×C37—21no—
253C2×C4×C37—21no—
254C2×C4×C37—41no—
255C2×C4×C37—41no—
256C2×C4×C37—41no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—41no—
260C2×C4×C37—41no—
261C2×C4×C37—41no—
262C2×C4×C37—41no—
263C2×C4×C37—41no—
264C2×C4×C37—41no—
265C2×C4×C37—41no—
266C2×C4×C37—41no—
267C2×C4×C37—41no—
268C2×C4×C37—41no—
269C2×C4×C37—41no—
270C2×C4×C37—41no—
271C2×C4×C37—41no—
272C2×C4×C37—41no—
273C2×C4×C37—41no—
274C2×C4×C37—41no—
275C2×C4×C37—41no—
276C2×C4×C37—41no—
277C2×C4×C37—41no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—84no—
281C2×C4×C37—84no—
282C2×C4×C37—84no—
283C2×C4×C37#12312yes—
284C2×C4×C37C2×Q1612yes—
285C2×C4×C37C2×#4111yescharacteristic
286C2×C4×C37C2×#4111yescharacteristic
287C2×C4×C37C2×#4111yescharacteristic
288C2×C4×C37C2×#4111yescharacteristic
289C2×C4×C37H(5,𝔽2)11yescharacteristic
290C2×C4×C37H(5,𝔽2)11yescharacteristic
291C8×C37—41no—
292C8×C37—41no—
293C8×C37—41no—
294C8×C37—41no—
295#26204C3711yesmaximal, characteristic, direct product factor, Sylow
296C22×C37—22no—
297C22×C37—22no—
298C22×C37—22no—
299C22×C37—22no—
300C22×C37—22no—
301C22×C37—22no—
302C22×C37—22no—
303C22×C37—22no—
304C22×C37—22no—
305C22×C37—41no—
306C22×C37—41no—
307C22×C37—41no—
308C22×C37—41no—
309C22×C37#48414yes—
310C22×C37C2×#12311yescharacteristic
311C22×C37#54611yescharacteristic
312C22×C37#54611yescharacteristic
313C22×C37C22×Q1611yescharacteristic
314C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C37#57711yescharacteristic
316C22×C37#57711yescharacteristic
317C4×C37—22no—
318C4×C37—22no—
319C4×C37—41no—
320C4×C37—41no—
321C4×C37—42no—
322C4×C37—42no—
323C4×C37—81no—
324C4×C37—81no—
325C4×C37—81no—
326C4×C37—81no—
327C4×C37—81no—
328C4×C37—81no—
329C4×C37#52911yescharacteristic
330C4×C37#53811yescharacteristic
331C4×C37#55311yescharacteristic
332C4×C37#55311yescharacteristic
333#2417C2×C3711yescharacteristic
334D4×C4⋊C4C2×C3711yescharacteristic
335#2100C2×C3711yescharacteristic, complemented
336#2076C2×C3711yescharacteristic, complemented
337#2072C2×C3711yescharacteristic, complemented
338#2036C2×C3711yescharacteristic, complemented
339#1928C2×C3711yescharacteristic, complemented
340#1921C2×C3711yescharacteristic, complemented
341#1892C2×C3711yescharacteristic, complemented
342#1872C2×C3711yescharacteristic, complemented
343#1872C2×C3711yescharacteristic, complemented
344#1869C2×C3711yescharacteristic
345#1852C2×C3711yescharacteristic, complemented
346#1824C2×C3711yescharacteristic, complemented
347C2×#340C2×C3711yescharacteristic, complemented
348C2×C37—24no—
349C2×C37—42no—
350C2×C37#244411yescharacteristic
351C2×C37C2×#48411yescharacteristic
352C2×C37#309911yescharacteristic
353C2×C37#329911yescharacteristic
354C2×C37#329911yescharacteristic
355C2×C37#330611yescharacteristic
356C2×C37#331011yescharacteristic
357C23×C8C22×C3711yescharacteristic
358C2×C22⋊Q8C22×C3711yescharacteristic
359C2×C22⋊Q8C22×C3711yescharacteristic
360C2×C4×D4—21no—
361C2×C4×D4C22×C3711yescharacteristic
362C22×C4⋊C4C22×C3711yescharacteristic
363C22×C4⋊C4C22×C3711yescharacteristic
364C22×C4⋊C4C22×C3711yescharacteristic
365C2×#107C22×C3711yescharacteristic
366C2×#107C22×C3711yescharacteristic
367C2×#103C22×C3711yescharacteristic
368C2×#103C22×C3711yescharacteristic
369C2×#103C22×C3711yescharacteristic
370C2×#103C22×C3711yescharacteristic
371C2×C22⋊C8C22×C3711yescharacteristic
372C2×C22⋊C8C22×C3711yescharacteristic
373C2×C22⋊C8C22×C3711yescharacteristic
374#398—21no—
375#396—21no—
376#391C22×C3711yescharacteristic
377#389—21no—
378#389C22×C3711yescharacteristic
379#386—21no—
380#385—21no—
381#385—21no—
382#384C22×C3711yescharacteristic
383#380—21no—
384#380C22×C3711yescharacteristic
385#380C22×C3711yescharacteristic
386#380C22×C3711yescharacteristic
387C4×C4⋊C4C22×C3711yescharacteristic
388#340C22×C3711yescharacteristic
389#340C22×C3711yescharacteristic
390#340C22×C3711yescharacteristic
391#340C22×C3711yescharacteristic
392#340C22×C3711yescharacteristic
393#340C22×C3711yescharacteristic
394#340C22×C3711yescharacteristic
395#340C22×C3711yescharacteristic
396#340C22×C3711yescharacteristic
397#340C22×C3711yescharacteristic
398#336C22×C3711yescharacteristic
399#336C22×C3711yescharacteristic
400C37#2620411yescharacteristic, direct product factor, Sylow
401C22×Q8C23×C3711yescharacteristic
402C22×D4D4×C3711yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—21no—
406C23×C4C23×C3711yescharacteristic
407C23×C4C23×C3711yescharacteristic
408C22×C8—22no—
409C22×C8—41no—
410C22×C8—41no—
411C22×C8C23×C3711yescharacteristic
412C22×C8C23×C3711yescharacteristic
413C22×C8C23×C3711yescharacteristic
414C22×C8C23×C3711yescharacteristic
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—41no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—44no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4D4×C3711yescharacteristic
437C2×C4⋊C4C23×C3711yescharacteristic
438C2×C4⋊C4C23×C3711yescharacteristic
439C2×C4⋊C4C23×C3711yescharacteristic
440C2×C4⋊C4C23×C3711yescharacteristic
441C2×C4⋊C4C23×C3711yescharacteristic
442C2×C4⋊C4C23×C3711yescharacteristic
443C2×C4⋊C4C23×C3711yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4D4×C3711yescharacteristic
450C2×C22⋊C4D4×C3711yescharacteristic
451C2×C42—21no—
452C2×C42C23×C3711yescharacteristic
453#107—22no—
454#107—41no—
455#103—22no—
456#103—41no—
457#103—41no—
458#103—41no—
459C22⋊C8—22no—
460C22⋊C8—41no—
461C22⋊C8—41no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469C24C2×D4×C3711yescharacteristic
470C24C2×D4×C3711yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4Q16×C3714yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4C2×D4×C3711yescharacteristic
508C22×C4C2×D4×C3711yescharacteristic
509C22×C4C2×D4×C3711yescharacteristic
510C22×C4C2×D4×C3711yescharacteristic
511C22×C4#41×C3712yes—
512C22×C4#41×C3712yes—
513C22×C4C24×C3711yescharacteristic
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—44no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C4⋊C4#41×C3712yes—
549C4⋊C4#41×C3712yes—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—42no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23#123×C3712yes—
571C23C2×Q16×C3712yes—
572C23C2×Q16×C3712yes—
573C23AGL(1,ℤ/8)×C3712yes—
574C23C22×D4×C3711yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—28no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—84no—
624C2×C4—84no—
625C2×C4#123×C3712yes—
626C2×C4C2×Q16×C3712yes—
627C2×C4C2×#41×C3711yescharacteristic
628C2×C4C2×#41×C3711yescharacteristic
629C2×C4C2×#41×C3711yescharacteristic
630C2×C4C2×#41×C3711yescharacteristic
631C2×C4H(5,𝔽2)×C3711yescharacteristic
632C2×C4H(5,𝔽2)×C3711yescharacteristic
633C8—41no—
634C8—41no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22C37×#48414yes—
651C22C2×#123×C3711yescharacteristic
652C22C37×#54611yescharacteristic
653C22C37×#54611yescharacteristic
654C22C22×Q16×C3711yescharacteristic
655C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
656C22C37×#57711yescharacteristic
657C22C37×#57711yescharacteristic
658C4—22no—
659C4—22no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C37×#52911yescharacteristic
671C4C37×#53811yescharacteristic
672C4C37×#55311yescharacteristic
673C4C37×#55311yescharacteristic
674C2—24no—
675C2—42no—
676C2C37×#244411yescharacteristic
677C2C2×C37×#48411yescharacteristic
678C2C37×#309911yescharacteristic
679C2C37×#329911yescharacteristic
680C2C37×#329911yescharacteristic
681C2C37×#330611yescharacteristic
682C2C37×#331011yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC22×D4×C37D4
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
3. C37×#2100C2semidirect
4. C37×#2076C2semidirect
5. C37×#2072C2semidirect
6. C37×#2036C2semidirect
7. C37×#1928C2semidirect
8. C37×#1921C2semidirect
9. C37×#1892C2semidirect
10. C37×#1872C2semidirect
11. C37×#1872C2semidirect
13. C37×#1852C2semidirect
14. C37×#1824C2semidirect
15. C2×C37×#340C2semidirect
295. #26204C37direct (N × H)
335. #2100C2×C37semidirect
336. #2076C2×C37semidirect
337. #2072C2×C37semidirect
338. #2036C2×C37semidirect
339. #1928C2×C37semidirect
340. #1921C2×C37semidirect
341. #1892C2×C37semidirect
342. #1872C2×C37semidirect
343. #1872C2×C37semidirect
345. #1852C2×C37semidirect
346. #1824C2×C37semidirect
347. C2×#340C2×C37semidirect
400. C37#26204direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#24172
D4×C4⋊C4×C372
C37×#21002
C37×#20762
C37×#20722
C37×#20362
C37×#19282
C37×#19212
C37×#18922
C37×#18722
C37×#18692
C37×#18522
C37×#18242
C2×C37×#3402
#2620437