Finite Group Databasebeta

← C137×#24467 #46873853

Subgroups — C137×#24467 #46873853

Order 35072.

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
1#3488×C137C211yesmaximal, characteristic
2#3056×C137C211yesmaximal, characteristic, complemented
3C2×#455×C137C211yesmaximal, characteristic, complemented
4#3007×C137C211yesmaximal, characteristic, complemented
5C22×#104×C137C211yesmaximal, characteristic, complemented
6#2850×C137C211yesmaximal, characteristic, complemented
7#2040×C137C211yesmaximal, characteristic, complemented
8#2037×C137C211yesmaximal, characteristic, complemented
9#2007×C137C211yesmaximal, characteristic, complemented
10#2004×C137C211yesmaximal, characteristic, complemented
11#1900×C137C211yesmaximal, characteristic, complemented
12#1896×C137C211yesmaximal, characteristic, complemented
13#1882×C137C211yesmaximal, characteristic, complemented
14#1860×C137C211yesmaximal, characteristic, complemented
15#1792×C137C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C2×#137×C137C2211yescharacteristic
19C2×#137×C137C2211yescharacteristic, complemented
20C2×#137×C137C2211yescharacteristic, complemented
21C22×M16×C137C2211yescharacteristic, complemented
22#550×C137—21no—
23#548×C137—21no—
24#546×C137—21no—
25#546×C137—22no—
26D42×C137—22no—
27D42×C137—21no—
28#537×C137—21no—
29#537×C137C2211yescharacteristic
30#535×C137—21no—
31#535×C137C2211yescharacteristic
32C2×#124×C137C2211yescharacteristic, complemented
33#525×C137—21no—
34#525×C137C2211yescharacteristic
35C2×C22⋊Q8×C137C2211yescharacteristic, complemented
36C2×#121×C137—21no—
37C2×#121×C137C2211yescharacteristic
38#520×C137C2211yescharacteristic
39C22×C42×C137C2211yescharacteristic, complemented
40#470×C137—21no—
41#468×C137—21no—
42#467×C137—21no—
43#465×C137—21no—
44#455×C137—24no—
45#452×C137—21no—
46#452×C137—21no—
47#451×C137—21no—
48#450×C137—21no—
49#428×C137C2211yescharacteristic, complemented
50C2×#104×C137—24no—
51C2×#104×C137C2211yescharacteristic
52C2×#104×C137C2211yescharacteristic
53C2×#104×C137C2211yescharacteristic, complemented
54C2×#104×C137C2211yescharacteristic, complemented
55C2×#104×C137C2211yescharacteristic, complemented
56C2×#104×C137C2211yescharacteristic, complemented
57#419×C137C2211yescharacteristic, complemented
58#417×C137C2211yescharacteristic
59#417×C137C2211yescharacteristic, complemented
60#417×C137C2211yescharacteristic, complemented
61C2×#100×C137C2211yescharacteristic, complemented
62C2×#100×C137C2211yescharacteristic, complemented
63#407×C137C2211yescharacteristic, complemented
64#391×C137C2211yescharacteristic, complemented
65#390×C137C2211yescharacteristic, complemented
66#388×C137—22no—
67#386×C137—22no—
68#382×C137C2211yescharacteristic, complemented
69#343×C137C2211yescharacteristic, complemented
70#343×C137C2211yescharacteristic, complemented
71#339×C137C2211yescharacteristic, complemented
72#339×C137C2211yescharacteristic, complemented
73H(5,𝔽2)×C137—22no—
74H(5,𝔽2)×C137—22no—
75H(5,𝔽2)×C137—41no—
76H(5,𝔽2)×C137—41no—
77C2×#41×C137—21no—
78C2×#41×C137—21no—
79C2×#41×C137—21no—
80C2×#41×C137—21no—
81C2×#41×C137—22no—
82C2×#41×C137—22no—
83C2×#41×C137—41no—
84C2×#41×C137—41no—
85C2×#41×C137D411yescharacteristic
86C2×#41×C137D411yescharacteristic
87C2×#41×C137C2311yescharacteristic
88C2×#41×C137C2311yescharacteristic
89C2×#41×C137C2311yescharacteristic
90C22×Q8×C137D411yescharacteristic
91C22×Q8×C137C2311yescharacteristic
92C22×D4×C137—21no—
93C22×D4×C137—22no—
94C22×D4×C137—22no—
95C22×D4×C137—21no—
96C22×D4×C137—21no—
97C22×D4×C137D411yescharacteristic
98C22×D4×C137D412yes—
99C22×D4×C137C2311yescharacteristic
100C23×C4×C137—21no—
101C23×C4×C137—21no—
102C23×C4×C137C2311yescharacteristic
103#137×C137—22no—
104#137×C137—22no—
105#137×C137—22no—
106#137×C137—41no—
107#137×C137—41no—
108#137×C137—41no—
109C2×Q16×C137—21no—
110C2×Q16×C137—21no—
111C2×Q16×C137—21no—
112C2×SD16×C137—21no—
113C2×SD16×C137—21no—
114C2×SD16×C137—21no—
115C2×M16×C137—21no—
116C2×M16×C137—22no—
117C2×M16×C137—41no—
118C2×M16×C137C2311yescharacteristic
119C2×M16×C137C2311yescharacteristic
120C2×M16×C137C2311yescharacteristic
121C2×M16×C137C2311yescharacteristic
122C22×C8×C137—21no—
123#127×C137—22no—
124#127×C137—21no—
125#124×C137—22no—
126#124×C137—21no—
127#124×C137—22no—
128#124×C137—41no—
129#123×C137—22no—
130#123×C137—21no—
131C22⋊Q8×C137—22no—
132C22⋊Q8×C137—21no—
133C22⋊Q8×C137—21no—
134C22⋊Q8×C137—21no—
135C22⋊Q8×C137—21no—
136C22⋊Q8×C137—21no—
137C22⋊Q8×C137—21no—
138C22⋊Q8×C137D411yescharacteristic
139C22⋊Q8×C137D411yescharacteristic
140#121×C137—22no—
141#121×C137—22no—
142#121×C137—22no—
143#121×C137—22no—
144#121×C137—22no—
145#121×C137—21no—
146#121×C137—21no—
147#121×C137—21no—
148#121×C137—21no—
149#121×C137—21no—
150#121×C137—21no—
151#121×C137—22no—
152#121×C137—21no—
153#121×C137—21no—
154#121×C137D411yescharacteristic
155#121×C137D411yescharacteristic
156#120×C137—22no—
157#120×C137—22no—
158#120×C137—22no—
159#120×C137—21no—
160#120×C137—22no—
161C4×Q8×C137—21no—
162C4×D4×C137—22no—
163C4×D4×C137—22no—
164C4×D4×C137—21no—
165C4×D4×C137—22no—
166C4×D4×C137—21no—
167C4×D4×C137—21no—
168#117×C137—21no—
169#117×C137C2311yescharacteristic
170C2×C4⋊C4×C137—21no—
171C2×C4⋊C4×C137—21no—
172C2×C4⋊C4×C137C2311yescharacteristic
173C2×C4⋊C4×C137C2311yescharacteristic
174C2×C22⋊C4×C137—22no—
175C2×C22⋊C4×C137—21no—
176C2×C22⋊C4×C137—22no—
177C2×C22⋊C4×C137—22no—
178C2×C22⋊C4×C137D412yes—
179C2×C42×C137—22no—
180C2×C42×C137—21no—
181C2×C42×C137—41no—
182C2×C42×C137C2311yescharacteristic
183C2×C42×C137C2311yescharacteristic
184#107×C137—21no—
185#106×C137—21no—
186#104×C137—22no—
187#104×C137—22no—
188#104×C137—22no—
189#104×C137—22no—
190#104×C137—41no—
191#104×C137D414yescomplemented
192#103×C137—21no—
193#103×C137—21no—
194#103×C137—21no—
195#103×C137—21no—
196#103×C137—21no—
197#102×C137—21no—
198#102×C137—21no—
199#102×C137—21no—
200#100×C137—22no—
201#100×C137—41no—
202C22⋊C8×C137—21no—
203C22⋊C8×C137—21no—
204#95×C137—22no—
205#95×C137—22no—
206C24×C137—22no—
207C24×C137—21no—
208C24×C137C2×D411yescharacteristic
209C24×C137C2×D412yes—
210#41×C137—21no—
211#41×C137—21no—
212#41×C137—22no—
213#41×C137—22no—
214#41×C137—21no—
215#41×C137—21no—
216#41×C137—21no—
217#41×C137—21no—
218#41×C137—21no—
219#41×C137—21no—
220#41×C137—21no—
221#41×C137—21no—
222#41×C137—42no—
223#41×C137—42no—
224#41×C137—41no—
225#41×C137—41no—
226#41×C137—42no—
227#41×C137—42no—
228#41×C137—42no—
229#41×C137—42no—
230#41×C137—42no—
231#41×C137—42no—
232#41×C137C2×D412yes—
233#41×C137#4112yes—
234C2×Q8×C137—21no—
235C2×Q8×C137—22no—
236C2×Q8×C137—21no—
237C2×Q8×C137—21no—
238C2×Q8×C137—21no—
239C2×Q8×C137—21no—
240C2×Q8×C137—21no—
241C2×Q8×C137—21no—
242C2×Q8×C137—41no—
243C2×Q8×C137C2×D411yescharacteristic
244C2×Q8×C137C2×D411yescharacteristic
245C2×Q8×C137C2×D411yescharacteristic
246C2×D4×C137—21no—
247C2×D4×C137—22no—
248C2×D4×C137—22no—
249C2×D4×C137—22no—
250C2×D4×C137—22no—
251C2×D4×C137—21no—
252C2×D4×C137—21no—
253C2×D4×C137—21no—
254C2×D4×C137—21no—
255C2×D4×C137—21no—
256C2×D4×C137—22no—
257C2×D4×C137—22no—
258C2×D4×C137—22no—
259C2×D4×C137—21no—
260C2×D4×C137—22no—
261C2×D4×C137—21no—
262C2×D4×C137—21no—
263C2×D4×C137—21no—
264C2×D4×C137—21no—
265C2×D4×C137—21no—
266C2×D4×C137—21no—
267C2×D4×C137—21no—
268C2×D4×C137—41no—
269C2×D4×C137—42no—
270C2×D4×C137—42no—
271C2×D4×C137—42no—
272C2×D4×C137—42no—
273C2×D4×C137—44no—
274C2×D4×C137—44no—
275C2×D4×C137—42no—
276C2×D4×C137—42no—
277C2×D4×C137—44no—
278C2×D4×C137—84no—
279C2×D4×C137C2×D411yescharacteristic
280C2×D4×C137C2×D411yescharacteristic
281C2×D4×C137C2×D411yescharacteristic
282C22×C4×C137—21no—
283C22×C4×C137—21no—
284C22×C4×C137—21no—
285C22×C4×C137—21no—
286C22×C4×C137—21no—
287C22×C4×C137—22no—
288C22×C4×C137—21no—
289C22×C4×C137—21no—
290C22×C4×C137—21no—
291C22×C4×C137—22no—
292C22×C4×C137—21no—
293C22×C4×C137—21no—
294C22×C4×C137—21no—
295C22×C4×C137—21no—
296C22×C4×C137—21no—
297C22×C4×C137—21no—
298C22×C4×C137—42no—
299C22×C4×C137—42no—
300C22×C4×C137—42no—
301C22×C4×C137—42no—
302C22×C4×C137—42no—
303C22×C4×C137C2×D411yescharacteristic
304C22×C4×C137C2×D411yescharacteristic
305C22×C4×C137C2×D411yescharacteristic
306C22×C4×C137C2×D411yescharacteristic
307C22×C4×C137C2×D411yescharacteristic
308C22×C4×C137C2×D412yes—
309C22×C4×C137C2411yescharacteristic
310Q16×C137—42no—
311Q16×C137—42no—
312Q16×C137—42no—
313SD16×C137—42no—
314SD16×C137—42no—
315SD16×C137—42no—
316M16×C137—21no—
317M16×C137—21no—
318M16×C137—21no—
319M16×C137—21no—
320M16×C137—21no—
321M16×C137—21no—
322M16×C137—21no—
323M16×C137—42no—
324M16×C137C2×D412yescomplemented
325C2×C8×C137—21no—
326C2×C8×C137—21no—
327C2×C8×C137—21no—
328C2×C8×C137—21no—
329C2×C8×C137—42no—
330C4⋊C4×C137—22no—
331C4⋊C4×C137—22no—
332C4⋊C4×C137—21no—
333C4⋊C4×C137—21no—
334C4⋊C4×C137—21no—
335C4⋊C4×C137—21no—
336C4⋊C4×C137—21no—
337C4⋊C4×C137—21no—
338C4⋊C4×C137—41no—
339C4⋊C4×C137—41no—
340C4⋊C4×C137C2×D411yescharacteristic
341C4⋊C4×C137C2×D411yescharacteristic
342C22⋊C4×C137—22no—
343C22⋊C4×C137—22no—
344C22⋊C4×C137—22no—
345C22⋊C4×C137—22no—
346C22⋊C4×C137—22no—
347C22⋊C4×C137—21no—
348C22⋊C4×C137—21no—
349C22⋊C4×C137—21no—
350C22⋊C4×C137—21no—
351C22⋊C4×C137—22no—
352C22⋊C4×C137—22no—
353C22⋊C4×C137—21no—
354C22⋊C4×C137—44no—
355C22⋊C4×C137—44no—
356C22⋊C4×C137—41no—
357C22⋊C4×C137—41no—
358C42×C137—22no—
359C42×C137—21no—
360C42×C137—21no—
361C42×C137—21no—
362C42×C137—21no—
363C42×C137—42no—
364C42×C137C2×D412yescomplemented
365C23×C137—21no—
366C23×C137—21no—
367C23×C137—21no—
368C23×C137—22no—
369C23×C137—22no—
370C23×C137—21no—
371C23×C137—21no—
372C23×C137—22no—
373C23×C137—22no—
374C23×C137—41no—
375C23×C137—42no—
376C23×C137—44no—
377C23×C137—42no—
378C23×C137—42no—
379C23×C137—42no—
380C23×C137—81no—
381C23×C137—82no—
382C23×C137—82no—
383C23×C137#12011yescharacteristic
384C23×C137#12011yescharacteristic
385C23×C137C22×D411yescharacteristic
386Q8×C137—21no—
387Q8×C137—21no—
388Q8×C137—21no—
389Q8×C137—21no—
390Q8×C137—21no—
391Q8×C137—42no—
392Q8×C137—41no—
393Q8×C137—41no—
394Q8×C137—41no—
395Q8×C137—41no—
396Q8×C137#12112yes—
397D4×C137—22no—
398D4×C137—22no—
399D4×C137—21no—
400D4×C137—21no—
401D4×C137—21no—
402D4×C137—21no—
403D4×C137—21no—
404D4×C137—42no—
405D4×C137—42no—
406D4×C137—44no—
407D4×C137—42no—
408D4×C137—44no—
409D4×C137—41no—
410D4×C137—41no—
411D4×C137—41no—
412D4×C137—41no—
413D4×C137—44no—
414D4×C137—42no—
415D4×C137—41no—
416D4×C137—41no—
417D4×C137—41no—
418D4×C137—41no—
419D4×C137—81no—
420D4×C137—82no—
421D4×C137—82no—
422D4×C137—82no—
423D4×C137—82no—
424D4×C137#12112yes—
425C2×C4×C137—21no—
426C2×C4×C137—21no—
427C2×C4×C137—21no—
428C2×C4×C137—21no—
429C2×C4×C137—21no—
430C2×C4×C137—21no—
431C2×C4×C137—21no—
432C2×C4×C137—21no—
433C2×C4×C137—21no—
434C2×C4×C137—22no—
435C2×C4×C137—21no—
436C2×C4×C137—21no—
437C2×C4×C137—22no—
438C2×C4×C137—22no—
439C2×C4×C137—21no—
440C2×C4×C137—22no—
441C2×C4×C137—21no—
442C2×C4×C137—21no—
443C2×C4×C137—21no—
444C2×C4×C137—22no—
445C2×C4×C137—42no—
446C2×C4×C137—42no—
447C2×C4×C137—42no—
448C2×C4×C137—44no—
449C2×C4×C137—41no—
450C2×C4×C137—41no—
451C2×C4×C137—41no—
452C2×C4×C137—48no—
453C2×C4×C137—41no—
454C2×C4×C137—41no—
455C2×C4×C137—41no—
456C2×C4×C137—41no—
457C2×C4×C137—41no—
458C2×C4×C137—42no—
459C2×C4×C137—42no—
460C2×C4×C137—41no—
461C2×C4×C137—41no—
462C2×C4×C137—41no—
463C2×C4×C137—41no—
464C2×C4×C137—82no—
465C2×C4×C137#12011yescharacteristic
466C2×C4×C137#12011yescharacteristic
467C2×C4×C137C22×D411yescharacteristic
468C2×C4×C137C22×D411yescharacteristic
469C2×C4×C137C22×D411yescharacteristic
470C2×C4×C137C2×#4111yescharacteristic
471C2×C4×C137H(5,𝔽2)11yescharacteristic
472C2×C4×C137H(5,𝔽2)11yescharacteristic
473C8×C137—22no—
474C8×C137—41no—
475C8×C137—41no—
476C8×C137—41no—
477C22×C137—21no—
478C22×C137—21no—
479C22×C137—21no—
480C22×C137—21no—
481C22×C137—21no—
482C22×C137—22no—
483C22×C137—21no—
484C22×C137—21no—
485C22×C137—42no—
486C22×C137—42no—
487C22×C137—41no—
488C22×C137—41no—
489C22×C137—41no—
490C22×C137—41no—
491C22×C137—42no—
492C22×C137—42no—
493C22×C137—41no—
494C22×C137—41no—
495C22×C137—41no—
496C22×C137—42no—
497C22×C137—41no—
498C22×C137—84no—
499C22×C137—82no—
500C22×C137—82no—
501C22×C137—164no—
502C22×C137#45512yescomplemented
503C22×C137C2×#12011yescharacteristic
504C22×C137D4211yescharacteristic
505C22×C137#54611yescharacteristic
506C4×C137—21no—
507C4×C137—21no—
508C4×C137—22no—
509C4×C137—42no—
510C4×C137—42no—
511C4×C137—41no—
512C4×C137—41no—
513C4×C137—42no—
514C4×C137—41no—
515C4×C137—41no—
516C4×C137—81no—
517C4×C137—81no—
518C4×C137C2×#12111yescharacteristic
519C4×C137#53411yescharacteristic
520C4×C137D4211yescharacteristic
521C4×C137#54611yescharacteristic
522C2×C137—21no—
523C2×C137—21no—
524C2×C137—22no—
525C2×C137—41no—
526C2×C137—42no—
527C2×C137—81no—
528C2×C137—82no—
529C2×C137—81no—
530C2×C137#241011yescharacteristic
531C2×C137C2×#45511yescharacteristic
532C2×C137#301811yescharacteristic
533#24467C13711yesmaximal, characteristic, direct product factor, Sylow
534C137#2446711yescharacteristic, direct product factor, Sylow
535#3488C2×C13711yescharacteristic
536#3056C2×C13711yescharacteristic, complemented
537C2×#455C2×C13711yescharacteristic, complemented
538#3007C2×C13711yescharacteristic, complemented
539C22×#104C2×C13711yescharacteristic, complemented
540#2850C2×C13711yescharacteristic, complemented
541#2040C2×C13711yescharacteristic, complemented
542#2037C2×C13711yescharacteristic, complemented
543#2007C2×C13711yescharacteristic, complemented
544#2004C2×C13711yescharacteristic, complemented
545#1900C2×C13711yescharacteristic, complemented
546#1896C2×C13711yescharacteristic, complemented
547#1882C2×C13711yescharacteristic, complemented
548#1860C2×C13711yescharacteristic, complemented
549#1792C2×C13711yescharacteristic, complemented
550C2×H(5,𝔽2)C22×C13711yescharacteristic
551C22×#41C22×C13711yescharacteristic
552C2×#137C22×C13711yescharacteristic
553C2×#137C22×C13711yescharacteristic, complemented
554C2×#137C22×C13711yescharacteristic, complemented
555C22×M16C22×C13711yescharacteristic, complemented
556#550—21no—
557#548—21no—
558#546—21no—
559#546—22no—
560D42—22no—
561D42—21no—
562#537—21no—
563#537C22×C13711yescharacteristic
564#535—21no—
565#535C22×C13711yescharacteristic
566C2×#124C22×C13711yescharacteristic, complemented
567#525—21no—
568#525C22×C13711yescharacteristic
569C2×C22⋊Q8C22×C13711yescharacteristic, complemented
570C2×#121—21no—
571C2×#121C22×C13711yescharacteristic
572#520C22×C13711yescharacteristic
573C22×C42C22×C13711yescharacteristic, complemented
574#470—21no—
575#468—21no—
576#467—21no—
577#465—21no—
578#455—24no—
579#452—21no—
580#452—21no—
581#451—21no—
582#450—21no—
583#428C22×C13711yescharacteristic, complemented
584C2×#104—24no—
585C2×#104C22×C13711yescharacteristic
586C2×#104C22×C13711yescharacteristic
587C2×#104C22×C13711yescharacteristic, complemented
588C2×#104C22×C13711yescharacteristic, complemented
589C2×#104C22×C13711yescharacteristic, complemented
590C2×#104C22×C13711yescharacteristic, complemented
591#419C22×C13711yescharacteristic, complemented
592#417C22×C13711yescharacteristic
593#417C22×C13711yescharacteristic, complemented
594#417C22×C13711yescharacteristic, complemented
595C2×#100C22×C13711yescharacteristic, complemented
596C2×#100C22×C13711yescharacteristic, complemented
597#407C22×C13711yescharacteristic, complemented
598#391C22×C13711yescharacteristic, complemented
599#390C22×C13711yescharacteristic, complemented
600#388—22no—
601#386—22no—
602#382C22×C13711yescharacteristic, complemented
603#343C22×C13711yescharacteristic, complemented
604#343C22×C13711yescharacteristic, complemented
605#339C22×C13711yescharacteristic, complemented
606#339C22×C13711yescharacteristic, complemented
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×C13711yescharacteristic
620C2×#41D4×C13711yescharacteristic
621C2×#41C23×C13711yescharacteristic
622C2×#41C23×C13711yescharacteristic
623C2×#41C23×C13711yescharacteristic
624C22×Q8D4×C13711yescharacteristic
625C22×Q8C23×C13711yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4D4×C13711yescharacteristic
632C22×D4D4×C13712yes—
633C22×D4C23×C13711yescharacteristic
634C23×C4—21no—
635C23×C4—21no—
636C23×C4C23×C13711yescharacteristic
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×C13711yescharacteristic
653C2×M16C23×C13711yescharacteristic
654C2×M16C23×C13711yescharacteristic
655C2×M16C23×C13711yescharacteristic
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×C13711yescharacteristic
673C22⋊Q8D4×C13711yescharacteristic
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×C13711yescharacteristic
689#121D4×C13711yescharacteristic
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×C13711yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4C23×C13711yescharacteristic
707C2×C4⋊C4C23×C13711yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4D4×C13712yes—
713C2×C42—22no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42C23×C13711yescharacteristic
717C2×C42C23×C13711yescharacteristic
718#107—21no—
719#106—21no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—22no—
724#104—41no—
725#104D4×C13714yescomplemented
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×C13711yescharacteristic
743C24C2×D4×C13712yes—
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×C13712yes—
767#41#41×C13712yes—
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×C13711yescharacteristic
778C2×Q8C2×D4×C13711yescharacteristic
779C2×Q8C2×D4×C13711yescharacteristic
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×C13711yescharacteristic
814C2×D4C2×D4×C13711yescharacteristic
815C2×D4C2×D4×C13711yescharacteristic
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×C13711yescharacteristic
838C22×C4C2×D4×C13711yescharacteristic
839C22×C4C2×D4×C13711yescharacteristic
840C22×C4C2×D4×C13711yescharacteristic
841C22×C4C2×D4×C13711yescharacteristic
842C22×C4C2×D4×C13712yes—
843C22×C4C24×C13711yescharacteristic
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×C13712yescomplemented
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×C13711yescharacteristic
875C4⋊C4C2×D4×C13711yescharacteristic
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×C13712yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
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×C13711yescharacteristic
918C23#120×C13711yescharacteristic
919C23C22×D4×C13711yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8#121×C13712yes—
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—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#121×C13712yes—
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×C13711yescharacteristic
1000C2×C4#120×C13711yescharacteristic
1001C2×C4C22×D4×C13711yescharacteristic
1002C2×C4C22×D4×C13711yescharacteristic
1003C2×C4C22×D4×C13711yescharacteristic
1004C2×C4C2×#41×C13711yescharacteristic
1005C2×C4H(5,𝔽2)×C13711yescharacteristic
1006C2×C4H(5,𝔽2)×C13711yescharacteristic
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—
1036C22#455×C13712yescomplemented
1037C22C2×#120×C13711yescharacteristic
1038C22D42×C13711yescharacteristic
1039C22#546×C13711yescharacteristic
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×C13711yescharacteristic
1053C4#534×C13711yescharacteristic
1054C4D42×C13711yescharacteristic
1055C4#546×C13711yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2#2410×C13711yescharacteristic
1065C2C2×#455×C13711yescharacteristic
1066C2#3018×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3488×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3056×C137C2semidirect
3. C2×#455×C137C2semidirect
4. #3007×C137C2semidirect
5. C22×#104×C137C2semidirect
6. #2850×C137C2semidirect
7. #2040×C137C2semidirect
8. #2037×C137C2semidirect
9. #2007×C137C2semidirect
10. #2004×C137C2semidirect
11. #1900×C137C2semidirect
12. #1896×C137C2semidirect
13. #1882×C137C2semidirect
14. #1860×C137C2semidirect
15. #1792×C137C2semidirect
19. C2×#137×C137C22semidirect
20. C2×#137×C137C22semidirect
21. C22×M16×C137C22semidirect
32. C2×#124×C137C22semidirect
35. C2×C22⋊Q8×C137C22semidirect
39. C22×C42×C137C22semidirect
49. #428×C137C22semidirect
53. C2×#104×C137C22semidirect
54. C2×#104×C137C22semidirect
55. C2×#104×C137C22semidirect
56. C2×#104×C137C22semidirect
57. #419×C137C22semidirect
59. #417×C137C22semidirect
60. #417×C137C22semidirect
61. C2×#100×C137C22semidirect
62. C2×#100×C137C22semidirect
63. #407×C137C22semidirect
64. #391×C137C22semidirect
65. #390×C137C22semidirect
68. #382×C137C22semidirect
69. #343×C137C22semidirect
70. #343×C137C22semidirect
71. #339×C137C22semidirect
72. #339×C137C22semidirect
191. #104×C137D4semidirect
324. M16×C137C2×D4semidirect
364. C42×C137C2×D4semidirect
502. C22×C137#455semidirect
533. #24467C137direct (N × H)
534. C137#24467direct (N × H)
536. #3056C2×C137semidirect
537. C2×#455C2×C137semidirect
538. #3007C2×C137semidirect
539. C22×#104C2×C137semidirect
540. #2850C2×C137semidirect
541. #2040C2×C137semidirect
542. #2037C2×C137semidirect
543. #2007C2×C137semidirect
544. #2004C2×C137semidirect
545. #1900C2×C137semidirect
546. #1896C2×C137semidirect
547. #1882C2×C137semidirect
548. #1860C2×C137semidirect
549. #1792C2×C137semidirect
553. C2×#137C22×C137semidirect
554. C2×#137C22×C137semidirect
555. C22×M16C22×C137semidirect
566. C2×#124C22×C137semidirect
569. C2×C22⋊Q8C22×C137semidirect
573. C22×C42C22×C137semidirect
583. #428C22×C137semidirect
587. C2×#104C22×C137semidirect
588. C2×#104C22×C137semidirect
589. C2×#104C22×C137semidirect
590. C2×#104C22×C137semidirect
591. #419C22×C137semidirect
593. #417C22×C137semidirect
594. #417C22×C137semidirect
595. C2×#100C22×C137semidirect
596. C2×#100C22×C137semidirect
597. #407C22×C137semidirect
598. #391C22×C137semidirect
599. #390C22×C137semidirect
602. #382C22×C137semidirect
603. #343C22×C137semidirect
604. #343C22×C137semidirect
605. #339C22×C137semidirect
606. #339C22×C137semidirect
725. #104D4×C137semidirect
858. M16C2×D4×C137semidirect
898. C42C2×D4×C137semidirect
1036. C22#455×C137semidirect

Maximal subgroups

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

subgroupindex
#3488×C1372
#3056×C1372
C2×#455×C1372
#3007×C1372
C22×#104×C1372
#2850×C1372
#2040×C1372
#2037×C1372
#2007×C1372
#2004×C1372
#1900×C1372
#1896×C1372
#1882×C1372
#1860×C1372
#1792×C1372
#24467137