Finite Group Databasebeta

← C137×#25843 #46875229

Subgroups — C137×#25843 #46875229

Order 35072.

1046 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C137C211yesmaximal, characteristic
2C2×#499×C137C211yesmaximal, characteristic, complemented
3C2×#478×C137C211yesmaximal, characteristic
4#2584×C137C211yesmaximal, characteristic, complemented
5#2059×C137C211yesmaximal, characteristic, complemented
6#2059×C137C211yesmaximal, characteristic, complemented
7#2058×C137C211yesmaximal, characteristic, complemented
8#2057×C137C211yesmaximal, characteristic, complemented
9#1989×C137C211yesmaximal, characteristic, complemented
10#1984×C137C211yesmaximal, characteristic, complemented
11#1864×C137C211yesmaximal, characteristic
12#1864×C137C211yesmaximal, characteristic
13#1862×C137C211yesmaximal, characteristic
14#1862×C137C211yesmaximal, characteristic
15C4×#102×C137C211yesmaximal, characteristic
16#554×C137—24no—
17#554×C137—24no—
18C2×C4⋊Q8×C137C2211yescharacteristic
19C2×#125×C137C2211yescharacteristic
20C2×#125×C137C2211yescharacteristic
21C2×#125×C137C2211yescharacteristic
22C2×C22⋊Q8×C137—21no—
23C2×C22⋊Q8×C137—21no—
24C2×C22⋊Q8×C137—21no—
25C2×C4×Q8×C137C2211yescharacteristic
26C2×C4×D4×C137C2211yescharacteristic
27C2×C4×D4×C137C2211yescharacteristic
28C2×C4×D4×C137C2211yescharacteristic
29C22×C4⋊C4×C137—21no—
30#499×C137—24no—
31#478×C137—24no—
32C2×#107×C137C2211yescharacteristic
33C2×#107×C137C2211yescharacteristic
34C2×#107×C137C2211yescharacteristic
35C2×#106×C137C2211yescharacteristic
36C2×#106×C137C2211yescharacteristic
37C2×#106×C137C2211yescharacteristic
38C2×C4⋊C8×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×C4×C8×C137C2211yescharacteristic
44#398×C137—21no—
45#395×C137—21no—
46#389×C137—21no—
47#389×C137—21no—
48#389×C137C2211yescharacteristic
49#389×C137C2211yescharacteristic
50#389×C137C2211yescharacteristic
51#389×C137C2211yescharacteristic
52C4×C4⋊C4×C137C2211yescharacteristic
53#340×C137C2211yescharacteristic
54#340×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#336×C137C2211yescharacteristic
60#336×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62#336×C137C2211yescharacteristic
63C22×Q8×C137—21no—
64C22×Q8×C137D411yescharacteristic
65C22×D4×C137C2311yescharacteristic
66C23×C4×C137—21no—
67C23×C4×C137—21no—
68C23×C4×C137—21no—
69C22×C8×C137C2311yescharacteristic
70C22×C8×C137C2311yescharacteristic
71C22×C8×C137C2311yescharacteristic
72C22×C8×C137C2311yescharacteristic
73C4⋊Q8×C137—22no—
74C4⋊Q8×C137—22no—
75#125×C137—22no—
76#125×C137—22no—
77#125×C137—22no—
78#125×C137—22no—
79#125×C137—22no—
80#125×C137D414yes—
81C22⋊Q8×C137—28no—
82C22⋊Q8×C137—28no—
83C22⋊Q8×C137—28no—
84C4×Q8×C137—22no—
85C4×Q8×C137—22no—
86C4×D4×C137—22no—
87C4×D4×C137—22no—
88C4×D4×C137—22no—
89C4×D4×C137—22no—
90C4×D4×C137—22no—
91C4×D4×C137D414yes—
92C2×C4⋊C4×C137—28no—
93C2×C4⋊C4×C137—21no—
94C2×C4⋊C4×C137—21no—
95C2×C4⋊C4×C137—21no—
96C2×C4⋊C4×C137—21no—
97C2×C4⋊C4×C137—21no—
98C2×C4⋊C4×C137—21no—
99C2×C4⋊C4×C137—21no—
100C2×C4⋊C4×C137—21no—
101C2×C4⋊C4×C137—21no—
102C2×C4⋊C4×C137—21no—
103C2×C4⋊C4×C137—21no—
104C2×C4⋊C4×C137D411yescharacteristic
105C2×C4⋊C4×C137D411yescharacteristic
106C2×C4⋊C4×C137D411yescharacteristic
107C2×C4⋊C4×C137C2311yescharacteristic
108C2×C4⋊C4×C137C2311yescharacteristic
109C2×C4⋊C4×C137C2311yescharacteristic
110C2×C4⋊C4×C137C2311yescharacteristic
111C2×C4⋊C4×C137C2311yescharacteristic
112C2×C4⋊C4×C137C2311yescharacteristic
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C22⋊C4×C137—21no—
115C2×C22⋊C4×C137—21no—
116C2×C22⋊C4×C137—21no—
117C2×C42×C137—21no—
118C2×C42×C137C2311yescharacteristic
119C2×C42×C137C2311yescharacteristic
120C2×C42×C137C2311yescharacteristic
121#107×C137—22no—
122#107×C137—22no—
123#107×C137—22no—
124#106×C137—22no—
125#106×C137—22no—
126#106×C137—22no—
127C4⋊C8×C137—22no—
128#102×C137—22no—
129#102×C137—22no—
130#102×C137Q814yescomplemented
131#102×C137Q814yescomplemented
132C4×C8×C137—22no—
133#95×C137—21no—
134#95×C137—21no—
135#95×C137—21no—
136#95×C137—21no—
137#95×C137—21no—
138C24×C137—21no—
139C2×Q8×C137—24no—
140C2×Q8×C137—22no—
141C2×Q8×C137—22no—
142C2×Q8×C137—41no—
143C2×Q8×C137—81no—
144C2×Q8×C137—81no—
145C2×D4×C137—21no—
146C2×D4×C137—21no—
147C2×D4×C137—21no—
148C2×D4×C137C2×D412yes—
149C2×D4×C137C2×Q812yes—
150C2×D4×C137C2×Q812yes—
151C22×C4×C137—24no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—21no—
157C22×C4×C137—24no—
158C22×C4×C137—24no—
159C22×C4×C137—21no—
160C22×C4×C137—21no—
161C22×C4×C137—42no—
162C22×C4×C137—42no—
163C22×C4×C137—81no—
164C22×C4×C137—81no—
165C22×C4×C137—81no—
166C22×C4×C137—81no—
167C22×C4×C137C2×D411yescharacteristic
168C22×C4×C137C2×D411yescharacteristic
169C22×C4×C137C2×D411yescharacteristic
170C22×C4×C137C2×D411yescharacteristic
171C22×C4×C137C2×D411yescharacteristic
172C22×C4×C137C2×D411yescharacteristic
173C22×C4×C137C2411yescharacteristic
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137—21no—
177C2×C8×C137—21no—
178C2×C8×C137—21no—
179C2×C8×C137—21no—
180C2×C8×C137—21no—
181C2×C8×C137—21no—
182C2×C8×C137—21no—
183C2×C8×C137—21no—
184C2×C8×C137C2×Q812yes—
185C2×C8×C137C2×Q812yes—
186C4⋊C4×C137—24no—
187C4⋊C4×C137—24no—
188C4⋊C4×C137—24no—
189C4⋊C4×C137—22no—
190C4⋊C4×C137—24no—
191C4⋊C4×C137—24no—
192C4⋊C4×C137—22no—
193C4⋊C4×C137—22no—
194C4⋊C4×C137—21no—
195C4⋊C4×C137—21no—
196C4⋊C4×C137—21no—
197C4⋊C4×C137—21no—
198C4⋊C4×C137—21no—
199C4⋊C4×C137—21no—
200C4⋊C4×C137—21no—
201C4⋊C4×C137—21no—
202C4⋊C4×C137—21no—
203C4⋊C4×C137—42no—
204C4⋊C4×C137—42no—
205C4⋊C4×C137—42no—
206C4⋊C4×C137—42no—
207C4⋊C4×C137—81no—
208C4⋊C4×C137—81no—
209C4⋊C4×C137C2×D412yes—
210C4⋊C4×C137C2×D412yes—
211C4⋊C4×C137C2×D412yes—
212C4⋊C4×C137C2×Q812yes—
213C4⋊C4×C137C2×Q812yes—
214C22⋊C4×C137—24no—
215C22⋊C4×C137—24no—
216C22⋊C4×C137—24no—
217C42×C137—21no—
218C42×C137—21no—
219C42×C137—21no—
220C42×C137—21no—
221C42×C137—81no—
222C42×C137C2×D412yes—
223C42×C137C2×D412yes—
224C23×C137—22no—
225C23×C137—22no—
226C23×C137—22no—
227C23×C137—41no—
228C23×C137—41no—
229C23×C137—41no—
230C23×C137—41no—
231C23×C137C22×D411yescharacteristic
232Q8×C137—44no—
233Q8×C137—84no—
234D4×C137—22no—
235D4×C137—22no—
236D4×C137—22no—
237D4×C137C4⋊Q814yes—
238C2×C4×C137—21no—
239C2×C4×C137—21no—
240C2×C4×C137—21no—
241C2×C4×C137—21no—
242C2×C4×C137—21no—
243C2×C4×C137—21no—
244C2×C4×C137—21no—
245C2×C4×C137—21no—
246C2×C4×C137—21no—
247C2×C4×C137—22no—
248C2×C4×C137—22no—
249C2×C4×C137—22no—
250C2×C4×C137—22no—
251C2×C4×C137—22no—
252C2×C4×C137—21no—
253C2×C4×C137—21no—
254C2×C4×C137—21no—
255C2×C4×C137—21no—
256C2×C4×C137—21no—
257C2×C4×C137—21no—
258C2×C4×C137—48no—
259C2×C4×C137—41no—
260C2×C4×C137—41no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—41no—
268C2×C4×C137—41no—
269C2×C4×C137—41no—
270C2×C4×C137—41no—
271C2×C4×C137—41no—
272C2×C4×C137—41no—
273C2×C4×C137—41no—
274C2×C4×C137—41no—
275C2×C4×C137—84no—
276C2×C4×C137—84no—
277C2×C4×C137#12012yes—
278C2×C4×C137#12012yes—
279C2×C4×C137#13512yes—
280C2×C4×C137C22×D411yescharacteristic
281C2×C4×C137C22×D411yescharacteristic
282C2×C4×C137C22×Q811yescharacteristic
283C2×C4×C137C22×Q811yescharacteristic
284C2×C4×C1372−1+411yescharacteristic
285C2×C4×C1372−1+411yescharacteristic
286C8×C137—22no—
287C8×C137—22no—
288C8×C137—41no—
289C8×C137—41no—
290C22×C137—24no—
291C22×C137—42no—
292C22×C137—42no—
293C22×C137—42no—
294C22×C137—42no—
295C22×C137—42no—
296C22×C137—42no—
297C22×C137C2×#12011yescharacteristic
298C22×C137D4×Q811yescharacteristic
299C22×C137D4×Q811yescharacteristic
300C22×C137C2×#13511yescharacteristic
301C22×C137#57511yescharacteristic
302C22×C137#57611yescharacteristic
303C22×C137#57711yescharacteristic
304C4×C137—22no—
305C4×C137—22no—
306C4×C137—22no—
307C4×C137—42no—
308C4×C137—42no—
309C4×C137—41no—
310C4×C137—42no—
311C4×C137—41no—
312C4×C137—41no—
313C4×C137—42no—
314C4×C137—42no—
315C4×C137—81no—
316C4×C137—81no—
317C4×C137C2×C4⋊Q811yescharacteristic
318C4×C137#53611yescharacteristic
319C4×C137D4×Q811yescharacteristic
320C4×C137D4×Q811yescharacteristic
321C2×C137—44no—
322C2×C137#243411yescharacteristic
323C2×C137#300211yescharacteristic
324C2×C137#301211yescharacteristic
325C2×C137#338011yescharacteristic
326C2×C137#338111yescharacteristic
327C2×C137#338811yescharacteristic
328C2×C137#338911yescharacteristic
329#25843C13711yesmaximal, characteristic, direct product factor, Sylow
330C137#2584311yescharacteristic, direct product factor, Sylow
331C2×#554C2×C13711yescharacteristic
332C2×#499C2×C13711yescharacteristic, complemented
333C2×#478C2×C13711yescharacteristic
334#2584C2×C13711yescharacteristic, complemented
335#2059C2×C13711yescharacteristic, complemented
336#2059C2×C13711yescharacteristic, complemented
337#2058C2×C13711yescharacteristic, complemented
338#2057C2×C13711yescharacteristic, complemented
339#1989C2×C13711yescharacteristic, complemented
340#1984C2×C13711yescharacteristic, complemented
341#1864C2×C13711yescharacteristic
342#1864C2×C13711yescharacteristic
343#1862C2×C13711yescharacteristic
344#1862C2×C13711yescharacteristic
345C4×#102C2×C13711yescharacteristic
346#554—24no—
347#554—24no—
348C2×C4⋊Q8C22×C13711yescharacteristic
349C2×#125C22×C13711yescharacteristic
350C2×#125C22×C13711yescharacteristic
351C2×#125C22×C13711yescharacteristic
352C2×C22⋊Q8—21no—
353C2×C22⋊Q8—21no—
354C2×C22⋊Q8—21no—
355C2×C4×Q8C22×C13711yescharacteristic
356C2×C4×D4C22×C13711yescharacteristic
357C2×C4×D4C22×C13711yescharacteristic
358C2×C4×D4C22×C13711yescharacteristic
359C22×C4⋊C4—21no—
360#499—24no—
361#478—24no—
362C2×#107C22×C13711yescharacteristic
363C2×#107C22×C13711yescharacteristic
364C2×#107C22×C13711yescharacteristic
365C2×#106C22×C13711yescharacteristic
366C2×#106C22×C13711yescharacteristic
367C2×#106C22×C13711yescharacteristic
368C2×C4⋊C8C22×C13711yescharacteristic
369C2×#102C22×C13711yescharacteristic
370C2×#102C22×C13711yescharacteristic
371C2×#102C22×C13711yescharacteristic
372C2×#102C22×C13711yescharacteristic
373C2×C4×C8C22×C13711yescharacteristic
374#398—21no—
375#395—21no—
376#389—21no—
377#389—21no—
378#389C22×C13711yescharacteristic
379#389C22×C13711yescharacteristic
380#389C22×C13711yescharacteristic
381#389C22×C13711yescharacteristic
382C4×C4⋊C4C22×C13711yescharacteristic
383#340C22×C13711yescharacteristic
384#340C22×C13711yescharacteristic
385#340C22×C13711yescharacteristic
386#340C22×C13711yescharacteristic
387#340C22×C13711yescharacteristic
388#340C22×C13711yescharacteristic
389#336C22×C13711yescharacteristic
390#336C22×C13711yescharacteristic
391#336C22×C13711yescharacteristic
392#336C22×C13711yescharacteristic
393C22×Q8—21no—
394C22×Q8D4×C13711yescharacteristic
395C22×D4C23×C13711yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C22×C8C23×C13711yescharacteristic
400C22×C8C23×C13711yescharacteristic
401C22×C8C23×C13711yescharacteristic
402C22×C8C23×C13711yescharacteristic
403C4⋊Q8—22no—
404C4⋊Q8—22no—
405#125—22no—
406#125—22no—
407#125—22no—
408#125—22no—
409#125—22no—
410#125D4×C13714yes—
411C22⋊Q8—28no—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4D4×C13714yes—
422C2×C4⋊C4—28no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4D4×C13711yescharacteristic
435C2×C4⋊C4D4×C13711yescharacteristic
436C2×C4⋊C4D4×C13711yescharacteristic
437C2×C4⋊C4C23×C13711yescharacteristic
438C2×C4⋊C4C23×C13711yescharacteristic
439C2×C4⋊C4C23×C13711yescharacteristic
440C2×C4⋊C4C23×C13711yescharacteristic
441C2×C4⋊C4C23×C13711yescharacteristic
442C2×C4⋊C4C23×C13711yescharacteristic
443C2×C4⋊C4C23×C13711yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42—21no—
448C2×C42C23×C13711yescharacteristic
449C2×C42C23×C13711yescharacteristic
450C2×C42C23×C13711yescharacteristic
451#107—22no—
452#107—22no—
453#107—22no—
454#106—22no—
455#106—22no—
456#106—22no—
457C4⋊C8—22no—
458#102—22no—
459#102—22no—
460#102Q8×C13714yescomplemented
461#102Q8×C13714yescomplemented
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468C24—21no—
469C2×Q8—24no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—41no—
473C2×Q8—81no—
474C2×Q8—81no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4C2×D4×C13712yes—
479C2×D4C2×Q8×C13712yes—
480C2×D4C2×Q8×C13712yes—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4C2×D4×C13711yescharacteristic
498C22×C4C2×D4×C13711yescharacteristic
499C22×C4C2×D4×C13711yescharacteristic
500C22×C4C2×D4×C13711yescharacteristic
501C22×C4C2×D4×C13711yescharacteristic
502C22×C4C2×D4×C13711yescharacteristic
503C22×C4C24×C13711yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8C2×Q8×C13712yes—
515C2×C8C2×Q8×C13712yes—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4C2×D4×C13712yes—
540C4⋊C4C2×D4×C13712yes—
541C4⋊C4C2×D4×C13712yes—
542C4⋊C4C2×Q8×C13712yes—
543C4⋊C4C2×Q8×C13712yes—
544C22⋊C4—24no—
545C22⋊C4—24no—
546C22⋊C4—24no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—81no—
552C42C2×D4×C13712yes—
553C42C2×D4×C13712yes—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×D4×C13711yescharacteristic
562Q8—44no—
563Q8—84no—
564D4—22no—
565D4—22no—
566D4—22no—
567D4C4⋊Q8×C13714yes—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—48no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—84no—
607C2×C4#120×C13712yes—
608C2×C4#120×C13712yes—
609C2×C4#135×C13712yes—
610C2×C4C22×D4×C13711yescharacteristic
611C2×C4C22×D4×C13711yescharacteristic
612C2×C4C22×Q8×C13711yescharacteristic
613C2×C4C22×Q8×C13711yescharacteristic
614C2×C42−1+4×C13711yescharacteristic
615C2×C42−1+4×C13711yescharacteristic
616C8—22no—
617C8—22no—
618C8—41no—
619C8—41no—
620C22—24no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22C2×#120×C13711yescharacteristic
628C22D4×Q8×C13711yescharacteristic
629C22D4×Q8×C13711yescharacteristic
630C22C2×#135×C13711yescharacteristic
631C22#575×C13711yescharacteristic
632C22#576×C13711yescharacteristic
633C22#577×C13711yescharacteristic
634C4—22no—
635C4—22no—
636C4—22no—
637C4—42no—
638C4—42no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4C2×C4⋊Q8×C13711yescharacteristic
648C4#536×C13711yescharacteristic
649C4D4×Q8×C13711yescharacteristic
650C4D4×Q8×C13711yescharacteristic
651C2—44no—
652C2#2434×C13711yescharacteristic
653C2#3002×C13711yescharacteristic
654C2#3012×C13711yescharacteristic
655C2#3380×C13711yescharacteristic
656C2#3381×C13711yescharacteristic
657C2#3388×C13711yescharacteristic
658C2#3389×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC22×D4×C137C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×Q8×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#499×C137C2semidirect
4. #2584×C137C2semidirect
5. #2059×C137C2semidirect
6. #2059×C137C2semidirect
7. #2058×C137C2semidirect
8. #2057×C137C2semidirect
9. #1989×C137C2semidirect
10. #1984×C137C2semidirect
130. #102×C137Q8semidirect
131. #102×C137Q8semidirect
329. #25843C137direct (N × H)
330. C137#25843direct (N × H)
332. C2×#499C2×C137semidirect
334. #2584C2×C137semidirect
335. #2059C2×C137semidirect
336. #2059C2×C137semidirect
337. #2058C2×C137semidirect
338. #2057C2×C137semidirect
339. #1989C2×C137semidirect
340. #1984C2×C137semidirect
460. #102Q8×C137semidirect
461. #102Q8×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1372
C2×#499×C1372
C2×#478×C1372
#2584×C1372
#2059×C1372
#2058×C1372
#2057×C1372
#1989×C1372
#1984×C1372
#1864×C1372
#1862×C1372
C4×#102×C1372
#25843137