Finite Group Databasebeta

← #15790528

Subgroups — #15790528

Order 3328.

1266 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718891C211yesmaximal, characteristic
2C2×#11718598C211yesmaximal, characteristic
3#13113107C211yesmaximal, characteristic
4#13113098C211yesmaximal, characteristic
5#13113098C211yesmaximal, characteristic
6#13113093C211yesmaximal, characteristic
7#13113093C211yesmaximal, characteristic
8#13113089C211yesmaximal, characteristic
9#13113070C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic
11#13113068C211yesmaximal, characteristic
12#13113063C211yesmaximal, characteristic
13#13113061C211yesmaximal, characteristic
14#13113061C211yesmaximal, characteristic
15C2×C13×#391C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C13×#391C418yescomplemented
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28#11718891—24no—
29C2×#88071C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718598—24no—
54C22×Q8×C13—22no—
55C22×Q8×C13—22no—
56C22×Q8×C13—22no—
57C22×Q8×C13—22no—
58C22×Q8×C13—41no—
59C22×Q8×C13—41no—
60C22×Q8×C13C2×C414yes—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4C2×C414yes—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13C2×C414yes—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—41no—
86C2×C4⋊Dic13—41no—
87C2×C4⋊Dic13—41no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—41no—
92C2×C4×Dic13—41no—
93C2×C4×Dic13—41no—
94C13×#95C2×C414yes—
95C13×#95C2×C414yes—
96C13×#95C2×C414yes—
97C13×#95C2×C414yes—
98#88071—22no—
99#88071—22no—
100#88071—22no—
101#88071—22no—
102#88071—22no—
103#88071—22no—
104#88071—22no—
105#88071—22no—
106#88071—22no—
107#88071—22no—
108#88071—22no—
109#88071—22no—
110#88071—22no—
111#88071—22no—
112#88071—22no—
113#88071—41no—
114#88071—41no—
115#88071—41no—
116#88071—41no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071D414yes—
122#14380—131nomaximal, Sylow
123C24×C13C2411yescharacteristic
124C2×Q8×C13—28no—
125C2×Q8×C13—28no—
126C2×Q8×C13—44no—
127C2×Q8×C13—44no—
128C2×Q8×C13—44no—
129C2×Q8×C13—44no—
130C2×Q8×C13—44no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C22×C412yes—
171C22×C4×C13C22×C412yes—
172C22×C4×C13C22×C412yes—
173C22×C4×C13C22×C412yes—
174C22×C4×C13C22×C412yes—
175C22×C4×C13C22×C412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13#4112yes—
178C22×C4×C13#4112yes—
179C22×C4×C13#4112yes—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13C2×D412yes—
233C22×Dic13C2×D412yes—
234C22×Dic13#4112yes—
235C22×Dic13#4112yes—
236C13×C4⋊C4—44no—
237C42×C13—28no—
238C4⋊Dic13—44no—
239C4⋊Dic13—44no—
240C4×Dic13—44no—
241C4×Dic13—44no—
242C2×#391—131no—
243C2×#391D1311yescharacteristic
244C2×#383—131no—
245#1446—131no—
246#1443—131no—
247#1443—131no—
248#1442—131no—
249#1442—131no—
250#1441—131no—
251#1436—131no—
252#1436—131no—
253#1436—131no—
254#1434—131no—
255#1434—131no—
256#1434—131no—
257C23×C13C23×C411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13H(5,𝔽2)11yescharacteristic
265C23×C13H(5,𝔽2)11yescharacteristic
266C23×C13H(5,𝔽2)11yescharacteristic
267C23×C132−1+411yescharacteristic
268C23×C132−1+411yescharacteristic
269C23×C132−1+411yescharacteristic
270C23×C132−1+411yescharacteristic
271C23×C132−1+411yescharacteristic
272Q8×C13—416no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13#11714yes—
321C2×C4×C13C4×D414yes—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—41no—
359C2×Dic13—41no—
360C2×Dic13—41no—
361C2×Dic13—41no—
362C2×Dic13—41no—
363C2×Dic13—41no—
364C2×Dic13—41no—
365C2×Dic13—41no—
366C2×Dic13—41no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13—41no—
376C2×Dic13—41no—
377C2×Dic13—41no—
378C23×Q8C2×D1311yescharacteristic
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4C2×D1311yescharacteristic
382C22×C42—131no—
383C22×C42—131no—
384C22×C42C2×D1311yescharacteristic
385#391—264no—
386#391Dic1318yescomplemented
387#383—264no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95—131no—
392C2×#95—131no—
393C2×#95—131no—
394C2×#95—131no—
395C2×#95—131no—
396C2×#95—131no—
397C2×#95—131no—
398C2×#95—131no—
399C2×#95—131no—
400C2×#95—131no—
401C2×#95—131no—
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95C2×D1311yescharacteristic
413C2×#95C2×D1311yescharacteristic
414C2×#95C2×D1311yescharacteristic
415C2×#95C2×D1311yescharacteristic
416C22×C13C2×#11711yescharacteristic
417C22×C13C2×C4×D411yescharacteristic
418C22×C13C4×#4111yescharacteristic
419C22×C13#51811yescharacteristic
420C22×C13#51911yescharacteristic
421C22×C13#51911yescharacteristic
422C22×C13#52011yescharacteristic
423C22×C13#53611yescharacteristic
424C22×C13#53711yescharacteristic
425C22×C13#53811yescharacteristic
426C22×C13#53811yescharacteristic
427C22×C13#54111yescharacteristic
428C22×C13#54111yescharacteristic
429C22×C13#54111yescharacteristic
430C22×C13#54211yescharacteristic
431C22×C13#54211yescharacteristic
432C22×C13#54211yescharacteristic
433C22×C13#54211yescharacteristic
434C22×C13#54211yescharacteristic
435C22×C13#54611yescharacteristic
436C22×C13#54611yescharacteristic
437C22×C13#54711yescharacteristic
438C22×C13#54811yescharacteristic
439C22×C13#55111yescharacteristic
440C22×C13#55111yescharacteristic
441C22×C13#55211yescharacteristic
442C22×C13#55211yescharacteristic
443C22×C13#55211yescharacteristic
444C22×C13#55611yescharacteristic
445C22×C13#55611yescharacteristic
446C22×C13#55611yescharacteristic
447C22×C13#56311yescharacteristic
448C22×C13#56311yescharacteristic
449C22×C13#56311yescharacteristic
450C22×C13#56311yescharacteristic
451C4×C13—24no—
452C4×C13—24no—
453C4×C13—42no—
454C4×C13—42no—
455C4×C13—42no—
456C4×C13—42no—
457C4×C13—42no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461Dic13—42no—
462Dic13—81no—
463Dic13—81no—
464Dic13—81no—
465Dic13—81no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—41no—
471C22×Q8—41no—
472C22×Q8C2×Dic1314yes—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4C22×D1311yescharacteristic
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—521no—
494C2×C4⋊C4—521no—
495C2×C4⋊C4—521no—
496C2×C4⋊C4C2×Dic1314yes—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—262no—
500C2×C42—262no—
501C2×C42—262no—
502C2×C42—521no—
503C2×C42—521no—
504C2×C42—521no—
505C2×C42C2×Dic1314yes—
506#95—134no—
507#95—262no—
508#95—262no—
509#95—262no—
510#95—262no—
511#95—262no—
512#95—262no—
513#95—262no—
514#95—262no—
515#95—262no—
516#95—262no—
517#95—262no—
518#95—262no—
519#95—262no—
520#95—262no—
521#95—262no—
522#95—521no—
523#95—521no—
524#95—521no—
525#95—521no—
526#95—521no—
527#95—521no—
528#95—521no—
529#95—521no—
530#95C2×Dic1314yes—
531#95C2×Dic1314yes—
532#95C2×Dic1314yes—
533#95C2×Dic1314yes—
534C2×C13#232011yescharacteristic
535C2×C13#232311yescharacteristic
536C2×C13#233711yescharacteristic
537C2×C13#234211yescharacteristic
538C2×C13#235611yescharacteristic
539C2×C13#236211yescharacteristic
540C2×C13#238111yescharacteristic
541C2×C13#269811yescharacteristic
542C2×C13#270211yescharacteristic
543C2×C13#271511yescharacteristic
544C2×C13#271611yescharacteristic
545C2×C13#275811yescharacteristic
546C2×C13#275911yescharacteristic
547C2×C13#276211yescharacteristic
548C2×C13#276411yescharacteristic
549C24C23×D1311yescharacteristic
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—261no—
633C22×C4—261no—
634C22×C4—261no—
635C22×C4—261no—
636C22×C4—261no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—261no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—261no—
649C22×C4—261no—
650C22×C4—261no—
651C22×C4#612712yes—
652C22×C4#612712yes—
653C22×C4D4×D1312yes—
654C22×C4#612912yes—
655C22×C4C22×Dic1312yes—
656C22×C4C22×Dic1312yes—
657C22×C4C22×Dic1312yes—
658C22×C4C22×Dic1312yes—
659C22×C4C22×Dic1312yes—
660C22×C4C22×Dic1312yes—
661C22×C4C22×Dic1312yes—
662C4⋊C4—44no—
663C4⋊C4—524no—
664C4⋊C4—524no—
665C42—28no—
666C42—524no—
667C42—524no—
668C13#1438011yescharacteristic, complemented, Sylow
669C23C2×#612711yescharacteristic
670C23C2×#612711yescharacteristic
671C23C2×D4×D1311yescharacteristic
672C23C2×#612911yescharacteristic
673C23#8825111yescharacteristic
674C23#8825111yescharacteristic
675C23#8825411yescharacteristic
676C23#8825411yescharacteristic
677C23#8825411yescharacteristic
678C23#8825411yescharacteristic
679C23#41×D1311yescharacteristic
680C23#41×D1311yescharacteristic
681C23#8825611yescharacteristic
682C23#8825711yescharacteristic
683C23C23×Dic1311yescharacteristic
684Q8—416no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—521no—
763C2×C4—521no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—521no—
769C2×C4—521no—
770C2×C4—521no—
771C2×C4—521no—
772C2×C4—521no—
773C2×C4—521no—
774C2×C4—521no—
775C2×C4—521no—
776C2×C4—521no—
777C2×C4—521no—
778C2×C4—521no—
779C2×C4—521no—
780C2×C4—521no—
781C2×C4—521no—
782C2×C4—521no—
783C2×C4—521no—
784C2×C4—521no—
785C2×C4—521no—
786C2×C4—521no—
787C2×C4—521no—
788C2×C4#8818014yes—
789C2×C4D4×Dic1314yes—
790C22#1171919511yescharacteristic
791C22#1171919511yescharacteristic
792C22#1171920011yescharacteristic
793C22#1171920011yescharacteristic
794C22#1171927311yescharacteristic
795C22#1171927311yescharacteristic
796C22#1171928611yescharacteristic
797C22#1171928611yescharacteristic
798C22#1171928711yescharacteristic
799C22#1171928711yescharacteristic
800C22#1171928811yescharacteristic
801C22#1171928811yescharacteristic
802C22#1171933011yescharacteristic
803C22#1171933311yescharacteristic
804C22#1171933411yescharacteristic
805C22#1171933611yescharacteristic
806C22#1171933811yescharacteristic
807C22#1171934411yescharacteristic
808C22#1171934611yescharacteristic
809C22#1171934811yescharacteristic
810C22#1171937411yescharacteristic
811C22#1171937411yescharacteristic
812C22#1171938311yescharacteristic
813C22#1171938311yescharacteristic
814C22#1171944011yescharacteristic
815C22#1171944011yescharacteristic
816C22#1171944011yescharacteristic
817C22#1171944011yescharacteristic
818C22C2×#8818011yescharacteristic
819C22C2×D4×Dic1311yescharacteristic
820C22#1171950311yescharacteristic
821C22#1171951711yescharacteristic
822C22#1171951711yescharacteristic
823C22#41×Dic1311yescharacteristic
824C22#1171953211yescharacteristic
825C4—24no—
826C4—24no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—522no—
833C4—522no—
834C4—522no—
835C4—522no—
836C4—1041no—
837C4—1041no—
838C4—1041no—
839C4—1041no—
840C2#1311748711yescharacteristic
841C2#1311752011yescharacteristic
842C2#1311765111yescharacteristic
843C2#1311768511yescharacteristic
844C2#1311780111yescharacteristic
845C2#1311786711yescharacteristic
846C2#1311801711yescharacteristic
847C2#1312141311yescharacteristic
848C2#1312146711yescharacteristic
849C2#1312164711yescharacteristic
850C2#1312166211yescharacteristic
851C2#1312218811yescharacteristic
852C2#1312220311yescharacteristic
853C2#1312223211yescharacteristic
854C2#1312225611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#391D13
hypocenterC13#14380
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
23. C13×#391C4semidirect
386. #391Dic13semidirect
668. C13#14380semidirect

Maximal subgroups

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

subgroupindex
C2×#117188912
C2×#117185982
#131131072
#131130982
#131130932
#131130892
#131130702
#131130682
#131130632
#131130612
C2×C13×#3912
#1438013