Finite Group Databasebeta

← C2×#19144314 #25963991

Subgroups — C2×#19144314 #25963991

Order 11008.

2650 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583699C211yesmaximal, characteristic, complemented
2C2×#14583697C211yesmaximal, characteristic, complemented
3C22×#13063345C211yesmaximal, characteristic, complemented
4C22×#13063333C211yesmaximal, characteristic, complemented
5#19144314C2116yesmaximal, direct product factor
6C2×#14583173C212yesmaximal, complemented
7C2×#14583168C212yesmaximal, complemented
8C2×#14583165C212yesmaximal, complemented
9C2×#14583161C212yesmaximal, complemented
10C22×#13063260C211yesmaximal, characteristic, complemented
11C2×#14582881C211yesmaximal, characteristic, complemented
12C2×C43×#413C211yesmaximal, characteristic, complemented
13C22×#10621898C2211yescharacteristic
14C22×#10621898C2211yescharacteristic
15#14583699—24no—
16#14583699C2218yescomplemented
17#14583697—24no—
18#14583697C2218yescomplemented
19C2×#13063358—21no—
20C2×#13063358C2212yes—
21C2×#13063356C2212yes—
22C2×#13063355—21no—
23C2×#13063353—21no—
24C2×#13063353C2212yes—
25C2×#13063351C2212yes—
26C2×#13063350—21no—
27C2×#13063347—22no—
28C2×#13063345—22no—
29C2×#13063345—21no—
30C2×#13063345—21no—
31C2×#13063345—21no—
32C2×#13063345—21no—
33C2×#13063345—24no—
34C2×#13063345C2218yescomplemented
35C22×#10621885C2211yescharacteristic, complemented
36C22×#10621883C2211yescharacteristic, complemented
37C22×#10621884C2211yescharacteristic, complemented
38C22×#10621882C2211yescharacteristic, complemented
39C2×#13063333—21no—
40C2×#13063333—21no—
41C2×#13063333—24no—
42C2×#13063333C2212yes—
43C2×#13063333C2212yes—
44C2×#13063333C2218yescomplemented
45C22×#10621877C2211yescharacteristic
46C22×#10621872—21no—
47C23×C43⋊C8C2211yescharacteristic
48C22×C8×D43—21no—
49#14583173C22116yescomplemented
50#14583168C22116yescomplemented
51#14583165C22116yescomplemented
52#14583161C22116yescomplemented
53C2×#13063260C2212yescomplemented
54C2×#13063260C2212yescomplemented
55C2×#13063260C2218yescomplemented
56#14582881C2218yescomplemented
57C2×#13063243C2212yescomplemented
58C2×#13063241C2212yescomplemented
59C22×#41×C43C2211yescharacteristic
60C22×M16×C43C2211yescharacteristic
61C22×M16×C43C2211yescharacteristic
62C43×#413C2218yescomplemented
63C2×#101×C43C2212yescomplemented
64C2×#100×C43C2212yescomplemented
65C2×#10621898—21no—
66C2×#10621898—22no—
67C2×#10621898—21no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—21no—
71C2×#10621898—21no—
72C2×#10621898—22no—
73C2×#10621898—21no—
74C2×#10621898—21no—
75C2×#10621898—22no—
76C2×#10621898D412yes—
77C2×#10621898D414yes—
78C2×#10621898C2312yes—
79C2×#10621898C2314yes—
80C2×#10621898C2314yes—
81C22×Dic86D411yescharacteristic
82C22×Dic86C2311yescharacteristic
83C22×D172D411yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89#13063358—24no—
90#13063358—28no—
91#13063358C2318yes—
92#13063356—24no—
93#13063356C2318yes—
94#13063355—28no—
95#13063353—24no—
96#13063353—28no—
97#13063353C2318yes—
98#13063351—24no—
99#13063351C2318yes—
100#13063350—28no—
101#13063347—216no—
102#13063345—216no—
103#13063345—28no—
104#13063345—28no—
105#13063345—28no—
106#13063345—28no—
107C2×Dic172—22no—
108C2×#10621885—22no—
109C2×#10621885—21no—
110C2×#10621885—21no—
111C2×#10621885—22no—
112C2×#10621885C2314yescomplemented
113C2×#10621873—22no—
114C2×#10621873—22no—
115C2×#10621883—22no—
116C2×#10621883—21no—
117C2×#10621883—21no—
118C2×#10621883—22no—
119C2×#10621883C2314yescomplemented
120C2×#10621884—22no—
121C2×#10621884—21no—
122C2×#10621884—21no—
123C2×#10621884—22no—
124C2×#10621884C2314yescomplemented
125C2×D344—22no—
126C2×#10621882—22no—
127C2×#10621882—21no—
128C2×#10621882—21no—
129C2×#10621882—22no—
130C2×#10621882C2314yescomplemented
131#13063333—24no—
132#13063333—24no—
133#13063333—28no—
134#13063333—28no—
135#13063333C2318yes—
136#13063333C2318yes—
137C2×#10621877—21no—
138C2×#10621877—22no—
139C2×#10621877C2312yes—
140C2×#10621877C2314yes—
141C2×#10621872—22no—
142C2×#10621872—22no—
143C2×#10621872—28no—
144C22×C43⋊C8—21no—
145C22×C43⋊C8D411yescharacteristic
146C22×C43⋊C8D411yescharacteristic
147C22×C43⋊C8D411yescharacteristic
148C22×C43⋊C8D411yescharacteristic
149C22×C43⋊C8D414yes—
150C22×C43⋊C8C2311yescharacteristic
151C22×C43⋊C8C2311yescharacteristic
152C22×C43⋊C8C2314yes—
153C2×C8×D43—22no—
154C2×C8×D43—22no—
155C2×C8×D43—28no—
156#13063260C2318yescomplemented
157#13063260C2318yescomplemented
158#13063243C2318yescomplemented
159#13063241C2318yescomplemented
160C2×#41×C43—22no—
161C2×#41×C43—21no—
162C2×#41×C43—21no—
163C2×#41×C43—21no—
164C2×#41×C43—22no—
165C2×#41×C43—21no—
166C2×#41×C43—22no—
167C2×#41×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43—21no—
170C22×D4×C43C2311yescharacteristic
171C23×C4×C43—21no—
172C23×C4×C43C2311yescharacteristic
173C2×M16×C43—21no—
174C2×M16×C43—22no—
175C2×M16×C43—21no—
176C2×M16×C43—22no—
177C2×M16×C43C2312yes—
178C2×M16×C43C2314yes—
179C2×M16×C43C2312yes—
180C2×M16×C43C2314yes—
181C22×C8×C43—21no—
182C22×C8×C43—21no—
183#101×C43C2318yescomplemented
184#100×C43C2318yescomplemented
185C24×C43—21no—
186C24×C43#4111yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189#41×C43—24no—
190#41×C43—24no—
191#41×C43—24no—
192#41×C43—24no—
193#41×C43—42no—
194#41×C43—42no—
195#41×C43—42no—
196#41×C43—42no—
197C2×Q8×C43—21no—
198C2×Q8×C43—21no—
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—21no—
202C2×Q8×C43C2412yes—
203C2×D4×C43—21no—
204C2×D4×C43—24no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—41no—
210C2×D4×C43—41no—
211C2×D4×C43—42no—
212C2×D4×C43C2412yes—
213C22×C4×C43—24no—
214C22×C4×C43—21no—
215C22×C4×C43—41no—
216C22×C4×C43—42no—
217C22×C4×C43—41no—
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D412yes—
224C22×C4×C43#4111yescharacteristic
225C22×C4×C43#4112yes—
226C22×C4×C43C2411yescharacteristic
227C22×C4×C43C2412yes—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—22no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—24no—
233C2×C22⋊D43—41no—
234C2×C22⋊D43—41no—
235C2×C22⋊D43—42no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238#10621898—24no—
239#10621898—24no—
240#10621898—24no—
241#10621898—22no—
242#10621898—24no—
243#10621898—22no—
244#10621898—24no—
245#10621898—24no—
246#10621898—24no—
247#10621898—24no—
248#10621898—24no—
249#10621898—42no—
250#10621898—42no—
251#10621898—42no—
252#10621898—42no—
253#10621898C2×D418yes—
254#10621898C2×D414yes—
255#10621898C2414yes—
256C2×D172—21no—
257C2×D172—22no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172C2×D412yes—
264C2×D172C2×D414yes—
265C2×D172C2412yes—
266C2×C4×D43—24no—
267C2×C4×D43—22no—
268C2×C4×D43—22no—
269C2×C4×D43—24no—
270C2×C4×D43—24no—
271C2×C4×D43—41no—
272C2×C4×D43—42no—
273C2×C4×D43—41no—
274C2×Dic86—21no—
275C2×Dic86—22no—
276C2×Dic86—21no—
277C2×Dic86—21no—
278C2×Dic86—21no—
279C2×Dic86—21no—
280C2×Dic86—21no—
281C2×Dic86C2×D412yes—
282C2×Dic86C2×D414yes—
283C2×Dic86C2412yes—
284M16×C43—22no—
285M16×C43—24no—
286M16×C43—22no—
287M16×C43—24no—
288M16×C43C2414yes—
289M16×C43C2414yes—
290C2×C8×C43—22no—
291C2×C8×C43—24no—
292C2×C8×C43—22no—
293C2×C8×C43—24no—
294#10621885—28no—
295#10621885—24no—
296#10621885—24no—
297#10621884—28no—
298#10621884—24no—
299#10621884—24no—
300#10621883—28no—
301#10621883—24no—
302#10621883—24no—
303#10621882—28no—
304#10621882—24no—
305#10621882—24no—
306#10621877—24no—
307#10621877—22no—
308#10621877C2414yes—
309C2×C43⋊C8—22no—
310C2×C43⋊C8—24no—
311C2×C43⋊C8C2×D411yescharacteristic
312C2×C43⋊C8C2×D411yescharacteristic
313C2×C43⋊C8C2×D414yes—
314C2×C43⋊C8C2×D411yescharacteristic
315C2×C43⋊C8C2×D411yescharacteristic
316C2×C43⋊C8C2×D414yes—
317C2×C43⋊C8C2×D412yes—
318C2×C43⋊C8C2×D412yes—
319C2×C43⋊C8C2×D414yes—
320C2×C43⋊C8C2×D414yes—
321C2×C43⋊C8C2412yes—
322C2×C43⋊C8C2412yes—
323Dic172—28no—
324D344—28no—
325#10621873—28no—
326#10621873—28no—
327#10621872—28no—
328#10621872—28no—
329C8×D43—28no—
330C8×D43—28no—
331C23×C43—22no—
332C23×C43—42no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—82no—
336C23×C43#12111yescharacteristic
337C23×C43#12111yescharacteristic
338C23×C43#12112yes—
339C23×C43C2×#4111yescharacteristic
340C23×C43C2×#4112yes—
341C22×D43—24no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—44no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—82no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43—41no—
351Q8×C43—41no—
352D4×C43—22no—
353D4×C43—22no—
354D4×C43—44no—
355D4×C43—44no—
356D4×C43—41no—
357D4×C43—41no—
358C2×C4×C43—22no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—44no—
362C2×C4×C43—44no—
363C2×C4×C43#12111yescharacteristic
364C2×C4×C43#12112yes—
365C2×C4×C43#12112yes—
366C2×C4×C43#12112yes—
367C2×C4×C43#12112yes—
368C2×C4×C43#12112yes—
369C2×C4×C43#12111yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C22×D412yes—
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D412yes—
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D412yes—
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D412yes—
378C2×C4×C43C2×#4111yescharacteristic
379C2×C4×C43C2×#4112yes—
380C2×C4×C43C2511yescharacteristic
381C22⋊D43—24no—
382C22⋊D43—28no—
383C22⋊D43—24no—
384C22⋊D43—44no—
385C22⋊D43—44no—
386C2×Dic43—24no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391D172—22no—
392D172—24no—
393D172—22no—
394D172—22no—
395D172—41no—
396D172—41no—
397D172C22×D414yes—
398C4×D43—24no—
399C4×D43—28no—
400C4×D43—24no—
401C4×D43—44no—
402C4×D43—44no—
403Dic86—22no—
404Dic86—24no—
405Dic86—22no—
406Dic86—22no—
407Dic86—41no—
408Dic86—41no—
409Dic86C22×D414yes—
410C8×C43—24no—
411C8×C43—24no—
412C43⋊C8—24no—
413C43⋊C8C22×D412yes—
414C43⋊C8C22×D412yes—
415C43⋊C8C22×D412yes—
416C43⋊C8C22×D412yes—
417C2×#3067—431nomaximal, Sylow
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43—82no—
425C22×C43—82no—
426C22×C43—82no—
427C22×C43C2×#12112yes—
428C22×C43C2×#12111yescharacteristic
429C22×C43C2×#12112yes—
430C22×C43C2×#12111yescharacteristic
431C22×C43C22×#4111yescharacteristic
432C2×D43—24no—
433C2×D43—48no—
434C2×D43—44no—
435C2×D43—42no—
436C2×D43—82no—
437C2×D43—82no—
438C2×D43—82no—
439C4×C43—42no—
440C4×C43C2×#12111yescharacteristic
441C4×C43C2×#12112yes—
442C4×C43C2×#12111yescharacteristic
443C4×C43C2×#12112yes—
444C4×C43C23×D411yescharacteristic
445C4×C43C23×D411yescharacteristic
446Dic43—24no—
447Dic43—42no—
448C2×#575—431no—
449C2×#575—431no—
450C22×#135—431no—
451C22×#131—431no—
452#3067—4316no—
453C2×#473—432no—
454C2×#472—432no—
455C2×#471—432no—
456C2×#471—432no—
457C22×#108—431no—
458C2×#413—431no—
459C2×#413D4311yescharacteristic, complemented
460C2×C43—22no—
461C2×C43—21no—
462C2×C43—21no—
463C2×C43—22no—
464C2×C43—82no—
465C2×C43#306712yescomplemented
466C2×C43C22×#12111yescharacteristic
467D43—44no—
468D43—82no—
469C22×#41—431no—
470C22×#41—431no—
471C22×#41C2×D4311yescharacteristic
472#575—438no—
473#575—438no—
474#575—864no—
475#575—864no—
476C2×#137—432no—
477C2×#137—432no—
478C2×#137—861no—
479C2×#137—861no—
480C2×AGL(1,ℤ/8)—432no—
481C2×AGL(1,ℤ/8)—432no—
482C2×AGL(1,ℤ/8)—861no—
483C2×AGL(1,ℤ/8)—861no—
484C2×#135—438no—
485C2×#135—862no—
486C2×#135—861no—
487C2×#135—861no—
488C2×#135—861no—
489C2×#135—861no—
490C2×#135—864no—
491C2×#135—862no—
492C22×Q16—431no—
493C22×SD16—431no—
494C22×SD16—431no—
495C22×D8—431no—
496C2×#131—432no—
497C2×#131—432no—
498C2×#131—438no—
499C2×#131—861no—
500C2×#131—861no—
501C2×#131—864no—
502C22×M16—431no—
503C22×M16—861no—
504C22×M16C2×D4311yescharacteristic
505C22×M16C2×D4311yescharacteristic
506C23×C8—431no—
507C23×C8—861no—
508#473—4316no—
509#472—4316no—
510#471—4316no—
511#471—4316no—
512C2×#108—432no—
513C2×#108—432no—
514C2×#108—438no—
515#413—438no—
516#413C2×D4318yescomplemented
517C2×#101—432no—
518C2×#101C2×D4312yescomplemented
519C2×#100—432no—
520C2×#100C2×D4312yescomplemented
521C43C2×#306711yescharacteristic, complemented, Sylow
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—22no—
525C2×#41—21no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—22no—
529C2×#41—432no—
530C2×#41—434no—
531C2×#41—432no—
532C2×#41—434no—
533C2×#41—434no—
534C2×#41—862no—
535C2×#41—861no—
536C2×#41—862no—
537C2×#41—861no—
538C2×#41—862no—
539C2×#41—861no—
540C2×#41—862no—
541C2×#41—861no—
542C2×#41—861no—
543C2×#41—861no—
544C2×#41—862no—
545C2×#41C22×D4314yes—
546C22×Q8—431no—
547C22×Q8—431no—
548C22×Q8C22×D4311yescharacteristic
549C22×D4—21no—
550C22×D4—431no—
551C22×D4—431no—
552C22×D4—861no—
553C22×D4—861no—
554C22×D4C22×D4311yescharacteristic
555C23×C4—21no—
556C23×C4—861no—
557C23×C4—861no—
558C23×C4C22×D4311yescharacteristic
559#137—438no—
560#137—438no—
561#137—868no—
562#137—864no—
563#137—864no—
564#137—868no—
565AGL(1,ℤ/8)—438no—
566AGL(1,ℤ/8)—438no—
567AGL(1,ℤ/8)—868no—
568AGL(1,ℤ/8)—864no—
569AGL(1,ℤ/8)—864no—
570AGL(1,ℤ/8)—868no—
571#135—8616no—
572#135—868no—
573#135—868no—
574#135—868no—
575#135—868no—
576#135—8616no—
577C2×Q16—434no—
578C2×Q16—862no—
579C2×Q16—861no—
580C2×Q16—861no—
581C2×Q16—862no—
582C2×Q16—862no—
583C2×SD16—434no—
584C2×SD16—434no—
585C2×SD16—862no—
586C2×SD16—862no—
587C2×SD16—861no—
588C2×SD16—861no—
589C2×SD16—862no—
590C2×SD16—861no—
591C2×SD16—861no—
592C2×SD16—862no—
593C2×SD16—862no—
594C2×SD16—862no—
595C2×D8—434no—
596C2×D8—862no—
597C2×D8—861no—
598C2×D8—861no—
599C2×D8—862no—
600C2×D8—862no—
601#131—438no—
602#131—438no—
603#131—864no—
604#131—864no—
605#131—868no—
606#131—868no—
607C2×M16—21no—
608C2×M16—22no—
609C2×M16—21no—
610C2×M16—22no—
611C2×M16—432no—
612C2×M16—434no—
613C2×M16—862no—
614C2×M16—862no—
615C2×M16—868no—
616C2×M16—861no—
617C2×M16—862no—
618C2×M16C22×D4312yes—
619C2×M16C22×D4314yes—
620C2×M16C22×D4312yes—
621C2×M16C22×D4314yes—
622C22×C8—21no—
623C22×C8—21no—
624C22×C8—431no—
625C22×C8—431no—
626C22×C8—431no—
627C22×C8—431no—
628C22×C8—434no—
629C22×C8—431no—
630C22×C8—431no—
631C22×C8—434no—
632C22×C8—862no—
633C22×C8—862no—
634C22×C8—868no—
635C22×C8—861no—
636#108—438no—
637#108—438no—
638#101—438no—
639#101C22×D4318yescomplemented
640#100—438no—
641#100C22×D4318yescomplemented
642C24—21no—
643C24—861no—
644C24—861no—
645C24#1062189811yescharacteristic
646#41—24no—
647#41—24no—
648#41—24no—
649#41—24no—
650#41—42no—
651#41—42no—
652#41—42no—
653#41—42no—
654#41—438no—
655#41—434no—
656#41—434no—
657#41—864no—
658#41—864no—
659#41—864no—
660#41—862no—
661#41—864no—
662#41—864no—
663#41—862no—
664#41—864no—
665#41—864no—
666#41—864no—
667#41—864no—
668#41—1722no—
669#41—1722no—
670#41—1722no—
671#41—1722no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—432no—
678C2×Q8—434no—
679C2×Q8—432no—
680C2×Q8—861no—
681C2×Q8—862no—
682C2×Q8—861no—
683C2×Q8—861no—
684C2×Q8—861no—
685C2×Q8—861no—
686C2×Q8—861no—
687C2×Q8C23×D4312yes—
688C2×D4—24no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—42no—
697C2×D4—432no—
698C2×D4—434no—
699C2×D4—432no—
700C2×D4—862no—
701C2×D4—864no—
702C2×D4—862no—
703C2×D4—864no—
704C2×D4—864no—
705C2×D4—861no—
706C2×D4—862no—
707C2×D4—861no—
708C2×D4—861no—
709C2×D4—861no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—1721no—
713C2×D4—1721no—
714C2×D4—1722no—
715C2×D4C23×D4312yes—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—41no—
719C22×C4—42no—
720C22×C4—41no—
721C22×C4—861no—
722C22×C4—864no—
723C22×C4—862no—
724C22×C4—862no—
725C22×C4—864no—
726C22×C4—861no—
727C22×C4—864no—
728C22×C4—1721no—
729C22×C4—1722no—
730C22×C4—1721no—
731C22×C4#1062189812yes—
732C22×C4#1062189811yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4D4×D4312yes—
735C22×C4D4×D4311yescharacteristic
736C22×C4D4×D4312yes—
737C22×C4D4×D4311yescharacteristic
738C22×C4D4×D4311yescharacteristic
739C22×C4C23×D4311yescharacteristic
740C22×C4C23×D4312yes—
741Q16—868no—
742Q16—864no—
743Q16—864no—
744Q16—868no—
745SD16—868no—
746SD16—868no—
747SD16—864no—
748SD16—864no—
749SD16—864no—
750SD16—864no—
751SD16—868no—
752SD16—868no—
753D8—868no—
754D8—864no—
755D8—864no—
756D8—868no—
757M16—22no—
758M16—24no—
759M16—22no—
760M16—24no—
761M16—434no—
762M16—868no—
763M16—868no—
764M16—862no—
765M16—864no—
766M16C23×D4314yes—
767M16C23×D4314yes—
768C2×C8—22no—
769C2×C8—24no—
770C2×C8—22no—
771C2×C8—24no—
772C2×C8—431no—
773C2×C8—431no—
774C2×C8—434no—
775C2×C8—431no—
776C2×C8—431no—
777C2×C8—434no—
778C2×C8—432no—
779C2×C8—432no—
780C2×C8—434no—
781C2×C8—434no—
782C2×C8—432no—
783C2×C8—432no—
784C2×C8—868no—
785C2×C8—868no—
786C2×C8—862no—
787C2×C8—864no—
788C23—22no—
789C23—42no—
790C23—41no—
791C23—41no—
792C23—82no—
793C23—864no—
794C23—862no—
795C23—862no—
796C23—3442no—
797C23—1724no—
798C23—1721no—
799C23—1721no—
800C23#1306329811yescharacteristic
801C23#1306329811yescharacteristic
802C23#1306329812yes—
803C23C2×#1062189811yescharacteristic
804C23C2×#1062189812yes—
805Q8—22no—
806Q8—22no—
807Q8—41no—
808Q8—41no—
809Q8—434no—
810Q8—864no—
811Q8—862no—
812Q8—862no—
813Q8—862no—
814Q8—1721no—
815Q8—1721no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—44no—
820D4—41no—
821D4—41no—
822D4—434no—
823D4—864no—
824D4—868no—
825D4—864no—
826D4—864no—
827D4—862no—
828D4—862no—
829D4—862no—
830D4—1724no—
831D4—1724no—
832D4—1721no—
833D4—1721no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—864no—
840C2×C4—862no—
841C2×C4—868no—
842C2×C4—864no—
843C2×C4—864no—
844C2×C4—862no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1724no—
848C2×C4—1724no—
849C2×C4#1306329811yescharacteristic
850C2×C4#1306329812yes—
851C2×C4#1306329812yes—
852C2×C4#1306329812yes—
853C2×C4#1306329812yes—
854C2×C4#1306329812yes—
855C2×C4#1306329811yescharacteristic
856C2×C4C2×D4×D4311yescharacteristic
857C2×C4C2×D4×D4312yes—
858C2×C4C2×D4×D4311yescharacteristic
859C2×C4C2×D4×D4312yes—
860C2×C4C2×D4×D4311yescharacteristic
861C2×C4C2×D4×D4312yes—
862C2×C4C2×D4×D4311yescharacteristic
863C2×C4C2×D4×D4312yes—
864C2×C4C2×#1062189812yes—
865C2×C4C2×#1062189811yescharacteristic
866C2×C4C24×D4311yescharacteristic
867C8—24no—
868C8—24no—
869C8—432no—
870C8—432no—
871C8—432no—
872C8—432no—
873C8—864no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—864no—
884C22—3442no—
885C22—3442no—
886C22—3442no—
887C22—1728no—
888C22—1722no—
889C22—1724no—
890C22C2×#1306329811yescharacteristic
891C22C2×#1306329812yes—
892C22C2×#1306329812yes—
893C22C2×#1306329811yescharacteristic
894C22C22×#1062189811yescharacteristic
895C4—42no—
896C4—864no—
897C4—1722no—
898C4C2×#1306329812yes—
899C4C2×#1306329812yes—
900C4C2×#1306329811yescharacteristic
901C4C2×#1306329811yescharacteristic
902C4C22×D4×D4311yescharacteristic
903C4C22×D4×D4311yescharacteristic
904C2—21no—
905C2—21no—
906C2—22no—
907C2—22no—
908C2—82no—
909C2—3442no—
910C2—1724no—
911C2#1914431412yesdirect product factor
912C2C22×#1306329811yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#413C2
socleC22×C43C2×#121
hypercenterC2×#413D43
hypocenterC43C2×#3067
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#14583699C2semidirect
2. C2×#14583697C2semidirect
3. C22×#13063345C2semidirect
4. C22×#13063333C2semidirect
5. #19144314C2direct (N × H)
6. C2×#14583173C2semidirect
7. C2×#14583168C2semidirect
8. C2×#14583165C2semidirect
9. C2×#14583161C2semidirect
10. C22×#13063260C2semidirect
11. C2×#14582881C2semidirect
12. C2×C43×#413C2semidirect
16. #14583699C22semidirect
18. #14583697C22semidirect
34. C2×#13063345C22semidirect
35. C22×#10621885C22semidirect
36. C22×#10621883C22semidirect
37. C22×#10621884C22semidirect
38. C22×#10621882C22semidirect
44. C2×#13063333C22semidirect
49. #14583173C22semidirect
50. #14583168C22semidirect
51. #14583165C22semidirect
52. #14583161C22semidirect
53. C2×#13063260C22semidirect
54. C2×#13063260C22semidirect
55. C2×#13063260C22semidirect
56. #14582881C22semidirect
57. C2×#13063243C22semidirect
58. C2×#13063241C22semidirect
62. C43×#413C22semidirect
63. C2×#101×C43C22semidirect
64. C2×#100×C43C22semidirect
112. C2×#10621885C23semidirect
119. C2×#10621883C23semidirect
124. C2×#10621884C23semidirect
130. C2×#10621882C23semidirect
156. #13063260C23semidirect
157. #13063260C23semidirect
158. #13063243C23semidirect
159. #13063241C23semidirect
183. #101×C43C23semidirect
184. #100×C43C23semidirect
459. C2×#413D43semidirect
465. C2×C43#3067semidirect
516. #413C2×D43semidirect
518. C2×#101C2×D43semidirect
520. C2×#100C2×D43semidirect
521. C43C2×#3067semidirect
639. #101C22×D43semidirect
641. #100C22×D43semidirect
911. C2#19144314direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836992
C2×#145836972
C22×#130633452
C22×#130633332
#191443142
C2×#145831732
C2×#145831682
C2×#145831652
C2×#145831612
C22×#130632602
C2×#145828812
C2×C43×#4132
C2×#306743