Finite Group Databasebeta

← D43×#3497 #26004766

Subgroups — D43×#3497 #26004766

Order 11008.

11210 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D43C212yesmaximal, complemented
2#19148366C211yesmaximal, characteristic, complemented
3#19148365C214yesmaximal, complemented
4#19148364C216yesmaximal, complemented
5#19148363C218yesmaximal, complemented
6#19148362C212yesmaximal, complemented
7#19148361C216yesmaximal, complemented
8#19148360C214yesmaximal, complemented
9#550×D43C214yesmaximal, complemented
10D4×Q8×D43C214yesmaximal, complemented
11#548×D43C218yesmaximal, complemented
12#537×D43C216yesmaximal, complemented
13#532×D43C216yesmaximal, complemented
14C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
15C43×#3497C211yesmaximal, characteristic, complemented
16C2×#13063373C2212yescomplemented
17C2×#13063373C2218yescomplemented
18C2×#13063372C2218yescomplemented
19C2×#13063372C22112yescomplemented
202−1+4×D43—232no—
21C2×#41×D43C2218yes—
22C2×#41×D43C22112yes—
23C22×Q8×D43C2218yes—
24C22×Q8×D43C2211yescharacteristic
25#14583571C2214yescomplemented
26#14583570C22112yescomplemented
27#14583569C22112yescomplemented
28#14583568C2218yescomplemented
29#14583567C22124yescomplemented
30Q8×D172C2214yescomplemented
31D4×Dic86C22112yescomplemented
32#14583564C22112yescomplemented
33Q8×C22⋊D43C2218yescomplemented
34#14583562C22124yescomplemented
35#14583561C2218yescomplemented
36#14583560C2218yescomplemented
37#14583559C22124yescomplemented
38#14583558C22124yescomplemented
39#14583557C22124yescomplemented
40#14583556C2218yescomplemented
41#14583555C22124yescomplemented
42#14583480C2216yescomplemented
43#14583479C22124yescomplemented
44#14583478C22124yescomplemented
45#14583477C22112yescomplemented
46#14583476C22124yescomplemented
47#14583450C2216yescomplemented
48#14583449C2216yescomplemented
49#14583448C22112yescomplemented
50#14583447C2216yescomplemented
51#14583446C22112yescomplemented
52#14583446C22112yescomplemented
53#14583445C22112yescomplemented
54#14583444C22112yescomplemented
55#14583444C22112yescomplemented
56C4⋊Q8×D43C2216yes—
57#127×D43C2216yes—
58#124×D43C22112yes—
59C22⋊Q8×D43C22124yes—
60#121×D43C22124yes—
61#121×D43C2214yes—
62#121×D43C22112yes—
63C2×Q8×Dic43C2211yescharacteristic, complemented
64C2×C4×Dic86C2213yescomplemented
65C2×#13063290C2213yescomplemented
66C4×Q8×D43C2214yes—
67C4×Q8×D43C2214yes—
68C4×Q8×D43C2214yescomplemented
69C4×Q8×D43C2214yescomplemented
70C4×D4×D43C22112yes—
71C4×D4×D43C22112yes—
72C2×C4⋊C4×D43C2213yes—
73C2×C42×D43C2213yes—
74C2×2−1+4×C43C2212yescomplemented
75C43×#550C2214yescomplemented
76D4×Q8×C43C2214yescomplemented
77C43×#548C2218yescomplemented
78C43×#537C2216yescomplemented
79C43×#532C2216yescomplemented
80C2×C4×Q8×C43C2211yescharacteristic, complemented
81#13063373—216no—
82#13063373—264no—
83#13063372—264no—
84#13063372—296no—
85C2×#10621902C2318yes—
86C2×#10621902C23112yes—
87C2×#10621898C23124yes—
88C2×#10621898C23112yes—
89C2×#10621898C23124yes—
90C2×#10621900C23124yes—
91C2×#10621900C23124yes—
92C2×#10621900C23112yes—
93#41×D43—264no—
94#41×D43—296no—
95C22×Dic86C23124yes—
96C22×Dic86C2313yes—
97C2×Q8×D43—264no—
98C2×Q8×D43D4116yescomplemented
99C2×Q8×D43C2318yes—
100C2×Q8×D43C23124yes—
101C2×Q8×D43C23112yes—
102C2×Q8×D43C2314yes—
103C2×Q8×D43C2314yes—
104C2×D4×D43C2314yes—
105C2×D4×D43C2318yes—
106C2×D4×D43C23112yes—
107C2×D4×D43C23112yes—
108C22×C4×D43C2311yescharacteristic
109C22×C4×D43C23124yes—
110C22×C4×D43C2313yes—
111C22×C4×D43C2313yes—
112#13063325C2316yes—
113#13063324C23112yes—
114#13063324C23112yes—
115#13063323C23112yes—
116#13063322C2316yes—
117#13063321C23112yes—
118#13063321C23112yes—
119#13063321C23112yes—
120#13063314C23112yes—
121#13063313C23112yes—
122#13063312C23112yes—
123#13063311C23124yes—
124#13063311C23124yes—
125#13063305C23124yes—
126#13063304C23124yes—
127#13063303C23148yes—
128#13063302C23148yes—
129#13063301C23124yes—
130#13063300C23124yes—
131#13063300C2314yes—
132#13063300C23112yes—
133#13063299C23124yes—
134#13063299C2314yes—
135#13063299C23112yes—
136#13063298C23148yes—
137#13063298C2318yes—
138#13063298C23124yes—
139#13063297C23148yes—
140#13063297C2318yes—
141#13063297C23124yes—
142#13063296C23124yes—
143#13063296C2314yes—
144#13063296C23112yes—
145Q8×Dic43C2314yes—
146Q8×Dic43C2314yes—
147C4×Dic86C23112yes—
148C4×Dic86C23112yes—
149#13063290C23112yes—
150#13063290C23112yes—
151C4×D172C23112yes—
152C4×D172C23112yes—
153D4×Dic43C23112yes—
154D4×Dic43C23112yes—
155#13063287C23112yes—
156#13063287C23112yes—
157C4×C22⋊D43C23124yes—
158C4×C22⋊D43C23124yes—
159(C22⋊D43)⋊C4C23124yes—
160(C22⋊D43)⋊C4C23124yes—
161C2×C4⋊Dic43C2313yes—
162C2×Dic43⋊C4C2316yes—
163C4⋊C4×D43C23112yes—
164C4⋊C4×D43C23112yes—
165C4⋊C4×D43C2314yes—
166C4⋊C4×D43C23112yes—
167C22⋊C4×D43C2318yes—
168C22⋊C4×D43C23124yes—
169C2×C4×Dic43C2313yes—
170C2×C4×Dic43C2313yes—
171C2×C4×Dic43C2313yes—
172C42×D43C2316yes—
173C42×D43C2316yes—
174C42×D43C2316yes—
175C42×D43C2316yes—
1762−1+4×C43—216no—
177C2×#41×C43C2318yes—
178C2×#41×C43C23112yes—
179C22×Q8×C43C2318yes—
180C22×Q8×C43C2311yescharacteristic
181C4⋊Q8×C43C2316yes—
182#127×C43C2316yes—
183#124×C43C23112yes—
184C22⋊Q8×C43C23124yes—
185#121×C43C23124yes—
186#121×C43C2314yes—
187#121×C43C23112yes—
188C4×Q8×C43C2314yes—
189C4×Q8×C43C2314yes—
190C4×D4×C43C23112yes—
191C4×D4×C43C23112yes—
192C2×C4⋊C4×C43C2313yes—
193C2×C42×C43C2313yes—
194C23×D43C2418yes—
195C23×D43C2411yescharacteristic
196#41×C43—232no—
197#41×C43—248no—
198C2×Q8×C43—232no—
199C2×Q8×C43C2×D418yescomplemented
200C2×Q8×C43C24112yes—
201C2×Q8×C43C2414yes—
202C2×D4×C43C2414yes—
203C2×D4×C43C2418yes—
204C2×D4×C43C24112yes—
205C2×D4×C43C24112yes—
206C22×C4×C43C2411yescharacteristic
207C22×C4×C43C24124yes—
208C22×C4×C43C2413yes—
209C22×C4×C43C2413yes—
210C2×C22⋊D43C2418yes—
211C2×C22⋊D43C2418yes—
212C2×C22⋊D43C2418yes—
213C2×C22⋊D43C24124yes—
214C2×C22⋊D43C24124yes—
215C22×Dic43C2411yescharacteristic
216C22×Dic43C24124yes—
217C22×Dic43C2413yes—
218C22×Dic43C2413yes—
219#10621902—232no—
220#10621902—248no—
221Q8×D43—232no—
222Q8×D43—248no—
223Q8×D43—296no—
224Q8×D43C2×D4132yes—
225Q8×D43C2×D4132yescomplemented
226#10621900—296no—
227#10621900—248no—
228#10621900—296no—
229D4×D43—248no—
230D4×D43—216no—
231D4×D43—232no—
232D4×D43—424no—
233#10621898—248no—
234#10621898—296no—
235#10621898—296no—
236C2×D172C2414yes—
237C2×D172C2418yes—
238C2×D172C24112yes—
239C2×D172C24112yes—
240C2×C4×D43—296no—
241C2×C4×D43—24no—
242C2×C4×D43—46no—
243C2×C4×D43C2×D4124yes—
244C2×C4×D43C2411yescharacteristic
245C2×C4×D43C2411yescharacteristic
246C2×C4×D43C2411yescharacteristic
247C2×C4×D43C2416yes—
248C2×C4×D43C2418yes—
249C2×C4×D43C24124yes—
250C2×C4×D43C24124yes—
251C2×C4×D43C2416yes—
252C2×C4×D43C2416yes—
253C2×C4×D43C2416yes—
254C2×C4×D43C2411yescharacteristic
255C2×Dic86—296no—
256C2×Dic86C2×D4124yescomplemented
257C2×Dic86C24124yes—
258C2×Dic86C24112yes—
259C2×Dic86C24112yes—
260C4⋊C4×C43C24112yes—
261C4⋊C4×C43C2414yes—
262C4⋊C4×C43C24112yes—
263C22⋊C4×C43C2418yes—
264C22⋊C4×C43C24124yes—
265C42×C43C2416yes—
266C42×C43C2416yes—
267C22⋊Dic43C2418yes—
268C22⋊Dic43C24124yes—
269(C2×D43)⋊C4C2418yes—
270(C2×D43)⋊C4C24124yes—
271(C2×D43)⋊C4C2418yes—
272(C2×D43)⋊C4C24124yes—
273C4⋊Dic43C24112yes—
274C4⋊Dic43C2414yes—
275C4⋊Dic43C24112yes—
276Dic43⋊C4C24124yes—
277Dic43⋊C4C2418yes—
278Dic43⋊C4C24124yes—
279C4×Dic43C2416yes—
280C4×Dic43C2416yes—
281C4×Dic43C2416yes—
282C4×Dic43C2416yes—
283C4×Dic43C2416yes—
284C4×Dic43C2416yes—
285C23×C43C2518yes—
286C23×C43C2511yescharacteristic
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—216no—
290C22×D43—216no—
291C22×D43—216no—
292C22×D43C22×D414yes—
293C22×D43C2518yes—
294C22×D43C2511yescharacteristic
295C22×D43C2511yescharacteristic
296Q8×C43—224no—
297Q8×C43C22×D4116yes—
298D4×C43—216no—
299D4×C43—224no—
300D4×C43—28no—
301D4×C43—412no—
302C2×C4×C43—248no—
303C2×C4×C43—22no—
304C2×C4×C43—43no—
305C2×C4×C43C22×D4112yes—
306C2×C4×C43C2511yescharacteristic
307C2×C4×C43C2516yes—
308C2×C4×C43C2518yes—
309C2×C4×C43C2516yes—
310C2×C4×C43C2511yescharacteristic
311C22⋊D43—216no—
312C22⋊D43—216no—
313C22⋊D43—248no—
314C22⋊D43—216no—
315C22⋊D43—424no—
316C2×Dic43—248no—
317C2×Dic43—22no—
318C2×Dic43—43no—
319C2×Dic43C22×D4112yes—
320C2×Dic43C2511yescharacteristic
321C2×Dic43C2516yes—
322C2×Dic43C2518yes—
323C2×Dic43C2516yes—
324C2×Dic43C2511yescharacteristic
325D172—216no—
326D172—224no—
327D172—28no—
328D172—412no—
329C4×D43—216no—
330C4×D43—22no—
331C4×D43—212no—
332C4×D43—248no—
333C4×D43—22no—
334C4×D43—248no—
335C4×D43—22no—
336C4×D43—46no—
337C4×D43C22×D4124yes—
338C4×D43C22×D4124yes—
339C4×D432−1+414yescomplemented
340Dic86—224no—
341Dic86—248no—
342Dic86C22×D4148yes—
343C2×#3497—431nomaximal, Sylow
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—28no—
347C22×C43—28no—
348C22×C43—28no—
349C22×C43C23×D412yes—
350C22×C43C2611yescharacteristic
351C2×D43—21no—
352C2×D43—21no—
353C2×D43—28no—
354C2×D43—28no—
355C2×D43—28no—
356C2×D43—28no—
357C2×D43—432no—
358C2×D43C23×D412yes—
359C2×D43C23×D412yes—
360C2×D43C2×2−1+412yes—
361C2×D43#58512yes—
362C4×C43—28no—
363C4×C43—21no—
364C4×C43—26no—
365C4×C43C23×D4112yes—
366C4×C43C2×2−1+412yescomplemented
367Dic43—28no—
368Dic43—21no—
369Dic43—26no—
370Dic43C23×D4112yes—
371Dic43C2×2−1+412yescomplemented
372C22×2−1+4—432no—
373#3497—432no—
374#3497—434no—
375#3497—434no—
376#3497—438no—
377#3497—436no—
378#3497—436no—
379#3497—431no—
380#3497D4311yescharacteristic, direct product factor
381C2×#550—434no—
382C2×D4×Q8—434no—
383C2×#548—438no—
384C2×#537—436no—
385C2×#532—436no—
386C22×C4×Q8—431no—
387C2×C43—22no—
388C2×C43—48no—
389C2×C43C24×D411yescharacteristic
390C2×C43C22×2−1+411yescharacteristic
391C2×C43C2×#58511yescharacteristic
392D43—22no—
393D43—48no—
394D43#349714yesdirect product factor
395C2×2−1+4—438no—
396C2×2−1+4—4312no—
397C2×2−1+4—438no—
398C2×2−1+4—432no—
399C2×2−1+4—8632no—
400C2×2−1+4C2×D4312yescomplemented
401C22×#41—4312no—
402C22×#41—438no—
403C23×Q8—431no—
404C23×Q8—438no—
405#550—438no—
406#550—4312no—
407#550—4324no—
408#550—434no—
409#550—4312no—
410#550C2×D4314yescomplemented
411D4×Q8—438no—
412D4×Q8—4312no—
413D4×Q8—4324no—
414D4×Q8—434no—
415D4×Q8—4312no—
416D4×Q8C2×D4314yescomplemented
417#548—438no—
418#548—438no—
419#548—4324no—
420#548—4324no—
421#548—4324no—
422#548—438no—
423#548—4324no—
424#548C2×D4318yescomplemented
425#537—4312no—
426#537—4324no—
427#537—4324no—
428#537—4324no—
429#537—436no—
430#537C2×D4316yescomplemented
431#532—4312no—
432#532—436no—
433#532—436no—
434#532—4312no—
435#532—4312no—
436#532—4312no—
437#532—4312no—
438#532—4312no—
439#532—436no—
440#532C2×D4316yescomplemented
441C2×C4⋊Q8—436no—
442C2×#127—436no—
443C2×#124—4312no—
444C2×C22⋊Q8—4324no—
445C2×#121—434no—
446C2×#121—4312no—
447C2×#121—4324no—
448C2×C4×Q8—431no—
449C2×C4×Q8—434no—
450C2×C4×Q8—434no—
451C2×C4×Q8—434no—
452C2×C4×Q8—434no—
453C2×C4×Q8—433no—
454C2×C4×Q8—433no—
455C2×C4×Q8C2×D4311yescharacteristic, complemented
456C2×C4×D4—4312no—
457C2×C4×D4—4312no—
458C22×C4⋊C4—433no—
459C22×C42—433no—
460C43C2×#349711yescharacteristic, complemented, Sylow
4612−1+4—216no—
4622−1+4—8664no—
4632−1+4—8664no—
4642−1+4—8696no—
4652−1+4—8616no—
466C2×#41—4312no—
467C2×#41—438no—
468C2×#41—4324no—
469C2×#41—4312no—
470C2×#41—4324no—
471C2×#41—4324no—
472C2×#41—4312no—
473C2×#41—4324no—
474C2×#41—8696no—
475C2×#41—8664no—
476C2×#41C22×D43112yes—
477C2×#41C22×D4318yes—
478C22×Q8—4316no—
479C22×Q8—434no—
480C22×Q8—434no—
481C22×Q8—4312no—
482C22×Q8—4324no—
483C22×Q8—438no—
484C22×Q8—433no—
485C22×Q8—4324no—
486C22×Q8—8664no—
487C22×Q8C22×D4318yes—
488C22×Q8C22×D4311yescharacteristic
489C22×D4—434no—
490C22×D4—438no—
491C22×D4—4312no—
492C22×D4—4312no—
493C23×C4—433no—
494C23×C4—4324no—
495C23×C4—431no—
496C23×C4—433no—
497C4⋊Q8—4312no—
498C4⋊Q8—4312no—
499C4⋊Q8—4312no—
500C4⋊Q8—436no—
501C4⋊Q8C22×D4316yes—
502#127—4312no—
503#127—4312no—
504#127—4312no—
505#127—436no—
506#127C22×D4316yes—
507#124—4312no—
508#124—4312no—
509#124—4324no—
510#124—4324no—
511#124—4312no—
512#124C22×D43112yes—
513C22⋊Q8—4324no—
514C22⋊Q8—4324no—
515C22⋊Q8—4348no—
516C22⋊Q8—4324no—
517C22⋊Q8—4348no—
518C22⋊Q8C22×D43124yes—
519#121—434no—
520#121—438no—
521#121—4312no—
522#121—4324no—
523#121—4324no—
524#121—4348no—
525#121—434no—
526#121—4312no—
527#121—4324no—
528#121—434no—
529#121—4312no—
530#121—4324no—
531#121—438no—
532#121—4324no—
533#121—4348no—
534#121C22×D4314yes—
535#121C22×D43112yes—
536#121C22×D43124yes—
537C4×Q8—434no—
538C4×Q8—434no—
539C4×Q8—4312no—
540C4×Q8—4312no—
541C4×Q8—4312no—
542C4×Q8—4312no—
543C4×Q8C22×D4314yes—
544C4×Q8C22×D4314yes—
545C4×D4—4312no—
546C4×D4—4312no—
547C4×D4—4324no—
548C4×D4—4324no—
549C4×D4—4312no—
550C4×D4—4312no—
551C4×D4—4324no—
552C4×D4—4324no—
553C4×D4—4312no—
554C4×D4—4312no—
555C4×D4C22×D43112yes—
556C4×D4C22×D43112yes—
557C2×C4⋊C4—436no—
558C2×C4⋊C4—433no—
559C2×C4⋊C4—4312no—
560C2×C4⋊C4—4312no—
561C2×C4⋊C4—434no—
562C2×C4⋊C4—4312no—
563C2×C4⋊C4C22×D4313yes—
564C2×C22⋊C4—438no—
565C2×C22⋊C4—4324no—
566C2×C42—433no—
567C2×C42—433no—
568C2×C42—433no—
569C2×C42—436no—
570C2×C42—436no—
571C2×C42—436no—
572C2×C42—436no—
573C2×C42C22×D4313yes—
574C24—431no—
575C24—438no—
576#41—232no—
577#41—248no—
578#41—8696no—
579#41—8696no—
580#41—8696no—
581#41—8648no—
582#41—8648no—
583#41—8696no—
584#41—8632no—
585#41—8648no—
586C2×Q8—232no—
587C2×Q8—4332no—
588C2×Q8—4332no—
589C2×Q8—4324no—
590C2×Q8—4312no—
591C2×Q8—4324no—
592C2×Q8—4312no—
593C2×Q8—8696no—
594C2×Q8—8648no—
595C2×Q8—8696no—
596C2×Q8—8632no—
597C2×Q8D4×D4318yescomplemented
598C2×Q8C23×D43112yes—
599C2×Q8C23×D4314yes—
600C2×D4—438no—
601C2×D4—438no—
602C2×D4—438no—
603C2×D4—4324no—
604C2×D4—4324no—
605C2×D4—434no—
606C2×D4—438no—
607C2×D4—4312no—
608C2×D4—4312no—
609C2×D4—8648no—
610C2×D4—8616no—
611C2×D4—8632no—
612C2×D4—17224no—
613C2×D4C23×D4314yes—
614C2×D4C23×D4318yes—
615C2×D4C23×D43112yes—
616C2×D4C23×D43112yes—
617C22×C4—433no—
618C22×C4—4324no—
619C22×C4—431no—
620C22×C4—436no—
621C22×C4—436no—
622C22×C4—431no—
623C22×C4—4324no—
624C22×C4—433no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—436no—
629C22×C4—438no—
630C22×C4—4324no—
631C22×C4—4324no—
632C22×C4—436no—
633C22×C4—8696no—
634C22×C4—864no—
635C22×C4—1726no—
636C22×C4C23×D4311yescharacteristic
637C22×C4C23×D43124yes—
638C22×C4C23×D4313yes—
639C22×C4C23×D4313yes—
640C4⋊C4—4324no—
641C4⋊C4—4312no—
642C4⋊C4—438no—
643C4⋊C4—434no—
644C4⋊C4—4324no—
645C4⋊C4—4312no—
646C4⋊C4C23×D43112yes—
647C4⋊C4C23×D4314yes—
648C4⋊C4C23×D43112yes—
649C22⋊C4—438no—
650C22⋊C4—4324no—
651C22⋊C4—438no—
652C22⋊C4—438no—
653C22⋊C4—4324no—
654C22⋊C4—4324no—
655C22⋊C4C23×D4318yes—
656C22⋊C4C23×D43124yes—
657C42—436no—
658C42—436no—
659C42—436no—
660C42—436no—
661C42—436no—
662C42—436no—
663C42C23×D4316yes—
664C42C23×D4316yes—
665C23—431no—
666C23—434no—
667C23—431no—
668C23—438no—
669C23—862no—
670C23—862no—
671C23—8616no—
672C23—8616no—
673C23—8616no—
674C23C24×D4318yes—
675C23C24×D4311yescharacteristic
676Q8—224no—
677Q8—4348no—
678Q8—8648no—
679Q8—8624no—
680Q8C2×D4×D43116yes—
681D4—216no—
682D4—224no—
683D4—28no—
684D4—412no—
685D4—8616no—
686D4—8648no—
687D4—8616no—
688D4—8616no—
689D4—8616no—
690D4—8624no—
691D4—868no—
692D4—17212no—
693D4—17224no—
694C2×C4—248no—
695C2×C4—22no—
696C2×C4—43no—
697C2×C4—4312no—
698C2×C4—431no—
699C2×C4—436no—
700C2×C4—4324no—
701C2×C4—4324no—
702C2×C4—434no—
703C2×C4—431no—
704C2×C4—436no—
705C2×C4—438no—
706C2×C4—8648no—
707C2×C4—862no—
708C2×C4—8616no—
709C2×C4—862no—
710C2×C4—8612no—
711C2×C4—8648no—
712C2×C4—862no—
713C2×C4—8648no—
714C2×C4—862no—
715C2×C4—1726no—
716C2×C4—1723no—
717C2×C4C2×D4×D43112yes—
718C2×C4C24×D4311yescharacteristic
719C2×C4C24×D4316yes—
720C2×C4C24×D4318yes—
721C2×C4C24×D4316yes—
722C2×C4C24×D4311yescharacteristic
723C22—21no—
724C22—21no—
725C22—28no—
726C22—28no—
727C22—28no—
728C22—432no—
729C22—432no—
730C22—432no—
731C22—432no—
732C22—868no—
733C22—861no—
734C22—861no—
735C22—868no—
736C22—868no—
737C22—868no—
738C22—17232no—
739C22C22×D4×D4312yes—
740C22C25×D4311yescharacteristic
741C4—28no—
742C4—21no—
743C4—26no—
744C4—4312no—
745C4—432no—
746C4—868no—
747C4—861no—
748C4—866no—
749C4C22×D4×D43112yes—
750C42−1+4×D4312yescomplemented
751C2—22no—
752C2—48no—
753C2—434no—
754C2—862no—
755C2—1728no—
756C2C23×D4×D4311yescharacteristic
757C2C2×2−1+4×D4311yescharacteristic
758C2#585×D4311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3497C2
hypercenter#3497D43
hypocenterC43C2×#3497
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D43C2semidirect
2. #19148366C2semidirect
3. #19148365C2semidirect
4. #19148364C2semidirect
5. #19148363C2semidirect
6. #19148362C2semidirect
7. #19148361C2semidirect
8. #19148360C2semidirect
9. #550×D43C2semidirect
10. D4×Q8×D43C2semidirect
11. #548×D43C2semidirect
12. #537×D43C2semidirect
13. #532×D43C2semidirect
14. C2×C4×Q8×D43C2semidirect
15. C43×#3497C2semidirect
16. C2×#13063373C22semidirect
17. C2×#13063373C22semidirect
18. C2×#13063372C22semidirect
19. C2×#13063372C22semidirect
25. #14583571C22semidirect
26. #14583570C22semidirect
27. #14583569C22semidirect
28. #14583568C22semidirect
29. #14583567C22semidirect
30. Q8×D172C22semidirect
31. D4×Dic86C22semidirect
32. #14583564C22semidirect
33. Q8×C22⋊D43C22semidirect
34. #14583562C22semidirect
35. #14583561C22semidirect
36. #14583560C22semidirect
37. #14583559C22semidirect
38. #14583558C22semidirect
39. #14583557C22semidirect
40. #14583556C22semidirect
41. #14583555C22semidirect
42. #14583480C22semidirect
43. #14583479C22semidirect
44. #14583478C22semidirect
45. #14583477C22semidirect
46. #14583476C22semidirect
47. #14583450C22semidirect
48. #14583449C22semidirect
49. #14583448C22semidirect
50. #14583447C22semidirect
51. #14583446C22semidirect
52. #14583446C22semidirect
53. #14583445C22semidirect
54. #14583444C22semidirect
55. #14583444C22semidirect
63. C2×Q8×Dic43C22semidirect
64. C2×C4×Dic86C22semidirect
65. C2×#13063290C22semidirect
68. C4×Q8×D43C22semidirect
69. C4×Q8×D43C22semidirect
74. C2×2−1+4×C43C22semidirect
75. C43×#550C22semidirect
76. D4×Q8×C43C22semidirect
77. C43×#548C22semidirect
78. C43×#537C22semidirect
79. C43×#532C22semidirect
80. C2×C4×Q8×C43C22semidirect
98. C2×Q8×D43D4semidirect
199. C2×Q8×C43C2×D4semidirect
225. Q8×D43C2×D4semidirect
256. C2×Dic86C2×D4semidirect
339. C4×D432−1+4semidirect
366. C4×C43C2×2−1+4semidirect
371. Dic43C2×2−1+4semidirect
380. #3497D43direct (N × H)
394. D43#3497direct (N × H)
400. C2×2−1+4C2×D43semidirect
410. #550C2×D43semidirect
416. D4×Q8C2×D43semidirect
424. #548C2×D43semidirect
430. #537C2×D43semidirect
440. #532C2×D43semidirect
455. C2×C4×Q8C2×D43semidirect
460. C43C2×#3497semidirect
597. C2×Q8D4×D43semidirect
750. C42−1+4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D432
#191483662
#191483652
#191483642
#191483632
#191483622
#191483612
#191483602
#550×D432
D4×Q8×D432
#548×D432
#537×D432
#532×D432
C2×C4×Q8×D432
C43×#34972
C2×#349743