Finite Group Databasebeta

← C37×#24443 #22645696

Subgroups — C37×#24443 #22645696

Order 9472.

1510 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#550C211yesmaximal, characteristic
2C2×C37×#468C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C2×C37×#452C211yesmaximal, characteristic, complemented
5C2×C37×#417C211yesmaximal, characteristic, complemented
6C37×#2417C211yesmaximal, characteristic, complemented
7C37×#2041C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2014C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1878C211yesmaximal, characteristic, complemented
12C37×#1874C211yesmaximal, characteristic, complemented
13C37×#1870C211yesmaximal, characteristic, complemented
14C37×#1863C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C22×M16×C37C2211yescharacteristic
22C37×#550—24no—
23C37×#550—24no—
24C2×#127×C37—21no—
25C2×#127×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic
28C2×#121×C37—21no—
29C2×#121×C37—21no—
30C2×#121×C37C2211yescharacteristic
31C2×#121×C37C2211yescharacteristic
32C2×C4×Q8×C37C2211yescharacteristic
33C2×C4×D4×C37—21no—
34C2×C4×D4×C37C2211yescharacteristic
35C22×C4⋊C4×C37C2211yescharacteristic
36C37×#468—24no—
37C37×#452—24no—
38C37×#452—24no—
39C2×#107×C37C2211yescharacteristic
40C37×#417—24no—
41C2×#103×C37C2211yescharacteristic
42C2×#103×C37C2211yescharacteristic
43C2×#103×C37C2211yescharacteristic
44C2×#103×C37C2211yescharacteristic
45C2×#102×C37C2211yescharacteristic
46C2×#102×C37C2211yescharacteristic
47C2×#102×C37C2211yescharacteristic
48C2×#102×C37C2211yescharacteristic
49C2×#102×C37C2211yescharacteristic
50C2×#102×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C37×#398—21no—
55C37×#396—21no—
56C37×#391C2211yescharacteristic
57C37×#389C2211yescharacteristic
58C37×#386—21no—
59C37×#380—21no—
60C37×#380C2211yescharacteristic
61C37×#340C2211yescharacteristic
62C37×#340C2211yescharacteristic
63C37×#336C2211yescharacteristic
64C37×#336C2211yescharacteristic
65C2×#41×C37—22no—
66C2×#41×C37—22no—
67C2×#41×C37—22no—
68C2×#41×C37—22no—
69C2×#41×C37—22no—
70C2×#41×C37—22no—
71C2×#41×C37—22no—
72C2×#41×C37—41no—
73C2×#41×C37—41no—
74C2×#41×C37—41no—
75C2×#41×C37—41no—
76C2×#41×C37D414yes—
77C22×Q8×C37C2311yescharacteristic
78C22×Q8×C37C2311yescharacteristic
79C22×D4×C37—21no—
80C22×D4×C37—21no—
81C22×D4×C37—21no—
82C22×D4×C37—21no—
83C22×D4×C37—21no—
84C22×D4×C37—21no—
85C22×D4×C37D411yescharacteristic
86C22×D4×C37C2311yescharacteristic
87C22×D4×C37C2311yescharacteristic
88C23×C4×C37—21no—
89C23×C4×C37—21no—
90C23×C4×C37—21no—
91C23×C4×C37C2311yescharacteristic
92C23×C4×C37C2311yescharacteristic
93C2×Q16×C37—22no—
94C2×Q16×C37—22no—
95C2×Q16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37—22no—
98C2×SD16×C37—22no—
99C2×SD16×C37—41no—
100C2×SD16×C37—41no—
101C2×SD16×C37—41no—
102C2×M16×C37—22no—
103C2×M16×C37—22no—
104C2×M16×C37—41no—
105C22×C8×C37C2311yescharacteristic
106C22×C8×C37C2311yescharacteristic
107C22×C8×C37C2311yescharacteristic
108C22×C8×C37C2311yescharacteristic
109#127×C37—28no—
110#127×C37—22no—
111#127×C37—22no—
112C22⋊Q8×C37—22no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—41no—
116#121×C37—28no—
117#121×C37—28no—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37D414yes—
122C4×Q8×C37—22no—
123C4×Q8×C37—22no—
124C4×D4×C37—28no—
125C4×D4×C37—22no—
126C4×D4×C37—22no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37—22no—
129C2×C4⋊C4×C37—21no—
130C2×C4⋊C4×C37—21no—
131C2×C4⋊C4×C37—21no—
132C2×C4⋊C4×C37—21no—
133C2×C4⋊C4×C37—41no—
134C2×C4⋊C4×C37D411yescharacteristic
135C2×C4⋊C4×C37C2311yescharacteristic
136C2×C4⋊C4×C37C2311yescharacteristic
137C2×C4⋊C4×C37C2311yescharacteristic
138C2×C4⋊C4×C37C2311yescharacteristic
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×C37D411yescharacteristic
145C2×C22⋊C4×C37D411yescharacteristic
146C2×C42×C37—21no—
147C2×C42×C37C2311yescharacteristic
148#107×C37—22no—
149#103×C37—22no—
150#103×C37—22no—
151#103×C37—22no—
152#103×C37D414yescomplemented
153#102×C37—22no—
154#102×C37—22no—
155#102×C37—22no—
156#102×C37—22no—
157#102×C37—22no—
158#102×C37—41no—
159C22⋊C8×C37—22no—
160C22⋊C8×C37—22no—
161C22⋊C8×C37—41no—
162#95×C37—21no—
163#95×C37—21no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—21no—
167C24×C37—21no—
168C24×C37C2×D411yescharacteristic
169C24×C37C2×D411yescharacteristic
170#41×C37—28no—
171#41×C37—44no—
172#41×C37—44no—
173#41×C37—44no—
174#41×C37—44no—
175#41×C37—44no—
176#41×C37—44no—
177#41×C37—44no—
178C2×Q8×C37—21no—
179C2×Q8×C37—21no—
180C2×Q8×C37—21no—
181C2×Q8×C37—21no—
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×Q8×C37C2×D412yes—
189C2×Q8×C37#4112yes—
190C2×D4×C37—24no—
191C2×D4×C37—24no—
192C2×D4×C37—22no—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—24no—
196C2×D4×C37—24no—
197C2×D4×C37—22no—
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—21no—
208C2×D4×C37—41no—
209C2×D4×C37—42no—
210C2×D4×C37—42no—
211C2×D4×C37—42no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—42no—
215C2×D4×C37—81no—
216C2×D4×C37—81no—
217C2×D4×C37—81no—
218C2×D4×C37—81no—
219C2×D4×C37—81no—
220C2×D4×C37—81no—
221C2×D4×C37C2×D412yes—
222C2×D4×C37C2×D412yes—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—24no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—24no—
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—42no—
242C22×C4×C37—42no—
243C22×C4×C37—42no—
244C22×C4×C37—42no—
245C22×C4×C37—42no—
246C22×C4×C37—42no—
247C22×C4×C37—81no—
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D411yescharacteristic
251C22×C4×C37C2×D412yes—
252C22×C4×C37C2×D412yes—
253C22×C4×C37C2×D411yescharacteristic
254C22×C4×C37C2411yescharacteristic
255Q16×C37—44no—
256SD16×C37—44no—
257SD16×C37—44no—
258M16×C37—44no—
259C2×C8×C37—21no—
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×C37C2×D412yes—
271C4⋊C4×C37—24no—
272C4⋊C4×C37—22no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—21no—
275C4⋊C4×C37—21no—
276C4⋊C4×C37—21no—
277C4⋊C4×C37—21no—
278C4⋊C4×C37—21no—
279C4⋊C4×C37—42no—
280C4⋊C4×C37—42no—
281C4⋊C4×C37—42no—
282C4⋊C4×C37—81no—
283C4⋊C4×C37C2×D412yes—
284C4⋊C4×C37C2×D412yes—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—22no—
287C22⋊C4×C37—24no—
288C22⋊C4×C37—22no—
289C22⋊C4×C37—42no—
290C22⋊C4×C37—42no—
291C22⋊C4×C37—81no—
292C42×C37—24no—
293C42×C37—21no—
294C42×C37—21no—
295C23×C37—21no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—21no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—22no—
303C23×C37—22no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—41no—
311C23×C37—41no—
312C23×C37—41no—
313C23×C37—41no—
314C23×C37—41no—
315C23×C37—41no—
316C23×C37—41no—
317C23×C37—41no—
318C23×C37—41no—
319C23×C37—41no—
320C23×C37—41no—
321C23×C37—41no—
322C23×C37#12012yes—
323C23×C37C22×D411yescharacteristic
324Q8×C37—22no—
325Q8×C37—22no—
326Q8×C37—22no—
327Q8×C37—41no—
328Q8×C37—41no—
329Q8×C37—41no—
330Q8×C37—41no—
331Q8×C37#12114yes—
332D4×C37—22no—
333D4×C37—22no—
334D4×C37—22no—
335D4×C37—22no—
336D4×C37—44no—
337D4×C37—48no—
338D4×C37—48no—
339D4×C37—48no—
340D4×C37—41no—
341D4×C37—41no—
342D4×C37—41no—
343D4×C37—41no—
344D4×C37—84no—
345D4×C37—84no—
346D4×C37—84no—
347C2×C4×C37—21no—
348C2×C4×C37—22no—
349C2×C4×C37—21no—
350C2×C4×C37—22no—
351C2×C4×C37—21no—
352C2×C4×C37—22no—
353C2×C4×C37—21no—
354C2×C4×C37—22no—
355C2×C4×C37—22no—
356C2×C4×C37—22no—
357C2×C4×C37—22no—
358C2×C4×C37—21no—
359C2×C4×C37—22no—
360C2×C4×C37—21no—
361C2×C4×C37—22no—
362C2×C4×C37—21no—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—21no—
366C2×C4×C37—48no—
367C2×C4×C37—48no—
368C2×C4×C37—41no—
369C2×C4×C37—41no—
370C2×C4×C37—41no—
371C2×C4×C37—41no—
372C2×C4×C37—41no—
373C2×C4×C37—41no—
374C2×C4×C37—41no—
375C2×C4×C37—41no—
376C2×C4×C37—41no—
377C2×C4×C37—41no—
378C2×C4×C37—41no—
379C2×C4×C37—41no—
380C2×C4×C37—41no—
381C2×C4×C37—41no—
382C2×C4×C37—41no—
383C2×C4×C37—41no—
384C2×C4×C37—41no—
385C2×C4×C37—84no—
386C2×C4×C37#12012yes—
387C2×C4×C37#13712yes—
388C2×C4×C37C22×D411yescharacteristic
389C2×C4×C37C22×D411yescharacteristic
390C2×C4×C37C22×D411yescharacteristic
391C2×C4×C37C2×#4111yescharacteristic
392C2×C4×C37H(5,𝔽2)11yescharacteristic
393C2×C4×C37H(5,𝔽2)11yescharacteristic
394C8×C37—22no—
395C8×C37—41no—
396C8×C37—41no—
397C8×C37—41no—
398#24443C3711yesmaximal, characteristic, direct product factor, Sylow
399C22×C37—22no—
400C22×C37—22no—
401C22×C37—22no—
402C22×C37—41no—
403C22×C37—41no—
404C22×C37—41no—
405C22×C37—41no—
406C22×C37—41no—
407C22×C37—42no—
408C22×C37—42no—
409C22×C37—41no—
410C22×C37—41no—
411C22×C37—42no—
412C22×C37—42no—
413C22×C37—41no—
414C22×C37—42no—
415C22×C37—42no—
416C22×C37—41no—
417C22×C37—41no—
418C22×C37—41no—
419C22×C37—81no—
420C22×C37—81no—
421C22×C37—81no—
422C22×C37—81no—
423C22×C37—81no—
424C22×C37—81no—
425C22×C37—81no—
426C22×C37—81no—
427C22×C37C2×#12011yescharacteristic
428C22×C37D4211yescharacteristic
429C22×C37#54611yescharacteristic
430C22×C37C2×#13711yescharacteristic
431C22×C37#57511yescharacteristic
432C22×C37#57611yescharacteristic
433C22×C37#57711yescharacteristic
434C4×C37—22no—
435C4×C37—24no—
436C4×C37—22no—
437C4×C37—41no—
438C4×C37—41no—
439C4×C37—42no—
440C4×C37—42no—
441C4×C37—81no—
442C4×C37—81no—
443C4×C37—81no—
444C4×C37C2×#12111yescharacteristic
445C4×C37#53411yescharacteristic
446C4×C37D4211yescharacteristic
447C4×C37#54611yescharacteristic
448C2×#550C2×C3711yescharacteristic
449C2×#468C2×C3711yescharacteristic, complemented
450C2×#452C2×C3711yescharacteristic, complemented
451C2×#452C2×C3711yescharacteristic, complemented
452C2×#417C2×C3711yescharacteristic, complemented
453#2417C2×C3711yescharacteristic, complemented
454#2041C2×C3711yescharacteristic, complemented
455#2033C2×C3711yescharacteristic, complemented
456#2014C2×C3711yescharacteristic, complemented
457#2000C2×C3711yescharacteristic, complemented
458#1878C2×C3711yescharacteristic, complemented
459#1874C2×C3711yescharacteristic, complemented
460#1870C2×C3711yescharacteristic, complemented
461#1863C2×C3711yescharacteristic, complemented
462#1788C2×C3711yescharacteristic, complemented
463C2×C37—42no—
464C2×C37—81no—
465C2×C37—82no—
466C2×C37—82no—
467C2×C37#241011yescharacteristic
468C2×C37#300711yescharacteristic
469C2×C37#301211yescharacteristic
470C2×C37#326811yescharacteristic
471C2×C37#327811yescharacteristic
472C2×C37#331711yescharacteristic
473C2×C37#333311yescharacteristic
474C22×#41C22×C3711yescharacteristic
475C22×#41C22×C3711yescharacteristic
476C22×Q16C22×C3711yescharacteristic
477C22×SD16C22×C3711yescharacteristic
478C22×SD16C22×C3711yescharacteristic
479C22×M16C22×C3711yescharacteristic
480#550—24no—
481#550—24no—
482C2×#127—21no—
483C2×#127C22×C3711yescharacteristic
484C2×C22⋊Q8C22×C3711yescharacteristic
485C2×C22⋊Q8C22×C3711yescharacteristic
486C2×#121—21no—
487C2×#121—21no—
488C2×#121C22×C3711yescharacteristic
489C2×#121C22×C3711yescharacteristic
490C2×C4×Q8C22×C3711yescharacteristic
491C2×C4×D4—21no—
492C2×C4×D4C22×C3711yescharacteristic
493C22×C4⋊C4C22×C3711yescharacteristic
494#468—24no—
495#452—24no—
496#452—24no—
497C2×#107C22×C3711yescharacteristic
498#417—24no—
499C2×#103C22×C3711yescharacteristic
500C2×#103C22×C3711yescharacteristic
501C2×#103C22×C3711yescharacteristic
502C2×#103C22×C3711yescharacteristic
503C2×#102C22×C3711yescharacteristic
504C2×#102C22×C3711yescharacteristic
505C2×#102C22×C3711yescharacteristic
506C2×#102C22×C3711yescharacteristic
507C2×#102C22×C3711yescharacteristic
508C2×#102C22×C3711yescharacteristic
509C2×C22⋊C8C22×C3711yescharacteristic
510C2×C22⋊C8C22×C3711yescharacteristic
511C2×C22⋊C8C22×C3711yescharacteristic
512#398—21no—
513#396—21no—
514#391C22×C3711yescharacteristic
515#389C22×C3711yescharacteristic
516#386—21no—
517#380—21no—
518#380C22×C3711yescharacteristic
519#340C22×C3711yescharacteristic
520#340C22×C3711yescharacteristic
521#336C22×C3711yescharacteristic
522#336C22×C3711yescharacteristic
523C37#2444311yescharacteristic, direct product factor, Sylow
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C3714yes—
536C22×Q8C23×C3711yescharacteristic
537C22×Q8C23×C3711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4D4×C3711yescharacteristic
545C22×D4C23×C3711yescharacteristic
546C22×D4C23×C3711yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C3711yescharacteristic
551C23×C4C23×C3711yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8C23×C3711yescharacteristic
565C22×C8C23×C3711yescharacteristic
566C22×C8C23×C3711yescharacteristic
567C22×C8C23×C3711yescharacteristic
568#127—28no—
569#127—22no—
570#127—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575#121—28no—
576#121—28no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121D4×C3714yes—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—28no—
584C4×D4—22no—
585C4×D4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4D4×C3711yescharacteristic
594C2×C4⋊C4C23×C3711yescharacteristic
595C2×C4⋊C4C23×C3711yescharacteristic
596C2×C4⋊C4C23×C3711yescharacteristic
597C2×C4⋊C4C23×C3711yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4D4×C3711yescharacteristic
604C2×C22⋊C4D4×C3711yescharacteristic
605C2×C42—21no—
606C2×C42C23×C3711yescharacteristic
607#107—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103D4×C3714yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C3711yescharacteristic
628C24C2×D4×C3711yescharacteristic
629#41—28no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8C2×D4×C3712yes—
647C2×Q8C2×D4×C3712yes—
648C2×Q8#41×C3712yes—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4—81no—
680C2×D4C2×D4×C3712yes—
681C2×D4C2×D4×C3712yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—81no—
707C22×C4C2×D4×C3711yescharacteristic
708C22×C4C2×D4×C3711yescharacteristic
709C22×C4C2×D4×C3711yescharacteristic
710C22×C4C2×D4×C3712yes—
711C22×C4C2×D4×C3712yes—
712C22×C4C2×D4×C3711yescharacteristic
713C22×C4C24×C3711yescharacteristic
714Q16—44no—
715SD16—44no—
716SD16—44no—
717M16—44no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8C2×D4×C3712yes—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C3712yes—
743C4⋊C4C2×D4×C3712yes—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—81no—
751C42—24no—
752C42—21no—
753C42—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—22no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23#120×C3712yes—
782C23C22×D4×C3711yescharacteristic
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8#121×C3714yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—48no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—84no—
804D4—84no—
805D4—84no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—48no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C3712yes—
846C2×C4#137×C3712yes—
847C2×C4C22×D4×C3711yescharacteristic
848C2×C4C22×D4×C3711yescharacteristic
849C2×C4C22×D4×C3711yescharacteristic
850C2×C4C2×#41×C3711yescharacteristic
851C2×C4H(5,𝔽2)×C3711yescharacteristic
852C2×C4H(5,𝔽2)×C3711yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C3711yescharacteristic
886C22D42×C3711yescharacteristic
887C22C37×#54611yescharacteristic
888C22C2×#137×C3711yescharacteristic
889C22C37×#57511yescharacteristic
890C22C37×#57611yescharacteristic
891C22C37×#57711yescharacteristic
892C4—22no—
893C4—24no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—42no—
898C4—42no—
899C4—81no—
900C4—81no—
901C4—81no—
902C4C2×#121×C3711yescharacteristic
903C4C37×#53411yescharacteristic
904C4D42×C3711yescharacteristic
905C4C37×#54611yescharacteristic
906C2—42no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2C37×#241011yescharacteristic
911C2C37×#300711yescharacteristic
912C2C37×#301211yescharacteristic
913C2C37×#326811yescharacteristic
914C2C37×#327811yescharacteristic
915C2C37×#331711yescharacteristic
916C2C37×#333311yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#550C2
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
2. C2×C37×#468C2semidirect
3. C2×C37×#452C2semidirect
4. C2×C37×#452C2semidirect
5. C2×C37×#417C2semidirect
6. C37×#2417C2semidirect
7. C37×#2041C2semidirect
8. C37×#2033C2semidirect
9. C37×#2014C2semidirect
10. C37×#2000C2semidirect
11. C37×#1878C2semidirect
12. C37×#1874C2semidirect
13. C37×#1870C2semidirect
14. C37×#1863C2semidirect
15. C37×#1788C2semidirect
152. #103×C37D4semidirect
398. #24443C37direct (N × H)
449. C2×#468C2×C37semidirect
450. C2×#452C2×C37semidirect
451. C2×#452C2×C37semidirect
452. C2×#417C2×C37semidirect
453. #2417C2×C37semidirect
454. #2041C2×C37semidirect
455. #2033C2×C37semidirect
456. #2014C2×C37semidirect
457. #2000C2×C37semidirect
458. #1878C2×C37semidirect
459. #1874C2×C37semidirect
460. #1870C2×C37semidirect
461. #1863C2×C37semidirect
462. #1788C2×C37semidirect
523. C37#24443direct (N × H)
611. #103D4×C37semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#5502
C2×C37×#4682
C2×C37×#4522
C2×C37×#4172
C37×#24172
C37×#20412
C37×#20332
C37×#20142
C37×#20002
C37×#18782
C37×#18742
C37×#18702
C37×#18632
C37×#17882
#2444337