Finite Group Databasebeta

← C137×#24469 #46873855

Subgroups — C137×#24469 #46873855

Order 35072.

1402 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3489×C137C211yesmaximal, characteristic, complemented
2#3055×C137C211yesmaximal, characteristic, complemented
3C2×#454×C137C211yesmaximal, characteristic, complemented
4#3006×C137C211yesmaximal, characteristic, complemented
5C2×#421×C137C211yesmaximal, characteristic, complemented
6#2620×C137C211yesmaximal, characteristic, complemented
7#2039×C137C211yesmaximal, characteristic, complemented
8#2038×C137C211yesmaximal, characteristic, complemented
9#2006×C137C211yesmaximal, characteristic, complemented
10#2003×C137C211yesmaximal, characteristic, complemented
11#1901×C137C211yesmaximal, characteristic, complemented
12#1897×C137C211yesmaximal, characteristic, complemented
13#1883×C137C211yesmaximal, characteristic, complemented
14#1859×C137C211yesmaximal, characteristic, complemented
15#1793×C137C211yesmaximal, characteristic, complemented
16C2×2−1+4×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C137C2211yescharacteristic, complemented
21C22×M16×C137C2211yescharacteristic
22D4×Q8×C137—21no—
23#548×C137—21no—
24#547×C137—21no—
25#547×C137—22no—
26#546×C137—21no—
27#546×C137—22no—
28#537×C137—21no—
29#537×C137C2211yescharacteristic
30#536×C137—21no—
31#536×C137C2211yescharacteristic
32C2×#124×C137C2211yescharacteristic, complemented
33#525×C137—21no—
34#525×C137C2211yescharacteristic
35C2×C22⋊Q8×C137—21no—
36C2×C22⋊Q8×C137C2211yescharacteristic
37C2×#121×C137C2211yescharacteristic
38#520×C137C2211yescharacteristic
39C2×#117×C137C2211yescharacteristic
40#469×C137—21no—
41#468×C137—21no—
42#466×C137—21no—
43#465×C137—21no—
44#454×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
54C2×#104×C137C2211yescharacteristic
55C2×#104×C137C2211yescharacteristic, complemented
56C2×#104×C137C2211yescharacteristic, complemented
57#418×C137C2211yescharacteristic, complemented
58#417×C137C2211yescharacteristic
59#417×C137C2211yescharacteristic
60#417×C137C2211yescharacteristic, complemented
61C2×#101×C137C2211yescharacteristic, complemented
62C2×#101×C137C2211yescharacteristic, complemented
63#407×C137C2211yescharacteristic
64#396×C137—22no—
65#394×C137—22no—
66#391×C137C2211yescharacteristic, complemented
67#390×C137C2211yescharacteristic, complemented
68#384×C137C2211yescharacteristic, complemented
69#343×C137C2211yescharacteristic, complemented
70#343×C137C2211yescharacteristic, complemented
71#339×C137C2211yescharacteristic, complemented
72#339×C137C2211yescharacteristic, complemented
732−1+4×C137—22no—
742−1+4×C137—22no—
752−1+4×C137—41no—
762−1+4×C137—41no—
77C2×#41×C137—21no—
78C2×#41×C137—21no—
79C2×#41×C137—21no—
80C2×#41×C137—22no—
81C2×#41×C137—21no—
82C2×#41×C137—22no—
83C2×#41×C137—22no—
84C2×#41×C137—41no—
85C2×#41×C137—41no—
86C2×#41×C137D411yescharacteristic
87C2×#41×C137D411yescharacteristic
88C2×#41×C137C2311yescharacteristic
89C2×#41×C137C2311yescharacteristic
90C2×#41×C137C2311yescharacteristic
91C22×Q8×C137—21no—
92C22×Q8×C137—21no—
93C22×Q8×C137D411yescharacteristic
94C22×Q8×C137C2311yescharacteristic
95C22×D4×C137—21no—
96C22×D4×C137—21no—
97C22×D4×C137D411yescharacteristic
98C22×D4×C137C2311yescharacteristic
99C23×C4×C137—21no—
100C23×C4×C137C2311yescharacteristic
101AGL(1,ℤ/8)×C137—22no—
102AGL(1,ℤ/8)×C137—22no—
103AGL(1,ℤ/8)×C137—22no—
104AGL(1,ℤ/8)×C137—41no—
105AGL(1,ℤ/8)×C137—41no—
106AGL(1,ℤ/8)×C137—41no—
107C2×SD16×C137—21no—
108C2×SD16×C137—21no—
109C2×SD16×C137—21no—
110C2×D8×C137—21no—
111C2×D8×C137—21no—
112C2×D8×C137—21no—
113C2×M16×C137—21no—
114C2×M16×C137—22no—
115C2×M16×C137—41no—
116C2×M16×C137C2311yescharacteristic
117C2×M16×C137C2311yescharacteristic
118C2×M16×C137C2311yescharacteristic
119C2×M16×C137C2311yescharacteristic
120C22×C8×C137—21no—
121C4⋊Q8×C137—22no—
122C4⋊Q8×C137—21no—
123#124×C137—22no—
124#124×C137—21no—
125#124×C137—22no—
126#124×C137—41no—
127#123×C137—22no—
128#123×C137—22no—
129#123×C137—22no—
130#123×C137—21no—
131#123×C137—22no—
132C22⋊Q8×C137—22no—
133C22⋊Q8×C137—22no—
134C22⋊Q8×C137—22no—
135C22⋊Q8×C137—21no—
136C22⋊Q8×C137—21no—
137C22⋊Q8×C137—21no—
138C22⋊Q8×C137—21no—
139C22⋊Q8×C137—21no—
140C22⋊Q8×C137—21no—
141C22⋊Q8×C137—21no—
142C22⋊Q8×C137—21no—
143C22⋊Q8×C137D411yescharacteristic
144C22⋊Q8×C137D411yescharacteristic
145#121×C137—22no—
146#121×C137—22no—
147#121×C137—22no—
148#121×C137—21no—
149#121×C137—21no—
150#121×C137—22no—
151#121×C137—21no—
152#121×C137—21no—
153#121×C137—21no—
154#121×C137—21no—
155#121×C137D411yescharacteristic
156#121×C137D411yescharacteristic
157#120×C137—22no—
158#120×C137—21no—
159C4×Q8×C137—21no—
160C4×D4×C137—22no—
161C4×D4×C137—22no—
162C4×D4×C137—21no—
163C4×D4×C137—22no—
164C4×D4×C137—21no—
165C4×D4×C137—21no—
166#117×C137—21no—
167#117×C137—22no—
168#117×C137—41no—
169#117×C137C2311yescharacteristic
170C2×C4⋊C4×C137—22no—
171C2×C4⋊C4×C137—21no—
172C2×C4⋊C4×C137—21no—
173C2×C4⋊C4×C137—22no—
174C2×C4⋊C4×C137D412yes—
175C2×C4⋊C4×C137C2311yescharacteristic
176C2×C4⋊C4×C137C2311yescharacteristic
177C2×C22⋊C4×C137—22no—
178C2×C22⋊C4×C137—21no—
179C2×C22⋊C4×C137—22no—
180C2×C22⋊C4×C137—21no—
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#101×C137—22no—
202#101×C137—41no—
203C22⋊C8×C137—21no—
204C22⋊C8×C137—21no—
205#95×C137—22no—
206C24×C137—21no—
207C24×C137—21no—
208C24×C137C2×D411yescharacteristic
209#41×C137—21no—
210#41×C137—21no—
211#41×C137—22no—
212#41×C137—22no—
213#41×C137—21no—
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—42no—
222#41×C137—42no—
223#41×C137—41no—
224#41×C137—41no—
225#41×C137—42no—
226#41×C137—42no—
227#41×C137—42no—
228#41×C137—42no—
229#41×C137—44no—
230#41×C137—44no—
231#41×C137—42no—
232#41×C137—42no—
233#41×C137C2×D412yes—
234#41×C137#4112yes—
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—21no—
243C2×Q8×C137—22no—
244C2×Q8×C137—41no—
245C2×Q8×C137—42no—
246C2×Q8×C137—42no—
247C2×Q8×C137—42no—
248C2×Q8×C137—42no—
249C2×Q8×C137C2×D411yescharacteristic
250C2×Q8×C137C2×D411yescharacteristic
251C2×Q8×C137C2×D411yescharacteristic
252C2×D4×C137—21no—
253C2×D4×C137—22no—
254C2×D4×C137—22no—
255C2×D4×C137—21no—
256C2×D4×C137—21no—
257C2×D4×C137—21no—
258C2×D4×C137—21no—
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—21no—
269C2×D4×C137—41no—
270C2×D4×C137—42no—
271C2×D4×C137—42no—
272C2×D4×C137—41no—
273C2×D4×C137—41no—
274C2×D4×C137—82no—
275C2×D4×C137C2×D411yescharacteristic
276C2×D4×C137C2×D411yescharacteristic
277C2×D4×C137C2×D411yescharacteristic
278C22×C4×C137—21no—
279C22×C4×C137—21no—
280C22×C4×C137—21no—
281C22×C4×C137—21no—
282C22×C4×C137—21no—
283C22×C4×C137—22no—
284C22×C4×C137—22no—
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—21no—
292C22×C4×C137—21no—
293C22×C4×C137—21no—
294C22×C4×C137—42no—
295C22×C4×C137—42no—
296C22×C4×C137C2×D412yes—
297C22×C4×C137C2×D411yescharacteristic
298C22×C4×C137C2×D411yescharacteristic
299C22×C4×C137C2×D411yescharacteristic
300C22×C4×C137C2×D411yescharacteristic
301C22×C4×C137C2×D411yescharacteristic
302C22×C4×C137C2×D412yes—
303C22×C4×C137C2411yescharacteristic
304SD16×C137—42no—
305SD16×C137—42no—
306SD16×C137—42no—
307D8×C137—42no—
308D8×C137—42no—
309D8×C137—42no—
310M16×C137—21no—
311M16×C137—21no—
312M16×C137—21no—
313M16×C137—21no—
314M16×C137—21no—
315M16×C137—21no—
316M16×C137—21no—
317M16×C137—42no—
318M16×C137C2×D412yes—
319C2×C8×C137—21no—
320C2×C8×C137—21no—
321C2×C8×C137—21no—
322C2×C8×C137—21no—
323C2×C8×C137—42no—
324C4⋊C4×C137—22no—
325C4⋊C4×C137—22no—
326C4⋊C4×C137—22no—
327C4⋊C4×C137—22no—
328C4⋊C4×C137—21no—
329C4⋊C4×C137—22no—
330C4⋊C4×C137—22no—
331C4⋊C4×C137—21no—
332C4⋊C4×C137—21no—
333C4⋊C4×C137—21no—
334C4⋊C4×C137—21no—
335C4⋊C4×C137—21no—
336C4⋊C4×C137—42no—
337C4⋊C4×C137—82no—
338C4⋊C4×C137C2×D411yescharacteristic
339C4⋊C4×C137C2×D411yescharacteristic
340C22⋊C4×C137—22no—
341C22⋊C4×C137—22no—
342C22⋊C4×C137—22no—
343C22⋊C4×C137—22no—
344C22⋊C4×C137—22no—
345C22⋊C4×C137—21no—
346C22⋊C4×C137—22no—
347C22⋊C4×C137—22no—
348C22⋊C4×C137—21no—
349C22⋊C4×C137—21no—
350C22⋊C4×C137—21no—
351C22⋊C4×C137—21no—
352C22⋊C4×C137—44no—
353C22⋊C4×C137—42no—
354C22⋊C4×C137—41no—
355C22⋊C4×C137—41no—
356C22⋊C4×C137—82no—
357C42×C137—22no—
358C42×C137—21no—
359C42×C137—21no—
360C42×C137—21no—
361C42×C137—21no—
362C42×C137C2×D412yes—
363C23×C137—21no—
364C23×C137—21no—
365C23×C137—21no—
366C23×C137—21no—
367C23×C137—21no—
368C23×C137—41no—
369C23×C137—41no—
370C23×C137—42no—
371C23×C137—42no—
372C23×C137—42no—
373C23×C137—42no—
374C23×C137—41no—
375C23×C137—41no—
376C23×C137—41no—
377C23×C137—81no—
378C23×C137#12011yescharacteristic
379C23×C137#12011yescharacteristic
380C23×C137C22×D411yescharacteristic
381Q8×C137—21no—
382Q8×C137—21no—
383Q8×C137—21no—
384Q8×C137—21no—
385Q8×C137—21no—
386Q8×C137—42no—
387Q8×C137—44no—
388Q8×C137—41no—
389Q8×C137—41no—
390Q8×C137—41no—
391Q8×C137—41no—
392Q8×C137#12112yes—
393D4×C137—22no—
394D4×C137—22no—
395D4×C137—21no—
396D4×C137—21no—
397D4×C137—21no—
398D4×C137—21no—
399D4×C137—21no—
400D4×C137—42no—
401D4×C137—42no—
402D4×C137—42no—
403D4×C137—42no—
404D4×C137—44no—
405D4×C137—41no—
406D4×C137—41no—
407D4×C137—41no—
408D4×C137—41no—
409D4×C137—41no—
410D4×C137—41no—
411D4×C137—41no—
412D4×C137—41no—
413D4×C137—81no—
414D4×C137—82no—
415D4×C137—82no—
416D4×C137—82no—
417D4×C137#12112yes—
418C2×C4×C137—21no—
419C2×C4×C137—21no—
420C2×C4×C137—21no—
421C2×C4×C137—21no—
422C2×C4×C137—21no—
423C2×C4×C137—21no—
424C2×C4×C137—21no—
425C2×C4×C137—21no—
426C2×C4×C137—21no—
427C2×C4×C137—22no—
428C2×C4×C137—21no—
429C2×C4×C137—21no—
430C2×C4×C137—22no—
431C2×C4×C137—21no—
432C2×C4×C137—22no—
433C2×C4×C137—21no—
434C2×C4×C137—21no—
435C2×C4×C137—22no—
436C2×C4×C137—21no—
437C2×C4×C137—22no—
438C2×C4×C137—22no—
439C2×C4×C137—22no—
440C2×C4×C137—42no—
441C2×C4×C137—42no—
442C2×C4×C137—42no—
443C2×C4×C137—44no—
444C2×C4×C137—41no—
445C2×C4×C137—41no—
446C2×C4×C137—44no—
447C2×C4×C137—41no—
448C2×C4×C137—41no—
449C2×C4×C137—41no—
450C2×C4×C137—41no—
451C2×C4×C137—42no—
452C2×C4×C137—41no—
453C2×C4×C137—42no—
454C2×C4×C137—41no—
455C2×C4×C137—41no—
456C2×C4×C137—41no—
457C2×C4×C137—82no—
458C2×C4×C137#12011yescharacteristic
459C2×C4×C137#12011yescharacteristic
460C2×C4×C137C22×D411yescharacteristic
461C2×C4×C137C22×D411yescharacteristic
462C2×C4×C137C22×D411yescharacteristic
463C2×C4×C137C2×#4111yescharacteristic
464C2×C4×C137H(5,𝔽2)11yescharacteristic
465C2×C4×C137H(5,𝔽2)11yescharacteristic
466C8×C137—22no—
467C8×C137—41no—
468C8×C137—41no—
469C8×C137—41no—
470C22×C137—21no—
471C22×C137—21no—
472C22×C137—21no—
473C22×C137—21no—
474C22×C137—22no—
475C22×C137—21no—
476C22×C137—21no—
477C22×C137—21no—
478C22×C137—21no—
479C22×C137—41no—
480C22×C137—41no—
481C22×C137—41no—
482C22×C137—41no—
483C22×C137—41no—
484C22×C137—41no—
485C22×C137—41no—
486C22×C137—41no—
487C22×C137—81no—
488C22×C137—81no—
489C22×C137—82no—
490C22×C137—82no—
491C22×C137—84no—
492C22×C137—81no—
493C22×C137—81no—
494C22×C137—81no—
495C22×C137C2×#12011yescharacteristic
496C22×C137D4211yescharacteristic
497C22×C137#54611yescharacteristic
498C4×C137—21no—
499C4×C137—21no—
500C4×C137—22no—
501C4×C137—42no—
502C4×C137—42no—
503C4×C137—41no—
504C4×C137—41no—
505C4×C137—41no—
506C4×C137—42no—
507C4×C137—41no—
508C4×C137—81no—
509C4×C137—81no—
510C4×C137C2×#12111yescharacteristic
511C4×C137#53411yescharacteristic
512C4×C137D4211yescharacteristic
513C4×C137#54611yescharacteristic
514C2×C137—21no—
515C2×C137—21no—
516C2×C137—41no—
517C2×C137—41no—
518C2×C137—42no—
519C2×C137—81no—
520C2×C137—81no—
521C2×C137—161no—
522C2×C137#241011yescharacteristic
523C2×C137#302011yescharacteristic
524C2×C137#302111yescharacteristic
525#24469C13711yesmaximal, characteristic, direct product factor, Sylow
526C137#2446911yescharacteristic, direct product factor, Sylow
527#3489C2×C13711yescharacteristic, complemented
528#3055C2×C13711yescharacteristic, complemented
529C2×#454C2×C13711yescharacteristic, complemented
530#3006C2×C13711yescharacteristic, complemented
531C2×#421C2×C13711yescharacteristic, complemented
532#2620C2×C13711yescharacteristic, complemented
533#2039C2×C13711yescharacteristic, complemented
534#2038C2×C13711yescharacteristic, complemented
535#2006C2×C13711yescharacteristic, complemented
536#2003C2×C13711yescharacteristic, complemented
537#1901C2×C13711yescharacteristic, complemented
538#1897C2×C13711yescharacteristic, complemented
539#1883C2×C13711yescharacteristic, complemented
540#1859C2×C13711yescharacteristic, complemented
541#1793C2×C13711yescharacteristic, complemented
542C2×2−1+4C22×C13711yescharacteristic
543C22×#41C22×C13711yescharacteristic
544C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
545C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
546C2×AGL(1,ℤ/8)C22×C13711yescharacteristic, complemented
547C22×M16C22×C13711yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C13711yescharacteristic
556#536—21no—
557#536C22×C13711yescharacteristic
558C2×#124C22×C13711yescharacteristic, complemented
559#525—21no—
560#525C22×C13711yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C13711yescharacteristic
563C2×#121C22×C13711yescharacteristic
564#520C22×C13711yescharacteristic
565C2×#117C22×C13711yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C13711yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C13711yescharacteristic
578C2×#104C22×C13711yescharacteristic
579C2×#104C22×C13711yescharacteristic
580C2×#104C22×C13711yescharacteristic
581C2×#104C22×C13711yescharacteristic, complemented
582C2×#104C22×C13711yescharacteristic, complemented
583#418C22×C13711yescharacteristic, complemented
584#417C22×C13711yescharacteristic
585#417C22×C13711yescharacteristic
586#417C22×C13711yescharacteristic, complemented
587C2×#101C22×C13711yescharacteristic, complemented
588C2×#101C22×C13711yescharacteristic, complemented
589#407C22×C13711yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C13711yescharacteristic, complemented
593#390C22×C13711yescharacteristic, complemented
594#384C22×C13711yescharacteristic, complemented
595#343C22×C13711yescharacteristic, complemented
596#343C22×C13711yescharacteristic, complemented
597#339C22×C13711yescharacteristic, complemented
598#339C22×C13711yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C13711yescharacteristic
613C2×#41D4×C13711yescharacteristic
614C2×#41C23×C13711yescharacteristic
615C2×#41C23×C13711yescharacteristic
616C2×#41C23×C13711yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C13711yescharacteristic
620C22×Q8C23×C13711yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C13711yescharacteristic
624C22×D4C23×C13711yescharacteristic
625C23×C4—21no—
626C23×C4C23×C13711yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C13711yescharacteristic
643C2×M16C23×C13711yescharacteristic
644C2×M16C23×C13711yescharacteristic
645C2×M16C23×C13711yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C13711yescharacteristic
670C22⋊Q8D4×C13711yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C13711yescharacteristic
682#121D4×C13711yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C13711yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C13712yes—
701C2×C4⋊C4C23×C13711yescharacteristic
702C2×C4⋊C4C23×C13711yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C13712yes—
709C2×C42C23×C13711yescharacteristic
710C2×C42C23×C13711yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C13714yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C13711yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C13712yes—
760#41#41×C13712yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C13711yescharacteristic
776C2×Q8C2×D4×C13711yescharacteristic
777C2×Q8C2×D4×C13711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C13711yescharacteristic
802C2×D4C2×D4×C13711yescharacteristic
803C2×D4C2×D4×C13711yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C13712yes—
823C22×C4C2×D4×C13711yescharacteristic
824C22×C4C2×D4×C13711yescharacteristic
825C22×C4C2×D4×C13711yescharacteristic
826C22×C4C2×D4×C13711yescharacteristic
827C22×C4C2×D4×C13711yescharacteristic
828C22×C4C2×D4×C13712yes—
829C22×C4C24×C13711yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C13712yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C13711yescharacteristic
865C4⋊C4C2×D4×C13711yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C13712yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C13711yescharacteristic
905C23#120×C13711yescharacteristic
906C23C22×D4×C13711yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C13712yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C13712yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C13711yescharacteristic
985C2×C4#120×C13711yescharacteristic
986C2×C4C22×D4×C13711yescharacteristic
987C2×C4C22×D4×C13711yescharacteristic
988C2×C4C22×D4×C13711yescharacteristic
989C2×C4C2×#41×C13711yescharacteristic
990C2×C4H(5,𝔽2)×C13711yescharacteristic
991C2×C4H(5,𝔽2)×C13711yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C13711yescharacteristic
1022C22D42×C13711yescharacteristic
1023C22#546×C13711yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C13711yescharacteristic
1037C4#534×C13711yescharacteristic
1038C4D42×C13711yescharacteristic
1039C4#546×C13711yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2#2410×C13711yescharacteristic
1049C2#3020×C13711yescharacteristic
1050C2#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. #3489×C137C2semidirect
2. #3055×C137C2semidirect
3. C2×#454×C137C2semidirect
4. #3006×C137C2semidirect
5. C2×#421×C137C2semidirect
6. #2620×C137C2semidirect
7. #2039×C137C2semidirect
8. #2038×C137C2semidirect
9. #2006×C137C2semidirect
10. #2003×C137C2semidirect
11. #1901×C137C2semidirect
12. #1897×C137C2semidirect
13. #1883×C137C2semidirect
14. #1859×C137C2semidirect
15. #1793×C137C2semidirect
20. C2×AGL(1,ℤ/8)×C137C22semidirect
32. C2×#124×C137C22semidirect
49. #428×C137C22semidirect
55. C2×#104×C137C22semidirect
56. C2×#104×C137C22semidirect
57. #418×C137C22semidirect
60. #417×C137C22semidirect
61. C2×#101×C137C22semidirect
62. C2×#101×C137C22semidirect
66. #391×C137C22semidirect
67. #390×C137C22semidirect
68. #384×C137C22semidirect
69. #343×C137C22semidirect
70. #343×C137C22semidirect
71. #339×C137C22semidirect
72. #339×C137C22semidirect
192. #104×C137D4semidirect
525. #24469C137direct (N × H)
526. C137#24469direct (N × H)
527. #3489C2×C137semidirect
528. #3055C2×C137semidirect
529. C2×#454C2×C137semidirect
530. #3006C2×C137semidirect
531. C2×#421C2×C137semidirect
532. #2620C2×C137semidirect
533. #2039C2×C137semidirect
534. #2038C2×C137semidirect
535. #2006C2×C137semidirect
536. #2003C2×C137semidirect
537. #1901C2×C137semidirect
538. #1897C2×C137semidirect
539. #1883C2×C137semidirect
540. #1859C2×C137semidirect
541. #1793C2×C137semidirect
546. C2×AGL(1,ℤ/8)C22×C137semidirect
558. C2×#124C22×C137semidirect
575. #428C22×C137semidirect
581. C2×#104C22×C137semidirect
582. C2×#104C22×C137semidirect
583. #418C22×C137semidirect
586. #417C22×C137semidirect
587. C2×#101C22×C137semidirect
588. C2×#101C22×C137semidirect
592. #391C22×C137semidirect
593. #390C22×C137semidirect
594. #384C22×C137semidirect
595. #343C22×C137semidirect
596. #343C22×C137semidirect
597. #339C22×C137semidirect
598. #339C22×C137semidirect
718. #104D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3489×C1372
#3055×C1372
C2×#454×C1372
#3006×C1372
C2×#421×C1372
#2620×C1372
#2039×C1372
#2038×C1372
#2006×C1372
#2003×C1372
#1901×C1372
#1897×C1372
#1883×C1372
#1859×C1372
#1793×C1372
#24469137