Finite Group Databasebeta

← C37×#26239 #22647492

Subgroups — C37×#26239 #22647492

Order 9472.

918 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#482C211yesmaximal, characteristic, complemented
2C2×C37×#483C211yesmaximal, characteristic, complemented
3C37×#2540C211yesmaximal, characteristic
4C37×#2352C211yesmaximal, characteristic, complemented
5C37×#2036C211yesmaximal, characteristic, complemented
6C37×#2035C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#1983C211yesmaximal, characteristic, complemented
10C37×#1958C211yesmaximal, characteristic, complemented
11C37×#1954C211yesmaximal, characteristic, complemented
12C37×#1949C211yesmaximal, characteristic, complemented
13C37×#1874C211yesmaximal, characteristic, complemented
14C37×#1873C211yesmaximal, characteristic, complemented
15C4×#106×C37C211yesmaximal, characteristic, complemented
16C2×#124×C37C2211yescharacteristic
17C2×C22⋊Q8×C37C2211yescharacteristic
18C2×C22⋊Q8×C37C2211yescharacteristic
19C2×#121×C37C2211yescharacteristic
20C2×#121×C37C2211yescharacteristic
21C2×C4×D4×C37C2211yescharacteristic
22C2×#117×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic
24C37×#483—24no—
25C37×#482—24no—
26C2×#107×C37C2211yescharacteristic
27C2×#106×C37C2211yescharacteristic
28C2×#106×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×C4⋊C8×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×#102×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×C22⋊C8×C37C2211yescharacteristic
40C2×C22⋊C8×C37C2211yescharacteristic
41C2×C22⋊C8×C37C2211yescharacteristic
42C2×C22⋊C8×C37C2211yescharacteristic
43C2×C4×C8×C37C2211yescharacteristic
44C37×#399—21no—
45C37×#392—21no—
46C37×#390—21no—
47C37×#390—21no—
48C37×#388—21no—
49C37×#387—21no—
50C37×#386—21no—
51C37×#382C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C37×#380C2211yescharacteristic
54C4×C4⋊C4×C37C2211yescharacteristic
55C4×C4⋊C4×C37C2211yescharacteristic
56C4×C22⋊C4×C37—21no—
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—21no—
63C22×D4×C37—21no—
64C22×D4×C37D411yescharacteristic
65C22×D4×C37C2311yescharacteristic
66C23×C4×C37—21no—
67C23×C4×C37C2311yescharacteristic
68C23×C4×C37C2311yescharacteristic
69C22×C8×C37C2311yescharacteristic
70C22×C8×C37C2311yescharacteristic
71C22×C8×C37C2311yescharacteristic
72C22×C8×C37C2311yescharacteristic
73#124×C37—22no—
74#124×C37—22no—
75C22⋊Q8×C37—22no—
76C22⋊Q8×C37—22no—
77C22⋊Q8×C37—41no—
78C22⋊Q8×C37—41no—
79#121×C37—22no—
80#121×C37—22no—
81#121×C37—41no—
82#121×C37—41no—
83C4×D4×C37—22no—
84C4×D4×C37—22no—
85#117×C37—22no—
86#117×C37—41no—
87C2×C4⋊C4×C37—22no—
88C2×C4⋊C4×C37—21no—
89C2×C4⋊C4×C37—21no—
90C2×C4⋊C4×C37—21no—
91C2×C4⋊C4×C37—41no—
92C2×C4⋊C4×C37D411yescharacteristic
93C2×C4⋊C4×C37C2311yescharacteristic
94C2×C4⋊C4×C37C2311yescharacteristic
95C2×C4⋊C4×C37C2311yescharacteristic
96C2×C4⋊C4×C37C2311yescharacteristic
97C2×C4⋊C4×C37C2311yescharacteristic
98C2×C4⋊C4×C37C2311yescharacteristic
99C2×C22⋊C4×C37—21no—
100C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
109C2×C22⋊C4×C37D411yescharacteristic
110C2×C42×C37—21no—
111C2×C42×C37—21no—
112C2×C42×C37—21no—
113C2×C42×C37C2311yescharacteristic
114#107×C37—22no—
115#106×C37—22no—
116#106×C37—22no—
117#106×C37D414yescomplemented
118C4⋊C8×C37—22no—
119#103×C37—22no—
120#103×C37—22no—
121#103×C37—41no—
122#103×C37—41no—
123#102×C37—22no—
124#102×C37—22no—
125#102×C37—41no—
126#102×C37—41no—
127C22⋊C8×C37—22no—
128C22⋊C8×C37—22no—
129C22⋊C8×C37—41no—
130C22⋊C8×C37—41no—
131C4×C8×C37—22no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37—21no—
137#95×C37—21no—
138C24×C37—21no—
139C24×C37C2×D411yescharacteristic
140C24×C37C2×D411yescharacteristic
141C2×Q8×C37—21no—
142C2×Q8×C37—21no—
143C2×Q8×C37—21no—
144C2×Q8×C37—21no—
145C2×Q8×C37—21no—
146C2×Q8×C37—21no—
147C2×D4×C37—22no—
148C2×D4×C37—22no—
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—41no—
156C2×D4×C37—42no—
157C2×D4×C37—42no—
158C2×D4×C37—42no—
159C2×D4×C37—42no—
160C2×D4×C37—81no—
161C2×D4×C37—81no—
162C22×C4×C37—21no—
163C22×C4×C37—21no—
164C22×C4×C37—21no—
165C22×C4×C37—21no—
166C22×C4×C37—21no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—21no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37—21no—
173C22×C4×C37—21no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—21no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—42no—
182C22×C4×C37—42no—
183C22×C4×C37—81no—
184C22×C4×C37C2×D411yescharacteristic
185C22×C4×C37C2×D411yescharacteristic
186C22×C4×C37C2×D411yescharacteristic
187C22×C4×C37C2×D411yescharacteristic
188C22×C4×C37C2411yescharacteristic
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37—21no—
193C2×C8×C37—21no—
194C2×C8×C37—21no—
195C2×C8×C37—21no—
196C2×C8×C37—21no—
197C2×C8×C37—21no—
198C2×C8×C37—21no—
199C2×C8×C37—21no—
200C2×C8×C37C2×D412yes—
201C4⋊C4×C37—22no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—21no—
206C4⋊C4×C37—21no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37—21no—
210C4⋊C4×C37—21no—
211C4⋊C4×C37—42no—
212C4⋊C4×C37—42no—
213C4⋊C4×C37—42no—
214C4⋊C4×C37C2×D412yes—
215C4⋊C4×C37C2×D412yes—
216C4⋊C4×C37#4112yes—
217C22⋊C4×C37—22no—
218C22⋊C4×C37—22no—
219C22⋊C4×C37—42no—
220C22⋊C4×C37—42no—
221C22⋊C4×C37—42no—
222C22⋊C4×C37—42no—
223C22⋊C4×C37—42no—
224C22⋊C4×C37—42no—
225C22⋊C4×C37—42no—
226C22⋊C4×C37—42no—
227C22⋊C4×C37—81no—
228C42×C37—42no—
229C42×C37—81no—
230C42×C37—81no—
231C42×C37#4112yes—
232C42×C37#4112yes—
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—21no—
236C23×C37—21no—
237C23×C37—21no—
238C23×C37—21no—
239C23×C37—21no—
240C23×C37—21no—
241C23×C37—21no—
242C23×C37—21no—
243C23×C37—21no—
244C23×C37—21no—
245C23×C37—21no—
246C23×C37—41no—
247C23×C37—41no—
248C23×C37—41no—
249C23×C37—41no—
250C23×C37—41no—
251C23×C37—41no—
252C23×C37—41no—
253C23×C37#13512yes—
254C23×C37C22×D411yescharacteristic
255Q8×C37—41no—
256Q8×C37—41no—
257Q8×C37—41no—
258Q8×C37—41no—
259D4×C37—44no—
260D4×C37—41no—
261D4×C37—41no—
262D4×C37—41no—
263D4×C37—41no—
264D4×C37—84no—
265D4×C37—84no—
266C2×C4×C37—21no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—21no—
271C2×C4×C37—21no—
272C2×C4×C37—21no—
273C2×C4×C37—22no—
274C2×C4×C37—22no—
275C2×C4×C37—21no—
276C2×C4×C37—22no—
277C2×C4×C37—21no—
278C2×C4×C37—21no—
279C2×C4×C37—41no—
280C2×C4×C37—41no—
281C2×C4×C37—41no—
282C2×C4×C37—41no—
283C2×C4×C37—41no—
284C2×C4×C37—41no—
285C2×C4×C37—41no—
286C2×C4×C37—41no—
287C2×C4×C37—41no—
288C2×C4×C37—41no—
289C2×C4×C37—41no—
290C2×C4×C37—41no—
291C2×C4×C37—41no—
292C2×C4×C37—41no—
293C2×C4×C37—41no—
294C2×C4×C37—41no—
295C2×C4×C37—41no—
296C2×C4×C37—41no—
297C2×C4×C37—41no—
298C2×C4×C37—41no—
299C2×C4×C37—41no—
300C2×C4×C37—41no—
301C2×C4×C37—41no—
302C2×C4×C37—41no—
303C2×C4×C37—41no—
304C2×C4×C37—41no—
305C2×C4×C37—84no—
306C2×C4×C37#12312yes—
307C2×C4×C37#12312yes—
308C2×C4×C37C22×D411yescharacteristic
309C2×C4×C37C2×#4111yescharacteristic
310C2×C4×C37C2×#4111yescharacteristic
311C2×C4×C37C2×#4111yescharacteristic
312C2×C4×C37H(5,𝔽2)11yescharacteristic
313C2×C4×C37H(5,𝔽2)11yescharacteristic
314C8×C37—22no—
315C8×C37—41no—
316C8×C37—41no—
317C8×C37—41no—
318#26239C3711yesmaximal, characteristic, direct product factor, Sylow
319C22×C37—22no—
320C22×C37—22no—
321C22×C37—22no—
322C22×C37—41no—
323C22×C37—41no—
324C22×C37—41no—
325C22×C37—41no—
326C22×C37—41no—
327C22×C37—41no—
328C22×C37—41no—
329C22×C37—41no—
330C22×C37—41no—
331C22×C37—41no—
332C22×C37—41no—
333C22×C37—81no—
334C22×C37—81no—
335C22×C37—81no—
336C22×C37—81no—
337C22×C37—81no—
338C22×C37—81no—
339C22×C37—81no—
340C22×C37C2×#12311yescharacteristic
341C22×C37D4211yescharacteristic
342C22×C37#54611yescharacteristic
343C22×C37C2×#13511yescharacteristic
344C22×C37#57511yescharacteristic
345C22×C37#57711yescharacteristic
346C22×C37#57711yescharacteristic
347C4×C37—22no—
348C4×C37—22no—
349C4×C37—41no—
350C4×C37—41no—
351C4×C37—42no—
352C4×C37—42no—
353C4×C37—42no—
354C4×C37—81no—
355C4×C37—81no—
356C4×C37—81no—
357C4×C37—81no—
358C4×C37#53211yescharacteristic
359C4×C37#54011yescharacteristic
360C4×C37#55011yescharacteristic
361C4×C37#55911yescharacteristic
362C2×#482C2×C3711yescharacteristic, complemented
363C2×#483C2×C3711yescharacteristic, complemented
364#2540C2×C3711yescharacteristic
365#2352C2×C3711yescharacteristic, complemented
366#2036C2×C3711yescharacteristic, complemented
367#2035C2×C3711yescharacteristic, complemented
368#2034C2×C3711yescharacteristic, complemented
369#2034C2×C3711yescharacteristic, complemented
370#1983C2×C3711yescharacteristic, complemented
371#1958C2×C3711yescharacteristic, complemented
372#1954C2×C3711yescharacteristic, complemented
373#1949C2×C3711yescharacteristic, complemented
374#1874C2×C3711yescharacteristic, complemented
375#1873C2×C3711yescharacteristic, complemented
376C4×#106C2×C3711yescharacteristic, complemented
377C2×C37—42no—
378C2×C37—81no—
379C2×C37—161no—
380C2×C37#244511yescharacteristic
381C2×C37#309111yescharacteristic
382C2×C37#309911yescharacteristic
383C2×C37#327511yescharacteristic
384C2×C37#328211yescharacteristic
385C2×C37#329611yescharacteristic
386C2×C37#332611yescharacteristic
387C2×#124C22×C3711yescharacteristic
388C2×C22⋊Q8C22×C3711yescharacteristic
389C2×C22⋊Q8C22×C3711yescharacteristic
390C2×#121C22×C3711yescharacteristic
391C2×#121C22×C3711yescharacteristic
392C2×C4×D4C22×C3711yescharacteristic
393C2×#117C22×C3711yescharacteristic
394C22×C4⋊C4C22×C3711yescharacteristic
395#483—24no—
396#482—24no—
397C2×#107C22×C3711yescharacteristic
398C2×#106C22×C3711yescharacteristic
399C2×#106C22×C3711yescharacteristic
400C2×#106C22×C3711yescharacteristic
401C2×C4⋊C8C22×C3711yescharacteristic
402C2×#103C22×C3711yescharacteristic
403C2×#103C22×C3711yescharacteristic
404C2×#103C22×C3711yescharacteristic
405C2×#103C22×C3711yescharacteristic
406C2×#102C22×C3711yescharacteristic
407C2×#102C22×C3711yescharacteristic
408C2×#102C22×C3711yescharacteristic
409C2×#102C22×C3711yescharacteristic
410C2×C22⋊C8C22×C3711yescharacteristic
411C2×C22⋊C8C22×C3711yescharacteristic
412C2×C22⋊C8C22×C3711yescharacteristic
413C2×C22⋊C8C22×C3711yescharacteristic
414C2×C4×C8C22×C3711yescharacteristic
415#399—21no—
416#392—21no—
417#390—21no—
418#390—21no—
419#388—21no—
420#387—21no—
421#386—21no—
422#382C22×C3711yescharacteristic
423#380C22×C3711yescharacteristic
424#380C22×C3711yescharacteristic
425C4×C4⋊C4C22×C3711yescharacteristic
426C4×C4⋊C4C22×C3711yescharacteristic
427C4×C22⋊C4—21no—
428#340C22×C3711yescharacteristic
429#340C22×C3711yescharacteristic
430#340C22×C3711yescharacteristic
431#340C22×C3711yescharacteristic
432C37#2623911yescharacteristic, direct product factor, Sylow
433C22×Q8C23×C3711yescharacteristic
434C22×D4—21no—
435C22×D4—21no—
436C22×D4D4×C3711yescharacteristic
437C22×D4C23×C3711yescharacteristic
438C23×C4—21no—
439C23×C4C23×C3711yescharacteristic
440C23×C4C23×C3711yescharacteristic
441C22×C8C23×C3711yescharacteristic
442C22×C8C23×C3711yescharacteristic
443C22×C8C23×C3711yescharacteristic
444C22×C8C23×C3711yescharacteristic
445#124—22no—
446#124—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—41no—
450C22⋊Q8—41no—
451#121—22no—
452#121—22no—
453#121—41no—
454#121—41no—
455C4×D4—22no—
456C4×D4—22no—
457#117—22no—
458#117—41no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4D4×C3711yescharacteristic
465C2×C4⋊C4C23×C3711yescharacteristic
466C2×C4⋊C4C23×C3711yescharacteristic
467C2×C4⋊C4C23×C3711yescharacteristic
468C2×C4⋊C4C23×C3711yescharacteristic
469C2×C4⋊C4C23×C3711yescharacteristic
470C2×C4⋊C4C23×C3711yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C3711yescharacteristic
481C2×C22⋊C4D4×C3711yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C23×C3711yescharacteristic
486#107—22no—
487#106—22no—
488#106—22no—
489#106D4×C3714yescomplemented
490C4⋊C8—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—41no—
498#102—41no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—41no—
502C22⋊C8—41no—
503C4×C8—22no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510C24—21no—
511C24C2×D4×C3711yescharacteristic
512C24C2×D4×C3711yescharacteristic
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4C2×D4×C3711yescharacteristic
557C22×C4C2×D4×C3711yescharacteristic
558C22×C4C2×D4×C3711yescharacteristic
559C22×C4C2×D4×C3711yescharacteristic
560C22×C4C24×C3711yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8C2×D4×C3712yes—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4C2×D4×C3712yes—
587C4⋊C4C2×D4×C3712yes—
588C4⋊C4#41×C3712yes—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—81no—
600C42—42no—
601C42—81no—
602C42—81no—
603C42#41×C3712yes—
604C42#41×C3712yes—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23#135×C3712yes—
626C23C22×D4×C3711yescharacteristic
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631D4—44no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—84no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—84no—
678C2×C4#123×C3712yes—
679C2×C4#123×C3712yes—
680C2×C4C22×D4×C3711yescharacteristic
681C2×C4C2×#41×C3711yescharacteristic
682C2×C4C2×#41×C3711yescharacteristic
683C2×C4C2×#41×C3711yescharacteristic
684C2×C4H(5,𝔽2)×C3711yescharacteristic
685C2×C4H(5,𝔽2)×C3711yescharacteristic
686C8—22no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×#123×C3711yescharacteristic
712C22D42×C3711yescharacteristic
713C22C37×#54611yescharacteristic
714C22C2×#135×C3711yescharacteristic
715C22C37×#57511yescharacteristic
716C22C37×#57711yescharacteristic
717C22C37×#57711yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4C37×#53211yescharacteristic
730C4C37×#54011yescharacteristic
731C4C37×#55011yescharacteristic
732C4C37×#55911yescharacteristic
733C2—42no—
734C2—81no—
735C2—161no—
736C2C37×#244511yescharacteristic
737C2C37×#309111yescharacteristic
738C2C37×#309911yescharacteristic
739C2C37×#327511yescharacteristic
740C2C37×#328211yescharacteristic
741C2C37×#329611yescharacteristic
742C2C37×#332611yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#2540C2
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×#482C2semidirect
2. C2×C37×#483C2semidirect
4. C37×#2352C2semidirect
5. C37×#2036C2semidirect
6. C37×#2035C2semidirect
7. C37×#2034C2semidirect
8. C37×#2034C2semidirect
9. C37×#1983C2semidirect
10. C37×#1958C2semidirect
11. C37×#1954C2semidirect
12. C37×#1949C2semidirect
13. C37×#1874C2semidirect
14. C37×#1873C2semidirect
15. C4×#106×C37C2semidirect
117. #106×C37D4semidirect
318. #26239C37direct (N × H)
362. C2×#482C2×C37semidirect
363. C2×#483C2×C37semidirect
365. #2352C2×C37semidirect
366. #2036C2×C37semidirect
367. #2035C2×C37semidirect
368. #2034C2×C37semidirect
369. #2034C2×C37semidirect
370. #1983C2×C37semidirect
371. #1958C2×C37semidirect
372. #1954C2×C37semidirect
373. #1949C2×C37semidirect
374. #1874C2×C37semidirect
375. #1873C2×C37semidirect
376. C4×#106C2×C37semidirect
432. C37#26239direct (N × H)
489. #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×#4832
C37×#25402
C37×#23522
C37×#20362
C37×#20352
C37×#20342
C37×#19832
C37×#19582
C37×#19542
C37×#19492
C37×#18742
C37×#18732
C4×#106×C372
#2623937