Finite Group Databasebeta

← #15768782

Subgroups — #15768782

Order 3328.

1338 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718603C211yesmaximal, characteristic
2C2×#11718603C211yesmaximal, characteristic
3C2×C22⋊C4×Dic13C211yesmaximal, characteristic
4C2×#11718118C211yesmaximal, characteristic
5C2×#11718119C211yesmaximal, characteristic
6C2×#11718119C211yesmaximal, characteristic
7C2×C13×#342C211yesmaximal, characteristic
8C24×Dic13C2211yescharacteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C13×C22⋊C4C2211yescharacteristic
11C22×C13×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic13C2211yescharacteristic
13C22×C22⋊Dic13C2211yescharacteristic
14C22×C22⋊Dic13C2211yescharacteristic
15C22×#6101—21no—
16C22×#6101C412yescomplemented
17C22×C4×Dic13—21no—
18C2×#88071—21no—
19C2×#88071—21no—
20C2×#88071C412yescomplemented
21#11718603—21no—
22#11718603—21no—
23#11718603—21no—
24#11718603—21no—
25#11718603—22no—
26#11718603C414yescomplemented
27C22⋊C4×Dic13—22no—
28C22⋊C4×Dic13C414yescomplemented
29C13×#342—22no—
30#11718119—22no—
31#11718119—22no—
32#11718118—22no—
33C25×C13C2311yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13—21no—
36C23×C4×C13C2×C412yes—
37C23×Dic13—21no—
38C23×Dic13—21no—
39C23×Dic13—44no—
40C23×Dic13C2×C411yescharacteristic
41C23×Dic13C2×C412yes—
42C23×Dic13C2×C412yes—
43C23×Dic13C2×C412yes—
44C23×Dic13C2×C411yescharacteristic
45C23×Dic13D411yescharacteristic
46C23×Dic13D411yescharacteristic
47C23×Dic13D412yes—
48C23×Dic13D411yescharacteristic
49C23×Dic13D411yescharacteristic
50C23×Dic13Q812yes—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—21no—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4C2×C412yes—
66C2×C13×C22⋊C4C2×C412yes—
67C2×C13×C22⋊C4D412yes—
68C2×C13×C22⋊C4Q812yes—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—21no—
71C2×C22⋊Dic13—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13C2×C412yes—
84C2×C22⋊Dic13C2×C412yes—
85C2×C22⋊Dic13D412yes—
86C2×C22⋊Dic13Q812yes—
87C2×#6101—24no—
88C2×#6101—22no—
89C2×#6101—22no—
90C2×#6101—44no—
91C2×#6101—44no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—44no—
94#88071—24no—
95#88071—22no—
96#88071—22no—
97#88071—24no—
98#10854—131nomaximal, Sylow
99C24×C13—42no—
100C24×C13—42no—
101C24×C13C22×C411yescharacteristic
102C24×C13C22×C411yescharacteristic
103C24×C13C22×C411yescharacteristic
104C24×C13C2×D411yescharacteristic
105C24×C13C2×D411yescharacteristic
106C24×C13C2×D411yescharacteristic
107C24×C13C2×D411yescharacteristic
108C24×C13C2×D411yescharacteristic
109C24×C13C2×Q811yescharacteristic
110C24×C13C2×Q811yescharacteristic
111C24×C13C2×Q811yescharacteristic
112C24×C13#4111yescharacteristic
113C24×C13#4111yescharacteristic
114C24×C13#4111yescharacteristic
115C24×C13#4111yescharacteristic
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×Dic13—24no—
132C22×Dic13—24no—
133C22×Dic13—24no—
134C22×Dic13—22no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—22no—
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—22no—
141C22×Dic13—44no—
142C22×Dic13—44no—
143C22×Dic13—44no—
144C22×Dic13—44no—
145C22×Dic13—42no—
146C22×Dic13—42no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C22×Dic13—42no—
152C22×Dic13—41no—
153C22×Dic13—41no—
154C22×Dic13—42no—
155C22×Dic13—42no—
156C22×Dic13C4212yes—
157C22×Dic13C4212yes—
158C22×Dic13C22⋊C411yescharacteristic
159C22×Dic13C22⋊C411yescharacteristic
160C22×Dic13C22⋊C412yes—
161C22×Dic13C22⋊C411yescharacteristic
162C22×Dic13C22⋊C412yes—
163C22×Dic13C22⋊C412yes—
164C22×Dic13C22⋊C412yes—
165C22×Dic13C22⋊C411yescharacteristic
166C22×Dic13C4⋊C412yes—
167C22×Dic13C4⋊C412yes—
168C22×Dic13C4⋊C412yes—
169C22×Dic13C4⋊C412yes—
170C22×Dic13C4⋊C412yes—
171C22×Dic13C4⋊C412yes—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—41no—
179C13×C22⋊C4—41no—
180C13×C22⋊C4—41no—
181C13×C22⋊C4—41no—
182C13×C22⋊C4—41no—
183C13×C22⋊C4C4⋊C414yescomplemented
184C22⋊Dic13—22no—
185C22⋊Dic13—22no—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C22⋊Dic13—22no—
189C22⋊Dic13—41no—
190C22⋊Dic13—41no—
191C22⋊Dic13—41no—
192C22⋊Dic13—41no—
193C22⋊Dic13—41no—
194C22⋊Dic13—41no—
195C22⋊Dic13C4⋊C414yescomplemented
196#6101—44no—
197#6101—48no—
198#6101—44no—
199C4×Dic13—48no—
200C2×#380—131no—
201C2×#380—131no—
202C2×C4×C22⋊C4—131no—
203C2×#342—131no—
204C2×#342—131no—
205C2×#342—131no—
206C2×#342D1311yescharacteristic
207C23×C13—22no—
208C23×C13—22no—
209C23×C13—22no—
210C23×C13—22no—
211C23×C13—22no—
212C23×C13—22no—
213C23×C13—41no—
214C23×C13—41no—
215C23×C13—41no—
216C23×C13—41no—
217C23×C13—41no—
218C23×C13—41no—
219C23×C13—42no—
220C23×C13—42no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13—42no—
226C23×C13—42no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13C2×C4211yescharacteristic
230C23×C13C2×C22⋊C411yescharacteristic
231C23×C13C2×C22⋊C411yescharacteristic
232C23×C13C2×C22⋊C411yescharacteristic
233C23×C13C2×C4⋊C411yescharacteristic
234C23×C13C2×C4⋊C411yescharacteristic
235C23×C13C2×C4⋊C411yescharacteristic
236C23×C13C2×C4⋊C411yescharacteristic
237C23×C13C2×C4⋊C411yescharacteristic
238C23×C13#11711yescharacteristic
239C23×C13#11711yescharacteristic
240C23×C13C4×D411yescharacteristic
241C23×C13C4×D411yescharacteristic
242C23×C13C4×D411yescharacteristic
243C23×C13C4×D411yescharacteristic
244C23×C13C4×Q811yescharacteristic
245C23×C13C4×Q811yescharacteristic
246C23×C13C4×Q811yescharacteristic
247C23×C13C4×Q811yescharacteristic
248C23×C13#12111yescharacteristic
249C23×C13#12111yescharacteristic
250C23×C13#12111yescharacteristic
251C23×C13#12111yescharacteristic
252C23×C13C22⋊Q811yescharacteristic
253C23×C13C22⋊Q811yescharacteristic
254C23×C13C22⋊Q811yescharacteristic
255C23×C13C22⋊Q811yescharacteristic
256C23×C13#12411yescharacteristic
257C23×C13#12411yescharacteristic
258C23×C13#12511yescharacteristic
259C23×C13#12511yescharacteristic
260C23×C13#12711yescharacteristic
261C23×C13C4⋊Q811yescharacteristic
262C23×C13C4⋊Q811yescharacteristic
263C23×C13C4⋊Q811yescharacteristic
264C2×C4×C13—24no—
265C2×C4×C13—42no—
266C2×C4×C13—44no—
267C2×C4×C13—42no—
268C2×C4×C13—44no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—42no—
272C2×C4×C13—42no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—82no—
276C2×C4×C13—82no—
277C2×C4×C13—82no—
278C2×C4×C13—82no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—44no—
297C2×Dic13—42no—
298C2×Dic13—44no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13—42no—
304C2×Dic13—42no—
305C2×Dic13—82no—
306C2×Dic13—82no—
307C2×Dic13—82no—
308C2×Dic13—82no—
309C2×Dic13#9512yes—
310C2×Dic13#9512yes—
311C2×Dic13#9512yes—
312C2×Dic13#9512yes—
313C2×Dic13#9914yes—
314C24×C4—131no—
315C22×C4⋊C4—132no—
316C22×C4⋊C4—261no—
317C22×C22⋊C4—131no—
318C22×C22⋊C4—131no—
319C22×C22⋊C4—131no—
320C22×C22⋊C4C2×D1311yescharacteristic
321C22×C22⋊C4C2×D1311yescharacteristic
322C22×C22⋊C4C2×D1311yescharacteristic
323C22×C42—261no—
324#380—134no—
325#380—261no—
326#380—261no—
327#380—261no—
328#380—261no—
329#380—262no—
330C4×C22⋊C4—134no—
331C4×C22⋊C4—262no—
332C2×#95—132no—
333C2×#95—261no—
334C2×#95—261no—
335#342—22no—
336#342—262no—
337#342—262no—
338#342—262no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—21no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—21no—
349C22×C13—21no—
350C22×C13—21no—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—22no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—41no—
374C22×C13—41no—
375C22×C13—41no—
376C22×C13—41no—
377C22×C13—41no—
378C22×C13—41no—
379C22×C13C2×#9511yescharacteristic
380C22×C13C4×C4⋊C411yescharacteristic
381C22×C13C4×C4⋊C411yescharacteristic
382C22×C13#38011yescharacteristic
383C22×C13#38011yescharacteristic
384C22×C13#38211yescharacteristic
385C22×C13#38411yescharacteristic
386C22×C13#38911yescharacteristic
387C22×C13#38911yescharacteristic
388C22×C13#38911yescharacteristic
389C22×C13#38911yescharacteristic
390C22×C13#39011yescharacteristic
391C22×C13#39011yescharacteristic
392C22×C13#39111yescharacteristic
393C22×C13#39111yescharacteristic
394C22×C13C2×#9912yes—
395C22×C13#41012yes—
396C4×C13—44no—
397C4×C13—82no—
398C4×C13—82no—
399Dic13—22no—
400Dic13—22no—
401Dic13—22no—
402Dic13—44no—
403Dic13—82no—
404Dic13—82no—
405Dic13#34214yescomplemented
406C25C22×D1311yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C23×C4—131no—
410C23×C4—131no—
411C23×C4—131no—
412C23×C4—131no—
413C23×C4—132no—
414C23×C4—132no—
415C23×C4—131no—
416C23×C4—131no—
417C23×C4—132no—
418C23×C4—132no—
419C23×C4—132no—
420C23×C4—261no—
421C23×C4—261no—
422C23×C4—524no—
423C23×C4C4×D1312yes—
424C2×C4⋊C4—262no—
425C2×C4⋊C4—262no—
426C2×C4⋊C4—264no—
427C2×C4⋊C4—524no—
428C2×C4⋊C4—524no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—132no—
444C2×C22⋊C4—132no—
445C2×C22⋊C4—132no—
446C2×C22⋊C4—132no—
447C2×C22⋊C4—261no—
448C2×C22⋊C4—261no—
449C2×C22⋊C4—261no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4—261no—
452C2×C22⋊C4—261no—
453C2×C22⋊C4—261no—
454C2×C22⋊C4—261no—
455C2×C22⋊C4—261no—
456C2×C22⋊C4—261no—
457C2×C22⋊C4—261no—
458C2×C22⋊C4—261no—
459C2×C22⋊C4—261no—
460C2×C22⋊C4—261no—
461C2×C22⋊C4Dic2612yes—
462C2×C22⋊C4C4×D1312yes—
463C2×C22⋊C4C4×D1312yes—
464C2×C22⋊C4C22⋊D1312yes—
465C2×C42—264no—
466C2×C42—524no—
467#95—262no—
468#95—262no—
469#95—264no—
470#95—264no—
471C2×C13—21no—
472C2×C13—21no—
473C2×C13—21no—
474C2×C13—21no—
475C2×C13—21no—
476C2×C13—21no—
477C2×C13—21no—
478C2×C13—21no—
479C2×C13—21no—
480C2×C13—21no—
481C2×C13—21no—
482C2×C13—21no—
483C2×C13C4⋊#9511yescharacteristic
484C2×C13C2×#34211yescharacteristic
485C2×C13#174011yescharacteristic
486C2×C13#196412yes—
487C2×C13#199612yes—
488C24—42no—
489C24—42no—
490C24C2×Dic2611yescharacteristic
491C24C2×C4×D1311yescharacteristic
492C24C2×C4×D1311yescharacteristic
493C24C2×C4×D1311yescharacteristic
494C24#612711yescharacteristic
495C24#612711yescharacteristic
496C24D4×D1311yescharacteristic
497C24D4×D1311yescharacteristic
498C24D4×D1311yescharacteristic
499C24D4×D1311yescharacteristic
500C24#612911yescharacteristic
501C24#612911yescharacteristic
502C24Q8×D1311yescharacteristic
503C24Q8×D1311yescharacteristic
504C24C2×C22⋊D1311yescharacteristic
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—131no—
521C22×C4—132no—
522C22×C4—132no—
523C22×C4—132no—
524C22×C4—131no—
525C22×C4—131no—
526C22×C4—131no—
527C22×C4—132no—
528C22×C4—132no—
529C22×C4—132no—
530C22×C4—132no—
531C22×C4—132no—
532C22×C4—132no—
533C22×C4—132no—
534C22×C4—132no—
535C22×C4—132no—
536C22×C4—264no—
537C22×C4—264no—
538C22×C4—264no—
539C22×C4—262no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4—262no—
543C22×C4—262no—
544C22×C4—262no—
545C22×C4—262no—
546C22×C4—524no—
547C22×C4—524no—
548C22×C4—524no—
549C22×C4—524no—
550C22×C4—522no—
551C22×C4—522no—
552C22×C4—522no—
553C22×C4—522no—
554C22×C4—522no—
555C22×C4—522no—
556C22×C4—522no—
557C22×C4—521no—
558C22×C4—521no—
559C22×C4—522no—
560C22×C4—522no—
561C4⋊C4—524no—
562C4⋊C4—528no—
563C4⋊C4—524no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—134no—
576C22⋊C4—262no—
577C22⋊C4—262no—
578C22⋊C4—262no—
579C22⋊C4—262no—
580C22⋊C4—262no—
581C22⋊C4—521no—
582C22⋊C4—521no—
583C22⋊C4—521no—
584C22⋊C4—521no—
585C22⋊C4—521no—
586C22⋊C4—521no—
587C22⋊C4#610114yescomplemented
588C42—528no—
589C13#1085411yescharacteristic, complemented, Sylow
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—42no—
612C23C4×Dic2611yescharacteristic
613C23C4×Dic2611yescharacteristic
614C23C42×D1311yescharacteristic
615C23#8812611yescharacteristic
616C23#8813111yescharacteristic
617C23#8813211yescharacteristic
618C23#8813211yescharacteristic
619C23C22⋊C4×D1311yescharacteristic
620C23C22⋊C4×D1311yescharacteristic
621C23C22⋊C4×D1311yescharacteristic
622C23#8813511yescharacteristic
623C23#8813511yescharacteristic
624C23#8813811yescharacteristic
625C23#8813811yescharacteristic
626C23#8813911yescharacteristic
627C23#8813911yescharacteristic
628C23#8814111yescharacteristic
629C23#8814111yescharacteristic
630C23#8814211yescharacteristic
631C23#8814211yescharacteristic
632C23#8814311yescharacteristic
633C23#8814311yescharacteristic
634C23C4⋊C4×D1311yescharacteristic
635C23C4⋊C4×D1311yescharacteristic
636C23C4⋊C4×D1311yescharacteristic
637C23C4⋊C4×D1311yescharacteristic
638C23#8815011yescharacteristic
639C23#8815011yescharacteristic
640C23C2×#610111yescharacteristic
641C23C4×C22⋊D1311yescharacteristic
642C23C4×C22⋊D1311yescharacteristic
643C23#8819311yescharacteristic
644C23#8819311yescharacteristic
645C23#8819411yescharacteristic
646C23#8819811yescharacteristic
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—82no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4—134no—
663C2×C4—132no—
664C2×C4—132no—
665C2×C4—132no—
666C2×C4—132no—
667C2×C4—264no—
668C2×C4—264no—
669C2×C4—264no—
670C2×C4—264no—
671C2×C4—264no—
672C2×C4—264no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—264no—
677C2×C4—522no—
678C2×C4—522no—
679C2×C4—522no—
680C2×C4—522no—
681C2×C4—522no—
682C2×C4—522no—
683C2×C4—522no—
684C2×C4—524no—
685C2×C4—524no—
686C2×C4—522no—
687C2×C4—522no—
688C2×C4—522no—
689C2×C4—522no—
690C2×C4—522no—
691C2×C4—522no—
692C2×C4—522no—
693C2×C4—1042no—
694C2×C4—1042no—
695C2×C4—1042no—
696C2×C4—1042no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22#1171830711yescharacteristic
738C22#1171830711yescharacteristic
739C22#1171830811yescharacteristic
740C22#1171830811yescharacteristic
741C22#1171831011yescharacteristic
742C22#1171831111yescharacteristic
743C22D13×#9511yescharacteristic
744C22#1171832811yescharacteristic
745C22#1171840112yes—
746C22D13×#9912yes—
747C22C4×#610111yescharacteristic
748C22#1171860311yescharacteristic
749C22#1171861811yescharacteristic
750C22#1171861811yescharacteristic
751C22#1171863311yescharacteristic
752C22#1171863311yescharacteristic
753C22#1171863711yescharacteristic
754C4—44no—
755C4—82no—
756C4—82no—
757C4—134no—
758C4—262no—
759C4—262no—
760C4—262no—
761C4—524no—
762C4—1042no—
763C4—1042no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2#1311306411yescharacteristic
777C2D13×#34211yescharacteristic
778C2#1311456711yescharacteristic
779C2#1311567012yes—
780C2#1311581912yes—
subgroupG/H
centerC23C22⋊C4×D13
commutatorC23×C13C2×C42
FrattiniC25C22×D13
FittingC2×C13×#342C2
socleC23×C13C2×C22⋊C4
prime radical, cosocleC25×C13C23
hypercenterC2×#342D13
hypocenterC13#10854
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
16. C22×#6101C4semidirect
20. C2×#88071C4semidirect
26. #11718603C4semidirect
28. C22⋊C4×Dic13C4semidirect
183. C13×C22⋊C4C4⋊C4semidirect
195. C22⋊Dic13C4⋊C4semidirect
405. Dic13#342semidirect
587. C22⋊C4#6101semidirect
589. C13#10854semidirect

Maximal subgroups

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

subgroupindex
C2×#117186032
C2×C22⋊C4×Dic132
C2×#117181182
C2×#117181192
C2×C13×#3422
#1085413