Finite Group Databasebeta

← #15793721

Subgroups — #15793721

Order 3328.

1378 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718609C211yesmaximal, characteristic
2#13113103C211yesmaximal, characteristic, complemented
3#13113102C211yesmaximal, characteristic, complemented
4#13113102C211yesmaximal, characteristic, complemented
5#13113099C211yesmaximal, characteristic, complemented
6#13113096C211yesmaximal, characteristic, complemented
7#13113088C211yesmaximal, characteristic, complemented
8#13113087C211yesmaximal, characteristic, complemented
9#13113086C211yesmaximal, characteristic, complemented
10#13113079C211yesmaximal, characteristic
11#13113079C211yesmaximal, characteristic
12#13113058C211yesmaximal, characteristic
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
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
51#11718609C418yescomplemented
52C25×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×Dic13—41no—
60C23×Dic13—41no—
61C23×Dic13—41no—
62C23×Dic13—41no—
63C23×Dic13—41no—
64C23×Dic13—41no—
65C23×Dic13Q814yes—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—41no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4—41no—
83C2×C13×C22⋊C4—41no—
84C2×C13×C22⋊C4—41no—
85C2×C13×C22⋊C4C2×C414yes—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—41no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13—41no—
90C2×C22⋊Dic13—41no—
91C2×C22⋊Dic13—41no—
92C2×C22⋊Dic13—41no—
93C2×C22⋊Dic13C2×C414yes—
94C2×C22⋊Dic13C2×C414yes—
95C2×C4⋊Dic13—41no—
96C2×C4⋊Dic13—41no—
97C2×C4⋊Dic13C2×C414yescomplemented
98C2×#6101—41no—
99C2×#6101—41no—
100C2×#6101—41no—
101C2×#6101—41no—
102C2×#6101—41no—
103C2×#6101—41no—
104C2×#6101—41no—
105C2×#6101—41no—
106C2×#6101—41no—
107C2×#6101—41no—
108C2×#6101C2×C414yescomplemented
109C2×#6101C2×C414yescomplemented
110C13×#95—41no—
111C13×#95—41no—
112C13×#95—41no—
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#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071—41no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071C2×C414yescomplemented
132#14637—131nomaximal, Sylow
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13C22×C412yes—
146C24×C13C2×Q812yes—
147C24×C13#4112yes—
148C24×C13C2411yescharacteristic
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×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
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×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—44no—
242C22×Dic13—44no—
243C22×Dic13—44no—
244C22×Dic13—44no—
245C22×Dic13—44no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248C22×Dic13C22×C412yes—
249C22×Dic13C22×C412yes—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C2×Q812yes—
253C22×Dic13C2×Q812yes—
254C13×C4⋊C4—44no—
255C13×C22⋊C4—44no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4—44no—
258C22⋊Dic13—44no—
259C22⋊Dic13—44no—
260C22⋊Dic13—44no—
261C4⋊Dic13—44no—
262#6101—44no—
263#6101—44no—
264#6101—44no—
265#6101—44no—
266C2×#396—131no—
267#1445—131no—
268#1445—131no—
269#1445—131no—
270#1444—131no—
271#1443—131no—
272#1441—131no—
273#1441—131no—
274#1441—131no—
275#1439—131no—
276#1439—131no—
277#1439D1311yescharacteristic
278C22⋊#95—131no—
279C22⋊#95—131no—
280C22⋊#95—131no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13C4×Q814yes—
316C23×C13C23×C411yescharacteristic
317C23×C13C22×Q811yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13H(5,𝔽2)11yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C132−1+411yescharacteristic
329C23×C132−1+411yescharacteristic
330C23×C132−1+411yescharacteristic
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—416no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C24×C4—131no—
431C22×C4⋊C4—131no—
432C22×C4⋊C4—131no—
433C22×C4⋊C4—131no—
434C22×C4⋊C4—131no—
435C22×C4⋊C4—131no—
436C22×C4⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4—131no—
438C22×C22⋊C4—131no—
439C22×C22⋊C4—131no—
440C22×C22⋊C4C2×D1311yescharacteristic
441C22×C22⋊C4C2×D1311yescharacteristic
442C22×C22⋊C4C2×D1311yescharacteristic
443#396—138no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C2×#95C2×D1311yescharacteristic
466C22×C13—24no—
467C22×C13—24no—
468C22×C13—24no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13C2×C4×Q811yescharacteristic
482C22×C13#51811yescharacteristic
483C22×C13#51811yescharacteristic
484C22×C13#51811yescharacteristic
485C22×C13#52011yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#52011yescharacteristic
488C22×C13#53811yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53911yescharacteristic
492C22×C13#53911yescharacteristic
493C22×C13#53911yescharacteristic
494C22×C13#54311yescharacteristic
495C22×C13#54311yescharacteristic
496C22×C13#54311yescharacteristic
497C22×C13#54411yescharacteristic
498C22×C13#54411yescharacteristic
499C22×C13#54411yescharacteristic
500C22×C13#56011yescharacteristic
501C22×C13#56011yescharacteristic
502C22×C13#56011yescharacteristic
503C22×C13#56011yescharacteristic
504C22×C13#56011yescharacteristic
505C22×C13#56011yescharacteristic
506C22×C13#56011yescharacteristic
507C22×C13#56211yescharacteristic
508C22×C13#56211yescharacteristic
509C22×C13#56211yescharacteristic
510C22×C13#56211yescharacteristic
511C22×C13#56211yescharacteristic
512C22×C13#56211yescharacteristic
513C22×C13#56311yescharacteristic
514C22×C13#56311yescharacteristic
515C22×C13#56311yescharacteristic
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—81no—
519C4×C13—81no—
520C4×C13—81no—
521C4×C13—81no—
522Dic13—42no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—81no—
529Dic13—81no—
530C25C22×D1311yescharacteristic
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—134no—
538C23×C4—131no—
539C23×C4—131no—
540C23×C4—521no—
541C23×C4—521no—
542C23×C4—521no—
543C23×C4—521no—
544C23×C4—521no—
545C23×C4—521no—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1311yescharacteristic
549C23×C4C22×D1311yescharacteristic
550C23×C4C22×D1311yescharacteristic
551C23×C4C22×D1311yescharacteristic
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—134no—
556C2×C4⋊C4—134no—
557C2×C4⋊C4—134no—
558C2×C4⋊C4—521no—
559C2×C4⋊C4—521no—
560C2×C4⋊C4—521no—
561C2×C4⋊C4—521no—
562C2×C4⋊C4—521no—
563C2×C4⋊C4—521no—
564C2×C4⋊C4—521no—
565C2×C4⋊C4—521no—
566C2×C4⋊C4—521no—
567C2×C4⋊C4—521no—
568C2×C4⋊C4—521no—
569C2×C4⋊C4—521no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—134no—
579C2×C22⋊C4—134no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—521no—
582C2×C22⋊C4—521no—
583C2×C22⋊C4—521no—
584C2×C22⋊C4—521no—
585C2×C22⋊C4—521no—
586C2×C22⋊C4—521no—
587C2×C22⋊C4C4×D1314yes—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—134no—
592#95—521no—
593#95—521no—
594#95—521no—
595#95—521no—
596#95—521no—
597#95—521no—
598#95—521no—
599#95—521no—
600#95—521no—
601#95—521no—
602#95—521no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95—521no—
609#95—521no—
610C2×C13—44no—
611C2×C13#232911yescharacteristic
612C2×C13#232911yescharacteristic
613C2×C13#232911yescharacteristic
614C2×C13#237711yescharacteristic
615C2×C13#237711yescharacteristic
616C2×C13#237711yescharacteristic
617C2×C13#238311yescharacteristic
618C2×C13#282511yescharacteristic
619C2×C13#282711yescharacteristic
620C2×C13#282711yescharacteristic
621C2×C13#282711yescharacteristic
622C2×C13#284111yescharacteristic
623C2×C13#284111yescharacteristic
624C2×C13#284111yescharacteristic
625C2×C13#284211yescharacteristic
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24C2×C4×D1312yes—
639C24#612912yes—
640C24Q8×D1312yes—
641C24C23×D1311yescharacteristic
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—524no—
739C22×C4—524no—
740C22×C4—524no—
741C22×C4—524no—
742C22×C4—524no—
743C22×C4—524no—
744C22×C4—524no—
745C22×C4C2×C4×D1312yes—
746C22×C4C2×C4×D1312yes—
747C4⋊C4—44no—
748C4⋊C4—524no—
749C4⋊C4—524no—
750C4⋊C4—524no—
751C4⋊C4—524no—
752C4⋊C4—524no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—524no—
757C22⋊C4—524no—
758C22⋊C4—524no—
759C13#1463711yescharacteristic, complemented, Sylow
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23#8814114yes—
795C23C22×C4×D1311yescharacteristic
796C23C2×#612911yescharacteristic
797C23#8825111yescharacteristic
798C23#8825111yescharacteristic
799C23#8825111yescharacteristic
800C23#8825111yescharacteristic
801C23#8825111yescharacteristic
802C23#8825111yescharacteristic
803C23C2×Q8×D1311yescharacteristic
804C23#8825611yescharacteristic
805C23#8825611yescharacteristic
806C23#8825611yescharacteristic
807C23#8825711yescharacteristic
808C23#8825711yescharacteristic
809C23#8825711yescharacteristic
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—5216no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4—521no—
902C2×C4—521no—
903C2×C4—521no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C22—24no—
910C22—24no—
911C22—24no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22#1171919111yescharacteristic
925C22C2×#8814111yescharacteristic
926C22#1171922811yescharacteristic
927C22#1171925011yescharacteristic
928C22#1171925011yescharacteristic
929C22#1171925111yescharacteristic
930C22#1171925111yescharacteristic
931C22#1171929811yescharacteristic
932C22#1171929811yescharacteristic
933C22#1171930011yescharacteristic
934C22#1171930711yescharacteristic
935C22#1171932211yescharacteristic
936C22#1171932511yescharacteristic
937C22#1171932511yescharacteristic
938C22#1171932511yescharacteristic
939C22#1171932511yescharacteristic
940C22#1171932611yescharacteristic
941C22#1171932611yescharacteristic
942C22#1171932811yescharacteristic
943C22#1171932811yescharacteristic
944C22#1171932811yescharacteristic
945C22#1171933911yescharacteristic
946C22#1171933911yescharacteristic
947C22#1171933911yescharacteristic
948C22#1171935611yescharacteristic
949C22#1171937011yescharacteristic
950C22#1171937011yescharacteristic
951C22#1171937211yescharacteristic
952C22#1171937211yescharacteristic
953C22#1171937711yescharacteristic
954C22#1171938911yescharacteristic
955C22#1171938911yescharacteristic
956C22#1171941611yescharacteristic
957C22#1171941711yescharacteristic
958C22#1171942511yescharacteristic
959C4—42no—
960C4—42no—
961C4—81no—
962C4—81no—
963C4—81no—
964C4—81no—
965C4—522no—
966C4—522no—
967C4—522no—
968C4—522no—
969C4—522no—
970C4—522no—
971C4—1041no—
972C4—1041no—
973C2—44no—
974C2#1311756611yescharacteristic
975C2#1311756711yescharacteristic
976C2#1311756711yescharacteristic
977C2#1311798711yescharacteristic
978C2#1311798811yescharacteristic
979C2#1311798911yescharacteristic
980C2#1311802311yescharacteristic
981C2#1312292411yescharacteristic
982C2#1312294411yescharacteristic
983C2#1312294611yescharacteristic
984C2#1312294811yescharacteristic
985C2#1312309611yescharacteristic
986C2#1312309711yescharacteristic
987C2#1312309811yescharacteristic
988C2#1312309911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14637
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13113103C2semidirect
3. #13113102C2semidirect
4. #13113102C2semidirect
5. #13113099C2semidirect
6. #13113096C2semidirect
7. #13113088C2semidirect
8. #13113087C2semidirect
9. #13113086C2semidirect
51. #11718609C4semidirect
97. C2×C4⋊Dic13C2×C4semidirect
108. C2×#6101C2×C4semidirect
109. C2×#6101C2×C4semidirect
131. #88071C2×C4semidirect
759. C13#14637semidirect

Maximal subgroups

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

subgroupindex
C2×#117186092
#131131032
#131131022
#131130992
#131130962
#131130882
#131130872
#131130862
#131130792
#131130582
C13×#14392
#1463713