Finite Group Databasebeta

← C2×C37×#2585 #22656087

Subgroups — C2×C37×#2585 #22656087

Order 9472.

1966 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#2585C2116yesmaximal, direct product factor
2C2×C37×#400C211yesmaximal, characteristic
3C2×C37×#398C211yesmaximal, characteristic
4C2×C37×#398C211yesmaximal, characteristic
5C2×C37×#398C211yesmaximal, characteristic
6C2×C37×#389C211yesmaximal, characteristic
7C2×C37×#389C211yesmaximal, characteristic
8C2×C37×#389C211yesmaximal, characteristic
9C2×C37×#387C211yesmaximal, characteristic
10C2×C37×#387C211yesmaximal, characteristic
11C2×C37×#387C211yesmaximal, characteristic
12C2×C37×#387C211yesmaximal, characteristic
13C2×C37×#387C211yesmaximal, characteristic
14C2×C37×#387C211yesmaximal, characteristic
15C2×C4×C4⋊C4×C37C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C37C211yesmaximal, characteristic
17C22×C4⋊C4×C37C2211yescharacteristic
18C22×C4⋊C4×C37C2211yescharacteristic
19C22×C4⋊C4×C37C2211yescharacteristic
20C22×C4⋊C4×C37C2211yescharacteristic
21C22×C4⋊C4×C37C2211yescharacteristic
22C22×C4⋊C4×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic
24C22×C4⋊C4×C37C2211yescharacteristic
25C22×C4⋊C4×C37C2211yescharacteristic
26C22×C4⋊C4×C37C2211yescharacteristic
27C22×C4⋊C4×C37C2211yescharacteristic
28C22×C4⋊C4×C37C2211yescharacteristic
29C22×C4⋊C4×C37C2211yescharacteristic
30C22×C4⋊C4×C37C2211yescharacteristic
31C22×C42×C37C2211yescharacteristic
32C22×C42×C37C2211yescharacteristic
33C22×C42×C37C2211yescharacteristic
34C22×C42×C37C2211yescharacteristic
35C22×C42×C37C2211yescharacteristic
36C37×#400C2218yes—
37C37×#398C2218yes—
38C37×#398C2218yes—
39C37×#398C2218yes—
40C37×#389C2218yes—
41C37×#389C2218yes—
42C37×#389C2218yes—
43C37×#387C2218yes—
44C37×#387C2218yes—
45C37×#387C2218yes—
46C37×#387C2218yes—
47C37×#387C2218yes—
48C37×#387C2218yes—
49C4×C4⋊C4×C37C2218yes—
50C4×C4⋊C4×C37C2218yes—
51C2×#95×C37C2211yescharacteristic
52C2×#95×C37C2211yescharacteristic
53C2×#95×C37C2211yescharacteristic
54C2×#95×C37C2211yescharacteristic
55C2×#95×C37C2211yescharacteristic
56C2×#95×C37C2211yescharacteristic
57C2×#95×C37C2211yescharacteristic
58C2×#95×C37C2211yescharacteristic
59C2×#95×C37C2211yescharacteristic
60C2×#95×C37C2211yescharacteristic
61C2×#95×C37C2211yescharacteristic
62C2×#95×C37C2211yescharacteristic
63C2×#95×C37C2211yescharacteristic
64C2×#95×C37C2211yescharacteristic
65C2×#95×C37C2211yescharacteristic
66C2×#95×C37C2211yescharacteristic
67C23×C4×C37C2311yescharacteristic
68C23×C4×C37C2311yescharacteristic
69C23×C4×C37C2311yescharacteristic
70C23×C4×C37C2311yescharacteristic
71C23×C4×C37C2311yescharacteristic
72C23×C4×C37C2311yescharacteristic
73C23×C4×C37C2311yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C23×C4×C37C2311yescharacteristic
76C23×C4×C37C2311yescharacteristic
77C23×C4×C37C2311yescharacteristic
78C23×C4×C37C2311yescharacteristic
79C23×C4×C37C2311yescharacteristic
80C23×C4×C37C2311yescharacteristic
81C23×C4×C37C2311yescharacteristic
82C2×C4⋊C4×C37—24no—
83C2×C4⋊C4×C37—24no—
84C2×C4⋊C4×C37—24no—
85C2×C4⋊C4×C37—24no—
86C2×C4⋊C4×C37—24no—
87C2×C4⋊C4×C37—24no—
88C2×C4⋊C4×C37—24no—
89C2×C4⋊C4×C37—24no—
90C2×C4⋊C4×C37—24no—
91C2×C4⋊C4×C37—24no—
92C2×C4⋊C4×C37—42no—
93C2×C4⋊C4×C37—42no—
94C2×C4⋊C4×C37—42no—
95C2×C4⋊C4×C37Q818yes—
96C2×C4⋊C4×C37C2314yes—
97C2×C4⋊C4×C37C2314yes—
98C2×C4⋊C4×C37C2314yes—
99C2×C4⋊C4×C37C2314yes—
100C2×C4⋊C4×C37C2314yes—
101C2×C4⋊C4×C37C2314yes—
102C2×C4⋊C4×C37C2314yes—
103C2×C4⋊C4×C37C2314yes—
104C2×C4⋊C4×C37C2314yes—
105C2×C4⋊C4×C37C2314yes—
106C2×C4⋊C4×C37C2314yes—
107C2×C4⋊C4×C37C2314yes—
108C2×C4⋊C4×C37C2314yes—
109C2×C4⋊C4×C37C2314yes—
110C2×C42×C37—24no—
111C2×C42×C37—24no—
112C2×C42×C37—42no—
113C2×C42×C37—42no—
114C2×C42×C37—42no—
115C2×C42×C37C2314yes—
116C2×C42×C37C2314yes—
117C2×C42×C37C2314yes—
118C2×C42×C37C2314yes—
119C2×C42×C37C2314yes—
120#95×C37C2314yes—
121#95×C37C2314yes—
122#95×C37C2314yes—
123#95×C37C2314yes—
124#95×C37C2314yes—
125#95×C37C2314yes—
126#95×C37C2314yes—
127#95×C37C2314yes—
128#95×C37C2314yes—
129#95×C37C2314yes—
130#95×C37C2314yes—
131#95×C37C2314yes—
132#95×C37C2314yes—
133#95×C37C2314yes—
134#95×C37C2314yes—
135#95×C37C2314yes—
136C24×C37C2411yescharacteristic
137C22×C4×C37—22no—
138C22×C4×C37—22no—
139C22×C4×C37—22no—
140C22×C4×C37—22no—
141C22×C4×C37—22no—
142C22×C4×C37—22no—
143C22×C4×C37—22no—
144C22×C4×C37—22no—
145C22×C4×C37—22no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—22no—
156C22×C4×C37—22no—
157C22×C4×C37—22no—
158C22×C4×C37—22no—
159C22×C4×C37—22no—
160C22×C4×C37—22no—
161C22×C4×C37—22no—
162C22×C4×C37—22no—
163C22×C4×C37—22no—
164C22×C4×C37—22no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—22no—
171C22×C4×C37—22no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—22no—
175C22×C4×C37C2×Q814yes—
176C22×C4×C37C2×Q814yes—
177C22×C4×C37C2×Q814yes—
178C22×C4×C37#4114yes—
179C22×C4×C37#4114yes—
180C22×C4×C37#4114yes—
181C22×C4×C37#4114yes—
182C22×C4×C37C2412yes—
183C22×C4×C37C2412yes—
184C22×C4×C37C2412yes—
185C22×C4×C37C2412yes—
186C22×C4×C37C2412yes—
187C22×C4×C37C2412yes—
188C22×C4×C37C2412yes—
189C22×C4×C37C2412yes—
190C22×C4×C37C2412yes—
191C22×C4×C37C2412yes—
192C22×C4×C37C2412yes—
193C22×C4×C37C2412yes—
194C22×C4×C37C2412yes—
195C22×C4×C37C2412yes—
196C22×C4×C37C2412yes—
197C4⋊C4×C37—28no—
198C4⋊C4×C37—28no—
199C4⋊C4×C37—28no—
200C4⋊C4×C37—28no—
201C4⋊C4×C37—28no—
202C4⋊C4×C37—28no—
203C4⋊C4×C37—28no—
204C4⋊C4×C37—28no—
205C4⋊C4×C37—28no—
206C4⋊C4×C37—28no—
207C4⋊C4×C37—44no—
208C4⋊C4×C37—44no—
209C4⋊C4×C37—44no—
210C4⋊C4×C37C2×Q8116yes—
211C42×C37—28no—
212C42×C37—28no—
213C42×C37—44no—
214C42×C37—44no—
215C42×C37—44no—
216C23×C37C22×Q812yes—
217C23×C37C2×#4112yes—
218C23×C37C2×#4112yes—
219C23×C37C2×#4112yes—
220C23×C37C2×#4112yes—
221C23×C37H(5,𝔽2)12yes—
222C23×C372−1+412yes—
223C23×C37C2511yescharacteristic
224C2×C4×C37—28no—
225C2×C4×C37—28no—
226C2×C4×C37—28no—
227C2×C4×C37—28no—
228C2×C4×C37—28no—
229C2×C4×C37—28no—
230C2×C4×C37—28no—
231C2×C4×C37—22no—
232C2×C4×C37—22no—
233C2×C4×C37—22no—
234C2×C4×C37—22no—
235C2×C4×C37—22no—
236C2×C4×C37—22no—
237C2×C4×C37—22no—
238C2×C4×C37—22no—
239C2×C4×C37—22no—
240C2×C4×C37—22no—
241C2×C4×C37—22no—
242C2×C4×C37—22no—
243C2×C4×C37—22no—
244C2×C4×C37—22no—
245C2×C4×C37—22no—
246C2×C4×C37—22no—
247C2×C4×C37—22no—
248C2×C4×C37—22no—
249C2×C4×C37—22no—
250C2×C4×C37—22no—
251C2×C4×C37—22no—
252C2×C4×C37—22no—
253C2×C4×C37—22no—
254C2×C4×C37—22no—
255C2×C4×C37—22no—
256C2×C4×C37—22no—
257C2×C4×C37—22no—
258C2×C4×C37—22no—
259C2×C4×C37—22no—
260C2×C4×C37—22no—
261C2×C4×C37—22no—
262C2×C4×C37—22no—
263C2×C4×C37—22no—
264C2×C4×C37—22no—
265C2×C4×C37—22no—
266C2×C4×C37—22no—
267C2×C4×C37—22no—
268C2×C4×C37—22no—
269C2×C4×C37—44no—
270C2×C4×C37—44no—
271C2×C4×C37—44no—
272C2×C4×C37—44no—
273C2×C4×C37—44no—
274C2×C4×C37—44no—
275C2×C4×C37—44no—
276C2×C4×C37—44no—
277C2×C4×C37C22×Q814yes—
278C2×C4×C37C22×Q814yes—
279C2×C4×C37C22×Q814yes—
280C2×C4×C37C2×#4114yes—
281C2×C4×C37C2×#4114yes—
282C2×C4×C37C2×#4114yes—
283C2×C4×C37C2×#4114yes—
284C2×#2585C3711yesmaximal, characteristic, direct product factor, Sylow
285C22×C37#52914yes—
286C22×C37#53314yes—
287C22×C37#53914yes—
288C22×C37#55214yes—
289C22×C37#55314yes—
290C22×C37#55414yes—
291C22×C37#55714yes—
292C22×C37C23×Q811yescharacteristic
293C22×C37C22×#4111yescharacteristic
294C22×C37C22×#4111yescharacteristic
295C22×C37C22×#4111yescharacteristic
296C22×C37C22×#4111yescharacteristic
297C22×C37C2×H(5,𝔽2)11yescharacteristic
298C22×C37C2×2−1+411yescharacteristic
299C4×C37—24no—
300C4×C37—24no—
301C4×C37—24no—
302C4×C37—24no—
303C4×C37—24no—
304C4×C37—24no—
305C4×C37—24no—
306C4×C37—42no—
307C4×C37—42no—
308C4×C37—42no—
309C4×C37—42no—
310C4×C37—42no—
311C4×C37—42no—
312C4×C37—42no—
313C4×C37—42no—
314#2585C2×C37116yesdirect product factor
315C2×#400C2×C3711yescharacteristic
316C2×#398C2×C3711yescharacteristic
317C2×#398C2×C3711yescharacteristic
318C2×#398C2×C3711yescharacteristic
319C2×#389C2×C3711yescharacteristic
320C2×#389C2×C3711yescharacteristic
321C2×#389C2×C3711yescharacteristic
322C2×#387C2×C3711yescharacteristic
323C2×#387C2×C3711yescharacteristic
324C2×#387C2×C3711yescharacteristic
325C2×#387C2×C3711yescharacteristic
326C2×#387C2×C3711yescharacteristic
327C2×#387C2×C3711yescharacteristic
328C2×C4×C4⋊C4C2×C3711yescharacteristic
329C2×C4×C4⋊C4C2×C3711yescharacteristic
330C2×C37#258518yesdirect product factor
331C2×C37C2×#52911yescharacteristic
332C2×C37C2×#53311yescharacteristic
333C2×C37C2×#53911yescharacteristic
334C2×C37C2×#55211yescharacteristic
335C2×C37C2×#55311yescharacteristic
336C2×C37C2×#55411yescharacteristic
337C2×C37C2×#55711yescharacteristic
338C22×C4⋊C4C22×C3711yescharacteristic
339C22×C4⋊C4C22×C3711yescharacteristic
340C22×C4⋊C4C22×C3711yescharacteristic
341C22×C4⋊C4C22×C3711yescharacteristic
342C22×C4⋊C4C22×C3711yescharacteristic
343C22×C4⋊C4C22×C3711yescharacteristic
344C22×C4⋊C4C22×C3711yescharacteristic
345C22×C4⋊C4C22×C3711yescharacteristic
346C22×C4⋊C4C22×C3711yescharacteristic
347C22×C4⋊C4C22×C3711yescharacteristic
348C22×C4⋊C4C22×C3711yescharacteristic
349C22×C4⋊C4C22×C3711yescharacteristic
350C22×C4⋊C4C22×C3711yescharacteristic
351C22×C4⋊C4C22×C3711yescharacteristic
352C22×C42C22×C3711yescharacteristic
353C22×C42C22×C3711yescharacteristic
354C22×C42C22×C3711yescharacteristic
355C22×C42C22×C3711yescharacteristic
356C22×C42C22×C3711yescharacteristic
357#400C22×C3718yes—
358#398C22×C3718yes—
359#398C22×C3718yes—
360#398C22×C3718yes—
361#389C22×C3718yes—
362#389C22×C3718yes—
363#389C22×C3718yes—
364#387C22×C3718yes—
365#387C22×C3718yes—
366#387C22×C3718yes—
367#387C22×C3718yes—
368#387C22×C3718yes—
369#387C22×C3718yes—
370C4×C4⋊C4C22×C3718yes—
371C4×C4⋊C4C22×C3718yes—
372C2×#95C22×C3711yescharacteristic
373C2×#95C22×C3711yescharacteristic
374C2×#95C22×C3711yescharacteristic
375C2×#95C22×C3711yescharacteristic
376C2×#95C22×C3711yescharacteristic
377C2×#95C22×C3711yescharacteristic
378C2×#95C22×C3711yescharacteristic
379C2×#95C22×C3711yescharacteristic
380C2×#95C22×C3711yescharacteristic
381C2×#95C22×C3711yescharacteristic
382C2×#95C22×C3711yescharacteristic
383C2×#95C22×C3711yescharacteristic
384C2×#95C22×C3711yescharacteristic
385C2×#95C22×C3711yescharacteristic
386C2×#95C22×C3711yescharacteristic
387C2×#95C22×C3711yescharacteristic
388C37C2×#258511yescharacteristic, direct product factor, Sylow
389C23×C4C23×C3711yescharacteristic
390C23×C4C23×C3711yescharacteristic
391C23×C4C23×C3711yescharacteristic
392C23×C4C23×C3711yescharacteristic
393C23×C4C23×C3711yescharacteristic
394C23×C4C23×C3711yescharacteristic
395C23×C4C23×C3711yescharacteristic
396C23×C4C23×C3711yescharacteristic
397C23×C4C23×C3711yescharacteristic
398C23×C4C23×C3711yescharacteristic
399C23×C4C23×C3711yescharacteristic
400C23×C4C23×C3711yescharacteristic
401C23×C4C23×C3711yescharacteristic
402C23×C4C23×C3711yescharacteristic
403C23×C4C23×C3711yescharacteristic
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4Q8×C3718yes—
418C2×C4⋊C4C23×C3714yes—
419C2×C4⋊C4C23×C3714yes—
420C2×C4⋊C4C23×C3714yes—
421C2×C4⋊C4C23×C3714yes—
422C2×C4⋊C4C23×C3714yes—
423C2×C4⋊C4C23×C3714yes—
424C2×C4⋊C4C23×C3714yes—
425C2×C4⋊C4C23×C3714yes—
426C2×C4⋊C4C23×C3714yes—
427C2×C4⋊C4C23×C3714yes—
428C2×C4⋊C4C23×C3714yes—
429C2×C4⋊C4C23×C3714yes—
430C2×C4⋊C4C23×C3714yes—
431C2×C4⋊C4C23×C3714yes—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—42no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42C23×C3714yes—
438C2×C42C23×C3714yes—
439C2×C42C23×C3714yes—
440C2×C42C23×C3714yes—
441C2×C42C23×C3714yes—
442#95C23×C3714yes—
443#95C23×C3714yes—
444#95C23×C3714yes—
445#95C23×C3714yes—
446#95C23×C3714yes—
447#95C23×C3714yes—
448#95C23×C3714yes—
449#95C23×C3714yes—
450#95C23×C3714yes—
451#95C23×C3714yes—
452#95C23×C3714yes—
453#95C23×C3714yes—
454#95C23×C3714yes—
455#95C23×C3714yes—
456#95C23×C3714yes—
457#95C23×C3714yes—
458C24C24×C3711yescharacteristic
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4C2×Q8×C3714yes—
498C22×C4C2×Q8×C3714yes—
499C22×C4C2×Q8×C3714yes—
500C22×C4#41×C3714yes—
501C22×C4#41×C3714yes—
502C22×C4#41×C3714yes—
503C22×C4#41×C3714yes—
504C22×C4C24×C3712yes—
505C22×C4C24×C3712yes—
506C22×C4C24×C3712yes—
507C22×C4C24×C3712yes—
508C22×C4C24×C3712yes—
509C22×C4C24×C3712yes—
510C22×C4C24×C3712yes—
511C22×C4C24×C3712yes—
512C22×C4C24×C3712yes—
513C22×C4C24×C3712yes—
514C22×C4C24×C3712yes—
515C22×C4C24×C3712yes—
516C22×C4C24×C3712yes—
517C22×C4C24×C3712yes—
518C22×C4C24×C3712yes—
519C4⋊C4—28no—
520C4⋊C4—28no—
521C4⋊C4—28no—
522C4⋊C4—28no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—28no—
529C4⋊C4—44no—
530C4⋊C4—44no—
531C4⋊C4—44no—
532C4⋊C4C2×Q8×C37116yes—
533C42—28no—
534C42—28no—
535C42—44no—
536C42—44no—
537C42—44no—
538C23C22×Q8×C3712yes—
539C23C2×#41×C3712yes—
540C23C2×#41×C3712yes—
541C23C2×#41×C3712yes—
542C23C2×#41×C3712yes—
543C23H(5,𝔽2)×C3712yes—
544C232−1+4×C3712yes—
545C23C25×C3711yescharacteristic
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—28no—
550C2×C4—28no—
551C2×C4—28no—
552C2×C4—28no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4C22×Q8×C3714yes—
600C2×C4C22×Q8×C3714yes—
601C2×C4C22×Q8×C3714yes—
602C2×C4C2×#41×C3714yes—
603C2×C4C2×#41×C3714yes—
604C2×C4C2×#41×C3714yes—
605C2×C4C2×#41×C3714yes—
606C22C37×#52914yes—
607C22C37×#53314yes—
608C22C37×#53914yes—
609C22C37×#55214yes—
610C22C37×#55314yes—
611C22C37×#55414yes—
612C22C37×#55714yes—
613C22C23×Q8×C3711yescharacteristic
614C22C22×#41×C3711yescharacteristic
615C22C22×#41×C3711yescharacteristic
616C22C22×#41×C3711yescharacteristic
617C22C22×#41×C3711yescharacteristic
618C22C2×H(5,𝔽2)×C3711yescharacteristic
619C22C2×2−1+4×C3711yescharacteristic
620C4—24no—
621C4—24no—
622C4—24no—
623C4—24no—
624C4—24no—
625C4—24no—
626C4—24no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—42no—
635C2C37×#258518yesdirect product factor
636C2C2×C37×#52911yescharacteristic
637C2C2×C37×#53311yescharacteristic
638C2C2×C37×#53911yescharacteristic
639C2C2×C37×#55211yescharacteristic
640C2C2×C37×#55311yescharacteristic
641C2C2×C37×#55411yescharacteristic
642C2C2×C37×#55711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C37C24
commutator, Frattini, cosocleC23C25×C37
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#2585C2direct (N × H)
284. C2×#2585C37direct (N × H)
314. #2585C2×C37direct (N × H)
330. C2×C37#2585direct (N × H)
388. C37C2×#2585direct (N × H)
635. C2C37×#2585direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#25852
C2×C37×#4002
C2×C37×#3982
C2×C37×#3892
C2×C37×#3872
C2×C4×C4⋊C4×C372
C2×#258537