Finite Group Databasebeta

← C37×#25087 #22646340

Subgroups — C37×#25087 #22646340

Order 9472.

1192 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#466C211yesmaximal, characteristic, complemented
2C2×C37×#463C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C2×C37×#416C211yesmaximal, characteristic, complemented
5C37×#2431C211yesmaximal, characteristic, complemented
6C37×#2363C211yesmaximal, characteristic, complemented
7C37×#2067C211yesmaximal, characteristic, complemented
8C37×#2055C211yesmaximal, characteristic, complemented
9C37×#2042C211yesmaximal, characteristic, complemented
10C37×#2011C211yesmaximal, characteristic, complemented
11C37×#1982C211yesmaximal, characteristic, complemented
12C37×#1928C211yesmaximal, characteristic, complemented
13C37×#1879C211yesmaximal, characteristic, complemented
14C37×#1875C211yesmaximal, characteristic, complemented
15C37×#1850C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×SD16×C37C2211yescharacteristic
18C22×D8×C37C2211yescharacteristic
19C22×D8×C37C2211yescharacteristic
20C23×C8×C37C2211yescharacteristic
21C2×#127×C37C2211yescharacteristic
22C2×#124×C37C2211yescharacteristic
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×C4×D4×C37C2211yescharacteristic
26C2×#117×C37C2211yescharacteristic
27C37×#466—24no—
28C37×#463—24no—
29C37×#449—24no—
30C2×#107×C37C2211yescharacteristic
31C2×C4⋊C8×C37C2211yescharacteristic
32C2×C4⋊C8×C37C2211yescharacteristic
33C37×#416—24no—
34C2×#103×C37C2211yescharacteristic
35C2×#103×C37C2211yescharacteristic
36C2×#103×C37C2211yescharacteristic
37C2×#102×C37C2211yescharacteristic
38C2×#102×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×C22⋊C8×C37C2211yescharacteristic
45C37×#392—21no—
46C37×#392—21no—
47C37×#391C2211yescharacteristic
48C37×#390—21no—
49C37×#390C2211yescharacteristic
50C37×#390C2211yescharacteristic
51C37×#389C2211yescharacteristic
52C37×#388—21no—
53C37×#386—21no—
54C37×#386—21no—
55C37×#386—21no—
56C4×C4⋊C4×C37C2211yescharacteristic
57C4×C22⋊C4×C37—21no—
58C4×C22⋊C4×C37C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#336C2211yescharacteristic
62C37×#336C2211yescharacteristic
63C2×#41×C37—22no—
64C2×#41×C37—22no—
65C2×#41×C37—22no—
66C2×#41×C37—22no—
67C2×#41×C37—41no—
68C2×#41×C37—41no—
69C22×Q8×C37C2311yescharacteristic
70C22×D4×C37—21no—
71C22×D4×C37—21no—
72C22×D4×C37—21no—
73C22×D4×C37—21no—
74C22×D4×C37—21no—
75C22×D4×C37C2311yescharacteristic
76C22×D4×C37C2311yescharacteristic
77C22×D4×C37C2311yescharacteristic
78C23×C4×C37—21no—
79C23×C4×C37—21no—
80C23×C4×C37C2311yescharacteristic
81C2×SD16×C37—22no—
82C2×SD16×C37—22no—
83C2×SD16×C37—41no—
84C2×D8×C37—22no—
85C2×D8×C37—22no—
86C2×D8×C37—22no—
87C2×D8×C37—22no—
88C2×D8×C37—41no—
89C2×D8×C37—41no—
90C22×C8×C37—22no—
91C22×C8×C37—22no—
92C22×C8×C37—41no—
93C22×C8×C37C2311yescharacteristic
94C22×C8×C37C2311yescharacteristic
95C22×C8×C37C2311yescharacteristic
96C22×C8×C37C2311yescharacteristic
97#127×C37—22no—
98#127×C37—41no—
99#124×C37—22no—
100#124×C37—41no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37D414yescomplemented
105C4×D4×C37—22no—
106C4×D4×C37—41no—
107#117×C37—22no—
108#117×C37—41no—
109C2×C4⋊C4×C37—21no—
110C2×C4⋊C4×C37C2311yescharacteristic
111C2×C4⋊C4×C37C2311yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C22⋊C4×C37—21no—
115C2×C22⋊C4×C37—21no—
116C2×C22⋊C4×C37—21no—
117C2×C22⋊C4×C37—21no—
118C2×C22⋊C4×C37—21no—
119C2×C22⋊C4×C37—21no—
120C2×C22⋊C4×C37—21no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37D411yescharacteristic
125C2×C22⋊C4×C37D411yescharacteristic
126C2×C42×C37—21no—
127C2×C42×C37—21no—
128C2×C42×C37C2311yescharacteristic
129C2×C42×C37C2311yescharacteristic
130#107×C37—22no—
131C4⋊C8×C37—22no—
132C4⋊C8×C37—41no—
133#103×C37—22no—
134#103×C37—22no—
135#103×C37D414yescomplemented
136#102×C37—22no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—22no—
141#102×C37—22no—
142#102×C37—41no—
143C22⋊C8×C37—22no—
144#95×C37—21no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148#95×C37D411yescharacteristic
149#95×C37D411yescharacteristic
150C24×C37—21no—
151C24×C37—21no—
152C24×C37—21no—
153C24×C37C2×D411yescharacteristic
154#41×C37—28no—
155#41×C37—44no—
156#41×C37—44no—
157#41×C37—44no—
158C2×Q8×C37—21no—
159C2×Q8×C37—21no—
160C2×Q8×C37—21no—
161C2×Q8×C37—21no—
162C2×Q8×C37—21no—
163C2×Q8×C37C2×D412yes—
164C2×D4×C37—24no—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—21no—
171C2×D4×C37—21no—
172C2×D4×C37—21no—
173C2×D4×C37—21no—
174C2×D4×C37—21no—
175C2×D4×C37—21no—
176C2×D4×C37—21no—
177C2×D4×C37—21no—
178C2×D4×C37—21no—
179C2×D4×C37—21no—
180C2×D4×C37—21no—
181C2×D4×C37—42no—
182C2×D4×C37—42no—
183C2×D4×C37—42no—
184C2×D4×C37—42no—
185C2×D4×C37—42no—
186C2×D4×C37—42no—
187C2×D4×C37—42no—
188C2×D4×C37—42no—
189C2×D4×C37—81no—
190C2×D4×C37—81no—
191C2×D4×C37—81no—
192C2×D4×C37—81no—
193C2×D4×C37—81no—
194C2×D4×C37—81no—
195C2×D4×C37C2×D412yes—
196C2×D4×C37#4112yes—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—21no—
200C22×C4×C37—21no—
201C22×C4×C37—21no—
202C22×C4×C37—21no—
203C22×C4×C37—21no—
204C22×C4×C37—21no—
205C22×C4×C37—21no—
206C22×C4×C37—42no—
207C22×C4×C37—42no—
208C22×C4×C37—42no—
209C22×C4×C37—42no—
210C22×C4×C37—42no—
211C22×C4×C37—81no—
212C22×C4×C37C2×D411yescharacteristic
213C22×C4×C37C2×D411yescharacteristic
214C22×C4×C37C2×D411yescharacteristic
215C22×C4×C37C2×D411yescharacteristic
216C22×C4×C37C2×D412yes—
217C22×C4×C37C2×D411yescharacteristic
218C22×C4×C37#4112yes—
219C22×C4×C37C2411yescharacteristic
220SD16×C37—44no—
221D8×C37—44no—
222D8×C37—44no—
223C2×C8×C37—21no—
224C2×C8×C37—21no—
225C2×C8×C37—21no—
226C2×C8×C37—21no—
227C2×C8×C37—21no—
228C2×C8×C37—21no—
229C2×C8×C37—21no—
230C2×C8×C37—21no—
231C2×C8×C37—21no—
232C2×C8×C37—21no—
233C2×C8×C37—21no—
234C2×C8×C37—44no—
235C2×C8×C37C2×D412yes—
236C4⋊C4×C37—21no—
237C4⋊C4×C37—21no—
238C4⋊C4×C37—21no—
239C4⋊C4×C37—21no—
240C4⋊C4×C37—21no—
241C4⋊C4×C37—21no—
242C4⋊C4×C37—81no—
243C4⋊C4×C37C2×D412yes—
244C4⋊C4×C37C2×D412yes—
245C22⋊C4×C37—24no—
246C22⋊C4×C37—22no—
247C22⋊C4×C37—41no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—42no—
250C22⋊C4×C37—42no—
251C22⋊C4×C37—42no—
252C22⋊C4×C37—42no—
253C22⋊C4×C37—42no—
254C22⋊C4×C37—81no—
255C22⋊C4×C37—81no—
256C22⋊C4×C37—81no—
257C42×C37—21no—
258C42×C37—21no—
259C42×C37—21no—
260C42×C37—21no—
261C42×C37—42no—
262C42×C37—81no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—22no—
270C23×C37—22no—
271C23×C37—41no—
272C23×C37—41no—
273C23×C37—41no—
274C23×C37—41no—
275C23×C37—41no—
276C23×C37—41no—
277C23×C37—41no—
278C23×C37—41no—
279C23×C37—41no—
280C23×C37—41no—
281C23×C37—41no—
282C23×C37—41no—
283C23×C37—41no—
284C23×C37—41no—
285C23×C37—41no—
286C23×C37—41no—
287C23×C37—41no—
288C23×C37—41no—
289C23×C37—41no—
290C23×C37#12112yes—
291C23×C37C22×D411yescharacteristic
292Q8×C37—22no—
293Q8×C37—22no—
294Q8×C37—41no—
295Q8×C37—41no—
296D4×C37—22no—
297D4×C37—22no—
298D4×C37—22no—
299D4×C37—22no—
300D4×C37—48no—
301D4×C37—41no—
302D4×C37—41no—
303D4×C37—41no—
304D4×C37—41no—
305D4×C37—41no—
306D4×C37—41no—
307D4×C37—41no—
308D4×C37—41no—
309D4×C37—84no—
310D4×C37—84no—
311D4×C37—84no—
312D4×C37—84no—
313C2×C4×C37—21no—
314C2×C4×C37—21no—
315C2×C4×C37—21no—
316C2×C4×C37—21no—
317C2×C4×C37—22no—
318C2×C4×C37—22no—
319C2×C4×C37—22no—
320C2×C4×C37—22no—
321C2×C4×C37—22no—
322C2×C4×C37—21no—
323C2×C4×C37—21no—
324C2×C4×C37—22no—
325C2×C4×C37—22no—
326C2×C4×C37—21no—
327C2×C4×C37—21no—
328C2×C4×C37—21no—
329C2×C4×C37—21no—
330C2×C4×C37—21no—
331C2×C4×C37—21no—
332C2×C4×C37—21no—
333C2×C4×C37—48no—
334C2×C4×C37—41no—
335C2×C4×C37—41no—
336C2×C4×C37—41no—
337C2×C4×C37—41no—
338C2×C4×C37—41no—
339C2×C4×C37—41no—
340C2×C4×C37—41no—
341C2×C4×C37—41no—
342C2×C4×C37—41no—
343C2×C4×C37—41no—
344C2×C4×C37—41no—
345C2×C4×C37—41no—
346C2×C4×C37—84no—
347C2×C4×C37#12112yes—
348C2×C4×C37#13512yes—
349C2×C4×C37C22×D411yescharacteristic
350C2×C4×C37C22×D411yescharacteristic
351C2×C4×C37C2×#4111yescharacteristic
352C2×C4×C37C2×#4111yescharacteristic
353C2×C4×C37H(5,𝔽2)11yescharacteristic
354C2×C4×C37H(5,𝔽2)11yescharacteristic
355C8×C37—22no—
356C8×C37—41no—
357C8×C37—41no—
358C8×C37—41no—
359#25087C3711yesmaximal, characteristic, direct product factor, Sylow
360C22×C37—22no—
361C22×C37—22no—
362C22×C37—22no—
363C22×C37—41no—
364C22×C37—41no—
365C22×C37—41no—
366C22×C37—41no—
367C22×C37—42no—
368C22×C37—42no—
369C22×C37—42no—
370C22×C37—42no—
371C22×C37—42no—
372C22×C37—42no—
373C22×C37—81no—
374C22×C37—81no—
375C22×C37—81no—
376C22×C37—81no—
377C22×C37—81no—
378C22×C37—81no—
379C22×C37—81no—
380C22×C37—81no—
381C22×C37—81no—
382C22×C37—81no—
383C22×C37—81no—
384C22×C37—81no—
385C22×C37—81no—
386C22×C37—81no—
387C22×C37—81no—
388C22×C37C2×#12111yescharacteristic
389C22×C37D4211yescharacteristic
390C22×C37#54611yescharacteristic
391C22×C37C2×#13511yescharacteristic
392C22×C37#57511yescharacteristic
393C22×C37#57611yescharacteristic
394C22×C37#57611yescharacteristic
395C4×C37—22no—
396C4×C37—22no—
397C4×C37—42no—
398C4×C37—41no—
399C4×C37—42no—
400C4×C37—41no—
401C4×C37—42no—
402C4×C37—41no—
403C4×C37—81no—
404C4×C37—81no—
405C4×C37#52511yescharacteristic
406C4×C37#53811yescharacteristic
407C4×C37D4211yescharacteristic
408C4×C37#54611yescharacteristic
409C2×#466C2×C3711yescharacteristic, complemented
410C2×#463C2×C3711yescharacteristic, complemented
411C2×#449C2×C3711yescharacteristic, complemented
412C2×#416C2×C3711yescharacteristic, complemented
413#2431C2×C3711yescharacteristic, complemented
414#2363C2×C3711yescharacteristic, complemented
415#2067C2×C3711yescharacteristic, complemented
416#2055C2×C3711yescharacteristic, complemented
417#2042C2×C3711yescharacteristic, complemented
418#2011C2×C3711yescharacteristic, complemented
419#1982C2×C3711yescharacteristic, complemented
420#1928C2×C3711yescharacteristic, complemented
421#1879C2×C3711yescharacteristic, complemented
422#1875C2×C3711yescharacteristic, complemented
423#1850C2×C3711yescharacteristic, complemented
424C2×C37—42no—
425C2×C37—82no—
426C2×C37—82no—
427C2×C37—161no—
428C2×C37#242411yescharacteristic
429C2×C37#303511yescharacteristic
430C2×C37#304111yescharacteristic
431C2×C37#326811yescharacteristic
432C2×C37#328711yescharacteristic
433C2×C37#329711yescharacteristic
434C2×C37#331911yescharacteristic
435C22×#41C22×C3711yescharacteristic
436C22×SD16C22×C3711yescharacteristic
437C22×D8C22×C3711yescharacteristic
438C22×D8C22×C3711yescharacteristic
439C23×C8C22×C3711yescharacteristic
440C2×#127C22×C3711yescharacteristic
441C2×#124C22×C3711yescharacteristic
442C2×#121C22×C3711yescharacteristic
443C2×#121C22×C3711yescharacteristic
444C2×C4×D4C22×C3711yescharacteristic
445C2×#117C22×C3711yescharacteristic
446#466—24no—
447#463—24no—
448#449—24no—
449C2×#107C22×C3711yescharacteristic
450C2×C4⋊C8C22×C3711yescharacteristic
451C2×C4⋊C8C22×C3711yescharacteristic
452#416—24no—
453C2×#103C22×C3711yescharacteristic
454C2×#103C22×C3711yescharacteristic
455C2×#103C22×C3711yescharacteristic
456C2×#102C22×C3711yescharacteristic
457C2×#102C22×C3711yescharacteristic
458C2×#102C22×C3711yescharacteristic
459C2×#102C22×C3711yescharacteristic
460C2×#102C22×C3711yescharacteristic
461C2×#102C22×C3711yescharacteristic
462C2×#102C22×C3711yescharacteristic
463C2×C22⋊C8C22×C3711yescharacteristic
464#392—21no—
465#392—21no—
466#391C22×C3711yescharacteristic
467#390—21no—
468#390C22×C3711yescharacteristic
469#390C22×C3711yescharacteristic
470#389C22×C3711yescharacteristic
471#388—21no—
472#386—21no—
473#386—21no—
474#386—21no—
475C4×C4⋊C4C22×C3711yescharacteristic
476C4×C22⋊C4—21no—
477C4×C22⋊C4C22×C3711yescharacteristic
478#340C22×C3711yescharacteristic
479#340C22×C3711yescharacteristic
480#336C22×C3711yescharacteristic
481#336C22×C3711yescharacteristic
482C37#2508711yescharacteristic, direct product factor, Sylow
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8C23×C3711yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4C23×C3711yescharacteristic
496C22×D4C23×C3711yescharacteristic
497C22×D4C23×C3711yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4C23×C3711yescharacteristic
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8—22no—
511C22×C8—22no—
512C22×C8—41no—
513C22×C8C23×C3711yescharacteristic
514C22×C8C23×C3711yescharacteristic
515C22×C8C23×C3711yescharacteristic
516C22×C8C23×C3711yescharacteristic
517#127—22no—
518#127—41no—
519#124—22no—
520#124—41no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121D4×C3714yescomplemented
525C4×D4—22no—
526C4×D4—41no—
527#117—22no—
528#117—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4C23×C3711yescharacteristic
531C2×C4⋊C4C23×C3711yescharacteristic
532C2×C4⋊C4C23×C3711yescharacteristic
533C2×C4⋊C4C23×C3711yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4D4×C3711yescharacteristic
545C2×C22⋊C4D4×C3711yescharacteristic
546C2×C42—21no—
547C2×C42—21no—
548C2×C42C23×C3711yescharacteristic
549C2×C42C23×C3711yescharacteristic
550#107—22no—
551C4⋊C8—22no—
552C4⋊C8—41no—
553#103—22no—
554#103—22no—
555#103D4×C3714yescomplemented
556#102—22no—
557#102—22no—
558#102—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—41no—
563C22⋊C8—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95D4×C3711yescharacteristic
569#95D4×C3711yescharacteristic
570C24—21no—
571C24—21no—
572C24—21no—
573C24C2×D4×C3711yescharacteristic
574#41—28no—
575#41—44no—
576#41—44no—
577#41—44no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C3712yes—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C3712yes—
616C2×D4#41×C3712yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4C2×D4×C3711yescharacteristic
633C22×C4C2×D4×C3711yescharacteristic
634C22×C4C2×D4×C3711yescharacteristic
635C22×C4C2×D4×C3711yescharacteristic
636C22×C4C2×D4×C3712yes—
637C22×C4C2×D4×C3711yescharacteristic
638C22×C4#41×C3712yes—
639C22×C4C24×C3711yescharacteristic
640SD16—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8C2×D4×C3712yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C3712yes—
664C4⋊C4C2×D4×C3712yes—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—42no—
682C42—81no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#121×C3712yes—
711C23C22×D4×C3711yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—84no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—48no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—84no—
767C2×C4#121×C3712yes—
768C2×C4#135×C3712yes—
769C2×C4C22×D4×C3711yescharacteristic
770C2×C4C22×D4×C3711yescharacteristic
771C2×C4C2×#41×C3711yescharacteristic
772C2×C4C2×#41×C3711yescharacteristic
773C2×C4H(5,𝔽2)×C3711yescharacteristic
774C2×C4H(5,𝔽2)×C3711yescharacteristic
775C8—22no—
776C8—41no—
777C8—41no—
778C8—41no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C3711yescharacteristic
808C22D42×C3711yescharacteristic
809C22C37×#54611yescharacteristic
810C22C2×#135×C3711yescharacteristic
811C22C37×#57511yescharacteristic
812C22C37×#57611yescharacteristic
813C22C37×#57611yescharacteristic
814C4—22no—
815C4—22no—
816C4—42no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—42no—
821C4—41no—
822C4—81no—
823C4—81no—
824C4C37×#52511yescharacteristic
825C4C37×#53811yescharacteristic
826C4D42×C3711yescharacteristic
827C4C37×#54611yescharacteristic
828C2—42no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C37×#242411yescharacteristic
833C2C37×#303511yescharacteristic
834C2C37×#304111yescharacteristic
835C2C37×#326811yescharacteristic
836C2C37×#328711yescharacteristic
837C2C37×#329711yescharacteristic
838C2C37×#331911yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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×#466C2semidirect
2. C2×C37×#463C2semidirect
3. C2×C37×#449C2semidirect
4. C2×C37×#416C2semidirect
5. C37×#2431C2semidirect
6. C37×#2363C2semidirect
7. C37×#2067C2semidirect
8. C37×#2055C2semidirect
9. C37×#2042C2semidirect
10. C37×#2011C2semidirect
11. C37×#1982C2semidirect
12. C37×#1928C2semidirect
13. C37×#1879C2semidirect
14. C37×#1875C2semidirect
15. C37×#1850C2semidirect
104. #121×C37D4semidirect
135. #103×C37D4semidirect
359. #25087C37direct (N × H)
409. C2×#466C2×C37semidirect
410. C2×#463C2×C37semidirect
411. C2×#449C2×C37semidirect
412. C2×#416C2×C37semidirect
413. #2431C2×C37semidirect
414. #2363C2×C37semidirect
415. #2067C2×C37semidirect
416. #2055C2×C37semidirect
417. #2042C2×C37semidirect
418. #2011C2×C37semidirect
419. #1982C2×C37semidirect
420. #1928C2×C37semidirect
421. #1879C2×C37semidirect
422. #1875C2×C37semidirect
423. #1850C2×C37semidirect
482. C37#25087direct (N × H)
524. #121D4×C37semidirect
555. #103D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#4662
C2×C37×#4632
C2×C37×#4492
C2×C37×#4162
C37×#24312
C37×#23632
C37×#20672
C37×#20552
C37×#20422
C37×#20112
C37×#19822
C37×#19282
C37×#18792
C37×#18752
C37×#18502
#2508737