Finite Group Databasebeta

← C37×#24394 #22645647

Subgroups — C37×#24394 #22645647

Order 9472.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#535C211yesmaximal, characteristic
2C2×C37×#468C211yesmaximal, characteristic, complemented
3C2×C37×#465C211yesmaximal, characteristic, complemented
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C2×C37×#408C211yesmaximal, characteristic, complemented
6C37×#2616C211yesmaximal, characteristic, complemented
7C37×#2034C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2000C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1893C211yesmaximal, characteristic, complemented
13C37×#1873C211yesmaximal, characteristic, complemented
14C37×#1854C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C22×M16×C37C2211yescharacteristic, complemented
21C23×C8×C37C2211yescharacteristic, complemented
22C37×#535—24no—
23C37×#535—24no—
24C2×#127×C37—21no—
25C2×#124×C37—21no—
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic, complemented
28C2×C22⋊Q8×C37C2211yescharacteristic, complemented
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×#121×C37C2211yescharacteristic
32C2×#121×C37C2211yescharacteristic
33C2×#120×C37—21no—
34C2×#120×C37—21no—
35C2×#117×C37C2211yescharacteristic
36C37×#468—24no—
37C37×#465—24no—
38C37×#450—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C2×#106×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#102×C37C2211yescharacteristic
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C37×#408—24no—
50C2×C22⋊C8×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#395—21no—
55C37×#394—21no—
56C37×#394—21no—
57C37×#394—21no—
58C37×#380C2211yescharacteristic
59C37×#380C2211yescharacteristic, complemented
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C37×#340C2211yescharacteristic, complemented
65C25×C37—21no—
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—41no—
71C2×#41×C37—41no—
72C22×Q8×C37D411yescharacteristic
73C22×Q8×C37C2311yescharacteristic
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—22no—
79C22×D4×C37—22no—
80C22×D4×C37—21no—
81C22×D4×C37—22no—
82C22×D4×C37—22no—
83C22×D4×C37—41no—
84C22×D4×C37—41no—
85C22×D4×C37D411yescharacteristic
86C22×D4×C37D411yescharacteristic
87C22×D4×C37D411yescharacteristic
88C22×D4×C37C2311yescharacteristic
89C22×D4×C37C2311yescharacteristic
90C23×C4×C37C2311yescharacteristic
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C2×SD16×C37—22no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37—41no—
98C2×SD16×C37—41no—
99C2×M16×C37—22no—
100C2×M16×C37—22no—
101C2×M16×C37—41no—
102C22×C8×C37—22no—
103C22×C8×C37—22no—
104C22×C8×C37—41no—
105C22×C8×C37C2311yescharacteristic
106C22×C8×C37C2311yescharacteristic
107C22×C8×C37C2311yescharacteristic
108C22×C8×C37C2311yescharacteristic
109#127×C37—28no—
110#124×C37—28no—
111C22⋊Q8×C37—22no—
112C22⋊Q8×C37—22no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—41no—
116C22⋊Q8×C37—41no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37—22no—
122#121×C37—22no—
123#121×C37D414yes—
124#121×C37D414yes—
125#120×C37—28no—
126#120×C37—28no—
127#117×C37—22no—
128#117×C37—22no—
129C2×C4⋊C4×C37—21no—
130C2×C4⋊C4×C37—21no—
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37C2311yescharacteristic
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C4⋊C4×C37C2311yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C22⋊C4×C37—21no—
138C2×C22⋊C4×C37—21no—
139C2×C22⋊C4×C37—21no—
140C2×C22⋊C4×C37—21no—
141C2×C22⋊C4×C37—21no—
142C2×C22⋊C4×C37—21no—
143C2×C22⋊C4×C37—21no—
144C2×C22⋊C4×C37—21no—
145C2×C22⋊C4×C37—21no—
146C2×C22⋊C4×C37—21no—
147C2×C22⋊C4×C37—21no—
148C2×C42×C37—21no—
149#107×C37—22no—
150#106×C37—22no—
151#103×C37—22no—
152#103×C37—22no—
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—41no—
158#102×C37—41no—
159C22⋊C8×C37—22no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—22no—
162C22⋊C8×C37D414yescomplemented
163#95×C37—21no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—24no—
167C24×C37—21no—
168C24×C37—21no—
169C24×C37—42no—
170C24×C37—42no—
171C24×C37—81no—
172C24×C37—81no—
173C24×C37—81no—
174C24×C37—81no—
175C24×C37C2×D411yescharacteristic
176C24×C37C2×D411yescharacteristic
177C24×C37C2×D411yescharacteristic
178#41×C37—44no—
179#41×C37—44no—
180#41×C37—44no—
181#41×C37—44no—
182C2×Q8×C37—22no—
183C2×Q8×C37—22no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37—21no—
188C2×Q8×C37—21no—
189C2×Q8×C37—21no—
190C2×Q8×C37—41no—
191C2×D4×C37—24no—
192C2×D4×C37—22no—
193C2×D4×C37—22no—
194C2×D4×C37—22no—
195C2×D4×C37—22no—
196C2×D4×C37—24no—
197C2×D4×C37—24no—
198C2×D4×C37—24no—
199C2×D4×C37—24no—
200C2×D4×C37—22no—
201C2×D4×C37—22no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—21no—
208C2×D4×C37—21no—
209C2×D4×C37—21no—
210C2×D4×C37—21no—
211C2×D4×C37—21no—
212C2×D4×C37—44no—
213C2×D4×C37—44no—
214C2×D4×C37—44no—
215C2×D4×C37—44no—
216C2×D4×C37—41no—
217C2×D4×C37—41no—
218C2×D4×C37—41no—
219C2×D4×C37—42no—
220C2×D4×C37—42no—
221C2×D4×C37—81no—
222C2×D4×C37—81no—
223C2×D4×C37—81no—
224C2×D4×C37—81no—
225C2×D4×C37—81no—
226C2×D4×C37—81no—
227C2×D4×C37—81no—
228C2×D4×C37—81no—
229C2×D4×C37C2×D412yes—
230C2×D4×C37C2×D412yes—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—21no—
237C22×C4×C37—21no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—21no—
245C22×C4×C37—21no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—21no—
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37C2×D411yescharacteristic
253C22×C4×C37C2×D412yes—
254C22×C4×C37C2×D412yes—
255C22×C4×C37C2×D411yescharacteristic
256C22×C4×C37C2×D412yes—
257C22×C4×C37#4112yes—
258C22×C4×C37C2411yescharacteristic
259SD16×C37—44no—
260SD16×C37—44no—
261M16×C37—44no—
262C2×C8×C37—21no—
263C2×C8×C37—21no—
264C2×C8×C37—21no—
265C2×C8×C37—21no—
266C2×C8×C37—21no—
267C2×C8×C37—21no—
268C2×C8×C37—21no—
269C2×C8×C37—21no—
270C2×C8×C37—21no—
271C2×C8×C37—21no—
272C2×C8×C37—44no—
273C2×C8×C37C2×D412yes—
274C2×C8×C37C2×D412yes—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—21no—
281C4⋊C4×C37—21no—
282C4⋊C4×C37—21no—
283C4⋊C4×C37—42no—
284C4⋊C4×C37—42no—
285C4⋊C4×C37—42no—
286C4⋊C4×C37C2×D412yes—
287C4⋊C4×C37C2×D412yes—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—24no—
290C22⋊C4×C37—24no—
291C22⋊C4×C37—24no—
292C22⋊C4×C37—24no—
293C22⋊C4×C37—42no—
294C22⋊C4×C37—42no—
295C22⋊C4×C37—42no—
296C22⋊C4×C37—81no—
297C22⋊C4×C37—81no—
298C22⋊C4×C37—81no—
299C42×C37—24no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—21no—
303C23×C37—21no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—22no—
313C23×C37—22no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—21no—
317C23×C37—21no—
318C23×C37—21no—
319C23×C37—21no—
320C23×C37—21no—
321C23×C37—48no—
322C23×C37—41no—
323C23×C37—41no—
324C23×C37—41no—
325C23×C37—41no—
326C23×C37—41no—
327C23×C37—41no—
328C23×C37—41no—
329C23×C37—41no—
330C23×C37—41no—
331C23×C37—41no—
332C23×C37—41no—
333C23×C37—41no—
334C23×C37—84no—
335C23×C37—84no—
336C23×C37—84no—
337C23×C37—84no—
338C23×C37—84no—
339C23×C37—84no—
340C23×C37#12012yes—
341C23×C37#12112yes—
342C23×C37C22×D411yescharacteristic
343Q8×C37—44no—
344Q8×C37—41no—
345Q8×C37—41no—
346Q8×C37—41no—
347Q8×C37—41no—
348D4×C37—22no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—22no—
352D4×C37—44no—
353D4×C37—44no—
354D4×C37—48no—
355D4×C37—44no—
356D4×C37—41no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—84no—
361D4×C37—84no—
362D4×C37—84no—
363D4×C37—84no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—21no—
367C2×C4×C37—21no—
368C2×C4×C37—22no—
369C2×C4×C37—22no—
370C2×C4×C37—22no—
371C2×C4×C37—22no—
372C2×C4×C37—22no—
373C2×C4×C37—22no—
374C2×C4×C37—22no—
375C2×C4×C37—22no—
376C2×C4×C37—22no—
377C2×C4×C37—22no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—41no—
382C2×C4×C37—41no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37—41no—
392C2×C4×C37—41no—
393C2×C4×C37—41no—
394C2×C4×C37—41no—
395C2×C4×C37—41no—
396C2×C4×C37—41no—
397C2×C4×C37—41no—
398C2×C4×C37—41no—
399C2×C4×C37—41no—
400C2×C4×C37—41no—
401C2×C4×C37#12012yes—
402C2×C4×C37#12112yes—
403C2×C4×C37C22×D411yescharacteristic
404C2×C4×C37C22×D411yescharacteristic
405C2×C4×C37C22×D411yescharacteristic
406C2×C4×C37C2×#4111yescharacteristic
407C2×C4×C37H(5,𝔽2)11yescharacteristic
408C2×C4×C37H(5,𝔽2)11yescharacteristic
409C8×C37—22no—
410C8×C37—22no—
411C8×C37—41no—
412C8×C37—41no—
413#24394C3711yesmaximal, characteristic, direct product factor, Sylow
414C22×C37—22no—
415C22×C37—22no—
416C22×C37—22no—
417C22×C37—22no—
418C22×C37—22no—
419C22×C37—22no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—41no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—41no—
426C22×C37—41no—
427C22×C37—41no—
428C22×C37—41no—
429C22×C37—42no—
430C22×C37—42no—
431C22×C37—41no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—42no—
435C22×C37—42no—
436C22×C37—41no—
437C22×C37—42no—
438C22×C37—42no—
439C22×C37—41no—
440C22×C37—41no—
441C22×C37—816no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37—81no—
449C22×C37—81no—
450C22×C37C2×#12011yescharacteristic
451C22×C37C2×#12111yescharacteristic
452C22×C37#53411yescharacteristic
453C22×C37#57611yescharacteristic
454C22×C37#57711yescharacteristic
455C22×C37#57711yescharacteristic
456C22×C37#57711yescharacteristic
457C4×C37—22no—
458C4×C37—22no—
459C4×C37—41no—
460C4×C37—42no—
461C4×C37—42no—
462C4×C37—81no—
463C4×C37—81no—
464C4×C37—81no—
465C4×C37—81no—
466C4×C37D4211yescharacteristic
467C4×C37D4211yescharacteristic
468C4×C37#54611yescharacteristic
469C4×C37#54611yescharacteristic
470C2×#535C2×C3711yescharacteristic
471C2×#468C2×C3711yescharacteristic, complemented
472C2×#465C2×C3711yescharacteristic, complemented
473C2×#450C2×C3711yescharacteristic, complemented
474C2×#408C2×C3711yescharacteristic, complemented
475#2616C2×C3711yescharacteristic, complemented
476#2034C2×C3711yescharacteristic, complemented
477#2033C2×C3711yescharacteristic, complemented
478#2000C2×C3711yescharacteristic, complemented
479#2000C2×C3711yescharacteristic, complemented
480#1895C2×C3711yescharacteristic, complemented
481#1893C2×C3711yescharacteristic, complemented
482#1873C2×C3711yescharacteristic, complemented
483#1854C2×C3711yescharacteristic, complemented
484#1786C2×C3711yescharacteristic, complemented
485C2×C37—42no—
486C2×C37—42no—
487C2×C37—81no—
488C2×C37—82no—
489C2×C37—82no—
490C2×C37#241011yescharacteristic
491C2×C37#300911yescharacteristic
492C2×C37#301211yescharacteristic
493C2×C37#305711yescharacteristic
494C2×C37#306211yescharacteristic
495C2×C37#319811yescharacteristic
496C2×C37#320011yescharacteristic
497C22×#41C22×C3711yescharacteristic
498C23×D4C22×C3711yescharacteristic
499C22×SD16C22×C3711yescharacteristic
500C22×SD16C22×C3711yescharacteristic
501C22×M16C22×C3711yescharacteristic, complemented
502C23×C8C22×C3711yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127—21no—
506C2×#124—21no—
507C2×C22⋊Q8C22×C3711yescharacteristic
508C2×C22⋊Q8C22×C3711yescharacteristic, complemented
509C2×C22⋊Q8C22×C3711yescharacteristic, complemented
510C2×#121C22×C3711yescharacteristic
511C2×#121C22×C3711yescharacteristic
512C2×#121C22×C3711yescharacteristic
513C2×#121C22×C3711yescharacteristic
514C2×#120—21no—
515C2×#120—21no—
516C2×#117C22×C3711yescharacteristic
517#468—24no—
518#465—24no—
519#450—24no—
520C2×#107C22×C3711yescharacteristic, complemented
521C2×#106C22×C3711yescharacteristic, complemented
522C2×#103C22×C3711yescharacteristic, complemented
523C2×#103C22×C3711yescharacteristic, complemented
524C2×#102C22×C3711yescharacteristic
525C2×#102C22×C3711yescharacteristic
526C2×#102C22×C3711yescharacteristic
527C2×#102C22×C3711yescharacteristic
528C2×#102C22×C3711yescharacteristic
529C2×#102C22×C3711yescharacteristic
530#408—24no—
531C2×C22⋊C8C22×C3711yescharacteristic
532C2×C22⋊C8C22×C3711yescharacteristic
533C2×C22⋊C8C22×C3711yescharacteristic, complemented
534C2×C22⋊C8C22×C3711yescharacteristic, complemented
535#395—21no—
536#394—21no—
537#394—21no—
538#394—21no—
539#380C22×C3711yescharacteristic
540#380C22×C3711yescharacteristic, complemented
541#380C22×C3711yescharacteristic, complemented
542#340C22×C3711yescharacteristic, complemented
543#340C22×C3711yescharacteristic, complemented
544#340C22×C3711yescharacteristic, complemented
545#340C22×C3711yescharacteristic, complemented
546C37#2439411yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C3711yescharacteristic
555C22×Q8C23×C3711yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C3711yescharacteristic
568C22×D4D4×C3711yescharacteristic
569C22×D4D4×C3711yescharacteristic
570C22×D4C23×C3711yescharacteristic
571C22×D4C23×C3711yescharacteristic
572C23×C4C23×C3711yescharacteristic
573C23×C4C23×C3711yescharacteristic
574C23×C4C23×C3711yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C3711yescharacteristic
588C22×C8C23×C3711yescharacteristic
589C22×C8C23×C3711yescharacteristic
590C22×C8C23×C3711yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C3714yes—
606#121D4×C3714yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C3711yescharacteristic
615C2×C4⋊C4C23×C3711yescharacteristic
616C2×C4⋊C4C23×C3711yescharacteristic
617C2×C4⋊C4C23×C3711yescharacteristic
618C2×C4⋊C4C23×C3711yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C3714yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C3711yescharacteristic
658C24C2×D4×C3711yescharacteristic
659C24C2×D4×C3711yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C3712yes—
712C2×D4C2×D4×C3712yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C3711yescharacteristic
734C22×C4C2×D4×C3711yescharacteristic
735C22×C4C2×D4×C3712yes—
736C22×C4C2×D4×C3712yes—
737C22×C4C2×D4×C3711yescharacteristic
738C22×C4C2×D4×C3712yes—
739C22×C4#41×C3712yes—
740C22×C4C24×C3711yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C3712yes—
756C2×C8C2×D4×C3712yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C3712yes—
769C4⋊C4C2×D4×C3712yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C3712yes—
823C23#121×C3712yes—
824C23C22×D4×C3711yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C3712yes—
884C2×C4#121×C3712yes—
885C2×C4C22×D4×C3711yescharacteristic
886C2×C4C22×D4×C3711yescharacteristic
887C2×C4C22×D4×C3711yescharacteristic
888C2×C4C2×#41×C3711yescharacteristic
889C2×C4H(5,𝔽2)×C3711yescharacteristic
890C2×C4H(5,𝔽2)×C3711yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C3711yescharacteristic
932C22C2×#121×C3711yescharacteristic
933C22C37×#53411yescharacteristic
934C22C37×#57611yescharacteristic
935C22C37×#57711yescharacteristic
936C22C37×#57711yescharacteristic
937C22C37×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C3711yescharacteristic
948C4D42×C3711yescharacteristic
949C4C37×#54611yescharacteristic
950C4C37×#54611yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C37×#241011yescharacteristic
957C2C37×#300911yescharacteristic
958C2C37×#301211yescharacteristic
959C2C37×#305711yescharacteristic
960C2C37×#306211yescharacteristic
961C2C37×#319811yescharacteristic
962C2C37×#320011yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×#41×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#468C2semidirect
3. C2×C37×#465C2semidirect
4. C2×C37×#450C2semidirect
5. C2×C37×#408C2semidirect
6. C37×#2616C2semidirect
7. C37×#2034C2semidirect
8. C37×#2033C2semidirect
9. C37×#2000C2semidirect
10. C37×#2000C2semidirect
11. C37×#1895C2semidirect
12. C37×#1893C2semidirect
13. C37×#1873C2semidirect
14. C37×#1854C2semidirect
15. C37×#1786C2semidirect
20. C22×M16×C37C22semidirect
21. C23×C8×C37C22semidirect
27. C2×C22⋊Q8×C37C22semidirect
28. C2×C22⋊Q8×C37C22semidirect
39. C2×#107×C37C22semidirect
40. C2×#106×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
59. C37×#380C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
162. C22⋊C8×C37D4semidirect
413. #24394C37direct (N × H)
471. C2×#468C2×C37semidirect
472. C2×#465C2×C37semidirect
473. C2×#450C2×C37semidirect
474. C2×#408C2×C37semidirect
475. #2616C2×C37semidirect
476. #2034C2×C37semidirect
477. #2033C2×C37semidirect
478. #2000C2×C37semidirect
479. #2000C2×C37semidirect
480. #1895C2×C37semidirect
481. #1893C2×C37semidirect
482. #1873C2×C37semidirect
483. #1854C2×C37semidirect
484. #1786C2×C37semidirect
501. C22×M16C22×C37semidirect
502. C23×C8C22×C37semidirect
508. C2×C22⋊Q8C22×C37semidirect
509. C2×C22⋊Q8C22×C37semidirect
520. C2×#107C22×C37semidirect
521. C2×#106C22×C37semidirect
522. C2×#103C22×C37semidirect
523. C2×#103C22×C37semidirect
533. C2×C22⋊C8C22×C37semidirect
534. C2×C22⋊C8C22×C37semidirect
540. #380C22×C37semidirect
541. #380C22×C37semidirect
542. #340C22×C37semidirect
543. #340C22×C37semidirect
544. #340C22×C37semidirect
545. #340C22×C37semidirect
546. C37#24394direct (N × H)
644. C22⋊C8D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5352
C2×C37×#4682
C2×C37×#4652
C2×C37×#4502
C2×C37×#4082
C37×#26162
C37×#20342
C37×#20332
C37×#20002
C37×#18952
C37×#18932
C37×#18732
C37×#18542
C37×#17862
#2439437