Finite Group Databasebeta

← C37×#23853 #22645106

Subgroups — C37×#23853 #22645106

Order 9472.

1800 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C37C211yesmaximal, characteristic, complemented
2C2×C37×#547C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C2×C37×#452C211yesmaximal, characteristic, complemented
5C2×C37×#449C211yesmaximal, characteristic, complemented
6C37×#2407C211yesmaximal, characteristic, complemented
7C37×#2016C211yesmaximal, characteristic, complemented
8C37×#2013C211yesmaximal, characteristic, complemented
9C37×#2001C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1892C211yesmaximal, characteristic, complemented
12C37×#1879C211yesmaximal, characteristic, complemented
13C37×#1877C211yesmaximal, characteristic, complemented
14C37×#1869C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C22×#41×C37C2211yescharacteristic
19C2×#135×C37—24no—
20C2×#135×C37—24no—
21C2×#135×C37—24no—
22C22×Q16×C37C2211yescharacteristic
23C22×Q16×C37C2211yescharacteristic
24C22×SD16×C37C2211yescharacteristic
25C22×SD16×C37C2211yescharacteristic
26C22×SD16×C37C2211yescharacteristic
27C22×D8×C37C2211yescharacteristic
28C23×C8×C37C2211yescharacteristic
29C37×#547—24no—
30C37×#547—24no—
31C2×C4⋊Q8×C37C2211yescharacteristic
32C2×#123×C37—21no—
33C2×#123×C37—21no—
34C2×C22⋊Q8×C37C2211yescharacteristic
35C2×C22⋊Q8×C37C2211yescharacteristic
36C2×C22⋊Q8×C37C2211yescharacteristic
37C2×#121×C37—21no—
38C2×#121×C37C2211yescharacteristic
39C2×C4×D4×C37C2211yescharacteristic
40C2×C4×D4×C37C2211yescharacteristic
41C22×C4⋊C4×C37—21no—
42C37×#452—24no—
43C37×#452—24no—
44C37×#449—24no—
45C2×#103×C37C2211yescharacteristic
46C2×#103×C37C2211yescharacteristic
47C2×#103×C37C2211yescharacteristic
48C2×#103×C37C2211yescharacteristic
49C2×#103×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic
51C2×#102×C37C2211yescharacteristic
52C2×#102×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C2×C22⋊C8×C37C2211yescharacteristic
55C2×C22⋊C8×C37C2211yescharacteristic
56C37×#394—21no—
57C37×#392—21no—
58C37×#391C2211yescharacteristic
59C37×#390C2211yescharacteristic
60C37×#386—21no—
61C37×#385—21no—
62C37×#380C2211yescharacteristic
63C37×#340C2211yescharacteristic
64C37×#340C2211yescharacteristic
65C37×#336C2211yescharacteristic
66C37×#336C2211yescharacteristic
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—22no—
71C2×#41×C37—22no—
72C2×#41×C37—22no—
73C2×#41×C37—22no—
74C2×#41×C37—22no—
75C2×#41×C37—22no—
76C2×#41×C37—22no—
77C2×#41×C37—22no—
78C2×#41×C37—41no—
79C2×#41×C37—41no—
80C2×#41×C37—41no—
81C2×#41×C37—41no—
82C2×#41×C37—41no—
83C2×#41×C37—41no—
84C2×#41×C37D414yescomplemented
85C22×Q8×C37C2311yescharacteristic
86C22×Q8×C37C2311yescharacteristic
87C22×Q8×C37C2311yescharacteristic
88C22×D4×C37—21no—
89C22×D4×C37—21no—
90C22×D4×C37—21no—
91C22×D4×C37—21no—
92C22×D4×C37D411yescharacteristic
93C22×D4×C37C2311yescharacteristic
94C22×D4×C37C2311yescharacteristic
95C23×C4×C37—21no—
96C23×C4×C37—21no—
97C23×C4×C37—21no—
98C23×C4×C37—21no—
99C23×C4×C37C2311yescharacteristic
100C23×C4×C37C2311yescharacteristic
101#135×C37—232no—
102C2×Q16×C37—22no—
103C2×Q16×C37—22no—
104C2×Q16×C37—22no—
105C2×Q16×C37—22no—
106C2×Q16×C37—22no—
107C2×Q16×C37—41no—
108C2×SD16×C37—22no—
109C2×SD16×C37—22no—
110C2×SD16×C37—22no—
111C2×SD16×C37—22no—
112C2×SD16×C37—22no—
113C2×SD16×C37—22no—
114C2×SD16×C37—22no—
115C2×SD16×C37—41no—
116C2×SD16×C37D414yescomplemented
117C2×D8×C37—22no—
118C2×D8×C37—22no—
119C2×D8×C37D414yescomplemented
120C22×C8×C37—22no—
121C22×C8×C37—22no—
122C22×C8×C37—22no—
123C22×C8×C37C2311yescharacteristic
124C22×C8×C37C2311yescharacteristic
125C22×C8×C37C2311yescharacteristic
126C22×C8×C37C2311yescharacteristic
127C4⋊Q8×C37—22no—
128C4⋊Q8×C37—22no—
129#123×C37—28no—
130#123×C37—28no—
131C22⋊Q8×C37—22no—
132C22⋊Q8×C37—22no—
133C22⋊Q8×C37—22no—
134C22⋊Q8×C37—22no—
135C22⋊Q8×C37—41no—
136C22⋊Q8×C37D414yescomplemented
137#121×C37—28no—
138#121×C37—22no—
139#121×C37—41no—
140C4×D4×C37—22no—
141C4×D4×C37—22no—
142C4×D4×C37—22no—
143C4×D4×C37—22no—
144C2×C4⋊C4×C37—28no—
145C2×C4⋊C4×C37—21no—
146C2×C4⋊C4×C37—21no—
147C2×C4⋊C4×C37—21no—
148C2×C4⋊C4×C37—21no—
149C2×C4⋊C4×C37—21no—
150C2×C4⋊C4×C37D411yescharacteristic
151C2×C4⋊C4×C37C2311yescharacteristic
152C2×C4⋊C4×C37C2311yescharacteristic
153C2×C4⋊C4×C37C2311yescharacteristic
154C2×C22⋊C4×C37—21no—
155C2×C22⋊C4×C37—21no—
156C2×C22⋊C4×C37—21no—
157C2×C22⋊C4×C37—21no—
158C2×C22⋊C4×C37—21no—
159C2×C22⋊C4×C37—21no—
160C2×C22⋊C4×C37—21no—
161C2×C22⋊C4×C37—21no—
162C2×C22⋊C4×C37D411yescharacteristic
163C2×C22⋊C4×C37D411yescharacteristic
164C2×C42×C37C2311yescharacteristic
165#103×C37—22no—
166#103×C37—22no—
167#103×C37—22no—
168#103×C37—41no—
169#103×C37—41no—
170#102×C37—22no—
171#102×C37—22no—
172#102×C37—22no—
173C22⋊C8×C37—22no—
174C22⋊C8×C37—22no—
175C22⋊C8×C37—22no—
176#95×C37—21no—
177#95×C37—21no—
178#95×C37—21no—
179C24×C37—21no—
180C24×C37—21no—
181C24×C37C2×D411yescharacteristic
182C24×C37C2×D411yescharacteristic
183#41×C37—28no—
184#41×C37—28no—
185#41×C37—44no—
186#41×C37—44no—
187#41×C37—44no—
188#41×C37—44no—
189#41×C37—44no—
190#41×C37—44no—
191#41×C37—44no—
192#41×C37—44no—
193#41×C37—44no—
194#41×C37—44no—
195C2×Q8×C37—21no—
196C2×Q8×C37—21no—
197C2×Q8×C37—21no—
198C2×Q8×C37—21no—
199C2×Q8×C37—21no—
200C2×Q8×C37—21no—
201C2×Q8×C37—21no—
202C2×Q8×C37—21no—
203C2×Q8×C37—21no—
204C2×Q8×C37—21no—
205C2×Q8×C37—21no—
206C2×Q8×C37—21no—
207C2×Q8×C37—21no—
208C2×Q8×C37—21no—
209C2×Q8×C37—21no—
210C2×Q8×C37C2×D412yes—
211C2×Q8×C37C2×D412yes—
212C2×Q8×C37C2×D412yes—
213C2×D4×C37—24no—
214C2×D4×C37—22no—
215C2×D4×C37—24no—
216C2×D4×C37—22no—
217C2×D4×C37—21no—
218C2×D4×C37—21no—
219C2×D4×C37—21no—
220C2×D4×C37—21no—
221C2×D4×C37—21no—
222C2×D4×C37—21no—
223C2×D4×C37—21no—
224C2×D4×C37—21no—
225C2×D4×C37—41no—
226C2×D4×C37—42no—
227C2×D4×C37—42no—
228C2×D4×C37—42no—
229C2×D4×C37—42no—
230C2×D4×C37—42no—
231C2×D4×C37—42no—
232C2×D4×C37—42no—
233C2×D4×C37—42no—
234C2×D4×C37—42no—
235C2×D4×C37—81no—
236C2×D4×C37C2×D412yes—
237C2×D4×C37C2×D412yes—
238C2×D4×C37C2×D412yes—
239C2×D4×C37C2×D412yes—
240C22×C4×C37—21no—
241C22×C4×C37—21no—
242C22×C4×C37—21no—
243C22×C4×C37—21no—
244C22×C4×C37—24no—
245C22×C4×C37—24no—
246C22×C4×C37—21no—
247C22×C4×C37—21no—
248C22×C4×C37—21no—
249C22×C4×C37—21no—
250C22×C4×C37—24no—
251C22×C4×C37—21no—
252C22×C4×C37—21no—
253C22×C4×C37—21no—
254C22×C4×C37—21no—
255C22×C4×C37—21no—
256C22×C4×C37—21no—
257C22×C4×C37—21no—
258C22×C4×C37—21no—
259C22×C4×C37—42no—
260C22×C4×C37—42no—
261C22×C4×C37—42no—
262C22×C4×C37—42no—
263C22×C4×C37—42no—
264C22×C4×C37—42no—
265C22×C4×C37—42no—
266C22×C4×C37—42no—
267C22×C4×C37—42no—
268C22×C4×C37C2×D411yescharacteristic
269C22×C4×C37C2×D411yescharacteristic
270C22×C4×C37C2×D411yescharacteristic
271C22×C4×C37C2×D412yes—
272C22×C4×C37C2×D412yes—
273C22×C4×C37C2×D411yescharacteristic
274C22×C4×C37C2411yescharacteristic
275Q16×C37—28no—
276Q16×C37—44no—
277SD16×C37—28no—
278SD16×C37—28no—
279SD16×C37—44no—
280D8×C37—28no—
281C2×C8×C37—28no—
282C2×C8×C37—21no—
283C2×C8×C37—21no—
284C2×C8×C37—21no—
285C2×C8×C37—21no—
286C2×C8×C37—21no—
287C2×C8×C37—21no—
288C2×C8×C37—21no—
289C2×C8×C37—21no—
290C2×C8×C37—21no—
291C2×C8×C37—21no—
292C2×C8×C37C2×D412yes—
293C2×C8×C37C2×D412yes—
294C4⋊C4×C37—24no—
295C4⋊C4×C37—24no—
296C4⋊C4×C37—24no—
297C4⋊C4×C37—22no—
298C4⋊C4×C37—24no—
299C4⋊C4×C37—21no—
300C4⋊C4×C37—21no—
301C4⋊C4×C37—21no—
302C4⋊C4×C37—21no—
303C4⋊C4×C37—21no—
304C4⋊C4×C37—42no—
305C4⋊C4×C37C2×D412yes—
306C22⋊C4×C37—24no—
307C22⋊C4×C37—24no—
308C22⋊C4×C37—24no—
309C22⋊C4×C37—22no—
310C22⋊C4×C37—22no—
311C22⋊C4×C37—42no—
312C22⋊C4×C37—42no—
313C22⋊C4×C37—42no—
314C22⋊C4×C37—81no—
315C22⋊C4×C37—81no—
316C42×C37—21no—
317C42×C37—21no—
318C23×C37—22no—
319C23×C37—21no—
320C23×C37—21no—
321C23×C37—22no—
322C23×C37—22no—
323C23×C37—21no—
324C23×C37—21no—
325C23×C37—21no—
326C23×C37—21no—
327C23×C37—21no—
328C23×C37—21no—
329C23×C37—22no—
330C23×C37—21no—
331C23×C37—21no—
332C23×C37—21no—
333C23×C37—21no—
334C23×C37—21no—
335C23×C37—41no—
336C23×C37—41no—
337C23×C37—41no—
338C23×C37—41no—
339C23×C37—41no—
340C23×C37—41no—
341C23×C37—41no—
342C23×C37—41no—
343C23×C37—41no—
344C23×C37—41no—
345C23×C37#12012yes—
346C23×C37C22×D411yescharacteristic
347Q8×C37—22no—
348Q8×C37—22no—
349Q8×C37—22no—
350Q8×C37—22no—
351Q8×C37—22no—
352Q8×C37—22no—
353Q8×C37—41no—
354Q8×C37—41no—
355Q8×C37—41no—
356Q8×C37—41no—
357Q8×C37—41no—
358Q8×C37—41no—
359D4×C37—22no—
360D4×C37—22no—
361D4×C37—22no—
362D4×C37—22no—
363D4×C37—22no—
364D4×C37—44no—
365D4×C37—48no—
366D4×C37—48no—
367D4×C37—48no—
368D4×C37—41no—
369D4×C37—41no—
370D4×C37—84no—
371D4×C37#12014yes—
372C2×C4×C37—21no—
373C2×C4×C37—21no—
374C2×C4×C37—21no—
375C2×C4×C37—21no—
376C2×C4×C37—22no—
377C2×C4×C37—22no—
378C2×C4×C37—22no—
379C2×C4×C37—22no—
380C2×C4×C37—21no—
381C2×C4×C37—22no—
382C2×C4×C37—21no—
383C2×C4×C37—22no—
384C2×C4×C37—22no—
385C2×C4×C37—21no—
386C2×C4×C37—22no—
387C2×C4×C37—21no—
388C2×C4×C37—21no—
389C2×C4×C37—21no—
390C2×C4×C37—48no—
391C2×C4×C37—48no—
392C2×C4×C37—48no—
393C2×C4×C37—48no—
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—41no—
402C2×C4×C37—41no—
403C2×C4×C37—41no—
404C2×C4×C37—41no—
405C2×C4×C37—41no—
406C2×C4×C37—41no—
407C2×C4×C37—41no—
408C2×C4×C37—41no—
409C2×C4×C37—41no—
410C2×C4×C37—41no—
411C2×C4×C37—41no—
412C2×C4×C37#12012yes—
413C2×C4×C37#13512yescomplemented
414C2×C4×C37C22×D411yescharacteristic
415C2×C4×C37C22×D411yescharacteristic
416C2×C4×C37C22×D411yescharacteristic
417C2×C4×C37C22×D411yescharacteristic
418C2×C4×C37H(5,𝔽2)11yescharacteristic
419C2×C4×C37H(5,𝔽2)11yescharacteristic
420C8×C37—22no—
421C8×C37—22no—
422C8×C37—41no—
423C8×C37—41no—
424#23853C3711yesmaximal, characteristic, direct product factor, Sylow
425C22×C37—22no—
426C22×C37—24no—
427C22×C37—22no—
428C22×C37—22no—
429C22×C37—42no—
430C22×C37—41no—
431C22×C37—42no—
432C22×C37—42no—
433C22×C37—41no—
434C22×C37—42no—
435C22×C37—41no—
436C22×C37—42no—
437C22×C37—41no—
438C22×C37—42no—
439C22×C37—42no—
440C22×C37—41no—
441C22×C37—41no—
442C22×C37—41no—
443C22×C37—42no—
444C22×C37—41no—
445C22×C37—41no—
446C22×C37—41no—
447C22×C37—42no—
448C22×C37—41no—
449C22×C37—81no—
450C22×C37—81no—
451C22×C37—81no—
452C22×C37—81no—
453C22×C37C2×#12011yescharacteristic
454C22×C37D4211yescharacteristic
455C22×C37D4211yescharacteristic
456C22×C37C2×#13511yescharacteristic
457C22×C37#57511yescharacteristic
458C22×C37#57711yescharacteristic
459C22×C37#57811yescharacteristic
460C4×C37—22no—
461C4×C37—22no—
462C4×C37—41no—
463C4×C37—42no—
464C4×C37—42no—
465C4×C37—42no—
466C4×C37—42no—
467C4×C37—41no—
468C4×C37—81no—
469C4×C37—81no—
470C4×C37C2×#12011yescharacteristic
471C4×C37#53411yescharacteristic
472C4×C37D4211yescharacteristic
473C4×C37D4211yescharacteristic
474C22×#135C2×C3711yescharacteristic, complemented
475C2×#547C2×C3711yescharacteristic, complemented
476C2×#452C2×C3711yescharacteristic, complemented
477C2×#452C2×C3711yescharacteristic, complemented
478C2×#449C2×C3711yescharacteristic, complemented
479#2407C2×C3711yescharacteristic, complemented
480#2016C2×C3711yescharacteristic, complemented
481#2013C2×C3711yescharacteristic, complemented
482#2001C2×C3711yescharacteristic, complemented
483#2000C2×C3711yescharacteristic, complemented
484#1892C2×C3711yescharacteristic, complemented
485#1879C2×C3711yescharacteristic, complemented
486#1877C2×C3711yescharacteristic, complemented
487#1869C2×C3711yescharacteristic, complemented
488#1788C2×C3711yescharacteristic, complemented
489C2×C37—42no—
490C2×C37—44no—
491C2×C37—81no—
492C2×C37—82no—
493C2×C37#240311yescharacteristic
494C2×C37#300211yescharacteristic
495C2×C37#301311yescharacteristic
496C2×C37#326711yescharacteristic
497C2×C37#326911yescharacteristic
498C2×C37#328311yescharacteristic
499C2×C37#328411yescharacteristic
500C22×#41C22×C3711yescharacteristic
501C22×#41C22×C3711yescharacteristic
502C22×#41C22×C3711yescharacteristic
503C2×#135—24no—
504C2×#135—24no—
505C2×#135—24no—
506C22×Q16C22×C3711yescharacteristic
507C22×Q16C22×C3711yescharacteristic
508C22×SD16C22×C3711yescharacteristic
509C22×SD16C22×C3711yescharacteristic
510C22×SD16C22×C3711yescharacteristic
511C22×D8C22×C3711yescharacteristic
512C23×C8C22×C3711yescharacteristic
513#547—24no—
514#547—24no—
515C2×C4⋊Q8C22×C3711yescharacteristic
516C2×#123—21no—
517C2×#123—21no—
518C2×C22⋊Q8C22×C3711yescharacteristic
519C2×C22⋊Q8C22×C3711yescharacteristic
520C2×C22⋊Q8C22×C3711yescharacteristic
521C2×#121—21no—
522C2×#121C22×C3711yescharacteristic
523C2×C4×D4C22×C3711yescharacteristic
524C2×C4×D4C22×C3711yescharacteristic
525C22×C4⋊C4—21no—
526#452—24no—
527#452—24no—
528#449—24no—
529C2×#103C22×C3711yescharacteristic
530C2×#103C22×C3711yescharacteristic
531C2×#103C22×C3711yescharacteristic
532C2×#103C22×C3711yescharacteristic
533C2×#103C22×C3711yescharacteristic
534C2×#102C22×C3711yescharacteristic
535C2×#102C22×C3711yescharacteristic
536C2×#102C22×C3711yescharacteristic
537C2×C22⋊C8C22×C3711yescharacteristic
538C2×C22⋊C8C22×C3711yescharacteristic
539C2×C22⋊C8C22×C3711yescharacteristic
540#394—21no—
541#392—21no—
542#391C22×C3711yescharacteristic
543#390C22×C3711yescharacteristic
544#386—21no—
545#385—21no—
546#380C22×C3711yescharacteristic
547#340C22×C3711yescharacteristic
548#340C22×C3711yescharacteristic
549#336C22×C3711yescharacteristic
550#336C22×C3711yescharacteristic
551C37#2385311yescharacteristic, direct product factor, Sylow
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—41no—
564C2×#41—41no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C3714yescomplemented
570C22×Q8C23×C3711yescharacteristic
571C22×Q8C23×C3711yescharacteristic
572C22×Q8C23×C3711yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C3711yescharacteristic
578C22×D4C23×C3711yescharacteristic
579C22×D4C23×C3711yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C3711yescharacteristic
585C23×C4C23×C3711yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16—41no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C3714yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8D4×C3714yescomplemented
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C3711yescharacteristic
609C22×C8C23×C3711yescharacteristic
610C22×C8C23×C3711yescharacteristic
611C22×C8C23×C3711yescharacteristic
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614#123—28no—
615#123—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—41no—
621C22⋊Q8D4×C3714yescomplemented
622#121—28no—
623#121—22no—
624#121—41no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4D4×C3711yescharacteristic
636C2×C4⋊C4C23×C3711yescharacteristic
637C2×C4⋊C4C23×C3711yescharacteristic
638C2×C4⋊C4C23×C3711yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4D4×C3711yescharacteristic
648C2×C22⋊C4D4×C3711yescharacteristic
649C2×C42C23×C3711yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C3711yescharacteristic
667C24C2×D4×C3711yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676#41—44no—
677#41—44no—
678#41—44no—
679#41—44no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8C2×D4×C3712yes—
696C2×Q8C2×D4×C3712yes—
697C2×Q8C2×D4×C3712yes—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—22no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—41no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—81no—
721C2×D4C2×D4×C3712yes—
722C2×D4C2×D4×C3712yes—
723C2×D4C2×D4×C3712yes—
724C2×D4C2×D4×C3712yes—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C3711yescharacteristic
754C22×C4C2×D4×C3711yescharacteristic
755C22×C4C2×D4×C3711yescharacteristic
756C22×C4C2×D4×C3712yes—
757C22×C4C2×D4×C3712yes—
758C22×C4C2×D4×C3711yescharacteristic
759C22×C4C24×C3711yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8C2×D4×C3712yes—
778C2×C8C2×D4×C3712yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—24no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—42no—
790C4⋊C4C2×D4×C3712yes—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—42no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C42—21no—
802C42—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—22no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23#120×C3712yes—
831C23C22×D4×C3711yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844D4—22no—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—44no—
850D4—48no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—84no—
856D4#120×C3714yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4#120×C3712yes—
898C2×C4#135×C3712yescomplemented
899C2×C4C22×D4×C3711yescharacteristic
900C2×C4C22×D4×C3711yescharacteristic
901C2×C4C22×D4×C3711yescharacteristic
902C2×C4C22×D4×C3711yescharacteristic
903C2×C4H(5,𝔽2)×C3711yescharacteristic
904C2×C4H(5,𝔽2)×C3711yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—24no—
911C22—22no—
912C22—22no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C3711yescharacteristic
938C22D42×C3711yescharacteristic
939C22D42×C3711yescharacteristic
940C22C2×#135×C3711yescharacteristic
941C22C37×#57511yescharacteristic
942C22C37×#57711yescharacteristic
943C22C37×#57811yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C3711yescharacteristic
955C4C37×#53411yescharacteristic
956C4D42×C3711yescharacteristic
957C4D42×C3711yescharacteristic
958C2—42no—
959C2—44no—
960C2—81no—
961C2—82no—
962C2C37×#240311yescharacteristic
963C2C37×#300211yescharacteristic
964C2C37×#301311yescharacteristic
965C2C37×#326711yescharacteristic
966C2C37×#326911yescharacteristic
967C2C37×#328311yescharacteristic
968C2C37×#328411yescharacteristic
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. C22×#135×C37C2semidirect
2. C2×C37×#547C2semidirect
3. C2×C37×#452C2semidirect
4. C2×C37×#452C2semidirect
5. C2×C37×#449C2semidirect
6. C37×#2407C2semidirect
7. C37×#2016C2semidirect
8. C37×#2013C2semidirect
9. C37×#2001C2semidirect
10. C37×#2000C2semidirect
11. C37×#1892C2semidirect
12. C37×#1879C2semidirect
13. C37×#1877C2semidirect
14. C37×#1869C2semidirect
15. C37×#1788C2semidirect
84. C2×#41×C37D4semidirect
116. C2×SD16×C37D4semidirect
119. C2×D8×C37D4semidirect
136. C22⋊Q8×C37D4semidirect
413. C2×C4×C37#135semidirect
424. #23853C37direct (N × H)
474. C22×#135C2×C37semidirect
475. C2×#547C2×C37semidirect
476. C2×#452C2×C37semidirect
477. C2×#452C2×C37semidirect
478. C2×#449C2×C37semidirect
479. #2407C2×C37semidirect
480. #2016C2×C37semidirect
481. #2013C2×C37semidirect
482. #2001C2×C37semidirect
483. #2000C2×C37semidirect
484. #1892C2×C37semidirect
485. #1879C2×C37semidirect
486. #1877C2×C37semidirect
487. #1869C2×C37semidirect
488. #1788C2×C37semidirect
551. C37#23853direct (N × H)
569. C2×#41D4×C37semidirect
601. C2×SD16D4×C37semidirect
604. C2×D8D4×C37semidirect
621. C22⋊Q8D4×C37semidirect
898. C2×C4#135×C37semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C372
C2×C37×#5472
C2×C37×#4522
C2×C37×#4492
C37×#24072
C37×#20162
C37×#20132
C37×#20012
C37×#20002
C37×#18922
C37×#18792
C37×#18772
C37×#18692
C37×#17882
#2385337