Finite Group Databasebeta

← C37×#28925 #22650178

Subgroups — C37×#28925 #22650178

Order 9472.

836 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#487C211yesmaximal, characteristic, complemented
2C2×C37×#470C211yesmaximal, characteristic
3C37×#2492C211yesmaximal, characteristic
4C37×#2429C211yesmaximal, characteristic
5C37×#2058C211yesmaximal, characteristic, complemented
6C37×#2035C211yesmaximal, characteristic
7C37×#2016C211yesmaximal, characteristic, complemented
8C37×#2001C211yesmaximal, characteristic
9C37×#1971C211yesmaximal, characteristic, complemented
10C37×#1933C211yesmaximal, characteristic, complemented
11C37×#1927C211yesmaximal, characteristic, complemented
12C37×#1894C211yesmaximal, characteristic
13C37×#1878C211yesmaximal, characteristic, complemented
14C37×#1763C211yesmaximal, characteristic, complemented
15C37×#1753C211yesmaximal, characteristic
16C22×Q16×C37C2211yescharacteristic
17C22×Q16×C37C2211yescharacteristic
18C22×M16×C37C2211yescharacteristic
19C2×C4⋊Q8×C37C2211yescharacteristic
20C2×C4⋊Q8×C37C2211yescharacteristic
21C2×C22⋊Q8×C37C2211yescharacteristic
22C2×C22⋊Q8×C37C2211yescharacteristic
23C2×C22⋊Q8×C37C2211yescharacteristic
24C2×C4×Q8×C37C2211yescharacteristic
25C37×#487—24no—
26C37×#470—24no—
27C2×#106×C37C2211yescharacteristic
28C2×#106×C37C2211yescharacteristic
29C2×#103×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#103×C37C2211yescharacteristic
34C2×#103×C37C2211yescharacteristic
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×C22⋊C8×C37C2211yescharacteristic
38C2×#97×C37C2211yescharacteristic
39C2×C4×C8×C37C2211yescharacteristic
40C37×#400—21no—
41C37×#398—21no—
42C37×#396—21no—
43C37×#393—21no—
44C37×#391—21no—
45C37×#391C2211yescharacteristic
46C37×#391C2211yescharacteristic
47C37×#391C2211yescharacteristic
48C37×#389—21no—
49C37×#389C2211yescharacteristic
50C37×#388—21no—
51C37×#388—21no—
52C37×#380C2211yescharacteristic
53C4×C4⋊C4×C37C2211yescharacteristic
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37—21no—
62C22×Q8×C37C2311yescharacteristic
63C22×Q8×C37C2311yescharacteristic
64C22×Q8×C37C2311yescharacteristic
65C23×C4×C37C2311yescharacteristic
66C2×Q16×C37—22no—
67C2×Q16×C37—22no—
68C2×Q16×C37—22no—
69C2×Q16×C37—41no—
70C2×Q16×C37—41no—
71C2×Q16×C37—41no—
72C2×M16×C37—22no—
73C2×M16×C37—22no—
74C2×M16×C37—41no—
75C22×C8×C37C2311yescharacteristic
76C22×C8×C37C2311yescharacteristic
77C22×C8×C37C2311yescharacteristic
78C22×C8×C37C2311yescharacteristic
79C4⋊Q8×C37—22no—
80C4⋊Q8×C37—22no—
81C4⋊Q8×C37—41no—
82C4⋊Q8×C37—41no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—22no—
85C22⋊Q8×C37—22no—
86C22⋊Q8×C37—41no—
87C22⋊Q8×C37—41no—
88C22⋊Q8×C37—41no—
89C4×Q8×C37—22no—
90C4×Q8×C37—41no—
91C2×C4⋊C4×C37—21no—
92C2×C4⋊C4×C37—21no—
93C2×C4⋊C4×C37—21no—
94C2×C4⋊C4×C37—21no—
95C2×C4⋊C4×C37—21no—
96C2×C4⋊C4×C37—21no—
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×C37D411yescharacteristic
109C2×C22⋊C4×C37D411yescharacteristic
110C2×C42×C37—21no—
111C2×C42×C37—21no—
112C2×C42×C37C2311yescharacteristic
113C2×C42×C37C2311yescharacteristic
114#106×C37—22no—
115#106×C37—41no—
116#103×C37—22no—
117#103×C37—22no—
118#103×C37—22no—
119#103×C37—22no—
120#103×C37—22no—
121#103×C37—22no—
122#103×C37—22no—
123#103×C37D414yes—
124C22⋊C8×C37—22no—
125#97×C37—41no—
126C4×C8×C37—22no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—21no—
136#95×C37D411yescharacteristic
137#95×C37D411yescharacteristic
138C24×C37C2×D411yescharacteristic
139C2×Q8×C37—21no—
140C2×Q8×C37—21no—
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×Q8×C37—21no—
148C2×Q8×C37—21no—
149C2×Q8×C37—21no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—42no—
157C2×Q8×C37—42no—
158C2×Q8×C37—81no—
159C2×Q8×C37C2×D412yes—
160C22×C4×C37—21no—
161C22×C4×C37—21no—
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×C37C2×D411yescharacteristic
175C22×C4×C37C2×D411yescharacteristic
176C22×C4×C37C2×D411yescharacteristic
177C22×C4×C37C2×D411yescharacteristic
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2411yescharacteristic
180Q16×C37—44no—
181Q16×C37—44no—
182M16×C37—44no—
183C2×C8×C37—21no—
184C2×C8×C37—21no—
185C2×C8×C37—21no—
186C2×C8×C37—21no—
187C2×C8×C37—21no—
188C2×C8×C37—21no—
189C2×C8×C37—21no—
190C2×C8×C37—21no—
191C2×C8×C37—21no—
192C2×C8×C37C2×D412yes—
193C2×C8×C37#4112yes—
194C2×C8×C37#4112yes—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—42no—
204C4⋊C4×C37—42no—
205C4⋊C4×C37—42no—
206C4⋊C4×C37—42no—
207C4⋊C4×C37—42no—
208C4⋊C4×C37—42no—
209C4⋊C4×C37—42no—
210C4⋊C4×C37—42no—
211C4⋊C4×C37C2×D412yes—
212C4⋊C4×C37#4112yes—
213C22⋊C4×C37—22no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—42no—
216C22⋊C4×C37—42no—
217C22⋊C4×C37—42no—
218C22⋊C4×C37—81no—
219C42×C37—21no—
220C42×C37—21no—
221C42×C37—21no—
222C42×C37—21no—
223C42×C37—42no—
224C42×C37—81no—
225C23×C37—21no—
226C23×C37—21no—
227C23×C37—21no—
228C23×C37—21no—
229C23×C37—21no—
230C23×C37—21no—
231C23×C37—21no—
232C23×C37C22×D411yescharacteristic
233Q8×C37—22no—
234Q8×C37—22no—
235Q8×C37—41no—
236Q8×C37—41no—
237Q8×C37—41no—
238Q8×C37—41no—
239Q8×C37—41no—
240Q8×C37—41no—
241Q8×C37—41no—
242Q8×C37—41no—
243Q8×C37—41no—
244Q8×C37—41no—
245Q8×C37—84no—
246C2×C4×C37—21no—
247C2×C4×C37—21no—
248C2×C4×C37—21no—
249C2×C4×C37—21no—
250C2×C4×C37—21no—
251C2×C4×C37—22no—
252C2×C4×C37—22no—
253C2×C4×C37—21no—
254C2×C4×C37—21no—
255C2×C4×C37—21no—
256C2×C4×C37—22no—
257C2×C4×C37—21no—
258C2×C4×C37—21no—
259C2×C4×C37—21no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
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—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#13712yes—
288C2×C4×C37#13712yes—
289C2×C4×C37C22×D411yescharacteristic
290C2×C4×C37C2×#4111yescharacteristic
291C2×C4×C37C2×#4111yescharacteristic
292C2×C4×C37C2×#4111yescharacteristic
293C2×C4×C37H(5,𝔽2)11yescharacteristic
294C2×C4×C37H(5,𝔽2)11yescharacteristic
295C8×C37—22no—
296C8×C37—22no—
297C8×C37—22no—
298C8×C37—41no—
299#28925C3711yesmaximal, characteristic, direct product factor, Sylow
300C22×C37—41no—
301C22×C37—41no—
302C22×C37—41no—
303C22×C37—41no—
304C22×C37—41no—
305C22×C37—41no—
306C22×C37—41no—
307C22×C37#53211yescharacteristic
308C22×C37D4211yescharacteristic
309C22×C37#54611yescharacteristic
310C22×C37C2×#13711yescharacteristic
311C22×C37C2×#13711yescharacteristic
312C22×C37#57711yescharacteristic
313C22×C37#57811yescharacteristic
314C4×C37—22no—
315C4×C37—22no—
316C4×C37—41no—
317C4×C37—41no—
318C4×C37—42no—
319C4×C37—42no—
320C4×C37—41no—
321C4×C37—42no—
322C4×C37—81no—
323C4×C37—81no—
324C4×C37—81no—
325C4×C37—81no—
326C4×C37—81no—
327C4×C37#53211yescharacteristic
328C4×C37#53811yescharacteristic
329C4×C37#54611yescharacteristic
330C4×C37#55511yescharacteristic
331C2×#487C2×C3711yescharacteristic, complemented
332C2×#470C2×C3711yescharacteristic
333#2492C2×C3711yescharacteristic
334#2429C2×C3711yescharacteristic
335#2058C2×C3711yescharacteristic, complemented
336#2035C2×C3711yescharacteristic
337#2016C2×C3711yescharacteristic, complemented
338#2001C2×C3711yescharacteristic
339#1971C2×C3711yescharacteristic, complemented
340#1933C2×C3711yescharacteristic, complemented
341#1927C2×C3711yescharacteristic, complemented
342#1894C2×C3711yescharacteristic
343#1878C2×C3711yescharacteristic, complemented
344#1763C2×C3711yescharacteristic, complemented
345#1753C2×C3711yescharacteristic
346C2×C37—81no—
347C2×C37#255511yescharacteristic
348C2×C37#317811yescharacteristic
349C2×C37#318511yescharacteristic
350C2×C37#326611yescharacteristic
351C2×C37#327011yescharacteristic
352C2×C37#332811yescharacteristic
353C2×C37#333111yescharacteristic
354C22×Q16C22×C3711yescharacteristic
355C22×Q16C22×C3711yescharacteristic
356C22×M16C22×C3711yescharacteristic
357C2×C4⋊Q8C22×C3711yescharacteristic
358C2×C4⋊Q8C22×C3711yescharacteristic
359C2×C22⋊Q8C22×C3711yescharacteristic
360C2×C22⋊Q8C22×C3711yescharacteristic
361C2×C22⋊Q8C22×C3711yescharacteristic
362C2×C4×Q8C22×C3711yescharacteristic
363#487—24no—
364#470—24no—
365C2×#106C22×C3711yescharacteristic
366C2×#106C22×C3711yescharacteristic
367C2×#103C22×C3711yescharacteristic
368C2×#103C22×C3711yescharacteristic
369C2×#103C22×C3711yescharacteristic
370C2×#103C22×C3711yescharacteristic
371C2×#103C22×C3711yescharacteristic
372C2×#103C22×C3711yescharacteristic
373C2×#103C22×C3711yescharacteristic
374C2×#103C22×C3711yescharacteristic
375C2×C22⋊C8C22×C3711yescharacteristic
376C2×#97C22×C3711yescharacteristic
377C2×C4×C8C22×C3711yescharacteristic
378#400—21no—
379#398—21no—
380#396—21no—
381#393—21no—
382#391—21no—
383#391C22×C3711yescharacteristic
384#391C22×C3711yescharacteristic
385#391C22×C3711yescharacteristic
386#389—21no—
387#389C22×C3711yescharacteristic
388#388—21no—
389#388—21no—
390#380C22×C3711yescharacteristic
391C4×C4⋊C4C22×C3711yescharacteristic
392C4×C22⋊C4C22×C3711yescharacteristic
393#340C22×C3711yescharacteristic
394#340C22×C3711yescharacteristic
395#340C22×C3711yescharacteristic
396#340C22×C3711yescharacteristic
397#336C22×C3711yescharacteristic
398#336C22×C3711yescharacteristic
399C37#2892511yescharacteristic, direct product factor, Sylow
400C22×Q8—21no—
401C22×Q8C23×C3711yescharacteristic
402C22×Q8C23×C3711yescharacteristic
403C22×Q8C23×C3711yescharacteristic
404C23×C4C23×C3711yescharacteristic
405C2×Q16—22no—
406C2×Q16—22no—
407C2×Q16—22no—
408C2×Q16—41no—
409C2×Q16—41no—
410C2×Q16—41no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—41no—
414C22×C8C23×C3711yescharacteristic
415C22×C8C23×C3711yescharacteristic
416C22×C8C23×C3711yescharacteristic
417C22×C8C23×C3711yescharacteristic
418C4⋊Q8—22no—
419C4⋊Q8—22no—
420C4⋊Q8—41no—
421C4⋊Q8—41no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—41no—
426C22⋊Q8—41no—
427C22⋊Q8—41no—
428C4×Q8—22no—
429C4×Q8—41no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4C23×C3711yescharacteristic
439C2×C4⋊C4C23×C3711yescharacteristic
440C2×C4⋊C4C23×C3711yescharacteristic
441C2×C4⋊C4C23×C3711yescharacteristic
442C2×C4⋊C4C23×C3711yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4D4×C3711yescharacteristic
448C2×C22⋊C4D4×C3711yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C3711yescharacteristic
452C2×C42C23×C3711yescharacteristic
453#106—22no—
454#106—41no—
455#103—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—22no—
460#103—22no—
461#103—22no—
462#103D4×C3714yes—
463C22⋊C8—22no—
464#97—41no—
465C4×C8—22no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95D4×C3711yescharacteristic
476#95D4×C3711yescharacteristic
477C24C2×D4×C3711yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—81no—
498C2×Q8C2×D4×C3712yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4C2×D4×C3711yescharacteristic
514C22×C4C2×D4×C3711yescharacteristic
515C22×C4C2×D4×C3711yescharacteristic
516C22×C4C2×D4×C3711yescharacteristic
517C22×C4C2×D4×C3711yescharacteristic
518C22×C4C24×C3711yescharacteristic
519Q16—44no—
520Q16—44no—
521M16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8C2×D4×C3712yes—
532C2×C8#41×C3712yes—
533C2×C8#41×C3712yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4C2×D4×C3712yes—
551C4⋊C4#41×C3712yes—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C42—81no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23C22×D4×C3711yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—84no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
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—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4#137×C3712yes—
627C2×C4#137×C3712yes—
628C2×C4C22×D4×C3711yescharacteristic
629C2×C4C2×#41×C3711yescharacteristic
630C2×C4C2×#41×C3711yescharacteristic
631C2×C4C2×#41×C3711yescharacteristic
632C2×C4H(5,𝔽2)×C3711yescharacteristic
633C2×C4H(5,𝔽2)×C3711yescharacteristic
634C8—22no—
635C8—22no—
636C8—22no—
637C8—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C37×#53211yescharacteristic
646C22D42×C3711yescharacteristic
647C22C37×#54611yescharacteristic
648C22C2×#137×C3711yescharacteristic
649C22C2×#137×C3711yescharacteristic
650C22C37×#57711yescharacteristic
651C22C37×#57811yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4C37×#53211yescharacteristic
666C4C37×#53811yescharacteristic
667C4C37×#54611yescharacteristic
668C4C37×#55511yescharacteristic
669C2—81no—
670C2C37×#255511yescharacteristic
671C2C37×#317811yescharacteristic
672C2C37×#318511yescharacteristic
673C2C37×#326611yescharacteristic
674C2C37×#327011yescharacteristic
675C2C37×#332811yescharacteristic
676C2C37×#333111yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC24×C37C2×D4
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×#487C2semidirect
5. C37×#2058C2semidirect
7. C37×#2016C2semidirect
9. C37×#1971C2semidirect
10. C37×#1933C2semidirect
11. C37×#1927C2semidirect
13. C37×#1878C2semidirect
14. C37×#1763C2semidirect
299. #28925C37direct (N × H)
331. C2×#487C2×C37semidirect
335. #2058C2×C37semidirect
337. #2016C2×C37semidirect
339. #1971C2×C37semidirect
340. #1933C2×C37semidirect
341. #1927C2×C37semidirect
343. #1878C2×C37semidirect
344. #1763C2×C37semidirect
399. C37#28925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#4872
C2×C37×#4702
C37×#24922
C37×#24292
C37×#20582
C37×#20352
C37×#20162
C37×#20012
C37×#19712
C37×#19332
C37×#19272
C37×#18942
C37×#18782
C37×#17632
C37×#17532
#2892537