Finite Group Databasebeta

← C137×#24468 #46873854

Subgroups — C137×#24468 #46873854

Order 35072.

1502 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C137C211yesmaximal, characteristic, complemented
2#3055×C137C211yesmaximal, characteristic, complemented
3C2×#453×C137C211yesmaximal, characteristic, complemented
4#3006×C137C211yesmaximal, characteristic, complemented
5C2×#421×C137C211yesmaximal, characteristic, complemented
6#2619×C137C211yesmaximal, characteristic, complemented
7#2040×C137C211yesmaximal, characteristic, complemented
8#2037×C137C211yesmaximal, characteristic, complemented
9#2006×C137C211yesmaximal, characteristic, complemented
10#2002×C137C211yesmaximal, characteristic, complemented
11#1900×C137C211yesmaximal, characteristic, complemented
12#1897×C137C211yesmaximal, characteristic, complemented
13#1883×C137C211yesmaximal, characteristic, complemented
14#1860×C137C211yesmaximal, characteristic, complemented
15#1792×C137C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C137C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×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×#127×C137C2211yescharacteristic, complemented
33#525×C137—21no—
34#525×C137C2211yescharacteristic
35C2×#121×C137—21no—
36C2×#121×C137C2211yescharacteristic
37C2×#121×C137C2211yescharacteristic, complemented
38#520×C137C2211yescharacteristic
39C2×#117×C137C2211yescharacteristic, complemented
40#469×C137—21no—
41#468×C137—21no—
42#466×C137—21no—
43#465×C137—21no—
44#453×C137—24no—
45#449×C137—21no—
46#449×C137—21no—
47#448×C137—21no—
48#447×C137—21no—
49#428×C137C2211yescharacteristic, complemented
50#421×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#418×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#394×C137—22no—
65#392×C137—22no—
66#390×C137C2211yescharacteristic, complemented
67#390×C137C2211yescharacteristic, complemented
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, complemented
86C2×#41×C137D411yescharacteristic, complemented
87C2×#41×C137C2311yescharacteristic
88C2×#41×C137C2311yescharacteristic
89C2×#41×C137C2311yescharacteristic
90C22×Q8×C137D411yescharacteristic, complemented
91C22×D4×C137—21no—
92C22×D4×C137—22no—
93C22×D4×C137—22no—
94C22×D4×C137—21no—
95C22×D4×C137—21no—
96C22×D4×C137—21no—
97C22×D4×C137—22no—
98C22×D4×C137D412yes—
99C22×D4×C137D411yescharacteristic, complemented
100C22×D4×C137C2311yescharacteristic
101C22×D4×C137C2311yescharacteristic
102C23×C4×C137—21no—
103C23×C4×C137C2311yescharacteristic
104AGL(1,ℤ/8)×C137—22no—
105AGL(1,ℤ/8)×C137—22no—
106AGL(1,ℤ/8)×C137—22no—
107AGL(1,ℤ/8)×C137—41no—
108AGL(1,ℤ/8)×C137—41no—
109AGL(1,ℤ/8)×C137—41no—
110C2×SD16×C137—21no—
111C2×SD16×C137—21no—
112C2×SD16×C137—21no—
113C2×D8×C137—21no—
114C2×D8×C137—21no—
115C2×D8×C137—21no—
116C2×M16×C137—21no—
117C2×M16×C137—22no—
118C2×M16×C137—41no—
119C2×M16×C137C2311yescharacteristic
120C2×M16×C137C2311yescharacteristic
121C2×M16×C137C2311yescharacteristic
122C2×M16×C137C2311yescharacteristic
123C22×C8×C137—21no—
124#127×C137—22no—
125#127×C137—21no—
126#127×C137—22no—
127#127×C137—41no—
128#124×C137—22no—
129#124×C137—21no—
130#123×C137—22no—
131#123×C137—21no—
132C22⋊Q8×C137—22no—
133C22⋊Q8×C137—21no—
134C22⋊Q8×C137—21no—
135C22⋊Q8×C137D411yescharacteristic, complemented
136C22⋊Q8×C137D411yescharacteristic, complemented
137#121×C137—22no—
138#121×C137—22no—
139#121×C137—22no—
140#121×C137—22no—
141#121×C137—22no—
142#121×C137—21no—
143#121×C137—21no—
144#121×C137—21no—
145#121×C137—21no—
146#121×C137—21no—
147#121×C137—21no—
148#121×C137—22no—
149#121×C137—21no—
150#121×C137—21no—
151#121×C137—21no—
152#121×C137—21no—
153#121×C137—21no—
154#121×C137—21no—
155#121×C137D411yescharacteristic, complemented
156#121×C137D411yescharacteristic, complemented
157#120×C137—22no—
158#120×C137—22no—
159#120×C137—22no—
160#120×C137—21no—
161#120×C137—22no—
162C4×Q8×C137—21no—
163C4×D4×C137—22no—
164C4×D4×C137—22no—
165C4×D4×C137—21no—
166C4×D4×C137—22no—
167C4×D4×C137—21no—
168C4×D4×C137—21no—
169#117×C137—21no—
170#117×C137—22no—
171#117×C137—41no—
172#117×C137C2311yescharacteristic
173C2×C4⋊C4×C137—21no—
174C2×C4⋊C4×C137—21no—
175C2×C4⋊C4×C137C2311yescharacteristic
176C2×C4⋊C4×C137C2311yescharacteristic
177C2×C22⋊C4×C137—22no—
178C2×C22⋊C4×C137—21no—
179C2×C22⋊C4×C137—21no—
180C2×C22⋊C4×C137—22no—
181C2×C22⋊C4×C137—22no—
182C2×C22⋊C4×C137D412yes—
183C2×C42×C137C2311yescharacteristic
184C2×C42×C137C2311yescharacteristic
185#107×C137—21no—
186#106×C137—21no—
187#104×C137—22no—
188#104×C137—22no—
189#104×C137—22no—
190#104×C137—22no—
191#104×C137—41no—
192#104×C137D414yescomplemented
193#103×C137—21no—
194#103×C137—21no—
195#103×C137—21no—
196#102×C137—21no—
197#102×C137—21no—
198#102×C137—21no—
199#102×C137—21no—
200#102×C137—21no—
201#100×C137—22no—
202#100×C137—41no—
203C22⋊C8×C137—21no—
204C22⋊C8×C137—21no—
205#95×C137—22no—
206C24×C137—22no—
207C24×C137—21no—
208C24×C137—21no—
209C24×C137C2×D412yes—
210C24×C137C2×D411yescharacteristic
211#41×C137—21no—
212#41×C137—21no—
213#41×C137—22no—
214#41×C137—22no—
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—21no—
223#41×C137—42no—
224#41×C137—42no—
225#41×C137—41no—
226#41×C137—41no—
227#41×C137—42no—
228#41×C137—42no—
229#41×C137—42no—
230#41×C137—42no—
231#41×C137—42no—
232#41×C137—42no—
233#41×C137C2×D412yes—
234#41×C137#4112yes—
235C2×Q8×C137—21no—
236C2×Q8×C137—22no—
237C2×Q8×C137—41no—
238C2×Q8×C137C2×D411yescharacteristic
239C2×Q8×C137C2×D411yescharacteristic
240C2×Q8×C137C2×D411yescharacteristic
241C2×D4×C137—21no—
242C2×D4×C137—22no—
243C2×D4×C137—22no—
244C2×D4×C137—22no—
245C2×D4×C137—22no—
246C2×D4×C137—21no—
247C2×D4×C137—21no—
248C2×D4×C137—21no—
249C2×D4×C137—21no—
250C2×D4×C137—21no—
251C2×D4×C137—22no—
252C2×D4×C137—22no—
253C2×D4×C137—22no—
254C2×D4×C137—21no—
255C2×D4×C137—22no—
256C2×D4×C137—21no—
257C2×D4×C137—21no—
258C2×D4×C137—21no—
259C2×D4×C137—21no—
260C2×D4×C137—21no—
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—21no—
269C2×D4×C137—41no—
270C2×D4×C137—42no—
271C2×D4×C137—42no—
272C2×D4×C137—44no—
273C2×D4×C137—42no—
274C2×D4×C137—42no—
275C2×D4×C137—44no—
276C2×D4×C137—44no—
277C2×D4×C137—42no—
278C2×D4×C137—42no—
279C2×D4×C137—41no—
280C2×D4×C137—41no—
281C2×D4×C137—82no—
282C2×D4×C137—82no—
283C2×D4×C137—82no—
284C2×D4×C137—82no—
285C2×D4×C137—84no—
286C2×D4×C137C2×D411yescharacteristic
287C2×D4×C137C2×D411yescharacteristic
288C2×D4×C137C2×D411yescharacteristic
289C22×C4×C137—21no—
290C22×C4×C137—21no—
291C22×C4×C137—21no—
292C22×C4×C137—21no—
293C22×C4×C137—21no—
294C22×C4×C137—22no—
295C22×C4×C137—21no—
296C22×C4×C137—21no—
297C22×C4×C137—22no—
298C22×C4×C137—21no—
299C22×C4×C137—21no—
300C22×C4×C137—21no—
301C22×C4×C137—21no—
302C22×C4×C137—21no—
303C22×C4×C137—21no—
304C22×C4×C137—42no—
305C22×C4×C137—42no—
306C22×C4×C137C2×D411yescharacteristic
307C22×C4×C137C2×D411yescharacteristic
308C22×C4×C137C2×D411yescharacteristic
309C22×C4×C137C2×D411yescharacteristic
310C22×C4×C137C2×D411yescharacteristic
311C22×C4×C137C2×D412yes—
312C22×C4×C137C2411yescharacteristic
313SD16×C137—42no—
314SD16×C137—42no—
315SD16×C137—42no—
316D8×C137—42no—
317D8×C137—42no—
318D8×C137—42no—
319M16×C137—21no—
320M16×C137—21no—
321M16×C137—21no—
322M16×C137—21no—
323M16×C137—21no—
324M16×C137—21no—
325M16×C137—21no—
326M16×C137—42no—
327M16×C137C2×D412yescomplemented
328C2×C8×C137—21no—
329C2×C8×C137—21no—
330C2×C8×C137—21no—
331C2×C8×C137—21no—
332C2×C8×C137—42no—
333C4⋊C4×C137—22no—
334C4⋊C4×C137—22no—
335C4⋊C4×C137—21no—
336C4⋊C4×C137—21no—
337C4⋊C4×C137—21no—
338C4⋊C4×C137—21no—
339C4⋊C4×C137—21no—
340C4⋊C4×C137—21no—
341C4⋊C4×C137—42no—
342C4⋊C4×C137C2×D411yescharacteristic
343C4⋊C4×C137C2×D411yescharacteristic
344C22⋊C4×C137—22no—
345C22⋊C4×C137—22no—
346C22⋊C4×C137—22no—
347C22⋊C4×C137—22no—
348C22⋊C4×C137—22no—
349C22⋊C4×C137—21no—
350C22⋊C4×C137—21no—
351C22⋊C4×C137—21no—
352C22⋊C4×C137—21no—
353C22⋊C4×C137—22no—
354C22⋊C4×C137—22no—
355C22⋊C4×C137—21no—
356C22⋊C4×C137—42no—
357C22⋊C4×C137—41no—
358C22⋊C4×C137—41no—
359C22⋊C4×C137—82no—
360C22⋊C4×C137—82no—
361C42×C137—22no—
362C42×C137—21no—
363C42×C137—21no—
364C42×C137—21no—
365C42×C137—21no—
366C42×C137C2×D412yescomplemented
367C23×C137—21no—
368C23×C137—21no—
369C23×C137—21no—
370C23×C137—22no—
371C23×C137—21no—
372C23×C137—21no—
373C23×C137—22no—
374C23×C137—22no—
375C23×C137—41no—
376C23×C137—41no—
377C23×C137—42no—
378C23×C137—42no—
379C23×C137—44no—
380C23×C137—42no—
381C23×C137—42no—
382C23×C137—42no—
383C23×C137—42no—
384C23×C137—41no—
385C23×C137—41no—
386C23×C137—41no—
387C23×C137—81no—
388C23×C137—82no—
389C23×C137—82no—
390C23×C137#12011yescharacteristic
391C23×C137#12011yescharacteristic
392C23×C137C22×D411yescharacteristic
393Q8×C137—21no—
394Q8×C137—21no—
395Q8×C137—21no—
396Q8×C137—21no—
397Q8×C137—21no—
398Q8×C137—42no—
399Q8×C137#12112yes—
400D4×C137—22no—
401D4×C137—22no—
402D4×C137—21no—
403D4×C137—21no—
404D4×C137—21no—
405D4×C137—21no—
406D4×C137—21no—
407D4×C137—42no—
408D4×C137—42no—
409D4×C137—44no—
410D4×C137—42no—
411D4×C137—44no—
412D4×C137—44no—
413D4×C137—42no—
414D4×C137—41no—
415D4×C137—41no—
416D4×C137—41no—
417D4×C137—41no—
418D4×C137—41no—
419D4×C137—41no—
420D4×C137—41no—
421D4×C137—41no—
422D4×C137—41no—
423D4×C137—41no—
424D4×C137—41no—
425D4×C137—41no—
426D4×C137—81no—
427D4×C137—82no—
428D4×C137—82no—
429D4×C137—82no—
430D4×C137—82no—
431D4×C137—88no—
432D4×C137—82no—
433D4×C137—82no—
434D4×C137#12112yes—
435C2×C4×C137—21no—
436C2×C4×C137—21no—
437C2×C4×C137—21no—
438C2×C4×C137—21no—
439C2×C4×C137—21no—
440C2×C4×C137—21no—
441C2×C4×C137—21no—
442C2×C4×C137—21no—
443C2×C4×C137—21no—
444C2×C4×C137—22no—
445C2×C4×C137—21no—
446C2×C4×C137—21no—
447C2×C4×C137—22no—
448C2×C4×C137—21no—
449C2×C4×C137—22no—
450C2×C4×C137—21no—
451C2×C4×C137—21no—
452C2×C4×C137—21no—
453C2×C4×C137—22no—
454C2×C4×C137—42no—
455C2×C4×C137—42no—
456C2×C4×C137—42no—
457C2×C4×C137—44no—
458C2×C4×C137—41no—
459C2×C4×C137—41no—
460C2×C4×C137—41no—
461C2×C4×C137—41no—
462C2×C4×C137—41no—
463C2×C4×C137—41no—
464C2×C4×C137—42no—
465C2×C4×C137—41no—
466C2×C4×C137—41no—
467C2×C4×C137—42no—
468C2×C4×C137—41no—
469C2×C4×C137—41no—
470C2×C4×C137—82no—
471C2×C4×C137#12011yescharacteristic
472C2×C4×C137#12011yescharacteristic
473C2×C4×C137C22×D411yescharacteristic
474C2×C4×C137C22×D411yescharacteristic
475C2×C4×C137C22×D411yescharacteristic
476C2×C4×C137C2×#4111yescharacteristic
477C2×C4×C137H(5,𝔽2)11yescharacteristic
478C2×C4×C137H(5,𝔽2)11yescharacteristic
479C8×C137—22no—
480C8×C137—41no—
481C8×C137—41no—
482C8×C137—41no—
483C22×C137—21no—
484C22×C137—21no—
485C22×C137—21no—
486C22×C137—21no—
487C22×C137—22no—
488C22×C137—21no—
489C22×C137—21no—
490C22×C137—21no—
491C22×C137—21no—
492C22×C137—41no—
493C22×C137—41no—
494C22×C137—41no—
495C22×C137—41no—
496C22×C137—42no—
497C22×C137—42no—
498C22×C137—41no—
499C22×C137—41no—
500C22×C137—41no—
501C22×C137—42no—
502C22×C137—41no—
503C22×C137—81no—
504C22×C137—81no—
505C22×C137—82no—
506C22×C137—82no—
507C22×C137—82no—
508C22×C137—82no—
509C22×C137—84no—
510C22×C137—81no—
511C22×C137—81no—
512C22×C137—81no—
513C22×C137—164no—
514C22×C137C2×#12011yescharacteristic
515C22×C137D4211yescharacteristic
516C22×C137#54611yescharacteristic
517C4×C137—21no—
518C4×C137—21no—
519C4×C137—22no—
520C4×C137—42no—
521C4×C137—41no—
522C4×C137—41no—
523C4×C137—42no—
524C4×C137—41no—
525C4×C137—41no—
526C4×C137—81no—
527C4×C137—81no—
528C4×C137C2×#12111yescharacteristic
529C4×C137#53411yescharacteristic
530C4×C137D4211yescharacteristic
531C4×C137#54611yescharacteristic
532C2×C137—21no—
533C2×C137—21no—
534C2×C137—41no—
535C2×C137—41no—
536C2×C137—42no—
537C2×C137—81no—
538C2×C137—82no—
539C2×C137—81no—
540C2×C137—161no—
541C2×C137#241011yescharacteristic
542C2×C137#301911yescharacteristic
543C2×C137#302111yescharacteristic
544#24468C13711yesmaximal, characteristic, direct product factor, Sylow
545C137#2446811yescharacteristic, direct product factor, Sylow
546#3488C2×C13711yescharacteristic, complemented
547#3055C2×C13711yescharacteristic, complemented
548C2×#453C2×C13711yescharacteristic, complemented
549#3006C2×C13711yescharacteristic, complemented
550C2×#421C2×C13711yescharacteristic, complemented
551#2619C2×C13711yescharacteristic, complemented
552#2040C2×C13711yescharacteristic, complemented
553#2037C2×C13711yescharacteristic, complemented
554#2006C2×C13711yescharacteristic, complemented
555#2002C2×C13711yescharacteristic, complemented
556#1900C2×C13711yescharacteristic, complemented
557#1897C2×C13711yescharacteristic, complemented
558#1883C2×C13711yescharacteristic, complemented
559#1860C2×C13711yescharacteristic, complemented
560#1792C2×C13711yescharacteristic, complemented
561C2×H(5,𝔽2)C22×C13711yescharacteristic
562C22×#41C22×C13711yescharacteristic
563C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
564C2×AGL(1,ℤ/8)C22×C13711yescharacteristic, complemented
565C2×AGL(1,ℤ/8)C22×C13711yescharacteristic, complemented
566C22×M16C22×C13711yescharacteristic, complemented
567#550—21no—
568#548—21no—
569#546—21no—
570#546—22no—
571D42—22no—
572D42—21no—
573#537—21no—
574#537C22×C13711yescharacteristic
575#535—21no—
576#535C22×C13711yescharacteristic
577C2×#127C22×C13711yescharacteristic, complemented
578#525—21no—
579#525C22×C13711yescharacteristic
580C2×#121—21no—
581C2×#121C22×C13711yescharacteristic
582C2×#121C22×C13711yescharacteristic, complemented
583#520C22×C13711yescharacteristic
584C2×#117C22×C13711yescharacteristic, complemented
585#469—21no—
586#468—21no—
587#466—21no—
588#465—21no—
589#453—24no—
590#449—21no—
591#449—21no—
592#448—21no—
593#447—21no—
594#428C22×C13711yescharacteristic, complemented
595#421—24no—
596C2×#104C22×C13711yescharacteristic
597C2×#104C22×C13711yescharacteristic
598C2×#104C22×C13711yescharacteristic, complemented
599C2×#104C22×C13711yescharacteristic, complemented
600C2×#104C22×C13711yescharacteristic, complemented
601C2×#104C22×C13711yescharacteristic, complemented
602#418C22×C13711yescharacteristic, complemented
603#417C22×C13711yescharacteristic
604#417C22×C13711yescharacteristic, complemented
605#417C22×C13711yescharacteristic, complemented
606C2×#100C22×C13711yescharacteristic, complemented
607C2×#100C22×C13711yescharacteristic, complemented
608#407C22×C13711yescharacteristic, complemented
609#394—22no—
610#392—22no—
611#390C22×C13711yescharacteristic, complemented
612#390C22×C13711yescharacteristic, complemented
613#382C22×C13711yescharacteristic, complemented
614#343C22×C13711yescharacteristic, complemented
615#343C22×C13711yescharacteristic, complemented
616#339C22×C13711yescharacteristic, complemented
617#339C22×C13711yescharacteristic, complemented
618H(5,𝔽2)—22no—
619H(5,𝔽2)—22no—
620H(5,𝔽2)—41no—
621H(5,𝔽2)—41no—
622C2×#41—21no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—22no—
627C2×#41—22no—
628C2×#41—41no—
629C2×#41—41no—
630C2×#41D4×C13711yescharacteristic, complemented
631C2×#41D4×C13711yescharacteristic, complemented
632C2×#41C23×C13711yescharacteristic
633C2×#41C23×C13711yescharacteristic
634C2×#41C23×C13711yescharacteristic
635C22×Q8D4×C13711yescharacteristic, complemented
636C22×D4—21no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—21no—
640C22×D4—21no—
641C22×D4—21no—
642C22×D4—22no—
643C22×D4D4×C13712yes—
644C22×D4D4×C13711yescharacteristic, complemented
645C22×D4C23×C13711yescharacteristic
646C22×D4C23×C13711yescharacteristic
647C23×C4—21no—
648C23×C4C23×C13711yescharacteristic
649AGL(1,ℤ/8)—22no—
650AGL(1,ℤ/8)—22no—
651AGL(1,ℤ/8)—22no—
652AGL(1,ℤ/8)—41no—
653AGL(1,ℤ/8)—41no—
654AGL(1,ℤ/8)—41no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16—21no—
658C2×D8—21no—
659C2×D8—21no—
660C2×D8—21no—
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16C23×C13711yescharacteristic
665C2×M16C23×C13711yescharacteristic
666C2×M16C23×C13711yescharacteristic
667C2×M16C23×C13711yescharacteristic
668C22×C8—21no—
669#127—22no—
670#127—21no—
671#127—22no—
672#127—41no—
673#124—22no—
674#124—21no—
675#123—22no—
676#123—21no—
677C22⋊Q8—22no—
678C22⋊Q8—21no—
679C22⋊Q8—21no—
680C22⋊Q8D4×C13711yescharacteristic, complemented
681C22⋊Q8D4×C13711yescharacteristic, complemented
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—21no—
688#121—21no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—22no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—21no—
700#121D4×C13711yescharacteristic, complemented
701#121D4×C13711yescharacteristic, complemented
702#120—22no—
703#120—22no—
704#120—22no—
705#120—21no—
706#120—22no—
707C4×Q8—21no—
708C4×D4—22no—
709C4×D4—22no—
710C4×D4—21no—
711C4×D4—22no—
712C4×D4—21no—
713C4×D4—21no—
714#117—21no—
715#117—22no—
716#117—41no—
717#117C23×C13711yescharacteristic
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4C23×C13711yescharacteristic
721C2×C4⋊C4C23×C13711yescharacteristic
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4D4×C13712yes—
728C2×C42C23×C13711yescharacteristic
729C2×C42C23×C13711yescharacteristic
730#107—21no—
731#106—21no—
732#104—22no—
733#104—22no—
734#104—22no—
735#104—22no—
736#104—41no—
737#104D4×C13714yescomplemented
738#103—21no—
739#103—21no—
740#103—21no—
741#102—21no—
742#102—21no—
743#102—21no—
744#102—21no—
745#102—21no—
746#100—22no—
747#100—41no—
748C22⋊C8—21no—
749C22⋊C8—21no—
750#95—22no—
751C24—22no—
752C24—21no—
753C24—21no—
754C24C2×D4×C13712yes—
755C24C2×D4×C13711yescharacteristic
756#41—21no—
757#41—21no—
758#41—22no—
759#41—22no—
760#41—21no—
761#41—21no—
762#41—21no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—21no—
768#41—42no—
769#41—42no—
770#41—41no—
771#41—41no—
772#41—42no—
773#41—42no—
774#41—42no—
775#41—42no—
776#41—42no—
777#41—42no—
778#41C2×D4×C13712yes—
779#41#41×C13712yes—
780C2×Q8—21no—
781C2×Q8—22no—
782C2×Q8—41no—
783C2×Q8C2×D4×C13711yescharacteristic
784C2×Q8C2×D4×C13711yescharacteristic
785C2×Q8C2×D4×C13711yescharacteristic
786C2×D4—21no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—21no—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—41no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—41no—
825C2×D4—41no—
826C2×D4—82no—
827C2×D4—82no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—84no—
831C2×D4C2×D4×C13711yescharacteristic
832C2×D4C2×D4×C13711yescharacteristic
833C2×D4C2×D4×C13711yescharacteristic
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4C2×D4×C13711yescharacteristic
852C22×C4C2×D4×C13711yescharacteristic
853C22×C4C2×D4×C13711yescharacteristic
854C22×C4C2×D4×C13711yescharacteristic
855C22×C4C2×D4×C13711yescharacteristic
856C22×C4C2×D4×C13712yes—
857C22×C4C24×C13711yescharacteristic
858SD16—42no—
859SD16—42no—
860SD16—42no—
861D8—42no—
862D8—42no—
863D8—42no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—21no—
870M16—21no—
871M16—42no—
872M16C2×D4×C13712yescomplemented
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—42no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—42no—
887C4⋊C4C2×D4×C13711yescharacteristic
888C4⋊C4C2×D4×C13711yescharacteristic
889C22⋊C4—22no—
890C22⋊C4—22no—
891C22⋊C4—22no—
892C22⋊C4—22no—
893C22⋊C4—22no—
894C22⋊C4—21no—
895C22⋊C4—21no—
896C22⋊C4—21no—
897C22⋊C4—21no—
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—21no—
901C22⋊C4—42no—
902C22⋊C4—41no—
903C22⋊C4—41no—
904C22⋊C4—82no—
905C22⋊C4—82no—
906C42—22no—
907C42—21no—
908C42—21no—
909C42—21no—
910C42—21no—
911C42C2×D4×C13712yescomplemented
912C23—21no—
913C23—21no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—42no—
924C23—44no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—81no—
933C23—82no—
934C23—82no—
935C23#120×C13711yescharacteristic
936C23#120×C13711yescharacteristic
937C23C22×D4×C13711yescharacteristic
938Q8—21no—
939Q8—21no—
940Q8—21no—
941Q8—21no—
942Q8—21no—
943Q8—42no—
944Q8#121×C13712yes—
945D4—22no—
946D4—22no—
947D4—21no—
948D4—21no—
949D4—21no—
950D4—21no—
951D4—21no—
952D4—42no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—44no—
957D4—44no—
958D4—42no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—82no—
972D4—81no—
973D4—82no—
974D4—82no—
975D4—82no—
976D4—88no—
977D4—82no—
978D4—82no—
979D4#121×C13712yes—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—42no—
1000C2×C4—42no—
1001C2×C4—42no—
1002C2×C4—44no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—42no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—82no—
1016C2×C4#120×C13711yescharacteristic
1017C2×C4#120×C13711yescharacteristic
1018C2×C4C22×D4×C13711yescharacteristic
1019C2×C4C22×D4×C13711yescharacteristic
1020C2×C4C22×D4×C13711yescharacteristic
1021C2×C4C2×#41×C13711yescharacteristic
1022C2×C4H(5,𝔽2)×C13711yescharacteristic
1023C2×C4H(5,𝔽2)×C13711yescharacteristic
1024C8—22no—
1025C8—41no—
1026C8—41no—
1027C8—41no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—22no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—42no—
1042C22—42no—
1043C22—41no—
1044C22—41no—
1045C22—41no—
1046C22—42no—
1047C22—41no—
1048C22—81no—
1049C22—81no—
1050C22—82no—
1051C22—82no—
1052C22—82no—
1053C22—82no—
1054C22—84no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—164no—
1059C22C2×#120×C13711yescharacteristic
1060C22D42×C13711yescharacteristic
1061C22#546×C13711yescharacteristic
1062C4—21no—
1063C4—21no—
1064C4—22no—
1065C4—42no—
1066C4—41no—
1067C4—41no—
1068C4—42no—
1069C4—41no—
1070C4—41no—
1071C4—81no—
1072C4—81no—
1073C4C2×#121×C13711yescharacteristic
1074C4#534×C13711yescharacteristic
1075C4D42×C13711yescharacteristic
1076C4#546×C13711yescharacteristic
1077C2—21no—
1078C2—21no—
1079C2—41no—
1080C2—41no—
1081C2—42no—
1082C2—81no—
1083C2—82no—
1084C2—81no—
1085C2—161no—
1086C2#2410×C13711yescharacteristic
1087C2#3019×C13711yescharacteristic
1088C2#3021×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
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
1. #3488×C137C2semidirect
2. #3055×C137C2semidirect
3. C2×#453×C137C2semidirect
4. #3006×C137C2semidirect
5. C2×#421×C137C2semidirect
6. #2619×C137C2semidirect
7. #2040×C137C2semidirect
8. #2037×C137C2semidirect
9. #2006×C137C2semidirect
10. #2002×C137C2semidirect
11. #1900×C137C2semidirect
12. #1897×C137C2semidirect
13. #1883×C137C2semidirect
14. #1860×C137C2semidirect
15. #1792×C137C2semidirect
19. C2×AGL(1,ℤ/8)×C137C22semidirect
20. C2×AGL(1,ℤ/8)×C137C22semidirect
21. C22×M16×C137C22semidirect
32. C2×#127×C137C22semidirect
37. C2×#121×C137C22semidirect
39. C2×#117×C137C22semidirect
49. #428×C137C22semidirect
53. C2×#104×C137C22semidirect
54. C2×#104×C137C22semidirect
55. C2×#104×C137C22semidirect
56. C2×#104×C137C22semidirect
57. #418×C137C22semidirect
59. #417×C137C22semidirect
60. #417×C137C22semidirect
61. C2×#100×C137C22semidirect
62. C2×#100×C137C22semidirect
63. #407×C137C22semidirect
66. #390×C137C22semidirect
67. #390×C137C22semidirect
68. #382×C137C22semidirect
69. #343×C137C22semidirect
70. #343×C137C22semidirect
71. #339×C137C22semidirect
72. #339×C137C22semidirect
85. C2×#41×C137D4semidirect
86. C2×#41×C137D4semidirect
90. C22×Q8×C137D4semidirect
99. C22×D4×C137D4semidirect
135. C22⋊Q8×C137D4semidirect
136. C22⋊Q8×C137D4semidirect
155. #121×C137D4semidirect
156. #121×C137D4semidirect
192. #104×C137D4semidirect
327. M16×C137C2×D4semidirect
366. C42×C137C2×D4semidirect
544. #24468C137direct (N × H)
545. C137#24468direct (N × H)
546. #3488C2×C137semidirect
547. #3055C2×C137semidirect
548. C2×#453C2×C137semidirect
549. #3006C2×C137semidirect
550. C2×#421C2×C137semidirect
551. #2619C2×C137semidirect
552. #2040C2×C137semidirect
553. #2037C2×C137semidirect
554. #2006C2×C137semidirect
555. #2002C2×C137semidirect
556. #1900C2×C137semidirect
557. #1897C2×C137semidirect
558. #1883C2×C137semidirect
559. #1860C2×C137semidirect
560. #1792C2×C137semidirect
564. C2×AGL(1,ℤ/8)C22×C137semidirect
565. C2×AGL(1,ℤ/8)C22×C137semidirect
566. C22×M16C22×C137semidirect
577. C2×#127C22×C137semidirect
582. C2×#121C22×C137semidirect
584. C2×#117C22×C137semidirect
594. #428C22×C137semidirect
598. C2×#104C22×C137semidirect
599. C2×#104C22×C137semidirect
600. C2×#104C22×C137semidirect
601. C2×#104C22×C137semidirect
602. #418C22×C137semidirect
604. #417C22×C137semidirect
605. #417C22×C137semidirect
606. C2×#100C22×C137semidirect
607. C2×#100C22×C137semidirect
608. #407C22×C137semidirect
611. #390C22×C137semidirect
612. #390C22×C137semidirect
613. #382C22×C137semidirect
614. #343C22×C137semidirect
615. #343C22×C137semidirect
616. #339C22×C137semidirect
617. #339C22×C137semidirect
630. C2×#41D4×C137semidirect
631. C2×#41D4×C137semidirect
635. C22×Q8D4×C137semidirect
644. C22×D4D4×C137semidirect
680. C22⋊Q8D4×C137semidirect
681. C22⋊Q8D4×C137semidirect
700. #121D4×C137semidirect
701. #121D4×C137semidirect
737. #104D4×C137semidirect
872. M16C2×D4×C137semidirect
911. C42C2×D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3488×C1372
#3055×C1372
C2×#453×C1372
#3006×C1372
C2×#421×C1372
#2619×C1372
#2040×C1372
#2037×C1372
#2006×C1372
#2002×C1372
#1900×C1372
#1897×C1372
#1883×C1372
#1860×C1372
#1792×C1372
#24468137