Finite Group Databasebeta

← #15793188

Subgroups — #15793188

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718612C211yesmaximal, characteristic
2C2×#11718642C211yesmaximal, characteristic, complemented
3#13113104C211yesmaximal, characteristic, complemented
4#13113089C211yesmaximal, characteristic, complemented
5#13113085C211yesmaximal, characteristic
6#13113085C211yesmaximal, characteristic
7#13113081C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113068C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113065C211yesmaximal, characteristic, complemented
14#13113061C211yesmaximal, characteristic, complemented
15C2×C13×#396C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#396C418yescomplemented
32C2×C13×#95C2211yescharacteristic
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
52#11718642—24no—
53#11718612—24no—
54C25×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4C2×C414yes—
76C2×C13×C4⋊C4C2×C414yes—
77C2×C13×C4⋊C4C2×C414yes—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4—41no—
83C2×C13×C22⋊C4—41no—
84C2×C13×C22⋊C4C2×C414yes—
85C2×C13×C22⋊C4C2×C414yes—
86C2×C13×C22⋊C4C2×C414yes—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—22no—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13—41no—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13—41no—
102C2×C4⋊Dic13—41no—
103C2×C4⋊Dic13—41no—
104C2×C4⋊Dic13D414yes—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13—41no—
114C13×#95C2×C414yes—
115#88071—22no—
116#88071—22no—
117#88071—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—41no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071—41no—
132#88071—41no—
133#88071—41no—
134#14588—131nomaximal, Sylow
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×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13C22×C412yes—
150C24×C13C2411yescharacteristic
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×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C22×C412yes—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13#4112yes—
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—21no—
242C22×Dic13—21no—
243C22×Dic13C2×D412yes—
244C22×Dic13C2×D412yes—
245C22×Dic13#4112yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C13×C4⋊C4—28no—
250C13×C4⋊C4—44no—
251C13×C4⋊C4—44no—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—44no—
254C13×C22⋊C4—44no—
255C22⋊Dic13—44no—
256C22⋊Dic13—44no—
257C22⋊Dic13—44no—
258C22⋊Dic13—44no—
259C4⋊Dic13—44no—
260C4⋊Dic13—44no—
261C4×Dic13—44no—
262C4×Dic13—44no—
263C4×Dic13—44no—
264C2×#396D1311yescharacteristic
265C2×#388—131no—
266C2×#387—131no—
267#1445—131no—
268#1441—131no—
269#1440—131no—
270#1440—131no—
271#1439—131no—
272#1437—131no—
273#1437—131no—
274#1436—131no—
275#1436—131no—
276#1436—131no—
277C4⋊#95—131no—
278#1434—131no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—41no—
287C23×C13—41no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13—41no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
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×C13C23×C411yescharacteristic
315C23×C13C22×D411yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
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×C132−1+411yescharacteristic
327C23×C132−1+411yescharacteristic
328C23×C132−1+411yescharacteristic
329C2×C4×C13—22no—
330C2×C4×C13—22no—
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—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
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×C13C4×D414yes—
371C2×Dic13—22no—
372C2×Dic13—22no—
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—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
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—
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C4⋊C4C2×D1311yescharacteristic
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4C2×D1311yescharacteristic
437C22×C22⋊C4C2×D1311yescharacteristic
438C22×C22⋊C4C2×D1311yescharacteristic
439C22×C42—131no—
440C22×C42—131no—
441C22×C42—131no—
442#396Dic1318yescomplemented
443#388—264no—
444#387—264no—
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×#95—131no—
464C2×#95C2×D1311yescharacteristic
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—81no—
473C22×C13—81no—
474C22×C13—81no—
475C22×C13—81no—
476C22×C13—81no—
477C22×C13—81no—
478C22×C13—81no—
479C22×C13—81no—
480C22×C13C2×C4×D411yescharacteristic
481C22×C13C4×#4111yescharacteristic
482C22×C13C4×#4111yescharacteristic
483C22×C13#51811yescharacteristic
484C22×C13#51811yescharacteristic
485C22×C13#51911yescharacteristic
486C22×C13#52011yescharacteristic
487C22×C13#53411yescharacteristic
488C22×C13#53711yescharacteristic
489C22×C13#53811yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53811yescharacteristic
492C22×C13#53911yescharacteristic
493C22×C13#53911yescharacteristic
494C22×C13#53911yescharacteristic
495C22×C13#54011yescharacteristic
496C22×C13#54011yescharacteristic
497C22×C13#54211yescharacteristic
498C22×C13#54211yescharacteristic
499C22×C13#54611yescharacteristic
500C22×C13#54711yescharacteristic
501C22×C13#54811yescharacteristic
502C22×C13#55011yescharacteristic
503C22×C13#55111yescharacteristic
504C22×C13#55211yescharacteristic
505C22×C13#55211yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55511yescharacteristic
509C22×C13#55611yescharacteristic
510C22×C13#55611yescharacteristic
511C22×C13#56211yescharacteristic
512C22×C13#56211yescharacteristic
513C22×C13#56311yescharacteristic
514C22×C13#56311yescharacteristic
515C4×C13—24no—
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521Dic13—42no—
522Dic13—42no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—42no—
527Dic13—81no—
528Dic13—81no—
529C25C22×D1311yescharacteristic
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4—131no—
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—134no—
551C2×C4⋊C4—262no—
552C2×C4⋊C4—521no—
553C2×C4⋊C4—521no—
554C2×C4⋊C4—521no—
555C2×C4⋊C4—521no—
556C2×C4⋊C4C2×Dic1314yes—
557C2×C4⋊C4C2×Dic1314yes—
558C2×C4⋊C4C2×Dic1314yes—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—262no—
566C2×C22⋊C4—262no—
567C2×C22⋊C4—262no—
568C2×C22⋊C4—262no—
569C2×C22⋊C4—262no—
570C2×C22⋊C4—262no—
571C2×C22⋊C4—521no—
572C2×C22⋊C4—521no—
573C2×C22⋊C4—521no—
574C2×C22⋊C4—521no—
575C2×C22⋊C4—521no—
576C2×C22⋊C4—521no—
577C2×C22⋊C4C2×Dic1314yes—
578C2×C22⋊C4C2×Dic1314yes—
579C2×C22⋊C4C2×Dic1314yes—
580C2×C42—262no—
581C2×C42—262no—
582C2×C42—262no—
583C2×C42—262no—
584C2×C42—521no—
585C2×C42—521no—
586C2×C42—521no—
587C2×C42—521no—
588C2×C42—521no—
589#95—262no—
590#95—262no—
591#95—262no—
592#95—262no—
593#95—262no—
594#95—262no—
595#95—262no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—521no—
602#95—521no—
603#95—521no—
604#95—521no—
605#95—521no—
606#95—521no—
607#95—521no—
608#95C2×Dic1314yes—
609C2×C13—82no—
610C2×C13#232511yescharacteristic
611C2×C13#233211yescharacteristic
612C2×C13#233311yescharacteristic
613C2×C13#236211yescharacteristic
614C2×C13#236311yescharacteristic
615C2×C13#237311yescharacteristic
616C2×C13#237811yescharacteristic
617C2×C13#270111yescharacteristic
618C2×C13#270711yescharacteristic
619C2×C13#272711yescharacteristic
620C2×C13#273011yescharacteristic
621C2×C13#277511yescharacteristic
622C2×C13#278111yescharacteristic
623C2×C13#278611yescharacteristic
624C2×C13#279311yescharacteristic
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24C22×Dic1312yes—
640C24C23×D1311yescharacteristic
641C22×C4—21no—
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—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
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×C4D4×D1312yes—
732C22×C4#612912yes—
733C22×C4C22×Dic1312yes—
734C22×C4C22×Dic1312yes—
735C22×C4C22×Dic1312yes—
736C22×C4C22×Dic1312yes—
737C22×C4C22×Dic1312yes—
738C22×C4C22×Dic1312yes—
739C4⋊C4—28no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—524no—
743C4⋊C4—524no—
744C22⋊C4—28no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—524no—
748C22⋊C4—524no—
749C22⋊C4—524no—
750C22⋊C4—524no—
751C42—524no—
752C42—524no—
753C42—524no—
754C13#1458811yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23C2×D4×D1311yescharacteristic
791C23C2×#612911yescharacteristic
792C23#8825111yescharacteristic
793C23#8825111yescharacteristic
794C23#8825111yescharacteristic
795C23#8825111yescharacteristic
796C23#8825411yescharacteristic
797C23#8825411yescharacteristic
798C23#41×D1311yescharacteristic
799C23#41×D1311yescharacteristic
800C23#41×D1311yescharacteristic
801C23#41×D1311yescharacteristic
802C23#8825611yescharacteristic
803C23#8825711yescharacteristic
804C23C23×Dic1311yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
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—262no—
847C2×C4—262no—
848C2×C4—262no—
849C2×C4—262no—
850C2×C4—262no—
851C2×C4—262no—
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—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
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×C4D4×Dic1314yes—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22#1171930211yescharacteristic
919C22#1171930411yescharacteristic
920C22#1171930711yescharacteristic
921C22#1171931011yescharacteristic
922C22#1171931711yescharacteristic
923C22#1171931811yescharacteristic
924C22#1171931811yescharacteristic
925C22#1171931911yescharacteristic
926C22#1171932011yescharacteristic
927C22#1171932011yescharacteristic
928C22#1171932111yescharacteristic
929C22#1171932211yescharacteristic
930C22#1171933611yescharacteristic
931C22#1171933811yescharacteristic
932C22#1171934311yescharacteristic
933C22#1171934311yescharacteristic
934C22#1171934411yescharacteristic
935C22#1171934511yescharacteristic
936C22#1171934511yescharacteristic
937C22#1171934611yescharacteristic
938C22#1171935111yescharacteristic
939C22#1171935111yescharacteristic
940C22#1171935211yescharacteristic
941C22#1171935211yescharacteristic
942C22#1171940711yescharacteristic
943C22#1171941011yescharacteristic
944C22#1171941311yescharacteristic
945C22#1171941411yescharacteristic
946C22C2×D4×Dic1311yescharacteristic
947C22#1171950311yescharacteristic
948C22#1171950311yescharacteristic
949C22#1171951711yescharacteristic
950C22#41×Dic1311yescharacteristic
951C22#41×Dic1311yescharacteristic
952C22#1171953211yescharacteristic
953C4—24no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—522no—
960C4—522no—
961C4—522no—
962C4—522no—
963C4—522no—
964C4—522no—
965C4—1041no—
966C4—1041no—
967C2—82no—
968C2#1311754111yescharacteristic
969C2#1311759411yescharacteristic
970C2#1311760311yescharacteristic
971C2#1311786711yescharacteristic
972C2#1311787811yescharacteristic
973C2#1311796011yescharacteristic
974C2#1311800211yescharacteristic
975C2#1312144211yescharacteristic
976C2#1312153211yescharacteristic
977C2#1312179311yescharacteristic
978C2#1312183211yescharacteristic
979C2#1312240811yescharacteristic
980C2#1312249811yescharacteristic
981C2#1312255411yescharacteristic
982C2#1312264711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#396C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#396D13
hypocenterC13#14588
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C2×#11718642C2semidirect
3. #13113104C2semidirect
4. #13113089C2semidirect
10. #13113070C2semidirect
11. #13113068C2semidirect
12. #13113068C2semidirect
13. #13113065C2semidirect
14. #13113061C2semidirect
31. C13×#396C4semidirect
442. #396Dic13semidirect
754. C13#14588semidirect

Maximal subgroups

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

subgroupindex
C2×#117186122
C2×#117186422
#131131042
#131130892
#131130852
#131130812
#131130732
#131130702
#131130682
#131130652
#131130612
C2×C13×#3962
#1458813