Finite Group Databasebeta

← C2×#13116013 #15890357

Subgroups — C2×#13116013 #15890357

Order 3328.

1434 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719188C211yesmaximal, characteristic, complemented
2C22×#88074C211yesmaximal, characteristic
3C22×#88074C211yesmaximal, characteristic
4#13116013C218yesmaximal, direct product factor
5C2×#11718118C211yesmaximal, characteristic, complemented
6C2×#11718119C211yesmaximal, characteristic, complemented
7C2×#11718119C211yesmaximal, characteristic, complemented
8C22×C13×#99C211yesmaximal, characteristic
9C23×D4×C13C2211yescharacteristic
10C22×C13×C22⋊C4C2211yescharacteristic
11C22×C13×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic13C2211yescharacteristic
13C22×C22⋊Dic13C2211yescharacteristic
14C22×C22⋊Dic13C2211yescharacteristic
15C22×C22⋊Dic13C2211yescharacteristic
16C2×#88178—22no—
17#11719188—22no—
18#11719188—22no—
19#11719188—22no—
20#11719188C2214yescomplemented
21C2×#88132—22no—
22C2×#88132—22no—
23C2×C13×#99—22no—
24C2×C13×#99—22no—
25C2×C13×#99C2214yes—
26C2×#88074—22no—
27C2×#88074—22no—
28C2×#88074—22no—
29C2×#88074—22no—
30C2×#88074C2214yes—
31C2×#88074C2214yes—
32#11718119C2214yescomplemented
33#11718119C2214yescomplemented
34#11718118C2214yescomplemented
35C25×C13Q811yescharacteristic, complemented
36C25×C13C2311yescharacteristic
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13—21no—
42C22×D4×C13—21no—
43C22×D4×C13—21no—
44C22×D4×C13—21no—
45C22×D4×C13—21no—
46C22×D4×C13—21no—
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13Q812yescomplemented
50C22×D4×C13C2312yes—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13Q811yescharacteristic, complemented
54C23×Dic13—21no—
55C23×Dic13—21no—
56C23×Dic13—21no—
57C23×Dic13—21no—
58C22×Dic26—22no—
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⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4D412yes—
68C2×C13×C22⋊C4D412yes—
69C2×C13×C22⋊C4C2312yes—
70C2×C13×C22⋊C4C2312yes—
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⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13D412yes—
88C2×C22⋊Dic13D412yes—
89C2×C22⋊Dic13D412yes—
90C2×C22⋊Dic13D412yes—
91C2×C22⋊Dic13C2312yes—
92C2×C22⋊Dic13C2312yes—
93C2×C22⋊Dic13C2312yes—
94C2×C22⋊Dic13C2312yes—
95C2×C4⋊Dic13—22no—
96#88178—28no—
97#88178—28no—
98C2×#6101—24no—
99#88132—28no—
100#88132—28no—
101#88132—28no—
102#88132—28no—
103C13×#99—28no—
104#88074—28no—
105#88074—28no—
106C2×#2032—131nomaximal, Sylow
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—82no—
114C24×C13—82no—
115C24×C13C2×D411yescharacteristic
116C24×C13C2×D411yescharacteristic
117C24×C13C2×D411yescharacteristic
118C24×C13C2×D411yescharacteristic
119C24×C13C2×D411yescharacteristic
120C24×C13C2×D411yescharacteristic
121C24×C13C2×Q811yescharacteristic
122C24×C13C2×Q811yescharacteristic
123C24×C13C2×Q812yescomplemented
124C24×C13#4111yescharacteristic
125C24×C13#4111yescharacteristic
126C24×C13#4111yescharacteristic
127C24×C13#4111yescharacteristic
128C24×C13#4111yescharacteristic
129C24×C13#4111yescharacteristic
130C24×C13C2411yescharacteristic
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—22no—
134C2×D4×C13—22no—
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—22no—
138C2×D4×C13—22no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—41no—
144C2×D4×C13—41no—
145C2×D4×C13—41no—
146C2×D4×C13—41no—
147C2×D4×C13—41no—
148C2×D4×C13—41no—
149C2×D4×C13—41no—
150C2×D4×C13—41no—
151C2×D4×C13—41no—
152C2×D4×C13—41no—
153C2×D4×C13—41no—
154C2×D4×C13—41no—
155C2×D4×C13—41no—
156C2×D4×C13—41no—
157C2×D4×C13—41no—
158C2×D4×C13—41no—
159C22×C4×C13—22no—
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—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—41no—
170C22×C4×C13—41no—
171C22×C4×C13—82no—
172C22×C4×C13—82no—
173C22×C4×C13C2×Q812yescomplemented
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—41no—
183C22×Dic13—41no—
184C22×Dic13—41no—
185C22×Dic13—41no—
186C22×Dic13—82no—
187C22×Dic13—82no—
188C22×Dic13—82no—
189C22×Dic13—82no—
190C2×Dic26—28no—
191C2×Dic26—84no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4C2×D414yes—
200C22⋊Dic13—22no—
201C22⋊Dic13—22no—
202C22⋊Dic13—22no—
203C22⋊Dic13—22no—
204C22⋊Dic13—22no—
205C22⋊Dic13—22no—
206C22⋊Dic13—22no—
207C22⋊Dic13—22no—
208C22⋊Dic13—22no—
209C22⋊Dic13—22no—
210C22⋊Dic13—41no—
211C22⋊Dic13—41no—
212C22⋊Dic13—41no—
213C22⋊Dic13—41no—
214C22⋊Dic13C2×D414yes—
215C22⋊Dic13C2×D414yes—
216C4⋊Dic13—28no—
217#6101—216no—
218C2×#543—131no—
219C22×#99—131no—
220C22×#99—131no—
221C22×#99D1311yescharacteristic
222#2032—138no—
223C2×#342—131no—
224C2×#342—131no—
225C2×#342—131no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—42no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—42no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—82no—
241C23×C13—82no—
242C23×C13—82no—
243C23×C13—81no—
244C23×C13—81no—
245C23×C13—81no—
246C23×C13—81no—
247C23×C13—81no—
248C23×C13—81no—
249C23×C13—81no—
250C23×C13—81no—
251C23×C13—82no—
252C23×C13—82no—
253C23×C13—82no—
254C23×C13—82no—
255C23×C13#12011yescharacteristic
256C23×C13#12011yescharacteristic
257C23×C13#12011yescharacteristic
258C23×C13#12011yescharacteristic
259C23×C13C22⋊Q811yescharacteristic
260C23×C13C22⋊Q811yescharacteristic
261C23×C13C22⋊Q811yescharacteristic
262C23×C13C22⋊Q811yescharacteristic
263C23×C13C22⋊Q811yescharacteristic
264C23×C13C22⋊Q811yescharacteristic
265C23×C13C22⋊Q811yescharacteristic
266C23×C13C22⋊Q811yescharacteristic
267C23×C13C22⋊Q811yescharacteristic
268C23×C13C22⋊Q811yescharacteristic
269C23×C13C22⋊Q811yescharacteristic
270C23×C13C22⋊Q811yescharacteristic
271C23×C13#12411yescharacteristic
272C23×C13#12411yescharacteristic
273C23×C13#12411yescharacteristic
274C23×C13#12411yescharacteristic
275C23×C13#12411yescharacteristic
276C23×C13#12411yescharacteristic
277C23×C13#12411yescharacteristic
278C23×C13#12411yescharacteristic
279C23×C13#12411yescharacteristic
280C23×C13#12411yescharacteristic
281C23×C13#12411yescharacteristic
282C23×C13#12411yescharacteristic
283C23×C13C22×D411yescharacteristic
284C23×C13C22×D411yescharacteristic
285C23×C13C22×D411yescharacteristic
286C23×C13C22×Q811yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290D4×C13—42no—
291D4×C13—42no—
292D4×C13—42no—
293D4×C13—42no—
294D4×C13—42no—
295D4×C13—42no—
296D4×C13—42no—
297D4×C13—42no—
298C2×C4×C13—24no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—44no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—42no—
308C2×C4×C13—82no—
309C2×C4×C13—82no—
310C2×C4×C13—82no—
311C2×C4×C13—82no—
312C2×C4×C13—82no—
313C2×Dic13—24no—
314C2×Dic13—24no—
315C2×Dic13—44no—
316C2×Dic13—44no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13—82no—
320C2×Dic13—82no—
321C2×Dic13—82no—
322C2×Dic13—82no—
323C2×Dic13—82no—
324C2×Dic13—82no—
325C2×Dic13—82no—
326C2×Dic13—82no—
327C2×Dic13—82no—
328C2×Dic13—82no—
329Dic26—88no—
330C23×D4C2×D1311yescharacteristic
331#543—134no—
332#543—262no—
333#543—262no—
334#543—262no—
335C2×C22⋊Q8—262no—
336C2×C22⋊Q8—262no—
337C2×C22⋊Q8—262no—
338C22×C22⋊C4—131no—
339C22×C22⋊C4—131no—
340C22×C22⋊C4—131no—
341C22×C22⋊C4—131no—
342C22×C22⋊C4C2×D1311yescharacteristic
343C22×C22⋊C4C2×D1311yescharacteristic
344C2×#99—22no—
345C2×#99—22no—
346C2×#99—134no—
347C2×#99—134no—
348C2×#99—262no—
349C2×#99—262no—
350C2×#99—262no—
351C2×#99—262no—
352C2×#99C2×D1314yes—
353#342—134no—
354#342—134no—
355#342—134no—
356C22×C13—22no—
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×C13—41no—
380C22×C13—41no—
381C22×C13—41no—
382C22×C13—41no—
383C22×C13—41no—
384C22×C13—41no—
385C22×C13—41no—
386C22×C13—41no—
387C22×C13—41no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13—41no—
391C22×C13—42no—
392C22×C13—82no—
393C22×C13—82no—
394C22×C13—82no—
395C22×C13—82no—
396C22×C13—82no—
397C22×C13—82no—
398C22×C13—82no—
399C22×C13#39311yescharacteristic
400C22×C13#39311yescharacteristic
401C22×C13#39311yescharacteristic
402C22×C13#39311yescharacteristic
403C22×C13#39311yescharacteristic
404C22×C13#39311yescharacteristic
405C22×C13#39311yescharacteristic
406C22×C13#39311yescharacteristic
407C22×C13C2×#12011yescharacteristic
408C22×C13C2×C22⋊Q811yescharacteristic
409C22×C13C2×C22⋊Q811yescharacteristic
410C22×C13C2×C22⋊Q811yescharacteristic
411C22×C13C2×#12411yescharacteristic
412C22×C13C2×#12411yescharacteristic
413C22×C13C2×#12411yescharacteristic
414C4×C13—44no—
415C4×C13—42no—
416C4×C13—82no—
417Dic13—44no—
418Dic13—44no—
419Dic13—82no—
420Dic13—82no—
421C25Dic2611yescharacteristic, complemented
422C25C22×D1311yescharacteristic
423C22×Q8—262no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4Dic2612yescomplemented
437C22×D4C22×D1312yes—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—261no—
441C23×C4—261no—
442C23×C4—261no—
443C23×C4—261no—
444C23×C4Dic2611yescharacteristic, complemented
445C22⋊Q8—268no—
446C22⋊Q8—268no—
447C22⋊Q8—268no—
448C22⋊Q8—268no—
449C22⋊Q8—268no—
450C22⋊Q8—268no—
451C2×C4⋊C4—264no—
452C2×C4⋊C4—262no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—132no—
462C2×C22⋊C4—132no—
463C2×C22⋊C4—132no—
464C2×C22⋊C4—132no—
465C2×C22⋊C4—132no—
466C2×C22⋊C4—132no—
467C2×C22⋊C4—132no—
468C2×C22⋊C4—132no—
469C2×C22⋊C4—261no—
470C2×C22⋊C4—261no—
471C2×C22⋊C4—261no—
472C2×C22⋊C4—261no—
473C2×C22⋊C4—261no—
474C2×C22⋊C4—261no—
475C2×C22⋊C4—261no—
476C2×C22⋊C4—261no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4—261no—
482C2×C22⋊C4—261no—
483C2×C22⋊C4—261no—
484C2×C22⋊C4—261no—
485C2×C22⋊C4C22⋊D1312yes—
486C2×C22⋊C4C22⋊D1312yes—
487C2×C22⋊C4C22×D1312yes—
488C2×C22⋊C4C22×D1312yes—
489#99—28no—
490#99—268no—
491#99—268no—
492C2×C13—21no—
493C2×C13—21no—
494C2×C13—21no—
495C2×C13—21no—
496C2×C13—21no—
497C2×C13—21no—
498C2×C13—21no—
499C2×C13—21no—
500C2×C13—21no—
501C2×C13—21no—
502C2×C13—21no—
503C2×C13—21no—
504C2×C13—21no—
505C2×C13—21no—
506C2×C13—82no—
507C2×C13#203212yescomplemented
508C2×C13C2×#39311yescharacteristic
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—82no—
516C24—82no—
517C24C2×Dic2611yescharacteristic
518C24C2×Dic2611yescharacteristic
519C24C2×Dic2612yescomplemented
520C24#612711yescharacteristic
521C24#612711yescharacteristic
522C24D4×D1311yescharacteristic
523C24D4×D1311yescharacteristic
524C24D4×D1311yescharacteristic
525C24D4×D1311yescharacteristic
526C24#612911yescharacteristic
527C24#612911yescharacteristic
528C24#612911yescharacteristic
529C24#612911yescharacteristic
530C24C2×C22⋊D1311yescharacteristic
531C24C2×C22⋊D1311yescharacteristic
532C24C23×D1311yescharacteristic
533C2×Q8—268no—
534C2×Q8—1044no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—521no—
586C22×C4—521no—
587C22×C4—521no—
588C22×C4—521no—
589C22×C4—1042no—
590C22×C4—1042no—
591C22×C4—1042no—
592C22×C4—1042no—
593C22×C4C2×Dic2612yescomplemented
594C4⋊C4—2616no—
595C4⋊C4—268no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—134no—
604C22⋊C4—134no—
605C22⋊C4—262no—
606C22⋊C4—262no—
607C22⋊C4—262no—
608C22⋊C4—262no—
609C22⋊C4—262no—
610C22⋊C4—262no—
611C22⋊C4—262no—
612C22⋊C4—262no—
613C22⋊C4—262no—
614C22⋊C4—262no—
615C22⋊C4—521no—
616C22⋊C4—521no—
617C22⋊C4—521no—
618C22⋊C4—521no—
619C22⋊C4C2×C22⋊D1314yes—
620C13C2×#203211yescharacteristic, complemented, Sylow
621C23—22no—
622C23—22no—
623C23—22no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—82no—
636C23—82no—
637C23—82no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—81no—
645C23—81no—
646C23—82no—
647C23—82no—
648C23—82no—
649C23—82no—
650C23#8813211yescharacteristic
651C23#8813211yescharacteristic
652C23#8813211yescharacteristic
653C23#8813211yescharacteristic
654C23#8813211yescharacteristic
655C23#8813211yescharacteristic
656C23#8813211yescharacteristic
657C23#8813211yescharacteristic
658C23#8813911yescharacteristic
659C23#8813911yescharacteristic
660C23#8813911yescharacteristic
661C23#8813911yescharacteristic
662C23#8813911yescharacteristic
663C23#8813911yescharacteristic
664C23#8813911yescharacteristic
665C23#8813911yescharacteristic
666C23#8817811yescharacteristic
667C23#8817811yescharacteristic
668C23#8817811yescharacteristic
669C23#8817811yescharacteristic
670C23#8819011yescharacteristic
671C23#8819011yescharacteristic
672C23#8819011yescharacteristic
673C23#8819011yescharacteristic
674C23#8819111yescharacteristic
675C23#8819111yescharacteristic
676C23#8819111yescharacteristic
677C23#8819111yescharacteristic
678C23C22×Dic2611yescharacteristic
679C23C2×#612711yescharacteristic
680C23C2×D4×D1311yescharacteristic
681C23C2×D4×D1311yescharacteristic
682C23C2×#612911yescharacteristic
683C23C2×#612911yescharacteristic
684C23C22×C22⋊D1311yescharacteristic
685Q8—1048no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—264no—
710C2×C4—264no—
711C2×C4—524no—
712C2×C4—524no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—1042no—
716C2×C4—1042no—
717C2×C4—1042no—
718C2×C4—1042no—
719C2×C4—1042no—
720C2×C4—1042no—
721C2×C4—1042no—
722C2×C4—1042no—
723C2×C4—1042no—
724C2×C4—1042no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22#1171860811yescharacteristic
769C22#1171860811yescharacteristic
770C22#1171860811yescharacteristic
771C22#1171860811yescharacteristic
772C22#1171860811yescharacteristic
773C22#1171860811yescharacteristic
774C22#1171860811yescharacteristic
775C22#1171860811yescharacteristic
776C22C2×#8813211yescharacteristic
777C22C2×#8813211yescharacteristic
778C22C2×#8813911yescharacteristic
779C22C2×#8813911yescharacteristic
780C22C2×#8817811yescharacteristic
781C22C2×#8819011yescharacteristic
782C22C2×#8819111yescharacteristic
783C4—44no—
784C4—42no—
785C4—82no—
786C4—524no—
787C4—524no—
788C4—1042no—
789C4—1042no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—82no—
805C2#1311601312yesdirect product factor
806C2C2×#1171860811yescharacteristic
subgroupG/H
centerC22#11718608
commutator, cosocleC24×C13C24
FrattiniC24C23×D13
FittingC22×C13×#99C2
socleC22×C13#393
prime radicalC23×D4×C13C22
hypercenterC22×#99D13
hypocenterC13C2×#2032
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
1. C2×#11719188C2semidirect
4. #13116013C2direct (N × H)
5. C2×#11718118C2semidirect
6. C2×#11718119C2semidirect
7. C2×#11718119C2semidirect
20. #11719188C22semidirect
32. #11718119C22semidirect
33. #11718119C22semidirect
34. #11718118C22semidirect
35. C25×C13Q8semidirect
49. C22×D4×C13Q8semidirect
53. C23×C4×C13Q8semidirect
123. C24×C13C2×Q8semidirect
173. C22×C4×C13C2×Q8semidirect
421. C25Dic26semidirect
436. C22×D4Dic26semidirect
444. C23×C4Dic26semidirect
507. C2×C13#2032semidirect
519. C24C2×Dic26semidirect
593. C22×C4C2×Dic26semidirect
620. C13C2×#2032semidirect
805. C2#13116013direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191882
C22×#880742
#131160132
C2×#117181182
C2×#117181192
C22×C13×#992
C2×#203213