Finite Group Databasebeta

← #15769697

Subgroups — #15769697

Order 3328.

1338 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718897C211yesmaximal, characteristic, complemented
2C22×#88077C211yesmaximal, characteristic, complemented
3C2×#11718901C211yesmaximal, characteristic, complemented
4#13117327C211yesmaximal, characteristic, complemented
5C2×#11718151C211yesmaximal, characteristic, complemented
6C2×#11718147C211yesmaximal, characteristic, complemented
7C2×C13×#575C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C22×C13×#41C2211yescharacteristic
10C13×#575—22no—
11C13×#575—22no—
12C13×#575—22no—
13C13×#575—22no—
14C2×C13×#137—21no—
15C2×C13×#137C412yescomplemented
16C2×C13×AGL(1,ℤ/8)—21no—
17C2×C13×AGL(1,ℤ/8)C412yescomplemented
18C2×C13×#135—22no—
19C22×C13×M16C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24#11718901—22no—
25#11718901—22no—
26#11718897—22no—
27#11718897—22no—
28C2×#88077—22no—
29C2×#88077—22no—
30C2×#88077—22no—
31C2×#88077—22no—
32#11718891—21no—
33#11718882—21no—
34#11718881—22no—
35C2×#88074—22no—
36C4×C22⋊Dic13—22no—
37#11718151—22no—
38#11718147—22no—
39C2×C13×#41—21no—
40C2×C13×#41—21no—
41C2×C13×#41—21no—
42C2×C13×#41—21no—
43C2×C13×#41—21no—
44C2×C13×#41—21no—
45C2×C13×#41—21no—
46C2×C13×#41—21no—
47C2×C13×#41—21no—
48C2×C13×#41—21no—
49C2×C13×#41—21no—
50C2×C13×#41—21no—
51C2×C13×#41—21no—
52C2×C13×#41—21no—
53C2×C13×#41—21no—
54C2×C13×#41—21no—
55C2×C13×#41—21no—
56C2×C13×#41—21no—
57C2×C13×#41—21no—
58C2×C13×#41—21no—
59C2×C13×#41C2×C412yes—
60C2×C13×#41D412yes—
61C2×C13×#41D412yes—
62C2×C13×#41D412yes—
63C22×Q8×C13C2×C411yescharacteristic
64C22×Q8×C13D411yescharacteristic
65C22×D4×C13—21no—
66C22×D4×C13—21no—
67C22×D4×C13C2×C411yescharacteristic
68C22×D4×C13D411yescharacteristic
69C23×C4×C13—21no—
70C23×C4×C13—21no—
71C23×C4×C13C2311yescharacteristic
72C23×Dic13—21no—
73C13×#137—24no—
74C13×#137—24no—
75C13×#137—24no—
76C13×#137—24no—
77C13×AGL(1,ℤ/8)—24no—
78C13×AGL(1,ℤ/8)—24no—
79C13×AGL(1,ℤ/8)—24no—
80C13×AGL(1,ℤ/8)—24no—
81C13×#135—28no—
82C13×#135—28no—
83C2×C13×Q16—22no—
84C2×C13×SD16—22no—
85C2×C13×SD16—22no—
86C2×C13×D8—22no—
87C2×C13×M16—21no—
88C2×C13×M16—21no—
89C2×C13×M16—21no—
90C2×C13×M16C2×C412yes—
91C2×C13×M16D412yes—
92C2×C13×M16D412yes—
93C22×C8×C13—21no—
94C2×C22⋊Dic13—21no—
95C2×C22⋊Dic13—24no—
96C2×C22⋊Dic13D412yes—
97#88180—21no—
98#88180—21no—
99#88180—21no—
100#88180—21no—
101#88180—21no—
102#88180—21no—
103#88180—21no—
104#88180D412yes—
105C2×C4⋊Dic13—21no—
106C2×C4⋊Dic13—21no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—21no—
110C2×C4×Dic13—21no—
111C2×C4×Dic13—21no—
112C2×C4×Dic13—21no—
113C2×C4×Dic13—21no—
114C2×C4×Dic13D412yes—
115C2×#6099—21no—
116C2×#6099—21no—
117C2×#6099—21no—
118C2×#6099—21no—
119C2×#6099—21no—
120C2×#6099D412yes—
121C22×#1055—21no—
122#88077—28no—
123#88077—28no—
124#88074—28no—
125#88071—24no—
126#11019—131nomaximal, Sylow
127C24×C13—21no—
128C24×C13—21no—
129C24×C13C2×D411yescharacteristic
130C13×#41—22no—
131C13×#41—22no—
132C13×#41—22no—
133C13×#41—22no—
134C13×#41—22no—
135C13×#41—22no—
136C13×#41—22no—
137C13×#41—22no—
138C13×#41—22no—
139C13×#41—22no—
140C13×#41—22no—
141C13×#41—22no—
142C13×#41—22no—
143C13×#41—22no—
144C13×#41—22no—
145C13×#41—22no—
146C13×#41—41no—
147C13×#41—41no—
148C13×#41—41no—
149C13×#41—41no—
150C13×#41—41no—
151C13×#41—41no—
152C13×#41—41no—
153C13×#41—41no—
154C13×#41—41no—
155C13×#41—41no—
156C13×#41—41no—
157C13×#41—41no—
158C13×#41—41no—
159C13×#41—41no—
160C13×#41—41no—
161C13×#41—41no—
162C2×Q8×C13—21no—
163C2×Q8×C13—21no—
164C2×Q8×C13—21no—
165C2×Q8×C13—21no—
166C2×Q8×C13—21no—
167C2×Q8×C13—21no—
168C2×Q8×C13—21no—
169C2×Q8×C13—21no—
170C2×Q8×C13—21no—
171C2×Q8×C13—21no—
172C2×Q8×C13C22⋊C412yes—
173C2×Q8×C13C22⋊C412yescomplemented
174C2×D4×C13—22no—
175C2×D4×C13—22no—
176C2×D4×C13—22no—
177C2×D4×C13—22no—
178C2×D4×C13—21no—
179C2×D4×C13—21no—
180C2×D4×C13—21no—
181C2×D4×C13—21no—
182C2×D4×C13—21no—
183C2×D4×C13—21no—
184C2×D4×C13—21no—
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—41no—
189C2×D4×C13—41no—
190C2×D4×C13—41no—
191C2×D4×C13—41no—
192C2×D4×C13—41no—
193C2×D4×C13—41no—
194C2×D4×C13—41no—
195C2×D4×C13—41no—
196C2×D4×C13C22⋊C412yes—
197C2×D4×C13C22⋊C412yescomplemented
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—22no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—41no—
205C22×C4×C13—41no—
206C22×C4×C13—41no—
207C22×C4×C13—41no—
208C22×C4×C13—41no—
209C22×C4×C13—41no—
210C22×C4×C13—41no—
211C22×C4×C13—41no—
212C22×C4×C13C22×C411yescharacteristic
213C22×C4×C13C2×D411yescharacteristic
214C22×C4×C13C2×D411yescharacteristic
215C22×C4×C13C2×D411yescharacteristic
216C22×C4×C13C2×D411yescharacteristic
217C22×C4×C13C2×D411yescharacteristic
218C22×C4×C13C2×D411yescharacteristic
219C22×C4×C13C2×D411yescharacteristic
220C22×C4×C13C2×D411yescharacteristic
221C22×C4×C13C2×D411yescharacteristic
222C22×C4×C13#4111yescharacteristic
223C22×C4×C13#4111yescharacteristic
224C22×C4×C13#4111yescharacteristic
225C22×C4×C13#4111yescharacteristic
226C22×Dic13—22no—
227C22×Dic13—22no—
228C22×Dic13—44no—
229C22×Dic13—41no—
230C22×Dic13—41no—
231C22×Dic13—41no—
232C13×Q16—28no—
233C13×SD16—28no—
234C13×SD16—28no—
235C13×D8—28no—
236C13×M16—22no—
237C13×M16—22no—
238C13×M16—22no—
239C13×M16C22⋊C414yescomplemented
240C2×C8×C13—22no—
241C2×C8×C13—22no—
242C2×C8×C13—22no—
243C22⋊Dic13—22no—
244C22⋊Dic13—22no—
245C22⋊Dic13—22no—
246C22⋊Dic13—48no—
247C22⋊Dic13—41no—
248C4⋊Dic13—22no—
249C4⋊Dic13—41no—
250C4⋊Dic13—41no—
251C4⋊Dic13—41no—
252C4×Dic13—22no—
253C4×Dic13—22no—
254C4×Dic13—22no—
255C4×Dic13—41no—
256C4×Dic13—41no—
257C4×Dic13—41no—
258C4×Dic13—41no—
259C4×Dic13—41no—
260#6099—22no—
261#6099—22no—
262#6099—41no—
263#6099—41no—
264C2×#1055—22no—
265C2×#1055—41no—
266C2×#1055—41no—
267C2×#575D1311yescharacteristic
268C2×#421—131no—
269C22×#104—131no—
270C2×#410—131no—
271#2297—131no—
272C2×#344—131no—
273C2×#339—131no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—42no—
277C23×C13—44no—
278C23×C13—41no—
279C23×C13—41no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—82no—
283C23×C13C4×D411yescharacteristic
284C23×C13#12011yescharacteristic
285C23×C13#12011yescharacteristic
286C23×C13#12111yescharacteristic
287C23×C13#12111yescharacteristic
288C23×C13#12111yescharacteristic
289C23×C13#12711yescharacteristic
290Q8×C13—22no—
291Q8×C13—22no—
292Q8×C13—22no—
293Q8×C13—22no—
294Q8×C13—41no—
295Q8×C13—41no—
296Q8×C13—41no—
297Q8×C13—41no—
298D4×C13—22no—
299D4×C13—22no—
300D4×C13—22no—
301D4×C13—22no—
302D4×C13—42no—
303D4×C13—42no—
304D4×C13—42no—
305D4×C13—42no—
306D4×C13—42no—
307D4×C13—42no—
308D4×C13—42no—
309D4×C13—42no—
310D4×C13—41no—
311D4×C13—41no—
312D4×C13—41no—
313D4×C13—41no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13C2×C22⋊C411yescharacteristic
329C2×C4×C13C2×C22⋊C411yescharacteristic
330C2×C4×C13C2×C22⋊C411yescharacteristic
331C2×C4×C13C4×D411yescharacteristic
332C2×C4×C13C4×D411yescharacteristic
333C2×C4×C13C4×D411yescharacteristic
334C2×C4×C13#12011yescharacteristic
335C2×C4×C13#12011yescharacteristic
336C2×C4×C13#12011yescharacteristic
337C2×C4×C13#12011yescharacteristic
338C2×C4×C13#12011yescharacteristic
339C2×C4×C13#12011yescharacteristic
340C2×C4×C13#12111yescharacteristic
341C2×C4×C13#12111yescharacteristic
342C2×C4×C13#12111yescharacteristic
343C2×C4×C13#12111yescharacteristic
344C2×C4×C13#12111yescharacteristic
345C2×C4×C13#12111yescharacteristic
346C2×C4×C13#12111yescharacteristic
347C2×C4×C13#12111yescharacteristic
348C2×C4×C13#12111yescharacteristic
349C2×C4×C13#12311yescharacteristic
350C2×C4×C13#12311yescharacteristic
351C2×C4×C13#12311yescharacteristic
352C2×C4×C13#12311yescharacteristic
353C2×C4×C13#12411yescharacteristic
354C2×C4×C13#12411yescharacteristic
355C2×C4×C13#12711yescharacteristic
356C2×Dic13—24no—
357C2×Dic13—42no—
358C2×Dic13—44no—
359C2×Dic13—44no—
360C2×Dic13—42no—
361C2×Dic13—44no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—82no—
365C8×C13—24no—
366#1055—42no—
367C22×#41C2×D1311yescharacteristic
368C22×#41C2×D1311yescharacteristic
369#575—22no—
370#575—22no—
371#575—22no—
372#575—22no—
373C2×#137—21no—
374C2×#137Dic1312yescomplemented
375C2×AGL(1,ℤ/8)—21no—
376C2×AGL(1,ℤ/8)Dic1312yescomplemented
377C2×#135—22no—
378C22×M16—131no—
379C22×M16C2×D1311yescharacteristic
380C2×#117—131no—
381C2×#117—131no—
382C22×C42—131no—
383#421—262no—
384#421—262no—
385C2×#104—262no—
386C2×#104—262no—
387C2×#104—262no—
388C2×#104—262no—
389#410—262no—
390#410—262no—
391C2×#99—262no—
392#391—261no—
393#390—261no—
394#386—262no—
395C4×C22⋊C4—262no—
396#344—262no—
397#339—262no—
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—44no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—82no—
409C22×C13—82no—
410C22×C13—82no—
411C22×C13—82no—
412C22×C13—82no—
413C22×C13#38611yescharacteristic
414C22×C13#38611yescharacteristic
415C22×C13#39011yescharacteristic
416C22×C13#39211yescharacteristic
417C22×C13#39211yescharacteristic
418C22×C13#39211yescharacteristic
419C22×C13#39411yescharacteristic
420C4×C13—42no—
421C4×C13—42no—
422C4×C13#37911yescharacteristic
423C4×C13#38611yescharacteristic
424C4×C13#38611yescharacteristic
425C4×C13#39011yescharacteristic
426C4×C13#39211yescharacteristic
427C4×C13#39411yescharacteristic
428C4×C13#39411yescharacteristic
429C4×C13#39411yescharacteristic
430Dic13—44no—
431Dic13—82no—
432Dic13—82no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41C2×Dic1312yes—
454C2×#41C22⋊D1312yes—
455C2×#41C22⋊D1312yes—
456C2×#41C22⋊D1312yes—
457C22×Q8C2×Dic1311yescharacteristic
458C22×Q8C22⋊D1311yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C2×Dic1311yescharacteristic
462C22×D4C22⋊D1311yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—261no—
466C23×C4C22×D1311yescharacteristic
467#137—24no—
468#137—24no—
469#137—24no—
470#137—24no—
471AGL(1,ℤ/8)—24no—
472AGL(1,ℤ/8)—24no—
473AGL(1,ℤ/8)—24no—
474AGL(1,ℤ/8)—24no—
475#135—28no—
476#135—28no—
477C2×Q16—22no—
478C2×SD16—22no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—132no—
485C2×M16—261no—
486C2×M16—261no—
487C2×M16—261no—
488C2×M16—261no—
489C2×M16—261no—
490C2×M16C2×Dic1312yes—
491C2×M16C22⋊D1312yes—
492C2×M16C22⋊D1312yes—
493C22×C8—21no—
494C22×C8—261no—
495#117—132no—
496#117—261no—
497#117—261no—
498#117—261no—
499#117—261no—
500#117—261no—
501#117—261no—
502#117—261no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C22⋊C4—132no—
506C2×C22⋊C4—261no—
507C2×C22⋊C4—264no—
508C2×C42—132no—
509C2×C42—261no—
510C2×C42—261no—
511C2×C42—261no—
512C2×C42—261no—
513C2×C42—261no—
514C2×C42—261no—
515C2×C42—261no—
516#104—268no—
517#104—268no—
518#99—268no—
519#95—264no—
520C2×C13—21no—
521C2×C13—21no—
522C2×C13—21no—
523C2×C13—21no—
524C2×C13—21no—
525C2×C13—21no—
526C2×C13—82no—
527C2×C13—82no—
528C2×C13#143811yescharacteristic
529C2×C13#190612yes—
530C24—21no—
531C24—21no—
532C24D4×D1311yescharacteristic
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8C22⋊Dic1312yes—
576C2×Q8C22⋊Dic1312yescomplemented
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4C22⋊Dic1312yes—
600C2×D4C22⋊Dic1312yescomplemented
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—524no—
618C22×C4—521no—
619C22×C4—521no—
620C22×C4—521no—
621C22×C4D4×D1311yescharacteristic
622C22×C4D4×D1311yescharacteristic
623C22×C4D4×D1311yescharacteristic
624C22×C4#612911yescharacteristic
625C22×C4#612911yescharacteristic
626C22×C4#612911yescharacteristic
627C22×C4#612911yescharacteristic
628C22×C4C22×Dic1311yescharacteristic
629C22×C4C2×C22⋊D1311yescharacteristic
630C22×C4C2×C22⋊D1311yescharacteristic
631C22×C4C2×C22⋊D1311yescharacteristic
632C22×C4C2×C22⋊D1311yescharacteristic
633C22×C4C2×C22⋊D1311yescharacteristic
634C22×C4C2×C22⋊D1311yescharacteristic
635Q16—28no—
636SD16—28no—
637SD16—28no—
638D8—28no—
639M16—22no—
640M16—22no—
641M16—22no—
642M16—262no—
643M16—262no—
644M16—521no—
645M16—521no—
646M16C22⋊Dic1314yescomplemented
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—262no—
651C2×C8—521no—
652C2×C8—521no—
653C4⋊C4—262no—
654C4⋊C4—521no—
655C4⋊C4—521no—
656C4⋊C4—521no—
657C22⋊C4—262no—
658C22⋊C4—262no—
659C22⋊C4—262no—
660C22⋊C4—528no—
661C22⋊C4—521no—
662C42—262no—
663C42—262no—
664C42—262no—
665C42—521no—
666C42—521no—
667C42—521no—
668C42—521no—
669C42—521no—
670C13#1101911yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—42no—
674C23—44no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—82no—
680C23D4×Dic1311yescharacteristic
681C23#8819111yescharacteristic
682C23#8819111yescharacteristic
683C23#8819211yescharacteristic
684C23#8819311yescharacteristic
685C23#8819311yescharacteristic
686C23#8819411yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—264no—
726C2×C4—522no—
727C2×C4—524no—
728C2×C4—524no—
729C2×C4—522no—
730C2×C4—524no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—1042no—
734C2×C4D4×Dic1311yescharacteristic
735C2×C4D4×Dic1311yescharacteristic
736C2×C4D4×Dic1311yescharacteristic
737C2×C4#8818911yescharacteristic
738C2×C4#8818911yescharacteristic
739C2×C4#8818911yescharacteristic
740C2×C4#8818911yescharacteristic
741C2×C4#8819011yescharacteristic
742C2×C4#8819011yescharacteristic
743C2×C4#8819111yescharacteristic
744C2×C4#8819111yescharacteristic
745C2×C4#8819211yescharacteristic
746C2×C4#8819211yescharacteristic
747C2×C4#8819211yescharacteristic
748C2×C4#8819311yescharacteristic
749C2×C4#8819311yescharacteristic
750C2×C4#8819311yescharacteristic
751C2×C4#8819311yescharacteristic
752C2×C4#8819311yescharacteristic
753C2×C4#8819311yescharacteristic
754C2×C4#8819411yescharacteristic
755C2×C4C2×C22⋊Dic1311yescharacteristic
756C2×C4C2×C22⋊Dic1311yescharacteristic
757C2×C4C2×C22⋊Dic1311yescharacteristic
758C2×C4#8820711yescharacteristic
759C2×C4#8820711yescharacteristic
760C2×C4#8820711yescharacteristic
761C2×C4#8820711yescharacteristic
762C8—24no—
763C8—522no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—44no—
772C22—42no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22#1171888111yescharacteristic
780C22#1171888111yescharacteristic
781C22#1171888211yescharacteristic
782C22#1171888311yescharacteristic
783C22#1171888411yescharacteristic
784C22#1171888411yescharacteristic
785C22#1171888411yescharacteristic
786C4—42no—
787C4—42no—
788C4—524no—
789C4—1042no—
790C4—1042no—
791C4#1171888111yescharacteristic
792C4#1171888111yescharacteristic
793C4#1171888211yescharacteristic
794C4#1171888311yescharacteristic
795C4#1171888311yescharacteristic
796C4#1171888311yescharacteristic
797C4#1171888411yescharacteristic
798C4#1171890811yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—82no—
806C2—82no—
807C2#1311307711yescharacteristic
808C2#1311533912yes—
subgroupG/H
centerC2×C4#88193
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC2×C13×#575C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenterC2×#575D13
hypocenterC13#11019
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#11718897C2semidirect
2. C22×#88077C2semidirect
3. C2×#11718901C2semidirect
4. #13117327C2semidirect
5. C2×#11718151C2semidirect
6. C2×#11718147C2semidirect
15. C2×C13×#137C4semidirect
17. C2×C13×AGL(1,ℤ/8)C4semidirect
173. C2×Q8×C13C22⋊C4semidirect
197. C2×D4×C13C22⋊C4semidirect
239. C13×M16C22⋊C4semidirect
374. C2×#137Dic13semidirect
376. C2×AGL(1,ℤ/8)Dic13semidirect
576. C2×Q8C22⋊Dic13semidirect
600. C2×D4C22⋊Dic13semidirect
646. M16C22⋊Dic13semidirect
670. C13#11019semidirect

Maximal subgroups

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

subgroupindex
C2×#117188972
C22×#880772
C2×#117189012
#131173272
C2×#117181512
C2×#117181472
C2×C13×#5752
#1101913