Finite Group Databasebeta

← C2×#20275612 #27388065

Subgroups — C2×#20275612 #27388065

Order 13568.

1474 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133237C211yesmaximal, characteristic
2C2×#16810659C211yesmaximal, characteristic, complemented
3C2×#16810639C211yesmaximal, characteristic, complemented
4C2×#16810597C211yesmaximal, characteristic, complemented
5C2×#16810596C211yesmaximal, characteristic, complemented
6C2×#16810581C211yesmaximal, characteristic, complemented
7#20275612C218yesmaximal, direct product factor
8C2×C53×#421C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10C2×#13133237—21no—
11C2×#13133237—21no—
12C2×#13133237—22no—
13C2×#13133237—21no—
14C2×#13133237—21no—
15C2×#13133237—22no—
16C2×#13133237C414yescomplemented
17C2×#13133237C2214yes—
18C22×#11719925C411yescharacteristic, complemented
19C22×#11719923C411yescharacteristic, complemented
20C22×#11719924C411yescharacteristic, complemented
21C22×#11719922C411yescharacteristic, complemented
22C23×#88322C2211yescharacteristic
23C2×#13133176C2211yescharacteristic
24C2×#13133176C2211yescharacteristic
25#16810659—22no—
26#16810659C2214yescomplemented
27C2×#13133150—21no—
28C2×#13133148—21no—
29#16810639—22no—
30#16810639C2214yescomplemented
31C2×#13133143—22no—
32#16810597—22no—
33#16810597C2214yescomplemented
34#16810596—22no—
35#16810596C2214yescomplemented
36C2×#13133132—22no—
37C2×#13133131—22no—
38#16810581—22no—
39#16810581C2214yescomplemented
40C2×#13133127—21no—
41C2×C8×Dic53—21no—
42C22×#41×C53C2211yescharacteristic
43C22×M16×C53C2211yescharacteristic
44C2×#117×C53C2211yescharacteristic
45C53×#421—22no—
46C53×#421C2214yescomplemented
47C2×#104×C53—22no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945—21no—
52C2×#11719945—21no—
53C2×#11719945—21no—
54C2×#11719945—21no—
55C2×#11719945—21no—
56C2×#11719945—21no—
57C2×#11719945—21no—
58C2×#11719945C2×C412yes—
59C2×#11719945C2312yes—
60C22×Dic106C2×C411yescharacteristic
61C22×D212C2×C411yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53—21no—
64#13133237—24no—
65#13133237—24no—
66#13133237—24no—
67#13133237—24no—
68#13133237—24no—
69#13133237—24no—
70#13133237—24no—
71#13133237—24no—
72C2×#11719925—21no—
73C2×#11719925—21no—
74C2×#11719925—22no—
75C2×#11719925C2×C414yescomplemented
76C2×#11719923—21no—
77C2×#11719923—21no—
78C2×#11719923—22no—
79C2×#11719923C2×C414yescomplemented
80C2×#11719924—21no—
81C2×#11719924—21no—
82C2×#11719924—22no—
83C2×#11719924C2×C414yescomplemented
84C2×#11719922—21no—
85C2×#11719922—21no—
86C2×#11719922—22no—
87C2×#11719922C2×C414yescomplemented
88C22×#88322C2×C411yescharacteristic
89C22×#88322C2×C411yescharacteristic
90C22×#88322C2×C412yes—
91C22×#88322D411yescharacteristic
92C22×#88322D411yescharacteristic
93C22×#88322D412yes—
94C22×#88322D411yescharacteristic
95C22×#88322D411yescharacteristic
96C22×#88322D412yes—
97C22×#88322C2312yes—
98#13133176—21no—
99#13133176—21no—
100#13133176—21no—
101#13133176—21no—
102#13133176—21no—
103#13133176D412yes—
104#13133176C2312yes—
105#13133176C2312yes—
106C2×C4⋊Dic53—21no—
107C2×C4⋊Dic53—21no—
108C2×C22⋊Dic53—21no—
109C2×C22⋊Dic53D412yes—
110C2×C4×Dic53—21no—
111C2×C4×Dic53—21no—
112#13133150—24no—
113#13133148—24no—
114#13133143—28no—
115#13133132—28no—
116#13133131—28no—
117#13133127—24no—
118C8×Dic53—24no—
119C2×#41×C53—21no—
120C2×#41×C53—21no—
121C2×#41×C53—21no—
122C2×#41×C53—21no—
123C2×#41×C53—21no—
124C2×#41×C53—21no—
125C2×#41×C53—21no—
126C2×#41×C53—21no—
127C2×#41×C53—21no—
128C2×#41×C53—21no—
129C2×#41×C53C2×C412yes—
130C2×#41×C53C2312yes—
131C22×Q8×C53C2×C411yescharacteristic
132C22×D4×C53—21no—
133C22×D4×C53C2×C411yescharacteristic
134C23×C4×C53—21no—
135C23×C4×C53C2311yescharacteristic
136C2×M16×C53—21no—
137C2×M16×C53—21no—
138C2×M16×C53—21no—
139C2×M16×C53D412yes—
140C2×M16×C53D412yes—
141C2×M16×C53C2312yes—
142C22×C8×C53—21no—
143#117×C53—21no—
144#117×C53—21no—
145#117×C53—21no—
146#117×C53C2312yes—
147C2×C4⋊C4×C53—21no—
148C2×C22⋊C4×C53—21no—
149C2×C42×C53—21no—
150#104×C53—28no—
151C24×C53—21no—
152C24×C53C2×D411yescharacteristic
153C23×D53—21no—
154#41×C53—22no—
155#41×C53—22no—
156#41×C53—22no—
157#41×C53—22no—
158#41×C53—22no—
159#41×C53—22no—
160#41×C53—22no—
161#41×C53—22no—
162#41×C53—41no—
163#41×C53—41no—
164#41×C53—41no—
165#41×C53—41no—
166#41×C53—41no—
167#41×C53—41no—
168#41×C53—41no—
169#41×C53—41no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53—21no—
173C2×Q8×C53—21no—
174C2×Q8×C53—21no—
175C2×Q8×C53C22×C412yes—
176C2×D4×C53—22no—
177C2×D4×C53—22no—
178C2×D4×C53—21no—
179C2×D4×C53—21no—
180C2×D4×C53—21no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—41no—
184C2×D4×C53—41no—
185C2×D4×C53—41no—
186C2×D4×C53—41no—
187C2×D4×C53C22×C412yes—
188C22×C4×C53—21no—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—41no—
192C22×C4×C53—41no—
193C22×C4×C53—41no—
194C22×C4×C53—41no—
195C22×C4×C53—41no—
196C22×C4×C53C22×C411yescharacteristic
197C22×C4×C53C22×C411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53#4111yescharacteristic
206C22×C4×C53#4111yescharacteristic
207C22×C4×C53#4111yescharacteristic
208C22×C4×C53#4111yescharacteristic
209C22×C4×C53C2411yescharacteristic
210C2×C22⋊D53—22no—
211C2×C22⋊D53—22no—
212C2×C22⋊D53—41no—
213C2×C22⋊D53—41no—
214C2×C22⋊D53—41no—
215C2×C22⋊D53—41no—
216C22×Dic53—21no—
217C22×Dic53—22no—
218C22×Dic53—41no—
219#11719945—22no—
220#11719945—22no—
221#11719945—22no—
222#11719945—22no—
223#11719945—22no—
224#11719945—22no—
225#11719945—22no—
226#11719945—22no—
227#11719945—41no—
228#11719945—41no—
229#11719945—41no—
230#11719945—41no—
231#11719945—41no—
232#11719945—41no—
233#11719945—41no—
234#11719945—41no—
235C2×D212—21no—
236C2×D212—21no—
237C2×D212—21no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212C22×C412yes—
241C2×C4×D53—22no—
242C2×C4×D53—22no—
243C2×C4×D53—41no—
244C2×C4×D53—41no—
245C2×C4×D53—41no—
246C2×C4×D53—41no—
247C2×Dic106—21no—
248C2×Dic106—21no—
249C2×Dic106—21no—
250C2×Dic106—21no—
251C2×Dic106—21no—
252C2×Dic106C22×C412yes—
253M16×C53—22no—
254M16×C53—22no—
255M16×C53—22no—
256M16×C53C2×D414yes—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53—22no—
260C4⋊C4×C53—22no—
261C4⋊C4×C53—41no—
262C22⋊C4×C53—22no—
263C22⋊C4×C53—41no—
264C42×C53—22no—
265C42×C53—41no—
266C22⋊Dic53—22no—
267C22⋊Dic53—22no—
268C22⋊Dic53—41no—
269C22⋊Dic53C2×D414yes—
270#11719925—24no—
271#11719925—24no—
272#11719924—24no—
273#11719924—24no—
274#11719923—24no—
275#11719923—24no—
276#11719922—24no—
277#11719922—24no—
278C4⋊Dic53—22no—
279C4⋊Dic53—22no—
280C4⋊Dic53—22no—
281C4⋊Dic53—41no—
282C4×Dic53—22no—
283C4×Dic53—22no—
284C4×Dic53—22no—
285C4×Dic53—41no—
286C2×#88322C22⋊C411yescharacteristic
287C2×#88322C22⋊C411yescharacteristic
288C2×#88322C22⋊C412yes—
289C2×#88322C22⋊C411yescharacteristic
290C2×#88322C22⋊C411yescharacteristic
291C2×#88322C22⋊C412yes—
292C2×#88322C22⋊C412yes—
293C2×#88322C22⋊C412yes—
294C2×#88322C22⋊C412yes—
295C2×#88322C22⋊C412yes—
296C2×#88322C22×C412yes—
297C2×#88322C22×C412yes—
298C2×#88322C2×D412yes—
299C2×#88322C2×D412yes—
300C2×#88322C2×D412yes—
301C2×#88322C2×D412yes—
302C23×C53—22no—
303C23×C53—42no—
304C23×C53—41no—
305C23×C53—41no—
306C23×C53—82no—
307C23×C53C4×D411yescharacteristic
308C23×C53C4×D411yescharacteristic
309C23×C53#12111yescharacteristic
310C23×C53#12111yescharacteristic
311C23×C53#12711yescharacteristic
312C23×C53#12711yescharacteristic
313C23×C53C22×D411yescharacteristic
314C22×D53—22no—
315C22×D53—41no—
316C22×D53—41no—
317C22×D53—82no—
318Q8×C53—22no—
319Q8×C53—22no—
320Q8×C53—41no—
321Q8×C53—41no—
322D4×C53—22no—
323D4×C53—22no—
324D4×C53—42no—
325D4×C53—42no—
326D4×C53—42no—
327D4×C53—42no—
328D4×C53—41no—
329D4×C53—41no—
330C2×C4×C53—22no—
331C2×C4×C53—41no—
332C2×C4×C53—41no—
333C2×C4×C53—42no—
334C2×C4×C53—42no—
335C2×C4×C53—42no—
336C2×C4×C53—42no—
337C2×C4×C53—42no—
338C2×C4×C53—82no—
339C2×C4×C53C2×C22⋊C411yescharacteristic
340C2×C4×C53C2×C22⋊C411yescharacteristic
341C2×C4×C53C2×C22⋊C411yescharacteristic
342C2×C4×C53C2×C22⋊C411yescharacteristic
343C2×C4×C53C4×D411yescharacteristic
344C2×C4×C53C4×D411yescharacteristic
345C2×C4×C53C4×D411yescharacteristic
346C2×C4×C53C4×D411yescharacteristic
347C2×C4×C53C4×D411yescharacteristic
348C2×C4×C53C4×D411yescharacteristic
349C2×C4×C53#12111yescharacteristic
350C2×C4×C53#12111yescharacteristic
351C2×C4×C53#12111yescharacteristic
352C2×C4×C53#12111yescharacteristic
353C2×C4×C53#12111yescharacteristic
354C2×C4×C53#12111yescharacteristic
355C2×C4×C53#12411yescharacteristic
356C2×C4×C53#12411yescharacteristic
357C2×C4×C53#12411yescharacteristic
358C2×C4×C53#12411yescharacteristic
359C2×C4×C53#12711yescharacteristic
360C2×C4×C53#12711yescharacteristic
361C2×C4×C53C23×C411yescharacteristic
362C2×C4×C53C22×D411yescharacteristic
363C2×C4×C53C22×D411yescharacteristic
364C2×C4×C53C22×D411yescharacteristic
365C2×C4×C53C2×#4111yescharacteristic
366C2×C4×C53C2×#4111yescharacteristic
367C22⋊D53—42no—
368C22⋊D53—42no—
369C22⋊D53—42no—
370C22⋊D53—42no—
371C2×Dic53—22no—
372C2×Dic53—24no—
373C2×Dic53—44no—
374C2×Dic53—41no—
375C2×Dic53—41no—
376C2×Dic53—42no—
377C2×Dic53—82no—
378D212—22no—
379D212—22no—
380D212—41no—
381D212—41no—
382C4×D53—42no—
383C4×D53—42no—
384C4×D53—42no—
385C4×D53—42no—
386Dic106—22no—
387Dic106—22no—
388Dic106—41no—
389Dic106—41no—
390C8×C53—24no—
391#88322C2×C22⋊C412yes—
392#88322C2×C22⋊C412yes—
393#88322C2×C22⋊C412yes—
394#88322C2×C22⋊C412yes—
395C2×#1976—531nomaximal, Sylow
396C22×C53—22no—
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—41no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—41no—
403C22×C53—42no—
404C22×C53—82no—
405C22×C53—82no—
406C22×C53—82no—
407C22×C53#39011yescharacteristic
408C22×C53#39011yescharacteristic
409C22×C53#39011yescharacteristic
410C22×C53#39011yescharacteristic
411C22×C53C2×C4×D411yescharacteristic
412C22×C53C2×#12111yescharacteristic
413C22×C53C2×#12711yescharacteristic
414C2×D53—42no—
415C2×D53—82no—
416C2×D53—82no—
417C2×D53—82no—
418C4×C53—42no—
419C4×C53—82no—
420C4×C53#39011yescharacteristic
421C4×C53#39011yescharacteristic
422C4×C53#39011yescharacteristic
423C4×C53#39011yescharacteristic
424C4×C53C22×C22⋊C411yescharacteristic
425C4×C53C2×C4×D411yescharacteristic
426C4×C53C2×#12111yescharacteristic
427C4×C53C2×#12411yescharacteristic
428Dic53—44no—
429Dic53—42no—
430Dic53—82no—
431C22×#135—531no—
432C2×#427—531no—
433C2×#421—531no—
434C2×#421D5311yescharacteristic, complemented
435C2×#410—531no—
436C2×#410—531no—
437C2×#405—531no—
438#1976—538no—
439C2×C53—21no—
440C2×C53—21no—
441C2×C53—21no—
442C2×C53—21no—
443C2×C53—21no—
444C2×C53—21no—
445C2×C53—82no—
446C2×C53#197612yescomplemented
447C2×C53C2×#39011yescharacteristic
448D53—82no—
449C22×#41—531no—
450C22×#41C2×D5311yescharacteristic
451C2×#135—534no—
452C2×#135—534no—
453C2×#135—1061no—
454C2×#135—1061no—
455C2×#135—1062no—
456C2×#135—1061no—
457C2×#135—1061no—
458C2×#135—1062no—
459C22×Q16—531no—
460C22×SD16—531no—
461C22×SD16—531no—
462C22×D8—531no—
463C22×M16C2×D5311yescharacteristic
464C23×C8—531no—
465C2×#117—531no—
466C2×#117—531no—
467C2×#117C2×D5311yescharacteristic
468#427—534no—
469#427—1062no—
470C2×#107—1061no—
471C2×#106—1061no—
472#421—22no—
473#421—534no—
474#421—1062no—
475#421C2×D5314yescomplemented
476C2×#104—22no—
477C2×#104—1062no—
478#410—534no—
479#410—534no—
480#410—1062no—
481#410—1062no—
482C2×#99—1062no—
483C2×#99—1062no—
484#405—534no—
485#405—1062no—
486C2×#97—1061no—
487C2×C4×C8—1061no—
488C53C2×#197611yescharacteristic, complemented, Sylow
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—532no—
500C2×#41—532no—
501C2×#41—1061no—
502C2×#41—1061no—
503C2×#41—1061no—
504C2×#41—1061no—
505C2×#41—1061no—
506C2×#41—1061no—
507C2×#41—1061no—
508C2×#41—1061no—
509C2×#41—1061no—
510C2×#41—1061no—
511C2×#41C4×D5312yes—
512C2×#41C22×D5312yes—
513C22×Q8—531no—
514C22×Q8C4×D5311yescharacteristic
515C22×D4—21no—
516C22×D4—531no—
517C22×D4—1061no—
518C22×D4C4×D5311yescharacteristic
519C23×C4—21no—
520C23×C4—1061no—
521C23×C4C22×D5311yescharacteristic
522#135—1064no—
523#135—1064no—
524#135—1064no—
525#135—1064no—
526#135—1064no—
527#135—1064no—
528#135—1064no—
529#135—1064no—
530C2×Q16—534no—
531C2×Q16—1061no—
532C2×Q16—1061no—
533C2×Q16—1062no—
534C2×SD16—534no—
535C2×SD16—534no—
536C2×SD16—1061no—
537C2×SD16—1061no—
538C2×SD16—1062no—
539C2×SD16—1061no—
540C2×SD16—1061no—
541C2×SD16—1062no—
542C2×D8—534no—
543C2×D8—1061no—
544C2×D8—1061no—
545C2×D8—1062no—
546C2×M16—21no—
547C2×M16—21no—
548C2×M16—21no—
549C2×M16C22⋊D5312yes—
550C2×M16C22⋊D5312yes—
551C2×M16C22×D5312yes—
552C22×C8—21no—
553C22×C8—531no—
554C22×C8—531no—
555C22×C8—532no—
556C22×C8—531no—
557C22×C8—531no—
558C22×C8—532no—
559C22×C8—531no—
560C22×C8—531no—
561C22×C8—532no—
562C22×C8—532no—
563#117—21no—
564#117—21no—
565#117—21no—
566#117—532no—
567#117—532no—
568#117—532no—
569#117—1061no—
570#117—1061no—
571#117—1061no—
572#117—1061no—
573#117—1061no—
574#117C22×D5312yes—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1061no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—532no—
580C2×C22⋊C4—1061no—
581C2×C42—21no—
582C2×C42—1061no—
583C2×C42—1061no—
584#107—1064no—
585#106—1064no—
586#104—28no—
587#104—1068no—
588#99—1068no—
589#99—1068no—
590#97—1064no—
591C4×C8—1064no—
592C24—21no—
593C24—1061no—
594C24D4×D5311yescharacteristic
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—41no—
611#41—1062no—
612#41—1062no—
613#41—1062no—
614#41—1062no—
615#41—1062no—
616#41—1062no—
617#41—1062no—
618#41—1062no—
619#41—2121no—
620#41—2121no—
621#41—2121no—
622#41—2121no—
623#41—2121no—
624#41—2121no—
625#41—2121no—
626#41—2121no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—532no—
633C2×Q8—1061no—
634C2×Q8—1061no—
635C2×Q8—1061no—
636C2×Q8—1061no—
637C2×Q8—1061no—
638C2×Q8C2×C4×D5312yes—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4—41no—
649C2×D4—41no—
650C2×D4—532no—
651C2×D4—1062no—
652C2×D4—1062no—
653C2×D4—1061no—
654C2×D4—1061no—
655C2×D4—1061no—
656C2×D4—1061no—
657C2×D4—1061no—
658C2×D4—2121no—
659C2×D4—2121no—
660C2×D4—2121no—
661C2×D4—2121no—
662C2×D4C2×C4×D5312yes—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—1061no—
672C22×C4—1062no—
673C22×C4—1062no—
674C22×C4—1062no—
675C22×C4—2121no—
676C22×C4—2121no—
677C22×C4—2121no—
678C22×C4—2121no—
679C22×C4—2121no—
680C22×C4C2×C4×D5311yescharacteristic
681C22×C4C2×C4×D5311yescharacteristic
682C22×C4#1171994511yescharacteristic
683C22×C4#1171994511yescharacteristic
684C22×C4D4×D5311yescharacteristic
685C22×C4D4×D5311yescharacteristic
686C22×C4D4×D5311yescharacteristic
687C22×C4D4×D5311yescharacteristic
688C22×C4D4×D5311yescharacteristic
689C22×C4#1171994711yescharacteristic
690C22×C4#1171994711yescharacteristic
691C22×C4C2×C22⋊D5311yescharacteristic
692C22×C4C2×C22⋊D5311yescharacteristic
693C22×C4C23×D5311yescharacteristic
694Q16—1064no—
695Q16—1064no—
696SD16—1064no—
697SD16—1064no—
698SD16—1064no—
699SD16—1064no—
700D8—1064no—
701D8—1064no—
702M16—22no—
703M16—22no—
704M16—22no—
705M16C2×C22⋊D5314yes—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—531no—
710C2×C8—531no—
711C2×C8—532no—
712C2×C8—531no—
713C2×C8—531no—
714C2×C8—532no—
715C2×C8—532no—
716C2×C8—532no—
717C2×C8—532no—
718C2×C8—532no—
719C2×C8—532no—
720C2×C8—532no—
721C2×C8—532no—
722C2×C8—532no—
723C2×C8—532no—
724C2×C8—532no—
725C4⋊C4—22no—
726C4⋊C4—41no—
727C4⋊C4—1062no—
728C4⋊C4—1062no—
729C4⋊C4—1062no—
730C4⋊C4—2121no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—534no—
734C22⋊C4—1062no—
735C22⋊C4—1062no—
736C22⋊C4—2121no—
737C42—22no—
738C42—41no—
739C42—1062no—
740C42—1062no—
741C42—1062no—
742C42—2121no—
743C23—22no—
744C23—42no—
745C23—41no—
746C23—41no—
747C23—82no—
748C23—1062no—
749C23—4242no—
750C23—2121no—
751C23—2121no—
752C23#1313317711yescharacteristic
753C23#1313317711yescharacteristic
754C23#1313319011yescharacteristic
755C23#1313319011yescharacteristic
756C23#1313321311yescharacteristic
757C23#1313321311yescharacteristic
758C23C2×D4×D5311yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763Q8—1062no—
764Q8—1062no—
765Q8—2121no—
766Q8—2121no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—41no—
774D4—41no—
775D4—1062no—
776D4—1062no—
777D4—2122no—
778D4—2122no—
779D4—2122no—
780D4—2122no—
781D4—2121no—
782D4—2121no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—82no—
792C2×C4—1062no—
793C2×C4—1064no—
794C2×C4—4242no—
795C2×C4—2122no—
796C2×C4—2124no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2122no—
800C2×C4—2122no—
801C2×C4—2122no—
802C2×C4—2122no—
803C2×C4C22⋊C4×D5311yescharacteristic
804C2×C4C22⋊C4×D5311yescharacteristic
805C2×C4C22⋊C4×D5311yescharacteristic
806C2×C4C22⋊C4×D5311yescharacteristic
807C2×C4#1313317711yescharacteristic
808C2×C4#1313317711yescharacteristic
809C2×C4C4×C22⋊D5311yescharacteristic
810C2×C4C4×C22⋊D5311yescharacteristic
811C2×C4C4×C22⋊D5311yescharacteristic
812C2×C4C4×C22⋊D5311yescharacteristic
813C2×C4#1313318911yescharacteristic
814C2×C4#1313318911yescharacteristic
815C2×C4#1313318911yescharacteristic
816C2×C4#1313318911yescharacteristic
817C2×C4#1313319011yescharacteristic
818C2×C4#1313319011yescharacteristic
819C2×C4#1313320311yescharacteristic
820C2×C4#1313320311yescharacteristic
821C2×C4#1313320311yescharacteristic
822C2×C4#1313320311yescharacteristic
823C2×C4#1313321311yescharacteristic
824C2×C4#1313321311yescharacteristic
825C2×C4C22×C4×D5311yescharacteristic
826C2×C4C2×D4×D5311yescharacteristic
827C2×C4C2×D4×D5311yescharacteristic
828C2×C4C22×C22⋊D5311yescharacteristic
829C2×C4C2×#1171994711yescharacteristic
830C2×C4C2×#1171994511yescharacteristic
831C8—24no—
832C8—532no—
833C8—532no—
834C8—532no—
835C8—532no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—42no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—4242no—
848C22—4242no—
849C22—4242no—
850C22—2122no—
851C22#1681052311yescharacteristic
852C22#1681052311yescharacteristic
853C22#1681052311yescharacteristic
854C22#1681052311yescharacteristic
855C22C2×#1313317711yescharacteristic
856C22C2×#1313319011yescharacteristic
857C22C2×#1313321311yescharacteristic
858C4—42no—
859C4—82no—
860C4—4242no—
861C4—2124no—
862C4—2122no—
863C4#1681052311yescharacteristic
864C4#1681052311yescharacteristic
865C4#1681052311yescharacteristic
866C4#1681052311yescharacteristic
867C4C2×C22⋊C4×D5311yescharacteristic
868C4C2×C4×C22⋊D5311yescharacteristic
869C4C2×#1313318911yescharacteristic
870C4C2×#1313320311yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—21no—
875C2—21no—
876C2—21no—
877C2—82no—
878C2—4242no—
879C2#2027561212yesdirect product factor
880C2C2×#1681052311yescharacteristic
subgroupG/H
centerC2×C4#13133189
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#421C2
socleC22×C53#390
prime radicalC22×#13133237C2
cosocleC22×C4×C53C24
hypercenterC2×#421D53
hypocenterC53C2×#1976
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16810659C2semidirect
3. C2×#16810639C2semidirect
4. C2×#16810597C2semidirect
5. C2×#16810596C2semidirect
6. C2×#16810581C2semidirect
7. #20275612C2direct (N × H)
8. C2×C53×#421C2semidirect
16. C2×#13133237C4semidirect
18. C22×#11719925C4semidirect
19. C22×#11719923C4semidirect
20. C22×#11719924C4semidirect
21. C22×#11719922C4semidirect
26. #16810659C22semidirect
30. #16810639C22semidirect
33. #16810597C22semidirect
35. #16810596C22semidirect
39. #16810581C22semidirect
46. C53×#421C22semidirect
75. C2×#11719925C2×C4semidirect
79. C2×#11719923C2×C4semidirect
83. C2×#11719924C2×C4semidirect
87. C2×#11719922C2×C4semidirect
434. C2×#421D53semidirect
446. C2×C53#1976semidirect
475. #421C2×D53semidirect
488. C53C2×#1976semidirect
879. C2#20275612direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332372
C2×#168106592
C2×#168106392
C2×#168105972
C2×#168105962
C2×#168105812
#202756122
C2×C53×#4212
C2×#197653