Finite Group Databasebeta

← C37×#24471 #22645724

Subgroups — C37×#24471 #22645724

Order 9472.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×C37×#421C211yesmaximal, characteristic, complemented
6C37×#2620C211yesmaximal, characteristic, complemented
7C37×#2039C211yesmaximal, characteristic, complemented
8C37×#2037C211yesmaximal, characteristic, complemented
9C37×#2007C211yesmaximal, characteristic, complemented
10C37×#2004C211yesmaximal, characteristic, complemented
11C37×#1900C211yesmaximal, characteristic, complemented
12C37×#1897C211yesmaximal, characteristic, complemented
13C37×#1882C211yesmaximal, characteristic, complemented
14C37×#1859C211yesmaximal, 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
39C2×#117×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
50C37×#421—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×#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
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×C37C2311yescharacteristic
102#137×C37—22no—
103#137×C37—22no—
104#137×C37—22no—
105#137×C37—41no—
106#137×C37—41no—
107#137×C37—41no—
108C2×Q16×C37—21no—
109C2×Q16×C37—21no—
110C2×Q16×C37—21no—
111C2×SD16×C37—21no—
112C2×SD16×C37—21no—
113C2×SD16×C37—21no—
114C2×M16×C37—21no—
115C2×M16×C37—22no—
116C2×M16×C37—41no—
117C2×M16×C37C2311yescharacteristic
118C2×M16×C37C2311yescharacteristic
119C2×M16×C37C2311yescharacteristic
120C2×M16×C37C2311yescharacteristic
121C22×C8×C37—21no—
122#127×C37—22no—
123#127×C37—21no—
124#124×C37—22no—
125#124×C37—21no—
126#124×C37—22no—
127#124×C37—41no—
128#123×C37—22no—
129#123×C37—21no—
130C22⋊Q8×C37—22no—
131C22⋊Q8×C37—21no—
132C22⋊Q8×C37—21no—
133C22⋊Q8×C37—21no—
134C22⋊Q8×C37—21no—
135C22⋊Q8×C37—21no—
136C22⋊Q8×C37—21no—
137C22⋊Q8×C37D411yescharacteristic
138C22⋊Q8×C37D411yescharacteristic
139#121×C37—22no—
140#121×C37—22no—
141#121×C37—22no—
142#121×C37—22no—
143#121×C37—22no—
144#121×C37—21no—
145#121×C37—21no—
146#121×C37—21no—
147#121×C37—21no—
148#121×C37—21no—
149#121×C37—21no—
150#121×C37—22no—
151#121×C37—21no—
152#121×C37—21no—
153#121×C37D411yescharacteristic
154#121×C37D411yescharacteristic
155#120×C37—22no—
156#120×C37—22no—
157#120×C37—22no—
158#120×C37—21no—
159#120×C37—22no—
160C4×Q8×C37—21no—
161C4×D4×C37—22no—
162C4×D4×C37—22no—
163C4×D4×C37—21no—
164C4×D4×C37—22no—
165C4×D4×C37—21no—
166C4×D4×C37—21no—
167#117×C37—21no—
168#117×C37—22no—
169#117×C37—41no—
170#117×C37C2311yescharacteristic
171C2×C4⋊C4×C37—21no—
172C2×C4⋊C4×C37—21no—
173C2×C4⋊C4×C37—21no—
174C2×C4⋊C4×C37—22no—
175C2×C4⋊C4×C37C2311yescharacteristic
176C2×C4⋊C4×C37C2311yescharacteristic
177C2×C22⋊C4×C37—22no—
178C2×C22⋊C4×C37—21no—
179C2×C22⋊C4×C37—22no—
180C2×C22⋊C4×C37—21no—
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#103×C37—21no—
197#103×C37—21no—
198#102×C37—21no—
199#102×C37—21no—
200#102×C37—21no—
201#100×C37—22no—
202#100×C37—41no—
203C22⋊C8×C37—21no—
204C22⋊C8×C37—21no—
205#95×C37—22no—
206C24×C37—22no—
207C24×C37—21no—
208C24×C37C2×D412yes—
209C24×C37C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C37—21no—
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×C37C2×D411yescharacteristic
301C22×C4×C37C2×D411yescharacteristic
302C22×C4×C37C2×D411yescharacteristic
303C22×C4×C37C2×D411yescharacteristic
304C22×C4×C37C2×D411yescharacteristic
305C22×C4×C37C2×D412yes—
306C22×C4×C37C2411yescharacteristic
307Q16×C37—42no—
308Q16×C37—42no—
309Q16×C37—42no—
310SD16×C37—42no—
311SD16×C37—42no—
312SD16×C37—42no—
313M16×C37—21no—
314M16×C37—21no—
315M16×C37—21no—
316M16×C37—21no—
317M16×C37—21no—
318M16×C37—21no—
319M16×C37—21no—
320M16×C37—42no—
321M16×C37C2×D412yescomplemented
322C2×C8×C37—21no—
323C2×C8×C37—21no—
324C2×C8×C37—21no—
325C2×C8×C37—21no—
326C2×C8×C37—42no—
327C4⋊C4×C37—22no—
328C4⋊C4×C37—22no—
329C4⋊C4×C37—21no—
330C4⋊C4×C37—21no—
331C4⋊C4×C37—21no—
332C4⋊C4×C37—21no—
333C4⋊C4×C37—21no—
334C4⋊C4×C37—21no—
335C4⋊C4×C37—42no—
336C4⋊C4×C37—41no—
337C4⋊C4×C37—41no—
338C4⋊C4×C37—82no—
339C4⋊C4×C37C2×D411yescharacteristic
340C4⋊C4×C37C2×D411yescharacteristic
341C22⋊C4×C37—22no—
342C22⋊C4×C37—22no—
343C22⋊C4×C37—22no—
344C22⋊C4×C37—22no—
345C22⋊C4×C37—22no—
346C22⋊C4×C37—21no—
347C22⋊C4×C37—21no—
348C22⋊C4×C37—21no—
349C22⋊C4×C37—21no—
350C22⋊C4×C37—22no—
351C22⋊C4×C37—22no—
352C22⋊C4×C37—21no—
353C22⋊C4×C37—42no—
354C22⋊C4×C37—44no—
355C22⋊C4×C37—41no—
356C22⋊C4×C37—41no—
357C22⋊C4×C37—82no—
358C42×C37—22no—
359C42×C37—21no—
360C42×C37—21no—
361C42×C37—21no—
362C42×C37—21no—
363C42×C37C2×D412yescomplemented
364C23×C37—21no—
365C23×C37—21no—
366C23×C37—21no—
367C23×C37—22no—
368C23×C37—21no—
369C23×C37—21no—
370C23×C37—22no—
371C23×C37—22no—
372C23×C37—41no—
373C23×C37—41no—
374C23×C37—42no—
375C23×C37—42no—
376C23×C37—44no—
377C23×C37—42no—
378C23×C37—42no—
379C23×C37—81no—
380C23×C37—82no—
381C23×C37—82no—
382C23×C37#12011yescharacteristic
383C23×C37#12011yescharacteristic
384C23×C37C22×D411yescharacteristic
385Q8×C37—21no—
386Q8×C37—21no—
387Q8×C37—21no—
388Q8×C37—21no—
389Q8×C37—21no—
390Q8×C37—42no—
391Q8×C37—41no—
392Q8×C37—41no—
393Q8×C37—41no—
394Q8×C37—41no—
395Q8×C37#12112yes—
396D4×C37—22no—
397D4×C37—22no—
398D4×C37—21no—
399D4×C37—21no—
400D4×C37—21no—
401D4×C37—21no—
402D4×C37—21no—
403D4×C37—42no—
404D4×C37—42no—
405D4×C37—44no—
406D4×C37—42no—
407D4×C37—44no—
408D4×C37—44no—
409D4×C37—42no—
410D4×C37—41no—
411D4×C37—41no—
412D4×C37—41no—
413D4×C37—41no—
414D4×C37—41no—
415D4×C37—41no—
416D4×C37—41no—
417D4×C37—41no—
418D4×C37—81no—
419D4×C37—82no—
420D4×C37—82no—
421D4×C37—82no—
422D4×C37—82no—
423D4×C37#12112yes—
424C2×C4×C37—21no—
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—22no—
434C2×C4×C37—21no—
435C2×C4×C37—21no—
436C2×C4×C37—22no—
437C2×C4×C37—21no—
438C2×C4×C37—22no—
439C2×C4×C37—21no—
440C2×C4×C37—21no—
441C2×C4×C37—21no—
442C2×C4×C37—22no—
443C2×C4×C37—42no—
444C2×C4×C37—42no—
445C2×C4×C37—42no—
446C2×C4×C37—44no—
447C2×C4×C37—41no—
448C2×C4×C37—41no—
449C2×C4×C37—41no—
450C2×C4×C37—41no—
451C2×C4×C37—41no—
452C2×C4×C37—41no—
453C2×C4×C37—42no—
454C2×C4×C37—41no—
455C2×C4×C37—42no—
456C2×C4×C37—41no—
457C2×C4×C37—41no—
458C2×C4×C37—41no—
459C2×C4×C37—41no—
460C2×C4×C37—41no—
461C2×C4×C37—41no—
462C2×C4×C37—82no—
463C2×C4×C37#12011yescharacteristic
464C2×C4×C37#12011yescharacteristic
465C2×C4×C37C22×D411yescharacteristic
466C2×C4×C37C22×D411yescharacteristic
467C2×C4×C37C22×D411yescharacteristic
468C2×C4×C37C2×#4111yescharacteristic
469C2×C4×C37H(5,𝔽2)11yescharacteristic
470C2×C4×C37H(5,𝔽2)11yescharacteristic
471C8×C37—22no—
472C8×C37—41no—
473C8×C37—41no—
474C8×C37—41no—
475#24471C3711yesmaximal, characteristic, direct product factor, Sylow
476C22×C37—21no—
477C22×C37—21no—
478C22×C37—21no—
479C22×C37—21no—
480C22×C37—22no—
481C22×C37—21no—
482C22×C37—21no—
483C22×C37—21no—
484C22×C37—21no—
485C22×C37—41no—
486C22×C37—41no—
487C22×C37—41no—
488C22×C37—41no—
489C22×C37—42no—
490C22×C37—42no—
491C22×C37—41no—
492C22×C37—41no—
493C22×C37—41no—
494C22×C37—42no—
495C22×C37—41no—
496C22×C37—81no—
497C22×C37—81no—
498C22×C37—82no—
499C22×C37—82no—
500C22×C37—84no—
501C22×C37—164no—
502C22×C37C2×#12011yescharacteristic
503C22×C37D4211yescharacteristic
504C22×C37#54611yescharacteristic
505C4×C37—21no—
506C4×C37—21no—
507C4×C37—22no—
508C4×C37—42no—
509C4×C37—41no—
510C4×C37—41no—
511C4×C37—42no—
512C4×C37—41no—
513C4×C37—41no—
514C4×C37—81no—
515C4×C37—81no—
516C4×C37—81no—
517C4×C37C2×#12111yescharacteristic
518C4×C37#53411yescharacteristic
519C4×C37D4211yescharacteristic
520C4×C37#54611yescharacteristic
521#3488C2×C3711yescharacteristic
522#3056C2×C3711yescharacteristic, complemented
523C2×#455C2×C3711yescharacteristic, complemented
524#3007C2×C3711yescharacteristic, complemented
525C2×#421C2×C3711yescharacteristic, complemented
526#2620C2×C3711yescharacteristic, complemented
527#2039C2×C3711yescharacteristic, complemented
528#2037C2×C3711yescharacteristic, complemented
529#2007C2×C3711yescharacteristic, complemented
530#2004C2×C3711yescharacteristic, complemented
531#1900C2×C3711yescharacteristic, complemented
532#1897C2×C3711yescharacteristic, complemented
533#1882C2×C3711yescharacteristic, complemented
534#1859C2×C3711yescharacteristic, complemented
535#1792C2×C3711yescharacteristic, complemented
536C2×C37—21no—
537C2×C37—21no—
538C2×C37—41no—
539C2×C37—41no—
540C2×C37—42no—
541C2×C37—81no—
542C2×C37—82no—
543C2×C37—81no—
544C2×C37#241011yescharacteristic
545C2×C37#301911yescharacteristic
546C2×C37#302211yescharacteristic
547C2×H(5,𝔽2)C22×C3711yescharacteristic
548C22×#41C22×C3711yescharacteristic
549C2×#137C22×C3711yescharacteristic
550C2×#137C22×C3711yescharacteristic, complemented
551C2×#137C22×C3711yescharacteristic, complemented
552C22×M16C22×C3711yescharacteristic, complemented
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C22×C3711yescharacteristic
561#535—21no—
562#535C22×C3711yescharacteristic
563C2×#124C22×C3711yescharacteristic, complemented
564#525—21no—
565#525C22×C3711yescharacteristic
566C2×C22⋊Q8C22×C3711yescharacteristic, complemented
567C2×#121—21no—
568C2×#121C22×C3711yescharacteristic
569#520C22×C3711yescharacteristic
570C2×#117C22×C3711yescharacteristic, complemented
571#470—21no—
572#468—21no—
573#467—21no—
574#465—21no—
575#455—24no—
576#452—21no—
577#452—21no—
578#451—21no—
579#450—21no—
580#428C22×C3711yescharacteristic, complemented
581#421—24no—
582C2×#104C22×C3711yescharacteristic
583C2×#104C22×C3711yescharacteristic
584C2×#104C22×C3711yescharacteristic, complemented
585C2×#104C22×C3711yescharacteristic, complemented
586C2×#104C22×C3711yescharacteristic, complemented
587C2×#104C22×C3711yescharacteristic, complemented
588#419C22×C3711yescharacteristic, complemented
589#417C22×C3711yescharacteristic
590#417C22×C3711yescharacteristic, complemented
591#417C22×C3711yescharacteristic, complemented
592C2×#100C22×C3711yescharacteristic, complemented
593C2×#100C22×C3711yescharacteristic, complemented
594#407C22×C3711yescharacteristic, complemented
595#396—22no—
596#394—22no—
597#391C22×C3711yescharacteristic, complemented
598#390C22×C3711yescharacteristic, complemented
599#384C22×C3711yescharacteristic, complemented
600#343C22×C3711yescharacteristic, complemented
601#343C22×C3711yescharacteristic, complemented
602#339C22×C3711yescharacteristic, complemented
603#339C22×C3711yescharacteristic, complemented
604C37#2447111yescharacteristic, direct product factor, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C3711yescharacteristic
618C2×#41D4×C3711yescharacteristic
619C2×#41C23×C3711yescharacteristic
620C2×#41C23×C3711yescharacteristic
621C2×#41C23×C3711yescharacteristic
622C22×Q8D4×C3711yescharacteristic
623C22×Q8C23×C3711yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C3711yescharacteristic
630C22×D4D4×C3712yes—
631C22×D4C23×C3711yescharacteristic
632C23×C4—21no—
633C23×C4C23×C3711yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C3711yescharacteristic
650C2×M16C23×C3711yescharacteristic
651C2×M16C23×C3711yescharacteristic
652C2×M16C23×C3711yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
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—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C3711yescharacteristic
686#121D4×C3711yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C3711yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C3711yescharacteristic
708C2×C4⋊C4C23×C3711yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C3712yes—
715C2×C42C23×C3711yescharacteristic
716C2×C42C23×C3711yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C3714yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C3712yes—
741C24C2×D4×C3711yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C3712yes—
765#41#41×C3712yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C3711yescharacteristic
776C2×Q8C2×D4×C3711yescharacteristic
777C2×Q8C2×D4×C3711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C3711yescharacteristic
812C2×D4C2×D4×C3711yescharacteristic
813C2×D4C2×D4×C3711yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C3711yescharacteristic
833C22×C4C2×D4×C3711yescharacteristic
834C22×C4C2×D4×C3711yescharacteristic
835C22×C4C2×D4×C3711yescharacteristic
836C22×C4C2×D4×C3711yescharacteristic
837C22×C4C2×D4×C3712yes—
838C22×C4C24×C3711yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C3712yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C3711yescharacteristic
872C4⋊C4C2×D4×C3711yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C3712yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C3711yescharacteristic
915C23#120×C3711yescharacteristic
916C23C22×D4×C3711yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C3712yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C3712yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C3711yescharacteristic
996C2×C4#120×C3711yescharacteristic
997C2×C4C22×D4×C3711yescharacteristic
998C2×C4C22×D4×C3711yescharacteristic
999C2×C4C22×D4×C3711yescharacteristic
1000C2×C4C2×#41×C3711yescharacteristic
1001C2×C4H(5,𝔽2)×C3711yescharacteristic
1002C2×C4H(5,𝔽2)×C3711yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C3711yescharacteristic
1034C22D42×C3711yescharacteristic
1035C22C37×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C3711yescharacteristic
1049C4C37×#53411yescharacteristic
1050C4D42×C3711yescharacteristic
1051C4C37×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C37×#241011yescharacteristic
1061C2C37×#301911yescharacteristic
1062C2C37×#302211yescharacteristic
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. C2×C37×#421C2semidirect
6. C37×#2620C2semidirect
7. C37×#2039C2semidirect
8. C37×#2037C2semidirect
9. C37×#2007C2semidirect
10. C37×#2004C2semidirect
11. C37×#1900C2semidirect
12. C37×#1897C2semidirect
13. C37×#1882C2semidirect
14. C37×#1859C2semidirect
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. C2×#117×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
66. C37×#391C22semidirect
67. C37×#390C22semidirect
68. C37×#384C22semidirect
69. C37×#343C22semidirect
70. C37×#343C22semidirect
71. C37×#339C22semidirect
72. C37×#339C22semidirect
192. #104×C37D4semidirect
321. M16×C37C2×D4semidirect
363. C42×C37C2×D4semidirect
475. #24471C37direct (N × H)
522. #3056C2×C37semidirect
523. C2×#455C2×C37semidirect
524. #3007C2×C37semidirect
525. C2×#421C2×C37semidirect
526. #2620C2×C37semidirect
527. #2039C2×C37semidirect
528. #2037C2×C37semidirect
529. #2007C2×C37semidirect
530. #2004C2×C37semidirect
531. #1900C2×C37semidirect
532. #1897C2×C37semidirect
533. #1882C2×C37semidirect
534. #1859C2×C37semidirect
535. #1792C2×C37semidirect
550. C2×#137C22×C37semidirect
551. C2×#137C22×C37semidirect
552. C22×M16C22×C37semidirect
563. C2×#124C22×C37semidirect
566. C2×C22⋊Q8C22×C37semidirect
570. C2×#117C22×C37semidirect
580. #428C22×C37semidirect
584. C2×#104C22×C37semidirect
585. C2×#104C22×C37semidirect
586. C2×#104C22×C37semidirect
587. C2×#104C22×C37semidirect
588. #419C22×C37semidirect
590. #417C22×C37semidirect
591. #417C22×C37semidirect
592. C2×#100C22×C37semidirect
593. C2×#100C22×C37semidirect
594. #407C22×C37semidirect
597. #391C22×C37semidirect
598. #390C22×C37semidirect
599. #384C22×C37semidirect
600. #343C22×C37semidirect
601. #343C22×C37semidirect
602. #339C22×C37semidirect
603. #339C22×C37semidirect
604. C37#24471direct (N × H)
724. #104D4×C37semidirect
853. M16C2×D4×C37semidirect
895. C42C2×D4×C37semidirect

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
C2×C37×#4212
C37×#26202
C37×#20392
C37×#20372
C37×#20072
C37×#20042
C37×#19002
C37×#18972
C37×#18822
C37×#18592
C37×#17922
#2447137