Finite Group Databasebeta

← C37×#25030 #22646283

Subgroups — C37×#25030 #22646283

Order 9472.

886 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
1C2×C37×#465C211yesmaximal, characteristic
2C2×C4×SD16×C37C211yesmaximal, characteristic, complemented
3C37×#2423C211yesmaximal, characteristic, complemented
4C37×#2422C211yesmaximal, characteristic
5C37×#2072C211yesmaximal, characteristic, complemented
6C37×#2071C211yesmaximal, characteristic, complemented
7C37×#2035C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic
9C37×#1968C211yesmaximal, characteristic, complemented
10C37×#1941C211yesmaximal, characteristic, complemented
11C37×#1865C211yesmaximal, characteristic, complemented
12C37×#1864C211yesmaximal, characteristic, complemented
13C37×#1844C211yesmaximal, characteristic, complemented
14C37×#1807C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C37C211yesmaximal, characteristic, complemented
16C22×SD16×C37C2211yescharacteristic
17C23×C8×C37C2211yescharacteristic
18C2×#123×C37—21no—
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×#121×C37C2211yescharacteristic
21C2×C4×Q8×C37C2211yescharacteristic
22C2×C4×D4×C37C2211yescharacteristic
23C37×#465—24no—
24C4×SD16×C37—24no—
25C2×#106×C37C2211yescharacteristic
26C2×#106×C37C2211yescharacteristic
27C2×#106×C37C2211yescharacteristic
28C2×#106×C37C2211yescharacteristic
29C2×#106×C37C2211yescharacteristic
30C2×#103×C37C2211yescharacteristic
31C2×#103×C37C2211yescharacteristic
32C2×#103×C37C2211yescharacteristic
33C2×#102×C37C2211yescharacteristic
34C2×#102×C37C2211yescharacteristic
35C2×#102×C37C2211yescharacteristic
36C2×C22⋊C8×C37C2211yescharacteristic
37C2×C4×C8×C37C2211yescharacteristic
38C2×C4×C8×C37C2211yescharacteristic
39C37×#399—21no—
40C37×#398—21no—
41C37×#397—21no—
42C37×#394—21no—
43C37×#391C2211yescharacteristic
44C37×#390C2211yescharacteristic
45C37×#389C2211yescharacteristic
46C37×#389C2211yescharacteristic
47C37×#388—21no—
48C37×#387—21no—
49C37×#385—21no—
50C37×#384C2211yescharacteristic
51C37×#384C2211yescharacteristic
52C37×#380C2211yescharacteristic
53C37×#380C2211yescharacteristic
54C4×C22⋊C4×C37C2211yescharacteristic
55C37×#340C2211yescharacteristic
56C37×#340C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#336C2211yescharacteristic
60C37×#336C2211yescharacteristic
61C22×Q8×C37C2311yescharacteristic
62C22×D4×C37—21no—
63C22×D4×C37C2311yescharacteristic
64C23×C4×C37—21no—
65C23×C4×C37C2311yescharacteristic
66C2×SD16×C37—22no—
67C2×SD16×C37—22no—
68C2×SD16×C37D414yes—
69C22×C8×C37—22no—
70C22×C8×C37—22no—
71C22×C8×C37—22no—
72C22×C8×C37C2311yescharacteristic
73C22×C8×C37C2311yescharacteristic
74C22×C8×C37C2311yescharacteristic
75C22×C8×C37C2311yescharacteristic
76#123×C37—44no—
77C22⋊Q8×C37—22no—
78C22⋊Q8×C37—41no—
79#121×C37—22no—
80#121×C37—41no—
81C4×Q8×C37—22no—
82C4×Q8×C37—41no—
83C4×D4×C37—22no—
84C4×D4×C37—41no—
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—21no—
92C2×C4⋊C4×C37—21no—
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×C37D411yescharacteristic
107C2×C22⋊C4×C37D411yescharacteristic
108C2×C42×C37—21no—
109C2×C42×C37C2311yescharacteristic
110C2×C42×C37C2311yescharacteristic
111#106×C37—22no—
112#106×C37—22no—
113#106×C37—22no—
114#106×C37—41no—
115#106×C37—41no—
116#103×C37—22no—
117#103×C37—22no—
118#103×C37—22no—
119#102×C37—22no—
120#102×C37—22no—
121#102×C37—22no—
122C22⋊C8×C37—22no—
123C4×C8×C37—22no—
124C4×C8×C37—22no—
125#95×C37—21no—
126#95×C37—21no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37D411yescharacteristic
132#95×C37D411yescharacteristic
133C24×C37—21no—
134C24×C37C2×D411yescharacteristic
135C2×Q8×C37—21no—
136C2×Q8×C37—21no—
137C2×Q8×C37—21no—
138C2×Q8×C37—21no—
139C2×Q8×C37—21no—
140C2×Q8×C37C2×D412yes—
141C2×D4×C37—21no—
142C2×D4×C37—21no—
143C2×D4×C37—21no—
144C2×D4×C37—21no—
145C2×D4×C37—21no—
146C2×D4×C37—42no—
147C2×D4×C37—42no—
148C2×D4×C37—81no—
149C2×D4×C37C2×D412yes—
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—21no—
157C22×C4×C37—21no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—21no—
162C22×C4×C37—21no—
163C22×C4×C37—42no—
164C22×C4×C37—42no—
165C22×C4×C37—81no—
166C22×C4×C37C2×D411yescharacteristic
167C22×C4×C37C2×D411yescharacteristic
168C22×C4×C37C2×D411yescharacteristic
169C22×C4×C37C2×D411yescharacteristic
170C22×C4×C37C2×D411yescharacteristic
171C22×C4×C37C2411yescharacteristic
172SD16×C37—28no—
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—44no—
182C2×C8×C37C2×D412yes—
183C2×C8×C37#4112yes—
184C2×C8×C37#4112yes—
185C2×C8×C37#4112yes—
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—81no—
204C4⋊C4×C37—81no—
205C4⋊C4×C37—81no—
206C22⋊C4×C37—22no—
207C22⋊C4×C37—42no—
208C22⋊C4×C37—42no—
209C22⋊C4×C37—42no—
210C22⋊C4×C37—42no—
211C22⋊C4×C37—42no—
212C22⋊C4×C37—42no—
213C22⋊C4×C37—81no—
214C22⋊C4×C37SD1614yescomplemented
215C42×C37—21no—
216C42×C37—21no—
217C42×C37—21no—
218C42×C37—21no—
219C42×C37—42no—
220C23×C37—21no—
221C23×C37—21no—
222C23×C37—21no—
223C23×C37—21no—
224C23×C37—21no—
225C23×C37—21no—
226C23×C37—22no—
227C23×C37—41no—
228C23×C37—41no—
229C23×C37—41no—
230C23×C37—41no—
231C23×C37—41no—
232C23×C37—41no—
233C23×C37C2×SD1612yes—
234C23×C37C22×D411yescharacteristic
235Q8×C37—22no—
236Q8×C37—22no—
237Q8×C37—41no—
238Q8×C37—41no—
239D4×C37—22no—
240D4×C37—22no—
241D4×C37—41no—
242D4×C37—41no—
243D4×C37—84no—
244C2×C4×C37—21no—
245C2×C4×C37—21no—
246C2×C4×C37—21no—
247C2×C4×C37—21no—
248C2×C4×C37—21no—
249C2×C4×C37—21no—
250C2×C4×C37—21no—
251C2×C4×C37—21no—
252C2×C4×C37—22no—
253C2×C4×C37—21no—
254C2×C4×C37—21no—
255C2×C4×C37—21no—
256C2×C4×C37—21no—
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—41no—
281C2×C4×C37—84no—
282C2×C4×C37C2×SD1612yes—
283C2×C4×C37C2×SD1612yes—
284C2×C4×C37#13512yes—
285C2×C4×C37C22×D411yescharacteristic
286C2×C4×C37C2×#4111yescharacteristic
287C2×C4×C37C2×#4111yescharacteristic
288C2×C4×C37C2×#4111yescharacteristic
289C2×C4×C37H(5,𝔽2)11yescharacteristic
290C2×C4×C372−1+411yescharacteristic
291C8×C37—22no—
292C8×C37—41no—
293C8×C37—41no—
294C8×C37#12314yescomplemented
295#25030C3711yesmaximal, characteristic, direct product factor, Sylow
296C22×C37—22no—
297C22×C37—22no—
298C22×C37—22no—
299C22×C37—41no—
300C22×C37—41no—
301C22×C37—41no—
302C22×C37—41no—
303C22×C37—42no—
304C22×C37—42no—
305C22×C37—42no—
306C22×C37—81no—
307C22×C37—81no—
308C22×C37—81no—
309C22×C37—81no—
310C22×C37#53211yescharacteristic
311C22×C37D4211yescharacteristic
312C22×C37#54711yescharacteristic
313C22×C37C22×SD1611yescharacteristic
314C22×C37C2×#13511yescharacteristic
315C22×C37#57711yescharacteristic
316C22×C37#57711yescharacteristic
317C4×C37—22no—
318C4×C37—22no—
319C4×C37—22no—
320C4×C37—41no—
321C4×C37—42no—
322C4×C37—41no—
323C4×C37—81no—
324C4×C37—81no—
325C4×C37—81no—
326C4×C37—81no—
327C4×C37—81no—
328C4×C37—81no—
329C4×C37C2×#12311yescharacteristic
330C4×C37#54211yescharacteristic
331C4×C37#54711yescharacteristic
332C4×C37#55311yescharacteristic
333C2×#465C2×C3711yescharacteristic
334C2×C4×SD16C2×C3711yescharacteristic, complemented
335#2423C2×C3711yescharacteristic, complemented
336#2422C2×C3711yescharacteristic
337#2072C2×C3711yescharacteristic, complemented
338#2071C2×C3711yescharacteristic, complemented
339#2035C2×C3711yescharacteristic, complemented
340#2034C2×C3711yescharacteristic
341#1968C2×C3711yescharacteristic, complemented
342#1941C2×C3711yescharacteristic, complemented
343#1865C2×C3711yescharacteristic, complemented
344#1864C2×C3711yescharacteristic, complemented
345#1844C2×C3711yescharacteristic, complemented
346#1807C2×C3711yescharacteristic, complemented
347C8×C22⋊C4C2×C3711yescharacteristic, complemented
348C2×C37—42no—
349C2×C37—82no—
350C2×C37#242211yescharacteristic
351C2×C37#316711yescharacteristic
352C2×C37#317311yescharacteristic
353C2×C37D4×SD1611yescharacteristic
354C2×C37#328411yescharacteristic
355C2×C37#333511yescharacteristic
356C2×C37#333711yescharacteristic
357C22×SD16C22×C3711yescharacteristic
358C23×C8C22×C3711yescharacteristic
359C2×#123—21no—
360C2×C22⋊Q8C22×C3711yescharacteristic
361C2×#121C22×C3711yescharacteristic
362C2×C4×Q8C22×C3711yescharacteristic
363C2×C4×D4C22×C3711yescharacteristic
364#465—24no—
365C4×SD16—24no—
366C2×#106C22×C3711yescharacteristic
367C2×#106C22×C3711yescharacteristic
368C2×#106C22×C3711yescharacteristic
369C2×#106C22×C3711yescharacteristic
370C2×#106C22×C3711yescharacteristic
371C2×#103C22×C3711yescharacteristic
372C2×#103C22×C3711yescharacteristic
373C2×#103C22×C3711yescharacteristic
374C2×#102C22×C3711yescharacteristic
375C2×#102C22×C3711yescharacteristic
376C2×#102C22×C3711yescharacteristic
377C2×C22⋊C8C22×C3711yescharacteristic
378C2×C4×C8C22×C3711yescharacteristic
379C2×C4×C8C22×C3711yescharacteristic
380#399—21no—
381#398—21no—
382#397—21no—
383#394—21no—
384#391C22×C3711yescharacteristic
385#390C22×C3711yescharacteristic
386#389C22×C3711yescharacteristic
387#389C22×C3711yescharacteristic
388#388—21no—
389#387—21no—
390#385—21no—
391#384C22×C3711yescharacteristic
392#384C22×C3711yescharacteristic
393#380C22×C3711yescharacteristic
394#380C22×C3711yescharacteristic
395C4×C22⋊C4C22×C3711yescharacteristic
396#340C22×C3711yescharacteristic
397#340C22×C3711yescharacteristic
398#340C22×C3711yescharacteristic
399#340C22×C3711yescharacteristic
400#336C22×C3711yescharacteristic
401#336C22×C3711yescharacteristic
402C37#2503011yescharacteristic, direct product factor, Sylow
403C22×Q8C23×C3711yescharacteristic
404C22×D4—21no—
405C22×D4C23×C3711yescharacteristic
406C23×C4—21no—
407C23×C4C23×C3711yescharacteristic
408C2×SD16—22no—
409C2×SD16—22no—
410C2×SD16D4×C3714yes—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8C23×C3711yescharacteristic
415C22×C8C23×C3711yescharacteristic
416C22×C8C23×C3711yescharacteristic
417C22×C8C23×C3711yescharacteristic
418#123—44no—
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421#121—22no—
422#121—41no—
423C4×Q8—22no—
424C4×Q8—41no—
425C4×D4—22no—
426C4×D4—41no—
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—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4C23×C3711yescharacteristic
436C2×C4⋊C4C23×C3711yescharacteristic
437C2×C4⋊C4C23×C3711yescharacteristic
438C2×C4⋊C4C23×C3711yescharacteristic
439C2×C4⋊C4C23×C3711yescharacteristic
440C2×C4⋊C4C23×C3711yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C3711yescharacteristic
449C2×C22⋊C4D4×C3711yescharacteristic
450C2×C42—21no—
451C2×C42C23×C3711yescharacteristic
452C2×C42C23×C3711yescharacteristic
453#106—22no—
454#106—22no—
455#106—22no—
456#106—41no—
457#106—41no—
458#103—22no—
459#103—22no—
460#103—22no—
461#102—22no—
462#102—22no—
463#102—22no—
464C22⋊C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95D4×C3711yescharacteristic
474#95D4×C3711yescharacteristic
475C24—21no—
476C24C2×D4×C3711yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8C2×D4×C3712yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—81no—
491C2×D4C2×D4×C3712yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4C2×D4×C3711yescharacteristic
509C22×C4C2×D4×C3711yescharacteristic
510C22×C4C2×D4×C3711yescharacteristic
511C22×C4C2×D4×C3711yescharacteristic
512C22×C4C2×D4×C3711yescharacteristic
513C22×C4C24×C3711yescharacteristic
514SD16—28no—
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—44no—
524C2×C8C2×D4×C3712yes—
525C2×C8#41×C3712yes—
526C2×C8#41×C3712yes—
527C2×C8#41×C3712yes—
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—81no—
546C4⋊C4—81no—
547C4⋊C4—81no—
548C22⋊C4—22no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4SD16×C3714yescomplemented
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23C2×SD16×C3712yes—
576C23C22×D4×C3711yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581D4—22no—
582D4—22no—
583D4—41no—
584D4—41no—
585D4—84no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
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—41no—
623C2×C4—84no—
624C2×C4C2×SD16×C3712yes—
625C2×C4C2×SD16×C3712yes—
626C2×C4#135×C3712yes—
627C2×C4C22×D4×C3711yescharacteristic
628C2×C4C2×#41×C3711yescharacteristic
629C2×C4C2×#41×C3711yescharacteristic
630C2×C4C2×#41×C3711yescharacteristic
631C2×C4H(5,𝔽2)×C3711yescharacteristic
632C2×C42−1+4×C3711yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8#123×C3714yescomplemented
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22C37×#53211yescharacteristic
652C22D42×C3711yescharacteristic
653C22C37×#54711yescharacteristic
654C22C22×SD16×C3711yescharacteristic
655C22C2×#135×C3711yescharacteristic
656C22C37×#57711yescharacteristic
657C22C37×#57711yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4C2×#123×C3711yescharacteristic
671C4C37×#54211yescharacteristic
672C4C37×#54711yescharacteristic
673C4C37×#55311yescharacteristic
674C2—42no—
675C2—82no—
676C2C37×#242211yescharacteristic
677C2C37×#316711yescharacteristic
678C2C37×#317311yescharacteristic
679C2D4×SD16×C3711yescharacteristic
680C2C37×#328411yescharacteristic
681C2C37×#333511yescharacteristic
682C2C37×#333711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
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
2. C2×C4×SD16×C37C2semidirect
3. C37×#2423C2semidirect
5. C37×#2072C2semidirect
6. C37×#2071C2semidirect
7. C37×#2035C2semidirect
9. C37×#1968C2semidirect
10. C37×#1941C2semidirect
11. C37×#1865C2semidirect
12. C37×#1864C2semidirect
13. C37×#1844C2semidirect
14. C37×#1807C2semidirect
15. C8×C22⋊C4×C37C2semidirect
214. C22⋊C4×C37SD16semidirect
294. C8×C37#123semidirect
295. #25030C37direct (N × H)
334. C2×C4×SD16C2×C37semidirect
335. #2423C2×C37semidirect
337. #2072C2×C37semidirect
338. #2071C2×C37semidirect
339. #2035C2×C37semidirect
341. #1968C2×C37semidirect
342. #1941C2×C37semidirect
343. #1865C2×C37semidirect
344. #1864C2×C37semidirect
345. #1844C2×C37semidirect
346. #1807C2×C37semidirect
347. C8×C22⋊C4C2×C37semidirect
402. C37#25030direct (N × H)
556. C22⋊C4SD16×C37semidirect
636. C8#123×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4652
C2×C4×SD16×C372
C37×#24232
C37×#24222
C37×#20722
C37×#20712
C37×#20352
C37×#20342
C37×#19682
C37×#19412
C37×#18652
C37×#18642
C37×#18442
C37×#18072
C8×C22⋊C4×C372
#2503037