Finite Group Databasebeta

← #25003440

Subgroups — #25003440

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143114C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3C2×#14582873C211yesmaximal, characteristic, complemented
4#19137177C211yesmaximal, characteristic, complemented
5C2×#14582671C211yesmaximal, characteristic, complemented
6#19134306C211yesmaximal, characteristic, complemented
7C22×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582908—21no—
13#14582904—22no—
14#14582904—22no—
15#14582904—21no—
16#14582900—22no—
17#14582895—22no—
18C2×#13063246—22no—
19#14582873—22no—
20#14582873—22no—
21C2×#13063240—22no—
22#14582802—22no—
23#14582802—22no—
24#14582755—22no—
25#14582671—22no—
26#14582660—22no—
27C22×#41×C43C2211yescharacteristic
28C23×D4×C43C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C43—22no—
30C2×AGL(1,ℤ/8)×C43—22no—
31C2×AGL(1,ℤ/8)×C43—22no—
32C2×AGL(1,ℤ/8)×C43—22no—
33C2×AGL(1,ℤ/8)×C43—22no—
34C2×AGL(1,ℤ/8)×C43C414yescomplemented
35C22×SD16×C43—21no—
36C22×D8×C43—21no—
37C22×M16×C43C2211yescharacteristic
38C2×#10621877—21no—
39C2×#10621877—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C22×C43⋊C8D412yes—
45#13063284—21no—
46#13063284—21no—
47#13063284—21no—
48#13063284—21no—
49#13063284—21no—
50#13063284—21no—
51#13063284—21no—
52#13063284—21no—
53#13063284—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284D412yes—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43D412yes—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—28no—
63C2×C22⋊Dic43D412yes—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66C2×C4×Dic43—21no—
67#13063249—24no—
68#13063246—28no—
69#13063246—24no—
70#13063240—28no—
71C25×C43—21no—
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×C43C2×C412yes—
83C2×#41×C43D412yes—
84C22×Q8×C43D411yescharacteristic
85C22×D4×C43—21no—
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43C2×C412yes—
98C22×D4×C43D412yes—
99C22×D4×C43D412yes—
100C22×D4×C43D411yescharacteristic
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103AGL(1,ℤ/8)×C43—28no—
104AGL(1,ℤ/8)×C43—28no—
105AGL(1,ℤ/8)×C43—28no—
106AGL(1,ℤ/8)×C43—28no—
107C2×SD16×C43—24no—
108C2×SD16×C43—24no—
109C2×SD16×C43—24no—
110C2×D8×C43—24no—
111C2×D8×C43—24no—
112C2×D8×C43—24no—
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43C2×C412yes—
117C2×M16×C43D412yes—
118C2×M16×C43D412yes—
119C22×C8×C43—21no—
120C24×C43—22no—
121C24×C43—22no—
122C24×C43—21no—
123C24×C43—22no—
124C24×C43—41no—
125C24×C43—41no—
126C24×C43—41no—
127C24×C43—41no—
128C24×C43—84no—
129C24×C43C2×D411yescharacteristic
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—41no—
139#41×C43—41no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C22⋊C412yescomplemented
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—22no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—21no—
170C2×D4×C43—22no—
171C2×D4×C43—22no—
172C2×D4×C43—22no—
173C2×D4×C43—21no—
174C2×D4×C43—41no—
175C2×D4×C43—41no—
176C2×D4×C43—41no—
177C2×D4×C43—41no—
178C2×D4×C43—41no—
179C2×D4×C43—41no—
180C2×D4×C43—41no—
181C2×D4×C43—41no—
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43—41no—
185C2×D4×C43—41no—
186C2×D4×C43—41no—
187C2×D4×C43—41no—
188C2×D4×C43—41no—
189C2×D4×C43—41no—
190C2×D4×C43C22⋊C414yes—
191C2×D4×C43C22⋊C412yescomplemented
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—41no—
196C22×C4×C43—41no—
197C22×C4×C43—41no—
198C22×C4×C43—41no—
199C22×C4×C43C22×C411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43#4111yescharacteristic
210C22×C4×C43#4111yescharacteristic
211C22×C4×C43#4111yescharacteristic
212C22×C4×C43#4111yescharacteristic
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—41no—
216SD16×C43—216no—
217D8×C43—216no—
218M16×C43—22no—
219M16×C43—22no—
220M16×C43—22no—
221M16×C43C22⋊C414yescomplemented
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—41no—
229C22⋊Dic43—41no—
230C22⋊Dic43—41no—
231C22⋊Dic43—88no—
232C4⋊Dic43—22no—
233C4⋊Dic43—22no—
234C4⋊Dic43—22no—
235C4⋊Dic43—41no—
236C4⋊Dic43—41no—
237C4⋊Dic43—41no—
238C4×Dic43—22no—
239C4×Dic43—41no—
240C4×Dic43—41no—
241C4×Dic43—41no—
242C4×Dic43—41no—
243C4×Dic43—41no—
244#10621877—41no—
245#10621877—41no—
246#10621877—41no—
247#10621877—41no—
248C2×C43⋊C8—22no—
249C2×C43⋊C8—22no—
250C2×C43⋊C8—22no—
251C23×C43—24no—
252C23×C43—22no—
253C23×C43—42no—
254C23×C43—48no—
255C23×C43—42no—
256C23×C43—42no—
257C23×C43—41no—
258C23×C43—42no—
259C23×C43—42no—
260C23×C43—42no—
261C23×C43—41no—
262C23×C43—42no—
263C23×C43—82no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43C4×D411yescharacteristic
271C23×C43#12011yescharacteristic
272C23×C43#12011yescharacteristic
273C23×C43#12111yescharacteristic
274C23×C43#12111yescharacteristic
275C23×C43#12111yescharacteristic
276C23×C43#12711yescharacteristic
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—41no—
280Q8×C43—41no—
281D4×C43—22no—
282D4×C43—24no—
283D4×C43—24no—
284D4×C43—22no—
285D4×C43—42no—
286D4×C43—42no—
287D4×C43—42no—
288D4×C43—42no—
289D4×C43—42no—
290D4×C43—42no—
291D4×C43—42no—
292D4×C43—41no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—41no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43C2×C22⋊C411yescharacteristic
305C2×C4×C43C2×C22⋊C411yescharacteristic
306C2×C4×C43C2×C22⋊C411yescharacteristic
307C2×C4×C43C4×D411yescharacteristic
308C2×C4×C43C4×D411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12011yescharacteristic
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12311yescharacteristic
326C2×C4×C43#12311yescharacteristic
327C2×C4×C43#12311yescharacteristic
328C2×C4×C43#12311yescharacteristic
329C2×C4×C43#12411yescharacteristic
330C2×C4×C43#12411yescharacteristic
331C2×C4×C43#12711yescharacteristic
332C2×Dic43—44no—
333C2×Dic43—44no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—82no—
338C8×C43—24no—
339C43⋊C8—42no—
340#11030—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—48no—
349C22×C43—44no—
350C22×C43—42no—
351C22×C43—82no—
352C22×C43—84no—
353C22×C43—82no—
354C22×C43—84no—
355C22×C43—84no—
356C22×C43—84no—
357C22×C43—84no—
358C22×C43—84no—
359C22×C43—82no—
360C22×C43#38611yescharacteristic
361C22×C43#38611yescharacteristic
362C22×C43#39011yescharacteristic
363C22×C43#39211yescharacteristic
364C22×C43#39211yescharacteristic
365C22×C43#39211yescharacteristic
366C22×C43#39411yescharacteristic
367C4×C43—42no—
368C4×C43#37911yescharacteristic
369C4×C43#38611yescharacteristic
370C4×C43#38611yescharacteristic
371C4×C43#39011yescharacteristic
372C4×C43#39211yescharacteristic
373C4×C43#39411yescharacteristic
374C4×C43#39411yescharacteristic
375C4×C43#39411yescharacteristic
376Dic43—82no—
377Dic43—82no—
378Dic43—82no—
379C22×AGL(1,ℤ/8)D4311yescharacteristic
380#2896—431no—
381C2×#418—431no—
382C2×#410—431no—
383#2309—431no—
384C2×#344—431no—
385#1733—431no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43—21no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—84no—
393C2×C43—82no—
394C2×C43#143811yescharacteristic
395C2×C43#200812yes—
396C22×#41C2×D4311yescharacteristic
397C23×D4C2×D4311yescharacteristic
398C2×AGL(1,ℤ/8)—22no—
399C2×AGL(1,ℤ/8)—22no—
400C2×AGL(1,ℤ/8)—22no—
401C2×AGL(1,ℤ/8)—22no—
402C2×AGL(1,ℤ/8)—22no—
403C2×AGL(1,ℤ/8)Dic4314yescomplemented
404C22×SD16—21no—
405C22×D8—21no—
406C22×M16—431no—
407C22×M16C2×D4311yescharacteristic
408C2×#117—431no—
409C2×#117—431no—
410C2×#117—431no—
411#419—861no—
412#418—862no—
413#418—862no—
414#418—861no—
415#417—862no—
416#416—862no—
417C2×#102—862no—
418#410—862no—
419#410—862no—
420C2×#99—862no—
421#390—862no—
422#390—862no—
423#379—862no—
424#344—862no—
425#339—862no—
426C43#1103011yescharacteristic, complemented, Sylow
427C25—21no—
428C2×#41—21no—
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×#41C2×Dic4312yes—
439C2×#41C22⋊D4312yes—
440C22×Q8C22⋊D4311yescharacteristic
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C2×Dic4312yes—
454C22×D4C22⋊D4312yes—
455C22×D4C22⋊D4312yes—
456C22×D4C22⋊D4311yescharacteristic
457C23×C4—21no—
458C23×C4C22×D4311yescharacteristic
459AGL(1,ℤ/8)—28no—
460AGL(1,ℤ/8)—28no—
461AGL(1,ℤ/8)—28no—
462AGL(1,ℤ/8)—28no—
463C2×SD16—24no—
464C2×SD16—24no—
465C2×SD16—24no—
466C2×D8—24no—
467C2×D8—24no—
468C2×D8—24no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—861no—
473C2×M16—861no—
474C2×M16—861no—
475C2×M16—861no—
476C2×M16—861no—
477C2×M16—861no—
478C2×M16C2×Dic4312yes—
479C2×M16C22⋊D4312yes—
480C2×M16C22⋊D4312yes—
481C22×C8—21no—
482C22×C8—432no—
483#117—432no—
484#117—861no—
485#117—861no—
486#117—861no—
487#117—861no—
488#117—861no—
489#117—861no—
490#117—861no—
491#117—861no—
492#117—861no—
493#117—861no—
494#117—861no—
495C2×C4⋊C4—432no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C22⋊C4—432no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—868no—
501C2×C22⋊C4—861no—
502C2×C42—861no—
503C2×C42—861no—
504C2×C42—861no—
505#103—864no—
506#102—868no—
507#102—864no—
508#99—868no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—22no—
513C24—41no—
514C24—41no—
515C24—41no—
516C24—41no—
517C24—84no—
518C24D4×D4311yescharacteristic
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C22⋊Dic4312yescomplemented
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4C22⋊Dic4314yes—
580C2×D4C22⋊Dic4312yescomplemented
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—1721no—
591C22×C4D4×D4311yescharacteristic
592C22×C4D4×D4311yescharacteristic
593C22×C4D4×D4311yescharacteristic
594C22×C4#1062190011yescharacteristic
595C22×C4#1062190011yescharacteristic
596C22×C4#1062190011yescharacteristic
597C22×C4#1062190011yescharacteristic
598C22×C4C22×Dic4311yescharacteristic
599C22×C4C2×C22⋊D4311yescharacteristic
600C22×C4C2×C22⋊D4311yescharacteristic
601C22×C4C2×C22⋊D4311yescharacteristic
602C22×C4C2×C22⋊D4311yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605SD16—216no—
606D8—216no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—1721no—
611M16—1721no—
612M16—1721no—
613M16—1721no—
614M16C22⋊Dic4314yescomplemented
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8—862no—
621C4⋊C4—862no—
622C4⋊C4—862no—
623C4⋊C4—862no—
624C4⋊C4—1721no—
625C4⋊C4—1721no—
626C4⋊C4—1721no—
627C22⋊C4—862no—
628C22⋊C4—862no—
629C22⋊C4—862no—
630C22⋊C4—3448no—
631C22⋊C4—1721no—
632C22⋊C4—1721no—
633C22⋊C4—1721no—
634C42—862no—
635C42—1721no—
636C42—1721no—
637C42—1721no—
638C42—1721no—
639C42—1721no—
640C23—24no—
641C23—22no—
642C23—42no—
643C23—48no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—82no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23D4×Dic4311yescharacteristic
660C23#1306329311yescharacteristic
661C23#1306329311yescharacteristic
662C23#1306329611yescharacteristic
663C23#1306329711yescharacteristic
664C23#1306329711yescharacteristic
665C23#1306332111yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670D4—22no—
671D4—24no—
672D4—24no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—41no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—41no—
685D4—42no—
686C2×C4—22no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—3442no—
694C2×C4—1724no—
695C2×C4—1724no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4C2×C22⋊Dic4311yescharacteristic
700C2×C4C2×C22⋊Dic4311yescharacteristic
701C2×C4C2×C22⋊Dic4311yescharacteristic
702C2×C4D4×Dic4311yescharacteristic
703C2×C4D4×Dic4311yescharacteristic
704C2×C4D4×Dic4311yescharacteristic
705C2×C4#1306329311yescharacteristic
706C2×C4#1306329311yescharacteristic
707C2×C4#1306329411yescharacteristic
708C2×C4#1306329411yescharacteristic
709C2×C4#1306329411yescharacteristic
710C2×C4#1306329411yescharacteristic
711C2×C4#1306329611yescharacteristic
712C2×C4#1306329611yescharacteristic
713C2×C4#1306329611yescharacteristic
714C2×C4#1306329711yescharacteristic
715C2×C4#1306329711yescharacteristic
716C2×C4#1306329711yescharacteristic
717C2×C4#1306329711yescharacteristic
718C2×C4#1306329711yescharacteristic
719C2×C4#1306329711yescharacteristic
720C2×C4#1306330611yescharacteristic
721C2×C4#1306330611yescharacteristic
722C2×C4#1306330611yescharacteristic
723C2×C4#1306330611yescharacteristic
724C2×C4#1306331211yescharacteristic
725C2×C4#1306331211yescharacteristic
726C2×C4#1306332111yescharacteristic
727C8—24no—
728C8—1722no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—48no—
737C22—42no—
738C22—44no—
739C22—82no—
740C22—84no—
741C22—84no—
742C22—84no—
743C22—84no—
744C22—84no—
745C22—82no—
746C22—84no—
747C22—82no—
748C22#1458277911yescharacteristic
749C22#1458277911yescharacteristic
750C22#1458280211yescharacteristic
751C22#1458280711yescharacteristic
752C22#1458280711yescharacteristic
753C22#1458280711yescharacteristic
754C22#1458281311yescharacteristic
755C4—42no—
756C4—3442no—
757C4—3442no—
758C4—3442no—
759C4#1458275511yescharacteristic
760C4#1458277911yescharacteristic
761C4#1458277911yescharacteristic
762C4#1458280211yescharacteristic
763C4#1458280711yescharacteristic
764C4#1458281311yescharacteristic
765C4#1458281311yescharacteristic
766C4#1458281311yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—84no—
774C2—82no—
775C2#1913283611yescharacteristic
776C2#1913564612yes—
subgroupG/H
centerC22#14582807
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC22×AGL(1,ℤ/8)×C43C2
socleC22×C43#392
cosocleC23×C4×C43C23
hypercenterC22×AGL(1,ℤ/8)D43
hypocenterC43#11030
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19143114C2semidirect
2. C2×#14582904C2semidirect
3. C2×#14582873C2semidirect
4. #19137177C2semidirect
5. C2×#14582671C2semidirect
6. #19134306C2semidirect
34. C2×AGL(1,ℤ/8)×C43C4semidirect
151. C2×Q8×C43C22⋊C4semidirect
191. C2×D4×C43C22⋊C4semidirect
221. M16×C43C22⋊C4semidirect
403. C2×AGL(1,ℤ/8)Dic43semidirect
426. C43#11030semidirect
540. C2×Q8C22⋊Dic43semidirect
580. C2×D4C22⋊Dic43semidirect
614. M16C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
#191431142
C2×#145829042
C2×#145828732
#191371772
C2×#145826712
#191343062
C22×AGL(1,ℤ/8)×C432
#1103043