Finite Group Databasebeta

← #15771840

Subgroups — #15771840

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88144C211yesmaximal, characteristic
2C2×#11718143C211yesmaximal, characteristic
3C2×#11718121C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic
5C2×#11718142C211yesmaximal, characteristic
6#13113065C211yesmaximal, characteristic
7C2×C13×#340C211yesmaximal, characteristic
8C23×C8×C13C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13—21no—
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6101—21no—
15C22×C4×Dic13C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C2×#88144—22no—
18C2×#88144—22no—
19C2×#88144—22no—
20C2×#88144—22no—
21C2×#88144—22no—
22C2×#88144C414yescomplemented
23C2×#88071—21no—
24C2×#88071—21no—
25C13×#340—22no—
26#11718143—22no—
27#11718142—22no—
28#11718121—22no—
29#11718121—22no—
30C23×C4×C13—21no—
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C23×Dic13—21no—
34C23×Dic13—21no—
35C23×Dic13D411yescharacteristic
36C23×Dic13D411yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13—21no—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13Q812yes—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2×C412yes—
53C2×C13×C4⋊C4D412yes—
54C2×C13×C4⋊C4D412yes—
55C2×C13×C4⋊C4Q812yes—
56C2×C4⋊Dic13—24no—
57C2×C4⋊Dic13—24no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—24no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13—21no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13C2×C412yes—
68C2×C4⋊Dic13D412yes—
69C2×C4⋊Dic13D412yes—
70C2×C4⋊Dic13Q812yes—
71C2×#6101—24no—
72C2×#6101—24no—
73C2×#6101—24no—
74C2×C4×Dic13—21no—
75C2×C4×Dic13—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13C2×C412yes—
79C2×C4×Dic13D412yes—
80C22×#1055—21no—
81C22×#1055—21no—
82C22×#1055—21no—
83C22×#1055—21no—
84C22×#1055—21no—
85C22×#1055—21no—
86C22×#1055Q812yes—
87#88144—28no—
88#88144—28no—
89#88144—28no—
90#88144—28no—
91#88071—42no—
92#88071—42no—
93#11385—131nomaximal, Sylow
94C24×C13C2×D411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—22no—
99C22×C4×C13—41no—
100C22×C4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13C22×C411yescharacteristic
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×Q811yescharacteristic
116C22×C4×C13C2×Q811yescharacteristic
117C22×C4×C13C2×Q811yescharacteristic
118C22×C4×C13C2×Q811yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C22×C4×C13#4111yescharacteristic
123C22×Dic13—22no—
124C22×Dic13—21no—
125C22×Dic13—21no—
126C22×Dic13—21no—
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—22no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13—21no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—22no—
139C22×Dic13—41no—
140C22×Dic13—41no—
141C22×Dic13—41no—
142C22×Dic13—41no—
143C22×Dic13—41no—
144C22×Dic13—41no—
145C22×Dic13—41no—
146C22×Dic13—41no—
147C22×Dic13—41no—
148C22×Dic13—41no—
149C22×Dic13C22⋊C412yes—
150C22×Dic13C22⋊C412yes—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C2×C8×C13—41no—
155C2×C8×C13—41no—
156C2×C8×C13—41no—
157C2×C8×C13—41no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—41no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4C22⋊C414yes—
166C4⋊Dic13—216no—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13—22no—
170C4⋊Dic13—22no—
171C4⋊Dic13—22no—
172C4⋊Dic13—41no—
173C4⋊Dic13—41no—
174C4⋊Dic13C22⋊C414yes—
175#6101—216no—
176C4×Dic13—22no—
177C4×Dic13—22no—
178C4×Dic13—22no—
179C4×Dic13—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—41no—
184C2×#1055—41no—
185C2×#1055—41no—
186C2×#1055—41no—
187C22×#125—131no—
188C2×#340—131no—
189C2×#340—131no—
190C2×#340—131no—
191C2×#340D1311yescharacteristic
192C2×#336—131no—
193C4⋊#95—131no—
194C23×C13C2×C22⋊C411yescharacteristic
195C23×C13#12011yescharacteristic
196C23×C13#12011yescharacteristic
197C23×C13C22⋊Q811yescharacteristic
198C23×C13C22⋊Q811yescharacteristic
199C23×C13#12411yescharacteristic
200C23×C13C4⋊Q811yescharacteristic
201C23×C13#13511yescharacteristic
202C23×C13#13511yescharacteristic
203C23×C13#13511yescharacteristic
204C23×C13#13511yescharacteristic
205C23×C13AGL(1,ℤ/8)11yescharacteristic
206C23×C13AGL(1,ℤ/8)11yescharacteristic
207C23×C13#13711yescharacteristic
208C23×C13#13711yescharacteristic
209C2×C4×C13—24no—
210C2×C4×C13—42no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—81no—
220C2×C4×C13—81no—
221C2×C4×C13—81no—
222C2×C4×C13—81no—
223C2×C4×C13C2×C22⋊C411yescharacteristic
224C2×C4×C13C2×C22⋊C411yescharacteristic
225C2×C4×C13C4×Q811yescharacteristic
226C2×C4×C13C4×Q811yescharacteristic
227C2×C4×C13C4×Q811yescharacteristic
228C2×C4×C13C4×Q811yescharacteristic
229C2×C4×C13#12011yescharacteristic
230C2×C4×C13#12011yescharacteristic
231C2×C4×C13C22⋊Q811yescharacteristic
232C2×C4×C13C22⋊Q811yescharacteristic
233C2×C4×C13C22⋊Q811yescharacteristic
234C2×C4×C13C22⋊Q811yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13C22⋊Q811yescharacteristic
237C2×C4×C13C22⋊Q811yescharacteristic
238C2×C4×C13C22⋊Q811yescharacteristic
239C2×C4×C13C22⋊Q811yescharacteristic
240C2×C4×C13C22⋊Q811yescharacteristic
241C2×C4×C13#12411yescharacteristic
242C2×C4×C13#12411yescharacteristic
243C2×C4×C13#12411yescharacteristic
244C2×C4×C13#12411yescharacteristic
245C2×C4×C13#12411yescharacteristic
246C2×C4×C13C4⋊Q811yescharacteristic
247C2×C4×C13C4⋊Q811yescharacteristic
248C2×C4×C13C4⋊Q811yescharacteristic
249C2×C4×C13C4⋊Q811yescharacteristic
250C2×C4×C13C4⋊Q811yescharacteristic
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—24no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13—42no—
273C2×Dic13—42no—
274C2×Dic13—42no—
275C2×Dic13—81no—
276C2×Dic13—81no—
277C2×Dic13—81no—
278C2×Dic13—81no—
279C8×C13—42no—
280#1055—42no—
281C23×C8—131no—
282C23×C8C2×D1311yescharacteristic
283C2×#125—134no—
284C2×#125—262no—
285C2×#125—262no—
286C2×#125—262no—
287C2×#125—262no—
288C2×#125—262no—
289C22×C4⋊C4—131no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—261no—
292C22×C4⋊C4—261no—
293C22×C4⋊C4C2×D1311yescharacteristic
294C22×C4⋊C4C2×D1311yescharacteristic
295C22×C42—131no—
296C2×#95—261no—
297C2×#95—261no—
298#340—22no—
299#340—262no—
300#340—262no—
301#340—262no—
302#336—262no—
303C22×C13#37911yescharacteristic
304C22×C13#39111yescharacteristic
305C22×C13#39111yescharacteristic
306C22×C13#39311yescharacteristic
307C22×C13#39311yescharacteristic
308C22×C13#39511yescharacteristic
309C22×C13#39511yescharacteristic
310C22×C13#41611yescharacteristic
311C22×C13#41611yescharacteristic
312C22×C13#41711yescharacteristic
313C22×C13#41711yescharacteristic
314C22×C13#44911yescharacteristic
315C22×C13#44911yescharacteristic
316C22×C13#44911yescharacteristic
317C22×C13#44911yescharacteristic
318C22×C13#45211yescharacteristic
319C22×C13#45211yescharacteristic
320C22×C13#45211yescharacteristic
321C22×C13#45211yescharacteristic
322C22×C13#47811yescharacteristic
323C22×C13#47811yescharacteristic
324C22×C13#47811yescharacteristic
325C22×C13#47811yescharacteristic
326C22×C13#47911yescharacteristic
327C22×C13#47911yescharacteristic
328C22×C13#47911yescharacteristic
329C22×C13#47911yescharacteristic
330C22×C13#48811yescharacteristic
331C22×C13#48811yescharacteristic
332C22×C13#49011yescharacteristic
333C22×C13#49111yescharacteristic
334C22×C13#49911yescharacteristic
335C22×C13#49911yescharacteristic
336C22×C13#50111yescharacteristic
337C22×C13#50111yescharacteristic
338C4×C13—44no—
339C4×C13—82no—
340C4×C13#39111yescharacteristic
341C4×C13#39111yescharacteristic
342C4×C13#39111yescharacteristic
343C4×C13#39111yescharacteristic
344C4×C13#39311yescharacteristic
345C4×C13#39311yescharacteristic
346C4×C13#39511yescharacteristic
347C4×C13#39511yescharacteristic
348Dic13—42no—
349Dic13—42no—
350Dic13—44no—
351Dic13—82no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—261no—
357C23×C4—261no—
358C23×C4C22×D1311yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—132no—
366C22×C8—261no—
367C22×C8—261no—
368C22×C8—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8Dic2612yes—
373#125—268no—
374#125—268no—
375#125—268no—
376#125—268no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—132no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—132no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—264no—
391C2×C4⋊C4—264no—
392C2×C4⋊C4—264no—
393C2×C4⋊C4—264no—
394C2×C4⋊C4—264no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4Dic2612yes—
404C2×C4⋊C4C4×D1312yes—
405C2×C4⋊C4D5212yes—
406C2×C4⋊C4C22⋊D1312yes—
407C2×C42—132no—
408C2×C42—132no—
409C2×C42—261no—
410C2×C42—261no—
411C2×C42—261no—
412C2×C42—261no—
413#95—522no—
414#95—522no—
415C2×C13#144611yescharacteristic
416C2×C13#178811yescharacteristic
417C2×C13#178811yescharacteristic
418C2×C13#198911yescharacteristic
419C2×C13#198911yescharacteristic
420C2×C13#199111yescharacteristic
421C2×C13#199211yescharacteristic
422C2×C13#202511yescharacteristic
423C2×C13#202511yescharacteristic
424C2×C13#202611yescharacteristic
425C2×C13#202611yescharacteristic
426C2×C13#205911yescharacteristic
427C2×C13#205911yescharacteristic
428C2×C13#205911yescharacteristic
429C2×C13#205911yescharacteristic
430C24D4×D1311yescharacteristic
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—132no—
446C22×C4—132no—
447C22×C4—262no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—262no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—262no—
462C22×C4—262no—
463C22×C4—521no—
464C22×C4—521no—
465C22×C4—521no—
466C22×C4—521no—
467C22×C4—521no—
468C22×C4—521no—
469C22×C4—521no—
470C22×C4—521no—
471C22×C4—521no—
472C22×C4—521no—
473C22×C4C2×Dic2611yescharacteristic
474C22×C4C2×Dic2611yescharacteristic
475C22×C4C2×C4×D1311yescharacteristic
476C22×C4C2×D5211yescharacteristic
477C22×C4#612711yescharacteristic
478C22×C4#612711yescharacteristic
479C22×C4D4×D1311yescharacteristic
480C22×C4D4×D1311yescharacteristic
481C22×C4D4×D1311yescharacteristic
482C22×C4#612911yescharacteristic
483C22×C4#612911yescharacteristic
484C22×C4Q8×D1311yescharacteristic
485C22×C4Q8×D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—262no—
495C2×C8—262no—
496C2×C8—262no—
497C2×C8—521no—
498C2×C8—521no—
499C2×C8—521no—
500C2×C8—521no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—134no—
509C4⋊C4—2616no—
510C4⋊C4—2616no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—262no—
514C4⋊C4—262no—
515C4⋊C4—262no—
516C4⋊C4—521no—
517C4⋊C4—521no—
518C4⋊C4#610314yes—
519C42—262no—
520C42—262no—
521C42—262no—
522C42—262no—
523C13#1138511yescharacteristic, complemented, Sylow
524C23#8813211yescharacteristic
525C23C22⋊C4×D1311yescharacteristic
526C23#8813611yescharacteristic
527C23#8813911yescharacteristic
528C23#8814211yescharacteristic
529C23#8815011yescharacteristic
530C23#8816511yescharacteristic
531C23#8816611yescharacteristic
532C23#8816811yescharacteristic
533C23#8816911yescharacteristic
534C23#8817011yescharacteristic
535C23#8817011yescharacteristic
536C23#8817211yescharacteristic
537C23#8817311yescharacteristic
538C23#8819111yescharacteristic
539C2×C4—24no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—262no—
554C2×C4—262no—
555C2×C4—262no—
556C2×C4—262no—
557C2×C4—262no—
558C2×C4—262no—
559C2×C4—264no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—521no—
565C2×C4—522no—
566C2×C4—521no—
567C2×C4—522no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—522no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—522no—
574C2×C4—522no—
575C2×C4—522no—
576C2×C4—522no—
577C2×C4—1041no—
578C2×C4—1041no—
579C2×C4—1041no—
580C2×C4—1041no—
581C2×C4C4×Dic2611yescharacteristic
582C2×C4C4×Dic2611yescharacteristic
583C2×C4#8812311yescharacteristic
584C2×C4#8812911yescharacteristic
585C2×C4#8813211yescharacteristic
586C2×C4#8813211yescharacteristic
587C2×C4#8813211yescharacteristic
588C2×C4C22⋊C4×D1311yescharacteristic
589C2×C4#8813611yescharacteristic
590C2×C4#8813911yescharacteristic
591C2×C4#8813911yescharacteristic
592C2×C4#8813911yescharacteristic
593C2×C4#8814111yescharacteristic
594C2×C4#8814111yescharacteristic
595C2×C4#8814211yescharacteristic
596C2×C4#8814211yescharacteristic
597C2×C4#8814211yescharacteristic
598C2×C4#8815011yescharacteristic
599C2×C4#8815011yescharacteristic
600C2×C4#8815011yescharacteristic
601C2×C4#8815111yescharacteristic
602C2×C4#8815111yescharacteristic
603C2×C4#8817811yescharacteristic
604C2×C4#8817811yescharacteristic
605C2×C4C2×#610311yescharacteristic
606C2×C4#8819011yescharacteristic
607C2×C4#8819111yescharacteristic
608C2×C4#8819811yescharacteristic
609C8—42no—
610C8—522no—
611C22#1171830711yescharacteristic
612C22#1171830711yescharacteristic
613C22#1171831711yescharacteristic
614C22#1171833411yescharacteristic
615C22#1171842411yescharacteristic
616C22#1171842511yescharacteristic
617C22#1171842711yescharacteristic
618C22#1171842911yescharacteristic
619C22#1171843211yescharacteristic
620C22#1171843311yescharacteristic
621C22#1171844211yescharacteristic
622C22#1171844411yescharacteristic
623C22#1171845711yescharacteristic
624C22#1171845811yescharacteristic
625C22#1171846011yescharacteristic
626C22#1171846111yescharacteristic
627C22#1171846411yescharacteristic
628C22#1171846511yescharacteristic
629C22#1171847111yescharacteristic
630C22#1171847211yescharacteristic
631C22#1171851711yescharacteristic
632C22#1171851811yescharacteristic
633C22#1171851911yescharacteristic
634C22#1171853211yescharacteristic
635C22#1171853711yescharacteristic
636C22#1171853811yescharacteristic
637C22#1171853911yescharacteristic
638C22#1171855211yescharacteristic
639C22#1171860811yescharacteristic
640C22#1171861611yescharacteristic
641C22#1171864011yescharacteristic
642C22#1171881911yescharacteristic
643C22#1171883311yescharacteristic
644C22#1171883411yescharacteristic
645C22#1171884811yescharacteristic
646C4—44no—
647C4—82no—
648C4—522no—
649C4—522no—
650C4—524no—
651C4—1042no—
652C4#1171830711yescharacteristic
653C4#1171830711yescharacteristic
654C4#1171831711yescharacteristic
655C4#1171833411yescharacteristic
656C4#1171859011yescharacteristic
657C4#1171860811yescharacteristic
658C4#1171863511yescharacteristic
659C4#1171864011yescharacteristic
660C2#1311310611yescharacteristic
661C2#1311477311yescharacteristic
662C2#1311477511yescharacteristic
663C2#1311579011yescharacteristic
664C2#1311579211yescharacteristic
665C2#1311579911yescharacteristic
666C2#1311580311yescharacteristic
667C2#1311598011yescharacteristic
668C2#1311598111yescharacteristic
669C2#1311598511yescharacteristic
670C2#1311598611yescharacteristic
671C2#1311617211yescharacteristic
672C2#1311617311yescharacteristic
673C2#1311617611yescharacteristic
674C2#1311617711yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#11385
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
22. C2×#88144C4semidirect
523. C13#11385semidirect

Maximal subgroups

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

subgroupindex
C22×#881442
C2×#117181432
C2×#117181212
C2×#117181422
#131130652
C2×C13×#3402
#1138513