Finite Group Databasebeta

← #15866898

Subgroups — #15866898

Order 3328.

1460 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719527C211yesmaximal, characteristic
2#13123425C211yesmaximal, characteristic, complemented
3C2×#11718800C211yesmaximal, characteristic, complemented
4C2×#11718901C211yesmaximal, characteristic, complemented
5C2×#11718667C211yesmaximal, characteristic, complemented
6#13123254C211yesmaximal, characteristic, complemented
7#13115733C218yesmaximal, complemented
8C2×C13×#421C211yesmaximal, characteristic, complemented
9C22×C13×#41C2211yescharacteristic
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×C13×#117C2211yescharacteristic
13C2×#88205C412yescomplemented
14#11719527—22no—
15#11719527—22no—
16#11719527—22no—
17#11719527—22no—
18C2×#88204C2214yes—
19C2×#88203C412yescomplemented
20C2×#88196C412yescomplemented
21C2×#88186C412yescomplemented
22C2×#88180C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C13×#421—22no—
26C13×#421C2214yescomplemented
27C2×C13×#104—22no—
28#11718901—22no—
29#11718901C2214yescomplemented
30C2×#88074—22no—
31#11718800—22no—
32#11718800C2214yescomplemented
33C2×#88065—22no—
34#11718783C2214yescomplemented
35M16×Dic13—22no—
36#11718762—22no—
37#11718667—22no—
38#11718667C2214yescomplemented
39#11718659C2214yescomplemented
40#11718656—22no—
41#11718625—22no—
42C2×#88046—22no—
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×#41C2×C412yes—
54C2×C13×#41C2312yes—
55C22×Q8×C13C2×C411yescharacteristic
56C22×D4×C13—21no—
57C22×D4×C13C2×C411yescharacteristic
58C23×C4×C13—21no—
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C2×#6127—21no—
62C2×#6127—21no—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—21no—
66C2×#6127—21no—
67C2×#6127—21no—
68C2×#6127—21no—
69C2×#6127—21no—
70C2×#6127—21no—
71C2×#6127C2×C412yes—
72C2×#6127C2312yes—
73C22×D52C2×C411yescharacteristic
74C22×C4×D13—21no—
75C22×Dic26C2×C411yescharacteristic
76C2×C13×M16—21no—
77C2×C13×M16—21no—
78C2×C13×M16—21no—
79C2×C13×M16D412yes—
80C2×C13×M16D412yes—
81C2×C13×M16C2312yes—
82C22×C8×C13—21no—
83C13×#117—21no—
84C13×#117—21no—
85C13×#117—21no—
86C13×#117C2312yes—
87C2×C13×C4⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C42×C13—21no—
90C2×C22⋊Dic13—21no—
91C2×C22⋊Dic13D412yes—
92#88205—24no—
93#88205—24no—
94#88204—28no—
95#88204—28no—
96#88203—24no—
97#88203—24no—
98C2×#6107C2×C414yescomplemented
99#88196—24no—
100#88196—24no—
101C2×#6106C2×C414yescomplemented
102C2×#6105C2×C414yescomplemented
103#88186—24no—
104#88186—24no—
105C2×#6104C2×C414yescomplemented
106#88180—21no—
107#88180—21no—
108#88180—21no—
109#88180—21no—
110#88180—21no—
111#88180D412yes—
112#88180C2312yes—
113#88180C2312yes—
114C2×C4⋊Dic13—21no—
115C2×C4⋊Dic13—21no—
116C2×C4×Dic13—21no—
117C2×C4×Dic13—21no—
118C2×#6099C2×C412yes—
119C2×#6099C2×C412yes—
120C2×#6099D412yes—
121C2×#6099D412yes—
122C2×#6099D412yes—
123C2×#6099D412yes—
124C22×#1055C2312yes—
125C13×#104—28no—
126#88074—28no—
127#88065—28no—
128#88055—24no—
129C8×Dic13—24no—
130#88048—24no—
131#88047—24no—
132#88046—28no—
133#21244—131nomaximal, Sylow
134C24×C13—21no—
135C24×C13C2×D411yescharacteristic
136C23×D13—21no—
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—41no—
146C13×#41—41no—
147C13×#41—41no—
148C13×#41—41no—
149C13×#41—41no—
150C13×#41—41no—
151C13×#41—41no—
152C13×#41—41no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—21no—
158C2×Q8×C13C22×C412yes—
159C2×D4×C13—22no—
160C2×D4×C13—22no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—21no—
166C2×D4×C13—41no—
167C2×D4×C13—41no—
168C2×D4×C13—41no—
169C2×D4×C13—41no—
170C2×D4×C13C22×C412yes—
171C22×C4×C13—21no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—41no—
175C22×C4×C13—41no—
176C22×C4×C13—41no—
177C22×C4×C13—41no—
178C22×C4×C13—41no—
179C22×C4×C13C22×C411yescharacteristic
180C22×C4×C13C22×C411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13#4111yescharacteristic
189C22×C4×C13#4111yescharacteristic
190C22×C4×C13#4111yescharacteristic
191C22×C4×C13#4111yescharacteristic
192C22×C4×C13C2411yescharacteristic
193C2×C22⋊D13—22no—
194C2×C22⋊D13—22no—
195C2×C22⋊D13—41no—
196C2×C22⋊D13—41no—
197C2×C22⋊D13—41no—
198C2×C22⋊D13—41no—
199C22×Dic13—21no—
200C22×Dic13—22no—
201C22×Dic13—41no—
202#6127—22no—
203#6127—22no—
204#6127—22no—
205#6127—22no—
206#6127—22no—
207#6127—22no—
208#6127—22no—
209#6127—22no—
210#6127—41no—
211#6127—41no—
212#6127—41no—
213#6127—41no—
214#6127—41no—
215#6127—41no—
216#6127—41no—
217#6127—41no—
218C2×D52—21no—
219C2×D52—21no—
220C2×D52—21no—
221C2×D52—21no—
222C2×D52—21no—
223C2×D52C22×C412yes—
224C2×C4×D13—22no—
225C2×C4×D13—22no—
226C2×C4×D13—41no—
227C2×C4×D13—41no—
228C2×C4×D13—41no—
229C2×C4×D13—41no—
230C2×Dic26—21no—
231C2×Dic26—21no—
232C2×Dic26—21no—
233C2×Dic26—21no—
234C2×Dic26—21no—
235C2×Dic26C22×C412yes—
236C13×M16—22no—
237C13×M16—22no—
238C13×M16—22no—
239C13×M16C2×D414yes—
240C2×C8×C13—22no—
241C2×C8×C13—22no—
242C2×C8×C13—22no—
243C13×C4⋊C4—22no—
244C13×C4⋊C4—41no—
245C13×C22⋊C4—22no—
246C13×C22⋊C4—41no—
247C42×C13—22no—
248C42×C13—41no—
249C22⋊Dic13—22no—
250C22⋊Dic13—22no—
251C22⋊Dic13—41no—
252C22⋊Dic13C2×D414yes—
253#6107—28no—
254#6106—28no—
255#6105—28no—
256#6104—28no—
257C4⋊Dic13—22no—
258C4⋊Dic13—22no—
259C4⋊Dic13—22no—
260C4⋊Dic13—41no—
261C4×Dic13—22no—
262C4×Dic13—22no—
263C4×Dic13—22no—
264C4×Dic13—41no—
265#6099C22⋊C414yes—
266#6099C22⋊C414yes—
267#6099C22⋊C414yes—
268#6099C22⋊C414yes—
269C2×#1055C22×C414yes—
270C2×#1055C2×D414yes—
271C2×#1055C2×D414yes—
272C2×#575—131no—
273#2911—131no—
274C2×#421—131no—
275C2×#421D1311yescharacteristic, complemented
276C2×#410—131no—
277C2×#410—131no—
278#2873—131no—
279#1976—138no—
280C23×C13—22no—
281C23×C13—41no—
282C23×C13—41no—
283C23×C13—81no—
284C23×C13—82no—
285C23×C13C4×D411yescharacteristic
286C23×C13C4×D411yescharacteristic
287C23×C13#12111yescharacteristic
288C23×C13#12111yescharacteristic
289C23×C13#12711yescharacteristic
290C23×C13#12711yescharacteristic
291C23×C13C22×D411yescharacteristic
292C22×D13—22no—
293C22×D13—41no—
294C22×D13—41no—
295C22×D13—82no—
296Q8×C13—22no—
297Q8×C13—22no—
298Q8×C13—41no—
299Q8×C13—41no—
300D4×C13—22no—
301D4×C13—22no—
302D4×C13—42no—
303D4×C13—42no—
304D4×C13—42no—
305D4×C13—42no—
306D4×C13—41no—
307D4×C13—41no—
308C2×C4×C13—22no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—82no—
317C2×C4×C13C2×C22⋊C411yescharacteristic
318C2×C4×C13C2×C22⋊C411yescharacteristic
319C2×C4×C13C2×C22⋊C411yescharacteristic
320C2×C4×C13C2×C22⋊C411yescharacteristic
321C2×C4×C13C4×D411yescharacteristic
322C2×C4×C13C4×D411yescharacteristic
323C2×C4×C13C4×D411yescharacteristic
324C2×C4×C13C4×D411yescharacteristic
325C2×C4×C13C4×D411yescharacteristic
326C2×C4×C13C4×D411yescharacteristic
327C2×C4×C13#12111yescharacteristic
328C2×C4×C13#12111yescharacteristic
329C2×C4×C13#12111yescharacteristic
330C2×C4×C13#12111yescharacteristic
331C2×C4×C13#12111yescharacteristic
332C2×C4×C13#12111yescharacteristic
333C2×C4×C13#12411yescharacteristic
334C2×C4×C13#12411yescharacteristic
335C2×C4×C13#12411yescharacteristic
336C2×C4×C13#12411yescharacteristic
337C2×C4×C13#12711yescharacteristic
338C2×C4×C13#12711yescharacteristic
339C2×C4×C13C23×C411yescharacteristic
340C2×C4×C13C22×D411yescharacteristic
341C2×C4×C13C22×D411yescharacteristic
342C2×C4×C13C22×D411yescharacteristic
343C2×C4×C13C2×#4111yescharacteristic
344C2×C4×C13C2×#4111yescharacteristic
345C22⋊D13—42no—
346C22⋊D13—42no—
347C22⋊D13—42no—
348C22⋊D13—42no—
349C2×Dic13—22no—
350C2×Dic13—24no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—42no—
354C2×Dic13—82no—
355C2×Dic13—82no—
356D52—22no—
357D52—22no—
358D52—41no—
359D52—41no—
360C4×D13—42no—
361C4×D13—42no—
362C4×D13—42no—
363C4×D13—42no—
364Dic26—22no—
365Dic26—22no—
366Dic26—41no—
367Dic26—41no—
368C8×C13—24no—
369#1055C2×C22⋊C418yes—
370C22×#41—131no—
371C22×#41C2×D1311yescharacteristic
372#575—262no—
373#575—262no—
374#575—262no—
375#575—262no—
376C2×#137—132no—
377C2×#137—132no—
378C2×AGL(1,ℤ/8)—132no—
379C2×AGL(1,ℤ/8)—132no—
380C2×#135—134no—
381C22×M16—131no—
382C22×M16C2×D1311yescharacteristic
383C2×#117—131no—
384C2×#117—131no—
385C2×#117C2×D1311yescharacteristic
386#428—262no—
387#428—262no—
388#427—134no—
389#421—22no—
390#421—134no—
391#421—262no—
392#421C2×D1314yescomplemented
393C2×#104—22no—
394C2×#104—262no—
395#410—134no—
396#410—134no—
397#410—262no—
398#410—262no—
399C2×#99—262no—
400C2×#99—262no—
401#405—134no—
402#405—262no—
403C4×M16—262no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—41no—
410C22×C13—41no—
411C22×C13—42no—
412C22×C13—82no—
413C22×C13—82no—
414C22×C13—82no—
415C22×C13#39011yescharacteristic
416C22×C13#39011yescharacteristic
417C22×C13#39011yescharacteristic
418C22×C13#39011yescharacteristic
419C22×C13C2×C4×D411yescharacteristic
420C22×C13C2×#12111yescharacteristic
421C22×C13C2×#12711yescharacteristic
422C2×D13—42no—
423C2×D13—82no—
424C2×D13—82no—
425C2×D13—82no—
426C4×C13—42no—
427C4×C13—82no—
428C4×C13#39011yescharacteristic
429C4×C13#39011yescharacteristic
430C4×C13#39011yescharacteristic
431C4×C13#39011yescharacteristic
432C4×C13C22×C22⋊C411yescharacteristic
433C4×C13C2×C4×D411yescharacteristic
434C4×C13C2×#12111yescharacteristic
435C4×C13C2×#12411yescharacteristic
436Dic13—44no—
437Dic13—42no—
438Dic13—82no—
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—132no—
450C2×#41—132no—
451C2×#41—261no—
452C2×#41—261no—
453C2×#41—261no—
454C2×#41—261no—
455C2×#41—261no—
456C2×#41—261no—
457C2×#41—261no—
458C2×#41—261no—
459C2×#41—261no—
460C2×#41—261no—
461C2×#41C4×D1312yes—
462C2×#41C22×D1312yes—
463C22×Q8—131no—
464C22×Q8C4×D1311yescharacteristic
465C22×D4—21no—
466C22×D4—131no—
467C22×D4—261no—
468C22×D4C4×D1311yescharacteristic
469C23×C4—21no—
470C23×C4—261no—
471C23×C4C22×D1311yescharacteristic
472#137—264no—
473#137—264no—
474#137—264no—
475#137—264no—
476AGL(1,ℤ/8)—264no—
477AGL(1,ℤ/8)—264no—
478AGL(1,ℤ/8)—264no—
479AGL(1,ℤ/8)—264no—
480#135—268no—
481#135—268no—
482C2×Q16—134no—
483C2×SD16—134no—
484C2×SD16—134no—
485C2×D8—134no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—132no—
490C2×M16—132no—
491C2×M16—132no—
492C2×M16—132no—
493C2×M16—132no—
494C2×M16—132no—
495C2×M16C22⋊D1312yes—
496C2×M16C22⋊D1312yes—
497C2×M16C22×D1312yes—
498C22×C8—21no—
499C22×C8—132no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117—132no—
504#117—132no—
505#117—132no—
506#117—261no—
507#117—261no—
508#117—261no—
509#117—261no—
510#117—261no—
511#117C22×D1312yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—261no—
514C2×C4⋊C4—261no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—132no—
517C2×C22⋊C4—261no—
518C2×C42—21no—
519C2×C42—261no—
520C2×C42—261no—
521#107—264no—
522#106—264no—
523#104—28no—
524#104—268no—
525#99—268no—
526#99—268no—
527#97—264no—
528C4×C8—264no—
529C2×C13—21no—
530C2×C13—21no—
531C2×C13—21no—
532C2×C13—21no—
533C2×C13—21no—
534C2×C13—21no—
535C2×C13—21no—
536C2×C13—82no—
537C2×C13C2×#39011yescharacteristic
538D13—82no—
539C24—21no—
540C24—261no—
541C24D4×D1311yescharacteristic
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
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—262no—
559#41—262no—
560#41—262no—
561#41—262no—
562#41—262no—
563#41—262no—
564#41—262no—
565#41—262no—
566#41—521no—
567#41—521no—
568#41—521no—
569#41—521no—
570#41—521no—
571#41—521no—
572#41—521no—
573#41—521no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—132no—
580C2×Q8—261no—
581C2×Q8—261no—
582C2×Q8—261no—
583C2×Q8—261no—
584C2×Q8—261no—
585C2×Q8C2×C4×D1312yes—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—132no—
598C2×D4—262no—
599C2×D4—262no—
600C2×D4—261no—
601C2×D4—261no—
602C2×D4—261no—
603C2×D4—261no—
604C2×D4—261no—
605C2×D4—521no—
606C2×D4—521no—
607C2×D4—521no—
608C2×D4—521no—
609C2×D4C2×C4×D1312yes—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—261no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—521no—
623C22×C4—521no—
624C22×C4—521no—
625C22×C4—521no—
626C22×C4—521no—
627C22×C4C2×C4×D1311yescharacteristic
628C22×C4C2×C4×D1311yescharacteristic
629C22×C4#612711yescharacteristic
630C22×C4#612711yescharacteristic
631C22×C4D4×D1311yescharacteristic
632C22×C4D4×D1311yescharacteristic
633C22×C4D4×D1311yescharacteristic
634C22×C4D4×D1311yescharacteristic
635C22×C4D4×D1311yescharacteristic
636C22×C4#612911yescharacteristic
637C22×C4#612911yescharacteristic
638C22×C4C2×C22⋊D1311yescharacteristic
639C22×C4C2×C22⋊D1311yescharacteristic
640C22×C4C23×D1311yescharacteristic
641Q16—268no—
642SD16—268no—
643SD16—268no—
644D8—268no—
645M16—22no—
646M16—22no—
647M16—22no—
648M16—134no—
649M16—134no—
650M16—134no—
651M16—134no—
652M16C2×C22⋊D1314yes—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—134no—
657C2×C8—134no—
658C2×C8—134no—
659C4⋊C4—22no—
660C4⋊C4—41no—
661C4⋊C4—262no—
662C4⋊C4—262no—
663C4⋊C4—262no—
664C4⋊C4—521no—
665C22⋊C4—22no—
666C22⋊C4—41no—
667C22⋊C4—134no—
668C22⋊C4—262no—
669C22⋊C4—262no—
670C22⋊C4—521no—
671C42—22no—
672C42—41no—
673C42—262no—
674C42—262no—
675C42—262no—
676C42—521no—
677C13#2124411yescharacteristic, complemented, Sylow
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—82no—
683C23—262no—
684C23—521no—
685C23—521no—
686C23—1042no—
687C23#8813511yescharacteristic
688C23#8813511yescharacteristic
689C23#8813811yescharacteristic
690C23#8813811yescharacteristic
691C23#8819411yescharacteristic
692C23#8819411yescharacteristic
693C23C2×D4×D1311yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—41no—
697Q8—41no—
698Q8—262no—
699Q8—262no—
700Q8—521no—
701Q8—521no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4—262no—
711D4—262no—
712D4—522no—
713D4—522no—
714D4—522no—
715D4—522no—
716D4—521no—
717D4—521no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—82no—
727C2×C4—262no—
728C2×C4—264no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—1042no—
737C2×C4—1042no—
738C2×C4C22⋊C4×D1311yescharacteristic
739C2×C4C22⋊C4×D1311yescharacteristic
740C2×C4C22⋊C4×D1311yescharacteristic
741C2×C4C22⋊C4×D1311yescharacteristic
742C2×C4#8813511yescharacteristic
743C2×C4#8813511yescharacteristic
744C2×C4#8813811yescharacteristic
745C2×C4#8813811yescharacteristic
746C2×C4#8813911yescharacteristic
747C2×C4#8813911yescharacteristic
748C2×C4#8813911yescharacteristic
749C2×C4#8813911yescharacteristic
750C2×C4C4×C22⋊D1311yescharacteristic
751C2×C4C4×C22⋊D1311yescharacteristic
752C2×C4C4×C22⋊D1311yescharacteristic
753C2×C4C4×C22⋊D1311yescharacteristic
754C2×C4#8819311yescharacteristic
755C2×C4#8819311yescharacteristic
756C2×C4#8819311yescharacteristic
757C2×C4#8819311yescharacteristic
758C2×C4#8819411yescharacteristic
759C2×C4#8819411yescharacteristic
760C2×C4C22×C4×D1311yescharacteristic
761C2×C4C2×#612711yescharacteristic
762C2×C4C2×D4×D1311yescharacteristic
763C2×C4C2×D4×D1311yescharacteristic
764C2×C4C2×#612911yescharacteristic
765C2×C4C22×C22⋊D1311yescharacteristic
766C8—24no—
767C8—138no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—522no—
780C22—1042no—
781C22—1042no—
782C22—1042no—
783C22#1171861811yescharacteristic
784C22#1171861811yescharacteristic
785C22#1171861811yescharacteristic
786C22#1171861811yescharacteristic
787C22C2×#8813511yescharacteristic
788C22C2×#8813811yescharacteristic
789C22C2×#8819411yescharacteristic
790C4—42no—
791C4—82no—
792C4—524no—
793C4—522no—
794C4—1042no—
795C4#1171861811yescharacteristic
796C4#1171861811yescharacteristic
797C4#1171861811yescharacteristic
798C4#1171861811yescharacteristic
799C4C2×C22⋊C4×D1311yescharacteristic
800C4C2×#8813911yescharacteristic
801C4C2×C4×C22⋊D1311yescharacteristic
802C4C2×#8819311yescharacteristic
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—82no—
811C2—1042no—
812C2C2×#1171861811yescharacteristic
subgroupG/H
centerC4C2×#88193
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#421C2
socleC2×C13C2×#390
prime radicalC2×#11719527C2
cosocleC22×C4×C13C24
hypercenterC2×#421D13
hypocenterC13#21244
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #13123425C2semidirect
3. C2×#11718800C2semidirect
4. C2×#11718901C2semidirect
5. C2×#11718667C2semidirect
6. #13123254C2semidirect
7. #13115733C2semidirect
8. C2×C13×#421C2semidirect
13. C2×#88205C4semidirect
19. C2×#88203C4semidirect
20. C2×#88196C4semidirect
21. C2×#88186C4semidirect
26. C13×#421C22semidirect
29. #11718901C22semidirect
32. #11718800C22semidirect
34. #11718783C22semidirect
38. #11718667C22semidirect
39. #11718659C22semidirect
98. C2×#6107C2×C4semidirect
101. C2×#6106C2×C4semidirect
102. C2×#6105C2×C4semidirect
105. C2×#6104C2×C4semidirect
275. C2×#421D13semidirect
392. #421C2×D13semidirect
677. C13#21244semidirect

Maximal subgroups

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

subgroupindex
C2×#117195272
#131234252
C2×#117188002
C2×#117189012
C2×#117186672
#131232542
#131157332
C2×C13×#4212
#2124413