Finite Group Databasebeta

← C37×#24259 #22645512

Subgroups — C37×#24259 #22645512

Order 9472.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#546C211yesmaximal, characteristic
2C2×C37×#464C211yesmaximal, characteristic, complemented
3C2×C37×#452C211yesmaximal, characteristic, complemented
4C2×C37×#450C211yesmaximal, characteristic, complemented
5C2×C37×#440C211yesmaximal, characteristic, complemented
6C37×#2538C211yesmaximal, characteristic, complemented
7C37×#2036C211yesmaximal, characteristic, complemented
8C37×#2033C211yesmaximal, characteristic, complemented
9C37×#2001C211yesmaximal, characteristic, complemented
10C37×#2000C211yesmaximal, characteristic, complemented
11C37×#1959C211yesmaximal, characteristic, complemented
12C37×#1955C211yesmaximal, characteristic, complemented
13C37×#1802C211yesmaximal, characteristic, complemented
14C37×#1788C211yesmaximal, characteristic, complemented
15C37×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C37C2211yescharacteristic
17C23×D4×C37C2211yescharacteristic
18C22×Q16×C37C2211yescharacteristic, complemented
19C22×SD16×C37C2211yescharacteristic
20C22×SD16×C37C2211yescharacteristic
21C37×#546—24no—
22C37×#546—24no—
23C2×#124×C37C2211yescharacteristic
24C2×#123×C37—21no—
25C2×C22⋊Q8×C37C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C2×C22⋊Q8×C37C2211yescharacteristic, complemented
28C2×#121×C37—21no—
29C2×#121×C37C2211yescharacteristic
30C2×#120×C37—21no—
31C2×C4×Q8×C37C2211yescharacteristic, complemented
32C2×C4×D4×C37C2211yescharacteristic
33C2×C4×D4×C37C2211yescharacteristic
34C22×C22⋊C4×C37—21no—
35C37×#464—24no—
36C37×#452—24no—
37C37×#450—24no—
38C37×#440—24no—
39C2×#107×C37C2211yescharacteristic, complemented
40C2×C4⋊C8×C37C2211yescharacteristic, complemented
41C2×#103×C37C2211yescharacteristic, complemented
42C2×#103×C37C2211yescharacteristic, complemented
43C2×#103×C37C2211yescharacteristic, complemented
44C2×#103×C37C2211yescharacteristic, complemented
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, complemented
54C2×C22⋊C8×C37C2211yescharacteristic, complemented
55C2×#97×C37C2211yescharacteristic, complemented
56C37×#396—21no—
57C37×#396—21no—
58C37×#390—21no—
59C37×#389—21no—
60C37×#384C2211yescharacteristic, complemented
61C37×#380C2211yescharacteristic
62C37×#380C2211yescharacteristic, 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×C37C2311yescharacteristic
73C22×Q8×C37C2311yescharacteristic
74C22×D4×C37—21no—
75C22×D4×C37—21no—
76C22×D4×C37—22no—
77C22×D4×C37—22no—
78C22×D4×C37—22no—
79C22×D4×C37—22no—
80C22×D4×C37—21no—
81C22×D4×C37—41no—
82C22×D4×C37—41no—
83C22×D4×C37D411yescharacteristic
84C22×D4×C37C2311yescharacteristic
85C22×D4×C37C2311yescharacteristic
86C23×C4×C37—21no—
87C23×C4×C37—21no—
88C23×C4×C37C2311yescharacteristic
89C23×C4×C37C2311yescharacteristic
90C2×Q16×C37—22no—
91C2×Q16×C37—22no—
92C2×Q16×C37—41no—
93C2×SD16×C37—22no—
94C2×SD16×C37—22no—
95C2×SD16×C37—22no—
96C2×SD16×C37—22no—
97C2×SD16×C37—41no—
98C2×SD16×C37D414yescomplemented
99C22×C8×C37C2311yescharacteristic
100C22×C8×C37C2311yescharacteristic
101C22×C8×C37C2311yescharacteristic
102C22×C8×C37C2311yescharacteristic
103#124×C37—22no—
104#124×C37D414yes—
105#123×C37—28no—
106C22⋊Q8×C37—22no—
107C22⋊Q8×C37—22no—
108C22⋊Q8×C37—22no—
109C22⋊Q8×C37—22no—
110C22⋊Q8×C37—41no—
111C22⋊Q8×C37—41no—
112#121×C37—28no—
113#121×C37—22no—
114#121×C37—22no—
115#120×C37—28no—
116C4×Q8×C37—22no—
117C4×Q8×C37—22no—
118C4×D4×C37—22no—
119C4×D4×C37—22no—
120C4×D4×C37—22no—
121C4×D4×C37D414yes—
122C2×C4⋊C4×C37—21no—
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37—21no—
125C2×C4⋊C4×C37—21no—
126C2×C4⋊C4×C37—21no—
127C2×C4⋊C4×C37—21no—
128C2×C4⋊C4×C37D411yescharacteristic
129C2×C4⋊C4×C37C2311yescharacteristic
130C2×C4⋊C4×C37C2311yescharacteristic
131C2×C4⋊C4×C37C2311yescharacteristic
132C2×C4⋊C4×C37C2311yescharacteristic
133C2×C22⋊C4×C37—28no—
134C2×C22⋊C4×C37—21no—
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×C37D411yescharacteristic
144C2×C22⋊C4×C37D411yescharacteristic
145C2×C42×C37—21no—
146C2×C42×C37C2311yescharacteristic
147#107×C37—22no—
148C4⋊C8×C37—22no—
149#103×C37—22no—
150#103×C37—22no—
151#103×C37—22no—
152#103×C37—41no—
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—
162C22⋊C8×C37—41no—
163#97×C37—22no—
164#95×C37—21no—
165#95×C37—21no—
166C24×C37—21no—
167C24×C37—24no—
168C24×C37—21no—
169C24×C37—42no—
170C24×C37—42no—
171C24×C37—42no—
172C24×C37—42no—
173C24×C37—81no—
174C24×C37—81no—
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×C37C2×D412yes—
192C2×Q8×C37C2×D412yes—
193C2×D4×C37—24no—
194C2×D4×C37—24no—
195C2×D4×C37—22no—
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—41no—
207C2×D4×C37—42no—
208C2×D4×C37—42no—
209C2×D4×C37—44no—
210C2×D4×C37—44no—
211C2×D4×C37—44no—
212C2×D4×C37—42no—
213C2×D4×C37—42no—
214C2×D4×C37—44no—
215C2×D4×C37—81no—
216C2×D4×C37—81no—
217C2×D4×C37C2×D412yes—
218C2×D4×C37C2×D412yes—
219C2×D4×C37C2×D412yes—
220C2×D4×C37#4112yes—
221C22×C4×C37—24no—
222C22×C4×C37—21no—
223C22×C4×C37—21no—
224C22×C4×C37—21no—
225C22×C4×C37—21no—
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—21no—
237C22×C4×C37—24no—
238C22×C4×C37—21no—
239C22×C4×C37—21no—
240C22×C4×C37—21no—
241C22×C4×C37—42no—
242C22×C4×C37—42no—
243C22×C4×C37—81no—
244C22×C4×C37—81no—
245C22×C4×C37C2×D411yescharacteristic
246C22×C4×C37C2×D411yescharacteristic
247C22×C4×C37C2×D411yescharacteristic
248C22×C4×C37C2×D411yescharacteristic
249C22×C4×C37C2411yescharacteristic
250Q16×C37—44no—
251SD16×C37—28no—
252SD16×C37—44no—
253C2×C8×C37—21no—
254C2×C8×C37—21no—
255C2×C8×C37—21no—
256C2×C8×C37—21no—
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×C37C2×D412yes—
265C4⋊C4×C37—24no—
266C4⋊C4×C37—22no—
267C4⋊C4×C37—21no—
268C4⋊C4×C37—21no—
269C4⋊C4×C37—21no—
270C4⋊C4×C37—21no—
271C4⋊C4×C37—21no—
272C4⋊C4×C37—21no—
273C4⋊C4×C37—21no—
274C4⋊C4×C37—42no—
275C4⋊C4×C37—42no—
276C4⋊C4×C37—42no—
277C4⋊C4×C37—42no—
278C4⋊C4×C37—81no—
279C4⋊C4×C37C2×D412yes—
280C22⋊C4×C37—24no—
281C22⋊C4×C37—24no—
282C22⋊C4×C37—22no—
283C22⋊C4×C37—24no—
284C22⋊C4×C37—24no—
285C22⋊C4×C37—24no—
286C22⋊C4×C37—22no—
287C22⋊C4×C37—42no—
288C22⋊C4×C37—42no—
289C22⋊C4×C37—81no—
290C22⋊C4×C37—81no—
291C42×C37—42no—
292C42×C37C2×D412yes—
293C42×C37C2×D412yes—
294C23×C37—21no—
295C23×C37—22no—
296C23×C37—21no—
297C23×C37—22no—
298C23×C37—21no—
299C23×C37—22no—
300C23×C37—21no—
301C23×C37—21no—
302C23×C37—21no—
303C23×C37—22no—
304C23×C37—21no—
305C23×C37—21no—
306C23×C37—21no—
307C23×C37—21no—
308C23×C37—21no—
309C23×C37—21no—
310C23×C37—21no—
311C23×C37—48no—
312C23×C37—48no—
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—41no—
323C23×C37—84no—
324C23×C37—84no—
325C23×C37—84no—
326C23×C37—84no—
327C23×C37—84no—
328C23×C37#13712yes—
329C23×C37C22×D411yescharacteristic
330Q8×C37—22no—
331Q8×C37—22no—
332Q8×C37—22no—
333Q8×C37—22no—
334Q8×C37—41no—
335Q8×C37—41no—
336Q8×C37—41no—
337Q8×C37—41no—
338D4×C37—22no—
339D4×C37—22no—
340D4×C37—22no—
341D4×C37—22no—
342D4×C37—22no—
343D4×C37—44no—
344D4×C37—48no—
345D4×C37—48no—
346D4×C37—41no—
347D4×C37—41no—
348D4×C37—84no—
349D4×C37#12114yes—
350C2×C4×C37—21no—
351C2×C4×C37—21no—
352C2×C4×C37—21no—
353C2×C4×C37—21no—
354C2×C4×C37—22no—
355C2×C4×C37—21no—
356C2×C4×C37—22no—
357C2×C4×C37—21no—
358C2×C4×C37—22no—
359C2×C4×C37—21no—
360C2×C4×C37—21no—
361C2×C4×C37—21no—
362C2×C4×C37—21no—
363C2×C4×C37—48no—
364C2×C4×C37—41no—
365C2×C4×C37—41no—
366C2×C4×C37—41no—
367C2×C4×C37—41no—
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—41no—
386C2×C4×C37—41no—
387C2×C4×C37—84no—
388C2×C4×C37#12012yes—
389C2×C4×C37#12012yes—
390C2×C4×C37C22×D411yescharacteristic
391C2×C4×C37C22×D411yescharacteristic
392C2×C4×C37C22×D411yescharacteristic
393C2×C4×C37C2×#4111yescharacteristic
394C2×C4×C37H(5,𝔽2)11yescharacteristic
395C2×C4×C37H(5,𝔽2)11yescharacteristic
396C8×C37—22no—
397C8×C37—41no—
398C8×C37—41no—
399C8×C37—41no—
400#24259C3711yesmaximal, characteristic, direct product factor, Sylow
401C22×C37—24no—
402C22×C37—22no—
403C22×C37—22no—
404C22×C37—22no—
405C22×C37—41no—
406C22×C37—42no—
407C22×C37—42no—
408C22×C37—42no—
409C22×C37—41no—
410C22×C37—41no—
411C22×C37—42no—
412C22×C37—41no—
413C22×C37—42no—
414C22×C37—42no—
415C22×C37—41no—
416C22×C37—42no—
417C22×C37—41no—
418C22×C37—42no—
419C22×C37—41no—
420C22×C37—41no—
421C22×C37—42no—
422C22×C37—41no—
423C22×C37—41no—
424C22×C37—41no—
425C22×C37—816no—
426C22×C37—81no—
427C22×C37—81no—
428C22×C37—81no—
429C22×C37—81no—
430C22×C37C2×#12011yescharacteristic
431C22×C37D4211yescharacteristic
432C22×C37#54611yescharacteristic
433C22×C37C2×#13711yescharacteristic
434C22×C37#57511yescharacteristic
435C22×C37#57611yescharacteristic
436C22×C37#57711yescharacteristic
437C4×C37—22no—
438C4×C37—22no—
439C4×C37—41no—
440C4×C37—41no—
441C4×C37—42no—
442C4×C37—42no—
443C4×C37—42no—
444C4×C37—81no—
445C4×C37—81no—
446C4×C37—81no—
447C4×C37C2×#12111yescharacteristic
448C4×C37#53511yescharacteristic
449C4×C37D4211yescharacteristic
450C4×C37#54611yescharacteristic
451C2×#546C2×C3711yescharacteristic
452C2×#464C2×C3711yescharacteristic, complemented
453C2×#452C2×C3711yescharacteristic, complemented
454C2×#450C2×C3711yescharacteristic, complemented
455C2×#440C2×C3711yescharacteristic, complemented
456#2538C2×C3711yescharacteristic, complemented
457#2036C2×C3711yescharacteristic, complemented
458#2033C2×C3711yescharacteristic, complemented
459#2001C2×C3711yescharacteristic, complemented
460#2000C2×C3711yescharacteristic, complemented
461#1959C2×C3711yescharacteristic, complemented
462#1955C2×C3711yescharacteristic, complemented
463#1802C2×C3711yescharacteristic, complemented
464#1788C2×C3711yescharacteristic, complemented
465#1786C2×C3711yescharacteristic, complemented
466C2×C37—42no—
467C2×C37—44no—
468C2×C37—81no—
469C2×C37—82no—
470C2×C37#240811yescharacteristic
471C2×C37#300711yescharacteristic
472C2×C37#301211yescharacteristic
473C2×C37#326611yescharacteristic
474C2×C37#326811yescharacteristic
475C2×C37#331111yescharacteristic
476C2×C37#331411yescharacteristic
477C22×#41C22×C3711yescharacteristic
478C23×D4C22×C3711yescharacteristic
479C22×Q16C22×C3711yescharacteristic, complemented
480C22×SD16C22×C3711yescharacteristic
481C22×SD16C22×C3711yescharacteristic
482#546—24no—
483#546—24no—
484C2×#124C22×C3711yescharacteristic
485C2×#123—21no—
486C2×C22⋊Q8C22×C3711yescharacteristic
487C2×C22⋊Q8C22×C3711yescharacteristic
488C2×C22⋊Q8C22×C3711yescharacteristic, complemented
489C2×#121—21no—
490C2×#121C22×C3711yescharacteristic
491C2×#120—21no—
492C2×C4×Q8C22×C3711yescharacteristic, complemented
493C2×C4×D4C22×C3711yescharacteristic
494C2×C4×D4C22×C3711yescharacteristic
495C22×C22⋊C4—21no—
496#464—24no—
497#452—24no—
498#450—24no—
499#440—24no—
500C2×#107C22×C3711yescharacteristic, complemented
501C2×C4⋊C8C22×C3711yescharacteristic, complemented
502C2×#103C22×C3711yescharacteristic, complemented
503C2×#103C22×C3711yescharacteristic, complemented
504C2×#103C22×C3711yescharacteristic, complemented
505C2×#103C22×C3711yescharacteristic, complemented
506C2×#102C22×C3711yescharacteristic
507C2×#102C22×C3711yescharacteristic
508C2×#102C22×C3711yescharacteristic
509C2×#102C22×C3711yescharacteristic
510C2×#102C22×C3711yescharacteristic
511C2×#102C22×C3711yescharacteristic
512C2×C22⋊C8C22×C3711yescharacteristic
513C2×C22⋊C8C22×C3711yescharacteristic
514C2×C22⋊C8C22×C3711yescharacteristic, complemented
515C2×C22⋊C8C22×C3711yescharacteristic, complemented
516C2×#97C22×C3711yescharacteristic, complemented
517#396—21no—
518#396—21no—
519#390—21no—
520#389—21no—
521#384C22×C3711yescharacteristic, complemented
522#380C22×C3711yescharacteristic
523#380C22×C3711yescharacteristic, complemented
524#340C22×C3711yescharacteristic, complemented
525#340C22×C3711yescharacteristic, complemented
526C37#2425911yescharacteristic, direct product factor, Sylow
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8C23×C3711yescharacteristic
535C22×Q8C23×C3711yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4D4×C3711yescharacteristic
546C22×D4C23×C3711yescharacteristic
547C22×D4C23×C3711yescharacteristic
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C3711yescharacteristic
551C23×C4C23×C3711yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C2×SD16D4×C3714yescomplemented
561C22×C8C23×C3711yescharacteristic
562C22×C8C23×C3711yescharacteristic
563C22×C8C23×C3711yescharacteristic
564C22×C8C23×C3711yescharacteristic
565#124—22no—
566#124D4×C3714yes—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574#121—28no—
575#121—22no—
576#121—22no—
577#120—28no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4D4×C3714yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C3711yescharacteristic
591C2×C4⋊C4C23×C3711yescharacteristic
592C2×C4⋊C4C23×C3711yescharacteristic
593C2×C4⋊C4C23×C3711yescharacteristic
594C2×C4⋊C4C23×C3711yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C3711yescharacteristic
606C2×C22⋊C4D4×C3711yescharacteristic
607C2×C42—21no—
608C2×C42C23×C3711yescharacteristic
609#107—22no—
610C4⋊C8—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—41no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—41no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624C22⋊C8—41no—
625#97—22no—
626#95—21no—
627#95—21no—
628C24—21no—
629C24—24no—
630C24—21no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24C2×D4×C3711yescharacteristic
638C24C2×D4×C3711yescharacteristic
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C3712yes—
654C2×Q8C2×D4×C3712yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C2×D4×C3712yes—
680C2×D4C2×D4×C3712yes—
681C2×D4C2×D4×C3712yes—
682C2×D4#41×C3712yes—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
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—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—81no—
706C22×C4—81no—
707C22×C4C2×D4×C3711yescharacteristic
708C22×C4C2×D4×C3711yescharacteristic
709C22×C4C2×D4×C3711yescharacteristic
710C22×C4C2×D4×C3711yescharacteristic
711C22×C4C24×C3711yescharacteristic
712Q16—44no—
713SD16—28no—
714SD16—44no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
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×C8C2×D4×C3712yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C3712yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C22⋊C4—81no—
753C42—42no—
754C42C2×D4×C3712yes—
755C42C2×D4×C3712yes—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—48no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23#137×C3712yes—
791C23C22×D4×C3711yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—44no—
806D4—48no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—84no—
811D4#121×C3714yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
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—41no—
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—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—84no—
850C2×C4#120×C3712yes—
851C2×C4#120×C3712yes—
852C2×C4C22×D4×C3711yescharacteristic
853C2×C4C22×D4×C3711yescharacteristic
854C2×C4C22×D4×C3711yescharacteristic
855C2×C4C2×#41×C3711yescharacteristic
856C2×C4H(5,𝔽2)×C3711yescharacteristic
857C2×C4H(5,𝔽2)×C3711yescharacteristic
858C8—22no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—24no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—816no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22C2×#120×C3711yescharacteristic
892C22D42×C3711yescharacteristic
893C22C37×#54611yescharacteristic
894C22C2×#137×C3711yescharacteristic
895C22C37×#57511yescharacteristic
896C22C37×#57611yescharacteristic
897C22C37×#57711yescharacteristic
898C4—22no—
899C4—22no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4C2×#121×C3711yescharacteristic
909C4C37×#53511yescharacteristic
910C4D42×C3711yescharacteristic
911C4C37×#54611yescharacteristic
912C2—42no—
913C2—44no—
914C2—81no—
915C2—82no—
916C2C37×#240811yescharacteristic
917C2C37×#300711yescharacteristic
918C2C37×#301211yescharacteristic
919C2C37×#326611yescharacteristic
920C2C37×#326811yescharacteristic
921C2C37×#331111yescharacteristic
922C2C37×#331411yescharacteristic
subgroupG/H
center, socleC23×C37C22×D4
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×C37×#546C2
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×#464C2semidirect
3. C2×C37×#452C2semidirect
4. C2×C37×#450C2semidirect
5. C2×C37×#440C2semidirect
6. C37×#2538C2semidirect
7. C37×#2036C2semidirect
8. C37×#2033C2semidirect
9. C37×#2001C2semidirect
10. C37×#2000C2semidirect
11. C37×#1959C2semidirect
12. C37×#1955C2semidirect
13. C37×#1802C2semidirect
14. C37×#1788C2semidirect
15. C37×#1786C2semidirect
18. C22×Q16×C37C22semidirect
27. C2×C22⋊Q8×C37C22semidirect
31. C2×C4×Q8×C37C22semidirect
39. C2×#107×C37C22semidirect
40. C2×C4⋊C8×C37C22semidirect
41. C2×#103×C37C22semidirect
42. C2×#103×C37C22semidirect
43. C2×#103×C37C22semidirect
44. C2×#103×C37C22semidirect
53. C2×C22⋊C8×C37C22semidirect
54. C2×C22⋊C8×C37C22semidirect
55. C2×#97×C37C22semidirect
60. C37×#384C22semidirect
62. C37×#380C22semidirect
63. C37×#340C22semidirect
64. C37×#340C22semidirect
98. C2×SD16×C37D4semidirect
400. #24259C37direct (N × H)
452. C2×#464C2×C37semidirect
453. C2×#452C2×C37semidirect
454. C2×#450C2×C37semidirect
455. C2×#440C2×C37semidirect
456. #2538C2×C37semidirect
457. #2036C2×C37semidirect
458. #2033C2×C37semidirect
459. #2001C2×C37semidirect
460. #2000C2×C37semidirect
461. #1959C2×C37semidirect
462. #1955C2×C37semidirect
463. #1802C2×C37semidirect
464. #1788C2×C37semidirect
465. #1786C2×C37semidirect
479. C22×Q16C22×C37semidirect
488. C2×C22⋊Q8C22×C37semidirect
492. C2×C4×Q8C22×C37semidirect
500. C2×#107C22×C37semidirect
501. C2×C4⋊C8C22×C37semidirect
502. C2×#103C22×C37semidirect
503. C2×#103C22×C37semidirect
504. C2×#103C22×C37semidirect
505. C2×#103C22×C37semidirect
514. C2×C22⋊C8C22×C37semidirect
515. C2×C22⋊C8C22×C37semidirect
516. C2×#97C22×C37semidirect
521. #384C22×C37semidirect
523. #380C22×C37semidirect
524. #340C22×C37semidirect
525. #340C22×C37semidirect
526. C37#24259direct (N × H)
560. C2×SD16D4×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×#4642
C2×C37×#4522
C2×C37×#4502
C2×C37×#4402
C37×#25382
C37×#20362
C37×#20332
C37×#20012
C37×#20002
C37×#19592
C37×#19552
C37×#18022
C37×#17882
C37×#17862
#2425937