Finite Group Databasebeta

← C37×#24124 #22645377

Subgroups — C37×#24124 #22645377

Order 9472.

1216 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#553C211yesmaximal, characteristic, complemented
2C2×C37×#478C211yesmaximal, characteristic, complemented
3C2×C4×D8×C37C211yesmaximal, characteristic, complemented
4C37×#2535C211yesmaximal, characteristic, complemented
5C37×#2034C211yesmaximal, characteristic, complemented
6C37×#2033C211yesmaximal, characteristic, complemented
7C37×#1999C211yesmaximal, characteristic, complemented
8C37×#1999C211yesmaximal, characteristic, complemented
9C37×#1991C211yesmaximal, characteristic, complemented
10C37×#1954C211yesmaximal, characteristic, complemented
11C37×#1875C211yesmaximal, characteristic, complemented
12C37×#1874C211yesmaximal, characteristic, complemented
13C37×#1854C211yesmaximal, characteristic, complemented
14C37×#1852C211yesmaximal, characteristic, complemented
15C37×#1804C211yesmaximal, characteristic, complemented
16C22×D8×C37C2211yescharacteristic
17C37×#553—24no—
18C37×#553—24no—
19C2×#126×C37—21no—
20C2×#125×C37C2211yescharacteristic
21C2×#123×C37—21no—
22C2×#121×C37—21no—
23C2×#121×C37C2211yescharacteristic
24C2×#121×C37C2211yescharacteristic
25C2×#121×C37C2211yescharacteristic
26C2×#121×C37C2211yescharacteristic
27C2×C4×D4×C37—21no—
28C2×C4×D4×C37C2211yescharacteristic
29C2×C4×D4×C37C2211yescharacteristic
30C2×C4×D4×C37C2211yescharacteristic
31C2×#117×C37C2211yescharacteristic
32C22×C4⋊C4×C37C2211yescharacteristic
33C37×#478—24no—
34C4×D8×C37—24no—
35C2×#107×C37C2211yescharacteristic
36C2×#107×C37C2211yescharacteristic
37C2×#106×C37C2211yescharacteristic
38C2×C4⋊C8×C37C2211yescharacteristic
39C2×#102×C37C2211yescharacteristic
40C2×#102×C37C2211yescharacteristic
41C2×#102×C37C2211yescharacteristic
42C2×#102×C37C2211yescharacteristic
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×C22⋊C8×C37C2211yescharacteristic
46C2×C22⋊C8×C37C2211yescharacteristic
47C2×C22⋊C8×C37C2211yescharacteristic
48C2×C22⋊C8×C37C2211yescharacteristic
49C2×C4×C8×C37C2211yescharacteristic
50C37×#397—21no—
51C37×#392—21no—
52C37×#386—21no—
53C37×#386—21no—
54C37×#382C2211yescharacteristic
55C37×#380C2211yescharacteristic
56C37×#380C2211yescharacteristic
57C37×#340C2211yescharacteristic
58C37×#340C2211yescharacteristic
59C37×#340C2211yescharacteristic
60C37×#340C2211yescharacteristic
61C37×#340C2211yescharacteristic
62C37×#340C2211yescharacteristic
63C22×D4×C37—21no—
64C22×D4×C37—21no—
65C22×D4×C37—21no—
66C22×D4×C37—21no—
67C22×D4×C37D411yescharacteristic
68C22×D4×C37C2311yescharacteristic
69C22×D4×C37C2311yescharacteristic
70C23×C4×C37—21no—
71C23×C4×C37—21no—
72C23×C4×C37—21no—
73C23×C4×C37C2311yescharacteristic
74C23×C4×C37C2311yescharacteristic
75C2×D8×C37—22no—
76C2×D8×C37—22no—
77C2×D8×C37—22no—
78C22×C8×C37C2311yescharacteristic
79C22×C8×C37C2311yescharacteristic
80C22×C8×C37C2311yescharacteristic
81C22×C8×C37C2311yescharacteristic
82#126×C37—28no—
83#125×C37—22no—
84#125×C37D414yescomplemented
85#123×C37—28no—
86#121×C37—28no—
87#121×C37—22no—
88#121×C37—22no—
89#121×C37—22no—
90#121×C37—22no—
91#121×C37—22no—
92#121×C37—22no—
93#121×C37—41no—
94#121×C37—41no—
95C4×D4×C37—28no—
96C4×D4×C37—22no—
97C4×D4×C37—22no—
98C4×D4×C37—22no—
99C4×D4×C37—22no—
100C4×D4×C37—22no—
101C4×D4×C37D414yescomplemented
102#117×C37—22no—
103#117×C37—22no—
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37—22no—
108C2×C4⋊C4×C37—22no—
109C2×C4⋊C4×C37D411yescharacteristic
110C2×C4⋊C4×C37C2311yescharacteristic
111C2×C4⋊C4×C37C2311yescharacteristic
112C2×C4⋊C4×C37C2311yescharacteristic
113C2×C4⋊C4×C37C2311yescharacteristic
114C2×C4⋊C4×C37C2311yescharacteristic
115C2×C4⋊C4×C37C2311yescharacteristic
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×C37—21no—
125C2×C22⋊C4×C37D411yescharacteristic
126C2×C22⋊C4×C37D411yescharacteristic
127C2×C42×C37—21no—
128C2×C42×C37C2311yescharacteristic
129#107×C37—22no—
130#107×C37—22no—
131#106×C37—22no—
132C4⋊C8×C37—22no—
133#102×C37—22no—
134#102×C37—22no—
135#102×C37—22no—
136#102×C37—22no—
137#102×C37—41no—
138#102×C37—41no—
139C22⋊C8×C37—22no—
140C22⋊C8×C37—22no—
141C22⋊C8×C37—41no—
142C22⋊C8×C37—41no—
143C4×C8×C37—22no—
144#95×C37—21no—
145#95×C37—21no—
146#95×C37—21no—
147#95×C37—21no—
148C24×C37—21no—
149C24×C37—21no—
150C24×C37C2×D411yescharacteristic
151C24×C37C2×D411yescharacteristic
152C2×D4×C37—24no—
153C2×D4×C37—22no—
154C2×D4×C37—24no—
155C2×D4×C37—22no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—21no—
163C2×D4×C37—21no—
164C2×D4×C37—21no—
165C2×D4×C37—21no—
166C2×D4×C37—41no—
167C2×D4×C37—42no—
168C2×D4×C37—42no—
169C2×D4×C37—42no—
170C2×D4×C37—42no—
171C2×D4×C37—42no—
172C2×D4×C37—42no—
173C2×D4×C37—81no—
174C2×D4×C37—81no—
175C2×D4×C37—81no—
176C2×D4×C37—81no—
177C2×D4×C37C2×D412yes—
178C2×D4×C37#4112yes—
179C22×C4×C37—21no—
180C22×C4×C37—21no—
181C22×C4×C37—21no—
182C22×C4×C37—24no—
183C22×C4×C37—21no—
184C22×C4×C37—21no—
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—24no—
196C22×C4×C37—21no—
197C22×C4×C37—21no—
198C22×C4×C37—21no—
199C22×C4×C37—42no—
200C22×C4×C37—81no—
201C22×C4×C37—81no—
202C22×C4×C37—81no—
203C22×C4×C37—81no—
204C22×C4×C37—81no—
205C22×C4×C37—81no—
206C22×C4×C37C2×D411yescharacteristic
207C22×C4×C37C2×D411yescharacteristic
208C22×C4×C37C2×D411yescharacteristic
209C22×C4×C37C2×D411yescharacteristic
210C22×C4×C37C2411yescharacteristic
211D8×C37—28no—
212C2×C8×C37—21no—
213C2×C8×C37—21no—
214C2×C8×C37—21no—
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#4112yes—
224C4⋊C4×C37—24no—
225C4⋊C4×C37—24no—
226C4⋊C4×C37—24no—
227C4⋊C4×C37—22no—
228C4⋊C4×C37—21no—
229C4⋊C4×C37—21no—
230C4⋊C4×C37—21no—
231C4⋊C4×C37—21no—
232C4⋊C4×C37—21no—
233C4⋊C4×C37—21no—
234C4⋊C4×C37—21no—
235C4⋊C4×C37—21no—
236C4⋊C4×C37—21no—
237C4⋊C4×C37C2×D412yes—
238C4⋊C4×C37C2×D412yes—
239C4⋊C4×C37C2×D412yes—
240C22⋊C4×C37—24no—
241C22⋊C4×C37—24no—
242C22⋊C4×C37—24no—
243C22⋊C4×C37—24no—
244C22⋊C4×C37—22no—
245C22⋊C4×C37—22no—
246C22⋊C4×C37—42no—
247C22⋊C4×C37—42no—
248C22⋊C4×C37—42no—
249C22⋊C4×C37—81no—
250C22⋊C4×C37—81no—
251C42×C37—24no—
252C42×C37C2×D412yes—
253C42×C37C2×D412yes—
254C23×C37—21no—
255C23×C37—21no—
256C23×C37—21no—
257C23×C37—21no—
258C23×C37—21no—
259C23×C37—21no—
260C23×C37—21no—
261C23×C37—22no—
262C23×C37—22no—
263C23×C37—21no—
264C23×C37—21no—
265C23×C37—21no—
266C23×C37—21no—
267C23×C37—21no—
268C23×C37—21no—
269C23×C37—41no—
270C23×C37—41no—
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#13512yes—
282C23×C37C22×D411yescharacteristic
283D4×C37—22no—
284D4×C37—22no—
285D4×C37—22no—
286D4×C37—22no—
287D4×C37—44no—
288D4×C37—48no—
289D4×C37—41no—
290D4×C37—41no—
291D4×C37—41no—
292D4×C37—41no—
293D4×C37—84no—
294D4×C37—84no—
295D4×C37—84no—
296C2×C4×C37—21no—
297C2×C4×C37—21no—
298C2×C4×C37—21no—
299C2×C4×C37—21no—
300C2×C4×C37—21no—
301C2×C4×C37—22no—
302C2×C4×C37—22no—
303C2×C4×C37—21no—
304C2×C4×C37—22no—
305C2×C4×C37—21no—
306C2×C4×C37—21no—
307C2×C4×C37—21no—
308C2×C4×C37—21no—
309C2×C4×C37—41no—
310C2×C4×C37—41no—
311C2×C4×C37—41no—
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—41no—
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—84no—
333C2×C4×C37—84no—
334C2×C4×C37—84no—
335C2×C4×C37#12012yes—
336C2×C4×C37#12012yes—
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#24124C3711yesmaximal, characteristic, direct product factor, Sylow
348C22×C37—22no—
349C22×C37—22no—
350C22×C37—22no—
351C22×C37—41no—
352C22×C37—41no—
353C22×C37—41no—
354C22×C37—41no—
355C22×C37—41no—
356C22×C37—41no—
357C22×C37—41no—
358C22×C37—42no—
359C22×C37—42no—
360C22×C37—41no—
361C22×C37—42no—
362C22×C37—42no—
363C22×C37—41no—
364C22×C37—42no—
365C22×C37—41no—
366C22×C37—41no—
367C22×C37—42no—
368C22×C37—81no—
369C22×C37—81no—
370C22×C37—81no—
371C22×C37—81no—
372C22×C37—81no—
373C22×C37—81no—
374C22×C37—81no—
375C22×C37—81no—
376C22×C37C2×#12011yescharacteristic
377C22×C37#54611yescharacteristic
378C22×C37#54711yescharacteristic
379C22×C37C2×#13511yescharacteristic
380C22×C37#57511yescharacteristic
381C22×C37#57611yescharacteristic
382C22×C37#57611yescharacteristic
383C4×C37—22no—
384C4×C37—22no—
385C4×C37—41no—
386C4×C37—41no—
387C4×C37—42no—
388C4×C37—42no—
389C4×C37—42no—
390C4×C37—81no—
391C4×C37—81no—
392C4×C37—81no—
393C4×C37#52511yescharacteristic
394C4×C37#53711yescharacteristic
395C4×C37#54811yescharacteristic
396C4×C37#55011yescharacteristic
397C2×#553C2×C3711yescharacteristic, complemented
398C2×#478C2×C3711yescharacteristic, complemented
399C2×C4×D8C2×C3711yescharacteristic, complemented
400#2535C2×C3711yescharacteristic, complemented
401#2034C2×C3711yescharacteristic, complemented
402#2033C2×C3711yescharacteristic, complemented
403#1999C2×C3711yescharacteristic, complemented
404#1999C2×C3711yescharacteristic, complemented
405#1991C2×C3711yescharacteristic, complemented
406#1954C2×C3711yescharacteristic, complemented
407#1875C2×C3711yescharacteristic, complemented
408#1874C2×C3711yescharacteristic, complemented
409#1854C2×C3711yescharacteristic, complemented
410#1852C2×C3711yescharacteristic, complemented
411#1804C2×C3711yescharacteristic, complemented
412C2×C37—42no—
413C2×C37—81no—
414C2×C37—82no—
415C2×C37—82no—
416C2×C37#240711yescharacteristic
417C2×C37#300211yescharacteristic
418C2×C37#300811yescharacteristic
419C2×C37#329711yescharacteristic
420C2×C37#332211yescharacteristic
421C2×C37#333911yescharacteristic
422C2×C37#335511yescharacteristic
423C22×D8C22×C3711yescharacteristic
424#553—24no—
425#553—24no—
426C2×#126—21no—
427C2×#125C22×C3711yescharacteristic
428C2×#123—21no—
429C2×#121—21no—
430C2×#121C22×C3711yescharacteristic
431C2×#121C22×C3711yescharacteristic
432C2×#121C22×C3711yescharacteristic
433C2×#121C22×C3711yescharacteristic
434C2×C4×D4—21no—
435C2×C4×D4C22×C3711yescharacteristic
436C2×C4×D4C22×C3711yescharacteristic
437C2×C4×D4C22×C3711yescharacteristic
438C2×#117C22×C3711yescharacteristic
439C22×C4⋊C4C22×C3711yescharacteristic
440#478—24no—
441C4×D8—24no—
442C2×#107C22×C3711yescharacteristic
443C2×#107C22×C3711yescharacteristic
444C2×#106C22×C3711yescharacteristic
445C2×C4⋊C8C22×C3711yescharacteristic
446C2×#102C22×C3711yescharacteristic
447C2×#102C22×C3711yescharacteristic
448C2×#102C22×C3711yescharacteristic
449C2×#102C22×C3711yescharacteristic
450C2×#102C22×C3711yescharacteristic
451C2×#102C22×C3711yescharacteristic
452C2×C22⋊C8C22×C3711yescharacteristic
453C2×C22⋊C8C22×C3711yescharacteristic
454C2×C22⋊C8C22×C3711yescharacteristic
455C2×C22⋊C8C22×C3711yescharacteristic
456C2×C4×C8C22×C3711yescharacteristic
457#397—21no—
458#392—21no—
459#386—21no—
460#386—21no—
461#382C22×C3711yescharacteristic
462#380C22×C3711yescharacteristic
463#380C22×C3711yescharacteristic
464#340C22×C3711yescharacteristic
465#340C22×C3711yescharacteristic
466#340C22×C3711yescharacteristic
467#340C22×C3711yescharacteristic
468#340C22×C3711yescharacteristic
469#340C22×C3711yescharacteristic
470C37#2412411yescharacteristic, direct product factor, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C3711yescharacteristic
476C22×D4C23×C3711yescharacteristic
477C22×D4C23×C3711yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C3711yescharacteristic
482C23×C4C23×C3711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C22×C8C23×C3711yescharacteristic
487C22×C8C23×C3711yescharacteristic
488C22×C8C23×C3711yescharacteristic
489C22×C8C23×C3711yescharacteristic
490#126—28no—
491#125—22no—
492#125D4×C3714yescomplemented
493#123—28no—
494#121—28no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C3714yescomplemented
510#117—22no—
511#117—22no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4D4×C3711yescharacteristic
518C2×C4⋊C4C23×C3711yescharacteristic
519C2×C4⋊C4C23×C3711yescharacteristic
520C2×C4⋊C4C23×C3711yescharacteristic
521C2×C4⋊C4C23×C3711yescharacteristic
522C2×C4⋊C4C23×C3711yescharacteristic
523C2×C4⋊C4C23×C3711yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
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⋊C4—21no—
533C2×C22⋊C4D4×C3711yescharacteristic
534C2×C22⋊C4D4×C3711yescharacteristic
535C2×C42—21no—
536C2×C42C23×C3711yescharacteristic
537#107—22no—
538#107—22no—
539#106—22no—
540C4⋊C8—22no—
541#102—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—41no—
550C22⋊C8—41no—
551C4×C8—22no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C3711yescharacteristic
559C24C2×D4×C3711yescharacteristic
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—24no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C2×D4×C3712yes—
586C2×D4#41×C3712yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
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—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—42no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C2×D4×C3711yescharacteristic
615C22×C4C2×D4×C3711yescharacteristic
616C22×C4C2×D4×C3711yescharacteristic
617C22×C4C2×D4×C3711yescharacteristic
618C22×C4C24×C3711yescharacteristic
619D8—28no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8#41×C3712yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4C2×D4×C3712yes—
646C4⋊C4C2×D4×C3712yes—
647C4⋊C4C2×D4×C3712yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42C2×D4×C3712yes—
661C42C2×D4×C3712yes—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23#135×C3712yes—
690C23C22×D4×C3711yescharacteristic
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—44no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4—84no—
703D4—84no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
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—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4#120×C3712yes—
744C2×C4#120×C3712yes—
745C2×C4C22×D4×C3711yescharacteristic
746C2×C4C22×D4×C3711yescharacteristic
747C2×C4C2×#41×C3711yescharacteristic
748C2×C4C2×#41×C3711yescharacteristic
749C2×C4H(5,𝔽2)×C3711yescharacteristic
750C2×C42−1+4×C3711yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C3711yescharacteristic
784C22C37×#54611yescharacteristic
785C22C37×#54711yescharacteristic
786C22C2×#135×C3711yescharacteristic
787C22C37×#57511yescharacteristic
788C22C37×#57611yescharacteristic
789C22C37×#57611yescharacteristic
790C4—22no—
791C4—22no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4C37×#52511yescharacteristic
801C4C37×#53711yescharacteristic
802C4C37×#54811yescharacteristic
803C4C37×#55011yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—82no—
808C2C37×#240711yescharacteristic
809C2C37×#300211yescharacteristic
810C2C37×#300811yescharacteristic
811C2C37×#329711yescharacteristic
812C2C37×#332211yescharacteristic
813C2C37×#333911yescharacteristic
814C2C37×#335511yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
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
1. C2×C37×#553C2semidirect
2. C2×C37×#478C2semidirect
3. C2×C4×D8×C37C2semidirect
4. C37×#2535C2semidirect
5. C37×#2034C2semidirect
6. C37×#2033C2semidirect
7. C37×#1999C2semidirect
8. C37×#1999C2semidirect
9. C37×#1991C2semidirect
10. C37×#1954C2semidirect
11. C37×#1875C2semidirect
12. C37×#1874C2semidirect
13. C37×#1854C2semidirect
14. C37×#1852C2semidirect
15. C37×#1804C2semidirect
84. #125×C37D4semidirect
101. C4×D4×C37D4semidirect
347. #24124C37direct (N × H)
397. C2×#553C2×C37semidirect
398. C2×#478C2×C37semidirect
399. C2×C4×D8C2×C37semidirect
400. #2535C2×C37semidirect
401. #2034C2×C37semidirect
402. #2033C2×C37semidirect
403. #1999C2×C37semidirect
404. #1999C2×C37semidirect
405. #1991C2×C37semidirect
406. #1954C2×C37semidirect
407. #1875C2×C37semidirect
408. #1874C2×C37semidirect
409. #1854C2×C37semidirect
410. #1852C2×C37semidirect
411. #1804C2×C37semidirect
470. C37#24124direct (N × H)
492. #125D4×C37semidirect
509. C4×D4D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5532
C2×C37×#4782
C2×C4×D8×C372
C37×#25352
C37×#20342
C37×#20332
C37×#19992
C37×#19912
C37×#19542
C37×#18752
C37×#18742
C37×#18542
C37×#18522
C37×#18042
#2412437