Finite Group Databasebeta

← C137×#18262 #46867648

Subgroups — C137×#18262 #46867648

Order 35072.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C137C211yesmaximal, characteristic
2#3094×C137C211yesmaximal, characteristic, complemented
3#3091×C137C211yesmaximal, characteristic, complemented
4#2498×C137C211yesmaximal, characteristic, complemented
5#1618×C137C211yesmaximal, characteristic, complemented
6#1616×C137C211yesmaximal, characteristic, complemented
7#1615×C137C211yesmaximal, characteristic, complemented
8#1613×C137C211yesmaximal, characteristic, complemented
9#1612×C137C211yesmaximal, characteristic, complemented
10#1610×C137C211yesmaximal, characteristic, complemented
11#1609×C137C211yesmaximal, characteristic, complemented
12#1607×C137C211yesmaximal, characteristic, complemented
13#1504×C137C211yesmaximal, characteristic, complemented
14C2×#327×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×#117×C137C2211yescharacteristic, complemented
36#485×C137—21no—
37#484×C137C2211yescharacteristic, complemented
38#483×C137C2211yescharacteristic, complemented
39#482×C137—21no—
40#482×C137—21no—
41#482×C137—21no—
42#481×C137C2211yescharacteristic
43#481×C137C2211yescharacteristic, complemented
44#481×C137C2211yescharacteristic, complemented
45#480×C137C2211yescharacteristic
46#480×C137C2211yescharacteristic, complemented
47#480×C137C2211yescharacteristic, complemented
48#428×C137—21no—
49#427×C137—21no—
50#418×C137—21no—
51#416×C137—21no—
52#407×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#400×C137C2211yescharacteristic, complemented
55#399×C137C2211yescharacteristic, complemented
56#398×C137C2211yescharacteristic, complemented
57#397×C137C2211yescharacteristic, complemented
58#388×C137—21no—
59#387×C137—21no—
60#386×C137—21no—
61#380×C137—21no—
62C2×#95×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
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137D411yescharacteristic
81C22×D4×C137D411yescharacteristic
82C23×C4×C137—21no—
83C23×C4×C137C2311yescharacteristic
84C2×M16×C137—21no—
85C22×C8×C137—21no—
86#127×C137—21no—
87#126×C137—21no—
88#126×C137—21no—
89#126×C137—21no—
90#126×C137—21no—
91#125×C137—21no—
92#125×C137—21no—
93#124×C137—21no—
94#124×C137—21no—
95#124×C137—21no—
96#123×C137—21no—
97#123×C137—21no—
98#123×C137—21no—
99#123×C137—21no—
100#123×C137—21no—
101#123×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—
110C22⋊Q8×C137—21no—
111C22⋊Q8×C137—21no—
112C22⋊Q8×C137—21no—
113C22⋊Q8×C137—21no—
114C22⋊Q8×C137—21no—
115C22⋊Q8×C137D411yescharacteristic
116C22⋊Q8×C137C2311yescharacteristic
117#121×C137—21no—
118#121×C137—21no—
119#121×C137—21no—
120#121×C137—21no—
121#121×C137—21no—
122#121×C137—21no—
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×C137D411yescharacteristic
133#121×C137D411yescharacteristic
134#121×C137D411yescharacteristic
135#121×C137C2311yescharacteristic
136#121×C137C2311yescharacteristic
137#121×C137C2311yescharacteristic
138#120×C137—21no—
139#120×C137—21no—
140#120×C137—21no—
141#120×C137—21no—
142#120×C137—21no—
143#120×C137—21no—
144#120×C137—21no—
145#120×C137—21no—
146C4×D4×C137—21no—
147C4×D4×C137—21no—
148C4×D4×C137—21no—
149C4×D4×C137—21no—
150C4×D4×C137—21no—
151C4×D4×C137—21no—
152C4×D4×C137—21no—
153C4×D4×C137—21no—
154#117×C137—21no—
155#117×C137—21no—
156#117×C137—21no—
157#117×C137—21no—
158#117×C137—21no—
159#117×C137D411yescharacteristic
160C2×C4⋊C4×C137—21no—
161C2×C4⋊C4×C137—21no—
162C2×C4⋊C4×C137D411yescharacteristic
163C2×C4⋊C4×C137D411yescharacteristic
164C2×C4⋊C4×C137C2311yescharacteristic
165C2×C4⋊C4×C137C2311yescharacteristic
166C2×C4⋊C4×C137C2311yescharacteristic
167C2×C22⋊C4×C137—21no—
168C2×C22⋊C4×C137—21no—
169C2×C22⋊C4×C137—21no—
170C2×C22⋊C4×C137—21no—
171C2×C22⋊C4×C137—21no—
172C2×C22⋊C4×C137—21no—
173C2×C22⋊C4×C137D411yescharacteristic
174C2×C22⋊C4×C137D411yescharacteristic
175C2×C22⋊C4×C137C2311yescharacteristic
176C2×C42×C137—21no—
177#107×C137—21no—
178#107×C137—21no—
179#107×C137—21no—
180#107×C137—21no—
181#106×C137—21no—
182#106×C137—21no—
183#106×C137—21no—
184#106×C137—21no—
185#103×C137—21no—
186#103×C137—21no—
187#102×C137—21no—
188#102×C137—21no—
189#102×C137—21no—
190#102×C137—21no—
191#102×C137—21no—
192#102×C137—21no—
193C22⋊C8×C137—21no—
194C22⋊C8×C137—21no—
195C22⋊C8×C137C2311yescharacteristic
196C22⋊C8×C137C2311yescharacteristic
197C22⋊C8×C137C2311yescharacteristic
198C22⋊C8×C137C2311yescharacteristic
199#95×C137—21no—
200#95×C137—21no—
201#95×C137—21no—
202#95×C137—21no—
203#95×C137—21no—
204#95×C137C2311yescharacteristic
205#95×C137C2311yescharacteristic
206C24×C137—21no—
207C24×C137—21no—
208C24×C137C2×D411yescharacteristic
209C24×C137C2×D411yescharacteristic
210#41×C137—42no—
211#41×C137—81no—
212#41×C137—81no—
213C2×Q8×C137—21no—
214C2×Q8×C137C2×D411yescharacteristic
215C2×D4×C137—21no—
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—42no—
233C2×D4×C137—42no—
234C2×D4×C137—81no—
235C2×D4×C137—81no—
236C2×D4×C137—81no—
237C2×D4×C137—81no—
238C2×D4×C137—82no—
239C2×D4×C137C2×D411yescharacteristic
240C2×D4×C137C2×D411yescharacteristic
241C2×D4×C137C2×D411yescharacteristic
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—21no—
249C22×C4×C137—21no—
250C22×C4×C137—21no—
251C22×C4×C137—21no—
252C22×C4×C137—21no—
253C22×C4×C137—42no—
254C22×C4×C137—42no—
255C22×C4×C137—42no—
256C22×C4×C137—81no—
257C22×C4×C137C2×D411yescharacteristic
258C22×C4×C137C2×D411yescharacteristic
259C22×C4×C137C2×D411yescharacteristic
260C22×C4×C137C2×D411yescharacteristic
261C22×C4×C137C2×D411yescharacteristic
262C22×C4×C137C2×D411yescharacteristic
263C22×C4×C137C2×D411yescharacteristic
264C22×C4×C137C2×D411yescharacteristic
265C22×C4×C137C2411yescharacteristic
266M16×C137—42no—
267C2×C8×C137—21no—
268C2×C8×C137—21no—
269C2×C8×C137—21no—
270C2×C8×C137—21no—
271C2×C8×C137—42no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
280C4⋊C4×C137—21no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—21no—
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—42no—
290C4⋊C4×C137—81no—
291C4⋊C4×C137C2×D411yescharacteristic
292C4⋊C4×C137C2×D411yescharacteristic
293C4⋊C4×C137C2×D411yescharacteristic
294C4⋊C4×C137C2×D411yescharacteristic
295C22⋊C4×C137—21no—
296C22⋊C4×C137—21no—
297C22⋊C4×C137—21no—
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—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—42no—
321C22⋊C4×C137—41no—
322C22⋊C4×C137—41no—
323C22⋊C4×C137—81no—
324C42×C137—21no—
325C42×C137—21no—
326C42×C137—21no—
327C42×C137—41no—
328C42×C137—41no—
329C23×C137—21no—
330C23×C137—21no—
331C23×C137—22no—
332C23×C137—21no—
333C23×C137—21no—
334C23×C137—21no—
335C23×C137—21no—
336C23×C137—21no—
337C23×C137—21no—
338C23×C137—41no—
339C23×C137—41no—
340C23×C137—41no—
341C23×C137—42no—
342C23×C137—81no—
343C23×C137—81no—
344C23×C137—81no—
345C23×C137—81no—
346C23×C137—81no—
347C23×C137#12011yescharacteristic
348C23×C137#12011yescharacteristic
349C23×C137C22×D411yescharacteristic
350Q8×C137—41no—
351Q8×C137—81no—
352D4×C137—41no—
353D4×C137—41no—
354D4×C137—41no—
355D4×C137—41no—
356D4×C137—41no—
357D4×C137—41no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—42no—
362D4×C137—42no—
363D4×C137—81no—
364D4×C137—81no—
365D4×C137—81no—
366D4×C137—81no—
367D4×C137—81no—
368D4×C137—81no—
369D4×C137—81no—
370D4×C137—81no—
371D4×C137—81no—
372D4×C137—81no—
373D4×C137—81no—
374D4×C137—81no—
375C2×C4×C137—22no—
376C2×C4×C137—22no—
377C2×C4×C137—22no—
378C2×C4×C137—21no—
379C2×C4×C137—21no—
380C2×C4×C137—21no—
381C2×C4×C137—21no—
382C2×C4×C137—21no—
383C2×C4×C137—21no—
384C2×C4×C137—21no—
385C2×C4×C137—21no—
386C2×C4×C137—21no—
387C2×C4×C137—21no—
388C2×C4×C137—41no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—41no—
400C2×C4×C137—41no—
401C2×C4×C137—41no—
402C2×C4×C137—41no—
403C2×C4×C137—41no—
404C2×C4×C137—41no—
405C2×C4×C137—81no—
406C2×C4×C137—81no—
407C2×C4×C137—81no—
408C2×C4×C137—81no—
409C2×C4×C137—81no—
410C2×C4×C137—81no—
411C2×C4×C137—81no—
412C2×C4×C137—84no—
413C2×C4×C137#12011yescharacteristic
414C2×C4×C137#12011yescharacteristic
415C2×C4×C137C22×D411yescharacteristic
416C2×C4×C137C22×D411yescharacteristic
417C8×C137—41no—
418C8×C137—41no—
419C8×C137—41no—
420C8×C137—41no—
421C22×C137—21no—
422C22×C137—21no—
423C22×C137—21no—
424C22×C137—21no—
425C22×C137—21no—
426C22×C137—21no—
427C22×C137—21no—
428C22×C137—42no—
429C22×C137—42no—
430C22×C137—41no—
431C22×C137—41no—
432C22×C137—41no—
433C22×C137—41no—
434C22×C137—41no—
435C22×C137—41no—
436C22×C137—41no—
437C22×C137—41no—
438C22×C137—41no—
439C22×C137—41no—
440C22×C137—41no—
441C22×C137—41no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137—162no—
445C22×C137—162no—
446C22×C137#45812yes—
447C22×C137C2×#12011yescharacteristic
448C22×C137#57611yescharacteristic
449C22×C137#57711yescharacteristic
450C4×C137—21no—
451C4×C137—21no—
452C4×C137—21no—
453C4×C137—21no—
454C4×C137—42no—
455C4×C137—41no—
456C4×C137—41no—
457C4×C137—41no—
458C4×C137—41no—
459C4×C137—41no—
460C4×C137—41no—
461C4×C137—41no—
462C4×C137—41no—
463C4×C137—81no—
464C4×C137—81no—
465C4×C137—81no—
466C2×C137—21no—
467C2×C137—21no—
468C2×C137—22no—
469C2×C137—41no—
470C2×C137—81no—
471C2×C137—81no—
472C2×C137—81no—
473C2×C137—81no—
474C2×C137#301211yescharacteristic
475C2×C137#301811yescharacteristic
476C2×C137C2×#45811yescharacteristic
477#18262C13711yesmaximal, characteristic, direct product factor, Sylow
478C137#1826211yescharacteristic, direct product factor, Sylow
479#3534C2×C13711yescharacteristic
480#3094C2×C13711yescharacteristic, complemented
481#3091C2×C13711yescharacteristic, complemented
482#2498C2×C13711yescharacteristic, complemented
483#1618C2×C13711yescharacteristic, complemented
484#1616C2×C13711yescharacteristic, complemented
485#1615C2×C13711yescharacteristic, complemented
486#1613C2×C13711yescharacteristic, complemented
487#1612C2×C13711yescharacteristic, complemented
488#1610C2×C13711yescharacteristic, complemented
489#1609C2×C13711yescharacteristic, complemented
490#1607C2×C13711yescharacteristic, complemented
491#1504C2×C13711yescharacteristic, complemented
492C2×#327C2×C13711yescharacteristic, complemented
493#1468C2×C13711yescharacteristic, complemented
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C13711yescharacteristic
505#538—21no—
506#538C22×C13711yescharacteristic
507#537C22×C13711yescharacteristic
508#534—21no—
509#534C22×C13711yescharacteristic
510#525C22×C13711yescharacteristic
511C2×#123C22×C13711yescharacteristic
512C2×#121C22×C13711yescharacteristic
513C2×#117C22×C13711yescharacteristic, complemented
514#485—21no—
515#484C22×C13711yescharacteristic, complemented
516#483C22×C13711yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C13711yescharacteristic
521#481C22×C13711yescharacteristic, complemented
522#481C22×C13711yescharacteristic, complemented
523#480C22×C13711yescharacteristic
524#480C22×C13711yescharacteristic, complemented
525#480C22×C13711yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C13711yescharacteristic, complemented
531C2×C22⋊C8C22×C13711yescharacteristic, complemented
532#400C22×C13711yescharacteristic, complemented
533#399C22×C13711yescharacteristic, complemented
534#398C22×C13711yescharacteristic, complemented
535#397C22×C13711yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C13711yescharacteristic, complemented
541#328C22×C13711yescharacteristic, complemented
542#328C22×C13711yescharacteristic, complemented
543#327C22×C13711yescharacteristic
544#327C22×C13711yescharacteristic
545#327C22×C13711yescharacteristic, complemented
546#327C22×C13711yescharacteristic, complemented
547#327C22×C13711yescharacteristic, complemented
548#327C22×C13711yescharacteristic, complemented
549#324C22×C13711yescharacteristic, complemented
550#324C22×C13711yescharacteristic, complemented
551#323C22×C13711yescharacteristic, complemented
552#323C22×C13711yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C13711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C13711yescharacteristic
559C22×D4D4×C13711yescharacteristic
560C23×C4—21no—
561C23×C4C23×C13711yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C13711yescharacteristic
594C22⋊Q8C23×C13711yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C13711yescharacteristic
611#121D4×C13711yescharacteristic
612#121D4×C13711yescharacteristic
613#121C23×C13711yescharacteristic
614#121C23×C13711yescharacteristic
615#121C23×C13711yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C13711yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C13711yescharacteristic
641C2×C4⋊C4D4×C13711yescharacteristic
642C2×C4⋊C4C23×C13711yescharacteristic
643C2×C4⋊C4C23×C13711yescharacteristic
644C2×C4⋊C4C23×C13711yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C13711yescharacteristic
652C2×C22⋊C4D4×C13711yescharacteristic
653C2×C22⋊C4C23×C13711yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C13711yescharacteristic
674C22⋊C8C23×C13711yescharacteristic
675C22⋊C8C23×C13711yescharacteristic
676C22⋊C8C23×C13711yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C13711yescharacteristic
683#95C23×C13711yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C13711yescharacteristic
687C24C2×D4×C13711yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C13711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C13711yescharacteristic
718C2×D4C2×D4×C13711yescharacteristic
719C2×D4C2×D4×C13711yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C13711yescharacteristic
736C22×C4C2×D4×C13711yescharacteristic
737C22×C4C2×D4×C13711yescharacteristic
738C22×C4C2×D4×C13711yescharacteristic
739C22×C4C2×D4×C13711yescharacteristic
740C22×C4C2×D4×C13711yescharacteristic
741C22×C4C2×D4×C13711yescharacteristic
742C22×C4C2×D4×C13711yescharacteristic
743C22×C4C24×C13711yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C13711yescharacteristic
770C4⋊C4C2×D4×C13711yescharacteristic
771C4⋊C4C2×D4×C13711yescharacteristic
772C4⋊C4C2×D4×C13711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C13711yescharacteristic
826C23#120×C13711yescharacteristic
827C23C22×D4×C13711yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C13711yescharacteristic
892C2×C4#120×C13711yescharacteristic
893C2×C4C22×D4×C13711yescharacteristic
894C2×C4C22×D4×C13711yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C13712yes—
925C22C2×#120×C13711yescharacteristic
926C22#576×C13711yescharacteristic
927C22#577×C13711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2#3012×C13711yescharacteristic
953C2#3018×C13711yescharacteristic
954C2C2×#458×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3534×C137C2
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
2. #3094×C137C2semidirect
3. #3091×C137C2semidirect
4. #2498×C137C2semidirect
5. #1618×C137C2semidirect
6. #1616×C137C2semidirect
7. #1615×C137C2semidirect
8. #1613×C137C2semidirect
9. #1612×C137C2semidirect
10. #1610×C137C2semidirect
11. #1609×C137C2semidirect
12. #1607×C137C2semidirect
13. #1504×C137C2semidirect
14. C2×#327×C137C2semidirect
15. #1468×C137C2semidirect
35. C2×#117×C137C22semidirect
37. #484×C137C22semidirect
38. #483×C137C22semidirect
43. #481×C137C22semidirect
44. #481×C137C22semidirect
46. #480×C137C22semidirect
47. #480×C137C22semidirect
52. #407×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
54. #400×C137C22semidirect
55. #399×C137C22semidirect
56. #398×C137C22semidirect
57. #397×C137C22semidirect
62. C2×#95×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
477. #18262C137direct (N × H)
478. C137#18262direct (N × H)
480. #3094C2×C137semidirect
481. #3091C2×C137semidirect
482. #2498C2×C137semidirect
483. #1618C2×C137semidirect
484. #1616C2×C137semidirect
485. #1615C2×C137semidirect
486. #1613C2×C137semidirect
487. #1612C2×C137semidirect
488. #1610C2×C137semidirect
489. #1609C2×C137semidirect
490. #1607C2×C137semidirect
491. #1504C2×C137semidirect
492. C2×#327C2×C137semidirect
493. #1468C2×C137semidirect
513. C2×#117C22×C137semidirect
515. #484C22×C137semidirect
516. #483C22×C137semidirect
521. #481C22×C137semidirect
522. #481C22×C137semidirect
524. #480C22×C137semidirect
525. #480C22×C137semidirect
530. #407C22×C137semidirect
531. C2×C22⋊C8C22×C137semidirect
532. #400C22×C137semidirect
533. #399C22×C137semidirect
534. #398C22×C137semidirect
535. #397C22×C137semidirect
540. C2×#95C22×C137semidirect
541. #328C22×C137semidirect
542. #328C22×C137semidirect
545. #327C22×C137semidirect
546. #327C22×C137semidirect
547. #327C22×C137semidirect
548. #327C22×C137semidirect
549. #324C22×C137semidirect
550. #324C22×C137semidirect
551. #323C22×C137semidirect
552. #323C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3534×C1372
#3094×C1372
#3091×C1372
#2498×C1372
#1618×C1372
#1616×C1372
#1615×C1372
#1613×C1372
#1612×C1372
#1610×C1372
#1609×C1372
#1607×C1372
#1504×C1372
C2×#327×C1372
#1468×C1372
#18262137