Finite Group Databasebeta

← #25003368

Subgroups — #25003368

Order 11008.

1270 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582916C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic, complemented
3#19143040C211yesmaximal, characteristic, complemented
4C2×#14582866C211yesmaximal, characteristic, complemented
5C2×#14582671C211yesmaximal, characteristic, complemented
6C2×#14582663C211yesmaximal, characteristic, complemented
7C2×C43×#575C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C23×C43⋊C8C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582916—22no—
13#14582916—22no—
14C2×#13063252—22no—
15#14582895—22no—
16#14582895—22no—
17C2×#13063249—21no—
18C2×#13063246—21no—
19#14582866—22no—
20#14582866—22no—
21#14582866—22no—
22#14582866—22no—
23#14582863—22no—
24C2×C22⋊(C43⋊C8)—22no—
25#14582671—22no—
26#14582663—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
39C2×#10621877—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877D412yes—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8D412yes—
59C22×C43⋊C8D412yes—
60#13063284—21no—
61#13063284—21no—
62#13063284—21no—
63#13063284D412yes—
64C2×C4⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C4×Dic43—21no—
67#13063252—28no—
68#13063249—24no—
69#13063246—24no—
70C22⋊(C43⋊C8)—28no—
71C22⋊(C43⋊C8)—28no—
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×C43#4111yescharacteristic
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⋊C412yes—
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⋊C412yes—
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×C43C2×D411yescharacteristic
222C22×C4×C43#4111yescharacteristic
223C22×C4×C43#4111yescharacteristic
224C22×C4×C43#4111yescharacteristic
225C22×Dic43—41no—
226Q16×C43—28no—
227SD16×C43—28no—
228SD16×C43—28no—
229D8×C43—28no—
230M16×C43—22no—
231M16×C43—22no—
232M16×C43—22no—
233M16×C43C22⋊C414yes—
234C2×C8×C43—22no—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C22⋊Dic43—22no—
238C22⋊Dic43—41no—
239C4⋊Dic43—22no—
240C4⋊Dic43—41no—
241C4×Dic43—22no—
242C4×Dic43—41no—
243#10621877—22no—
244#10621877—22no—
245#10621877—41no—
246#10621877—41no—
247#10621877—41no—
248#10621877—41no—
249#10621877—41no—
250#10621877—41no—
251C2×C43⋊C8—22no—
252C2×C43⋊C8—22no—
253C2×C43⋊C8—22no—
254C2×C43⋊C8—22no—
255C2×C43⋊C8—22no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—41no—
259C2×C43⋊C8—41no—
260C2×C43⋊C8—41no—
261C2×C43⋊C8—41no—
262C2×C43⋊C8—41no—
263C2×C43⋊C8—41no—
264C23×C43—22no—
265C23×C43—22no—
266C23×C43—42no—
267C23×C43—44no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—82no—
273C23×C43C4×D411yescharacteristic
274C23×C43#12111yescharacteristic
275C23×C43#12111yescharacteristic
276C23×C43#12111yescharacteristic
277C23×C43#12311yescharacteristic
278C23×C43#12311yescharacteristic
279C23×C43#12411yescharacteristic
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—22no—
283Q8×C43—22no—
284Q8×C43—41no—
285Q8×C43—41no—
286Q8×C43—41no—
287Q8×C43—41no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—42no—
300D4×C43—41no—
301D4×C43—41no—
302D4×C43—41no—
303D4×C43—41no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
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×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C4×D411yescharacteristic
322C2×C4×C43C4×D411yescharacteristic
323C2×C4×C43C4×D411yescharacteristic
324C2×C4×C43#12011yescharacteristic
325C2×C4×C43#12011yescharacteristic
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#12411yescharacteristic
344C2×C4×C43#12711yescharacteristic
345C2×C4×C43#12711yescharacteristic
346C2×Dic43—42no—
347C2×Dic43—82no—
348C8×C43—24no—
349C43⋊C8—42no—
350C43⋊C8—42no—
351C43⋊C8—42no—
352#11018—431nomaximal, Sylow
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—44no—
361C22×C43—44no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—82no—
365C22×C43—82no—
366C22×C43—82no—
367C22×C43—82no—
368C22×C43#38611yescharacteristic
369C22×C43#38611yescharacteristic
370C22×C43#39011yescharacteristic
371C22×C43#39211yescharacteristic
372C22×C43#39411yescharacteristic
373C22×C43#39411yescharacteristic
374C22×C43#39411yescharacteristic
375C4×C43—42no—
376C4×C43—42no—
377C4×C43#37911yescharacteristic
378C4×C43#38611yescharacteristic
379C4×C43#38611yescharacteristic
380C4×C43#39011yescharacteristic
381C4×C43#39211yescharacteristic
382C4×C43#39211yescharacteristic
383C4×C43#39211yescharacteristic
384C4×C43#39411yescharacteristic
385Dic43—82no—
386C2×#575D4311yescharacteristic
387C2×#421—431no—
388C2×#416—431no—
389#2879—431no—
390C2×#408—431no—
391C2×#344—431no—
392C2×#341—431no—
393C2×C43—21no—
394C2×C43—21no—
395C2×C43—21no—
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—21no—
399C2×C43—82no—
400C2×C43—82no—
401C2×C43#143811yescharacteristic
402C2×C43#188112yes—
403C22×#41C2×D4311yescharacteristic
404C22×#41C2×D4311yescharacteristic
405#575—22no—
406#575—22no—
407#575—22no—
408#575—22no—
409C2×#137—21no—
410C2×#137Dic4312yescomplemented
411C2×AGL(1,ℤ/8)—21no—
412C2×AGL(1,ℤ/8)Dic4312yescomplemented
413C2×#135—22no—
414C22×M16—431no—
415C22×M16—431no—
416C22×M16C2×D4311yescharacteristic
417C23×C8—431no—
418C2×#117—431no—
419#421—862no—
420#421—862no—
421C2×#104—862no—
422#416—862no—
423#416—862no—
424C2×#103—861no—
425C2×#102—861no—
426#408—862no—
427#408—862no—
428#408—862no—
429#408—862no—
430#407—862no—
431C2×C22⋊C8—862no—
432#344—862no—
433#341—862no—
434C43#1101811yescharacteristic, complemented, Sylow
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×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41C2×Dic4312yes—
456C2×#41C22⋊D4312yes—
457C2×#41C22⋊D4312yes—
458C2×#41C22⋊D4312yes—
459C22×Q8C2×Dic4311yescharacteristic
460C22×Q8C22⋊D4311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C2×Dic4311yescharacteristic
464C22×D4C22⋊D4311yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C22×D4311yescharacteristic
468#137—24no—
469#137—24no—
470#137—24no—
471#137—24no—
472AGL(1,ℤ/8)—24no—
473AGL(1,ℤ/8)—24no—
474AGL(1,ℤ/8)—24no—
475AGL(1,ℤ/8)—24no—
476#135—28no—
477#135—28no—
478C2×Q16—22no—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×D8—22no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—432no—
486C2×M16—861no—
487C2×M16—861no—
488C2×M16—861no—
489C2×M16—861no—
490C2×M16—861no—
491C2×M16—861no—
492C2×M16—861no—
493C2×M16—861no—
494C2×M16—861no—
495C2×M16—861no—
496C2×M16—861no—
497C2×M16C2×Dic4312yes—
498C2×M16C22⋊D4312yes—
499C2×M16C22⋊D4312yes—
500C22×C8—21no—
501C22×C8—432no—
502C22×C8—432no—
503C22×C8—861no—
504C22×C8—861no—
505C22×C8—861no—
506C22×C8—861no—
507C22×C8—861no—
508C22×C8—861no—
509C22×C8—861no—
510#117—432no—
511#117—861no—
512#117—861no—
513#117—861no—
514C2×C4⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—861no—
517#104—868no—
518#103—864no—
519#102—864no—
520C22⋊C8—868no—
521C22⋊C8—868no—
522C24—21no—
523C24—21no—
524C24#1062190011yescharacteristic
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
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—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—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C22⋊Dic4312yes—
568C2×Q8C22⋊Dic4312yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4C22⋊Dic4312yes—
592C2×D4C22⋊Dic4312yes—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—1721no—
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610C22×C4D4×D4311yescharacteristic
611C22×C4D4×D4311yescharacteristic
612C22×C4#1062190011yescharacteristic
613C22×C4#1062190011yescharacteristic
614C22×C4#1062190011yescharacteristic
615C22×C4C22×Dic4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C2×C22⋊D4311yescharacteristic
622Q16—28no—
623SD16—28no—
624SD16—28no—
625D8—28no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—862no—
630M16—862no—
631M16—1721no—
632M16—1721no—
633M16—1721no—
634M16—1721no—
635M16—1721no—
636M16—1721no—
637M16C22⋊Dic4314yes—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—862no—
642C2×C8—862no—
643C2×C8—862no—
644C2×C8—862no—
645C2×C8—862no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—1721no—
649C2×C8—1721no—
650C2×C8—1721no—
651C2×C8—1721no—
652C2×C8—1721no—
653C2×C8—1721no—
654C4⋊C4—862no—
655C4⋊C4—1721no—
656C22⋊C4—862no—
657C22⋊C4—1721no—
658C42—862no—
659C42—1721no—
660C23—22no—
661C23—22no—
662C23—42no—
663C23—44no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—82no—
669C23D4×Dic4311yescharacteristic
670C23#1306329611yescharacteristic
671C23#1306329711yescharacteristic
672C23#1306329711yescharacteristic
673C23#1306330611yescharacteristic
674C23#1306330611yescharacteristic
675C23#1306331211yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—3442no—
715C2×C4—1722no—
716C2×C4C2×C22⋊Dic4311yescharacteristic
717C2×C4C2×C22⋊Dic4311yescharacteristic
718C2×C4C2×C22⋊Dic4311yescharacteristic
719C2×C4D4×Dic4311yescharacteristic
720C2×C4D4×Dic4311yescharacteristic
721C2×C4D4×Dic4311yescharacteristic
722C2×C4#1306329311yescharacteristic
723C2×C4#1306329311yescharacteristic
724C2×C4#1306329311yescharacteristic
725C2×C4#1306329311yescharacteristic
726C2×C4#1306329411yescharacteristic
727C2×C4#1306329411yescharacteristic
728C2×C4#1306329411yescharacteristic
729C2×C4#1306329411yescharacteristic
730C2×C4#1306329611yescharacteristic
731C2×C4#1306329611yescharacteristic
732C2×C4#1306329611yescharacteristic
733C2×C4#1306329711yescharacteristic
734C2×C4#1306329711yescharacteristic
735C2×C4#1306329711yescharacteristic
736C2×C4#1306329711yescharacteristic
737C2×C4#1306329711yescharacteristic
738C2×C4#1306329711yescharacteristic
739C2×C4#1306330611yescharacteristic
740C2×C4#1306330611yescharacteristic
741C2×C4#1306331211yescharacteristic
742C2×C4#1306332111yescharacteristic
743C2×C4#1306332111yescharacteristic
744C8—24no—
745C8—1722no—
746C8—1722no—
747C8—1722no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22#1458277911yescharacteristic
764C22#1458277911yescharacteristic
765C22#1458280211yescharacteristic
766C22#1458280711yescharacteristic
767C22#1458281311yescharacteristic
768C22#1458281311yescharacteristic
769C22#1458281311yescharacteristic
770C4—42no—
771C4—42no—
772C4—3442no—
773C4#1458275511yescharacteristic
774C4#1458277911yescharacteristic
775C4#1458277911yescharacteristic
776C4#1458280211yescharacteristic
777C4#1458280711yescharacteristic
778C4#1458280711yescharacteristic
779C4#1458280711yescharacteristic
780C4#1458281311yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—82no—
788C2—82no—
789C2#1913283611yescharacteristic
790C2#1913495912yes—
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#575C2
socleC22×C43#386
cosocleC23×C4×C43C23
hypercenterC2×#575D43
hypocenterC43#11018
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. C2×#14582895C2semidirect
3. #19143040C2semidirect
4. C2×#14582866C2semidirect
5. C2×#14582671C2semidirect
6. C2×#14582663C2semidirect
34. C2×#137×C43C4semidirect
36. C2×AGL(1,ℤ/8)×C43C4semidirect
410. C2×#137Dic43semidirect
412. C2×AGL(1,ℤ/8)Dic43semidirect
434. C43#11018semidirect

Maximal subgroups

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

subgroupindex
C2×#145829162
C2×#145828952
#191430402
C2×#145828662
C2×#145826712
C2×#145826632
C2×C43×#5752
#1101843