Finite Group Databasebeta

← #15791334

Subgroups — #15791334

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718600C211yesmaximal, characteristic
2C2×#11718326C212yesmaximal
3C2×#11718329C212yesmaximal, complemented
4C2×#11718650C212yesmaximal, complemented
5#13113088C212yesmaximal, complemented
6#13113082C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9C13×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D52C2211yescharacteristic
11C23×C4×D13C2212yes—
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6103C2212yes—
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C2×C13×#95C2212yes—
25C2×C13×#95C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31#11718650—28no—
32#11718600C418yescomplemented
33#11718329—28no—
34#11718326—28no—
35C24×D13C2312yes—
36C23×C4×C13C2312yes—
37C23×C4×C13C2312yes—
38C23×C4×C13C2311yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×C4×C13C2311yescharacteristic
41C23×Dic13C2312yes—
42C23×Dic13C2312yes—
43C23×Dic13C2312yes—
44C22×D52—41no—
45C22×D52—41no—
46C22×D52—41no—
47C22×D52—41no—
48C22×D52C2×C414yes—
49C22×D52D414yes—
50C22×D52Q814yes—
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13—24no—
54C22×C4×D13—42no—
55C22×C4×D13—42no—
56C22×C4×D13—42no—
57C22×C4×D13—42no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—41no—
60C2×C13×C4⋊C4—41no—
61C2×C13×C4⋊C4—41no—
62C2×C13×C4⋊C4—41no—
63C2×C13×C4⋊C4D414yescomplemented
64C2×C42×C13—41no—
65C2×C42×C13—41no—
66C2×C42×C13C2×C414yescomplemented
67C2×#6103—24no—
68C2×#6103—24no—
69C2×#6103—24no—
70C2×#6103—24no—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—42no—
77C2×#6103—42no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×#6103C2×C418yescomplemented
81C2×#6103C2×C418yescomplemented
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—41no—
84C2×C4⋊Dic13—41no—
85C2×C4⋊Dic13—41no—
86C2×C4⋊Dic13—41no—
87C2×C4⋊Dic13—41no—
88C2×C4⋊Dic13—41no—
89C2×C4⋊Dic13C2×C414yescomplemented
90C2×C4⋊Dic13D414yescomplemented
91C2×#6101—24no—
92C2×#6101—24no—
93C2×#6101—42no—
94C13×#95—24no—
95C13×#95—24no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—42no—
101#14440—131nomaximal, Sylow
102C24×C13C2411yescharacteristic
103C23×D13—22no—
104C23×D13—22no—
105C23×D13—22no—
106C23×D13—22no—
107C23×D13—22no—
108C23×D13—22no—
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13C22×C414yes—
116C23×D13C2×D414yes—
117C23×D13C2×Q814yes—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13C22×C412yes—
144C22×C4×C13C22×C412yes—
145C22×C4×C13C22×C412yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×Q812yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13C22×C414yes—
173C22×Dic13C2×D414yes—
174C2×D52—44no—
175C2×D52—44no—
176C2×D52—44no—
177C2×D52—44no—
178C2×D52—44no—
179C2×D52—44no—
180C2×D52C4⋊C4116yescomplemented
181C2×C4×D13—48no—
182C2×C4×D13—48no—
183C2×C4×D13—48no—
184C2×C4×D13—48no—
185C2×C4×D13—48no—
186C2×C4×D13—48no—
187C2×C4×D13—48no—
188C13×C4⋊C4—44no—
189C13×C4⋊C4—44no—
190C42×C13—44no—
191#6103—216no—
192#6103—216no—
193#6103—48no—
194#6103—48no—
195#6103—48no—
196C4⋊Dic13—44no—
197C4⋊Dic13—44no—
198C4⋊Dic13—44no—
199#6101—48no—
200C2×#390—131no—
201C2×#386—132no—
202C2×#385—132no—
203C2×#385—132no—
204#1441—132no—
205#1439—132no—
206#1439—132no—
207C4⋊#95—131no—
208C4⋊#95D1311yescharacteristic, complemented
209C23×C13C23×C411yescharacteristic
210C23×C13C22×D411yescharacteristic
211C23×C13C22×D411yescharacteristic
212C23×C13C22×D411yescharacteristic
213C23×C13C22×Q811yescharacteristic
214C23×C13C2×#4111yescharacteristic
215C23×C13C2×#4111yescharacteristic
216C23×C13H(5,𝔽2)11yescharacteristic
217C23×C13H(5,𝔽2)11yescharacteristic
218C23×C13H(5,𝔽2)11yescharacteristic
219C23×C13H(5,𝔽2)11yescharacteristic
220C23×C13H(5,𝔽2)11yescharacteristic
221C23×C13H(5,𝔽2)11yescharacteristic
222C23×C132−1+411yescharacteristic
223C23×C132−1+411yescharacteristic
224C22×D13—24no—
225C22×D13—24no—
226C22×D13—24no—
227C22×D13—24no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—24no—
233C22×D13—24no—
234C22×D13—24no—
235C22×D13—24no—
236C22×D13—24no—
237C22×D13—24no—
238C22×D13—24no—
239C22×D13—24no—
240C22×D13—24no—
241C22×D13—24no—
242C22×D13—42no—
243C22×D13—42no—
244C22×D13—42no—
245C22×D13—42no—
246C22×D13—42no—
247C22×D13—42no—
248C22×D13—42no—
249C22×D13—42no—
250C22×D13—42no—
251C22×D13—42no—
252C22×D13—42no—
253C22×D13—42no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13C2×C4⋊C418yes—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13C2×C4⋊C414yes—
292C2×C4×C13C4×D414yes—
293C2×C4×C13C4×D414yes—
294C2×Dic13—24no—
295C2×Dic13—24no—
296C2×Dic13—24no—
297C2×Dic13—24no—
298C2×Dic13—24no—
299C2×Dic13—24no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13—42no—
304C2×Dic13—42no—
305C2×Dic13—42no—
306C2×Dic13—42no—
307C2×Dic13—42no—
308C2×Dic13—42no—
309C2×Dic13—42no—
310C2×Dic13—42no—
311C2×Dic13—42no—
312C2×Dic13—42no—
313C2×Dic13—42no—
314C2×Dic13—42no—
315D52—416no—
316C4×D13—432no—
317C23×D4—131no—
318C24×C4—132no—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—132no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4C2×D1311yescharacteristic
324C22×C4⋊C4C2×D1311yescharacteristic
325C22×C22⋊C4—132no—
326C22×C22⋊C4—132no—
327C22×C22⋊C4—132no—
328C22×C22⋊C4—132no—
329C22×C22⋊C4—132no—
330C22×C42C2×D1311yescharacteristic
331#390—138no—
332#386—268no—
333#385—268no—
334#385—268no—
335C2×#95—132no—
336C2×#95—132no—
337C2×#95—132no—
338C2×#95—132no—
339C2×#95—132no—
340C2×#95C2×D1312yes—
341C2×#95C2×D1312yes—
342C22×C13C22×C4⋊C411yescharacteristic
343C22×C13C2×C4×D411yescharacteristic
344C22×C13C2×C4×D411yescharacteristic
345C22×C13#51811yescharacteristic
346C22×C13#51811yescharacteristic
347C22×C13#52011yescharacteristic
348C22×C13#52011yescharacteristic
349C22×C13#53411yescharacteristic
350C22×C13#53411yescharacteristic
351C22×C13#53411yescharacteristic
352C22×C13#53411yescharacteristic
353C22×C13#53711yescharacteristic
354C22×C13#53711yescharacteristic
355C22×C13#53811yescharacteristic
356C22×C13#53811yescharacteristic
357C22×C13#53911yescharacteristic
358C22×C13#53911yescharacteristic
359C22×C13#54311yescharacteristic
360C22×C13#54311yescharacteristic
361C22×C13D4211yescharacteristic
362C22×C13D4211yescharacteristic
363C22×C13D4211yescharacteristic
364C22×C13#54711yescharacteristic
365C22×C13#54711yescharacteristic
366C22×C13D4×Q811yescharacteristic
367C22×C13D4×Q811yescharacteristic
368C22×C13#55011yescharacteristic
369C22×C13#55011yescharacteristic
370C22×C13#55411yescharacteristic
371C22×C13#55411yescharacteristic
372C22×C13#55911yescharacteristic
373C22×C13H(3,𝔽4)11yescharacteristic
374C22×C13#56211yescharacteristic
375C22×C13#56211yescharacteristic
376C22×C13#56311yescharacteristic
377C2×D13—28no—
378C2×D13—28no—
379C2×D13—28no—
380C2×D13—44no—
381C2×D13—44no—
382C2×D13—44no—
383C2×D13—44no—
384C2×D13—44no—
385C2×D13—44no—
386C2×D13—44no—
387C2×D13—44no—
388C2×D13—44no—
389C2×D13—44no—
390C2×D13—44no—
391C2×D13—44no—
392C4×C13—24no—
393C4×C13—24no—
394C4×C13—24no—
395C4×C13—44no—
396C4×C13—82no—
397Dic13—44no—
398Dic13—44no—
399Dic13—82no—
400C25—132no—
401C22×D4—134no—
402C22×D4—134no—
403C22×D4—134no—
404C22×D4—521no—
405C22×D4—521no—
406C22×D4—521no—
407C22×D4—521no—
408C23×C4—132no—
409C23×C4—132no—
410C23×C4—132no—
411C23×C4—264no—
412C23×C4—264no—
413C23×C4—264no—
414C23×C4—522no—
415C23×C4—522no—
416C23×C4—522no—
417C23×C4—522no—
418C23×C4C22×D1312yes—
419C23×C4C22×D1312yes—
420C23×C4C22×D1311yescharacteristic
421C23×C4C22×D1311yescharacteristic
422C23×C4C22×D1311yescharacteristic
423C2×C4⋊C4—22no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—134no—
429C2×C4⋊C4—134no—
430C2×C4⋊C4—264no—
431C2×C4⋊C4—264no—
432C2×C4⋊C4—262no—
433C2×C4⋊C4—522no—
434C2×C4⋊C4—521no—
435C2×C4⋊C4—521no—
436C2×C4⋊C4—521no—
437C2×C4⋊C4—521no—
438C2×C4⋊C4—521no—
439C2×C4⋊C4—521no—
440C2×C4⋊C4D5214yescomplemented
441C2×C22⋊C4—138no—
442C2×C22⋊C4—138no—
443C2×C22⋊C4—264no—
444C2×C22⋊C4—264no—
445C2×C22⋊C4—264no—
446C2×C22⋊C4—264no—
447C2×C22⋊C4—264no—
448C2×C22⋊C4—264no—
449C2×C22⋊C4—264no—
450C2×C22⋊C4—264no—
451C2×C22⋊C4—264no—
452C2×C22⋊C4—522no—
453C2×C22⋊C4—522no—
454C2×C22⋊C4—522no—
455C2×C22⋊C4—522no—
456C2×C42—41no—
457C2×C42—41no—
458C2×C42C4×D1314yescomplemented
459#95—24no—
460#95—24no—
461#95—264no—
462#95—264no—
463#95—264no—
464#95—264no—
465#95—522no—
466C2×C13#231511yescharacteristic
467C2×C13#232511yescharacteristic
468C2×C13#232511yescharacteristic
469C2×C13D4×C4⋊C411yescharacteristic
470C2×C13D4×C4⋊C411yescharacteristic
471C2×C13#236611yescharacteristic
472C2×C13#237911yescharacteristic
473C2×C13#267911yescharacteristic
474C2×C13#268211yescharacteristic
475C2×C13#268211yescharacteristic
476C2×C13#268311yescharacteristic
477C2×C13#272411yescharacteristic
478C2×C13#273211yescharacteristic
479C2×C13#273211yescharacteristic
480C2×C13#280411yescharacteristic
481D13—48no—
482C24—134no—
483C24—134no—
484C24—134no—
485C24—262no—
486C24—262no—
487C24—262no—
488C24—262no—
489C24—262no—
490C24—262no—
491C24—262no—
492C24—262no—
493C24—262no—
494C24—262no—
495C24—262no—
496C24—262no—
497C24C23×D1311yescharacteristic
498C2×D4—1316no—
499C2×D4—524no—
500C2×D4—524no—
501C2×D4—524no—
502C2×D4—524no—
503C2×D4—524no—
504C2×D4—524no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—134no—
531C22×C4—134no—
532C22×C4—262no—
533C22×C4—262no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—262no—
547C22×C4—262no—
548C22×C4—262no—
549C22×C4—262no—
550C22×C4—262no—
551C22×C4—528no—
552C22×C4—528no—
553C22×C4—528no—
554C22×C4—528no—
555C22×C4—528no—
556C22×C4—528no—
557C22×C4—528no—
558C22×C4C2×C4×D1312yes—
559C22×C4C2×C4×D1312yes—
560C22×C4C2×C4×D1312yes—
561C22×C4C2×D5214yes—
562C22×C4C2×D5212yes—
563C22×C4#612712yes—
564C22×C4D4×D1312yes—
565C22×C4D4×D1312yes—
566C22×C4Q8×D1312yes—
567C22×C4#613112yes—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—524no—
571C4⋊C4—524no—
572C4⋊C4—528no—
573C4⋊C4—524no—
574C22⋊C4—2616no—
575C22⋊C4—2616no—
576C22⋊C4—528no—
577C22⋊C4—528no—
578C22⋊C4—528no—
579C42—44no—
580C13#1444011yescharacteristic, complemented, Sylow
581C23—138no—
582C23—264no—
583C23—264no—
584C23—264no—
585C23—264no—
586C23—264no—
587C23—264no—
588C23—264no—
589C23—264no—
590C23—264no—
591C23—264no—
592C23—264no—
593C23—264no—
594C23—264no—
595C23—264no—
596C23—264no—
597C23—264no—
598C23—264no—
599C23—264no—
600C23—522no—
601C23—522no—
602C23—522no—
603C23—522no—
604C23—522no—
605C23—522no—
606C23—522no—
607C23—522no—
608C23—522no—
609C23—522no—
610C23—522no—
611C23—522no—
612C23—522no—
613C23—522no—
614C23—522no—
615C23—522no—
616C23C22×C4×D1311yescharacteristic
617C23C22×D5211yescharacteristic
618C23C2×#612711yescharacteristic
619C23C2×D4×D1311yescharacteristic
620C23C2×D4×D1311yescharacteristic
621C23#8825111yescharacteristic
622C23#8825111yescharacteristic
623C23#8825111yescharacteristic
624C23C2×Q8×D1311yescharacteristic
625C23C2×#613111yescharacteristic
626C23#8825411yescharacteristic
627C23#8825611yescharacteristic
628C23#8825611yescharacteristic
629C23#8825611yescharacteristic
630C23#8825711yescharacteristic
631D4—5216no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—264no—
665C2×C4—264no—
666C2×C4—264no—
667C2×C4—264no—
668C2×C4—264no—
669C2×C4—264no—
670C2×C4—5232no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—522no—
674C2×C4—522no—
675C2×C4—522no—
676C2×C4—522no—
677C2×C4—522no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—522no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—522no—
685C2×C4—522no—
686C2×C4C4×D5214yes—
687C2×C4C4⋊C4×D1314yes—
688C2×C4#8814714yes—
689C22—268no—
690C22—268no—
691C22—268no—
692C22—524no—
693C22—524no—
694C22—524no—
695C22—524no—
696C22—524no—
697C22—524no—
698C22—524no—
699C22—524no—
700C22—524no—
701C22—524no—
702C22—524no—
703C22—524no—
704C22C2×C4×D5211yescharacteristic
705C22#1171919111yescharacteristic
706C22#1171919811yescharacteristic
707C22#1171919911yescharacteristic
708C22C2×C4⋊C4×D1311yescharacteristic
709C22C2×#8814711yescharacteristic
710C22#1171920911yescharacteristic
711C22#1171921511yescharacteristic
712C22#1171922011yescharacteristic
713C22#1171922611yescharacteristic
714C22#1171922811yescharacteristic
715C22D4×D5211yescharacteristic
716C22D4×D5211yescharacteristic
717C22#1171925611yescharacteristic
718C22#1171925811yescharacteristic
719C22Q8×D5211yescharacteristic
720C22#1171928211yescharacteristic
721C22#1171928411yescharacteristic
722C22#1171929011yescharacteristic
723C22#1171930211yescharacteristic
724C22#1171931011yescharacteristic
725C22#1171931011yescharacteristic
726C22#1171931011yescharacteristic
727C22#1171933911yescharacteristic
728C22#1171933911yescharacteristic
729C22#1171934911yescharacteristic
730C22#1171935011yescharacteristic
731C22#1171938811yescharacteristic
732C22#1171938911yescharacteristic
733C22#1171940411yescharacteristic
734C22#1171940511yescharacteristic
735C22#1171942211yescharacteristic
736C22#1171943111yescharacteristic
737C22#1171943211yescharacteristic
738C22#1171943511yescharacteristic
739C4—24no—
740C4—24no—
741C4—24no—
742C4—44no—
743C4—82no—
744C4—524no—
745C4—524no—
746C4—1042no—
747C2—528no—
748C2#1311744911yescharacteristic
749C2#1311753611yescharacteristic
750C2#1311753911yescharacteristic
751C2#1311773611yescharacteristic
752C2C4⋊C4×D5211yescharacteristic
753C2#1311790011yescharacteristic
754C2#1311800711yescharacteristic
755C2#1312117111yescharacteristic
756C2#1312119811yescharacteristic
757C2#1312119911yescharacteristic
758C2#1312120711yescharacteristic
759C2#1312176511yescharacteristic
760C2#1312185211yescharacteristic
761C2#1312185411yescharacteristic
762C2#1312278011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#14440
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11718329C2semidirect
4. C2×#11718650C2semidirect
5. #13113088C2semidirect
6. #13113082C2semidirect
7. #13113078C2semidirect
8. #13113066C2semidirect
9. C13×C4⋊#95C2semidirect
32. #11718600C4semidirect
63. C2×C13×C4⋊C4D4semidirect
66. C2×C42×C13C2×C4semidirect
80. C2×#6103C2×C4semidirect
81. C2×#6103C2×C4semidirect
89. C2×C4⋊Dic13C2×C4semidirect
90. C2×C4⋊Dic13D4semidirect
180. C2×D52C4⋊C4semidirect
208. C4⋊#95D13semidirect
440. C2×C4⋊C4D52semidirect
458. C2×C42C4×D13semidirect
580. C13#14440semidirect

Maximal subgroups

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

subgroupindex
C2×#117186002
C2×#117183262
C2×#117183292
C2×#117186502
#131130882
#131130822
#131130782
#131130662
C13×C4⋊#952
#1444013