Finite Group Databasebeta

← #15786830

Subgroups — #15786830

Order 3328.

1426 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718589C211yesmaximal, characteristic
2C2×#11718633C211yesmaximal, characteristic
3C2×#11718314C211yesmaximal, characteristic
4C2×#11718639C211yesmaximal, characteristic
5#13113103C211yesmaximal, characteristic
6#13113088C211yesmaximal, characteristic
7#13113086C211yesmaximal, characteristic
8#13113086C211yesmaximal, characteristic
9#13113070C211yesmaximal, characteristic
10#13113069C211yesmaximal, characteristic
11#13113069C211yesmaximal, characteristic
12#13113063C211yesmaximal, characteristic
13#13113063C211yesmaximal, characteristic
14C4×#88071C211yesmaximal, characteristic
15C2×C4×C13×C4⋊C4C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C4×C13×C4⋊C4—24no—
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
51C2×#88071C2211yescharacteristic
52#11718639—24no—
53#11718633—24no—
54#11718589C418yescomplemented
55#11718314—24no—
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4D414yes—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
81C2×C42×C13—22no—
82C2×C42×C13—22no—
83C2×C42×C13—41no—
84C2×C42×C13—41no—
85C2×C42×C13C2×C414yes—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13C2×C414yes—
91C2×C4⋊Dic13C2×C414yes—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—41no—
102C2×#6101C2×C414yes—
103C2×#6101C2×C414yes—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—41no—
110C13×#95—22no—
111C13×#95D414yes—
112#88071—22no—
113#88071—22no—
114#88071—22no—
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#88071C2×C414yes—
130#88071C2×C414yes—
131#88071Q814yes—
132#14060—131nomaximal, Sylow
133C24×C13C2411yescharacteristic
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×C13C22×C412yes—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C22×C412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×Q812yes—
178C22×C4×C13#4112yes—
179C22×C4×C13#4112yes—
180C22×C4×C13#4112yes—
181C22×C4×C13#4112yes—
182C22×C4×C13#4112yes—
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×Dic13C22×C412yes—
232C22×Dic13C22×C412yes—
233C22×Dic13C22×C412yes—
234C22×Dic13C22×C412yes—
235C22×Dic13C2×Q812yes—
236C22×Dic13C2×Q812yes—
237C22×Dic13#4112yes—
238C22×Dic13#4112yes—
239C13×C4⋊C4—28no—
240C13×C4⋊C4—28no—
241C42×C13—28no—
242C42×C13—44no—
243C42×C13—44no—
244C4⋊Dic13—28no—
245C4⋊Dic13—28no—
246#6101—28no—
247#6101—28no—
248#6101—44no—
249#6101—44no—
250C4×Dic13—44no—
251C4×Dic13—44no—
252C2×#389—131no—
253C2×#389—131no—
254C2×#387—131no—
255C2×#387—131no—
256C2×C4×C4⋊C4D1311yescharacteristic
257#1445—131no—
258#1441—131no—
259#1441—131no—
260#1441—131no—
261#1436—131no—
262#1436—131no—
263#1436—131no—
264#1434—131no—
265#1434—131no—
266C4×#95—131no—
267C23×C13C23×C411yescharacteristic
268C23×C13C22×D411yescharacteristic
269C23×C13C22×D411yescharacteristic
270C23×C13C22×Q811yescharacteristic
271C23×C13C2×#4111yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13C2×#4111yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13H(5,𝔽2)11yescharacteristic
279C23×C132−1+411yescharacteristic
280C23×C132−1+411yescharacteristic
281C23×C132−1+411yescharacteristic
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—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13C4×D414yes—
328C2×C4×C13C4×D414yes—
329C2×C4×C13C4×Q814yes—
330C2×C4×C13#12114yes—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
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—
378C2×Dic13—41no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13#11714yes—
387C22×C4⋊C4—131no—
388C22×C4⋊C4—131no—
389C22×C4⋊C4—131no—
390C22×C4⋊C4—131no—
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4C2×D1311yescharacteristic
394C22×C4⋊C4C2×D1311yescharacteristic
395C22×C42—131no—
396C22×C42—131no—
397C22×C42C2×D1311yescharacteristic
398C22×C42C2×D1311yescharacteristic
399C22×C42C2×D1311yescharacteristic
400#389—138no—
401#389—264no—
402#387—264no—
403#387—264no—
404C4×C4⋊C4—24no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95—131no—
411C2×#95—131no—
412C2×#95—131no—
413C2×#95—131no—
414C2×#95—131no—
415C2×#95—131no—
416C2×#95—131no—
417C2×#95—131no—
418C2×#95—131no—
419C2×#95—131no—
420C2×#95—131no—
421C2×#95—131no—
422C2×#95—131no—
423C2×#95—131no—
424C2×#95—131no—
425C2×#95C2×D1311yescharacteristic
426C2×#95C2×D1311yescharacteristic
427C22×C13C2×#11711yescharacteristic
428C22×C13C2×C4×D411yescharacteristic
429C22×C13C2×C4×D411yescharacteristic
430C22×C13C2×C4×Q811yescharacteristic
431C22×C13C4×#4111yescharacteristic
432C22×C13#51911yescharacteristic
433C22×C13#52011yescharacteristic
434C22×C13C2×#12111yescharacteristic
435C22×C13#52511yescharacteristic
436C22×C13#52911yescharacteristic
437C22×C13#52911yescharacteristic
438C22×C13#52911yescharacteristic
439C22×C13#53211yescharacteristic
440C22×C13#53311yescharacteristic
441C22×C13#53311yescharacteristic
442C22×C13#53911yescharacteristic
443C22×C13#53911yescharacteristic
444C22×C13#54111yescharacteristic
445C22×C13#54111yescharacteristic
446C22×C13#54611yescharacteristic
447C22×C13#54611yescharacteristic
448C22×C13#54711yescharacteristic
449C22×C13#54711yescharacteristic
450C22×C13#54711yescharacteristic
451C22×C13#54811yescharacteristic
452C22×C13D4×Q811yescharacteristic
453C22×C13D4×Q811yescharacteristic
454C22×C13#55211yescharacteristic
455C22×C13#55211yescharacteristic
456C22×C13#55211yescharacteristic
457C22×C13#55211yescharacteristic
458C22×C13#55311yescharacteristic
459C22×C13#55411yescharacteristic
460C22×C13#55611yescharacteristic
461C22×C13#55711yescharacteristic
462C4×C13—24no—
463C4×C13—24no—
464C4×C13—24no—
465C4×C13—24no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13—42no—
469Dic13—24no—
470Dic13—42no—
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474Dic13—42no—
475Dic13—81no—
476Dic13—81no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4—131no—
482C23×C4—131no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—134no—
498C2×C4⋊C4—134no—
499C2×C4⋊C4—134no—
500C2×C4⋊C4—134no—
501C2×C4⋊C4—262no—
502C2×C4⋊C4—262no—
503C2×C4⋊C4—262no—
504C2×C4⋊C4—262no—
505C2×C4⋊C4—262no—
506C2×C4⋊C4—262no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—262no—
509C2×C4⋊C4—262no—
510C2×C4⋊C4—262no—
511C2×C4⋊C4—262no—
512C2×C4⋊C4—262no—
513C2×C4⋊C4—262no—
514C2×C4⋊C4—521no—
515C2×C4⋊C4D5214yes—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—41no—
523C2×C42—41no—
524C2×C42—262no—
525C2×C42—262no—
526C2×C42—262no—
527C2×C42—262no—
528C2×C42—262no—
529C2×C42—521no—
530C2×C42C4×D1314yes—
531#95—22no—
532#95—134no—
533#95—134no—
534#95—134no—
535#95—262no—
536#95—262no—
537#95—262no—
538#95—262no—
539#95—262no—
540#95—262no—
541#95—262no—
542#95—262no—
543#95—262no—
544#95—262no—
545#95—262no—
546#95—262no—
547#95—262no—
548#95—262no—
549#95—262no—
550#95—521no—
551#95—521no—
552#95C22⋊D1314yes—
553C2×C13#229511yescharacteristic
554C2×C13C4×#12111yescharacteristic
555C2×C13#233611yescharacteristic
556C2×C13#234411yescharacteristic
557C2×C13#235211yescharacteristic
558C2×C13#236011yescharacteristic
559C2×C13#236511yescharacteristic
560C2×C13#242511yescharacteristic
561C2×C13#242911yescharacteristic
562C2×C13#246211yescharacteristic
563C2×C13#246611yescharacteristic
564C2×C13#251911yescharacteristic
565C2×C13#253311yescharacteristic
566C2×C13#255611yescharacteristic
567C2×C13#259011yescharacteristic
568C24C23×D1311yescharacteristic
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—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—132no—
604C22×C4—132no—
605C22×C4—132no—
606C22×C4—132no—
607C22×C4—132no—
608C22×C4—132no—
609C22×C4—132no—
610C22×C4—132no—
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—261no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4—261no—
658C22×C4—261no—
659C22×C4C2×C4×D1312yes—
660C22×C4C2×C4×D1312yes—
661C22×C4C2×C4×D1312yes—
662C22×C4C2×D5212yes—
663C22×C4C2×D5212yes—
664C22×C4C2×D5212yes—
665C22×C4#612712yes—
666C22×C4#612712yes—
667C22×C4#612712yes—
668C22×C4#612712yes—
669C22×C4#612912yes—
670C22×C4Q8×D1312yes—
671C22×C4C2×C22⋊D1312yes—
672C22×C4C2×C22⋊D1312yes—
673C22×C4C2×C22⋊D1312yes—
674C4⋊C4—28no—
675C4⋊C4—28no—
676C4⋊C4—268no—
677C4⋊C4—268no—
678C4⋊C4—268no—
679C4⋊C4—268no—
680C4⋊C4—524no—
681C4⋊C4—524no—
682C42—28no—
683C42—44no—
684C42—44no—
685C42—524no—
686C42—524no—
687C13#1406011yescharacteristic, complemented, Sylow
688C23C22×C4×D1311yescharacteristic
689C23C22×D5211yescharacteristic
690C23C2×#612711yescharacteristic
691C23C2×#612711yescharacteristic
692C23C2×#612711yescharacteristic
693C23C2×#612711yescharacteristic
694C23C2×#612911yescharacteristic
695C23#8825111yescharacteristic
696C23C2×Q8×D1311yescharacteristic
697C23#8825411yescharacteristic
698C23#41×D1311yescharacteristic
699C23#41×D1311yescharacteristic
700C23#8825711yescharacteristic
701C23#8825711yescharacteristic
702C23C22×C22⋊D1311yescharacteristic
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—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—134no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
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—521no—
789C2×C4—521no—
790C2×C4—521no—
791C2×C4—521no—
792C2×C4—521no—
793C2×C4—521no—
794C2×C4—521no—
795C2×C4—521no—
796C2×C4—521no—
797C2×C4—521no—
798C2×C4—521no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4—521no—
802C2×C4—521no—
803C2×C4—521no—
804C2×C4C4×D5214yes—
805C2×C4#8814114yes—
806C2×C4C4×C22⋊D1314yes—
807C2×C4#8818414yes—
808C22C2×C4×D5211yescharacteristic
809C22C4×#612711yescharacteristic
810C22#1171918211yescharacteristic
811C22#1171918411yescharacteristic
812C22C2×#8814111yescharacteristic
813C22#1171920911yescharacteristic
814C22#1171921611yescharacteristic
815C22#1171921811yescharacteristic
816C22#1171922111yescharacteristic
817C22D13×#11711yescharacteristic
818C22#1171923611yescharacteristic
819C22#1171923611yescharacteristic
820C22#1171924311yescharacteristic
821C22#1171924311yescharacteristic
822C22#1171924711yescharacteristic
823C22#1171925911yescharacteristic
824C22#1171926011yescharacteristic
825C22#1171926311yescharacteristic
826C22#1171926911yescharacteristic
827C22#1171926911yescharacteristic
828C22#1171927211yescharacteristic
829C22Q8×D5211yescharacteristic
830C22#1171928111yescharacteristic
831C22#1171928311yescharacteristic
832C22#1171928311yescharacteristic
833C22#1171928611yescharacteristic
834C22#1171928811yescharacteristic
835C22#1171928811yescharacteristic
836C22C2×C4×C22⋊D1311yescharacteristic
837C22C2×#8818411yescharacteristic
838C22#1171949611yescharacteristic
839C22#1171951111yescharacteristic
840C22Q8×C22⋊D1311yescharacteristic
841C22#1171952911yescharacteristic
842C22#1171952911yescharacteristic
843C4—24no—
844C4—24no—
845C4—24no—
846C4—24no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—264no—
851C4—522no—
852C4—522no—
853C4—522no—
854C4—522no—
855C4—522no—
856C4—1041no—
857C4—1041no—
858C2#1311731211yescharacteristic
859C2C4×#8818411yescharacteristic
860C2#1311764011yescharacteristic
861C2#1311770611yescharacteristic
862C2#1311776811yescharacteristic
863C2#1311784111yescharacteristic
864C2#1311789411yescharacteristic
865C2#1311838111yescharacteristic
866C2#1311842911yescharacteristic
867C2#1311881211yescharacteristic
868C2#1311886611yescharacteristic
869C2#1311950911yescharacteristic
870C2#1311971311yescharacteristic
871C2#1311991411yescharacteristic
872C2#1312030211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#14060
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
54. #11718589C4semidirect
687. C13#14060semidirect

Maximal subgroups

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

subgroupindex
C2×#117185892
C2×#117186332
C2×#117183142
C2×#117186392
#131131032
#131130882
#131130862
#131130702
#131130692
#131130632
C4×#880712
C2×C4×C13×C4⋊C42
#1406013