Finite Group Databasebeta

← C37×#24469 #22645722

Subgroups — C37×#24469 #22645722

Order 9472.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3489C211yesmaximal, characteristic, complemented
2C37×#3055C211yesmaximal, characteristic, complemented
3C2×C37×#454C211yesmaximal, characteristic, complemented
4C37×#3006C211yesmaximal, characteristic, complemented
5C2×C37×#421C211yesmaximal, characteristic, complemented
6C37×#2620C211yesmaximal, characteristic, complemented
7C37×#2039C211yesmaximal, characteristic, complemented
8C37×#2038C211yesmaximal, characteristic, complemented
9C37×#2006C211yesmaximal, characteristic, complemented
10C37×#2003C211yesmaximal, characteristic, complemented
11C37×#1901C211yesmaximal, characteristic, complemented
12C37×#1897C211yesmaximal, characteristic, complemented
13C37×#1883C211yesmaximal, characteristic, complemented
14C37×#1859C211yesmaximal, characteristic, complemented
15C37×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C37C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C37C2211yescharacteristic, complemented
21C22×M16×C37C2211yescharacteristic
22D4×Q8×C37—21no—
23C37×#548—21no—
24C37×#547—21no—
25C37×#547—22no—
26C37×#546—21no—
27C37×#546—22no—
28C37×#537—21no—
29C37×#537C2211yescharacteristic
30C37×#536—21no—
31C37×#536C2211yescharacteristic
32C2×#124×C37C2211yescharacteristic, complemented
33C37×#525—21no—
34C37×#525C2211yescharacteristic
35C2×C22⋊Q8×C37—21no—
36C2×C22⋊Q8×C37C2211yescharacteristic
37C2×#121×C37C2211yescharacteristic
38C37×#520C2211yescharacteristic
39C2×#117×C37C2211yescharacteristic
40C37×#469—21no—
41C37×#468—21no—
42C37×#466—21no—
43C37×#465—21no—
44C37×#454—24no—
45C37×#449—21no—
46C37×#449—21no—
47C37×#448—21no—
48C37×#447—21no—
49C37×#428C2211yescharacteristic, complemented
50C37×#421—24no—
51C2×#104×C37C2211yescharacteristic
52C2×#104×C37C2211yescharacteristic
53C2×#104×C37C2211yescharacteristic
54C2×#104×C37C2211yescharacteristic
55C2×#104×C37C2211yescharacteristic, complemented
56C2×#104×C37C2211yescharacteristic, complemented
57C37×#418C2211yescharacteristic, complemented
58C37×#417C2211yescharacteristic
59C37×#417C2211yescharacteristic
60C37×#417C2211yescharacteristic, complemented
61C2×#101×C37C2211yescharacteristic, complemented
62C2×#101×C37C2211yescharacteristic, complemented
63C37×#407C2211yescharacteristic
64C37×#396—22no—
65C37×#394—22no—
66C37×#391C2211yescharacteristic, complemented
67C37×#390C2211yescharacteristic, complemented
68C37×#384C2211yescharacteristic, complemented
69C37×#343C2211yescharacteristic, complemented
70C37×#343C2211yescharacteristic, complemented
71C37×#339C2211yescharacteristic, complemented
72C37×#339C2211yescharacteristic, complemented
732−1+4×C37—22no—
742−1+4×C37—22no—
752−1+4×C37—41no—
762−1+4×C37—41no—
77C2×#41×C37—21no—
78C2×#41×C37—21no—
79C2×#41×C37—21no—
80C2×#41×C37—22no—
81C2×#41×C37—21no—
82C2×#41×C37—22no—
83C2×#41×C37—22no—
84C2×#41×C37—41no—
85C2×#41×C37—41no—
86C2×#41×C37D411yescharacteristic
87C2×#41×C37D411yescharacteristic
88C2×#41×C37C2311yescharacteristic
89C2×#41×C37C2311yescharacteristic
90C2×#41×C37C2311yescharacteristic
91C22×Q8×C37—21no—
92C22×Q8×C37—21no—
93C22×Q8×C37D411yescharacteristic
94C22×Q8×C37C2311yescharacteristic
95C22×D4×C37—21no—
96C22×D4×C37—21no—
97C22×D4×C37D411yescharacteristic
98C22×D4×C37C2311yescharacteristic
99C23×C4×C37—21no—
100C23×C4×C37C2311yescharacteristic
101AGL(1,ℤ/8)×C37—22no—
102AGL(1,ℤ/8)×C37—22no—
103AGL(1,ℤ/8)×C37—22no—
104AGL(1,ℤ/8)×C37—41no—
105AGL(1,ℤ/8)×C37—41no—
106AGL(1,ℤ/8)×C37—41no—
107C2×SD16×C37—21no—
108C2×SD16×C37—21no—
109C2×SD16×C37—21no—
110C2×D8×C37—21no—
111C2×D8×C37—21no—
112C2×D8×C37—21no—
113C2×M16×C37—21no—
114C2×M16×C37—22no—
115C2×M16×C37—41no—
116C2×M16×C37C2311yescharacteristic
117C2×M16×C37C2311yescharacteristic
118C2×M16×C37C2311yescharacteristic
119C2×M16×C37C2311yescharacteristic
120C22×C8×C37—21no—
121C4⋊Q8×C37—22no—
122C4⋊Q8×C37—21no—
123#124×C37—22no—
124#124×C37—21no—
125#124×C37—22no—
126#124×C37—41no—
127#123×C37—22no—
128#123×C37—22no—
129#123×C37—22no—
130#123×C37—21no—
131#123×C37—22no—
132C22⋊Q8×C37—22no—
133C22⋊Q8×C37—22no—
134C22⋊Q8×C37—22no—
135C22⋊Q8×C37—21no—
136C22⋊Q8×C37—21no—
137C22⋊Q8×C37—21no—
138C22⋊Q8×C37—21no—
139C22⋊Q8×C37—21no—
140C22⋊Q8×C37—21no—
141C22⋊Q8×C37—21no—
142C22⋊Q8×C37—21no—
143C22⋊Q8×C37D411yescharacteristic
144C22⋊Q8×C37D411yescharacteristic
145#121×C37—22no—
146#121×C37—22no—
147#121×C37—22no—
148#121×C37—21no—
149#121×C37—21no—
150#121×C37—22no—
151#121×C37—21no—
152#121×C37—21no—
153#121×C37—21no—
154#121×C37—21no—
155#121×C37D411yescharacteristic
156#121×C37D411yescharacteristic
157#120×C37—22no—
158#120×C37—21no—
159C4×Q8×C37—21no—
160C4×D4×C37—22no—
161C4×D4×C37—22no—
162C4×D4×C37—21no—
163C4×D4×C37—22no—
164C4×D4×C37—21no—
165C4×D4×C37—21no—
166#117×C37—21no—
167#117×C37—22no—
168#117×C37—41no—
169#117×C37C2311yescharacteristic
170C2×C4⋊C4×C37—22no—
171C2×C4⋊C4×C37—21no—
172C2×C4⋊C4×C37—21no—
173C2×C4⋊C4×C37—22no—
174C2×C4⋊C4×C37D412yes—
175C2×C4⋊C4×C37C2311yescharacteristic
176C2×C4⋊C4×C37C2311yescharacteristic
177C2×C22⋊C4×C37—22no—
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—21no—
180C2×C22⋊C4×C37—22no—
181C2×C22⋊C4×C37—22no—
182C2×C22⋊C4×C37D412yes—
183C2×C42×C37C2311yescharacteristic
184C2×C42×C37C2311yescharacteristic
185#107×C37—21no—
186#106×C37—21no—
187#104×C37—22no—
188#104×C37—22no—
189#104×C37—22no—
190#104×C37—22no—
191#104×C37—41no—
192#104×C37D414yescomplemented
193#103×C37—21no—
194#103×C37—21no—
195#103×C37—21no—
196#102×C37—21no—
197#102×C37—21no—
198#102×C37—21no—
199#102×C37—21no—
200#102×C37—21no—
201#101×C37—22no—
202#101×C37—41no—
203C22⋊C8×C37—21no—
204C22⋊C8×C37—21no—
205#95×C37—22no—
206C24×C37—21no—
207C24×C37—21no—
208C24×C37C2×D411yescharacteristic
209#41×C37—21no—
210#41×C37—21no—
211#41×C37—22no—
212#41×C37—22no—
213#41×C37—21no—
214#41×C37—21no—
215#41×C37—21no—
216#41×C37—21no—
217#41×C37—21no—
218#41×C37—21no—
219#41×C37—21no—
220#41×C37—21no—
221#41×C37—42no—
222#41×C37—42no—
223#41×C37—41no—
224#41×C37—41no—
225#41×C37—42no—
226#41×C37—42no—
227#41×C37—42no—
228#41×C37—42no—
229#41×C37—44no—
230#41×C37—44no—
231#41×C37—42no—
232#41×C37—42no—
233#41×C37C2×D412yes—
234#41×C37#4112yes—
235C2×Q8×C37—22no—
236C2×Q8×C37—21no—
237C2×Q8×C37—21no—
238C2×Q8×C37—21no—
239C2×Q8×C37—21no—
240C2×Q8×C37—21no—
241C2×Q8×C37—21no—
242C2×Q8×C37—21no—
243C2×Q8×C37—22no—
244C2×Q8×C37—41no—
245C2×Q8×C37—42no—
246C2×Q8×C37—42no—
247C2×Q8×C37—42no—
248C2×Q8×C37—42no—
249C2×Q8×C37C2×D411yescharacteristic
250C2×Q8×C37C2×D411yescharacteristic
251C2×Q8×C37C2×D411yescharacteristic
252C2×D4×C37—21no—
253C2×D4×C37—22no—
254C2×D4×C37—22no—
255C2×D4×C37—21no—
256C2×D4×C37—21no—
257C2×D4×C37—21no—
258C2×D4×C37—21no—
259C2×D4×C37—21no—
260C2×D4×C37—22no—
261C2×D4×C37—21no—
262C2×D4×C37—21no—
263C2×D4×C37—21no—
264C2×D4×C37—21no—
265C2×D4×C37—21no—
266C2×D4×C37—21no—
267C2×D4×C37—21no—
268C2×D4×C37—21no—
269C2×D4×C37—41no—
270C2×D4×C37—42no—
271C2×D4×C37—42no—
272C2×D4×C37—41no—
273C2×D4×C37—41no—
274C2×D4×C37—82no—
275C2×D4×C37C2×D411yescharacteristic
276C2×D4×C37C2×D411yescharacteristic
277C2×D4×C37C2×D411yescharacteristic
278C22×C4×C37—21no—
279C22×C4×C37—21no—
280C22×C4×C37—21no—
281C22×C4×C37—21no—
282C22×C4×C37—21no—
283C22×C4×C37—22no—
284C22×C4×C37—22no—
285C22×C4×C37—21no—
286C22×C4×C37—21no—
287C22×C4×C37—22no—
288C22×C4×C37—21no—
289C22×C4×C37—21no—
290C22×C4×C37—21no—
291C22×C4×C37—21no—
292C22×C4×C37—21no—
293C22×C4×C37—21no—
294C22×C4×C37—42no—
295C22×C4×C37—42no—
296C22×C4×C37C2×D412yes—
297C22×C4×C37C2×D411yescharacteristic
298C22×C4×C37C2×D411yescharacteristic
299C22×C4×C37C2×D411yescharacteristic
300C22×C4×C37C2×D411yescharacteristic
301C22×C4×C37C2×D411yescharacteristic
302C22×C4×C37C2×D412yes—
303C22×C4×C37C2411yescharacteristic
304SD16×C37—42no—
305SD16×C37—42no—
306SD16×C37—42no—
307D8×C37—42no—
308D8×C37—42no—
309D8×C37—42no—
310M16×C37—21no—
311M16×C37—21no—
312M16×C37—21no—
313M16×C37—21no—
314M16×C37—21no—
315M16×C37—21no—
316M16×C37—21no—
317M16×C37—42no—
318M16×C37C2×D412yes—
319C2×C8×C37—21no—
320C2×C8×C37—21no—
321C2×C8×C37—21no—
322C2×C8×C37—21no—
323C2×C8×C37—42no—
324C4⋊C4×C37—22no—
325C4⋊C4×C37—22no—
326C4⋊C4×C37—22no—
327C4⋊C4×C37—22no—
328C4⋊C4×C37—21no—
329C4⋊C4×C37—22no—
330C4⋊C4×C37—22no—
331C4⋊C4×C37—21no—
332C4⋊C4×C37—21no—
333C4⋊C4×C37—21no—
334C4⋊C4×C37—21no—
335C4⋊C4×C37—21no—
336C4⋊C4×C37—42no—
337C4⋊C4×C37—82no—
338C4⋊C4×C37C2×D411yescharacteristic
339C4⋊C4×C37C2×D411yescharacteristic
340C22⋊C4×C37—22no—
341C22⋊C4×C37—22no—
342C22⋊C4×C37—22no—
343C22⋊C4×C37—22no—
344C22⋊C4×C37—22no—
345C22⋊C4×C37—21no—
346C22⋊C4×C37—22no—
347C22⋊C4×C37—22no—
348C22⋊C4×C37—21no—
349C22⋊C4×C37—21no—
350C22⋊C4×C37—21no—
351C22⋊C4×C37—21no—
352C22⋊C4×C37—44no—
353C22⋊C4×C37—42no—
354C22⋊C4×C37—41no—
355C22⋊C4×C37—41no—
356C22⋊C4×C37—82no—
357C42×C37—22no—
358C42×C37—21no—
359C42×C37—21no—
360C42×C37—21no—
361C42×C37—21no—
362C42×C37C2×D412yes—
363C23×C37—21no—
364C23×C37—21no—
365C23×C37—21no—
366C23×C37—21no—
367C23×C37—21no—
368C23×C37—41no—
369C23×C37—41no—
370C23×C37—42no—
371C23×C37—42no—
372C23×C37—42no—
373C23×C37—42no—
374C23×C37—41no—
375C23×C37—41no—
376C23×C37—41no—
377C23×C37—81no—
378C23×C37#12011yescharacteristic
379C23×C37#12011yescharacteristic
380C23×C37C22×D411yescharacteristic
381Q8×C37—21no—
382Q8×C37—21no—
383Q8×C37—21no—
384Q8×C37—21no—
385Q8×C37—21no—
386Q8×C37—42no—
387Q8×C37—44no—
388Q8×C37—41no—
389Q8×C37—41no—
390Q8×C37—41no—
391Q8×C37—41no—
392Q8×C37#12112yes—
393D4×C37—22no—
394D4×C37—22no—
395D4×C37—21no—
396D4×C37—21no—
397D4×C37—21no—
398D4×C37—21no—
399D4×C37—21no—
400D4×C37—42no—
401D4×C37—42no—
402D4×C37—42no—
403D4×C37—42no—
404D4×C37—44no—
405D4×C37—41no—
406D4×C37—41no—
407D4×C37—41no—
408D4×C37—41no—
409D4×C37—41no—
410D4×C37—41no—
411D4×C37—41no—
412D4×C37—41no—
413D4×C37—81no—
414D4×C37—82no—
415D4×C37—82no—
416D4×C37—82no—
417D4×C37#12112yes—
418C2×C4×C37—21no—
419C2×C4×C37—21no—
420C2×C4×C37—21no—
421C2×C4×C37—21no—
422C2×C4×C37—21no—
423C2×C4×C37—21no—
424C2×C4×C37—21no—
425C2×C4×C37—21no—
426C2×C4×C37—21no—
427C2×C4×C37—22no—
428C2×C4×C37—21no—
429C2×C4×C37—21no—
430C2×C4×C37—22no—
431C2×C4×C37—21no—
432C2×C4×C37—22no—
433C2×C4×C37—21no—
434C2×C4×C37—21no—
435C2×C4×C37—22no—
436C2×C4×C37—21no—
437C2×C4×C37—22no—
438C2×C4×C37—22no—
439C2×C4×C37—22no—
440C2×C4×C37—42no—
441C2×C4×C37—42no—
442C2×C4×C37—42no—
443C2×C4×C37—44no—
444C2×C4×C37—41no—
445C2×C4×C37—41no—
446C2×C4×C37—44no—
447C2×C4×C37—41no—
448C2×C4×C37—41no—
449C2×C4×C37—41no—
450C2×C4×C37—41no—
451C2×C4×C37—42no—
452C2×C4×C37—41no—
453C2×C4×C37—42no—
454C2×C4×C37—41no—
455C2×C4×C37—41no—
456C2×C4×C37—41no—
457C2×C4×C37—82no—
458C2×C4×C37#12011yescharacteristic
459C2×C4×C37#12011yescharacteristic
460C2×C4×C37C22×D411yescharacteristic
461C2×C4×C37C22×D411yescharacteristic
462C2×C4×C37C22×D411yescharacteristic
463C2×C4×C37C2×#4111yescharacteristic
464C2×C4×C37H(5,𝔽2)11yescharacteristic
465C2×C4×C37H(5,𝔽2)11yescharacteristic
466C8×C37—22no—
467C8×C37—41no—
468C8×C37—41no—
469C8×C37—41no—
470#24469C3711yesmaximal, characteristic, direct product factor, Sylow
471C22×C37—21no—
472C22×C37—21no—
473C22×C37—21no—
474C22×C37—21no—
475C22×C37—22no—
476C22×C37—21no—
477C22×C37—21no—
478C22×C37—21no—
479C22×C37—21no—
480C22×C37—41no—
481C22×C37—41no—
482C22×C37—41no—
483C22×C37—41no—
484C22×C37—41no—
485C22×C37—41no—
486C22×C37—41no—
487C22×C37—41no—
488C22×C37—81no—
489C22×C37—81no—
490C22×C37—82no—
491C22×C37—82no—
492C22×C37—84no—
493C22×C37—81no—
494C22×C37—81no—
495C22×C37—81no—
496C22×C37C2×#12011yescharacteristic
497C22×C37D4211yescharacteristic
498C22×C37#54611yescharacteristic
499C4×C37—21no—
500C4×C37—21no—
501C4×C37—22no—
502C4×C37—42no—
503C4×C37—42no—
504C4×C37—41no—
505C4×C37—41no—
506C4×C37—41no—
507C4×C37—42no—
508C4×C37—41no—
509C4×C37—81no—
510C4×C37—81no—
511C4×C37C2×#12111yescharacteristic
512C4×C37#53411yescharacteristic
513C4×C37D4211yescharacteristic
514C4×C37#54611yescharacteristic
515#3489C2×C3711yescharacteristic, complemented
516#3055C2×C3711yescharacteristic, complemented
517C2×#454C2×C3711yescharacteristic, complemented
518#3006C2×C3711yescharacteristic, complemented
519C2×#421C2×C3711yescharacteristic, complemented
520#2620C2×C3711yescharacteristic, complemented
521#2039C2×C3711yescharacteristic, complemented
522#2038C2×C3711yescharacteristic, complemented
523#2006C2×C3711yescharacteristic, complemented
524#2003C2×C3711yescharacteristic, complemented
525#1901C2×C3711yescharacteristic, complemented
526#1897C2×C3711yescharacteristic, complemented
527#1883C2×C3711yescharacteristic, complemented
528#1859C2×C3711yescharacteristic, complemented
529#1793C2×C3711yescharacteristic, complemented
530C2×C37—21no—
531C2×C37—21no—
532C2×C37—41no—
533C2×C37—41no—
534C2×C37—42no—
535C2×C37—81no—
536C2×C37—81no—
537C2×C37—161no—
538C2×C37#241011yescharacteristic
539C2×C37#302011yescharacteristic
540C2×C37#302111yescharacteristic
541C2×2−1+4C22×C3711yescharacteristic
542C22×#41C22×C3711yescharacteristic
543C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
544C2×AGL(1,ℤ/8)C22×C3711yescharacteristic
545C2×AGL(1,ℤ/8)C22×C3711yescharacteristic, complemented
546C22×M16C22×C3711yescharacteristic
547D4×Q8—21no—
548#548—21no—
549#547—21no—
550#547—22no—
551#546—21no—
552#546—22no—
553#537—21no—
554#537C22×C3711yescharacteristic
555#536—21no—
556#536C22×C3711yescharacteristic
557C2×#124C22×C3711yescharacteristic, complemented
558#525—21no—
559#525C22×C3711yescharacteristic
560C2×C22⋊Q8—21no—
561C2×C22⋊Q8C22×C3711yescharacteristic
562C2×#121C22×C3711yescharacteristic
563#520C22×C3711yescharacteristic
564C2×#117C22×C3711yescharacteristic
565#469—21no—
566#468—21no—
567#466—21no—
568#465—21no—
569#454—24no—
570#449—21no—
571#449—21no—
572#448—21no—
573#447—21no—
574#428C22×C3711yescharacteristic, complemented
575#421—24no—
576C2×#104C22×C3711yescharacteristic
577C2×#104C22×C3711yescharacteristic
578C2×#104C22×C3711yescharacteristic
579C2×#104C22×C3711yescharacteristic
580C2×#104C22×C3711yescharacteristic, complemented
581C2×#104C22×C3711yescharacteristic, complemented
582#418C22×C3711yescharacteristic, complemented
583#417C22×C3711yescharacteristic
584#417C22×C3711yescharacteristic
585#417C22×C3711yescharacteristic, complemented
586C2×#101C22×C3711yescharacteristic, complemented
587C2×#101C22×C3711yescharacteristic, complemented
588#407C22×C3711yescharacteristic
589#396—22no—
590#394—22no—
591#391C22×C3711yescharacteristic, complemented
592#390C22×C3711yescharacteristic, complemented
593#384C22×C3711yescharacteristic, complemented
594#343C22×C3711yescharacteristic, complemented
595#343C22×C3711yescharacteristic, complemented
596#339C22×C3711yescharacteristic, complemented
597#339C22×C3711yescharacteristic, complemented
598C37#2446911yescharacteristic, direct product factor, Sylow
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C3711yescharacteristic
613C2×#41D4×C3711yescharacteristic
614C2×#41C23×C3711yescharacteristic
615C2×#41C23×C3711yescharacteristic
616C2×#41C23×C3711yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C3711yescharacteristic
620C22×Q8C23×C3711yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C3711yescharacteristic
624C22×D4C23×C3711yescharacteristic
625C23×C4—21no—
626C23×C4C23×C3711yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C3711yescharacteristic
643C2×M16C23×C3711yescharacteristic
644C2×M16C23×C3711yescharacteristic
645C2×M16C23×C3711yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C3711yescharacteristic
670C22⋊Q8D4×C3711yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C3711yescharacteristic
682#121D4×C3711yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C3711yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C3712yes—
701C2×C4⋊C4C23×C3711yescharacteristic
702C2×C4⋊C4C23×C3711yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C3712yes—
709C2×C42C23×C3711yescharacteristic
710C2×C42C23×C3711yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C3714yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C3711yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C3712yes—
760#41#41×C3712yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C3711yescharacteristic
776C2×Q8C2×D4×C3711yescharacteristic
777C2×Q8C2×D4×C3711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C3711yescharacteristic
802C2×D4C2×D4×C3711yescharacteristic
803C2×D4C2×D4×C3711yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C3712yes—
823C22×C4C2×D4×C3711yescharacteristic
824C22×C4C2×D4×C3711yescharacteristic
825C22×C4C2×D4×C3711yescharacteristic
826C22×C4C2×D4×C3711yescharacteristic
827C22×C4C2×D4×C3711yescharacteristic
828C22×C4C2×D4×C3712yes—
829C22×C4C24×C3711yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C3712yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C3711yescharacteristic
865C4⋊C4C2×D4×C3711yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C3712yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C3711yescharacteristic
905C23#120×C3711yescharacteristic
906C23C22×D4×C3711yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C3712yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C3712yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C3711yescharacteristic
985C2×C4#120×C3711yescharacteristic
986C2×C4C22×D4×C3711yescharacteristic
987C2×C4C22×D4×C3711yescharacteristic
988C2×C4C22×D4×C3711yescharacteristic
989C2×C4C2×#41×C3711yescharacteristic
990C2×C4H(5,𝔽2)×C3711yescharacteristic
991C2×C4H(5,𝔽2)×C3711yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C3711yescharacteristic
1022C22D42×C3711yescharacteristic
1023C22C37×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C3711yescharacteristic
1037C4C37×#53411yescharacteristic
1038C4D42×C3711yescharacteristic
1039C4C37×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C37×#241011yescharacteristic
1049C2C37×#302011yescharacteristic
1050C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3489C2semidirect
2. C37×#3055C2semidirect
3. C2×C37×#454C2semidirect
4. C37×#3006C2semidirect
5. C2×C37×#421C2semidirect
6. C37×#2620C2semidirect
7. C37×#2039C2semidirect
8. C37×#2038C2semidirect
9. C37×#2006C2semidirect
10. C37×#2003C2semidirect
11. C37×#1901C2semidirect
12. C37×#1897C2semidirect
13. C37×#1883C2semidirect
14. C37×#1859C2semidirect
15. C37×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C37C22semidirect
32. C2×#124×C37C22semidirect
49. C37×#428C22semidirect
55. C2×#104×C37C22semidirect
56. C2×#104×C37C22semidirect
57. C37×#418C22semidirect
60. C37×#417C22semidirect
61. C2×#101×C37C22semidirect
62. C2×#101×C37C22semidirect
66. C37×#391C22semidirect
67. C37×#390C22semidirect
68. C37×#384C22semidirect
69. C37×#343C22semidirect
70. C37×#343C22semidirect
71. C37×#339C22semidirect
72. C37×#339C22semidirect
192. #104×C37D4semidirect
470. #24469C37direct (N × H)
515. #3489C2×C37semidirect
516. #3055C2×C37semidirect
517. C2×#454C2×C37semidirect
518. #3006C2×C37semidirect
519. C2×#421C2×C37semidirect
520. #2620C2×C37semidirect
521. #2039C2×C37semidirect
522. #2038C2×C37semidirect
523. #2006C2×C37semidirect
524. #2003C2×C37semidirect
525. #1901C2×C37semidirect
526. #1897C2×C37semidirect
527. #1883C2×C37semidirect
528. #1859C2×C37semidirect
529. #1793C2×C37semidirect
545. C2×AGL(1,ℤ/8)C22×C37semidirect
557. C2×#124C22×C37semidirect
574. #428C22×C37semidirect
580. C2×#104C22×C37semidirect
581. C2×#104C22×C37semidirect
582. #418C22×C37semidirect
585. #417C22×C37semidirect
586. C2×#101C22×C37semidirect
587. C2×#101C22×C37semidirect
591. #391C22×C37semidirect
592. #390C22×C37semidirect
593. #384C22×C37semidirect
594. #343C22×C37semidirect
595. #343C22×C37semidirect
596. #339C22×C37semidirect
597. #339C22×C37semidirect
598. C37#24469direct (N × H)
718. #104D4×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#34892
C37×#30552
C2×C37×#4542
C37×#30062
C2×C37×#4212
C37×#26202
C37×#20392
C37×#20382
C37×#20062
C37×#20032
C37×#19012
C37×#18972
C37×#18832
C37×#18592
C37×#17932
#2446937