Finite Group Databasebeta

← #27290749

Subgroups — #27290749

Order 13568.

1310 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×#16810640C211yesmaximal, characteristic, complemented
2C2×#16810619C211yesmaximal, characteristic, complemented
3C2×#16810597C211yesmaximal, characteristic, complemented
4C2×#16810590C211yesmaximal, characteristic, complemented
5#20274431C211yesmaximal, characteristic, complemented
6#20274424C211yesmaximal, characteristic, complemented
7C53×#3449C211yesmaximal, characteristic
8C22×#11719917C2211yescharacteristic
9C23×#88322C2211yescharacteristic
10C2×#13133176C2211yescharacteristic
11C2×#13133176C2211yescharacteristic
12#16810640—22no—
13#16810640—22no—
14C2×#13133144—22no—
15#16810619—22no—
16#16810619—22no—
17C2×#13133141—21no—
18C2×#13133138—21no—
19#16810597—22no—
20#16810597—22no—
21C2×#13133132—22no—
22#16810590—22no—
23#16810590—22no—
24C2×C22⋊#88322—22no—
25#16810385—22no—
26#16810382—22no—
27C22×#41×C53C2211yescharacteristic
28C22×#41×C53C2211yescharacteristic
29C53×#537—22no—
30C53×#536—21no—
31C53×#536C412yescomplemented
32C53×#535—21no—
33C53×#535C412yescomplemented
34C53×#534—22no—
35C53×#532—22no—
36C53×#525—22no—
37C53×#525—22no—
38C2×#117×C53C2211yescharacteristic
39C2×#11719917—21no—
40C2×#11719917—21no—
41C2×#11719917—21no—
42C2×#11719917—21no—
43C2×#11719917—21no—
44C2×#11719917D412yescomplemented
45C22×#88322—21no—
46C22×#88322—21no—
47C22×#88322—21no—
48C22×#88322—21no—
49C22×#88322—21no—
50C22×#88322—21no—
51C22×#88322—21no—
52C22×#88322D412yescomplemented
53#13133176—21no—
54#13133176—21no—
55#13133176—21no—
56#13133176—21no—
57#13133176—21no—
58#13133176—21no—
59#13133176D412yescomplemented
60#13133176D412yescomplemented
61C2×C4⋊Dic53—21no—
62C2×C4⋊Dic53—21no—
63C2×C22⋊Dic53—21no—
64C2×C22⋊Dic53—21no—
65C2×C4×Dic53—21no—
66C2×C4×Dic53—21no—
67#13133144—28no—
68#13133141—24no—
69#13133138—24no—
70#13133132—28no—
71C22⋊#88322—28no—
72C2×#41×C53—21no—
73C2×#41×C53—21no—
74C2×#41×C53—21no—
75C2×#41×C53—21no—
76C2×#41×C53—21no—
77C2×#41×C53—21no—
78C2×#41×C53—21no—
79C2×#41×C53—21no—
80C2×#41×C53—21no—
81C2×#41×C53—21no—
82C2×#41×C53—21no—
83C2×#41×C53—21no—
84C2×#41×C53—21no—
85C2×#41×C53—21no—
86C2×#41×C53—21no—
87C2×#41×C53—21no—
88C2×#41×C53—21no—
89C2×#41×C53—21no—
90C2×#41×C53—21no—
91C2×#41×C53—21no—
92C2×#41×C53—21no—
93C2×#41×C53—21no—
94C2×#41×C53C2×C412yes—
95C2×#41×C53D412yes—
96C22×Q8×C53C2×C411yescharacteristic
97C22×Q8×C53D411yescharacteristic
98C22×D4×C53—21no—
99C22×D4×C53C2×C411yescharacteristic
100C22×D4×C53D412yes—
101C22×D4×C53D411yescharacteristic
102C23×C4×C53—21no—
103C23×C4×C53D412yes—
104C23×C4×C53C2311yescharacteristic
105C4⋊Q8×C53—22no—
106#127×C53—22no—
107#124×C53—22no—
108#124×C53—22no—
109#123×C53—24no—
110#123×C53—24no—
111C22⋊Q8×C53—24no—
112C22⋊Q8×C53—24no—
113#121×C53—24no—
114#121×C53—28no—
115#121×C53—24no—
116#120×C53—24no—
117#120×C53—24no—
118C4×D4×C53—28no—
119#117×C53—21no—
120#117×C53—21no—
121#117×C53C2×C412yes—
122#117×C53D412yes—
123C2×C4⋊C4×C53D412yes—
124C2×C22⋊C4×C53—21no—
125C2×C42×C53—21no—
126C24×C53—21no—
127C24×C53C22⋊C412yes—
128C24×C53C2×D411yescharacteristic
129#41×C53—22no—
130#41×C53—22no—
131#41×C53—22no—
132#41×C53—22no—
133#41×C53—22no—
134#41×C53—22no—
135#41×C53—22no—
136#41×C53—22no—
137#41×C53—41no—
138#41×C53—41no—
139#41×C53—41no—
140#41×C53—41no—
141#41×C53—41no—
142#41×C53—41no—
143#41×C53—41no—
144#41×C53—41no—
145#41×C53—41no—
146#41×C53—41no—
147#41×C53—41no—
148#41×C53—41no—
149#41×C53—41no—
150#41×C53—41no—
151#41×C53—41no—
152#41×C53—41no—
153#41×C53—41no—
154#41×C53—41no—
155#41×C53—41no—
156#41×C53—41no—
157#41×C53—41no—
158#41×C53—41no—
159#41×C53—41no—
160#41×C53—41no—
161C2×Q8×C53—21no—
162C2×Q8×C53—21no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—21no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53C22⋊C412yes—
173C2×D4×C53—22no—
174C2×D4×C53—22no—
175C2×D4×C53—22no—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—22no—
179C2×D4×C53—22no—
180C2×D4×C53—22no—
181C2×D4×C53—28no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53—21no—
185C2×D4×C53—21no—
186C2×D4×C53—21no—
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—21no—
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—41no—
194C2×D4×C53—41no—
195C2×D4×C53—41no—
196C2×D4×C53—41no—
197C2×D4×C53C22⋊C412yes—
198C22×C4×C53—21no—
199C22×C4×C53—22no—
200C22×C4×C53—22no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—22no—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—22no—
208C22×C4×C53—41no—
209C22×C4×C53—41no—
210C22×C4×C53—41no—
211C22×C4×C53—41no—
212C22×C4×C53C22⋊C412yes—
213C22×C4×C53C22×C411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53C2×D411yescharacteristic
220C22×C4×C53C2×D411yescharacteristic
221C22×C4×C53C2×D411yescharacteristic
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53#4111yescharacteristic
224C22×C4×C53#4111yescharacteristic
225C22×C4×C53#4111yescharacteristic
226C22×C4×C53#4111yescharacteristic
227C22×Dic53—41no—
228C22×Dic53—41no—
229C4⋊C4×C53—28no—
230C4⋊C4×C53—22no—
231C4⋊C4×C53C22⋊C414yes—
232C22⋊C4×C53—28no—
233C22⋊C4×C53—28no—
234C22⋊C4×C53—22no—
235C22⋊C4×C53—22no—
236C42×C53—22no—
237C42×C53—22no—
238C22⋊Dic53—22no—
239C22⋊Dic53—22no—
240C22⋊Dic53—41no—
241C22⋊Dic53—41no—
242C4⋊Dic53—22no—
243C4⋊Dic53—22no—
244C4⋊Dic53—41no—
245C4⋊Dic53—41no—
246C4×Dic53—22no—
247C4×Dic53—22no—
248C4×Dic53—41no—
249C4×Dic53—41no—
250#11719917—22no—
251#11719917—22no—
252#11719917—41no—
253#11719917—41no—
254C2×#88322—22no—
255C2×#88322—22no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322—41no—
259C2×#88322—41no—
260C2×#88322—41no—
261C2×#88322—41no—
262C2×#88322—41no—
263C2×#88322—41no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—42no—
269C23×C53—44no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—82no—
273C23×C53C2×C22⋊C411yescharacteristic
274C23×C53#12011yescharacteristic
275C23×C53#12011yescharacteristic
276C23×C53#12011yescharacteristic
277C23×C53#12111yescharacteristic
278C23×C53#12111yescharacteristic
279C23×C53#12311yescharacteristic
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—41no—
283Q8×C53—41no—
284Q8×C53—41no—
285Q8×C53—41no—
286Q8×C53—41no—
287Q8×C53—41no—
288D4×C53—22no—
289D4×C53—22no—
290D4×C53—42no—
291D4×C53—42no—
292D4×C53—42no—
293D4×C53—42no—
294D4×C53—42no—
295D4×C53—42no—
296D4×C53—42no—
297D4×C53—42no—
298D4×C53—41no—
299D4×C53—41no—
300D4×C53—41no—
301D4×C53—41no—
302D4×C53—41no—
303D4×C53—41no—
304D4×C53—88no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—24no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—42no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—82no—
321C2×C4×C53C2×C22⋊C411yescharacteristic
322C2×C4×C53C2×C22⋊C411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53C4×D411yescharacteristic
325C2×C4×C53C4×D411yescharacteristic
326C2×C4×C53C4×D411yescharacteristic
327C2×C4×C53#12011yescharacteristic
328C2×C4×C53#12011yescharacteristic
329C2×C4×C53#12011yescharacteristic
330C2×C4×C53#12011yescharacteristic
331C2×C4×C53#12011yescharacteristic
332C2×C4×C53#12111yescharacteristic
333C2×C4×C53#12111yescharacteristic
334C2×C4×C53#12111yescharacteristic
335C2×C4×C53#12111yescharacteristic
336C2×C4×C53#12111yescharacteristic
337C2×C4×C53#12111yescharacteristic
338C2×C4×C53#12111yescharacteristic
339C2×C4×C53#12111yescharacteristic
340C2×C4×C53#12111yescharacteristic
341C2×C4×C53#12111yescharacteristic
342C2×C4×C53#12311yescharacteristic
343C2×C4×C53#12311yescharacteristic
344C2×C4×C53#12311yescharacteristic
345C2×C4×C53#12411yescharacteristic
346C2×C4×C53#12411yescharacteristic
347C2×C4×C53#12711yescharacteristic
348C2×C4×C53#12711yescharacteristic
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—82no—
352C2×Dic53—82no—
353#88322—42no—
354#88322—42no—
355#10999—531nomaximal, Sylow
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53—44no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—82no—
369C22×C53—82no—
370C22×C53—82no—
371C22×C53#37911yescharacteristic
372C22×C53#38611yescharacteristic
373C22×C53#38611yescharacteristic
374C22×C53#39211yescharacteristic
375C22×C53#39211yescharacteristic
376C22×C53#39411yescharacteristic
377C22×C53#39411yescharacteristic
378C4×C53—44no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#38611yescharacteristic
382C4×C53#38611yescharacteristic
383C4×C53#39011yescharacteristic
384C4×C53#39011yescharacteristic
385C4×C53#39211yescharacteristic
386C4×C53#39211yescharacteristic
387C4×C53#39411yescharacteristic
388C4×C53#39411yescharacteristic
389Dic53—82no—
390Dic53—82no—
391#3449D5311yescharacteristic
392C2×#421—531no—
393C2×#416—531no—
394C2×#410—531no—
395C2×#408—531no—
396#1735—531no—
397#1733—531no—
398C2×C53—21no—
399C2×C53—21no—
400C2×C53—21no—
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—21no—
404C2×C53—82no—
405C2×C53—82no—
406C2×C53#143811yescharacteristic
407C2×C53#179412yes—
408C22×#41C2×D5311yescharacteristic
409C22×#41C2×D5311yescharacteristic
410C22×M16—531no—
411C23×C8—531no—
412#537—22no—
413#536—21no—
414#536Dic5312yescomplemented
415#535—21no—
416#535Dic5312yescomplemented
417#534—22no—
418#532—22no—
419#525—22no—
420#525—22no—
421C2×#117—531no—
422C2×#117—531no—
423C2×#117C2×D5311yescharacteristic
424#421—1062no—
425#421—1062no—
426C2×#104—1062no—
427#416—1062no—
428#416—1062no—
429C2×#103—1061no—
430C2×#102—1061no—
431#410—1062no—
432#410—1062no—
433C2×#99—1062no—
434#408—1062no—
435#408—1062no—
436C2×C22⋊C8—1062no—
437#340—1062no—
438#339—1062no—
439C53#1099911yescharacteristic, complemented, Sylow
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×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41C2×Dic5312yes—
463C2×#41C22⋊D5312yes—
464C22×Q8C2×Dic5311yescharacteristic
465C22×Q8C22⋊D5311yescharacteristic
466C22×D4—21no—
467C22×D4C2×Dic5311yescharacteristic
468C22×D4C22⋊D5311yescharacteristic
469C22×D4C22⋊D5312yes—
470C23×C4—21no—
471C23×C4C22⋊D5312yes—
472C23×C4C22×D5311yescharacteristic
473C2×M16—532no—
474C2×M16—1061no—
475C2×M16—1061no—
476C2×M16—1061no—
477C2×M16—1061no—
478C2×M16—1061no—
479C22×C8—532no—
480C22×C8—1061no—
481C22×C8—1061no—
482C22×C8—1061no—
483C22×C8—1061no—
484C22×C8—1061no—
485C22×C8—1061no—
486C22×C8—1061no—
487C4⋊Q8—22no—
488#127—22no—
489#124—22no—
490#124—22no—
491#123—24no—
492#123—24no—
493C22⋊Q8—24no—
494C22⋊Q8—24no—
495#121—24no—
496#121—28no—
497#121—24no—
498#120—24no—
499#120—24no—
500C4×D4—28no—
501#117—21no—
502#117—21no—
503#117—532no—
504#117—532no—
505#117—1061no—
506#117—1061no—
507#117—1061no—
508#117—1061no—
509#117—1061no—
510#117—1061no—
511#117C2×Dic5312yes—
512#117C22⋊D5312yes—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4C22⋊D5312yes—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C42—21no—
520C2×C42—1061no—
521C2×C42—1061no—
522#104—1068no—
523#103—1064no—
524#102—1064no—
525#99—1068no—
526C22⋊C8—1068no—
527C24—21no—
528C24C22⋊Dic5312yes—
529C24C2×C22⋊D5311yescharacteristic
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—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
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—
561#41—41no—
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×Q8—21no—
572C2×Q8—21no—
573C2×Q8C22⋊Dic5312yes—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—28no—
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—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4C22⋊Dic5312yes—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—2121no—
614C22×C4—2121no—
615C22×C4C22⋊Dic5312yes—
616C22×C4D4×D5311yescharacteristic
617C22×C4D4×D5311yescharacteristic
618C22×C4D4×D5311yescharacteristic
619C22×C4D4×D5311yescharacteristic
620C22×C4#1171994711yescharacteristic
621C22×C4#1171994711yescharacteristic
622C22×C4#1171994711yescharacteristic
623C22×C4#1171994711yescharacteristic
624C22×C4C22×Dic5311yescharacteristic
625C22×C4C2×C22⋊D5311yescharacteristic
626C22×C4C2×C22⋊D5311yescharacteristic
627C22×C4C2×C22⋊D5311yescharacteristic
628C22×C4C2×C22⋊D5311yescharacteristic
629C22×C4C2×C22⋊D5311yescharacteristic
630M16—1062no—
631M16—1062no—
632M16—2121no—
633M16—2121no—
634C2×C8—1062no—
635C2×C8—1062no—
636C2×C8—1062no—
637C2×C8—1062no—
638C2×C8—2121no—
639C2×C8—2121no—
640C2×C8—2121no—
641C2×C8—2121no—
642C2×C8—2121no—
643C2×C8—2121no—
644C4⋊C4—28no—
645C4⋊C4—22no—
646C4⋊C4—1062no—
647C4⋊C4—1062no—
648C4⋊C4—2121no—
649C4⋊C4—2121no—
650C4⋊C4C22⋊Dic5314yes—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—1062no—
656C22⋊C4—1062no—
657C22⋊C4—2121no—
658C22⋊C4—2121no—
659C42—22no—
660C42—22no—
661C42—1062no—
662C42—1062no—
663C42—2121no—
664C42—2121no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—44no—
671C23—41no—
672C23—41no—
673C23—82no—
674C23C2×C22⋊Dic5311yescharacteristic
675C23#1313318511yescharacteristic
676C23#1313318611yescharacteristic
677C23#1313318611yescharacteristic
678C23#1313318911yescharacteristic
679C23#1313318911yescharacteristic
680C23#1313319811yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—88no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
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—4242no—
723C2×C4—4242no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4C2×C22⋊Dic5311yescharacteristic
727C2×C4C2×C22⋊Dic5311yescharacteristic
728C2×C4D4×Dic5311yescharacteristic
729C2×C4D4×Dic5311yescharacteristic
730C2×C4D4×Dic5311yescharacteristic
731C2×C4D4×Dic5311yescharacteristic
732C2×C4#1313318511yescharacteristic
733C2×C4#1313318511yescharacteristic
734C2×C4#1313318511yescharacteristic
735C2×C4#1313318611yescharacteristic
736C2×C4#1313318611yescharacteristic
737C2×C4#1313318811yescharacteristic
738C2×C4#1313318811yescharacteristic
739C2×C4#1313318811yescharacteristic
740C2×C4#1313318811yescharacteristic
741C2×C4#1313318911yescharacteristic
742C2×C4#1313318911yescharacteristic
743C2×C4#1313318911yescharacteristic
744C2×C4#1313318911yescharacteristic
745C2×C4#1313318911yescharacteristic
746C2×C4#1313318911yescharacteristic
747C2×C4#1313319811yescharacteristic
748C2×C4#1313319811yescharacteristic
749C2×C4#1313319811yescharacteristic
750C2×C4#1313320411yescharacteristic
751C2×C4#1313320411yescharacteristic
752C2×C4#1313321311yescharacteristic
753C2×C4#1313321311yescharacteristic
754C8—2122no—
755C8—2122no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#1681047911yescharacteristic
772C22#1681050311yescharacteristic
773C22#1681050311yescharacteristic
774C22#1681053111yescharacteristic
775C22#1681053111yescharacteristic
776C22#1681053711yescharacteristic
777C22#1681053711yescharacteristic
778C4—42no—
779C4—42no—
780C4—44no—
781C4—4242no—
782C4—4242no—
783C4#1681050311yescharacteristic
784C4#1681050311yescharacteristic
785C4#1681052611yescharacteristic
786C4#1681052611yescharacteristic
787C4#1681053111yescharacteristic
788C4#1681053111yescharacteristic
789C4#1681053711yescharacteristic
790C4#1681053711yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—82no—
798C2—82no—
799C2#2027295611yescharacteristic
800C2#2027467912yes—
subgroupG/H
centerC2×C4#13133186
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
Fitting, prime radicalC53×#3449C2
socleC22×C53#379
cosocleC23×C4×C53C23
hypercenter#3449D53
hypocenterC53#10999
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16810640C2semidirect
2. C2×#16810619C2semidirect
3. C2×#16810597C2semidirect
4. C2×#16810590C2semidirect
5. #20274431C2semidirect
6. #20274424C2semidirect
31. C53×#536C4semidirect
33. C53×#535C4semidirect
44. C2×#11719917D4semidirect
52. C22×#88322D4semidirect
59. #13133176D4semidirect
60. #13133176D4semidirect
414. #536Dic53semidirect
416. #535Dic53semidirect
439. C53#10999semidirect

Maximal subgroups

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

subgroupindex
C2×#168106402
C2×#168106192
C2×#168105972
C2×#168105902
#202744312
#202744242
C53×#34492
#1099953