Finite Group Databasebeta

← C137×#18414 #46867800

Subgroups — C137×#18414 #46867800

Order 35072.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C137C211yesmaximal, characteristic, complemented
2#3194×C137C211yesmaximal, characteristic, complemented
3#3186×C137C211yesmaximal, characteristic, complemented
4#2661×C137C211yesmaximal, characteristic, complemented
5#1612×C137C211yesmaximal, characteristic, complemented
6#1610×C137C211yesmaximal, characteristic, complemented
7#1609×C137C211yesmaximal, characteristic, complemented
8#1607×C137C211yesmaximal, characteristic, complemented
9#1600×C137C211yesmaximal, characteristic, complemented
10#1598×C137C211yesmaximal, characteristic, complemented
11#1597×C137C211yesmaximal, characteristic, complemented
12#1595×C137C211yesmaximal, characteristic, complemented
13#1507×C137C211yesmaximal, characteristic, complemented
14#1501×C137C211yesmaximal, characteristic, complemented
15#1468×C137C211yesmaximal, characteristic, complemented
16#562×C137—21no—
17#560×C137—21no—
18#553×C137—21no—
19#551×C137—21no—
20#546×C137—21no—
21#546×C137—21no—
22#546×C137—21no—
23D42×C137—21no—
24#540×C137—21no—
25#539×C137—21no—
26#539×C137C2211yescharacteristic
27#538×C137—21no—
28#538×C137C2211yescharacteristic
29#537×C137C2211yescharacteristic
30#534×C137—21no—
31#534×C137C2211yescharacteristic
32#525×C137C2211yescharacteristic
33C2×#123×C137C2211yescharacteristic
34C2×#121×C137C2211yescharacteristic
35C2×#121×C137C2211yescharacteristic, complemented
36#483×C137C2211yescharacteristic, complemented
37#482×C137—21no—
38#480×C137—21no—
39#480×C137C2211yescharacteristic
40#480×C137C2211yescharacteristic, complemented
41#480×C137C2211yescharacteristic, complemented
42#469×C137—21no—
43#468×C137—21no—
44#466×C137—21no—
45#466×C137—21no—
46#450×C137C2211yescharacteristic, complemented
47#449×C137—21no—
48#447×C137—21no—
49#447×C137C2211yescharacteristic
50#447×C137C2211yescharacteristic, complemented
51#447×C137C2211yescharacteristic, complemented
52#407×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#398×C137C2211yescharacteristic, complemented
55#397×C137C2211yescharacteristic, complemented
56#394×C137—21no—
57#394×C137C2211yescharacteristic, complemented
58#392×C137—21no—
59#392×C137C2211yescharacteristic, complemented
60#390×C137—21no—
61#388×C137—21no—
62C4×C22⋊C4×C137C2211yescharacteristic, complemented
63#328×C137C2211yescharacteristic, complemented
64#328×C137C2211yescharacteristic, complemented
65#327×C137C2211yescharacteristic
66#327×C137C2211yescharacteristic
67#327×C137C2211yescharacteristic, complemented
68#327×C137C2211yescharacteristic, complemented
69#327×C137C2211yescharacteristic, complemented
70#327×C137C2211yescharacteristic, complemented
71#324×C137C2211yescharacteristic, complemented
72#324×C137C2211yescharacteristic, complemented
73#323×C137C2211yescharacteristic, complemented
74#323×C137C2211yescharacteristic, complemented
75C2×#41×C137—21no—
76C2×#41×C137D411yescharacteristic, complemented
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137D411yescharacteristic
83C22×D4×C137D411yescharacteristic, complemented
84C22×D4×C137C2311yescharacteristic
85C23×C4×C137C2311yescharacteristic
86C2×SD16×C137—21no—
87C2×D8×C137—21no—
88C2×D8×C137—21no—
89C2×D8×C137—21no—
90C2×M16×C137—21no—
91C22×C8×C137—21no—
92#127×C137—21no—
93#126×C137—21no—
94#126×C137—21no—
95#126×C137—21no—
96#126×C137—21no—
97#125×C137—21no—
98#125×C137—21no—
99#124×C137—21no—
100#124×C137—21no—
101#124×C137—21no—
102#123×C137—21no—
103#123×C137—21no—
104#123×C137—21no—
105#123×C137—21no—
106#123×C137—21no—
107#123×C137—21no—
108#123×C137—21no—
109#123×C137—21no—
110#123×C137—21no—
111#123×C137—21no—
112#123×C137—21no—
113#123×C137—21no—
114#123×C137—21no—
115#123×C137—21no—
116C22⋊Q8×C137—21no—
117C22⋊Q8×C137—21no—
118C22⋊Q8×C137—21no—
119C22⋊Q8×C137—21no—
120C22⋊Q8×C137—21no—
121C22⋊Q8×C137D411yescharacteristic, complemented
122C22⋊Q8×C137C2311yescharacteristic
123#121×C137—21no—
124#121×C137—21no—
125#121×C137—21no—
126#121×C137—21no—
127#121×C137—21no—
128#121×C137—21no—
129#121×C137—21no—
130#121×C137—21no—
131#121×C137—21no—
132#121×C137—21no—
133#121×C137—21no—
134#121×C137—21no—
135#121×C137—21no—
136#121×C137—21no—
137#121×C137—21no—
138#121×C137—21no—
139#121×C137—21no—
140#121×C137—21no—
141#121×C137—21no—
142#121×C137D411yescharacteristic, complemented
143#121×C137D411yescharacteristic, complemented
144#121×C137D411yescharacteristic, complemented
145#121×C137C2311yescharacteristic
146#121×C137C2311yescharacteristic
147#121×C137C2311yescharacteristic
148#120×C137—21no—
149#120×C137—21no—
150#120×C137—21no—
151#120×C137—21no—
152#120×C137—21no—
153#120×C137—21no—
154#120×C137—21no—
155#120×C137—21no—
156C4×D4×C137—21no—
157C4×D4×C137—21no—
158C4×D4×C137—21no—
159C4×D4×C137—21no—
160C4×D4×C137—21no—
161C4×D4×C137—21no—
162C4×D4×C137—21no—
163C4×D4×C137—21no—
164#117×C137—21no—
165#117×C137D411yescharacteristic, complemented
166C2×C4⋊C4×C137—21no—
167C2×C4⋊C4×C137D411yescharacteristic
168C2×C4⋊C4×C137D411yescharacteristic, complemented
169C2×C4⋊C4×C137C2311yescharacteristic
170C2×C4⋊C4×C137C2311yescharacteristic
171C2×C22⋊C4×C137—21no—
172C2×C22⋊C4×C137—21no—
173C2×C22⋊C4×C137—21no—
174C2×C22⋊C4×C137—21no—
175C2×C22⋊C4×C137—21no—
176C2×C22⋊C4×C137—21no—
177C2×C22⋊C4×C137—21no—
178C2×C22⋊C4×C137—21no—
179C2×C22⋊C4×C137—21no—
180C2×C22⋊C4×C137D411yescharacteristic
181C2×C22⋊C4×C137D411yescharacteristic
182C2×C22⋊C4×C137C2311yescharacteristic
183C2×C42×C137—21no—
184#107×C137—21no—
185#107×C137—21no—
186#107×C137—21no—
187#106×C137—21no—
188#103×C137—21no—
189#102×C137—21no—
190#102×C137—21no—
191#102×C137—21no—
192#102×C137—21no—
193#102×C137—21no—
194#102×C137—21no—
195#102×C137—21no—
196C22⋊C8×C137—21no—
197C22⋊C8×C137—21no—
198C22⋊C8×C137C2311yescharacteristic
199C22⋊C8×C137C2311yescharacteristic
200C22⋊C8×C137C2311yescharacteristic
201C22⋊C8×C137C2311yescharacteristic
202#95×C137—21no—
203#95×C137—21no—
204#95×C137C2311yescharacteristic
205#95×C137C2311yescharacteristic
206C24×C137—21no—
207C24×C137—21no—
208C24×C137—21no—
209C24×C137C2×D411yescharacteristic
210C24×C137C2×D411yescharacteristic
211#41×C137—81no—
212#41×C137—81no—
213#41×C137—81no—
214C2×Q8×C137—21no—
215C2×Q8×C137C2×D411yescharacteristic
216C2×D4×C137—21no—
217C2×D4×C137—21no—
218C2×D4×C137—21no—
219C2×D4×C137—21no—
220C2×D4×C137—21no—
221C2×D4×C137—21no—
222C2×D4×C137—21no—
223C2×D4×C137—21no—
224C2×D4×C137—21no—
225C2×D4×C137—21no—
226C2×D4×C137—21no—
227C2×D4×C137—21no—
228C2×D4×C137—21no—
229C2×D4×C137—21no—
230C2×D4×C137—21no—
231C2×D4×C137—21no—
232C2×D4×C137—21no—
233C2×D4×C137—21no—
234C2×D4×C137—21no—
235C2×D4×C137—42no—
236C2×D4×C137—41no—
237C2×D4×C137—41no—
238C2×D4×C137—81no—
239C2×D4×C137—81no—
240C2×D4×C137—81no—
241C2×D4×C137—81no—
242C2×D4×C137—81no—
243C2×D4×C137—81no—
244C2×D4×C137—81no—
245C2×D4×C137—81no—
246C2×D4×C137—81no—
247C2×D4×C137—81no—
248C2×D4×C137—81no—
249C2×D4×C137—82no—
250C2×D4×C137C2×D411yescharacteristic
251C2×D4×C137C2×D411yescharacteristic
252C2×D4×C137C2×D411yescharacteristic
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—21no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—21no—
259C22×C4×C137—21no—
260C22×C4×C137—21no—
261C22×C4×C137—21no—
262C22×C4×C137—21no—
263C22×C4×C137—81no—
264C22×C4×C137C2×D411yescharacteristic
265C22×C4×C137C2×D411yescharacteristic
266C22×C4×C137C2×D411yescharacteristic
267C22×C4×C137C2×D411yescharacteristic
268C22×C4×C137C2×D411yescharacteristic
269C22×C4×C137C2×D411yescharacteristic
270C22×C4×C137C2×D411yescharacteristic
271C22×C4×C137C2×D411yescharacteristic
272C22×C4×C137C2411yescharacteristic
273SD16×C137—81no—
274D8×C137—81no—
275D8×C137—81no—
276D8×C137—81no—
277M16×C137—81no—
278C2×C8×C137—21no—
279C2×C8×C137—21no—
280C2×C8×C137—21no—
281C2×C8×C137—21no—
282C2×C8×C137—81no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—21no—
285C4⋊C4×C137—21no—
286C4⋊C4×C137—21no—
287C4⋊C4×C137—21no—
288C4⋊C4×C137—21no—
289C4⋊C4×C137—21no—
290C4⋊C4×C137—21no—
291C4⋊C4×C137—21no—
292C4⋊C4×C137—21no—
293C4⋊C4×C137—21no—
294C4⋊C4×C137—21no—
295C4⋊C4×C137—21no—
296C4⋊C4×C137—21no—
297C4⋊C4×C137—21no—
298C4⋊C4×C137—81no—
299C4⋊C4×C137C2×D411yescharacteristic
300C4⋊C4×C137C2×D411yescharacteristic
301C4⋊C4×C137C2×D411yescharacteristic
302C4⋊C4×C137C2×D411yescharacteristic
303C22⋊C4×C137—21no—
304C22⋊C4×C137—21no—
305C22⋊C4×C137—21no—
306C22⋊C4×C137—21no—
307C22⋊C4×C137—21no—
308C22⋊C4×C137—21no—
309C22⋊C4×C137—21no—
310C22⋊C4×C137—21no—
311C22⋊C4×C137—21no—
312C22⋊C4×C137—21no—
313C22⋊C4×C137—21no—
314C22⋊C4×C137—21no—
315C22⋊C4×C137—21no—
316C22⋊C4×C137—21no—
317C22⋊C4×C137—21no—
318C22⋊C4×C137—21no—
319C22⋊C4×C137—21no—
320C22⋊C4×C137—21no—
321C22⋊C4×C137—21no—
322C22⋊C4×C137—21no—
323C22⋊C4×C137—21no—
324C22⋊C4×C137—21no—
325C22⋊C4×C137—21no—
326C22⋊C4×C137—21no—
327C22⋊C4×C137—21no—
328C22⋊C4×C137—42no—
329C22⋊C4×C137—42no—
330C22⋊C4×C137—41no—
331C22⋊C4×C137—41no—
332C22⋊C4×C137—81no—
333C22⋊C4×C137—81no—
334C22⋊C4×C137—81no—
335C42×C137—21no—
336C42×C137—21no—
337C42×C137—21no—
338C42×C137—81no—
339C23×C137—21no—
340C23×C137—21no—
341C23×C137—21no—
342C23×C137—21no—
343C23×C137—21no—
344C23×C137—21no—
345C23×C137—21no—
346C23×C137—21no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—42no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—41no—
357C23×C137—41no—
358C23×C137—41no—
359C23×C137—81no—
360C23×C137—81no—
361C23×C137—81no—
362C23×C137—81no—
363C23×C137—81no—
364C23×C137#12011yescharacteristic
365C23×C137#12011yescharacteristic
366C23×C137C22×D411yescharacteristic
367Q8×C137—41no—
368Q8×C137—81no—
369D4×C137—41no—
370D4×C137—41no—
371D4×C137—41no—
372D4×C137—41no—
373D4×C137—41no—
374D4×C137—41no—
375D4×C137—41no—
376D4×C137—42no—
377D4×C137—42no—
378D4×C137—41no—
379D4×C137—41no—
380D4×C137—41no—
381D4×C137—41no—
382D4×C137—41no—
383D4×C137—41no—
384D4×C137—81no—
385D4×C137—81no—
386D4×C137—81no—
387D4×C137—81no—
388D4×C137—81no—
389D4×C137—81no—
390D4×C137—81no—
391D4×C137—81no—
392D4×C137—81no—
393D4×C137—81no—
394D4×C137—81no—
395D4×C137—81no—
396D4×C137—84no—
397D4×C137—82no—
398D4×C137—82no—
399C2×C4×C137—22no—
400C2×C4×C137—21no—
401C2×C4×C137—21no—
402C2×C4×C137—21no—
403C2×C4×C137—21no—
404C2×C4×C137—21no—
405C2×C4×C137—21no—
406C2×C4×C137—21no—
407C2×C4×C137—21no—
408C2×C4×C137—21no—
409C2×C4×C137—21no—
410C2×C4×C137—41no—
411C2×C4×C137—41no—
412C2×C4×C137—41no—
413C2×C4×C137—41no—
414C2×C4×C137—41no—
415C2×C4×C137—41no—
416C2×C4×C137—41no—
417C2×C4×C137—41no—
418C2×C4×C137—41no—
419C2×C4×C137—41no—
420C2×C4×C137—41no—
421C2×C4×C137—41no—
422C2×C4×C137—41no—
423C2×C4×C137—41no—
424C2×C4×C137—41no—
425C2×C4×C137—41no—
426C2×C4×C137—81no—
427C2×C4×C137—81no—
428C2×C4×C137—81no—
429C2×C4×C137—81no—
430C2×C4×C137—81no—
431C2×C4×C137—81no—
432C2×C4×C137—81no—
433C2×C4×C137#12011yescharacteristic
434C2×C4×C137#12011yescharacteristic
435C2×C4×C137C22×D411yescharacteristic
436C2×C4×C137C22×D411yescharacteristic
437C8×C137—41no—
438C8×C137—41no—
439C8×C137—41no—
440C8×C137—41no—
441C22×C137—21no—
442C22×C137—21no—
443C22×C137—21no—
444C22×C137—21no—
445C22×C137—21no—
446C22×C137—21no—
447C22×C137—21no—
448C22×C137—21no—
449C22×C137—41no—
450C22×C137—41no—
451C22×C137—41no—
452C22×C137—41no—
453C22×C137—41no—
454C22×C137—41no—
455C22×C137—41no—
456C22×C137—41no—
457C22×C137—41no—
458C22×C137—41no—
459C22×C137—41no—
460C22×C137—41no—
461C22×C137—81no—
462C22×C137—81no—
463C22×C137—81no—
464C22×C137—81no—
465C22×C137—81no—
466C22×C137—81no—
467C22×C137—81no—
468C22×C137—81no—
469C22×C137—81no—
470C22×C137—81no—
471C22×C137—81no—
472C22×C137—162no—
473C22×C137—162no—
474C22×C137C2×#12011yescharacteristic
475C22×C137#57611yescharacteristic
476C22×C137#57611yescharacteristic
477C4×C137—21no—
478C4×C137—21no—
479C4×C137—21no—
480C4×C137—21no—
481C4×C137—42no—
482C4×C137—41no—
483C4×C137—41no—
484C4×C137—41no—
485C4×C137—41no—
486C4×C137—41no—
487C4×C137—41no—
488C4×C137—41no—
489C4×C137—41no—
490C4×C137—81no—
491C4×C137—81no—
492C2×C137—21no—
493C2×C137—21no—
494C2×C137—41no—
495C2×C137—41no—
496C2×C137—81no—
497C2×C137—81no—
498C2×C137—81no—
499C2×C137—81no—
500C2×C137—161no—
501C2×C137#300811yescharacteristic
502C2×C137#301811yescharacteristic
503C2×C137#302611yescharacteristic
504#18414C13711yesmaximal, characteristic, direct product factor, Sylow
505C137#1841411yescharacteristic, direct product factor, Sylow
506#3534C2×C13711yescharacteristic, complemented
507#3194C2×C13711yescharacteristic, complemented
508#3186C2×C13711yescharacteristic, complemented
509#2661C2×C13711yescharacteristic, complemented
510#1612C2×C13711yescharacteristic, complemented
511#1610C2×C13711yescharacteristic, complemented
512#1609C2×C13711yescharacteristic, complemented
513#1607C2×C13711yescharacteristic, complemented
514#1600C2×C13711yescharacteristic, complemented
515#1598C2×C13711yescharacteristic, complemented
516#1597C2×C13711yescharacteristic, complemented
517#1595C2×C13711yescharacteristic, complemented
518#1507C2×C13711yescharacteristic, complemented
519#1501C2×C13711yescharacteristic, complemented
520#1468C2×C13711yescharacteristic, complemented
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C13711yescharacteristic
532#538—21no—
533#538C22×C13711yescharacteristic
534#537C22×C13711yescharacteristic
535#534—21no—
536#534C22×C13711yescharacteristic
537#525C22×C13711yescharacteristic
538C2×#123C22×C13711yescharacteristic
539C2×#121C22×C13711yescharacteristic
540C2×#121C22×C13711yescharacteristic, complemented
541#483C22×C13711yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C13711yescharacteristic
545#480C22×C13711yescharacteristic, complemented
546#480C22×C13711yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C13711yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C13711yescharacteristic
555#447C22×C13711yescharacteristic, complemented
556#447C22×C13711yescharacteristic, complemented
557#407C22×C13711yescharacteristic, complemented
558C2×C22⋊C8C22×C13711yescharacteristic, complemented
559#398C22×C13711yescharacteristic, complemented
560#397C22×C13711yescharacteristic, complemented
561#394—21no—
562#394C22×C13711yescharacteristic, complemented
563#392—21no—
564#392C22×C13711yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C13711yescharacteristic, complemented
568#328C22×C13711yescharacteristic, complemented
569#328C22×C13711yescharacteristic, complemented
570#327C22×C13711yescharacteristic
571#327C22×C13711yescharacteristic
572#327C22×C13711yescharacteristic, complemented
573#327C22×C13711yescharacteristic, complemented
574#327C22×C13711yescharacteristic, complemented
575#327C22×C13711yescharacteristic, complemented
576#324C22×C13711yescharacteristic, complemented
577#324C22×C13711yescharacteristic, complemented
578#323C22×C13711yescharacteristic, complemented
579#323C22×C13711yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C13711yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C13711yescharacteristic
588C22×D4D4×C13711yescharacteristic, complemented
589C22×D4C23×C13711yescharacteristic
590C23×C4C23×C13711yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C13711yescharacteristic, complemented
627C22⋊Q8C23×C13711yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C13711yescharacteristic, complemented
648#121D4×C13711yescharacteristic, complemented
649#121D4×C13711yescharacteristic, complemented
650#121C23×C13711yescharacteristic
651#121C23×C13711yescharacteristic
652#121C23×C13711yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C13711yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C13711yescharacteristic
673C2×C4⋊C4D4×C13711yescharacteristic, complemented
674C2×C4⋊C4C23×C13711yescharacteristic
675C2×C4⋊C4C23×C13711yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C13711yescharacteristic
686C2×C22⋊C4D4×C13711yescharacteristic
687C2×C22⋊C4C23×C13711yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C13711yescharacteristic
704C22⋊C8C23×C13711yescharacteristic
705C22⋊C8C23×C13711yescharacteristic
706C22⋊C8C23×C13711yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C13711yescharacteristic
710#95C23×C13711yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C13711yescharacteristic
715C24C2×D4×C13711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C13711yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C13711yescharacteristic
756C2×D4C2×D4×C13711yescharacteristic
757C2×D4C2×D4×C13711yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C13711yescharacteristic
770C22×C4C2×D4×C13711yescharacteristic
771C22×C4C2×D4×C13711yescharacteristic
772C22×C4C2×D4×C13711yescharacteristic
773C22×C4C2×D4×C13711yescharacteristic
774C22×C4C2×D4×C13711yescharacteristic
775C22×C4C2×D4×C13711yescharacteristic
776C22×C4C2×D4×C13711yescharacteristic
777C22×C4C24×C13711yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C13711yescharacteristic
805C4⋊C4C2×D4×C13711yescharacteristic
806C4⋊C4C2×D4×C13711yescharacteristic
807C4⋊C4C2×D4×C13711yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C13711yescharacteristic
870C23#120×C13711yescharacteristic
871C23C22×D4×C13711yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C13711yescharacteristic
939C2×C4#120×C13711yescharacteristic
940C2×C4C22×D4×C13711yescharacteristic
941C2×C4C22×D4×C13711yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C13711yescharacteristic
980C22#576×C13711yescharacteristic
981C22#576×C13711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2#3008×C13711yescharacteristic
1007C2#3018×C13711yescharacteristic
1008C2#3026×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3534×C137C2semidirect
2. #3194×C137C2semidirect
3. #3186×C137C2semidirect
4. #2661×C137C2semidirect
5. #1612×C137C2semidirect
6. #1610×C137C2semidirect
7. #1609×C137C2semidirect
8. #1607×C137C2semidirect
9. #1600×C137C2semidirect
10. #1598×C137C2semidirect
11. #1597×C137C2semidirect
12. #1595×C137C2semidirect
13. #1507×C137C2semidirect
14. #1501×C137C2semidirect
15. #1468×C137C2semidirect
35. C2×#121×C137C22semidirect
36. #483×C137C22semidirect
40. #480×C137C22semidirect
41. #480×C137C22semidirect
46. #450×C137C22semidirect
50. #447×C137C22semidirect
51. #447×C137C22semidirect
52. #407×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
54. #398×C137C22semidirect
55. #397×C137C22semidirect
57. #394×C137C22semidirect
59. #392×C137C22semidirect
62. C4×C22⋊C4×C137C22semidirect
63. #328×C137C22semidirect
64. #328×C137C22semidirect
67. #327×C137C22semidirect
68. #327×C137C22semidirect
69. #327×C137C22semidirect
70. #327×C137C22semidirect
71. #324×C137C22semidirect
72. #324×C137C22semidirect
73. #323×C137C22semidirect
74. #323×C137C22semidirect
76. C2×#41×C137D4semidirect
83. C22×D4×C137D4semidirect
121. C22⋊Q8×C137D4semidirect
142. #121×C137D4semidirect
143. #121×C137D4semidirect
144. #121×C137D4semidirect
165. #117×C137D4semidirect
168. C2×C4⋊C4×C137D4semidirect
504. #18414C137direct (N × H)
505. C137#18414direct (N × H)
506. #3534C2×C137semidirect
507. #3194C2×C137semidirect
508. #3186C2×C137semidirect
509. #2661C2×C137semidirect
510. #1612C2×C137semidirect
511. #1610C2×C137semidirect
512. #1609C2×C137semidirect
513. #1607C2×C137semidirect
514. #1600C2×C137semidirect
515. #1598C2×C137semidirect
516. #1597C2×C137semidirect
517. #1595C2×C137semidirect
518. #1507C2×C137semidirect
519. #1501C2×C137semidirect
520. #1468C2×C137semidirect
540. C2×#121C22×C137semidirect
541. #483C22×C137semidirect
545. #480C22×C137semidirect
546. #480C22×C137semidirect
551. #450C22×C137semidirect
555. #447C22×C137semidirect
556. #447C22×C137semidirect
557. #407C22×C137semidirect
558. C2×C22⋊C8C22×C137semidirect
559. #398C22×C137semidirect
560. #397C22×C137semidirect
562. #394C22×C137semidirect
564. #392C22×C137semidirect
567. C4×C22⋊C4C22×C137semidirect
568. #328C22×C137semidirect
569. #328C22×C137semidirect
572. #327C22×C137semidirect
573. #327C22×C137semidirect
574. #327C22×C137semidirect
575. #327C22×C137semidirect
576. #324C22×C137semidirect
577. #324C22×C137semidirect
578. #323C22×C137semidirect
579. #323C22×C137semidirect
581. C2×#41D4×C137semidirect
588. C22×D4D4×C137semidirect
626. C22⋊Q8D4×C137semidirect
647. #121D4×C137semidirect
648. #121D4×C137semidirect
649. #121D4×C137semidirect
670. #117D4×C137semidirect
673. C2×C4⋊C4D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3534×C1372
#3194×C1372
#3186×C1372
#2661×C1372
#1612×C1372
#1610×C1372
#1609×C1372
#1607×C1372
#1600×C1372
#1598×C1372
#1597×C1372
#1595×C1372
#1507×C1372
#1501×C1372
#1468×C1372
#18414137