Finite Group Databasebeta

← C37×#24389 #22645642

Subgroups — C37×#24389 #22645642

Order 9472.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#525C211yesmaximal, characteristic
2C2×C37×#470C211yesmaximal, characteristic, complemented
3C2×C37×#468C211yesmaximal, characteristic, complemented
4C2×C37×#452C211yesmaximal, characteristic, complemented
5C2×C37×#407C211yesmaximal, characteristic, complemented
6C37×#2848C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2034C211yesmaximal, characteristic, complemented
9C37×#2001C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1895C211yesmaximal, characteristic, complemented
12C37×#1894C211yesmaximal, characteristic, complemented
13C37×#1873C211yesmaximal, characteristic, complemented
14C37×#1854C211yesmaximal, characteristic, complemented
15C37×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C24×C4×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic, complemented
19C22×SD16×C37C2211yescharacteristic, complemented
20C22×M16×C37C2211yescharacteristic
21C22×M16×C37C2211yescharacteristic
22C37×#525—24no—
23C37×#525—24no—
24C2×#123×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic
28C2×C22⋊Q8×C37C2211yescharacteristic
29C2×C22⋊Q8×C37C2211yescharacteristic
30C2×#121×C37C2211yescharacteristic
31C2×#121×C37C2211yescharacteristic
32C2×#120×C37—21no—
33C2×C4×D4×C37—21no—
34C2×C4×D4×C37—21no—
35C2×#117×C37C2211yescharacteristic
36C37×#470—24no—
37C37×#468—24no—
38C37×#452—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C2×#106×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#103×C37C2211yescharacteristic, complemented
45C2×#103×C37C2211yescharacteristic, complemented
46C2×#102×C37C2211yescharacteristic, complemented
47C2×#102×C37C2211yescharacteristic, complemented
48C2×#102×C37C2211yescharacteristic, complemented
49C37×#407—24no—
50C2×C22⋊C8×C37C2211yescharacteristic
51C2×C22⋊C8×C37C2211yescharacteristic
52C2×C22⋊C8×C37C2211yescharacteristic
53C2×C22⋊C8×C37C2211yescharacteristic
54C37×#385—21no—
55C37×#385—21no—
56C37×#385—21no—
57C37×#380C2211yescharacteristic
58C37×#380C2211yescharacteristic
59C37×#380C2211yescharacteristic
60C37×#379—21no—
61C37×#340C2211yescharacteristic, complemented
62C37×#340C2211yescharacteristic, complemented
63C37×#340C2211yescharacteristic, complemented
64C37×#340C2211yescharacteristic, complemented
65C25×C37D411yescharacteristic
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×Q8×C37C2311yescharacteristic
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—21no—
77C22×D4×C37C2311yescharacteristic
78C23×C4×C37—22no—
79C23×C4×C37—22no—
80C23×C4×C37—22no—
81C23×C4×C37—21no—
82C23×C4×C37—22no—
83C23×C4×C37—41no—
84C23×C4×C37—41no—
85C23×C4×C37D411yescharacteristic
86C23×C4×C37D411yescharacteristic
87C23×C4×C37D411yescharacteristic
88C23×C4×C37C2311yescharacteristic
89C23×C4×C37C2311yescharacteristic
90C23×C4×C37C2311yescharacteristic
91C2×Q16×C37—22no—
92C2×Q16×C37—22no—
93C2×Q16×C37—41no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—41no—
97C2×M16×C37—22no—
98C2×M16×C37—22no—
99C2×M16×C37—22no—
100C2×M16×C37—22no—
101C2×M16×C37—41no—
102C2×M16×C37—41no—
103C22×C8×C37C2311yescharacteristic
104C22×C8×C37C2311yescharacteristic
105C22×C8×C37C2311yescharacteristic
106C22×C8×C37C2311yescharacteristic
107#123×C37—28no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—22no—
110C22⋊Q8×C37—22no—
111C22⋊Q8×C37—22no—
112C22⋊Q8×C37—22no—
113C22⋊Q8×C37—22no—
114C22⋊Q8×C37—22no—
115C22⋊Q8×C37—41no—
116C22⋊Q8×C37—41no—
117C22⋊Q8×C37D414yes—
118#121×C37—22no—
119#121×C37—22no—
120#121×C37—22no—
121#121×C37D414yes—
122#120×C37—28no—
123C4×D4×C37—28no—
124C4×D4×C37—28no—
125#117×C37—22no—
126#117×C37—22no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37—21no—
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#103×C37—22no—
154#103×C37—22no—
155#103×C37—41no—
156#102×C37—22no—
157#102×C37—22no—
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—22no—
167C24×C37—22no—
168C24×C37—22no—
169C24×C37—21no—
170C24×C37—41no—
171C24×C37—41no—
172C24×C37—41no—
173C24×C37—41no—
174C24×C37C2×D411yescharacteristic
175C24×C37C2×D411yescharacteristic
176C24×C37C2×D411yescharacteristic
177#41×C37—44no—
178#41×C37—44no—
179#41×C37—44no—
180#41×C37—44no—
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×C37—21no—
188C2×Q8×C37—21no—
189C2×Q8×C37—21no—
190C2×Q8×C37—21no—
191C2×Q8×C37—21no—
192C2×Q8×C37C2×D412yes—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—24no—
196C2×D4×C37—21no—
197C2×D4×C37—21no—
198C2×D4×C37—21no—
199C2×D4×C37—21no—
200C2×D4×C37—21no—
201C2×D4×C37—42no—
202C2×D4×C37—42no—
203C2×D4×C37—42no—
204C2×D4×C37—42no—
205C2×D4×C37—42no—
206C2×D4×C37—42no—
207C2×D4×C37C2×D412yes—
208C22×C4×C37—21no—
209C22×C4×C37—21no—
210C22×C4×C37—21no—
211C22×C4×C37—21no—
212C22×C4×C37—21no—
213C22×C4×C37—21no—
214C22×C4×C37—21no—
215C22×C4×C37—21no—
216C22×C4×C37—24no—
217C22×C4×C37—22no—
218C22×C4×C37—22no—
219C22×C4×C37—21no—
220C22×C4×C37—21no—
221C22×C4×C37—21no—
222C22×C4×C37—22no—
223C22×C4×C37—22no—
224C22×C4×C37—22no—
225C22×C4×C37—22no—
226C22×C4×C37—21no—
227C22×C4×C37—21no—
228C22×C4×C37—21no—
229C22×C4×C37—21no—
230C22×C4×C37—21no—
231C22×C4×C37—21no—
232C22×C4×C37—21no—
233C22×C4×C37—21no—
234C22×C4×C37—21no—
235C22×C4×C37—21no—
236C22×C4×C37—41no—
237C22×C4×C37—41no—
238C22×C4×C37—41no—
239C22×C4×C37—44no—
240C22×C4×C37—44no—
241C22×C4×C37—44no—
242C22×C4×C37—44no—
243C22×C4×C37—42no—
244C22×C4×C37—42no—
245C22×C4×C37C2×D411yescharacteristic
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D412yes—
248C22×C4×C37C2×D412yes—
249C22×C4×C37C2×D411yescharacteristic
250C22×C4×C37C2×D412yes—
251C22×C4×C37#4112yes—
252C22×C4×C37C2411yescharacteristic
253Q16×C37—44no—
254SD16×C37—44no—
255M16×C37—44no—
256M16×C37—44no—
257C2×C8×C37—21no—
258C2×C8×C37—21no—
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×C37C2×D412yes—
268C2×C8×C37C2×D412yes—
269C4⋊C4×C37—24no—
270C4⋊C4×C37—24no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
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×C37C2×D412yes—
283C4⋊C4×C37C2×D412yes—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—24no—
287C22⋊C4×C37—24no—
288C22⋊C4×C37—24no—
289C22⋊C4×C37—42no—
290C22⋊C4×C37—42no—
291C22⋊C4×C37—42no—
292C22⋊C4×C37—42no—
293C22⋊C4×C37—42no—
294C22⋊C4×C37—42no—
295C42×C37—24no—
296C23×C37—21no—
297C23×C37—21no—
298C23×C37—21no—
299C23×C37—21no—
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—21no—
313C23×C37—21no—
314C23×C37—22no—
315C23×C37—44no—
316C23×C37—44no—
317C23×C37—44no—
318C23×C37—44no—
319C23×C37—44no—
320C23×C37—44no—
321C23×C37—44no—
322C23×C37—41no—
323C23×C37—41no—
324C23×C37—41no—
325C23×C37—41no—
326C23×C37—41no—
327C23×C37—41no—
328C23×C37#12012yes—
329C23×C37#12112yes—
330C23×C37#13712yes—
331C23×C37C22×D411yescharacteristic
332Q8×C37—22no—
333Q8×C37—22no—
334Q8×C37—41no—
335Q8×C37—41no—
336Q8×C37—41no—
337Q8×C37—41no—
338Q8×C37—41no—
339Q8×C37—41no—
340D4×C37—22no—
341D4×C37—22no—
342D4×C37—48no—
343D4×C37—48no—
344D4×C37—48no—
345D4×C37—41no—
346D4×C37—41no—
347C2×C4×C37—21no—
348C2×C4×C37—21no—
349C2×C4×C37—21no—
350C2×C4×C37—21no—
351C2×C4×C37—22no—
352C2×C4×C37—22no—
353C2×C4×C37—22no—
354C2×C4×C37—22no—
355C2×C4×C37—22no—
356C2×C4×C37—22no—
357C2×C4×C37—22no—
358C2×C4×C37—22no—
359C2×C4×C37—22no—
360C2×C4×C37—22no—
361C2×C4×C37—21no—
362C2×C4×C37—22no—
363C2×C4×C37—21no—
364C2×C4×C37—21no—
365C2×C4×C37—44no—
366C2×C4×C37—44no—
367C2×C4×C37—44no—
368C2×C4×C37—48no—
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—41no—
386C2×C4×C37—41no—
387C2×C4×C37—41no—
388C2×C4×C37—41no—
389C2×C4×C37—41no—
390C2×C4×C37—41no—
391C2×C4×C37#12012yes—
392C2×C4×C37#12112yes—
393C2×C4×C37C22×D411yescharacteristic
394C2×C4×C37C22×D411yescharacteristic
395C2×C4×C37C22×D411yescharacteristic
396C2×C4×C37C2×#4111yescharacteristic
397C2×C4×C37H(5,𝔽2)11yescharacteristic
398C2×C4×C37H(5,𝔽2)11yescharacteristic
399C8×C37—22no—
400C8×C37—22no—
401C8×C37—41no—
402C8×C37—41no—
403#24389C3711yesmaximal, characteristic, direct product factor, Sylow
404C22×C37—22no—
405C22×C37—22no—
406C22×C37—22no—
407C22×C37—22no—
408C22×C37—22no—
409C22×C37—22no—
410C22×C37—22no—
411C22×C37—22no—
412C22×C37—22no—
413C22×C37—416no—
414C22×C37—41no—
415C22×C37—41no—
416C22×C37—41no—
417C22×C37—41no—
418C22×C37—41no—
419C22×C37—41no—
420C22×C37—41no—
421C22×C37—41no—
422C22×C37—41no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—41no—
426C22×C37—42no—
427C22×C37—42no—
428C22×C37—42no—
429C22×C37—81no—
430C22×C37—81no—
431C22×C37—81no—
432C22×C37—81no—
433C22×C37C2×#12011yescharacteristic
434C22×C37C2×#12111yescharacteristic
435C22×C37#53411yescharacteristic
436C22×C37C2×#13711yescharacteristic
437C22×C37#57511yescharacteristic
438C22×C37#57511yescharacteristic
439C22×C37#57511yescharacteristic
440C4×C37—22no—
441C4×C37—22no—
442C4×C37—41no—
443C4×C37—42no—
444C4×C37—42no—
445C4×C37—42no—
446C4×C37—81no—
447C4×C37—81no—
448C4×C37—81no—
449C4×C37—81no—
450C4×C37D4211yescharacteristic
451C4×C37D4211yescharacteristic
452C4×C37#54611yescharacteristic
453C4×C37#54611yescharacteristic
454C2×#525C2×C3711yescharacteristic
455C2×#470C2×C3711yescharacteristic, complemented
456C2×#468C2×C3711yescharacteristic, complemented
457C2×#452C2×C3711yescharacteristic, complemented
458C2×#407C2×C3711yescharacteristic, complemented
459#2848C2×C3711yescharacteristic, complemented
460#2036C2×C3711yescharacteristic, complemented
461#2034C2×C3711yescharacteristic, complemented
462#2001C2×C3711yescharacteristic, complemented
463#2000C2×C3711yescharacteristic, complemented
464#1895C2×C3711yescharacteristic, complemented
465#1894C2×C3711yescharacteristic, complemented
466#1873C2×C3711yescharacteristic, complemented
467#1854C2×C3711yescharacteristic, complemented
468#1788C2×C3711yescharacteristic, complemented
469C2×C37—42no—
470C2×C37—42no—
471C2×C37—42no—
472C2×C37—82no—
473C2×C37#241011yescharacteristic
474C2×C37#300511yescharacteristic
475C2×C37#300711yescharacteristic
476C2×C37#305411yescharacteristic
477C2×C37#305611yescharacteristic
478C2×C37#319611yescharacteristic
479C2×C37#319711yescharacteristic
480C22×#41C22×C3711yescharacteristic
481C24×C4C22×C3711yescharacteristic
482C22×Q16C22×C3711yescharacteristic, complemented
483C22×SD16C22×C3711yescharacteristic, complemented
484C22×M16C22×C3711yescharacteristic
485C22×M16C22×C3711yescharacteristic
486#525—24no—
487#525—24no—
488C2×#123—21no—
489C2×C22⋊Q8C22×C3711yescharacteristic
490C2×C22⋊Q8C22×C3711yescharacteristic
491C2×C22⋊Q8C22×C3711yescharacteristic
492C2×C22⋊Q8C22×C3711yescharacteristic
493C2×C22⋊Q8C22×C3711yescharacteristic
494C2×#121C22×C3711yescharacteristic
495C2×#121C22×C3711yescharacteristic
496C2×#120—21no—
497C2×C4×D4—21no—
498C2×C4×D4—21no—
499C2×#117C22×C3711yescharacteristic
500#470—24no—
501#468—24no—
502#452—24no—
503C2×#107C22×C3711yescharacteristic, complemented
504C2×#106C22×C3711yescharacteristic, complemented
505C2×#103C22×C3711yescharacteristic, complemented
506C2×#103C22×C3711yescharacteristic, complemented
507C2×#103C22×C3711yescharacteristic, complemented
508C2×#103C22×C3711yescharacteristic, complemented
509C2×#103C22×C3711yescharacteristic, complemented
510C2×#102C22×C3711yescharacteristic, complemented
511C2×#102C22×C3711yescharacteristic, complemented
512C2×#102C22×C3711yescharacteristic, complemented
513#407—24no—
514C2×C22⋊C8C22×C3711yescharacteristic
515C2×C22⋊C8C22×C3711yescharacteristic
516C2×C22⋊C8C22×C3711yescharacteristic
517C2×C22⋊C8C22×C3711yescharacteristic
518#385—21no—
519#385—21no—
520#385—21no—
521#380C22×C3711yescharacteristic
522#380C22×C3711yescharacteristic
523#380C22×C3711yescharacteristic
524#379—21no—
525#340C22×C3711yescharacteristic, complemented
526#340C22×C3711yescharacteristic, complemented
527#340C22×C3711yescharacteristic, complemented
528#340C22×C3711yescharacteristic, complemented
529C37#2438911yescharacteristic, direct product factor, Sylow
530C25D4×C3711yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C3711yescharacteristic
538C22×Q8C23×C3711yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C3711yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C3711yescharacteristic
551C23×C4D4×C3711yescharacteristic
552C23×C4D4×C3711yescharacteristic
553C23×C4C23×C3711yescharacteristic
554C23×C4C23×C3711yescharacteristic
555C23×C4C23×C3711yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C3711yescharacteristic
569C22×C8C23×C3711yescharacteristic
570C22×C8C23×C3711yescharacteristic
571C22×C8C23×C3711yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C3714yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C3714yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C3711yescharacteristic
598C2×C4⋊C4C23×C3711yescharacteristic
599C2×C4⋊C4C23×C3711yescharacteristic
600C2×C4⋊C4C23×C3711yescharacteristic
601C2×C4⋊C4C23×C3711yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C3714yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C3711yescharacteristic
640C24C2×D4×C3711yescharacteristic
641C24C2×D4×C3711yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C3712yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C3712yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
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—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C3711yescharacteristic
711C22×C4C2×D4×C3711yescharacteristic
712C22×C4C2×D4×C3712yes—
713C22×C4C2×D4×C3712yes—
714C22×C4C2×D4×C3711yescharacteristic
715C22×C4C2×D4×C3712yes—
716C22×C4#41×C3712yes—
717C22×C4C24×C3711yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C3712yes—
733C2×C8C2×D4×C3712yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C3712yes—
748C4⋊C4C2×D4×C3712yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C3712yes—
794C23#121×C3712yes—
795C23#137×C3712yes—
796C23C22×D4×C3711yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
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—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C3712yes—
857C2×C4#121×C3712yes—
858C2×C4C22×D4×C3711yescharacteristic
859C2×C4C22×D4×C3711yescharacteristic
860C2×C4C22×D4×C3711yescharacteristic
861C2×C4C2×#41×C3711yescharacteristic
862C2×C4H(5,𝔽2)×C3711yescharacteristic
863C2×C4H(5,𝔽2)×C3711yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C3711yescharacteristic
898C22C2×#121×C3711yescharacteristic
899C22C37×#53411yescharacteristic
900C22C2×#137×C3711yescharacteristic
901C22C37×#57511yescharacteristic
902C22C37×#57511yescharacteristic
903C22C37×#57511yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C3711yescharacteristic
915C4D42×C3711yescharacteristic
916C4C37×#54611yescharacteristic
917C4C37×#54611yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C37×#241011yescharacteristic
923C2C37×#300511yescharacteristic
924C2C37×#300711yescharacteristic
925C2C37×#305411yescharacteristic
926C2C37×#305611yescharacteristic
927C2C37×#319611yescharacteristic
928C2C37×#319711yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C37 ◁ C24×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#470C2semidirect
3. C2×C37×#468C2semidirect
4. C2×C37×#452C2semidirect
5. C2×C37×#407C2semidirect
6. C37×#2848C2semidirect
7. C37×#2036C2semidirect
8. C37×#2034C2semidirect
9. C37×#2001C2semidirect
10. C37×#2000C2semidirect
11. C37×#1895C2semidirect
12. C37×#1894C2semidirect
13. C37×#1873C2semidirect
14. C37×#1854C2semidirect
15. C37×#1788C2semidirect
18. C22×Q16×C37C22semidirect
19. C22×SD16×C37C22semidirect
39. C2×#107×C37C22semidirect
40. C2×#106×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
44. C2×#103×C37C22semidirect
45. C2×#103×C37C22semidirect
46. C2×#102×C37C22semidirect
47. C2×#102×C37C22semidirect
48. C2×#102×C37C22semidirect
61. C37×#340C22semidirect
62. C37×#340C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
162. C22⋊C8×C37D4semidirect
403. #24389C37direct (N × H)
455. C2×#470C2×C37semidirect
456. C2×#468C2×C37semidirect
457. C2×#452C2×C37semidirect
458. C2×#407C2×C37semidirect
459. #2848C2×C37semidirect
460. #2036C2×C37semidirect
461. #2034C2×C37semidirect
462. #2001C2×C37semidirect
463. #2000C2×C37semidirect
464. #1895C2×C37semidirect
465. #1894C2×C37semidirect
466. #1873C2×C37semidirect
467. #1854C2×C37semidirect
468. #1788C2×C37semidirect
482. C22×Q16C22×C37semidirect
483. C22×SD16C22×C37semidirect
503. C2×#107C22×C37semidirect
504. C2×#106C22×C37semidirect
505. C2×#103C22×C37semidirect
506. C2×#103C22×C37semidirect
507. C2×#103C22×C37semidirect
508. C2×#103C22×C37semidirect
509. C2×#103C22×C37semidirect
510. C2×#102C22×C37semidirect
511. C2×#102C22×C37semidirect
512. C2×#102C22×C37semidirect
525. #340C22×C37semidirect
526. #340C22×C37semidirect
527. #340C22×C37semidirect
528. #340C22×C37semidirect
529. C37#24389direct (N × H)
627. 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×#5252
C2×C37×#4702
C2×C37×#4682
C2×C37×#4522
C2×C37×#4072
C37×#28482
C37×#20362
C37×#20342
C37×#20012
C37×#20002
C37×#18952
C37×#18942
C37×#18732
C37×#18542
C37×#17882
#2438937