Finite Group Databasebeta

← C37×#25531 #22646784

Subgroups — C37×#25531 #22646784

Order 9472.

1374 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#547C211yesmaximal, characteristic
2C2×C37×#483C211yesmaximal, characteristic, complemented
3C2×C37×#465C211yesmaximal, characteristic, complemented
4C37×#2417C211yesmaximal, characteristic, complemented
5C37×#2058C211yesmaximal, characteristic, complemented
6C37×#2034C211yesmaximal, characteristic, complemented
7C37×#2024C211yesmaximal, characteristic, complemented
8C37×#2000C211yesmaximal, characteristic, complemented
9C37×#1877C211yesmaximal, characteristic, complemented
10C37×#1874C211yesmaximal, characteristic, complemented
11C37×#1872C211yesmaximal, characteristic, complemented
12C37×#1869C211yesmaximal, characteristic, complemented
13C37×#1864C211yesmaximal, characteristic, complemented
14C37×#1853C211yesmaximal, characteristic, complemented
15C2×C37×#340C211yesmaximal, characteristic, complemented
16C22×#41×C37—21no—
17C22×SD16×C37C2211yescharacteristic
18C23×C8×C37C2211yescharacteristic
19C37×#547—24no—
20C37×#547—24no—
21C2×C4⋊Q8×C37C2211yescharacteristic
22C2×#123×C37—21no—
23C2×#123×C37—21no—
24C2×C22⋊Q8×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×#121×C37C2211yescharacteristic
28C2×#121×C37C2211yescharacteristic
29C2×C4×D4×C37C2211yescharacteristic
30C2×C4×D4×C37C2211yescharacteristic
31C22×C4⋊C4×C37C2211yescharacteristic
32C22×C4⋊C4×C37C2211yescharacteristic
33C22×C4⋊C4×C37C2211yescharacteristic
34C37×#483—24no—
35C37×#465—24no—
36C2×#106×C37C2211yescharacteristic
37C2×#106×C37C2211yescharacteristic
38C2×#106×C37C2211yescharacteristic
39C2×#103×C37C2211yescharacteristic
40C2×#103×C37C2211yescharacteristic
41C2×#103×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C37×#398—21no—
49C37×#396—21no—
50C37×#391C2211yescharacteristic
51C37×#389C2211yescharacteristic
52C37×#386—21no—
53C37×#380—21no—
54C37×#380C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C2×#41×C37—28no—
64C2×#41×C37—44no—
65C2×#41×C37—44no—
66C22×Q8×C37—21no—
67C22×Q8×C37C2311yescharacteristic
68C22×D4×C37—21no—
69C22×D4×C37—21no—
70C22×D4×C37D411yescharacteristic
71C22×D4×C37C2311yescharacteristic
72C23×C4×C37—21no—
73C23×C4×C37—21no—
74C23×C4×C37—21no—
75C23×C4×C37—21no—
76C23×C4×C37C2311yescharacteristic
77C23×C4×C37C2311yescharacteristic
78C2×SD16×C37—22no—
79C2×SD16×C37—22no—
80C2×SD16×C37—41no—
81C22×C8×C37—22no—
82C22×C8×C37—22no—
83C22×C8×C37—41no—
84C22×C8×C37C2311yescharacteristic
85C22×C8×C37C2311yescharacteristic
86C22×C8×C37C2311yescharacteristic
87C22×C8×C37C2311yescharacteristic
88C4⋊Q8×C37—22no—
89C4⋊Q8×C37—22no—
90#123×C37—28no—
91#123×C37—28no—
92C22⋊Q8×C37—28no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—22no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—41no—
97#121×C37—22no—
98#121×C37—22no—
99#121×C37—22no—
100#121×C37D414yes—
101C4×D4×C37—22no—
102C4×D4×C37—22no—
103C4×D4×C37—22no—
104C4×D4×C37—22no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37—21no—
108C2×C4⋊C4×C37—22no—
109C2×C4⋊C4×C37—22no—
110C2×C4⋊C4×C37—22no—
111C2×C4⋊C4×C37—22no—
112C2×C4⋊C4×C37—21no—
113C2×C4⋊C4×C37—21no—
114C2×C4⋊C4×C37—21no—
115C2×C4⋊C4×C37—21no—
116C2×C4⋊C4×C37—41no—
117C2×C4⋊C4×C37D411yescharacteristic
118C2×C4⋊C4×C37D414yes—
119C2×C4⋊C4×C37C2311yescharacteristic
120C2×C4⋊C4×C37C2311yescharacteristic
121C2×C4⋊C4×C37C2311yescharacteristic
122C2×C4⋊C4×C37C2311yescharacteristic
123C2×C4⋊C4×C37C2311yescharacteristic
124C2×C4⋊C4×C37C2311yescharacteristic
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37D411yescharacteristic
132C2×C22⋊C4×C37D411yescharacteristic
133C2×C42×C37C2311yescharacteristic
134#106×C37—22no—
135#106×C37—22no—
136#106×C37—22no—
137#103×C37—22no—
138#103×C37—22no—
139#103×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—41no—
143C22⋊C8×C37—22no—
144C22⋊C8×C37—22no—
145C22⋊C8×C37—41no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37—21no—
149#95×C37—21no—
150C24×C37—21no—
151C24×C37C2×D411yescharacteristic
152C24×C37C2×D411yescharacteristic
153#41×C37—432no—
154C2×Q8×C37—24no—
155C2×Q8×C37—21no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—21no—
159C2×Q8×C37—21no—
160C2×Q8×C37—21no—
161C2×Q8×C37—42no—
162C2×Q8×C37—42no—
163C2×D4×C37—22no—
164C2×D4×C37—22no—
165C2×D4×C37—24no—
166C2×D4×C37—24no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—42no—
173C2×D4×C37—42no—
174C2×D4×C37—42no—
175C2×D4×C37—42no—
176C2×D4×C37SD1614yescomplemented
177C2×D4×C37C2×D412yes—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—24no—
183C22×C4×C37—24no—
184C22×C4×C37—24no—
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—21no—
195C22×C4×C37—21no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—42no—
199C22×C4×C37—42no—
200C22×C4×C37—42no—
201C22×C4×C37—42no—
202C22×C4×C37—42no—
203C22×C4×C37—42no—
204C22×C4×C37—42no—
205C22×C4×C37—42no—
206C22×C4×C37—81no—
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D411yescharacteristic
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2×D412yes—
211C22×C4×C37C2×D412yes—
212C22×C4×C37C2×D411yescharacteristic
213C22×C4×C37C2411yescharacteristic
214SD16×C37—44no—
215C2×C8×C37—21no—
216C2×C8×C37—21no—
217C2×C8×C37—21no—
218C2×C8×C37—21no—
219C2×C8×C37—21no—
220C2×C8×C37—21no—
221C2×C8×C37—21no—
222C2×C8×C37—21no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—44no—
227C2×C8×C37#4112yescomplemented
228C4⋊C4×C37—24no—
229C4⋊C4×C37—24no—
230C4⋊C4×C37—24no—
231C4⋊C4×C37—22no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—42no—
241C4⋊C4×C37—42no—
242C4⋊C4×C37—42no—
243C4⋊C4×C37—81no—
244C4⋊C4×C37C2×D412yes—
245C4⋊C4×C37C2×D412yes—
246C4⋊C4×C37C2×D412yes—
247C4⋊C4×C37#4112yescomplemented
248C22⋊C4×C37—24no—
249C22⋊C4×C37—24no—
250C22⋊C4×C37—22no—
251C22⋊C4×C37—24no—
252C22⋊C4×C37—22no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—42no—
255C22⋊C4×C37—81no—
256C42×C37—21no—
257C42×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—21no—
262C23×C37—21no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—22no—
269C23×C37—41no—
270C23×C37—41no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37#12012yes—
276C23×C37C2×SD1612yes—
277C23×C37C2×SD1612yes—
278C23×C37AGL(1,ℤ/8)12yes—
279C23×C37C22×D411yescharacteristic
280Q8×C37—48no—
281Q8×C37—41no—
282Q8×C37—41no—
283Q8×C37—41no—
284Q8×C37—41no—
285D4×C37—28no—
286D4×C37—22no—
287D4×C37—22no—
288D4×C37—48no—
289D4×C37—48no—
290D4×C37—41no—
291D4×C37—41no—
292C2×C4×C37—21no—
293C2×C4×C37—21no—
294C2×C4×C37—21no—
295C2×C4×C37—21no—
296C2×C4×C37—22no—
297C2×C4×C37—22no—
298C2×C4×C37—22no—
299C2×C4×C37—22no—
300C2×C4×C37—21no—
301C2×C4×C37—21no—
302C2×C4×C37—22no—
303C2×C4×C37—22no—
304C2×C4×C37—22no—
305C2×C4×C37—22no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—21no—
310C2×C4×C37—48no—
311C2×C4×C37—48no—
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—48no—
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—41no—
333C2×C4×C37—41no—
334C2×C4×C37—84no—
335C2×C4×C37#12012yes—
336C2×C4×C37C2×SD1612yes—
337C2×C4×C37C22×D411yescharacteristic
338C2×C4×C37C22×D411yescharacteristic
339C2×C4×C37C2×#4111yescharacteristic
340C2×C4×C37C2×#4111yescharacteristic
341C2×C4×C37H(5,𝔽2)11yescharacteristic
342C2×C4×C372−1+411yescharacteristic
343C8×C37—22no—
344C8×C37—41no—
345C8×C37—41no—
346C8×C37—41no—
347#25531C3711yesmaximal, characteristic, direct product factor, Sylow
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—22no—
352C22×C37—22no—
353C22×C37—22no—
354C22×C37—22no—
355C22×C37—22no—
356C22×C37—22no—
357C22×C37—41no—
358C22×C37—41no—
359C22×C37—41no—
360C22×C37—41no—
361C22×C37—42no—
362C22×C37—42no—
363C22×C37—42no—
364C22×C37—81no—
365C22×C37—81no—
366C22×C37—81no—
367C22×C37—81no—
368C22×C37#45014yes—
369C22×C37C2×#12011yescharacteristic
370C22×C37#54611yescharacteristic
371C22×C37#54711yescharacteristic
372C22×C37C22×SD1611yescharacteristic
373C22×C37C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C37#57711yescharacteristic
375C22×C37#57811yescharacteristic
376C4×C37—22no—
377C4×C37—22no—
378C4×C37—41no—
379C4×C37—42no—
380C4×C37—42no—
381C4×C37—42no—
382C4×C37—41no—
383C4×C37—42no—
384C4×C37—81no—
385C4×C37—81no—
386C4×C37—81no—
387C4×C37#53211yescharacteristic
388C4×C37#53711yescharacteristic
389C4×C37#54611yescharacteristic
390C4×C37#54711yescharacteristic
391C2×#547C2×C3711yescharacteristic
392C2×#483C2×C3711yescharacteristic, complemented
393C2×#465C2×C3711yescharacteristic, complemented
394#2417C2×C3711yescharacteristic, complemented
395#2058C2×C3711yescharacteristic, complemented
396#2034C2×C3711yescharacteristic, complemented
397#2024C2×C3711yescharacteristic, complemented
398#2000C2×C3711yescharacteristic, complemented
399#1877C2×C3711yescharacteristic, complemented
400#1874C2×C3711yescharacteristic, complemented
401#1872C2×C3711yescharacteristic, complemented
402#1869C2×C3711yescharacteristic, complemented
403#1864C2×C3711yescharacteristic, complemented
404#1853C2×C3711yescharacteristic, complemented
405C2×#340C2×C3711yescharacteristic, complemented
406C2×C37—24no—
407C2×C37—42no—
408C2×C37—82no—
409C2×C37#243011yescharacteristic
410C2×C37C2×#45011yescharacteristic
411C2×C37#301311yescharacteristic
412C2×C37#329811yescharacteristic
413C2×C37#330611yescharacteristic
414C2×C37#333511yescharacteristic
415C2×C37#334311yescharacteristic
416C22×#41—21no—
417C22×SD16C22×C3711yescharacteristic
418C23×C8C22×C3711yescharacteristic
419#547—24no—
420#547—24no—
421C2×C4⋊Q8C22×C3711yescharacteristic
422C2×#123—21no—
423C2×#123—21no—
424C2×C22⋊Q8—21no—
425C2×C22⋊Q8C22×C3711yescharacteristic
426C2×C22⋊Q8C22×C3711yescharacteristic
427C2×#121C22×C3711yescharacteristic
428C2×#121C22×C3711yescharacteristic
429C2×C4×D4C22×C3711yescharacteristic
430C2×C4×D4C22×C3711yescharacteristic
431C22×C4⋊C4C22×C3711yescharacteristic
432C22×C4⋊C4C22×C3711yescharacteristic
433C22×C4⋊C4C22×C3711yescharacteristic
434#483—24no—
435#465—24no—
436C2×#106C22×C3711yescharacteristic
437C2×#106C22×C3711yescharacteristic
438C2×#106C22×C3711yescharacteristic
439C2×#103C22×C3711yescharacteristic
440C2×#103C22×C3711yescharacteristic
441C2×#103C22×C3711yescharacteristic
442C2×#102C22×C3711yescharacteristic
443C2×#102C22×C3711yescharacteristic
444C2×#102C22×C3711yescharacteristic
445C2×C22⋊C8C22×C3711yescharacteristic
446C2×C22⋊C8C22×C3711yescharacteristic
447C2×C22⋊C8C22×C3711yescharacteristic
448#398—21no—
449#396—21no—
450#391C22×C3711yescharacteristic
451#389C22×C3711yescharacteristic
452#386—21no—
453#380—21no—
454#380C22×C3711yescharacteristic
455#340C22×C3711yescharacteristic
456#340C22×C3711yescharacteristic
457#340C22×C3711yescharacteristic
458#340C22×C3711yescharacteristic
459#340C22×C3711yescharacteristic
460#340C22×C3711yescharacteristic
461#336C22×C3711yescharacteristic
462#336C22×C3711yescharacteristic
463C37#2553111yescharacteristic, direct product factor, Sylow
464C2×#41—28no—
465C2×#41—44no—
466C2×#41—44no—
467C22×Q8—21no—
468C22×Q8C23×C3711yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C3711yescharacteristic
472C22×D4C23×C3711yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4C23×C3711yescharacteristic
478C23×C4C23×C3711yescharacteristic
479C2×SD16—22no—
480C2×SD16—22no—
481C2×SD16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C3711yescharacteristic
486C22×C8C23×C3711yescharacteristic
487C22×C8C23×C3711yescharacteristic
488C22×C8C23×C3711yescharacteristic
489C4⋊Q8—22no—
490C4⋊Q8—22no—
491#123—28no—
492#123—28no—
493C22⋊Q8—28no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—41no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121D4×C3714yes—
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4D4×C3711yescharacteristic
519C2×C4⋊C4D4×C3714yes—
520C2×C4⋊C4C23×C3711yescharacteristic
521C2×C4⋊C4C23×C3711yescharacteristic
522C2×C4⋊C4C23×C3711yescharacteristic
523C2×C4⋊C4C23×C3711yescharacteristic
524C2×C4⋊C4C23×C3711yescharacteristic
525C2×C4⋊C4C23×C3711yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4D4×C3711yescharacteristic
533C2×C22⋊C4D4×C3711yescharacteristic
534C2×C42C23×C3711yescharacteristic
535#106—22no—
536#106—22no—
537#106—22no—
538#103—22no—
539#103—22no—
540#103—22no—
541#102—22no—
542#102—22no—
543#102—41no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—41no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551C24—21no—
552C24C2×D4×C3711yescharacteristic
553C24C2×D4×C3711yescharacteristic
554#41—432no—
555C2×Q8—24no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4SD16×C3714yescomplemented
578C2×D4C2×D4×C3712yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
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—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4C2×D4×C3711yescharacteristic
609C22×C4C2×D4×C3711yescharacteristic
610C22×C4C2×D4×C3711yescharacteristic
611C22×C4C2×D4×C3712yes—
612C22×C4C2×D4×C3712yes—
613C22×C4C2×D4×C3711yescharacteristic
614C22×C4C24×C3711yescharacteristic
615SD16—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—44no—
628C2×C8#41×C3712yescomplemented
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—42no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—81no—
645C4⋊C4C2×D4×C3712yes—
646C4⋊C4C2×D4×C3712yes—
647C4⋊C4C2×D4×C3712yes—
648C4⋊C4#41×C3712yescomplemented
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23#120×C3712yes—
677C23C2×SD16×C3712yes—
678C23C2×SD16×C3712yes—
679C23AGL(1,ℤ/8)×C3712yes—
680C23C22×D4×C3711yescharacteristic
681Q8—48no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686D4—28no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—48no—
691D4—41no—
692D4—41no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
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—21no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—48no—
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—84no—
736C2×C4#120×C3712yes—
737C2×C4C2×SD16×C3712yes—
738C2×C4C22×D4×C3711yescharacteristic
739C2×C4C22×D4×C3711yescharacteristic
740C2×C4C2×#41×C3711yescharacteristic
741C2×C4C2×#41×C3711yescharacteristic
742C2×C4H(5,𝔽2)×C3711yescharacteristic
743C2×C42−1+4×C3711yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22C37×#45014yes—
769C22C2×#120×C3711yescharacteristic
770C22C37×#54611yescharacteristic
771C22C37×#54711yescharacteristic
772C22C22×SD16×C3711yescharacteristic
773C22C2×AGL(1,ℤ/8)×C3711yescharacteristic
774C22C37×#57711yescharacteristic
775C22C37×#57811yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—41no—
783C4—42no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4C37×#53211yescharacteristic
788C4C37×#53711yescharacteristic
789C4C37×#54611yescharacteristic
790C4C37×#54711yescharacteristic
791C2—24no—
792C2—42no—
793C2—82no—
794C2C37×#243011yescharacteristic
795C2C2×C37×#45011yescharacteristic
796C2C37×#301311yescharacteristic
797C2C37×#329811yescharacteristic
798C2C37×#330611yescharacteristic
799C2C37×#333511yescharacteristic
800C2C37×#334311yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#547C2
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
2. C2×C37×#483C2semidirect
3. C2×C37×#465C2semidirect
4. C37×#2417C2semidirect
5. C37×#2058C2semidirect
6. C37×#2034C2semidirect
7. C37×#2024C2semidirect
8. C37×#2000C2semidirect
9. C37×#1877C2semidirect
10. C37×#1874C2semidirect
11. C37×#1872C2semidirect
12. C37×#1869C2semidirect
13. C37×#1864C2semidirect
14. C37×#1853C2semidirect
15. C2×C37×#340C2semidirect
176. C2×D4×C37SD16semidirect
227. C2×C8×C37#41semidirect
247. C4⋊C4×C37#41semidirect
347. #25531C37direct (N × H)
392. C2×#483C2×C37semidirect
393. C2×#465C2×C37semidirect
394. #2417C2×C37semidirect
395. #2058C2×C37semidirect
396. #2034C2×C37semidirect
397. #2024C2×C37semidirect
398. #2000C2×C37semidirect
399. #1877C2×C37semidirect
400. #1874C2×C37semidirect
401. #1872C2×C37semidirect
402. #1869C2×C37semidirect
403. #1864C2×C37semidirect
404. #1853C2×C37semidirect
405. C2×#340C2×C37semidirect
463. C37#25531direct (N × H)
577. C2×D4SD16×C37semidirect
628. C2×C8#41×C37semidirect
648. C4⋊C4#41×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5472
C2×C37×#4832
C2×C37×#4652
C37×#24172
C37×#20582
C37×#20342
C37×#20242
C37×#20002
C37×#18772
C37×#18742
C37×#18722
C37×#18692
C37×#18642
C37×#18532
C2×C37×#3402
#2553137