Finite Group Databasebeta

← D43×#3550 #26004401

Subgroups — D43×#3550 #26004401

Order 11008.

7074 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149009C211yesmaximal, characteristic, complemented
2#19149008C214yesmaximal, complemented
3#19149007C212yesmaximal, complemented
4#19149006C212yesmaximal, complemented
5#19149005C214yesmaximal, complemented
6#19149004C214yesmaximal, complemented
7#19149003C218yesmaximal, complemented
8#19149002C214yesmaximal, complemented
9#19149001C212yesmaximal, complemented
10#563×D43C214yesmaximal, complemented
11#559×D43C212yesmaximal, complemented
12Q82×D43C212yesmaximal, complemented
13#556×D43C214yesmaximal, complemented
14D4×Q8×D43C214yesmaximal, complemented
15#542×D43C218yesmaximal, complemented
16#536×D43C214yesmaximal, complemented
17#533×D43C212yesmaximal, complemented
18#532×D43C211yesmaximal, characteristic
19C43×#3550C211yesmaximal, characteristic, complemented
20C2×#41×D43C2212yes—
21C22×Q8×D43C2214yes—
22#14583653C2218yescomplemented
23#14583652C2218yescomplemented
24#14583651C22116yescomplemented
25#14583650C22116yescomplemented
26#14583649C2214yescomplemented
27#14583648C2218yescomplemented
28#14583635C2212yescomplemented
29#14583634C2214yescomplemented
30#14583633C2218yescomplemented
31#14583632C2218yescomplemented
32#14583631C2218yescomplemented
33Q8×Dic86C2218yescomplemented
34Q8×Dic86C2214yescomplemented
35#14583629C2212yescomplemented
36#14583629C2218yescomplemented
37#14583629C2218yescomplemented
38#14583623C2214yescomplemented
39#14583622C2214yescomplemented
40#14583621C2218yescomplemented
41#14583620C2218yescomplemented
42#14583619C2214yescomplemented
43#14583618C2218yescomplemented
44#14583617C2218yescomplemented
45#14583616C22116yescomplemented
46Q8×D172C2214yescomplemented
47D4×Dic86C2218yescomplemented
48D4×Dic86C2214yescomplemented
49#14583564C2218yescomplemented
50#14583564C2214yescomplemented
51Q8×C22⋊D43C2218yescomplemented
52#14583562C22116yescomplemented
53#14583562C2218yescomplemented
54#14583523C2218yescomplemented
55#14583522C2218yescomplemented
56#14583521C2218yescomplemented
57#14583520C2218yescomplemented
58#14583519C22116yescomplemented
59#14583518C2218yescomplemented
60#14583517C22116yescomplemented
61#14583516C2218yescomplemented
62#14583515C22116yescomplemented
63#14583514C2218yescomplemented
64#14583513C22116yescomplemented
65#14583475C2214yescomplemented
66#14583474C2218yescomplemented
67#14583473C2214yescomplemented
68#14583472C2218yescomplemented
69#14583472C2218yescomplemented
70#14583471C2218yescomplemented
71#14583471C2218yescomplemented
72#14583470C2214yescomplemented
73#14583469C2218yescomplemented
74#14583456C2212yescomplemented
75#14583455C2214yescomplemented
76#14583454C2212yescomplemented
77#14583454C2212yescomplemented
78#14583453C2214yescomplemented
79#14583453C2214yescomplemented
80#14583452C2214yescomplemented
81#14583451C2214yescomplemented
82#14583451C2214yescomplemented
83#14583450C2211yescharacteristic
84#14583449C2211yescharacteristic
85#14583448C2212yes—
86#14583447C2211yescharacteristic
87#14583446C2214yes—
88#14583445C2212yes—
89#14583444C2214yes—
90C4⋊Q8×D43C2212yes—
91C4⋊Q8×D43C2218yes—
92C4⋊Q8×D43C2211yescharacteristic
93C4⋊Q8×D43C2212yes—
94C4⋊Q8×D43C2218yes—
95#127×D43C2211yescharacteristic
96#126×D43C22116yes—
97#125×D43C2214yes—
98#124×D43C2212yes—
99#124×D43C2218yes—
100#124×D43C2218yes—
101#123×D43C2218yes—
102#123×D43C2218yes—
103C22⋊Q8×D43C2218yes—
104C22⋊Q8×D43C22116yes—
105C22⋊Q8×D43C2214yes—
106C22⋊Q8×D43C2214yes—
107#121×D43C2214yes—
108C4×Q8×D43C2214yes—
109C4×Q8×D43C2214yes—
110C4×Q8×D43C2218yes—
111C4×D4×D43C2214yes—
112C4×D4×D43C2218yes—
113#117×D43C2214yes—
114#117×D43C2214yes—
115C2×C42×D43C2211yescharacteristic
116C43×#563C2214yescomplemented
117C43×#559C2212yescomplemented
118Q82×C43C2212yescomplemented
119C43×#556C2214yescomplemented
120D4×Q8×C43C2214yescomplemented
121C43×#542C2218yescomplemented
122C43×#536C2214yescomplemented
123C43×#533C2212yescomplemented
124C43×#532C2211yescharacteristic
125C2×#10621902C2312yes—
126C2×#10621898C2312yes—
127C2×#10621898C2314yes—
128C2×#10621900C2314yes—
129C2×#10621900C2312yes—
130#41×D43—48no—
131C22×Dic86C2314yes—
132C22×Dic86C2318yes—
133C2×Q8×D43—416no—
134C2×Q8×D43C2314yes—
135C2×Q8×D43C2314yes—
136C2×Q8×D43C2318yes—
137C2×Q8×D43C2318yes—
138C2×Q8×D43C2318yes—
139C2×Q8×D43C2312yes—
140C2×D4×D43C2314yes—
141C2×D4×D43C2314yes—
142C2×D4×D43C2312yes—
143C22×C4×D43C2312yes—
144C22×C4×D43C2311yescharacteristic
145C22×C4×D43C2314yes—
146C22×C4×D43C2318yes—
147#13063325C2312yes—
148#13063325C2318yes—
149#13063325C2312yes—
150#13063325C2311yescharacteristic
151#13063325C2318yes—
152#13063324C2314yes—
153#13063324C23116yes—
154#13063324C2314yes—
155#13063324C2318yes—
156#13063324C2318yes—
157#13063324C2314yes—
158#13063324C2314yes—
159#13063324C2314yes—
160#13063324C23116yes—
161#13063324C23116yes—
162#13063323C2314yes—
163#13063323C23116yes—
164#13063323C2314yes—
165#13063323C2312yes—
166#13063323C2318yes—
167#13063323C2318yes—
168#13063322C2311yescharacteristic
169#13063321C2314yes—
170#13063321C2312yes—
171#13063320C23116yes—
172#13063320C23116yes—
173#13063320C23116yes—
174#13063319C23116yes—
175#13063318C23116yes—
176#13063318C23116yes—
177#13063318C23116yes—
178#13063317C2314yes—
179#13063316C2314yes—
180#13063316C2314yes—
181#13063315C2318yes—
182#13063315C2318yes—
183#13063314C2318yes—
184#13063314C2312yes—
185#13063314C2318yes—
186#13063313C2318yes—
187#13063313C2312yes—
188#13063313C2318yes—
189#13063312C2318yes—
190#13063312C2312yes—
191#13063312C2318yes—
192#13063311C23116yes—
193#13063311C23116yes—
194#13063311C2318yes—
195#13063311C23116yes—
196#13063311C23116yes—
197#13063310C23116yes—
198#13063310C23116yes—
199#13063309C2318yes—
200#13063309C2318yes—
201#13063308C2318yes—
202#13063308C2318yes—
203#13063307C23116yes—
204#13063307C23116yes—
205#13063306C2318yes—
206#13063306C2318yes—
207#13063305C2318yes—
208#13063305C23116yes—
209#13063305C2314yes—
210#13063305C2314yes—
211#13063304C2318yes—
212#13063304C23116yes—
213#13063304C2314yes—
214#13063304C2314yes—
215#13063303C23116yes—
216#13063303C23116yes—
217#13063303C23116yes—
218#13063303C2318yes—
219#13063303C2318yes—
220#13063302C23116yes—
221#13063302C23116yes—
222#13063302C23116yes—
223#13063302C2318yes—
224#13063302C2318yes—
225#13063301C2318yes—
226#13063301C23116yes—
227#13063301C2314yes—
228#13063301C2314yes—
229#13063300C2314yes—
230#13063299C2314yes—
231#13063298C2318yes—
232#13063297C2318yes—
233#13063296C2314yes—
234Q8×Dic43C2314yes—
235Q8×Dic43C2318yes—
236Q8×Dic43C2314yes—
237C4×Dic86C2318yes—
238C4×Dic86C2314yes—
239C4×Dic86C23116yes—
240C4×Dic86C2318yes—
241C4×Dic86C2318yes—
242C4×Dic86C2314yes—
243#13063290C2318yes—
244#13063290C2314yes—
245#13063290C23116yes—
246#13063290C2318yes—
247#13063290C2314yes—
248#13063290C2318yes—
249C4×D172C2314yes—
250C4×D172C2318yes—
251D4×Dic43C2314yes—
252D4×Dic43C2318yes—
253#13063287C2314yes—
254#13063287C2318yes—
255C4×C22⋊D43C2318yes—
256C4×C22⋊D43C23116yes—
257(C22⋊D43)⋊C4C2318yes—
258(C22⋊D43)⋊C4C23116yes—
259#13063284C2314yes—
260#13063284C2314yes—
261#13063283C2318yes—
262#13063283C2314yes—
263#13063283C2314yes—
264#13063282C2318yes—
265#13063282C2318yes—
266#13063281C2318yes—
267#13063281C2318yes—
268C4⋊C4×D43C2314yes—
269C4⋊C4×D43C2314yes—
270C4⋊C4×D43C2314yes—
271C4⋊C4×D43C2314yes—
272C4⋊C4×D43C2314yes—
273C4⋊C4×D43C2318yes—
274C4⋊C4×D43C23116yes—
275C4⋊C4×D43C2318yes—
276C22⋊C4×D43C2318yes—
277C22⋊C4×D43C2318yes—
278C22⋊C4×D43C2318yes—
279C22⋊C4×D43C23116yes—
280C2×C4×Dic43C2312yes—
281C2×C4×Dic43C2311yescharacteristic
282C42×D43C2312yes—
283C42×D43C2311yescharacteristic
284C42×D43C2311yescharacteristic
285C42×D43C2312yes—
286C42×D43C2311yescharacteristic
287C42×D43C2311yescharacteristic
288C42×D43C2318yes—
289C42×D43C2318yes—
290C2×#41×C43C2312yes—
291C22×Q8×C43C2314yes—
292C4⋊Q8×C43C2312yes—
293C4⋊Q8×C43C2318yes—
294C4⋊Q8×C43C2311yescharacteristic
295C4⋊Q8×C43C2312yes—
296C4⋊Q8×C43C2318yes—
297#127×C43C2311yescharacteristic
298#126×C43C23116yes—
299#125×C43C2314yes—
300#124×C43C2312yes—
301#124×C43C2318yes—
302#124×C43C2318yes—
303#123×C43C2318yes—
304#123×C43C2318yes—
305C22⋊Q8×C43C2318yes—
306C22⋊Q8×C43C23116yes—
307C22⋊Q8×C43C2314yes—
308C22⋊Q8×C43C2314yes—
309#121×C43C2314yes—
310C4×Q8×C43C2314yes—
311C4×Q8×C43C2314yes—
312C4×Q8×C43C2318yes—
313C4×D4×C43C2314yes—
314C4×D4×C43C2318yes—
315#117×C43C2314yes—
316#117×C43C2314yes—
317C2×C42×C43C2311yescharacteristic
318C23×D43C2414yes—
319C23×D43C2411yescharacteristic
320#41×C43—44no—
321C2×Q8×C43—48no—
322C2×Q8×C43C2414yes—
323C2×Q8×C43C2414yes—
324C2×Q8×C43C2418yes—
325C2×Q8×C43C2412yes—
326C2×D4×C43C2414yes—
327C2×D4×C43C2414yes—
328C2×D4×C43C2412yes—
329C22×C4×C43C2412yes—
330C22×C4×C43C2411yescharacteristic
331C22×C4×C43C2414yes—
332C22×C4×C43C2418yes—
333C2×C22⋊D43C2418yes—
334C2×C22⋊D43C2414yes—
335C2×C22⋊D43C2414yes—
336C2×C22⋊D43C2414yes—
337C22×Dic43C2412yes—
338C22×Dic43C2411yescharacteristic
339C22×Dic43C2414yes—
340C22×Dic43C2418yes—
341#10621902—44no—
342Q8×D43—216no—
343Q8×D43—216no—
344Q8×D43—416no—
345Q8×D43—416no—
346Q8×D43—416no—
347Q8×D43—44no—
348#10621900—44no—
349#10621900—48no—
350D4×D43—216no—
351D4×D43—44no—
352D4×D43—48no—
353#10621898—48no—
354#10621898—44no—
355C2×D172C2414yes—
356C2×D172C2414yes—
357C2×D172C2412yes—
358C2×C4×D43—216no—
359C2×C4×D43—24no—
360C2×C4×D43—28no—
361C2×C4×D43—416no—
362C2×C4×D43C2418yes—
363C2×C4×D43C2412yes—
364C2×C4×D43C2414yes—
365C2×C4×D43C2411yescharacteristic
366C2×C4×D43C2412yes—
367C2×C4×D43C2412yes—
368C2×C4×D43C2411yescharacteristic
369C2×C4×D43C2411yescharacteristic
370C2×C4×D43C2418yes—
371C2×C4×D43C2414yes—
372C2×C4×D43C2414yes—
373C2×C4×D43C24116yes—
374C2×C4×D43C2411yescharacteristic
375C2×C4×D43C2412yes—
376C2×Dic86—416no—
377C2×Dic86—48no—
378C2×Dic86C2418yes—
379C2×Dic86C2414yes—
380C2×Dic86C2418yes—
381C2×Dic86C2414yes—
382C2×Dic86C2418yes—
383C2×Dic86C24116yes—
384C2×Dic86C2414yes—
385C2×Dic86C2412yes—
386C4⋊C4×C43C2414yes—
387C4⋊C4×C43C2414yes—
388C4⋊C4×C43C2414yes—
389C4⋊C4×C43C2414yes—
390C4⋊C4×C43C2414yes—
391C4⋊C4×C43C2418yes—
392C4⋊C4×C43C24116yes—
393C4⋊C4×C43C2418yes—
394C22⋊C4×C43C2418yes—
395C22⋊C4×C43C2418yes—
396C22⋊C4×C43C2418yes—
397C22⋊C4×C43C24116yes—
398C42×C43C2412yes—
399C42×C43C2411yescharacteristic
400C42×C43C2411yescharacteristic
401C42×C43C2418yes—
402C42×C43C2418yes—
403C22⋊Dic43C2418yes—
404C22⋊Dic43C2418yes—
405C22⋊Dic43C2418yes—
406C22⋊Dic43C24116yes—
407(C2×D43)⋊C4C2418yes—
408(C2×D43)⋊C4C2418yes—
409(C2×D43)⋊C4C24116yes—
410(C2×D43)⋊C4C2418yes—
411(C2×D43)⋊C4C24116yes—
412(C2×D43)⋊C4C2418yes—
413(C2×D43)⋊C4C24116yes—
414C4⋊Dic43C2414yes—
415C4⋊Dic43C2414yes—
416C4⋊Dic43C2414yes—
417C4⋊Dic43C2414yes—
418C4⋊Dic43C2414yes—
419C4⋊Dic43C2418yes—
420C4⋊Dic43C24116yes—
421C4⋊Dic43C2418yes—
422Dic43⋊C4C2418yes—
423Dic43⋊C4C2418yes—
424Dic43⋊C4C2418yes—
425Dic43⋊C4C2418yes—
426Dic43⋊C4C2418yes—
427Dic43⋊C4C2418yes—
428Dic43⋊C4C24116yes—
429Dic43⋊C4C24116yes—
430Dic43⋊C4C2418yes—
431Dic43⋊C4C2418yes—
432Dic43⋊C4C2418yes—
433C4×Dic43C2412yes—
434C4×Dic43C2412yes—
435C4×Dic43C2412yes—
436C4×Dic43C2411yescharacteristic
437C4×Dic43C2412yes—
438C4×Dic43C2412yes—
439C4×Dic43C2411yescharacteristic
440C4×Dic43C2418yes—
441C4×Dic43C2418yes—
442C4×Dic43C24116yes—
443C4×Dic43C2418yes—
444C4×Dic43C2418yes—
445C23×C43C2514yes—
446C23×C43C2511yescharacteristic
447C22×D43—28no—
448C22×D43—22no—
449C22×D43—24no—
450C22×D43—216no—
451C22×D43C2514yes—
452C22×D43C2511yescharacteristic
453C22×D43C2511yescharacteristic
454Q8×C43—28no—
455Q8×C43—28no—
456Q8×C43—48no—
457Q8×C43—42no—
458D4×C43—28no—
459D4×C43—44no—
460D4×C43—42no—
461C2×C4×C43—28no—
462C2×C4×C43—22no—
463C2×C4×C43—24no—
464C2×C4×C43—48no—
465C2×C4×C43C2518yes—
466C2×C4×C43C2511yescharacteristic
467C2×C4×C43C2514yes—
468C2×C4×C43C2512yes—
469C2×C4×C43C2518yes—
470C2×C4×C43C2511yescharacteristic
471C2×C4×C43C2512yes—
472C22⋊D43—216no—
473C22⋊D43—44no—
474C22⋊D43—44no—
475C22⋊D43—44no—
476C2×Dic43—28no—
477C2×Dic43—22no—
478C2×Dic43—24no—
479C2×Dic43—48no—
480C2×Dic43C2518yes—
481C2×Dic43C2512yes—
482C2×Dic43C2511yescharacteristic
483C2×Dic43C2514yes—
484C2×Dic43C2518yes—
485C2×Dic43C2511yescharacteristic
486C2×Dic43C2512yes—
487D172—28no—
488D172—44no—
489D172—42no—
490C4×D43—22no—
491C4×D43—28no—
492C4×D43—216no—
493C4×D43—24no—
494C4×D43—216no—
495C4×D43—22no—
496C4×D43—28no—
497C4×D43—24no—
498C4×D43—22no—
499C4×D43—28no—
500C4×D43—24no—
501C4×D43—416no—
502C4×D43H(5,𝔽2)14yes—
503C4×D432−1+418yes—
504Dic86—28no—
505Dic86—28no—
506Dic86—216no—
507Dic86—216no—
508Dic86—48no—
509Dic86—416no—
510Dic86—42no—
511Dic86—44no—
512C2×#3550—431nomaximal, Sylow
513C22×C43—24no—
514C22×C43—21no—
515C22×C43—22no—
516C22×C43—28no—
517C22×C43C2611yescharacteristic
518C2×D43—24no—
519C2×D43—21no—
520C2×D43—22no—
521C2×D43—28no—
522C2×D43—416no—
523C2×D43—44no—
524C2×D43C2×H(5,𝔽2)12yes—
525C2×D43C2×2−1+414yes—
526C4×C43—28no—
527C4×C43—24no—
528C4×C43—21no—
529C4×C43—28no—
530C4×C43—22no—
531C4×C43C2×H(5,𝔽2)12yes—
532C4×C43C2×2−1+414yes—
533Dic43—28no—
534Dic43—24no—
535Dic43—21no—
536Dic43—28no—
537Dic43—22no—
538Dic43C2×H(5,𝔽2)12yes—
539Dic43C2×2−1+414yes—
540#3550—434no—
541#3550—432no—
542#3550—432no—
543#3550—434no—
544#3550—434no—
545#3550—438no—
546#3550—434no—
547#3550—432no—
548#3550—431no—
549#3550D4311yescharacteristic, direct product factor
550C2×#563—434no—
551C2×#559—432no—
552C2×Q82—432no—
553C2×#556—434no—
554C2×D4×Q8—434no—
555C2×#542—438no—
556C2×#536—434no—
557C2×#533—432no—
558C2×#532—431no—
559C2×C43—44no—
560C2×C43—41no—
561C2×C43C22×H(5,𝔽2)11yescharacteristic
562C2×C43C22×2−1+412yes—
563D43—44no—
564D43—41no—
565D43#355014yesdirect product factor
566C22×#41—432no—
567C23×Q8—434no—
568#563—438no—
569#563—4316no—
570#563—438no—
571#563—434no—
572#563—438no—
573#563—4316no—
574#563C2×D4314yescomplemented
575#559—432no—
576#559—438no—
577#559—438no—
578#559—434no—
579#559—438no—
580#559C2×D4312yescomplemented
581Q82—438no—
582Q82—438no—
583Q82—432no—
584Q82—438no—
585Q82—434no—
586Q82C2×D4312yescomplemented
587#556—434no—
588#556—4316no—
589#556—438no—
590#556—438no—
591#556—438no—
592#556—434no—
593#556—434no—
594#556—438no—
595#556C2×D4314yescomplemented
596D4×Q8—438no—
597D4×Q8—438no—
598D4×Q8—434no—
599D4×Q8—438no—
600D4×Q8—4316no—
601D4×Q8—434no—
602D4×Q8—438no—
603D4×Q8—434no—
604D4×Q8C2×D4314yescomplemented
605#542—438no—
606#542—4316no—
607#542—4316no—
608#542—438no—
609#542—4316no—
610#542—4316no—
611#542—438no—
612#542—438no—
613#542—438no—
614#542—438no—
615#542—438no—
616#542C2×D4318yescomplemented
617#536—434no—
618#536—434no—
619#536—438no—
620#536—438no—
621#536—438no—
622#536—438no—
623#536—438no—
624#536—438no—
625#536—434no—
626#536C2×D4314yescomplemented
627#533—432no—
628#533—432no—
629#533—434no—
630#533—434no—
631#533—434no—
632#533—434no—
633#533—434no—
634#533—434no—
635#533—432no—
636#533C2×D4312yescomplemented
637#532—432no—
638#532—431no—
639#532—431no—
640#532—432no—
641#532—434no—
642#532—434no—
643#532—431no—
644#532C2×D4311yescharacteristic
645C2×C4⋊Q8—431no—
646C2×C4⋊Q8—432no—
647C2×C4⋊Q8—432no—
648C2×C4⋊Q8—438no—
649C2×C4⋊Q8—438no—
650C2×#127—431no—
651C2×#126—4316no—
652C2×#125—434no—
653C2×#124—432no—
654C2×#124—438no—
655C2×#124—438no—
656C2×#123—438no—
657C2×#123—438no—
658C2×C22⋊Q8—434no—
659C2×C22⋊Q8—434no—
660C2×C22⋊Q8—438no—
661C2×C22⋊Q8—4316no—
662C2×#121—434no—
663C2×C4×Q8—434no—
664C2×C4×Q8—434no—
665C2×C4×Q8—438no—
666C2×C4×D4—434no—
667C2×C4×D4—438no—
668C2×#117—434no—
669C2×#117—434no—
670C22×C42—431no—
671C43C2×#355011yescharacteristic, complemented, Sylow
672C2×#41—432no—
673C2×#41—434no—
674C2×#41—432no—
675C2×#41—434no—
676C2×#41—432no—
677C2×#41—1728no—
678C2×#41C22×D4312yes—
679C22×Q8—434no—
680C22×Q8—434no—
681C22×Q8—438no—
682C22×Q8—432no—
683C22×Q8—438no—
684C22×Q8—438no—
685C22×Q8—438no—
686C22×Q8—434no—
687C22×Q8—17216no—
688C22×Q8C22×D4314yes—
689C22×D4—434no—
690C22×D4—434no—
691C22×D4—432no—
692C23×C4—432no—
693C23×C4—434no—
694C23×C4—431no—
695C23×C4—438no—
696C4⋊Q8—432no—
697C4⋊Q8—434no—
698C4⋊Q8—434no—
699C4⋊Q8—438no—
700C4⋊Q8—438no—
701C4⋊Q8—4316no—
702C4⋊Q8—434no—
703C4⋊Q8—434no—
704C4⋊Q8—434no—
705C4⋊Q8—434no—
706C4⋊Q8—434no—
707C4⋊Q8—4316no—
708C4⋊Q8—4316no—
709C4⋊Q8—4316no—
710C4⋊Q8—438no—
711C4⋊Q8—438no—
712C4⋊Q8—431no—
713C4⋊Q8—432no—
714C4⋊Q8—432no—
715C4⋊Q8—438no—
716C4⋊Q8—438no—
717C4⋊Q8C22×D4311yescharacteristic
718C4⋊Q8C22×D4312yes—
719C4⋊Q8C22×D4312yes—
720C4⋊Q8C22×D4318yes—
721C4⋊Q8C22×D4318yes—
722#127—432no—
723#127—434no—
724#127—431no—
725#127C22×D4311yescharacteristic
726#126—4316no—
727#126—4316no—
728#126—4316no—
729#126—4316no—
730#126—4316no—
731#126—4316no—
732#126—4316no—
733#126C22×D43116yes—
734#125—438no—
735#125—438no—
736#125—434no—
737#125—434no—
738#125—434no—
739#125C22×D4314yes—
740#124—432no—
741#124—438no—
742#124—438no—
743#124—432no—
744#124—438no—
745#124—438no—
746#124—438no—
747#124—4316no—
748#124—4316no—
749#124—4316no—
750#124—4316no—
751#124—432no—
752#124—438no—
753#124—438no—
754#124C22×D4312yes—
755#124C22×D4318yes—
756#124C22×D4318yes—
757#123—438no—
758#123—438no—
759#123—438no—
760#123—438no—
761#123—4316no—
762#123—4316no—
763#123—4316no—
764#123—438no—
765#123—4316no—
766#123—438no—
767#123C22×D4318yes—
768#123C22×D4318yes—
769C22⋊Q8—434no—
770C22⋊Q8—434no—
771C22⋊Q8—438no—
772C22⋊Q8—4316no—
773C22⋊Q8—434no—
774C22⋊Q8—434no—
775C22⋊Q8—438no—
776C22⋊Q8—4316no—
777C22⋊Q8—438no—
778C22⋊Q8—434no—
779C22⋊Q8—438no—
780C22⋊Q8—434no—
781C22⋊Q8—4316no—
782C22⋊Q8—438no—
783C22⋊Q8—4316no—
784C22⋊Q8—4316no—
785C22⋊Q8—4316no—
786C22⋊Q8—438no—
787C22⋊Q8—438no—
788C22⋊Q8—4316no—
789C22⋊Q8—4316no—
790C22⋊Q8—4316no—
791C22⋊Q8C22×D4314yes—
792C22⋊Q8C22×D4314yes—
793C22⋊Q8C22×D4318yes—
794C22⋊Q8C22×D43116yes—
795#121—434no—
796#121—438no—
797#121—434no—
798#121—434no—
799#121—438no—
800#121C22×D4314yes—
801C4×Q8—434no—
802C4×Q8—434no—
803C4×Q8—438no—
804C4×Q8—438no—
805C4×Q8—434no—
806C4×Q8—438no—
807C4×Q8—434no—
808C4×Q8—4316no—
809C4×Q8—438no—
810C4×Q8—438no—
811C4×Q8—434no—
812C4×Q8—438no—
813C4×Q8—434no—
814C4×Q8—4316no—
815C4×Q8—438no—
816C4×Q8C22×D4314yes—
817C4×Q8C22×D4314yes—
818C4×Q8C22×D4318yes—
819C4×D4—434no—
820C4×D4—438no—
821C4×D4—438no—
822C4×D4—4316no—
823C4×D4—434no—
824C4×D4—438no—
825C4×D4—438no—
826C4×D4—4316no—
827C4×D4—434no—
828C4×D4—438no—
829C4×D4C22×D4314yes—
830C4×D4C22×D4318yes—
831#117—434no—
832#117—434no—
833#117—434no—
834#117—434no—
835#117—438no—
836#117—438no—
837#117—438no—
838#117—438no—
839#117—438no—
840#117C22×D4314yes—
841#117C22×D4314yes—
842C2×C4⋊C4—434no—
843C2×C4⋊C4—434no—
844C2×C4⋊C4—434no—
845C2×C4⋊C4—434no—
846C2×C4⋊C4—434no—
847C2×C4⋊C4—438no—
848C2×C4⋊C4—4316no—
849C2×C4⋊C4—438no—
850C2×C22⋊C4—438no—
851C2×C22⋊C4—438no—
852C2×C22⋊C4—438no—
853C2×C22⋊C4—4316no—
854C2×C42—431no—
855C2×C42—432no—
856C2×C42—438no—
857C2×C42—438no—
858C2×C42—432no—
859C2×C42—431no—
860C2×C42—431no—
861C2×C42—431no—
862C2×C42—431no—
863C2×C42—432no—
864C2×C42C22×D4311yescharacteristic
865C24—434no—
866C24—431no—
867#41—44no—
868#41—1728no—
869#41—1724no—
870#41—1728no—
871#41—1724no—
872#41—1724no—
873C2×Q8—48no—
874C2×Q8—438no—
875C2×Q8—434no—
876C2×Q8—438no—
877C2×Q8—434no—
878C2×Q8—4316no—
879C2×Q8—438no—
880C2×Q8—432no—
881C2×Q8—434no—
882C2×Q8—8616no—
883C2×Q8—8616no—
884C2×Q8—1728no—
885C2×Q8—17216no—
886C2×Q8—17216no—
887C2×Q8—1724no—
888C2×Q8—17216no—
889C2×Q8—17216no—
890C2×Q8C23×D4314yes—
891C2×Q8C23×D4314yes—
892C2×Q8C23×D4318yes—
893C2×Q8C23×D4312yes—
894C2×D4—438no—
895C2×D4—434no—
896C2×D4—434no—
897C2×D4—434no—
898C2×D4—434no—
899C2×D4—434no—
900C2×D4—432no—
901C2×D4—8616no—
902C2×D4—1724no—
903C2×D4—1728no—
904C2×D4C23×D4314yes—
905C2×D4C23×D4314yes—
906C2×D4C23×D4312yes—
907C22×C4—432no—
908C22×C4—431no—
909C22×C4—432no—
910C22×C4—431no—
911C22×C4—434no—
912C22×C4—438no—
913C22×C4—438no—
914C22×C4—432no—
915C22×C4—434no—
916C22×C4—431no—
917C22×C4—432no—
918C22×C4—432no—
919C22×C4—431no—
920C22×C4—431no—
921C22×C4—438no—
922C22×C4—434no—
923C22×C4—434no—
924C22×C4—4316no—
925C22×C4—8616no—
926C22×C4—864no—
927C22×C4—868no—
928C22×C4—17216no—
929C22×C4C23×D4312yes—
930C22×C4C23×D4311yescharacteristic
931C22×C4C23×D4314yes—
932C22×C4C23×D4318yes—
933C4⋊C4—438no—
934C4⋊C4—434no—
935C4⋊C4—438no—
936C4⋊C4—434no—
937C4⋊C4—438no—
938C4⋊C4—434no—
939C4⋊C4—438no—
940C4⋊C4—434no—
941C4⋊C4—438no—
942C4⋊C4—434no—
943C4⋊C4—438no—
944C4⋊C4—438no—
945C4⋊C4—438no—
946C4⋊C4—4316no—
947C4⋊C4—4316no—
948C4⋊C4—4316no—
949C4⋊C4—438no—
950C4⋊C4—438no—
951C4⋊C4—438no—
952C4⋊C4C23×D4314yes—
953C4⋊C4C23×D4314yes—
954C4⋊C4C23×D4314yes—
955C4⋊C4C23×D4314yes—
956C4⋊C4C23×D4314yes—
957C4⋊C4C23×D4318yes—
958C4⋊C4C23×D43116yes—
959C4⋊C4C23×D4318yes—
960C22⋊C4—438no—
961C22⋊C4—438no—
962C22⋊C4—438no—
963C22⋊C4—4316no—
964C22⋊C4—438no—
965C22⋊C4—438no—
966C22⋊C4—4316no—
967C22⋊C4—438no—
968C22⋊C4—438no—
969C22⋊C4—4316no—
970C22⋊C4—4316no—
971C22⋊C4C23×D4318yes—
972C22⋊C4C23×D4318yes—
973C22⋊C4C23×D4318yes—
974C22⋊C4C23×D43116yes—
975C42—432no—
976C42—432no—
977C42—432no—
978C42—431no—
979C42—432no—
980C42—431no—
981C42—432no—
982C42—438no—
983C42—438no—
984C42—438no—
985C42—438no—
986C42—4316no—
987C42C23×D4312yes—
988C42C23×D4311yescharacteristic
989C42C23×D4311yescharacteristic
990C42C23×D4318yes—
991C42C23×D4318yes—
992C23—431no—
993C23—434no—
994C23—431no—
995C23—868no—
996C23—862no—
997C23—864no—
998C23—8616no—
999C23C24×D4314yes—
1000C23C24×D4311yescharacteristic
1001Q8—28no—
1002Q8—28no—
1003Q8—48no—
1004Q8—42no—
1005Q8—8616no—
1006Q8—8616no—
1007Q8—868no—
1008Q8—868no—
1009Q8—1728no—
1010Q8—17216no—
1011Q8—1722no—
1012Q8—1724no—
1013D4—28no—
1014D4—42no—
1015D4—44no—
1016D4—8616no—
1017D4—868no—
1018D4—1722no—
1019D4—1724no—
1020D4—1724no—
1021D4—1724no—
1022D4—1724no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—48no—
1027C2×C4—432no—
1028C2×C4—431no—
1029C2×C4—434no—
1030C2×C4—438no—
1031C2×C4—438no—
1032C2×C4—432no—
1033C2×C4—434no—
1034C2×C4—431no—
1035C2×C4—438no—
1036C2×C4—868no—
1037C2×C4—862no—
1038C2×C4—864no—
1039C2×C4—862no—
1040C2×C4—868no—
1041C2×C4—864no—
1042C2×C4—8616no—
1043C2×C4—8616no—
1044C2×C4—868no—
1045C2×C4—862no—
1046C2×C4—864no—
1047C2×C4—868no—
1048C2×C4—862no—
1049C2×C4—864no—
1050C2×C4—17216no—
1051C2×C4—1728no—
1052C2×C4C24×D4318yes—
1053C2×C4C24×D4312yes—
1054C2×C4C24×D4314yes—
1055C2×C4C24×D4311yescharacteristic
1056C2×C4C24×D4318yes—
1057C2×C4C24×D4311yescharacteristic
1058C2×C4C24×D4312yes—
1059C22—24no—
1060C22—21no—
1061C22—22no—
1062C22—28no—
1063C22—432no—
1064C22—434no—
1065C22—864no—
1066C22—861no—
1067C22—862no—
1068C22—868no—
1069C22—17216no—
1070C22—1724no—
1071C22C25×D4311yescharacteristic
1072C4—21no—
1073C4—24no—
1074C4—28no—
1075C4—22no—
1076C4—28no—
1077C4—432no—
1078C4—434no—
1079C4—861no—
1080C4—864no—
1081C4—868no—
1082C4—862no—
1083C4—868no—
1084C4H(5,𝔽2)×D4312yes—
1085C42−1+4×D4314yes—
1086C2—44no—
1087C2—41no—
1088C2—434no—
1089C2—1724no—
1090C2—1721no—
1091C2C2×H(5,𝔽2)×D4311yescharacteristic
1092C2C2×2−1+4×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3550C2
prime radical#532×D43C2
hypercenter#3550D43
hypocenterC43C2×#3550
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #19149009C2semidirect
2. #19149008C2semidirect
3. #19149007C2semidirect
4. #19149006C2semidirect
5. #19149005C2semidirect
6. #19149004C2semidirect
7. #19149003C2semidirect
8. #19149002C2semidirect
9. #19149001C2semidirect
10. #563×D43C2semidirect
11. #559×D43C2semidirect
12. Q82×D43C2semidirect
13. #556×D43C2semidirect
14. D4×Q8×D43C2semidirect
15. #542×D43C2semidirect
16. #536×D43C2semidirect
17. #533×D43C2semidirect
19. C43×#3550C2semidirect
22. #14583653C22semidirect
23. #14583652C22semidirect
24. #14583651C22semidirect
25. #14583650C22semidirect
26. #14583649C22semidirect
27. #14583648C22semidirect
28. #14583635C22semidirect
29. #14583634C22semidirect
30. #14583633C22semidirect
31. #14583632C22semidirect
32. #14583631C22semidirect
33. Q8×Dic86C22semidirect
34. Q8×Dic86C22semidirect
35. #14583629C22semidirect
36. #14583629C22semidirect
37. #14583629C22semidirect
38. #14583623C22semidirect
39. #14583622C22semidirect
40. #14583621C22semidirect
41. #14583620C22semidirect
42. #14583619C22semidirect
43. #14583618C22semidirect
44. #14583617C22semidirect
45. #14583616C22semidirect
46. Q8×D172C22semidirect
47. D4×Dic86C22semidirect
48. D4×Dic86C22semidirect
49. #14583564C22semidirect
50. #14583564C22semidirect
51. Q8×C22⋊D43C22semidirect
52. #14583562C22semidirect
53. #14583562C22semidirect
54. #14583523C22semidirect
55. #14583522C22semidirect
56. #14583521C22semidirect
57. #14583520C22semidirect
58. #14583519C22semidirect
59. #14583518C22semidirect
60. #14583517C22semidirect
61. #14583516C22semidirect
62. #14583515C22semidirect
63. #14583514C22semidirect
64. #14583513C22semidirect
65. #14583475C22semidirect
66. #14583474C22semidirect
67. #14583473C22semidirect
68. #14583472C22semidirect
69. #14583472C22semidirect
70. #14583471C22semidirect
71. #14583471C22semidirect
72. #14583470C22semidirect
73. #14583469C22semidirect
74. #14583456C22semidirect
75. #14583455C22semidirect
76. #14583454C22semidirect
77. #14583454C22semidirect
78. #14583453C22semidirect
79. #14583453C22semidirect
80. #14583452C22semidirect
81. #14583451C22semidirect
82. #14583451C22semidirect
116. C43×#563C22semidirect
117. C43×#559C22semidirect
118. Q82×C43C22semidirect
119. C43×#556C22semidirect
120. D4×Q8×C43C22semidirect
121. C43×#542C22semidirect
122. C43×#536C22semidirect
123. C43×#533C22semidirect
549. #3550D43direct (N × H)
565. D43#3550direct (N × H)
574. #563C2×D43semidirect
580. #559C2×D43semidirect
586. Q82C2×D43semidirect
595. #556C2×D43semidirect
604. D4×Q8C2×D43semidirect
616. #542C2×D43semidirect
626. #536C2×D43semidirect
636. #533C2×D43semidirect
671. C43C2×#3550semidirect

Maximal subgroups

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

subgroupindex
#191490092
#191490082
#191490072
#191490062
#191490052
#191490042
#191490032
#191490022
#191490012
#563×D432
#559×D432
Q82×D432
#556×D432
D4×Q8×D432
#542×D432
#536×D432
#533×D432
#532×D432
C43×#35502
C2×#355043