Finite Group Databasebeta

← C37×#24450 #22645703

Subgroups — C37×#24450 #22645703

Order 9472.

1620 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#546C211yesmaximal, characteristic, complemented
2C2×C37×#468C211yesmaximal, characteristic, complemented
3C2×C37×#449C211yesmaximal, characteristic, complemented
4C2×C37×#447C211yesmaximal, characteristic, complemented
5C2×C37×#418C211yesmaximal, characteristic, complemented
6C37×#2414C211yesmaximal, characteristic, complemented
7C37×#2042C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2012C211yesmaximal, characteristic, complemented
10C37×#1999C211yesmaximal, characteristic, complemented
11C37×#1879C211yesmaximal, characteristic, complemented
12C37×#1873C211yesmaximal, characteristic, complemented
13C37×#1870C211yesmaximal, characteristic, complemented
14C37×#1862C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×SD16×C37C2211yescharacteristic, complemented
19C22×D8×C37C2211yescharacteristic
20C22×D8×C37C2211yescharacteristic
21C22×M16×C37C2211yescharacteristic
22C37×#546—24no—
23C37×#546—24no—
24C2×#124×C37C2211yescharacteristic
25C2×#123×C37—21no—
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×#121×C37—21no—
28C2×#121×C37C2211yescharacteristic
29C2×#121×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic, complemented
31C2×#120×C37—21no—
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C2×#117×C37C2211yescharacteristic
35C22×C22⋊C4×C37—21no—
36C37×#468—24no—
37C37×#449—24no—
38C37×#447—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C37×#418—24no—
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#102×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic, complemented
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic, complemented
53C2×C22⋊C8×C37C2211yescharacteristic, complemented
54C37×#394—21no—
55C37×#392—21no—
56C37×#390—21no—
57C37×#390C2211yescharacteristic, complemented
58C37×#389C2211yescharacteristic, complemented
59C37×#388—21no—
60C37×#380C2211yescharacteristic, complemented
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#336C2211yescharacteristic, complemented
64C37×#336C2211yescharacteristic, 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×C37C2311yescharacteristic
73C22×D4×C37—22no—
74C22×D4×C37—22no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37—21no—
78C22×D4×C37—21no—
79C22×D4×C37—21no—
80C22×D4×C37—22no—
81C22×D4×C37—41no—
82C22×D4×C37—41no—
83C22×D4×C37D411yescharacteristic
84C22×D4×C37D414yescomplemented
85C22×D4×C37C2311yescharacteristic
86C22×D4×C37C2311yescharacteristic
87C22×D4×C37C2311yescharacteristic
88C23×C4×C37—21no—
89C23×C4×C37—21no—
90C23×C4×C37C2311yescharacteristic
91C23×C4×C37C2311yescharacteristic
92C2×SD16×C37—22no—
93C2×SD16×C37—22no—
94C2×SD16×C37—41no—
95C2×D8×C37—22no—
96C2×D8×C37—22no—
97C2×D8×C37—22no—
98C2×D8×C37—22no—
99C2×D8×C37—41no—
100C2×D8×C37—41no—
101C2×M16×C37—22no—
102C2×M16×C37—22no—
103C2×M16×C37—41no—
104C22×C8×C37C2311yescharacteristic
105C22×C8×C37C2311yescharacteristic
106C22×C8×C37C2311yescharacteristic
107C22×C8×C37C2311yescharacteristic
108#124×C37—22no—
109#124×C37—22no—
110#123×C37—28no—
111C22⋊Q8×C37—22no—
112C22⋊Q8×C37D414yescomplemented
113#121×C37—28no—
114#121×C37—22no—
115#121×C37—22no—
116#121×C37—22no—
117#121×C37—22no—
118#121×C37—22no—
119#121×C37—41no—
120#120×C37—28no—
121C4×D4×C37—22no—
122C4×D4×C37—22no—
123C4×D4×C37—22no—
124C4×D4×C37—22no—
125#117×C37—22no—
126#117×C37—41no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37—21no—
129C2×C4⋊C4×C37D411yescharacteristic
130C2×C4⋊C4×C37C2311yescharacteristic
131C2×C4⋊C4×C37C2311yescharacteristic
132C2×C4⋊C4×C37C2311yescharacteristic
133C2×C4⋊C4×C37C2311yescharacteristic
134C2×C22⋊C4×C37—28no—
135C2×C22⋊C4×C37—21no—
136C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
147C2×C22⋊C4×C37D411yescharacteristic
148C2×C42×C37—21no—
149C2×C42×C37C2311yescharacteristic
150#107×C37—22no—
151#103×C37—22no—
152#103×C37—22no—
153#103×C37—41no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—22no—
158#102×C37—22no—
159#102×C37—22no—
160#102×C37D414yescomplemented
161C22⋊C8×C37—22no—
162C22⋊C8×C37—22no—
163C22⋊C8×C37—41no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—21no—
167C24×C37—21no—
168C24×C37—24no—
169C24×C37—21no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—42no—
174C24×C37—81no—
175C24×C37—81no—
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—21no—
183C2×Q8×C37—21no—
184C2×Q8×C37—21no—
185C2×Q8×C37—21no—
186C2×Q8×C37—21no—
187C2×Q8×C37C2×D412yes—
188C2×D4×C37—28no—
189C2×D4×C37—24no—
190C2×D4×C37—22no—
191C2×D4×C37—24no—
192C2×D4×C37—24no—
193C2×D4×C37—21no—
194C2×D4×C37—21no—
195C2×D4×C37—21no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—21no—
202C2×D4×C37—21no—
203C2×D4×C37—21no—
204C2×D4×C37—21no—
205C2×D4×C37—21no—
206C2×D4×C37—21no—
207C2×D4×C37—44no—
208C2×D4×C37—44no—
209C2×D4×C37—44no—
210C2×D4×C37—41no—
211C2×D4×C37—41no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—42no—
216C2×D4×C37—42no—
217C2×D4×C37—42no—
218C2×D4×C37—42no—
219C2×D4×C37—81no—
220C2×D4×C37—81no—
221C2×D4×C37—81no—
222C2×D4×C37—81no—
223C2×D4×C37—81no—
224C2×D4×C37C2×D412yes—
225C2×D4×C37C2×D412yes—
226C2×D4×C37C2×D412yes—
227C2×D4×C37#4112yes—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—24no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—24no—
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—42no—
246C22×C4×C37—42no—
247C22×C4×C37—81no—
248C22×C4×C37—81no—
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D411yescharacteristic
251C22×C4×C37C2×D411yescharacteristic
252C22×C4×C37C2×D411yescharacteristic
253C22×C4×C37C2×D412yes—
254C22×C4×C37C2×D412yes—
255C22×C4×C37C2411yescharacteristic
256SD16×C37—44no—
257D8×C37—44no—
258D8×C37—44no—
259M16×C37—44no—
260C2×C8×C37—21no—
261C2×C8×C37—21no—
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×C37C2×D412yes—
272C4⋊C4×C37—24no—
273C4⋊C4×C37—22no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—21no—
280C4⋊C4×C37—81no—
281C4⋊C4×C37C2×D412yes—
282C4⋊C4×C37C2×D412yes—
283C22⋊C4×C37—24no—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—24no—
287C22⋊C4×C37—22no—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—22no—
290C22⋊C4×C37—42no—
291C22⋊C4×C37—42no—
292C22⋊C4×C37—42no—
293C22⋊C4×C37—42no—
294C22⋊C4×C37—81no—
295C22⋊C4×C37—81no—
296C42×C37—21no—
297C42×C37—21no—
298C42×C37—42no—
299C23×C37—22no—
300C23×C37—21no—
301C23×C37—22no—
302C23×C37—21no—
303C23×C37—22no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—22no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—21no—
312C23×C37—21no—
313C23×C37—21no—
314C23×C37—21no—
315C23×C37—21no—
316C23×C37—48no—
317C23×C37—48no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—41no—
321C23×C37—41no—
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—41no—
335C23×C37—84no—
336C23×C37—84no—
337C23×C37—84no—
338C23×C37—84no—
339C23×C37—84no—
340C23×C37#12012yes—
341C23×C37C22×D411yescharacteristic
342Q8×C37—22no—
343Q8×C37—22no—
344Q8×C37—41no—
345Q8×C37—41no—
346D4×C37—22no—
347D4×C37—22no—
348D4×C37—22no—
349D4×C37—22no—
350D4×C37—22no—
351D4×C37—48no—
352D4×C37—44no—
353D4×C37—48no—
354D4×C37—41no—
355D4×C37—41no—
356D4×C37—41no—
357D4×C37—41no—
358D4×C37—41no—
359D4×C37—41no—
360D4×C37—84no—
361D4×C37—84no—
362D4×C37—84no—
363D4×C37#12114yes—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—22no—
367C2×C4×C37—22no—
368C2×C4×C37—22no—
369C2×C4×C37—22no—
370C2×C4×C37—21no—
371C2×C4×C37—21no—
372C2×C4×C37—22no—
373C2×C4×C37—21no—
374C2×C4×C37—22no—
375C2×C4×C37—22no—
376C2×C4×C37—21no—
377C2×C4×C37—21no—
378C2×C4×C37—21no—
379C2×C4×C37—21no—
380C2×C4×C37—21no—
381C2×C4×C37—21no—
382C2×C4×C37—48no—
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—84no—
400C2×C4×C37#12012yes—
401C2×C4×C37C22×D411yescharacteristic
402C2×C4×C37C22×D411yescharacteristic
403C2×C4×C37C22×D411yescharacteristic
404C2×C4×C37C2×#4111yescharacteristic
405C2×C4×C37H(5,𝔽2)11yescharacteristic
406C2×C4×C37H(5,𝔽2)11yescharacteristic
407C8×C37—22no—
408C8×C37—41no—
409C8×C37—41no—
410C8×C37—41no—
411#24450C3711yesmaximal, characteristic, direct product factor, Sylow
412C22×C37—22no—
413C22×C37—24no—
414C22×C37—22no—
415C22×C37—22no—
416C22×C37—42no—
417C22×C37—42no—
418C22×C37—41no—
419C22×C37—42no—
420C22×C37—41no—
421C22×C37—42no—
422C22×C37—41no—
423C22×C37—42no—
424C22×C37—41no—
425C22×C37—42no—
426C22×C37—41no—
427C22×C37—42no—
428C22×C37—41no—
429C22×C37—42no—
430C22×C37—41no—
431C22×C37—42no—
432C22×C37—41no—
433C22×C37—41no—
434C22×C37—41no—
435C22×C37—41no—
436C22×C37—816no—
437C22×C37—81no—
438C22×C37—81no—
439C22×C37—81no—
440C22×C37—81no—
441C22×C37—81no—
442C22×C37—81no—
443C22×C37—81no—
444C22×C37—81no—
445C22×C37—81no—
446C22×C37—81no—
447C22×C37—81no—
448C22×C37C2×#12011yescharacteristic
449C22×C37D4211yescharacteristic
450C22×C37#54611yescharacteristic
451C22×C37#57511yescharacteristic
452C22×C37#57511yescharacteristic
453C22×C37#57611yescharacteristic
454C22×C37#57611yescharacteristic
455C4×C37—22no—
456C4×C37—41no—
457C4×C37—42no—
458C4×C37—41no—
459C4×C37—41no—
460C4×C37—42no—
461C4×C37—42no—
462C4×C37—81no—
463C4×C37—81no—
464C4×C37C2×#12111yescharacteristic
465C4×C37#53411yescharacteristic
466C4×C37D4211yescharacteristic
467C4×C37#54611yescharacteristic
468C2×#546C2×C3711yescharacteristic, complemented
469C2×#468C2×C3711yescharacteristic, complemented
470C2×#449C2×C3711yescharacteristic, complemented
471C2×#447C2×C3711yescharacteristic, complemented
472C2×#418C2×C3711yescharacteristic, complemented
473#2414C2×C3711yescharacteristic, complemented
474#2042C2×C3711yescharacteristic, complemented
475#2033C2×C3711yescharacteristic, complemented
476#2012C2×C3711yescharacteristic, complemented
477#1999C2×C3711yescharacteristic, complemented
478#1879C2×C3711yescharacteristic, complemented
479#1873C2×C3711yescharacteristic, complemented
480#1870C2×C3711yescharacteristic, complemented
481#1862C2×C3711yescharacteristic, complemented
482#1788C2×C3711yescharacteristic, complemented
483C2×C37—42no—
484C2×C37—44no—
485C2×C37—81no—
486C2×C37—82no—
487C2×C37—161no—
488C2×C37#241011yescharacteristic
489C2×C37#300511yescharacteristic
490C2×C37#300811yescharacteristic
491C2×C37#326811yescharacteristic
492C2×C37#327311yescharacteristic
493C2×C37#331911yescharacteristic
494C2×C37#332211yescharacteristic
495C22×#41C22×C3711yescharacteristic
496C23×D4C22×C3711yescharacteristic
497C22×SD16C22×C3711yescharacteristic, complemented
498C22×D8C22×C3711yescharacteristic
499C22×D8C22×C3711yescharacteristic
500C22×M16C22×C3711yescharacteristic
501#546—24no—
502#546—24no—
503C2×#124C22×C3711yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C3711yescharacteristic
506C2×#121—21no—
507C2×#121C22×C3711yescharacteristic
508C2×#121C22×C3711yescharacteristic
509C2×#121C22×C3711yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C3711yescharacteristic
512C2×C4×D4C22×C3711yescharacteristic
513C2×#117C22×C3711yescharacteristic
514C22×C22⋊C4—21no—
515#468—24no—
516#449—24no—
517#447—24no—
518C2×#107C22×C3711yescharacteristic, complemented
519#418—24no—
520C2×#103C22×C3711yescharacteristic, complemented
521C2×#103C22×C3711yescharacteristic, complemented
522C2×#103C22×C3711yescharacteristic, complemented
523C2×#102C22×C3711yescharacteristic
524C2×#102C22×C3711yescharacteristic
525C2×#102C22×C3711yescharacteristic
526C2×#102C22×C3711yescharacteristic
527C2×#102C22×C3711yescharacteristic
528C2×#102C22×C3711yescharacteristic
529C2×#102C22×C3711yescharacteristic, complemented
530C2×C22⋊C8C22×C3711yescharacteristic
531C2×C22⋊C8C22×C3711yescharacteristic, complemented
532C2×C22⋊C8C22×C3711yescharacteristic, complemented
533#394—21no—
534#392—21no—
535#390—21no—
536#390C22×C3711yescharacteristic, complemented
537#389C22×C3711yescharacteristic, complemented
538#388—21no—
539#380C22×C3711yescharacteristic, complemented
540#340C22×C3711yescharacteristic, complemented
541#340C22×C3711yescharacteristic, complemented
542#336C22×C3711yescharacteristic, complemented
543#336C22×C3711yescharacteristic, complemented
544C37#2445011yescharacteristic, direct product factor, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C3711yescharacteristic
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4D4×C3711yescharacteristic
564C22×D4D4×C3714yescomplemented
565C22×D4C23×C3711yescharacteristic
566C22×D4C23×C3711yescharacteristic
567C22×D4C23×C3711yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C3711yescharacteristic
571C23×C4C23×C3711yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8C23×C3711yescharacteristic
585C22×C8C23×C3711yescharacteristic
586C22×C8C23×C3711yescharacteristic
587C22×C8C23×C3711yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C3714yescomplemented
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C3711yescharacteristic
610C2×C4⋊C4C23×C3711yescharacteristic
611C2×C4⋊C4C23×C3711yescharacteristic
612C2×C4⋊C4C23×C3711yescharacteristic
613C2×C4⋊C4C23×C3711yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
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⋊C4D4×C3711yescharacteristic
627C2×C22⋊C4D4×C3711yescharacteristic
628C2×C42—21no—
629C2×C42C23×C3711yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102D4×C3714yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—24no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C3711yescharacteristic
657C24C2×D4×C3711yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C3712yes—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C3712yes—
705C2×D4C2×D4×C3712yes—
706C2×D4C2×D4×C3712yes—
707C2×D4#41×C3712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
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—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C3711yescharacteristic
730C22×C4C2×D4×C3711yescharacteristic
731C22×C4C2×D4×C3711yescharacteristic
732C22×C4C2×D4×C3711yescharacteristic
733C22×C4C2×D4×C3712yes—
734C22×C4C2×D4×C3712yes—
735C22×C4C24×C3711yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739M16—44no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8C2×D4×C3712yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C3712yes—
762C4⋊C4C2×D4×C3712yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23#120×C3712yes—
821C23C22×D4×C3711yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—48no—
832D4—48no—
833D4—44no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C3714yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
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—84no—
880C2×C4#120×C3712yes—
881C2×C4C22×D4×C3711yescharacteristic
882C2×C4C22×D4×C3711yescharacteristic
883C2×C4C22×D4×C3711yescharacteristic
884C2×C4C2×#41×C3711yescharacteristic
885C2×C4H(5,𝔽2)×C3711yescharacteristic
886C2×C4H(5,𝔽2)×C3711yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C3711yescharacteristic
928C22D42×C3711yescharacteristic
929C22C37×#54611yescharacteristic
930C22C37×#57511yescharacteristic
931C22C37×#57511yescharacteristic
932C22C37×#57611yescharacteristic
933C22C37×#57611yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C3711yescharacteristic
944C4C37×#53411yescharacteristic
945C4D42×C3711yescharacteristic
946C4C37×#54611yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—161no—
952C2C37×#241011yescharacteristic
953C2C37×#300511yescharacteristic
954C2C37×#300811yescharacteristic
955C2C37×#326811yescharacteristic
956C2C37×#327311yescharacteristic
957C2C37×#331911yescharacteristic
958C2C37×#332211yescharacteristic
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×#546C2semidirect
2. C2×C37×#468C2semidirect
3. C2×C37×#449C2semidirect
4. C2×C37×#447C2semidirect
5. C2×C37×#418C2semidirect
6. C37×#2414C2semidirect
7. C37×#2042C2semidirect
8. C37×#2033C2semidirect
9. C37×#2012C2semidirect
10. C37×#1999C2semidirect
11. C37×#1879C2semidirect
12. C37×#1873C2semidirect
13. C37×#1870C2semidirect
14. C37×#1862C2semidirect
15. C37×#1788C2semidirect
18. C22×SD16×C37C22semidirect
30. C2×#121×C37C22semidirect
39. C2×#107×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
50. C2×#102×C37C22semidirect
52. C2×C22⋊C8×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
57. C37×#390C22semidirect
58. C37×#389C22semidirect
60. C37×#380C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#336C22semidirect
64. C37×#336C22semidirect
84. C22×D4×C37D4semidirect
112. C22⋊Q8×C37D4semidirect
160. #102×C37D4semidirect
411. #24450C37direct (N × H)
468. C2×#546C2×C37semidirect
469. C2×#468C2×C37semidirect
470. C2×#449C2×C37semidirect
471. C2×#447C2×C37semidirect
472. C2×#418C2×C37semidirect
473. #2414C2×C37semidirect
474. #2042C2×C37semidirect
475. #2033C2×C37semidirect
476. #2012C2×C37semidirect
477. #1999C2×C37semidirect
478. #1879C2×C37semidirect
479. #1873C2×C37semidirect
480. #1870C2×C37semidirect
481. #1862C2×C37semidirect
482. #1788C2×C37semidirect
497. C22×SD16C22×C37semidirect
509. C2×#121C22×C37semidirect
518. C2×#107C22×C37semidirect
520. C2×#103C22×C37semidirect
521. C2×#103C22×C37semidirect
522. C2×#103C22×C37semidirect
529. C2×#102C22×C37semidirect
531. C2×C22⋊C8C22×C37semidirect
532. C2×C22⋊C8C22×C37semidirect
536. #390C22×C37semidirect
537. #389C22×C37semidirect
539. #380C22×C37semidirect
540. #340C22×C37semidirect
541. #340C22×C37semidirect
542. #336C22×C37semidirect
543. #336C22×C37semidirect
544. C37#24450direct (N × H)
564. C22×D4D4×C37semidirect
592. C22⋊Q8D4×C37semidirect
640. #102D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5462
C2×C37×#4682
C2×C37×#4492
C2×C37×#4472
C2×C37×#4182
C37×#24142
C37×#20422
C37×#20332
C37×#20122
C37×#19992
C37×#18792
C37×#18732
C37×#18702
C37×#18622
C37×#17882
#2445037