Finite Group Databasebeta

← C137×#13884 #46863270

Subgroups — C137×#13884 #46863270

Order 35072.

1486 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387×C137C212yesmaximal
2C2×#384×C137C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C137C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C137C211yesmaximal, characteristic
5#1442×C137C212yesmaximal
6#1441×C137C212yesmaximal
7#1436×C137C212yesmaximal
8C4⋊#95×C137C211yesmaximal, characteristic
9C4⋊#95×C137C211yesmaximal, characteristic
10C4⋊#95×C137C211yesmaximal, characteristic
11C4⋊#95×C137C211yesmaximal, characteristic
12C22×C4⋊C4×C137C2211yescharacteristic
13C22×C4⋊C4×C137C2211yescharacteristic
14C22×C4⋊C4×C137C2212yes—
15C22×C4⋊C4×C137C2212yes—
16C22×C4⋊C4×C137C2211yescharacteristic
17C22×C4⋊C4×C137C2211yescharacteristic
18C22×C4⋊C4×C137C2211yescharacteristic
19C22×C4⋊C4×C137C2211yescharacteristic
20C22×C42×C137C2212yes—
21C22×C42×C137C2211yescharacteristic
22C22×C42×C137C2211yescharacteristic
23C22×C42×C137C2211yescharacteristic
24#387×C137—28no—
25#384×C137—24no—
26C4×C4⋊C4×C137—24no—
27C4×C4⋊C4×C137C418yescomplemented
28C2×#95×C137C2212yes—
29C2×#95×C137C2212yes—
30C2×#95×C137C2212yes—
31C2×#95×C137C2212yes—
32C2×#95×C137C2212yes—
33C2×#95×C137C2212yes—
34C2×#95×C137C2212yes—
35C2×#95×C137C2212yes—
36C2×#95×C137C2212yes—
37C2×#95×C137C2211yescharacteristic
38C2×#95×C137C2211yescharacteristic
39C23×C4×C137C2312yes—
40C23×C4×C137C2312yes—
41C23×C4×C137C2311yescharacteristic
42C23×C4×C137C2311yescharacteristic
43C23×C4×C137C2312yes—
44C23×C4×C137C2312yes—
45C23×C4×C137C2311yescharacteristic
46C23×C4×C137C2311yescharacteristic
47C23×C4×C137C2311yescharacteristic
48C23×C4×C137C2311yescharacteristic
49C23×C4×C137C2311yescharacteristic
50C2×C4⋊C4×C137—22no—
51C2×C4⋊C4×C137—22no—
52C2×C4⋊C4×C137—22no—
53C2×C4⋊C4×C137—22no—
54C2×C4⋊C4×C137—22no—
55C2×C4⋊C4×C137—22no—
56C2×C4⋊C4×C137—24no—
57C2×C4⋊C4×C137—24no—
58C2×C4⋊C4×C137—22no—
59C2×C4⋊C4×C137—24no—
60C2×C4⋊C4×C137—24no—
61C2×C4⋊C4×C137—22no—
62C2×C4⋊C4×C137—22no—
63C2×C4⋊C4×C137—22no—
64C2×C4⋊C4×C137—22no—
65C2×C4⋊C4×C137—22no—
66C2×C4⋊C4×C137—42no—
67C2×C4⋊C4×C137—42no—
68C2×C4⋊C4×C137C2×C414yes—
69C2×C4⋊C4×C137C2×C414yes—
70C2×C4⋊C4×C137D414yes—
71C2×C4⋊C4×C137D414yes—
72C2×C4⋊C4×C137Q814yes—
73C2×C4⋊C4×C137Q814yes—
74C2×C42×C137—22no—
75C2×C42×C137—22no—
76C2×C42×C137—22no—
77C2×C42×C137—22no—
78C2×C42×C137—22no—
79C2×C42×C137—22no—
80C2×C42×C137—24no—
81C2×C42×C137—24no—
82C2×C42×C137—42no—
83C2×C42×C137C2×C414yes—
84C2×C42×C137C2×C414yes—
85C2×C42×C137C2×C414yes—
86#95×C137—24no—
87#95×C137—24no—
88#95×C137—24no—
89#95×C137—24no—
90#95×C137—24no—
91#95×C137—24no—
92#95×C137—42no—
93#95×C137—42no—
94#95×C137—42no—
95#95×C137C2×C414yes—
96#95×C137C2×C414yes—
97C24×C137C2411yescharacteristic
98C22×C4×C137—21no—
99C22×C4×C137—21no—
100C22×C4×C137—21no—
101C22×C4×C137—21no—
102C22×C4×C137—21no—
103C22×C4×C137—21no—
104C22×C4×C137—21no—
105C22×C4×C137—21no—
106C22×C4×C137—21no—
107C22×C4×C137—21no—
108C22×C4×C137—21no—
109C22×C4×C137—21no—
110C22×C4×C137—21no—
111C22×C4×C137—21no—
112C22×C4×C137—21no—
113C22×C4×C137—21no—
114C22×C4×C137—21no—
115C22×C4×C137—22no—
116C22×C4×C137—22no—
117C22×C4×C137—22no—
118C22×C4×C137—22no—
119C22×C4×C137—21no—
120C22×C4×C137—21no—
121C22×C4×C137—21no—
122C22×C4×C137—21no—
123C22×C4×C137—21no—
124C22×C4×C137—22no—
125C22×C4×C137—22no—
126C22×C4×C137—22no—
127C22×C4×C137—22no—
128C22×C4×C137—21no—
129C22×C4×C137—21no—
130C22×C4×C137—21no—
131C22×C4×C137—22no—
132C22×C4×C137—22no—
133C22×C4×C137—22no—
134C22×C4×C137—21no—
135C22×C4×C137—21no—
136C22×C4×C137—21no—
137C22×C4×C137—22no—
138C22×C4×C137—22no—
139C22×C4×C137—22no—
140C22×C4×C137—22no—
141C22×C4×C137—22no—
142C22×C4×C137—22no—
143C22×C4×C137—22no—
144C22×C4×C137—22no—
145C22×C4×C137—22no—
146C22×C4×C137—22no—
147C22×C4×C137—22no—
148C22×C4×C137—22no—
149C22×C4×C137—22no—
150C22×C4×C137—22no—
151C22×C4×C137—22no—
152C22×C4×C137C22×C412yes—
153C22×C4×C137C22×C412yes—
154C22×C4×C137C22×C412yes—
155C22×C4×C137C22×C412yes—
156C22×C4×C137C22×C412yes—
157C22×C4×C137C22×C412yes—
158C22×C4×C137C22×C412yes—
159C22×C4×C137C2×D414yes—
160C22×C4×C137C2×D412yes—
161C22×C4×C137C2×D412yes—
162C22×C4×C137C2×D412yes—
163C22×C4×C137C2×D412yes—
164C22×C4×C137C2×Q814yes—
165C22×C4×C137C2×Q812yes—
166C22×C4×C137C2×Q812yes—
167C22×C4×C137C2×Q812yes—
168C22×C4×C137C2×Q812yes—
169C22×C4×C137#4112yes—
170C22×C4×C137#4112yes—
171C22×C4×C137#4112yes—
172C22×C4×C137#4112yes—
173C22×C4×C137#4112yes—
174C22×C4×C137#4112yes—
175C4⋊C4×C137—28no—
176C4⋊C4×C137—28no—
177C4⋊C4×C137—28no—
178C4⋊C4×C137—48no—
179C4⋊C4×C137—48no—
180C4⋊C4×C137—44no—
181C4⋊C4×C137—44no—
182C4⋊C4×C137C4⋊C4116yescomplemented
183C42×C137—28no—
184C42×C137—28no—
185C42×C137—28no—
186C42×C137—48no—
187C23×C137C23×C411yescharacteristic
188C23×C137C22×D411yescharacteristic
189C23×C137C22×D411yescharacteristic
190C23×C137C22×Q811yescharacteristic
191C23×C137C22×Q811yescharacteristic
192C23×C137C2×#4111yescharacteristic
193C23×C137C2×#4111yescharacteristic
194C23×C137C2×#4111yescharacteristic
195C23×C137C2×#4111yescharacteristic
196C23×C137C2×#4111yescharacteristic
197C23×C137C2×#4111yescharacteristic
198C23×C137H(5,𝔽2)11yescharacteristic
199C23×C137H(5,𝔽2)11yescharacteristic
200C23×C1372−1+411yescharacteristic
201C23×C1372−1+411yescharacteristic
202C2×C4×C137—22no—
203C2×C4×C137—22no—
204C2×C4×C137—22no—
205C2×C4×C137—22no—
206C2×C4×C137—22no—
207C2×C4×C137—22no—
208C2×C4×C137—22no—
209C2×C4×C137—22no—
210C2×C4×C137—22no—
211C2×C4×C137—22no—
212C2×C4×C137—22no—
213C2×C4×C137—22no—
214C2×C4×C137—22no—
215C2×C4×C137—22no—
216C2×C4×C137—22no—
217C2×C4×C137—22no—
218C2×C4×C137—22no—
219C2×C4×C137—22no—
220C2×C4×C137—22no—
221C2×C4×C137—22no—
222C2×C4×C137—22no—
223C2×C4×C137—22no—
224C2×C4×C137—22no—
225C2×C4×C137—22no—
226C2×C4×C137—22no—
227C2×C4×C137—22no—
228C2×C4×C137—22no—
229C2×C4×C137—22no—
230C2×C4×C137—22no—
231C2×C4×C137—22no—
232C2×C4×C137—24no—
233C2×C4×C137—24no—
234C2×C4×C137—24no—
235C2×C4×C137—24no—
236C2×C4×C137—24no—
237C2×C4×C137—24no—
238C2×C4×C137—42no—
239C2×C4×C137—42no—
240C2×C4×C137—41no—
241C2×C4×C137—42no—
242C2×C4×C137—41no—
243C2×C4×C137—41no—
244C2×C4×C137—41no—
245C2×C4×C137—42no—
246C2×C4×C137—42no—
247C2×C4×C137—41no—
248C2×C4×C137—41no—
249C2×C4×C137—42no—
250C2×C4×C137—42no—
251C2×C4×C137—41no—
252C2×C4×C137—41no—
253C2×C4×C137—42no—
254C2×C4×C137—42no—
255C2×C4×C137—42no—
256C2×C4×C137—42no—
257C2×C4×C137—42no—
258C2×C4×C137—42no—
259C2×C4×C137—42no—
260C2×C4×C137—42no—
261C2×C4×C137—42no—
262C2×C4×C137—42no—
263C2×C4×C137—42no—
264C2×C4×C137—42no—
265C2×C4×C137—42no—
266C2×C4×C137—42no—
267C2×C4×C137—42no—
268C2×C4×C137C2×C4⋊C414yes—
269C2×C4×C137C2×C4⋊C414yes—
270C2×C4×C137C2×C4⋊C414yes—
271C2×C4×C137#11714yes—
272C2×C4×C137#11714yes—
273C2×C4×C137C4×D414yes—
274C2×C4×C137C4×Q814yes—
275C2×C4×C137C22⋊Q814yes—
276C2×C4×C137#12314yes—
277C2×C4×C137#12514yes—
278C2×C4×C137#12614yes—
279C22×C137C22×C4⋊C411yescharacteristic
280C22×C137C2×#11711yescharacteristic
281C22×C137C2×#11711yescharacteristic
282C22×C137C2×C4×D411yescharacteristic
283C22×C137C2×C4×Q811yescharacteristic
284C22×C137#52011yescharacteristic
285C22×C137#52011yescharacteristic
286C22×C137C2×C22⋊Q811yescharacteristic
287C22×C137C2×#12311yescharacteristic
288C22×C137C2×#12511yescharacteristic
289C22×C137C2×#12611yescharacteristic
290C22×C137#53211yescharacteristic
291C22×C137#53211yescharacteristic
292C22×C137#53311yescharacteristic
293C22×C137#53311yescharacteristic
294C22×C137#54011yescharacteristic
295C22×C137#54111yescharacteristic
296C22×C137#54211yescharacteristic
297C22×C137#54211yescharacteristic
298C22×C137D4211yescharacteristic
299C22×C137#54611yescharacteristic
300C22×C137#54711yescharacteristic
301C22×C137#54811yescharacteristic
302C22×C137D4×Q811yescharacteristic
303C22×C137D4×Q811yescharacteristic
304C22×C137#55011yescharacteristic
305C22×C137#55211yescharacteristic
306C22×C137#55311yescharacteristic
307C22×C137#55411yescharacteristic
308C22×C137#55411yescharacteristic
309C22×C137#55611yescharacteristic
310C22×C137#55711yescharacteristic
311C22×C137#55711yescharacteristic
312C22×C137Q8211yescharacteristic
313C22×C137#55911yescharacteristic
314C4×C137—24no—
315C4×C137—24no—
316C4×C137—24no—
317C4×C137—24no—
318C4×C137—42no—
319C4×C137—42no—
320C4×C137—44no—
321C4×C137—44no—
322C4×C137—82no—
323C4×C137—82no—
324C4×C137#38718yescomplemented
325C2×C137#228511yescharacteristic
326C2×C137C2×#38711yescharacteristic
327C2×C137#231411yescharacteristic
328C2×C137D4×C4⋊C411yescharacteristic
329C2×C137Q8×C4⋊C411yescharacteristic
330C2×C137#235211yescharacteristic
331C2×C137#235511yescharacteristic
332C2×C137#244511yescharacteristic
333C2×C137#244611yescharacteristic
334C2×C137#245111yescharacteristic
335C2×C137#245211yescharacteristic
336C2×C137#250611yescharacteristic
337C2×C137#250711yescharacteristic
338C2×C137#251111yescharacteristic
339C2×C137#251211yescharacteristic
340#13884C13711yesmaximal, characteristic, direct product factor, Sylow
341C137#1388411yescharacteristic, direct product factor, Sylow
342C2×#387C2×C13712yes—
343C2×#384C2×C13711yescharacteristic
344C2×C4×C4⋊C4C2×C13711yescharacteristic
345C2×C4×C4⋊C4C2×C13711yescharacteristic
346#1442C2×C13712yes—
347#1441C2×C13712yes—
348#1436C2×C13712yes—
349C4⋊#95C2×C13711yescharacteristic
350C4⋊#95C2×C13711yescharacteristic
351C4⋊#95C2×C13711yescharacteristic
352C4⋊#95C2×C13711yescharacteristic
353C22×C4⋊C4C22×C13711yescharacteristic
354C22×C4⋊C4C22×C13711yescharacteristic
355C22×C4⋊C4C22×C13712yes—
356C22×C4⋊C4C22×C13712yes—
357C22×C4⋊C4C22×C13711yescharacteristic
358C22×C4⋊C4C22×C13711yescharacteristic
359C22×C4⋊C4C22×C13711yescharacteristic
360C22×C4⋊C4C22×C13711yescharacteristic
361C22×C42C22×C13712yes—
362C22×C42C22×C13711yescharacteristic
363C22×C42C22×C13711yescharacteristic
364C22×C42C22×C13711yescharacteristic
365#387—28no—
366#384—24no—
367C4×C4⋊C4—24no—
368C4×C4⋊C4C4×C13718yescomplemented
369C2×#95C22×C13712yes—
370C2×#95C22×C13712yes—
371C2×#95C22×C13712yes—
372C2×#95C22×C13712yes—
373C2×#95C22×C13712yes—
374C2×#95C22×C13712yes—
375C2×#95C22×C13712yes—
376C2×#95C22×C13712yes—
377C2×#95C22×C13712yes—
378C2×#95C22×C13711yescharacteristic
379C2×#95C22×C13711yescharacteristic
380C23×C4C23×C13712yes—
381C23×C4C23×C13712yes—
382C23×C4C23×C13711yescharacteristic
383C23×C4C23×C13711yescharacteristic
384C23×C4C23×C13712yes—
385C23×C4C23×C13712yes—
386C23×C4C23×C13711yescharacteristic
387C23×C4C23×C13711yescharacteristic
388C23×C4C23×C13711yescharacteristic
389C23×C4C23×C13711yescharacteristic
390C23×C4C23×C13711yescharacteristic
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4C2×C4×C13714yes—
410C2×C4⋊C4C2×C4×C13714yes—
411C2×C4⋊C4D4×C13714yes—
412C2×C4⋊C4D4×C13714yes—
413C2×C4⋊C4Q8×C13714yes—
414C2×C4⋊C4Q8×C13714yes—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—42no—
424C2×C42C2×C4×C13714yes—
425C2×C42C2×C4×C13714yes—
426C2×C42C2×C4×C13714yes—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95C2×C4×C13714yes—
437#95C2×C4×C13714yes—
438C24C24×C13711yescharacteristic
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4C22×C4×C13712yes—
494C22×C4C22×C4×C13712yes—
495C22×C4C22×C4×C13712yes—
496C22×C4C22×C4×C13712yes—
497C22×C4C22×C4×C13712yes—
498C22×C4C22×C4×C13712yes—
499C22×C4C22×C4×C13712yes—
500C22×C4C2×D4×C13714yes—
501C22×C4C2×D4×C13712yes—
502C22×C4C2×D4×C13712yes—
503C22×C4C2×D4×C13712yes—
504C22×C4C2×D4×C13712yes—
505C22×C4C2×Q8×C13714yes—
506C22×C4C2×Q8×C13712yes—
507C22×C4C2×Q8×C13712yes—
508C22×C4C2×Q8×C13712yes—
509C22×C4C2×Q8×C13712yes—
510C22×C4#41×C13712yes—
511C22×C4#41×C13712yes—
512C22×C4#41×C13712yes—
513C22×C4#41×C13712yes—
514C22×C4#41×C13712yes—
515C22×C4#41×C13712yes—
516C4⋊C4—28no—
517C4⋊C4—28no—
518C4⋊C4—28no—
519C4⋊C4—48no—
520C4⋊C4—48no—
521C4⋊C4—44no—
522C4⋊C4—44no—
523C4⋊C4C4⋊C4×C137116yescomplemented
524C42—28no—
525C42—28no—
526C42—28no—
527C42—48no—
528C23C23×C4×C13711yescharacteristic
529C23C22×D4×C13711yescharacteristic
530C23C22×D4×C13711yescharacteristic
531C23C22×Q8×C13711yescharacteristic
532C23C22×Q8×C13711yescharacteristic
533C23C2×#41×C13711yescharacteristic
534C23C2×#41×C13711yescharacteristic
535C23C2×#41×C13711yescharacteristic
536C23C2×#41×C13711yescharacteristic
537C23C2×#41×C13711yescharacteristic
538C23C2×#41×C13711yescharacteristic
539C23H(5,𝔽2)×C13711yescharacteristic
540C23H(5,𝔽2)×C13711yescharacteristic
541C232−1+4×C13711yescharacteristic
542C232−1+4×C13711yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C4⋊C4×C13714yes—
610C2×C4C2×C4⋊C4×C13714yes—
611C2×C4C2×C4⋊C4×C13714yes—
612C2×C4#117×C13714yes—
613C2×C4#117×C13714yes—
614C2×C4C4×D4×C13714yes—
615C2×C4C4×Q8×C13714yes—
616C2×C4C22⋊Q8×C13714yes—
617C2×C4#123×C13714yes—
618C2×C4#125×C13714yes—
619C2×C4#126×C13714yes—
620C22C22×C4⋊C4×C13711yescharacteristic
621C22C2×#117×C13711yescharacteristic
622C22C2×#117×C13711yescharacteristic
623C22C2×C4×D4×C13711yescharacteristic
624C22C2×C4×Q8×C13711yescharacteristic
625C22#520×C13711yescharacteristic
626C22#520×C13711yescharacteristic
627C22C2×C22⋊Q8×C13711yescharacteristic
628C22C2×#123×C13711yescharacteristic
629C22C2×#125×C13711yescharacteristic
630C22C2×#126×C13711yescharacteristic
631C22#532×C13711yescharacteristic
632C22#532×C13711yescharacteristic
633C22#533×C13711yescharacteristic
634C22#533×C13711yescharacteristic
635C22#540×C13711yescharacteristic
636C22#541×C13711yescharacteristic
637C22#542×C13711yescharacteristic
638C22#542×C13711yescharacteristic
639C22D42×C13711yescharacteristic
640C22#546×C13711yescharacteristic
641C22#547×C13711yescharacteristic
642C22#548×C13711yescharacteristic
643C22D4×Q8×C13711yescharacteristic
644C22D4×Q8×C13711yescharacteristic
645C22#550×C13711yescharacteristic
646C22#552×C13711yescharacteristic
647C22#553×C13711yescharacteristic
648C22#554×C13711yescharacteristic
649C22#554×C13711yescharacteristic
650C22#556×C13711yescharacteristic
651C22#557×C13711yescharacteristic
652C22#557×C13711yescharacteristic
653C22Q82×C13711yescharacteristic
654C22#559×C13711yescharacteristic
655C4—24no—
656C4—24no—
657C4—24no—
658C4—24no—
659C4—42no—
660C4—42no—
661C4—44no—
662C4—44no—
663C4—82no—
664C4—82no—
665C4#387×C13718yescomplemented
666C2#2285×C13711yescharacteristic
667C2C2×#387×C13711yescharacteristic
668C2#2314×C13711yescharacteristic
669C2D4×C4⋊C4×C13711yescharacteristic
670C2Q8×C4⋊C4×C13711yescharacteristic
671C2#2352×C13711yescharacteristic
672C2#2355×C13711yescharacteristic
673C2#2445×C13711yescharacteristic
674C2#2446×C13711yescharacteristic
675C2#2451×C13711yescharacteristic
676C2#2452×C13711yescharacteristic
677C2#2506×C13711yescharacteristic
678C2#2507×C13711yescharacteristic
679C2#2511×C13711yescharacteristic
680C2#2512×C13711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
27. C4×C4⋊C4×C137C4semidirect
182. C4⋊C4×C137C4⋊C4semidirect
324. C4×C137#387semidirect
340. #13884C137direct (N × H)
341. C137#13884direct (N × H)
368. C4×C4⋊C4C4×C137semidirect
523. C4⋊C4C4⋊C4×C137semidirect
665. C4#387×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#387×C1372
C2×#384×C1372
C2×C4×C4⋊C4×C1372
#1442×C1372
#1441×C1372
#1436×C1372
C4⋊#95×C1372
#13884137