Finite Group Databasebeta

← #25003375

Subgroups — #25003375

Order 11008.

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×#14582916C211yesmaximal, characteristic, complemented
2C22×#13063252C211yesmaximal, characteristic, complemented
3C2×#14582873C211yesmaximal, characteristic, complemented
4#19137086C211yesmaximal, characteristic, complemented
5C2×#14582671C211yesmaximal, characteristic, complemented
6C2×#14582660C211yesmaximal, characteristic, complemented
7C2×C43×#575C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C22×C4×Dic43C2211yescharacteristic
12#14582916—22no—
13#14582916—22no—
14C2×#13063252—22no—
15C2×#13063252—22no—
16C2×#13063252—22no—
17C2×#13063252—22no—
18#14582873—22no—
19#14582873—22no—
20C2×#13063240—22no—
21#14582806—21no—
22#14582802—21no—
23#14582779—22no—
24C4×C22⋊Dic43—22no—
25#14582671—22no—
26#14582660—22no—
27C22×#41×C43C2211yescharacteristic
28C22×#41×C43C2211yescharacteristic
29C43×#575—22no—
30C43×#575—22no—
31C43×#575—22no—
32C43×#575—22no—
33C2×#137×C43—21no—
34C2×#137×C43C412yescomplemented
35C2×AGL(1,ℤ/8)×C43—21no—
36C2×AGL(1,ℤ/8)×C43C412yescomplemented
37C2×#135×C43—22no—
38C22×M16×C43C2211yescharacteristic
39C23×Dic43—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877D412yes—
46C22×C43⋊C8—21no—
47#13063284—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284—21no—
53#13063284—21no—
54#13063284D412yes—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—24no—
59C2×C22⋊Dic43D412yes—
60C2×C4×Dic43—21no—
61C2×C4×Dic43—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67C2×C4×Dic43D412yes—
68#13063252—28no—
69#13063252—28no—
70#13063240—28no—
71C43⋊#95—24no—
72C2×#41×C43—21no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43—21no—
83C2×#41×C43—21no—
84C2×#41×C43—21no—
85C2×#41×C43—21no—
86C2×#41×C43—21no—
87C2×#41×C43—21no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43—21no—
92C2×#41×C43C2×C412yes—
93C2×#41×C43D412yes—
94C2×#41×C43D412yes—
95C2×#41×C43D412yes—
96C22×Q8×C43C2×C411yescharacteristic
97C22×Q8×C43D411yescharacteristic
98C22×D4×C43—21no—
99C22×D4×C43—21no—
100C22×D4×C43C2×C411yescharacteristic
101C22×D4×C43D411yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43C2311yescharacteristic
105#137×C43—24no—
106#137×C43—24no—
107#137×C43—24no—
108#137×C43—24no—
109AGL(1,ℤ/8)×C43—24no—
110AGL(1,ℤ/8)×C43—24no—
111AGL(1,ℤ/8)×C43—24no—
112AGL(1,ℤ/8)×C43—24no—
113#135×C43—28no—
114#135×C43—28no—
115C2×Q16×C43—22no—
116C2×SD16×C43—22no—
117C2×SD16×C43—22no—
118C2×D8×C43—22no—
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43C2×C412yes—
123C2×M16×C43D412yes—
124C2×M16×C43D412yes—
125C22×C8×C43—21no—
126C24×C43—21no—
127C24×C43—21no—
128C24×C43C2×D411yescharacteristic
129#41×C43—22no—
130#41×C43—22no—
131#41×C43—22no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—22no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—22no—
144#41×C43—22no—
145#41×C43—41no—
146#41×C43—41no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156#41×C43—41no—
157#41×C43—41no—
158#41×C43—41no—
159#41×C43—41no—
160#41×C43—41no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43C22⋊C412yes—
172C2×Q8×C43C22⋊C412yescomplemented
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—22no—
176C2×D4×C43—22no—
177C2×D4×C43—22no—
178C2×D4×C43—22no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—41no—
188C2×D4×C43—41no—
189C2×D4×C43—41no—
190C2×D4×C43—41no—
191C2×D4×C43—41no—
192C2×D4×C43—41no—
193C2×D4×C43—41no—
194C2×D4×C43—41no—
195C2×D4×C43C22⋊C412yes—
196C2×D4×C43C22⋊C412yescomplemented
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—41no—
204C22×C4×C43—41no—
205C22×C4×C43—41no—
206C22×C4×C43—41no—
207C22×C4×C43—41no—
208C22×C4×C43—41no—
209C22×C4×C43—41no—
210C22×C4×C43—41no—
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43#4111yescharacteristic
222C22×C4×C43#4111yescharacteristic
223C22×C4×C43#4111yescharacteristic
224C22×C4×C43#4111yescharacteristic
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—44no—
228C22×Dic43—41no—
229C22×Dic43—41no—
230C22×Dic43—41no—
231Q16×C43—28no—
232SD16×C43—28no—
233SD16×C43—28no—
234D8×C43—28no—
235M16×C43—22no—
236M16×C43—22no—
237M16×C43—22no—
238M16×C43C22⋊C414yescomplemented
239C2×C8×C43—22no—
240C2×C8×C43—22no—
241C2×C8×C43—22no—
242C22⋊Dic43—22no—
243C22⋊Dic43—22no—
244C22⋊Dic43—22no—
245C22⋊Dic43—48no—
246C22⋊Dic43—41no—
247C4⋊Dic43—22no—
248C4⋊Dic43—41no—
249C4⋊Dic43—41no—
250C4⋊Dic43—41no—
251C4×Dic43—22no—
252C4×Dic43—22no—
253C4×Dic43—22no—
254C4×Dic43—41no—
255C4×Dic43—41no—
256C4×Dic43—41no—
257C4×Dic43—41no—
258C4×Dic43—41no—
259#10621877—22no—
260#10621877—22no—
261#10621877—41no—
262#10621877—41no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—41no—
265C2×C43⋊C8—41no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—42no—
269C23×C43—44no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—82no—
275C23×C43C4×D411yescharacteristic
276C23×C43#12011yescharacteristic
277C23×C43#12011yescharacteristic
278C23×C43#12111yescharacteristic
279C23×C43#12111yescharacteristic
280C23×C43#12111yescharacteristic
281C23×C43#12711yescharacteristic
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—41no—
287Q8×C43—41no—
288Q8×C43—41no—
289Q8×C43—41no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—22no—
293D4×C43—22no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—42no—
301D4×C43—42no—
302D4×C43—41no—
303D4×C43—41no—
304D4×C43—41no—
305D4×C43—41no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43C4×D411yescharacteristic
325C2×C4×C43C4×D411yescharacteristic
326C2×C4×C43#12011yescharacteristic
327C2×C4×C43#12011yescharacteristic
328C2×C4×C43#12011yescharacteristic
329C2×C4×C43#12011yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43#12011yescharacteristic
332C2×C4×C43#12111yescharacteristic
333C2×C4×C43#12111yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12111yescharacteristic
341C2×C4×C43#12311yescharacteristic
342C2×C4×C43#12311yescharacteristic
343C2×C4×C43#12311yescharacteristic
344C2×C4×C43#12311yescharacteristic
345C2×C4×C43#12411yescharacteristic
346C2×C4×C43#12411yescharacteristic
347C2×C4×C43#12711yescharacteristic
348C2×Dic43—24no—
349C2×Dic43—42no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43—42no—
353C2×Dic43—44no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—82no—
357C8×C43—24no—
358C43⋊C8—42no—
359#11019—431nomaximal, Sylow
360C22×C43—22no—
361C22×C43—22no—
362C22×C43—22no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—41no—
367C22×C43—44no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—82no—
371C22×C43—82no—
372C22×C43—82no—
373C22×C43—82no—
374C22×C43—82no—
375C22×C43#38611yescharacteristic
376C22×C43#38611yescharacteristic
377C22×C43#39011yescharacteristic
378C22×C43#39211yescharacteristic
379C22×C43#39211yescharacteristic
380C22×C43#39211yescharacteristic
381C22×C43#39411yescharacteristic
382C4×C43—42no—
383C4×C43—42no—
384C4×C43#37911yescharacteristic
385C4×C43#38611yescharacteristic
386C4×C43#38611yescharacteristic
387C4×C43#39011yescharacteristic
388C4×C43#39211yescharacteristic
389C4×C43#39411yescharacteristic
390C4×C43#39411yescharacteristic
391C4×C43#39411yescharacteristic
392Dic43—44no—
393Dic43—82no—
394Dic43—82no—
395C2×#575D4311yescharacteristic
396C2×#421—431no—
397C22×#104—431no—
398C2×#410—431no—
399#2297—431no—
400C2×#344—431no—
401C2×#339—431no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—82no—
409C2×C43—82no—
410C2×C43#143811yescharacteristic
411C2×C43#190612yes—
412C22×#41C2×D4311yescharacteristic
413C22×#41C2×D4311yescharacteristic
414#575—22no—
415#575—22no—
416#575—22no—
417#575—22no—
418C2×#137—21no—
419C2×#137Dic4312yescomplemented
420C2×AGL(1,ℤ/8)—21no—
421C2×AGL(1,ℤ/8)Dic4312yescomplemented
422C2×#135—22no—
423C22×M16—431no—
424C22×M16C2×D4311yescharacteristic
425C2×#117—431no—
426C2×#117—431no—
427C22×C42—431no—
428#421—862no—
429#421—862no—
430C2×#104—862no—
431C2×#104—862no—
432C2×#104—862no—
433C2×#104—862no—
434#410—862no—
435#410—862no—
436C2×#99—862no—
437#391—861no—
438#390—861no—
439#386—862no—
440C4×C22⋊C4—862no—
441#344—862no—
442#339—862no—
443C43#1101911yescharacteristic, complemented, Sylow
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×#41—21no—
463C2×#41—21no—
464C2×#41C2×Dic4312yes—
465C2×#41C22⋊D4312yes—
466C2×#41C22⋊D4312yes—
467C2×#41C22⋊D4312yes—
468C22×Q8C2×Dic4311yescharacteristic
469C22×Q8C22⋊D4311yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C2×Dic4311yescharacteristic
473C22×D4C22⋊D4311yescharacteristic
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—861no—
477C23×C4C22×D4311yescharacteristic
478#137—24no—
479#137—24no—
480#137—24no—
481#137—24no—
482AGL(1,ℤ/8)—24no—
483AGL(1,ℤ/8)—24no—
484AGL(1,ℤ/8)—24no—
485AGL(1,ℤ/8)—24no—
486#135—28no—
487#135—28no—
488C2×Q16—22no—
489C2×SD16—22no—
490C2×SD16—22no—
491C2×D8—22no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—432no—
496C2×M16—861no—
497C2×M16—861no—
498C2×M16—861no—
499C2×M16—861no—
500C2×M16—861no—
501C2×M16C2×Dic4312yes—
502C2×M16C22⋊D4312yes—
503C2×M16C22⋊D4312yes—
504C22×C8—21no—
505C22×C8—861no—
506#117—432no—
507#117—861no—
508#117—861no—
509#117—861no—
510#117—861no—
511#117—861no—
512#117—861no—
513#117—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C22⋊C4—432no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—864no—
519C2×C42—432no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42—861no—
524C2×C42—861no—
525C2×C42—861no—
526C2×C42—861no—
527#104—868no—
528#104—868no—
529#99—868no—
530#95—864no—
531C24—21no—
532C24—21no—
533C24D4×D4311yescharacteristic
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—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—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
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×Q8—21no—
576C2×Q8C22⋊Dic4312yes—
577C2×Q8C22⋊Dic4312yescomplemented
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
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—21no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4C22⋊Dic4312yes—
601C2×D4C22⋊Dic4312yescomplemented
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—1724no—
619C22×C4—1721no—
620C22×C4—1721no—
621C22×C4—1721no—
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4#1062190011yescharacteristic
626C22×C4#1062190011yescharacteristic
627C22×C4#1062190011yescharacteristic
628C22×C4#1062190011yescharacteristic
629C22×C4C22×Dic4311yescharacteristic
630C22×C4C2×C22⋊D4311yescharacteristic
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C2×C22⋊D4311yescharacteristic
634C22×C4C2×C22⋊D4311yescharacteristic
635C22×C4C2×C22⋊D4311yescharacteristic
636Q16—28no—
637SD16—28no—
638SD16—28no—
639D8—28no—
640M16—22no—
641M16—22no—
642M16—22no—
643M16—862no—
644M16—862no—
645M16—1721no—
646M16—1721no—
647M16C22⋊Dic4314yescomplemented
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—862no—
652C2×C8—1721no—
653C2×C8—1721no—
654C4⋊C4—862no—
655C4⋊C4—1721no—
656C4⋊C4—1721no—
657C4⋊C4—1721no—
658C22⋊C4—862no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—1728no—
662C22⋊C4—1721no—
663C42—862no—
664C42—862no—
665C42—862no—
666C42—1721no—
667C42—1721no—
668C42—1721no—
669C42—1721no—
670C42—1721no—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—44no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—82no—
680C23D4×Dic4311yescharacteristic
681C23#1306329311yescharacteristic
682C23#1306329311yescharacteristic
683C23#1306329611yescharacteristic
684C23#1306329711yescharacteristic
685C23#1306329711yescharacteristic
686C23#1306332111yescharacteristic
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—864no—
726C2×C4—3442no—
727C2×C4—1724no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1724no—
732C2×C4—1724no—
733C2×C4—1722no—
734C2×C4C2×C22⋊Dic4311yescharacteristic
735C2×C4C2×C22⋊Dic4311yescharacteristic
736C2×C4C2×C22⋊Dic4311yescharacteristic
737C2×C4D4×Dic4311yescharacteristic
738C2×C4D4×Dic4311yescharacteristic
739C2×C4D4×Dic4311yescharacteristic
740C2×C4#1306329311yescharacteristic
741C2×C4#1306329311yescharacteristic
742C2×C4#1306329411yescharacteristic
743C2×C4#1306329411yescharacteristic
744C2×C4#1306329411yescharacteristic
745C2×C4#1306329411yescharacteristic
746C2×C4#1306329611yescharacteristic
747C2×C4#1306329611yescharacteristic
748C2×C4#1306329611yescharacteristic
749C2×C4#1306329711yescharacteristic
750C2×C4#1306329711yescharacteristic
751C2×C4#1306329711yescharacteristic
752C2×C4#1306329711yescharacteristic
753C2×C4#1306329711yescharacteristic
754C2×C4#1306329711yescharacteristic
755C2×C4#1306330611yescharacteristic
756C2×C4#1306330611yescharacteristic
757C2×C4#1306330611yescharacteristic
758C2×C4#1306330611yescharacteristic
759C2×C4#1306331211yescharacteristic
760C2×C4#1306331211yescharacteristic
761C2×C4#1306332111yescharacteristic
762C8—24no—
763C8—1722no—
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#1458277911yescharacteristic
780C22#1458277911yescharacteristic
781C22#1458280211yescharacteristic
782C22#1458280711yescharacteristic
783C22#1458280711yescharacteristic
784C22#1458280711yescharacteristic
785C22#1458281311yescharacteristic
786C4—42no—
787C4—42no—
788C4—3442no—
789C4—3442no—
790C4—1724no—
791C4#1458275511yescharacteristic
792C4#1458277911yescharacteristic
793C4#1458277911yescharacteristic
794C4#1458280211yescharacteristic
795C4#1458280711yescharacteristic
796C4#1458281311yescharacteristic
797C4#1458281311yescharacteristic
798C4#1458281311yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—82no—
806C2—82no—
807C2#1913283611yescharacteristic
808C2#1913509812yes—
subgroupG/H
centerC2×C4#13063297
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#575C2
socleC22×C43#386
cosocleC23×C4×C43C23
hypercenterC2×#575D43
hypocenterC43#11019
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#14582916C2semidirect
2. C22×#13063252C2semidirect
3. C2×#14582873C2semidirect
4. #19137086C2semidirect
5. C2×#14582671C2semidirect
6. C2×#14582660C2semidirect
34. C2×#137×C43C4semidirect
36. C2×AGL(1,ℤ/8)×C43C4semidirect
172. C2×Q8×C43C22⋊C4semidirect
196. C2×D4×C43C22⋊C4semidirect
238. M16×C43C22⋊C4semidirect
419. C2×#137Dic43semidirect
421. C2×AGL(1,ℤ/8)Dic43semidirect
443. C43#11019semidirect
577. C2×Q8C22⋊Dic43semidirect
601. C2×D4C22⋊Dic43semidirect
647. M16C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829162
C22×#130632522
C2×#145828732
#191370862
C2×#145826712
C2×#145826602
C2×C43×#5752
#1101943