Finite Group Databasebeta

← C131×#23578 #45709462

Subgroups — C131×#23578 #45709462

Order 33536.

1176 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C131C211yesmaximal, characteristic
2C2×#441×C131C211yesmaximal, characteristic, complemented
3C2×#440×C131C211yesmaximal, characteristic, complemented
4C4×C22⋊Q8×C131C211yesmaximal, characteristic, complemented
5#2059×C131C211yesmaximal, characteristic, complemented
6#2042×C131C211yesmaximal, characteristic, complemented
7#2036×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic
9#2026×C131C211yesmaximal, characteristic, complemented
10#2015×C131C211yesmaximal, characteristic, complemented
11#2001×C131C211yesmaximal, characteristic, complemented
12#2000×C131C211yesmaximal, characteristic
13#1763×C131C211yesmaximal, characteristic, complemented
14#1762×C131C211yesmaximal, characteristic, complemented
15#1749×C131C211yesmaximal, characteristic, complemented
16C22×Q16×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18#529×C131—24no—
19#529×C131—24no—
20C2×#126×C131—21no—
21C2×#125×C131C2211yescharacteristic
22C2×#124×C131C2211yescharacteristic
23C2×#123×C131—21no—
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×#121×C131C2211yescharacteristic
27C2×C4×Q8×C131C2211yescharacteristic
28C2×C4×Q8×C131C2211yescharacteristic
29C2×C4×D4×C131—21no—
30C2×C4×D4×C131C2211yescharacteristic
31C2×#117×C131—21no—
32C22×C42×C131C2211yescharacteristic
33#441×C131—24no—
34#440×C131—24no—
35C2×#107×C131C2211yescharacteristic
36C2×#106×C131C2211yescharacteristic
37C2×#103×C131C2211yescharacteristic
38C2×#103×C131C2211yescharacteristic
39C2×#103×C131C2211yescharacteristic
40C2×#103×C131C2211yescharacteristic
41C2×#103×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic
46C2×C22⋊C8×C131C2211yescharacteristic
47C2×#97×C131C2211yescharacteristic
48C2×#97×C131C2211yescharacteristic
49#391×C131C2211yescharacteristic
50#389×C131C2211yescharacteristic
51#387×C131—21no—
52#385×C131—21no—
53#380×C131C2211yescharacteristic
54C4×C4⋊C4×C131—21no—
55C4×C4⋊C4×C131C2211yescharacteristic
56C4×C22⋊C4×C131—21no—
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#336×C131C2211yescharacteristic
62#336×C131C2211yescharacteristic
63C22×Q8×C131C2311yescharacteristic
64C22×Q8×C131C2311yescharacteristic
65C22×D4×C131—21no—
66C22×D4×C131C2311yescharacteristic
67C23×C4×C131—21no—
68C23×C4×C131D411yescharacteristic
69C23×C4×C131D411yescharacteristic
70C23×C4×C131C2311yescharacteristic
71C2×Q16×C131—22no—
72C2×Q16×C131—22no—
73C2×Q16×C131—22no—
74C2×SD16×C131—22no—
75C2×SD16×C131—22no—
76C2×SD16×C131—22no—
77C22×C8×C131C2311yescharacteristic
78C22×C8×C131C2311yescharacteristic
79C22×C8×C131C2311yescharacteristic
80C22×C8×C131C2311yescharacteristic
81#126×C131—28no—
82#125×C131—22no—
83#125×C131—22no—
84#124×C131—22no—
85#124×C131—22no—
86#123×C131—28no—
87C22⋊Q8×C131—22no—
88C22⋊Q8×C131—22no—
89C22⋊Q8×C131—22no—
90C22⋊Q8×C131—22no—
91#121×C131—22no—
92#121×C131—22no—
93C4×Q8×C131—22no—
94C4×Q8×C131—22no—
95C4×Q8×C131—22no—
96C4×Q8×C131D414yes—
97C4×D4×C131—28no—
98C4×D4×C131—22no—
99C4×D4×C131D414yes—
100#117×C131—28no—
101C2×C4⋊C4×C131—21no—
102C2×C4⋊C4×C131—21no—
103C2×C4⋊C4×C131—21no—
104C2×C4⋊C4×C131—21no—
105C2×C4⋊C4×C131—21no—
106C2×C4⋊C4×C131—21no—
107C2×C4⋊C4×C131—21no—
108C2×C4⋊C4×C131C2311yescharacteristic
109C2×C4⋊C4×C131C2311yescharacteristic
110C2×C4⋊C4×C131C2311yescharacteristic
111C2×C4⋊C4×C131C2311yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C22⋊C4×C131—21no—
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—21no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C42×C131—21no—
121C2×C42×C131—22no—
122C2×C42×C131—22no—
123C2×C42×C131—21no—
124C2×C42×C131—21no—
125C2×C42×C131D411yescharacteristic
126C2×C42×C131D411yescharacteristic
127C2×C42×C131C2311yescharacteristic
128C2×C42×C131C2311yescharacteristic
129#107×C131—22no—
130#106×C131—22no—
131#103×C131—22no—
132#103×C131—22no—
133#103×C131—22no—
134#103×C131—22no—
135#103×C131—22no—
136#102×C131—22no—
137#102×C131—22no—
138#102×C131—22no—
139C22⋊C8×C131—22no—
140C22⋊C8×C131—22no—
141#97×C131—22no—
142#97×C131—22no—
143#95×C131—21no—
144#95×C131—21no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148C24×C131—21no—
149C24×C131C2×D411yescharacteristic
150C2×Q8×C131—21no—
151C2×Q8×C131—21no—
152C2×Q8×C131—21no—
153C2×Q8×C131—21no—
154C2×Q8×C131—21no—
155C2×Q8×C131—21no—
156C2×Q8×C131—21no—
157C2×Q8×C131—21no—
158C2×Q8×C131—21no—
159C2×Q8×C131—21no—
160C2×Q8×C131C2×D412yes—
161C2×Q8×C131#4112yes—
162C2×D4×C131—24no—
163C2×D4×C131—21no—
164C2×D4×C131—21no—
165C2×D4×C131—21no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—42no—
169C2×D4×C131—42no—
170C2×D4×C131C2×D412yes—
171C22×C4×C131—22no—
172C22×C4×C131—21no—
173C22×C4×C131—21no—
174C22×C4×C131—21no—
175C22×C4×C131—21no—
176C22×C4×C131—21no—
177C22×C4×C131—22no—
178C22×C4×C131—22no—
179C22×C4×C131—24no—
180C22×C4×C131—21no—
181C22×C4×C131—21no—
182C22×C4×C131—21no—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—21no—
188C22×C4×C131—41no—
189C22×C4×C131—41no—
190C22×C4×C131—41no—
191C22×C4×C131—42no—
192C22×C4×C131—42no—
193C22×C4×C131C2×D411yescharacteristic
194C22×C4×C131C2×D411yescharacteristic
195C22×C4×C131C2×D411yescharacteristic
196C22×C4×C131C2×D411yescharacteristic
197C22×C4×C131C2×D411yescharacteristic
198C22×C4×C131C2411yescharacteristic
199Q16×C131—28no—
200SD16×C131—28no—
201C2×C8×C131—21no—
202C2×C8×C131—21no—
203C2×C8×C131—21no—
204C2×C8×C131—21no—
205C2×C8×C131—21no—
206C2×C8×C131—21no—
207C2×C8×C131—21no—
208C2×C8×C131—21no—
209C2×C8×C131—21no—
210C2×C8×C131—21no—
211C2×C8×C131#4112yes—
212C2×C8×C131#4112yes—
213C4⋊C4×C131—24no—
214C4⋊C4×C131—24no—
215C4⋊C4×C131—24no—
216C4⋊C4×C131—24no—
217C4⋊C4×C131—24no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—21no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—21no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—42no—
226C4⋊C4×C131—42no—
227C4⋊C4×C131C2×D412yes—
228C4⋊C4×C131C2×D412yes—
229C4⋊C4×C131#4112yes—
230C22⋊C4×C131—24no—
231C22⋊C4×C131—24no—
232C22⋊C4×C131—24no—
233C22⋊C4×C131—24no—
234C22⋊C4×C131—24no—
235C22⋊C4×C131—24no—
236C22⋊C4×C131—42no—
237C42×C131—22no—
238C42×C131—22no—
239C42×C131—24no—
240C42×C131—21no—
241C42×C131—21no—
242C42×C131—42no—
243C42×C131—42no—
244C42×C131C2×D412yes—
245C42×C131C2×D412yes—
246C23×C131—21no—
247C23×C131—21no—
248C23×C131—21no—
249C23×C131—21no—
250C23×C131—21no—
251C23×C131—21no—
252C23×C131—22no—
253C23×C131—41no—
254C23×C131—41no—
255C23×C131—41no—
256C23×C131—41no—
257C23×C131—41no—
258C23×C131—41no—
259C23×C131#13712yes—
260C23×C131C22×D411yescharacteristic
261Q8×C131—22no—
262Q8×C131—22no—
263Q8×C131—22no—
264Q8×C131—22no—
265Q8×C131—41no—
266Q8×C131—41no—
267Q8×C131—41no—
268Q8×C131—41no—
269D4×C131—22no—
270D4×C131—22no—
271D4×C131—48no—
272D4×C131—41no—
273D4×C131—41no—
274C2×C4×C131—21no—
275C2×C4×C131—21no—
276C2×C4×C131—21no—
277C2×C4×C131—21no—
278C2×C4×C131—21no—
279C2×C4×C131—21no—
280C2×C4×C131—21no—
281C2×C4×C131—22no—
282C2×C4×C131—22no—
283C2×C4×C131—22no—
284C2×C4×C131—22no—
285C2×C4×C131—22no—
286C2×C4×C131—21no—
287C2×C4×C131—21no—
288C2×C4×C131—21no—
289C2×C4×C131—21no—
290C2×C4×C131—21no—
291C2×C4×C131—21no—
292C2×C4×C131—44no—
293C2×C4×C131—44no—
294C2×C4×C131—48no—
295C2×C4×C131—41no—
296C2×C4×C131—41no—
297C2×C4×C131—41no—
298C2×C4×C131—41no—
299C2×C4×C131—41no—
300C2×C4×C131—41no—
301C2×C4×C131—41no—
302C2×C4×C131—41no—
303C2×C4×C131—41no—
304C2×C4×C131—41no—
305C2×C4×C131—41no—
306C2×C4×C131—41no—
307C2×C4×C131—41no—
308C2×C4×C131—41no—
309C2×C4×C131—41no—
310C2×C4×C131—41no—
311C2×C4×C131—41no—
312C2×C4×C131—41no—
313C2×C4×C131—41no—
314C2×C4×C131—41no—
315C2×C4×C131#12012yes—
316C2×C4×C131#12012yes—
317C2×C4×C131C22×D411yescharacteristic
318C2×C4×C131C22×D411yescharacteristic
319C2×C4×C131C2×#4111yescharacteristic
320C2×C4×C131C2×#4111yescharacteristic
321C2×C4×C131C2×#4111yescharacteristic
322C2×C4×C131C2×#4111yescharacteristic
323C8×C131—22no—
324C8×C131—22no—
325C8×C131—41no—
326C8×C131—41no—
327C22×C131—22no—
328C22×C131—22no—
329C22×C131—22no—
330C22×C131—41no—
331C22×C131—41no—
332C22×C131—41no—
333C22×C131—41no—
334C22×C131—42no—
335C22×C131—42no—
336C22×C131—42no—
337C22×C131—81no—
338C22×C131—81no—
339C22×C131—81no—
340C22×C131—81no—
341C22×C131C2×#12011yescharacteristic
342C22×C131#52511yescharacteristic
343C22×C131#53211yescharacteristic
344C22×C131C2×#13711yescharacteristic
345C22×C131#57511yescharacteristic
346C22×C131#57511yescharacteristic
347C22×C131#57511yescharacteristic
348C4×C131—22no—
349C4×C131—22no—
350C4×C131—42no—
351C4×C131—41no—
352C4×C131—42no—
353C4×C131—42no—
354C4×C131—41no—
355C4×C131—42no—
356C4×C131—41no—
357C4×C131—42no—
358C4×C131—81no—
359C4×C131—81no—
360C4×C131#52511yescharacteristic
361C4×C131#52511yescharacteristic
362C4×C131#53211yescharacteristic
363C4×C131#53211yescharacteristic
364C2×C131—42no—
365C2×C131—82no—
366C2×C131#238811yescharacteristic
367C2×C131#300511yescharacteristic
368C2×C131#300711yescharacteristic
369C2×C131#311111yescharacteristic
370C2×C131#311711yescharacteristic
371C2×C131#318111yescharacteristic
372C2×C131#318311yescharacteristic
373#23578C13111yesmaximal, characteristic, direct product factor, Sylow
374C131#2357811yescharacteristic, direct product factor, Sylow
375C2×#529C2×C13111yescharacteristic
376C2×#441C2×C13111yescharacteristic, complemented
377C2×#440C2×C13111yescharacteristic, complemented
378C4×C22⋊Q8C2×C13111yescharacteristic, complemented
379#2059C2×C13111yescharacteristic, complemented
380#2042C2×C13111yescharacteristic, complemented
381#2036C2×C13111yescharacteristic, complemented
382#2034C2×C13111yescharacteristic
383#2026C2×C13111yescharacteristic, complemented
384#2015C2×C13111yescharacteristic, complemented
385#2001C2×C13111yescharacteristic, complemented
386#2000C2×C13111yescharacteristic
387#1763C2×C13111yescharacteristic, complemented
388#1762C2×C13111yescharacteristic, complemented
389#1749C2×C13111yescharacteristic, complemented
390C22×Q16C22×C13111yescharacteristic
391C22×SD16C22×C13111yescharacteristic
392#529—24no—
393#529—24no—
394C2×#126—21no—
395C2×#125C22×C13111yescharacteristic
396C2×#124C22×C13111yescharacteristic
397C2×#123—21no—
398C2×C22⋊Q8C22×C13111yescharacteristic
399C2×C22⋊Q8C22×C13111yescharacteristic
400C2×#121C22×C13111yescharacteristic
401C2×C4×Q8C22×C13111yescharacteristic
402C2×C4×Q8C22×C13111yescharacteristic
403C2×C4×D4—21no—
404C2×C4×D4C22×C13111yescharacteristic
405C2×#117—21no—
406C22×C42C22×C13111yescharacteristic
407#441—24no—
408#440—24no—
409C2×#107C22×C13111yescharacteristic
410C2×#106C22×C13111yescharacteristic
411C2×#103C22×C13111yescharacteristic
412C2×#103C22×C13111yescharacteristic
413C2×#103C22×C13111yescharacteristic
414C2×#103C22×C13111yescharacteristic
415C2×#103C22×C13111yescharacteristic
416C2×#102C22×C13111yescharacteristic
417C2×#102C22×C13111yescharacteristic
418C2×#102C22×C13111yescharacteristic
419C2×C22⋊C8C22×C13111yescharacteristic
420C2×C22⋊C8C22×C13111yescharacteristic
421C2×#97C22×C13111yescharacteristic
422C2×#97C22×C13111yescharacteristic
423#391C22×C13111yescharacteristic
424#389C22×C13111yescharacteristic
425#387—21no—
426#385—21no—
427#380C22×C13111yescharacteristic
428C4×C4⋊C4—21no—
429C4×C4⋊C4C22×C13111yescharacteristic
430C4×C22⋊C4—21no—
431#340C22×C13111yescharacteristic
432#340C22×C13111yescharacteristic
433#340C22×C13111yescharacteristic
434#340C22×C13111yescharacteristic
435#336C22×C13111yescharacteristic
436#336C22×C13111yescharacteristic
437C22×Q8C23×C13111yescharacteristic
438C22×Q8C23×C13111yescharacteristic
439C22×D4—21no—
440C22×D4C23×C13111yescharacteristic
441C23×C4—21no—
442C23×C4D4×C13111yescharacteristic
443C23×C4D4×C13111yescharacteristic
444C23×C4C23×C13111yescharacteristic
445C2×Q16—22no—
446C2×Q16—22no—
447C2×Q16—22no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C22×C8C23×C13111yescharacteristic
452C22×C8C23×C13111yescharacteristic
453C22×C8C23×C13111yescharacteristic
454C22×C8C23×C13111yescharacteristic
455#126—28no—
456#125—22no—
457#125—22no—
458#124—22no—
459#124—22no—
460#123—28no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465#121—22no—
466#121—22no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8D4×C13114yes—
471C4×D4—28no—
472C4×D4—22no—
473C4×D4D4×C13114yes—
474#117—28no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4C23×C13111yescharacteristic
483C2×C4⋊C4C23×C13111yescharacteristic
484C2×C4⋊C4C23×C13111yescharacteristic
485C2×C4⋊C4C23×C13111yescharacteristic
486C2×C4⋊C4C23×C13111yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C42—21no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—21no—
498C2×C42—21no—
499C2×C42D4×C13111yescharacteristic
500C2×C42D4×C13111yescharacteristic
501C2×C42C23×C13111yescharacteristic
502C2×C42C23×C13111yescharacteristic
503#107—22no—
504#106—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#103—22no—
509#103—22no—
510#102—22no—
511#102—22no—
512#102—22no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515#97—22no—
516#97—22no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522C24—21no—
523C24C2×D4×C13111yescharacteristic
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8C2×D4×C13112yes—
535C2×Q8#41×C13112yes—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4C2×D4×C13112yes—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4C2×D4×C13111yescharacteristic
568C22×C4C2×D4×C13111yescharacteristic
569C22×C4C2×D4×C13111yescharacteristic
570C22×C4C2×D4×C13111yescharacteristic
571C22×C4C2×D4×C13111yescharacteristic
572C22×C4C24×C13111yescharacteristic
573Q16—28no—
574SD16—28no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8#41×C13112yes—
586C2×C8#41×C13112yes—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4C2×D4×C13112yes—
602C4⋊C4C2×D4×C13112yes—
603C4⋊C4#41×C13112yes—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—42no—
611C42—22no—
612C42—22no—
613C42—24no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42C2×D4×C13112yes—
619C42C2×D4×C13112yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23#137×C13112yes—
634C23C22×D4×C13111yescharacteristic
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—48no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4#120×C13112yes—
690C2×C4#120×C13112yes—
691C2×C4C22×D4×C13111yescharacteristic
692C2×C4C22×D4×C13111yescharacteristic
693C2×C4C2×#41×C13111yescharacteristic
694C2×C4C2×#41×C13111yescharacteristic
695C2×C4C2×#41×C13111yescharacteristic
696C2×C4C2×#41×C13111yescharacteristic
697C8—22no—
698C8—22no—
699C8—41no—
700C8—41no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×#120×C13111yescharacteristic
716C22#525×C13111yescharacteristic
717C22#532×C13111yescharacteristic
718C22C2×#137×C13111yescharacteristic
719C22#575×C13111yescharacteristic
720C22#575×C13111yescharacteristic
721C22#575×C13111yescharacteristic
722C4—22no—
723C4—22no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4#525×C13111yescharacteristic
735C4#525×C13111yescharacteristic
736C4#532×C13111yescharacteristic
737C4#532×C13111yescharacteristic
738C2—42no—
739C2—82no—
740C2#2388×C13111yescharacteristic
741C2#3005×C13111yescharacteristic
742C2#3007×C13111yescharacteristic
743C2#3111×C13111yescharacteristic
744C2#3117×C13111yescharacteristic
745C2#3181×C13111yescharacteristic
746C2#3183×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#441×C131C2semidirect
3. C2×#440×C131C2semidirect
4. C4×C22⋊Q8×C131C2semidirect
5. #2059×C131C2semidirect
6. #2042×C131C2semidirect
7. #2036×C131C2semidirect
9. #2026×C131C2semidirect
10. #2015×C131C2semidirect
11. #2001×C131C2semidirect
13. #1763×C131C2semidirect
14. #1762×C131C2semidirect
15. #1749×C131C2semidirect
373. #23578C131direct (N × H)
374. C131#23578direct (N × H)
376. C2×#441C2×C131semidirect
377. C2×#440C2×C131semidirect
378. C4×C22⋊Q8C2×C131semidirect
379. #2059C2×C131semidirect
380. #2042C2×C131semidirect
381. #2036C2×C131semidirect
383. #2026C2×C131semidirect
384. #2015C2×C131semidirect
385. #2001C2×C131semidirect
387. #1763C2×C131semidirect
388. #1762C2×C131semidirect
389. #1749C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1312
C2×#441×C1312
C2×#440×C1312
C4×C22⋊Q8×C1312
#2059×C1312
#2042×C1312
#2036×C1312
#2034×C1312
#2026×C1312
#2015×C1312
#2001×C1312
#2000×C1312
#1763×C1312
#1762×C1312
#1749×C1312
#23578131