Finite Group Databasebeta

← #15769600

Subgroups — #15769600

Order 3328.

1292 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718897C211yesmaximal, characteristic, complemented
2C2×#11718897C211yesmaximal, characteristic, complemented
3C2×#11718897C211yesmaximal, characteristic, complemented
4#13123355C211yesmaximal, characteristic, complemented
5C2×#11718125C211yesmaximal, characteristic, complemented
6#13114568C211yesmaximal, characteristic, complemented
7C13×#3449C211yesmaximal, characteristic
8C22×C13×#41C2211yescharacteristic
9C22×C13×#41C2211yescharacteristic
10C13×#537—22no—
11C13×#536—21no—
12C13×#536C412yescomplemented
13C13×#535—21no—
14C13×#535C412yescomplemented
15C13×#534—22no—
16C13×#532—22no—
17C13×#525—22no—
18C13×#525—22no—
19C2×C13×#117C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×#6099C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24#11718897—22no—
25#11718897—22no—
26#11718897—22no—
27#11718897—22no—
28#11718897—22no—
29#11718897—22no—
30C2×#88077—22no—
31C2×#88077—22no—
32C2×#88077—22no—
33#11718894—22no—
34#11718893—22no—
35#11718886—21no—
36#11718876—21no—
37#11718125—22no—
38#11718119—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
72C13×C4⋊Q8—22no—
73C13×#127—22no—
74C13×#124—22no—
75C13×#124—22no—
76C13×#123—24no—
77C13×#123—24no—
78C13×C22⋊Q8—24no—
79C13×C22⋊Q8—24no—
80C13×#121—24no—
81C13×#121—28no—
82C13×#121—24no—
83C13×#120—24no—
84C13×#120—24no—
85C4×D4×C13—28no—
86C13×#117—21no—
87C13×#117—21no—
88C13×#117C2×C412yes—
89C13×#117D412yes—
90C2×C13×C4⋊C4—21no—
91C2×C13×C22⋊C4D412yes—
92C2×C42×C13—21no—
93C2×C22⋊Dic13—21no—
94C2×C22⋊Dic13—21no—
95#88180—21no—
96#88180—21no—
97#88180—21no—
98#88180—21no—
99#88180—21no—
100#88180—21no—
101#88180—21no—
102#88180D412yescomplemented
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—21no—
105C2×C4×Dic13—21no—
106C2×C4×Dic13D412yescomplemented
107C2×#6099—21no—
108C2×#6099—21no—
109C2×#6099—21no—
110C2×#6099—21no—
111C2×#6099—21no—
112C2×#6099—21no—
113C2×#6099—21no—
114C2×#6099—21no—
115C2×#6099—21no—
116C2×#6099—21no—
117C2×#6099D412yescomplemented
118C2×#6099D412yescomplemented
119C22×#1055—21no—
120C22×#1055—21no—
121#88077—28no—
122#88077—28no—
123#88077—28no—
124#88075—24no—
125#88072—24no—
126#11003—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⋊C412yes—
174C2×D4×C13—22no—
175C2×D4×C13—22no—
176C2×D4×C13—22no—
177C2×D4×C13—22no—
178C2×D4×C13—28no—
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—21no—
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×C13—41no—
197C2×D4×C13C22⋊C412yes—
198C2×D4×C13C22⋊C412yes—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—22no—
202C22×C4×C13—22no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—22no—
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×C13—41no—
213C22×C4×C13—41no—
214C22×C4×C13C22×C411yescharacteristic
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×C13C2×D411yescharacteristic
223C22×C4×C13C2×D411yescharacteristic
224C22×C4×C13#4111yescharacteristic
225C22×C4×C13#4111yescharacteristic
226C22×C4×C13#4111yescharacteristic
227C22×C4×C13#4111yescharacteristic
228C22×Dic13—22no—
229C22×Dic13—41no—
230C13×C4⋊C4—28no—
231C13×C4⋊C4—22no—
232C13×C4⋊C4—22no—
233C13×C22⋊C4—28no—
234C13×C22⋊C4—28no—
235C13×C22⋊C4—22no—
236C13×C22⋊C4C22⋊C414yes—
237C42×C13—22no—
238C42×C13—22no—
239C22⋊Dic13—22no—
240C22⋊Dic13—41no—
241C22⋊Dic13—41no—
242C22⋊Dic13—41no—
243C4⋊Dic13—22no—
244C4⋊Dic13—41no—
245C4⋊Dic13—41no—
246C4⋊Dic13—41no—
247C4×Dic13—22no—
248C4×Dic13—22no—
249C4×Dic13—22no—
250C4×Dic13—41no—
251#6099—22no—
252#6099—22no—
253#6099—22no—
254#6099—22no—
255#6099—41no—
256#6099—41no—
257#6099—41no—
258#6099—41no—
259C2×#1055—22no—
260C2×#1055—22no—
261C2×#1055—41no—
262C2×#1055—41no—
263C2×#1055—41no—
264C2×#1055—41no—
265#3449D1311yescharacteristic
266C2×#421—131no—
267C2×#421—131no—
268C2×#421—131no—
269#2896—131no—
270C2×#344—131no—
271#1740—131no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13—81no—
279C23×C13—82no—
280C23×C13—82no—
281C23×C13C2×C22⋊C411yescharacteristic
282C23×C13#12011yescharacteristic
283C23×C13#12011yescharacteristic
284C23×C13#12111yescharacteristic
285C23×C13#12111yescharacteristic
286C23×C13#12411yescharacteristic
287C23×C13#12711yescharacteristic
288Q8×C13—22no—
289Q8×C13—22no—
290Q8×C13—22no—
291Q8×C13—22no—
292Q8×C13—41no—
293Q8×C13—41no—
294Q8×C13—41no—
295Q8×C13—41no—
296D4×C13—22no—
297D4×C13—22no—
298D4×C13—22no—
299D4×C13—22no—
300D4×C13—42no—
301D4×C13—42no—
302D4×C13—42no—
303D4×C13—42no—
304D4×C13—42no—
305D4×C13—42no—
306D4×C13—42no—
307D4×C13—42no—
308D4×C13—41no—
309D4×C13—41no—
310D4×C13—41no—
311D4×C13—41no—
312D4×C13—88no—
313C2×C4×C13—24no—
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×C13—82no—
329C2×C4×C13C2×C22⋊C411yescharacteristic
330C2×C4×C13C2×C22⋊C411yescharacteristic
331C2×C4×C13C4×D411yescharacteristic
332C2×C4×C13C4×D411yescharacteristic
333C2×C4×C13C4×D411yescharacteristic
334C2×C4×C13C4×D411yescharacteristic
335C2×C4×C13#12011yescharacteristic
336C2×C4×C13#12011yescharacteristic
337C2×C4×C13#12011yescharacteristic
338C2×C4×C13#12011yescharacteristic
339C2×C4×C13#12011yescharacteristic
340C2×C4×C13#12011yescharacteristic
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#12111yescharacteristic
350C2×C4×C13#12111yescharacteristic
351C2×C4×C13#12311yescharacteristic
352C2×C4×C13#12311yescharacteristic
353C2×C4×C13#12311yescharacteristic
354C2×C4×C13#12311yescharacteristic
355C2×C4×C13#12411yescharacteristic
356C2×C4×C13#12711yescharacteristic
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—82no—
360C2×Dic13—82no—
361#1055—42no—
362#1055—42no—
363C22×#41C2×D1311yescharacteristic
364C22×#41C2×D1311yescharacteristic
365C22×M16—131no—
366C22×M16—131no—
367#537—22no—
368#536—21no—
369#536Dic1312yescomplemented
370#535—21no—
371#535Dic1312yescomplemented
372#534—22no—
373#532—22no—
374#525—22no—
375#525—22no—
376C2×#117—131no—
377C2×#117—131no—
378C2×#117C2×D1311yescharacteristic
379#421—262no—
380#421—262no—
381#421—262no—
382#421—262no—
383#421—262no—
384#421—262no—
385C2×#104—262no—
386C2×#104—262no—
387C2×#104—262no—
388#419—261no—
389#418—261no—
390#417—262no—
391#416—262no—
392#344—262no—
393#342—262no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13—41no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—44no—
402C22×C13—44no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—82no—
406C22×C13—82no—
407C22×C13—82no—
408C22×C13—82no—
409C22×C13#37911yescharacteristic
410C22×C13#39011yescharacteristic
411C22×C13#39011yescharacteristic
412C22×C13#39211yescharacteristic
413C22×C13#39211yescharacteristic
414C22×C13#39411yescharacteristic
415C22×C13#39411yescharacteristic
416C4×C13—44no—
417C4×C13—42no—
418C4×C13—42no—
419C4×C13#38611yescharacteristic
420C4×C13#38611yescharacteristic
421C4×C13#38611yescharacteristic
422C4×C13#38611yescharacteristic
423C4×C13#39211yescharacteristic
424C4×C13#39211yescharacteristic
425C4×C13#39411yescharacteristic
426C4×C13#39411yescharacteristic
427Dic13—82no—
428Dic13—82no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
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×#41C2×Dic1312yes—
450C2×#41C22⋊D1312yes—
451C2×#41C22⋊D1312yes—
452C2×#41C22⋊D1312yes—
453C22×Q8C2×Dic1311yescharacteristic
454C22×Q8C22⋊D1311yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C2×Dic1311yescharacteristic
458C22×D4C22⋊D1311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C22×D1311yescharacteristic
462C2×M16—132no—
463C2×M16—132no—
464C2×M16—261no—
465C2×M16—261no—
466C2×M16—261no—
467C2×M16—261no—
468C2×M16—261no—
469C2×M16—261no—
470C2×M16—261no—
471C2×M16—261no—
472C2×M16—261no—
473C2×M16—261no—
474C22×C8—261no—
475C22×C8—261no—
476C4⋊Q8—22no—
477#127—22no—
478#124—22no—
479#124—22no—
480#123—24no—
481#123—24no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484#121—24no—
485#121—28no—
486#121—24no—
487#120—24no—
488#120—24no—
489C4×D4—28no—
490#117—21no—
491#117—21no—
492#117—132no—
493#117—261no—
494#117—261no—
495#117—261no—
496#117—261no—
497#117—261no—
498#117—261no—
499#117—261no—
500#117C2×Dic1312yes—
501#117C22⋊D1312yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—261no—
504C2×C4⋊C4—261no—
505C2×C22⋊C4—261no—
506C2×C22⋊C4—261no—
507C2×C22⋊C4C22⋊D1312yes—
508C2×C42—21no—
509C2×C42—132no—
510C2×C42—261no—
511#104—268no—
512#104—268no—
513#104—268no—
514#103—264no—
515#102—264no—
516C2×C13—21no—
517C2×C13—21no—
518C2×C13—21no—
519C2×C13—21no—
520C2×C13—21no—
521C2×C13—21no—
522C2×C13—21no—
523C2×C13—82no—
524C2×C13—82no—
525C2×C13#143811yescharacteristic
526C24—21no—
527C24—21no—
528C24C2×C22⋊D1311yescharacteristic
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
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—41no—
546#41—41no—
547#41—41no—
548#41—41no—
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—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C22⋊Dic1312yes—
572C2×Q8C22⋊Dic1312yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—28no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4C22⋊Dic1312yes—
597C2×D4C22⋊Dic1312yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—262no—
614C22×C4—521no—
615C22×C4D4×D1311yescharacteristic
616C22×C4D4×D1311yescharacteristic
617C22×C4D4×D1311yescharacteristic
618C22×C4D4×D1311yescharacteristic
619C22×C4#612911yescharacteristic
620C22×C4#612911yescharacteristic
621C22×C4#612911yescharacteristic
622C22×C4#612911yescharacteristic
623C22×C4C22×Dic1311yescharacteristic
624C22×C4C2×C22⋊D1311yescharacteristic
625C22×C4C2×C22⋊D1311yescharacteristic
626C22×C4C2×C22⋊D1311yescharacteristic
627C22×C4C2×C22⋊D1311yescharacteristic
628C22×C4C2×C22⋊D1311yescharacteristic
629M16—262no—
630M16—262no—
631M16—262no—
632M16—262no—
633M16—521no—
634M16—521no—
635M16—521no—
636M16—521no—
637C2×C8—262no—
638C2×C8—262no—
639C2×C8—521no—
640C2×C8—521no—
641C2×C8—521no—
642C2×C8—521no—
643C4⋊C4—28no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—262no—
647C4⋊C4—521no—
648C4⋊C4—521no—
649C4⋊C4—521no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—22no—
653C22⋊C4—262no—
654C22⋊C4—521no—
655C22⋊C4—521no—
656C22⋊C4—521no—
657C22⋊C4C22⋊Dic1314yes—
658C42—22no—
659C42—22no—
660C42—262no—
661C42—262no—
662C42—262no—
663C42—521no—
664C13#1100311yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—82no—
673C23—82no—
674C23#8819011yescharacteristic
675C23#8819211yescharacteristic
676C23#8819211yescharacteristic
677C23#8819411yescharacteristic
678C23C2×C22⋊Dic1311yescharacteristic
679C23#8820711yescharacteristic
680C23#8820711yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—88no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—82no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—1042no—
725C2×C4—1042no—
726C2×C4D4×Dic1311yescharacteristic
727C2×C4D4×Dic1311yescharacteristic
728C2×C4D4×Dic1311yescharacteristic
729C2×C4D4×Dic1311yescharacteristic
730C2×C4#8818911yescharacteristic
731C2×C4#8818911yescharacteristic
732C2×C4#8818911yescharacteristic
733C2×C4#8818911yescharacteristic
734C2×C4#8819011yescharacteristic
735C2×C4#8819111yescharacteristic
736C2×C4#8819111yescharacteristic
737C2×C4#8819111yescharacteristic
738C2×C4#8819111yescharacteristic
739C2×C4#8819211yescharacteristic
740C2×C4#8819211yescharacteristic
741C2×C4#8819311yescharacteristic
742C2×C4#8819311yescharacteristic
743C2×C4#8819311yescharacteristic
744C2×C4#8819311yescharacteristic
745C2×C4#8819311yescharacteristic
746C2×C4#8819311yescharacteristic
747C2×C4#8819311yescharacteristic
748C2×C4#8819311yescharacteristic
749C2×C4#8819411yescharacteristic
750C2×C4C2×C22⋊Dic1311yescharacteristic
751C2×C4C2×C22⋊Dic1311yescharacteristic
752C2×C4#8820711yescharacteristic
753C2×C4#8820711yescharacteristic
754C8—522no—
755C8—522no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#1171888211yescharacteristic
772C22#1171888211yescharacteristic
773C22#1171888311yescharacteristic
774C22#1171888311yescharacteristic
775C22#1171888411yescharacteristic
776C22#1171888411yescharacteristic
777C22#1171890811yescharacteristic
778C4—44no—
779C4—42no—
780C4—42no—
781C4—1042no—
782C4—1042no—
783C4#1171888111yescharacteristic
784C4#1171888111yescharacteristic
785C4#1171888111yescharacteristic
786C4#1171888111yescharacteristic
787C4#1171888311yescharacteristic
788C4#1171888311yescharacteristic
789C4#1171888411yescharacteristic
790C4#1171888411yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—82no—
799C2—82no—
800C2#1311307711yescharacteristic
subgroupG/H
centerC4#11718884
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#3449C2
socleC2×C13#1438
cosocleC23×C4×C13C23
hypercenter#3449D13
hypocenterC13#11003
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#11718897C2semidirect
2. C2×#11718897C2semidirect
3. C2×#11718897C2semidirect
4. #13123355C2semidirect
5. C2×#11718125C2semidirect
6. #13114568C2semidirect
12. C13×#536C4semidirect
14. C13×#535C4semidirect
102. #88180D4semidirect
106. C2×C4×Dic13D4semidirect
117. C2×#6099D4semidirect
118. C2×#6099D4semidirect
369. #536Dic13semidirect
371. #535Dic13semidirect
664. C13#11003semidirect

Maximal subgroups

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

subgroupindex
C2×#117188972
#131233552
C2×#117181252
#131145682
C13×#34492
#1100313