Finite Group Databasebeta

← C37×#24467 #22645720

Subgroups — C37×#24467 #22645720

Order 9472.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3488C211yesmaximal, characteristic
2C37×#3056C211yesmaximal, characteristic, complemented
3C2×C37×#455C211yesmaximal, characteristic, complemented
4C37×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C37C211yesmaximal, characteristic, complemented
6C37×#2850C211yesmaximal, characteristic, complemented
7C37×#2040C211yesmaximal, characteristic, complemented
8C37×#2037C211yesmaximal, characteristic, complemented
9C37×#2007C211yesmaximal, characteristic, complemented
10C37×#2004C211yesmaximal, characteristic, complemented
11C37×#1900C211yesmaximal, characteristic, complemented
12C37×#1896C211yesmaximal, characteristic, complemented
13C37×#1882C211yesmaximal, characteristic, complemented
14C37×#1860C211yesmaximal, characteristic, complemented
15C37×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C37C2211yescharacteristic
17C22×#41×C37C2211yescharacteristic
18C2×#137×C37C2211yescharacteristic
19C2×#137×C37C2211yescharacteristic, complemented
20C2×#137×C37C2211yescharacteristic, complemented
21C22×M16×C37C2211yescharacteristic, complemented
22C37×#550—21no—
23C37×#548—21no—
24C37×#546—21no—
25C37×#546—22no—
26D42×C37—22no—
27D42×C37—21no—
28C37×#537—21no—
29C37×#537C2211yescharacteristic
30C37×#535—21no—
31C37×#535C2211yescharacteristic
32C2×#124×C37C2211yescharacteristic, complemented
33C37×#525—21no—
34C37×#525C2211yescharacteristic
35C2×C22⋊Q8×C37C2211yescharacteristic, complemented
36C2×#121×C37—21no—
37C2×#121×C37C2211yescharacteristic
38C37×#520C2211yescharacteristic
39C22×C42×C37C2211yescharacteristic, complemented
40C37×#470—21no—
41C37×#468—21no—
42C37×#467—21no—
43C37×#465—21no—
44C37×#455—24no—
45C37×#452—21no—
46C37×#452—21no—
47C37×#451—21no—
48C37×#450—21no—
49C37×#428C2211yescharacteristic, complemented
50C2×#104×C37—24no—
51C2×#104×C37C2211yescharacteristic
52C2×#104×C37C2211yescharacteristic
53C2×#104×C37C2211yescharacteristic, complemented
54C2×#104×C37C2211yescharacteristic, complemented
55C2×#104×C37C2211yescharacteristic, complemented
56C2×#104×C37C2211yescharacteristic, complemented
57C37×#419C2211yescharacteristic, complemented
58C37×#417C2211yescharacteristic
59C37×#417C2211yescharacteristic, complemented
60C37×#417C2211yescharacteristic, complemented
61C2×#100×C37C2211yescharacteristic, complemented
62C2×#100×C37C2211yescharacteristic, complemented
63C37×#407C2211yescharacteristic, complemented
64C37×#391C2211yescharacteristic, complemented
65C37×#390C2211yescharacteristic, complemented
66C37×#388—22no—
67C37×#386—22no—
68C37×#382C2211yescharacteristic, complemented
69C37×#343C2211yescharacteristic, complemented
70C37×#343C2211yescharacteristic, complemented
71C37×#339C2211yescharacteristic, complemented
72C37×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C37—22no—
74H(5,𝔽2)×C37—22no—
75H(5,𝔽2)×C37—41no—
76H(5,𝔽2)×C37—41no—
77C2×#41×C37—21no—
78C2×#41×C37—21no—
79C2×#41×C37—21no—
80C2×#41×C37—21no—
81C2×#41×C37—22no—
82C2×#41×C37—22no—
83C2×#41×C37—41no—
84C2×#41×C37—41no—
85C2×#41×C37D411yescharacteristic
86C2×#41×C37D411yescharacteristic
87C2×#41×C37C2311yescharacteristic
88C2×#41×C37C2311yescharacteristic
89C2×#41×C37C2311yescharacteristic
90C22×Q8×C37D411yescharacteristic
91C22×Q8×C37C2311yescharacteristic
92C22×D4×C37—21no—
93C22×D4×C37—22no—
94C22×D4×C37—22no—
95C22×D4×C37—21no—
96C22×D4×C37—21no—
97C22×D4×C37D411yescharacteristic
98C22×D4×C37D412yes—
99C22×D4×C37C2311yescharacteristic
100C23×C4×C37—21no—
101C23×C4×C37—21no—
102C23×C4×C37C2311yescharacteristic
103#137×C37—22no—
104#137×C37—22no—
105#137×C37—22no—
106#137×C37—41no—
107#137×C37—41no—
108#137×C37—41no—
109C2×Q16×C37—21no—
110C2×Q16×C37—21no—
111C2×Q16×C37—21no—
112C2×SD16×C37—21no—
113C2×SD16×C37—21no—
114C2×SD16×C37—21no—
115C2×M16×C37—21no—
116C2×M16×C37—22no—
117C2×M16×C37—41no—
118C2×M16×C37C2311yescharacteristic
119C2×M16×C37C2311yescharacteristic
120C2×M16×C37C2311yescharacteristic
121C2×M16×C37C2311yescharacteristic
122C22×C8×C37—21no—
123#127×C37—22no—
124#127×C37—21no—
125#124×C37—22no—
126#124×C37—21no—
127#124×C37—22no—
128#124×C37—41no—
129#123×C37—22no—
130#123×C37—21no—
131C22⋊Q8×C37—22no—
132C22⋊Q8×C37—21no—
133C22⋊Q8×C37—21no—
134C22⋊Q8×C37—21no—
135C22⋊Q8×C37—21no—
136C22⋊Q8×C37—21no—
137C22⋊Q8×C37—21no—
138C22⋊Q8×C37D411yescharacteristic
139C22⋊Q8×C37D411yescharacteristic
140#121×C37—22no—
141#121×C37—22no—
142#121×C37—22no—
143#121×C37—22no—
144#121×C37—22no—
145#121×C37—21no—
146#121×C37—21no—
147#121×C37—21no—
148#121×C37—21no—
149#121×C37—21no—
150#121×C37—21no—
151#121×C37—22no—
152#121×C37—21no—
153#121×C37—21no—
154#121×C37D411yescharacteristic
155#121×C37D411yescharacteristic
156#120×C37—22no—
157#120×C37—22no—
158#120×C37—22no—
159#120×C37—21no—
160#120×C37—22no—
161C4×Q8×C37—21no—
162C4×D4×C37—22no—
163C4×D4×C37—22no—
164C4×D4×C37—21no—
165C4×D4×C37—22no—
166C4×D4×C37—21no—
167C4×D4×C37—21no—
168#117×C37—21no—
169#117×C37C2311yescharacteristic
170C2×C4⋊C4×C37—21no—
171C2×C4⋊C4×C37—21no—
172C2×C4⋊C4×C37C2311yescharacteristic
173C2×C4⋊C4×C37C2311yescharacteristic
174C2×C22⋊C4×C37—22no—
175C2×C22⋊C4×C37—21no—
176C2×C22⋊C4×C37—22no—
177C2×C22⋊C4×C37—22no—
178C2×C22⋊C4×C37D412yes—
179C2×C42×C37—22no—
180C2×C42×C37—21no—
181C2×C42×C37—41no—
182C2×C42×C37C2311yescharacteristic
183C2×C42×C37C2311yescharacteristic
184#107×C37—21no—
185#106×C37—21no—
186#104×C37—22no—
187#104×C37—22no—
188#104×C37—22no—
189#104×C37—22no—
190#104×C37—41no—
191#104×C37D414yescomplemented
192#103×C37—21no—
193#103×C37—21no—
194#103×C37—21no—
195#103×C37—21no—
196#103×C37—21no—
197#102×C37—21no—
198#102×C37—21no—
199#102×C37—21no—
200#100×C37—22no—
201#100×C37—41no—
202C22⋊C8×C37—21no—
203C22⋊C8×C37—21no—
204#95×C37—22no—
205#95×C37—22no—
206C24×C37—22no—
207C24×C37—21no—
208C24×C37C2×D411yescharacteristic
209C24×C37C2×D412yes—
210#41×C37—21no—
211#41×C37—21no—
212#41×C37—22no—
213#41×C37—22no—
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—21no—
222#41×C37—42no—
223#41×C37—42no—
224#41×C37—41no—
225#41×C37—41no—
226#41×C37—42no—
227#41×C37—42no—
228#41×C37—42no—
229#41×C37—42no—
230#41×C37—42no—
231#41×C37—42no—
232#41×C37C2×D412yes—
233#41×C37#4112yes—
234C2×Q8×C37—21no—
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—41no—
243C2×Q8×C37C2×D411yescharacteristic
244C2×Q8×C37C2×D411yescharacteristic
245C2×Q8×C37C2×D411yescharacteristic
246C2×D4×C37—21no—
247C2×D4×C37—22no—
248C2×D4×C37—22no—
249C2×D4×C37—22no—
250C2×D4×C37—22no—
251C2×D4×C37—21no—
252C2×D4×C37—21no—
253C2×D4×C37—21no—
254C2×D4×C37—21no—
255C2×D4×C37—21no—
256C2×D4×C37—22no—
257C2×D4×C37—22no—
258C2×D4×C37—22no—
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—41no—
269C2×D4×C37—42no—
270C2×D4×C37—42no—
271C2×D4×C37—42no—
272C2×D4×C37—42no—
273C2×D4×C37—44no—
274C2×D4×C37—44no—
275C2×D4×C37—42no—
276C2×D4×C37—42no—
277C2×D4×C37—44no—
278C2×D4×C37—84no—
279C2×D4×C37C2×D411yescharacteristic
280C2×D4×C37C2×D411yescharacteristic
281C2×D4×C37C2×D411yescharacteristic
282C22×C4×C37—21no—
283C22×C4×C37—21no—
284C22×C4×C37—21no—
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—22no—
292C22×C4×C37—21no—
293C22×C4×C37—21no—
294C22×C4×C37—21no—
295C22×C4×C37—21no—
296C22×C4×C37—21no—
297C22×C4×C37—21no—
298C22×C4×C37—42no—
299C22×C4×C37—42no—
300C22×C4×C37—42no—
301C22×C4×C37—42no—
302C22×C4×C37—42no—
303C22×C4×C37C2×D411yescharacteristic
304C22×C4×C37C2×D411yescharacteristic
305C22×C4×C37C2×D411yescharacteristic
306C22×C4×C37C2×D411yescharacteristic
307C22×C4×C37C2×D411yescharacteristic
308C22×C4×C37C2×D412yes—
309C22×C4×C37C2411yescharacteristic
310Q16×C37—42no—
311Q16×C37—42no—
312Q16×C37—42no—
313SD16×C37—42no—
314SD16×C37—42no—
315SD16×C37—42no—
316M16×C37—21no—
317M16×C37—21no—
318M16×C37—21no—
319M16×C37—21no—
320M16×C37—21no—
321M16×C37—21no—
322M16×C37—21no—
323M16×C37—42no—
324M16×C37C2×D412yescomplemented
325C2×C8×C37—21no—
326C2×C8×C37—21no—
327C2×C8×C37—21no—
328C2×C8×C37—21no—
329C2×C8×C37—42no—
330C4⋊C4×C37—22no—
331C4⋊C4×C37—22no—
332C4⋊C4×C37—21no—
333C4⋊C4×C37—21no—
334C4⋊C4×C37—21no—
335C4⋊C4×C37—21no—
336C4⋊C4×C37—21no—
337C4⋊C4×C37—21no—
338C4⋊C4×C37—41no—
339C4⋊C4×C37—41no—
340C4⋊C4×C37C2×D411yescharacteristic
341C4⋊C4×C37C2×D411yescharacteristic
342C22⋊C4×C37—22no—
343C22⋊C4×C37—22no—
344C22⋊C4×C37—22no—
345C22⋊C4×C37—22no—
346C22⋊C4×C37—22no—
347C22⋊C4×C37—21no—
348C22⋊C4×C37—21no—
349C22⋊C4×C37—21no—
350C22⋊C4×C37—21no—
351C22⋊C4×C37—22no—
352C22⋊C4×C37—22no—
353C22⋊C4×C37—21no—
354C22⋊C4×C37—44no—
355C22⋊C4×C37—44no—
356C22⋊C4×C37—41no—
357C22⋊C4×C37—41no—
358C42×C37—22no—
359C42×C37—21no—
360C42×C37—21no—
361C42×C37—21no—
362C42×C37—21no—
363C42×C37—42no—
364C42×C37C2×D412yescomplemented
365C23×C37—21no—
366C23×C37—21no—
367C23×C37—21no—
368C23×C37—22no—
369C23×C37—22no—
370C23×C37—21no—
371C23×C37—21no—
372C23×C37—22no—
373C23×C37—22no—
374C23×C37—41no—
375C23×C37—42no—
376C23×C37—44no—
377C23×C37—42no—
378C23×C37—42no—
379C23×C37—42no—
380C23×C37—81no—
381C23×C37—82no—
382C23×C37—82no—
383C23×C37#12011yescharacteristic
384C23×C37#12011yescharacteristic
385C23×C37C22×D411yescharacteristic
386Q8×C37—21no—
387Q8×C37—21no—
388Q8×C37—21no—
389Q8×C37—21no—
390Q8×C37—21no—
391Q8×C37—42no—
392Q8×C37—41no—
393Q8×C37—41no—
394Q8×C37—41no—
395Q8×C37—41no—
396Q8×C37#12112yes—
397D4×C37—22no—
398D4×C37—22no—
399D4×C37—21no—
400D4×C37—21no—
401D4×C37—21no—
402D4×C37—21no—
403D4×C37—21no—
404D4×C37—42no—
405D4×C37—42no—
406D4×C37—44no—
407D4×C37—42no—
408D4×C37—44no—
409D4×C37—41no—
410D4×C37—41no—
411D4×C37—41no—
412D4×C37—41no—
413D4×C37—44no—
414D4×C37—42no—
415D4×C37—41no—
416D4×C37—41no—
417D4×C37—41no—
418D4×C37—41no—
419D4×C37—81no—
420D4×C37—82no—
421D4×C37—82no—
422D4×C37—82no—
423D4×C37—82no—
424D4×C37#12112yes—
425C2×C4×C37—21no—
426C2×C4×C37—21no—
427C2×C4×C37—21no—
428C2×C4×C37—21no—
429C2×C4×C37—21no—
430C2×C4×C37—21no—
431C2×C4×C37—21no—
432C2×C4×C37—21no—
433C2×C4×C37—21no—
434C2×C4×C37—22no—
435C2×C4×C37—21no—
436C2×C4×C37—21no—
437C2×C4×C37—22no—
438C2×C4×C37—22no—
439C2×C4×C37—21no—
440C2×C4×C37—22no—
441C2×C4×C37—21no—
442C2×C4×C37—21no—
443C2×C4×C37—21no—
444C2×C4×C37—22no—
445C2×C4×C37—42no—
446C2×C4×C37—42no—
447C2×C4×C37—42no—
448C2×C4×C37—44no—
449C2×C4×C37—41no—
450C2×C4×C37—41no—
451C2×C4×C37—41no—
452C2×C4×C37—48no—
453C2×C4×C37—41no—
454C2×C4×C37—41no—
455C2×C4×C37—41no—
456C2×C4×C37—41no—
457C2×C4×C37—41no—
458C2×C4×C37—42no—
459C2×C4×C37—42no—
460C2×C4×C37—41no—
461C2×C4×C37—41no—
462C2×C4×C37—41no—
463C2×C4×C37—41no—
464C2×C4×C37—82no—
465C2×C4×C37#12011yescharacteristic
466C2×C4×C37#12011yescharacteristic
467C2×C4×C37C22×D411yescharacteristic
468C2×C4×C37C22×D411yescharacteristic
469C2×C4×C37C22×D411yescharacteristic
470C2×C4×C37C2×#4111yescharacteristic
471C2×C4×C37H(5,𝔽2)11yescharacteristic
472C2×C4×C37H(5,𝔽2)11yescharacteristic
473C8×C37—22no—
474C8×C37—41no—
475C8×C37—41no—
476C8×C37—41no—
477#24467C3711yesmaximal, characteristic, direct product factor, Sylow
478C22×C37—21no—
479C22×C37—21no—
480C22×C37—21no—
481C22×C37—21no—
482C22×C37—21no—
483C22×C37—22no—
484C22×C37—21no—
485C22×C37—21no—
486C22×C37—42no—
487C22×C37—42no—
488C22×C37—41no—
489C22×C37—41no—
490C22×C37—41no—
491C22×C37—41no—
492C22×C37—42no—
493C22×C37—42no—
494C22×C37—41no—
495C22×C37—41no—
496C22×C37—41no—
497C22×C37—42no—
498C22×C37—41no—
499C22×C37—84no—
500C22×C37—82no—
501C22×C37—82no—
502C22×C37—164no—
503C22×C37#45512yescomplemented
504C22×C37C2×#12011yescharacteristic
505C22×C37D4211yescharacteristic
506C22×C37#54611yescharacteristic
507C4×C37—21no—
508C4×C37—21no—
509C4×C37—22no—
510C4×C37—42no—
511C4×C37—42no—
512C4×C37—41no—
513C4×C37—41no—
514C4×C37—42no—
515C4×C37—41no—
516C4×C37—41no—
517C4×C37—81no—
518C4×C37—81no—
519C4×C37C2×#12111yescharacteristic
520C4×C37#53411yescharacteristic
521C4×C37D4211yescharacteristic
522C4×C37#54611yescharacteristic
523#3488C2×C3711yescharacteristic
524#3056C2×C3711yescharacteristic, complemented
525C2×#455C2×C3711yescharacteristic, complemented
526#3007C2×C3711yescharacteristic, complemented
527C22×#104C2×C3711yescharacteristic, complemented
528#2850C2×C3711yescharacteristic, complemented
529#2040C2×C3711yescharacteristic, complemented
530#2037C2×C3711yescharacteristic, complemented
531#2007C2×C3711yescharacteristic, complemented
532#2004C2×C3711yescharacteristic, complemented
533#1900C2×C3711yescharacteristic, complemented
534#1896C2×C3711yescharacteristic, complemented
535#1882C2×C3711yescharacteristic, complemented
536#1860C2×C3711yescharacteristic, complemented
537#1792C2×C3711yescharacteristic, complemented
538C2×C37—21no—
539C2×C37—21no—
540C2×C37—22no—
541C2×C37—41no—
542C2×C37—42no—
543C2×C37—81no—
544C2×C37—82no—
545C2×C37—81no—
546C2×C37#241011yescharacteristic
547C2×C37C2×#45511yescharacteristic
548C2×C37#301811yescharacteristic
549C2×H(5,𝔽2)C22×C3711yescharacteristic
550C22×#41C22×C3711yescharacteristic
551C2×#137C22×C3711yescharacteristic
552C2×#137C22×C3711yescharacteristic, complemented
553C2×#137C22×C3711yescharacteristic, complemented
554C22×M16C22×C3711yescharacteristic, complemented
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C22×C3711yescharacteristic
563#535—21no—
564#535C22×C3711yescharacteristic
565C2×#124C22×C3711yescharacteristic, complemented
566#525—21no—
567#525C22×C3711yescharacteristic
568C2×C22⋊Q8C22×C3711yescharacteristic, complemented
569C2×#121—21no—
570C2×#121C22×C3711yescharacteristic
571#520C22×C3711yescharacteristic
572C22×C42C22×C3711yescharacteristic, complemented
573#470—21no—
574#468—21no—
575#467—21no—
576#465—21no—
577#455—24no—
578#452—21no—
579#452—21no—
580#451—21no—
581#450—21no—
582#428C22×C3711yescharacteristic, complemented
583C2×#104—24no—
584C2×#104C22×C3711yescharacteristic
585C2×#104C22×C3711yescharacteristic
586C2×#104C22×C3711yescharacteristic, complemented
587C2×#104C22×C3711yescharacteristic, complemented
588C2×#104C22×C3711yescharacteristic, complemented
589C2×#104C22×C3711yescharacteristic, complemented
590#419C22×C3711yescharacteristic, complemented
591#417C22×C3711yescharacteristic
592#417C22×C3711yescharacteristic, complemented
593#417C22×C3711yescharacteristic, complemented
594C2×#100C22×C3711yescharacteristic, complemented
595C2×#100C22×C3711yescharacteristic, complemented
596#407C22×C3711yescharacteristic, complemented
597#391C22×C3711yescharacteristic, complemented
598#390C22×C3711yescharacteristic, complemented
599#388—22no—
600#386—22no—
601#382C22×C3711yescharacteristic, complemented
602#343C22×C3711yescharacteristic, complemented
603#343C22×C3711yescharacteristic, complemented
604#339C22×C3711yescharacteristic, complemented
605#339C22×C3711yescharacteristic, complemented
606C37#2446711yescharacteristic, direct product factor, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41D4×C3711yescharacteristic
620C2×#41D4×C3711yescharacteristic
621C2×#41C23×C3711yescharacteristic
622C2×#41C23×C3711yescharacteristic
623C2×#41C23×C3711yescharacteristic
624C22×Q8D4×C3711yescharacteristic
625C22×Q8C23×C3711yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C3711yescharacteristic
632C22×D4D4×C3712yes—
633C22×D4C23×C3711yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C3711yescharacteristic
637#137—22no—
638#137—22no—
639#137—22no—
640#137—41no—
641#137—41no—
642#137—41no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×Q16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×M16—21no—
650C2×M16—22no—
651C2×M16—41no—
652C2×M16C23×C3711yescharacteristic
653C2×M16C23×C3711yescharacteristic
654C2×M16C23×C3711yescharacteristic
655C2×M16C23×C3711yescharacteristic
656C22×C8—21no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—22no—
662#124—41no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8D4×C3711yescharacteristic
673C22⋊Q8D4×C3711yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121D4×C3711yescharacteristic
689#121D4×C3711yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C23×C3711yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C3711yescharacteristic
707C2×C4⋊C4C23×C3711yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C3712yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C3711yescharacteristic
717C2×C42C23×C3711yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C3714yescomplemented
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#103—21no—
731#102—21no—
732#102—21no—
733#102—21no—
734#100—22no—
735#100—41no—
736C22⋊C8—21no—
737C22⋊C8—21no—
738#95—22no—
739#95—22no—
740C24—22no—
741C24—21no—
742C24C2×D4×C3711yescharacteristic
743C24C2×D4×C3712yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C3712yes—
767#41#41×C3712yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C3711yescharacteristic
778C2×Q8C2×D4×C3711yescharacteristic
779C2×Q8C2×D4×C3711yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C3711yescharacteristic
814C2×D4C2×D4×C3711yescharacteristic
815C2×D4C2×D4×C3711yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C3711yescharacteristic
838C22×C4C2×D4×C3711yescharacteristic
839C22×C4C2×D4×C3711yescharacteristic
840C22×C4C2×D4×C3711yescharacteristic
841C22×C4C2×D4×C3711yescharacteristic
842C22×C4C2×D4×C3712yes—
843C22×C4C24×C3711yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C3712yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C3711yescharacteristic
875C4⋊C4C2×D4×C3711yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C3712yescomplemented
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#120×C3711yescharacteristic
918C23#120×C3711yescharacteristic
919C23C22×D4×C3711yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C3712yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—44no—
948D4—42no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C3712yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4#120×C3711yescharacteristic
1000C2×C4#120×C3711yescharacteristic
1001C2×C4C22×D4×C3711yescharacteristic
1002C2×C4C22×D4×C3711yescharacteristic
1003C2×C4C22×D4×C3711yescharacteristic
1004C2×C4C2×#41×C3711yescharacteristic
1005C2×C4H(5,𝔽2)×C3711yescharacteristic
1006C2×C4H(5,𝔽2)×C3711yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—22no—
1017C22—21no—
1018C22—21no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—41no—
1029C22—41no—
1030C22—42no—
1031C22—41no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C37×#45512yescomplemented
1037C22C2×#120×C3711yescharacteristic
1038C22D42×C3711yescharacteristic
1039C22C37×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×#121×C3711yescharacteristic
1053C4C37×#53411yescharacteristic
1054C4D42×C3711yescharacteristic
1055C4C37×#54611yescharacteristic
1056C2—21no—
1057C2—21no—
1058C2—22no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C37×#241011yescharacteristic
1065C2C2×C37×#45511yescharacteristic
1066C2C37×#301811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3488C2
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
2. C37×#3056C2semidirect
3. C2×C37×#455C2semidirect
4. C37×#3007C2semidirect
5. C22×#104×C37C2semidirect
6. C37×#2850C2semidirect
7. C37×#2040C2semidirect
8. C37×#2037C2semidirect
9. C37×#2007C2semidirect
10. C37×#2004C2semidirect
11. C37×#1900C2semidirect
12. C37×#1896C2semidirect
13. C37×#1882C2semidirect
14. C37×#1860C2semidirect
15. C37×#1792C2semidirect
19. C2×#137×C37C22semidirect
20. C2×#137×C37C22semidirect
21. C22×M16×C37C22semidirect
32. C2×#124×C37C22semidirect
35. C2×C22⋊Q8×C37C22semidirect
39. C22×C42×C37C22semidirect
49. C37×#428C22semidirect
53. C2×#104×C37C22semidirect
54. C2×#104×C37C22semidirect
55. C2×#104×C37C22semidirect
56. C2×#104×C37C22semidirect
57. C37×#419C22semidirect
59. C37×#417C22semidirect
60. C37×#417C22semidirect
61. C2×#100×C37C22semidirect
62. C2×#100×C37C22semidirect
63. C37×#407C22semidirect
64. C37×#391C22semidirect
65. C37×#390C22semidirect
68. C37×#382C22semidirect
69. C37×#343C22semidirect
70. C37×#343C22semidirect
71. C37×#339C22semidirect
72. C37×#339C22semidirect
191. #104×C37D4semidirect
324. M16×C37C2×D4semidirect
364. C42×C37C2×D4semidirect
477. #24467C37direct (N × H)
503. C22×C37#455semidirect
524. #3056C2×C37semidirect
525. C2×#455C2×C37semidirect
526. #3007C2×C37semidirect
527. C22×#104C2×C37semidirect
528. #2850C2×C37semidirect
529. #2040C2×C37semidirect
530. #2037C2×C37semidirect
531. #2007C2×C37semidirect
532. #2004C2×C37semidirect
533. #1900C2×C37semidirect
534. #1896C2×C37semidirect
535. #1882C2×C37semidirect
536. #1860C2×C37semidirect
537. #1792C2×C37semidirect
552. C2×#137C22×C37semidirect
553. C2×#137C22×C37semidirect
554. C22×M16C22×C37semidirect
565. C2×#124C22×C37semidirect
568. C2×C22⋊Q8C22×C37semidirect
572. C22×C42C22×C37semidirect
582. #428C22×C37semidirect
586. C2×#104C22×C37semidirect
587. C2×#104C22×C37semidirect
588. C2×#104C22×C37semidirect
589. C2×#104C22×C37semidirect
590. #419C22×C37semidirect
592. #417C22×C37semidirect
593. #417C22×C37semidirect
594. C2×#100C22×C37semidirect
595. C2×#100C22×C37semidirect
596. #407C22×C37semidirect
597. #391C22×C37semidirect
598. #390C22×C37semidirect
601. #382C22×C37semidirect
602. #343C22×C37semidirect
603. #343C22×C37semidirect
604. #339C22×C37semidirect
605. #339C22×C37semidirect
606. C37#24467direct (N × H)
725. #104D4×C37semidirect
858. M16C2×D4×C37semidirect
898. C42C2×D4×C37semidirect
1036. C22C37×#455semidirect

Maximal subgroups

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

subgroupindex
C37×#34882
C37×#30562
C2×C37×#4552
C37×#30072
C22×#104×C372
C37×#28502
C37×#20402
C37×#20372
C37×#20072
C37×#20042
C37×#19002
C37×#18962
C37×#18822
C37×#18602
C37×#17922
#2446737