Finite Group Databasebeta

← #26004823

Subgroups — #26004823

Order 11008.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148692C211yesmaximal, characteristic, complemented
2#19148690C213yesmaximal, complemented
3#19148677C213yesmaximal, complemented
4#19148675C211yesmaximal, characteristic, complemented
5#19148579C216yesmaximal, complemented
6#19148577C212yesmaximal, complemented
7#19148452C213yesmaximal, complemented
8#19148450C213yesmaximal, complemented
9#19148399C211yesmaximal, characteristic, complemented
10#19148360C211yesmaximal, characteristic, complemented
11#19148299C216yesmaximal, complemented
12#19148241C212yesmaximal, complemented
13#19148217C212yesmaximal, complemented
14#19148208C216yesmaximal, complemented
15#19148192C213yesmaximal, complemented
16Q8×#10621898C211yesmaximal, characteristic, complemented
17#41×Dic86C213yesmaximal, complemented
18#19148020C216yesmaximal, complemented
19#19147890C213yesmaximal, complemented
20#19147888C213yesmaximal, complemented
21C4×#13063372C212yesmaximal, complemented
22C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
23C43×#3480C211yesmaximal, characteristic, complemented
24C2×#13063372C2212yes—
25C22×Q8×D43C2211yescharacteristic
26#14583635C2213yescomplemented
27#14583631C2216yescomplemented
28Q8×Dic86C2211yescharacteristic, complemented
29Q8×Dic86C2213yescomplemented
30#14583628C2212yescomplemented
31#14583628C2213yescomplemented
32#14583627C2213yescomplemented
33#14583626C2216yescomplemented
34#14583625C2216yescomplemented
35#14583624C2213yescomplemented
36#14583623C2213yescomplemented
37#14583619C2216yescomplemented
38#14583618C2216yescomplemented
39#14583618C2216yescomplemented
40#14583616C22112yescomplemented
41#14583609C2213yescomplemented
42#14583608C22112yes—
43#14583608C2216yescomplemented
44#14583606C2216yes—
45#14583606C2213yescomplemented
46#14583604C2216yes—
47#14583601C2216yes—
48#14583592C22112yes—
49#14583591C2216yescomplemented
50#14583588C2216yes—
51#14583588C2216yescomplemented
52#14583587C2216yes—
53#14583586C22112yescomplemented
54#14583585C22112yes—
55#14583569C2213yescomplemented
56Q8×D172C2212yes—
57Q8×D172C2211yescharacteristic, complemented
58D4×Dic86C2216yes—
59D4×Dic86C2213yescomplemented
60Q8×C22⋊D43C2212yes—
61#14583562C2216yes—
62#14583557C2216yes—
63#14583556C2212yes—
64#14583556C2212yescomplemented
65#14583555C2216yes—
66#14583555C2216yescomplemented
67#14583554C2216yes—
68#14583549C2216yes—
69#14583547C22112yes—
70#14583529C2216yes—
71#14583518C2216yescomplemented
72#14583517C22112yescomplemented
73#14583516C2216yescomplemented
74#14583512C2216yescomplemented
75#14583509C2216yescomplemented
76#14583506C22112yescomplemented
77#14583492C22112yes—
78#14583490C22112yes—
79#14583478C2216yes—
80#14583472C2216yes—
81#14583469C2216yes—
82#14583456C2213yes—
83#14583456C2216yescomplemented
84#14583454C2213yes—
85#14583454C2213yes—
86#14583453C2213yes—
87#14583453C2213yes—
88#14583453C2216yescomplemented
89#14583452C2213yes—
90#14583452C22112yescomplemented
91#14583447C2213yes—
92#14583447C2213yes—
93#14583446C2213yes—
94#14583446C2213yes—
95#14583445C2213yes—
96#14583436C2213yes—
97#14583436C2213yes—
98#14583431C2213yes—
99#14583431C2213yes—
100#14583431C2216yes—
101#14583431C2216yes—
102#14583431C2216yescomplemented
103#14583430C2216yes—
104#14583430C2216yes—
105#14583429C2216yes—
106#14583429C2216yes—
107#14583429C22112yescomplemented
108#14583428C2216yes—
109#14583428C2216yes—
110#14583427C2216yes—
111#14583427C2216yes—
112#14583411C2211yescharacteristic
113#14583409C2216yes—
114#14583409C2216yes—
115#14583408C2216yes—
116#14583408C2216yes—
117#14583406C2213yes—
118#14583382C2212yescomplemented
119#14583379C2216yes—
120#14583378C2216yes—
121#14583378C2216yescomplemented
122#14583376C2216yescomplemented
123#14583375C2212yes—
124#14583375C2212yescomplemented
125#41×Dic43C2216yes—
126C4×#10621898C2216yes—
127C4×#10621898C2213yes—
128C4×#10621898C2216yes—
129C4×#10621900C2216yes—
130C4×#10621900C2216yes—
131C4×#10621900C2216yescomplemented
132C2×Q8×Dic43C2211yescharacteristic
133C2×C4×Dic86C2213yes—
134C2×C4×Dic86C2216yescomplemented
135C2×#13063290C2213yes—
136C4×Q8×D43C2211yescharacteristic
137C4×Q8×D43C2211yescharacteristic
138C4×Q8×D43C2211yescharacteristic
139C4×Q8×D43C2213yes—
140C4×Q8×D43C2213yes—
141C4×Q8×D43C2213yes—
142C4×Q8×D43C2211yescharacteristic
143C4×Q8×D43C2213yes—
144C4×Q8×D43C2212yescomplemented
145C2×C4⋊C4×D43C2213yes—
146C2×C42×D43C2213yes—
147C43×#559C2213yescomplemented
148C43×#557C2211yescharacteristic, complemented
149C43×#556C2213yescomplemented
150C43×#553C2216yes—
151C43×#550C2211yescharacteristic, complemented
152C43×#548C2212yes—
153C43×#532C2213yes—
154C43×#529C2216yescomplemented
155C4×#41×C43C2213yes—
156C4×#41×C43C2212yescomplemented
157C2×C4×Q8×C43C2211yescharacteristic
158#13063372—216no—
159C2×#10621898C2311yescharacteristic
160C2×#10621898C2316yes—
161C2×#10621898C2316yes—
162C2×#10621900C2316yes—
163C2×#10621900C2316yes—
164C2×#10621900C2316yes—
165C22×Dic86C2313yes—
166C22×Dic86C2316yes—
167C2×Q8×D43—28no—
168C2×Q8×D43C2311yescharacteristic
169C2×Q8×D43C2312yes—
170C2×Q8×D43C2313yes—
171C2×Q8×D43C2313yes—
172C2×Q8×D43C2311yescharacteristic
173C22×C4×D43C2311yescharacteristic
174C22×C4×D43C2313yes—
175C22×C4×D43C2313yes—
176#13063325C2316yes—
177#13063325C2316yes—
178#13063325C2313yes—
179#13063325C2313yes—
180#13063324C23112yes—
181#13063324C2313yes—
182#13063324C2316yes—
183#13063324C23112yes—
184#13063324C2313yes—
185#13063323C2316yes—
186#13063323C2313yes—
187#13063321C2313yes—
188#13063320C23112yes—
189#13063320C2316yes—
190#13063320C2316yes—
191#13063318C23112yes—
192#13063318C2316yes—
193#13063318C23112yes—
194#13063318C23112yes—
195#13063318C2316yes—
196#13063318C23112yes—
197#13063317C23112yes—
198#13063317C2316yes—
199#13063316C23112yes—
200#13063316C23112yes—
201#13063316C2316yes—
202#13063316C2316yes—
203#13063316C2313yes—
204#13063316C2313yes—
205#13063316C2316yes—
206#13063315C23112yes—
207#13063315C23112yes—
208#13063315C2316yes—
209#13063315C2316yes—
210#13063314C2313yes—
211#13063312C2316yes—
212#13063312C2316yes—
213#13063312C2313yes—
214#13063312C2316yes—
215#13063311C23112yes—
216#13063311C2316yes—
217#13063311C2316yes—
218#13063310C2316yes—
219#13063310C2316yes—
220#13063309C23112yes—
221#13063309C2312yes—
222#13063307C23112yes—
223#13063307C23112yes—
224#13063307C2316yes—
225#13063307C2316yes—
226#13063307C23112yes—
227#13063306C23112yes—
228#13063306C2316yes—
229#13063305C2316yes—
230#13063305C2316yes—
231#13063305C2316yes—
232#13063305C2316yes—
233#13063305C2311yescharacteristic
234#13063305C2311yescharacteristic
235#13063304C23112yes—
236#13063304C2316yes—
237#13063304C2316yes—
238#13063304C2316yes—
239#13063304C2316yes—
240#13063303C2316yes—
241#13063303C23112yes—
242#13063303C2316yes—
243#13063302C23112yes—
244#13063302C23112yes—
245#13063302C23112yes—
246#13063302C2316yes—
247#13063302C2316yes—
248#13063302C23112yes—
249#13063302C23112yes—
250#13063301C2316yes—
251#13063301C2313yes—
252#13063301C2313yes—
253#13063300C2311yescharacteristic
254#13063300C2311yescharacteristic
255#13063298C2316yes—
256#13063298C2316yes—
257#13063297C2316yes—
258#13063297C23112yes—
259#13063297C2316yes—
260#13063296C2316yes—
261#13063296C2316yes—
262#13063296C2313yes—
263#13063296C2313yes—
264#13063296C2316yes—
265#13063295C2312yes—
266#13063293C2316yes—
267Q8×Dic43C2312yes—
268Q8×Dic43C2311yescharacteristic
269Q8×Dic43C2313yes—
270Q8×Dic43C2311yescharacteristic
271Q8×Dic43C2313yes—
272Q8×Dic43C2316yes—
273Q8×Dic43C2316yes—
274C4×Dic86C2316yes—
275C4×Dic86C2313yes—
276C4×Dic86C23112yes—
277C4×Dic86C2316yes—
278C4×Dic86C2313yes—
279C4×Dic86C2316yes—
280C4×Dic86C2313yes—
281C4×Dic86C2316yes—
282C4×Dic86C2313yes—
283C4×Dic86C2316yes—
284C4×Dic86C2313yes—
285C4×Dic86C2316yes—
286C4×Dic86C2316yes—
287C4×Dic86C2316yes—
288C4×Dic86C2313yes—
289C4×Dic86C2316yes—
290C4×Dic86C2316yes—
291#13063290C2316yes—
292#13063290C2313yes—
293#13063290C2316yes—
294#13063290C2316yes—
295#13063290C2313yes—
296#13063290C2316yes—
297#13063290C2313yes—
298#13063290C2316yes—
299#13063290C2313yes—
300#13063290C2316yes—
301C4×D172C2316yes—
302C4×D172C2313yes—
303C4×D172C2313yes—
304C4×D172C2312yes—
305C4×D172C2312yes—
306C4×D172C2316yes—
307D4×Dic43C23112yes—
308D4×Dic43C2316yes—
309D4×Dic43C2316yes—
310D4×Dic43C23112yes—
311D4×Dic43C2316yes—
312D4×Dic43C2316yes—
313D4×Dic43C2316yes—
314C4×C22⋊D43C2316yes—
315C4×C22⋊D43C2316yes—
316C4×C22⋊D43C2316yes—
317C4×C22⋊D43C2316yes—
318C4×C22⋊D43C2316yes—
319C4×C22⋊D43C2316yes—
320C4×C22⋊D43C2316yes—
321C4×C22⋊D43C2316yes—
322C4×C22⋊D43C2316yes—
323C4×C22⋊D43C2316yes—
324(C22⋊D43)⋊C4C23112yes—
325(C22⋊D43)⋊C4C23112yes—
326(C22⋊D43)⋊C4C23112yes—
327#13063284C2316yes—
328#13063284C2313yes—
329#13063284C2316yes—
330#13063284C23112yes—
331#13063283C2316yes—
332#13063283C2316yes—
333#13063283C2316yes—
334#13063282C2316yes—
335#13063282C2316yes—
336#13063282C2316yes—
337#13063282C2316yes—
338#13063282C2316yes—
339#13063281C23112yes—
340#13063281C23112yes—
341#13063281C23112yes—
342C2×C4⋊Dic43C2316yes—
343C2×C4⋊Dic43C2313yes—
344C2×Dic43⋊C4C23112yes—
345C2×Dic43⋊C4C2316yes—
346C4⋊C4×D43C2313yes—
347C4⋊C4×D43C2316yes—
348C4⋊C4×D43C2316yes—
349C4⋊C4×D43C2313yes—
350C4⋊C4×D43C2313yes—
351C4⋊C4×D43C2313yes—
352C4⋊C4×D43C2316yes—
353C2×C4×Dic43C2313yes—
354C2×C4×Dic43C2313yes—
355C2×C4×Dic43C2313yes—
356C2×C4×Dic43C23112yes—
357C42×D43C2313yes—
358C42×D43C2313yes—
359C42×D43C2313yes—
360C42×D43C2313yes—
361C42×D43C2313yes—
362C42×D43C2313yes—
363C42×D43C2313yes—
364C42×D43C2313yes—
365C42×D43C2316yes—
366C2×#41×C43C2312yes—
367C2×#41×C43C2313yes—
368C22×Q8×C43C2311yescharacteristic
369C4⋊Q8×C43C2313yes—
370#127×C43C2313yes—
371#126×C43C23112yes—
372#125×C43C2316yes—
373#124×C43C2316yes—
374#124×C43C2316yes—
375#123×C43C23112yes—
376C22⋊Q8×C43C2316yes—
377#121×C43C2316yes—
378#121×C43C2316yes—
379#121×C43C2316yes—
380C4×Q8×C43C2312yes—
381C4×Q8×C43C2311yescharacteristic
382C4×Q8×C43C2311yescharacteristic
383C4×Q8×C43C2313yes—
384C4×Q8×C43C2313yes—
385C4×Q8×C43C2313yes—
386C4×Q8×C43C2313yes—
387C4×D4×C43C2316yes—
388C4×D4×C43C2316yes—
389C4×D4×C43C2313yes—
390C4×D4×C43C2316yes—
391C4×D4×C43C2313yes—
392C4×D4×C43C2316yes—
393C4×D4×C43C2316yes—
394#117×C43C2311yescharacteristic
395#117×C43C2316yes—
396#117×C43C2316yes—
397C2×C4⋊C4×C43C2313yes—
398C2×C42×C43C2313yes—
399C2×C42×C43C2316yes—
400C23×D43C2411yescharacteristic
401#41×C43—28no—
402#41×C43—212no—
403C2×Q8×C43—24no—
404C2×Q8×C43C2413yes—
405C2×Q8×C43C2413yes—
406C2×Q8×C43C2411yescharacteristic
407C2×D4×C43C2416yes—
408C2×D4×C43C2416yes—
409C2×D4×C43C2413yes—
410C2×D4×C43C2416yes—
411C22×C4×C43C2413yes—
412C22×C4×C43C2416yes—
413C22×C4×C43C2416yes—
414C22×C4×C43C2413yes—
415C22×C4×C43C2416yes—
416C22×C4×C43C2411yescharacteristic
417C2×C22⋊D43C2416yes—
418C2×C22⋊D43C2416yes—
419C2×C22⋊D43C2416yes—
420C2×C22⋊D43C2412yes—
421C2×C22⋊D43C2416yes—
422C22×Dic43C2411yescharacteristic
423C22×Dic43C2413yes—
424C22×Dic43C24112yes—
425C22×Dic43C2413yes—
426C22×Dic43C24112yes—
427Q8×D43—24no—
428Q8×D43—28no—
429Q8×D43—212no—
430Q8×D43—212no—
431Q8×D43#4118yescomplemented
432#10621900—224no—
433#10621900—224no—
434#10621900—412no—
435#10621898—24no—
436#10621898—224no—
437#10621898—412no—
438C2×D172C2411yescharacteristic
439C2×D172C2412yes—
440C2×D172C2412yes—
441C2×C4×D43—24no—
442C2×C4×D43—212no—
443C2×C4×D43—46no—
444C2×C4×D43C2411yescharacteristic
445C2×C4×D43C2411yescharacteristic
446C2×C4×D43C2411yescharacteristic
447C2×C4×D43C2411yescharacteristic
448C2×C4×D43C2412yes—
449C2×C4×D43C2413yes—
450C2×C4×D43C2413yes—
451C2×C4×D43C2413yes—
452C2×C4×D43C2413yes—
453C2×C4×D43C2413yes—
454C2×C4×D43C2416yes—
455C2×C4×D43C2413yes—
456C2×C4×D43C2413yes—
457C2×C4×D43C2416yes—
458C2×C4×D43C2413yes—
459C2×Dic86—212no—
460C2×Dic86—224no—
461C2×Dic86C2416yes—
462C2×Dic86C2413yes—
463C2×Dic86C2416yes—
464C2×Dic86C2411yescharacteristic
465C2×Dic86C2416yes—
466C2×Dic86C2416yes—
467C2×Dic86C2416yes—
468C2×Dic86C2413yes—
469C4⋊C4×C43C2413yes—
470C4⋊C4×C43C2413yes—
471C4⋊C4×C43C2416yes—
472C4⋊C4×C43C2411yescharacteristic
473C4⋊C4×C43C2411yescharacteristic
474C4⋊C4×C43C2416yes—
475C4⋊C4×C43C2416yes—
476C4⋊C4×C43C2416yes—
477C4⋊C4×C43C2416yes—
478C22⋊C4×C43C2412yes—
479C22⋊C4×C43C2416yes—
480C22⋊C4×C43C24112yes—
481C22⋊C4×C43C2416yes—
482C22⋊C4×C43C24112yes—
483C42×C43C2412yes—
484C42×C43C2413yes—
485C42×C43C2413yes—
486C42×C43C2416yes—
487C42×C43C2416yes—
488C42×C43C2413yes—
489C42×C43C2413yes—
490C22⋊Dic43C2416yes—
491C22⋊Dic43C2416yes—
492C22⋊Dic43C2416yes—
493C22⋊Dic43C2416yes—
494C22⋊Dic43C2416yes—
495C22⋊Dic43C24112yes—
496C22⋊Dic43C24112yes—
497(C2×D43)⋊C4C2412yes—
498(C2×D43)⋊C4C2412yes—
499(C2×D43)⋊C4C2412yes—
500(C2×D43)⋊C4C2412yes—
501(C2×D43)⋊C4C2416yes—
502(C2×D43)⋊C4C2416yes—
503(C2×D43)⋊C4C2416yes—
504(C2×D43)⋊C4C2416yes—
505(C2×D43)⋊C4C2416yes—
506(C2×D43)⋊C4C2416yes—
507C4⋊Dic43C2413yes—
508C4⋊Dic43C2413yes—
509C4⋊Dic43C2416yes—
510C4⋊Dic43C2416yes—
511C4⋊Dic43C2416yes—
512C4⋊Dic43C2416yes—
513C4⋊Dic43C2412yes—
514C4⋊Dic43C2412yes—
515C4⋊Dic43C2413yes—
516C4⋊Dic43C2413yes—
517C4⋊Dic43C24112yes—
518C4⋊Dic43C24112yes—
519C4⋊Dic43C2416yes—
520Dic43⋊C4C2416yes—
521Dic43⋊C4C2416yes—
522Dic43⋊C4C2416yes—
523Dic43⋊C4C2416yes—
524Dic43⋊C4C24112yes—
525Dic43⋊C4C2416yes—
526Dic43⋊C4C2416yes—
527Dic43⋊C4C2416yes—
528Dic43⋊C4C2416yes—
529Dic43⋊C4C2416yes—
530Dic43⋊C4C24112yes—
531Dic43⋊C4C2416yes—
532Dic43⋊C4C2416yes—
533Dic43⋊C4C2416yes—
534Dic43⋊C4C2416yes—
535Dic43⋊C4C2416yes—
536C4×Dic43C2413yes—
537C4×Dic43C2413yes—
538C4×Dic43C2413yes—
539C4×Dic43C2413yes—
540C4×Dic43C2413yes—
541C4×Dic43C2413yes—
542C4×Dic43C2413yes—
543C4×Dic43C2413yes—
544C4×Dic43C2413yes—
545C4×Dic43C2413yes—
546C4×Dic43C2413yes—
547C4×Dic43C2413yes—
548C4×Dic43C2416yes—
549C4×Dic43C2416yes—
550C4×Dic43C2416yes—
551C4×Dic43C24112yes—
552C4×Dic43C24112yes—
553C23×C43C2516yes—
554C23×C43C2511yescharacteristic
555C22×D43—22no—
556C22×D43—22no—
557C22×D43—22no—
558C22×D43C2512yes—
559C22×D43C2511yescharacteristic
560C22×D43C2511yescharacteristic
561Q8×C43—26no—
562Q8×C43—26no—
563Q8×C43C2×#4114yes—
564D4×C43—212no—
565D4×C43—212no—
566D4×C43—26no—
567D4×C43—46no—
568C2×C4×C43—26no—
569C2×C4×C43—212no—
570C2×C4×C43—212no—
571C2×C4×C43—43no—
572C2×C4×C43—46no—
573C2×C4×C432−1+414yescomplemented
574C2×C4×C43C2513yes—
575C2×C4×C43C2516yes—
576C2×C4×C43C2513yes—
577C2×C4×C43C2513yes—
578C2×C4×C43C2512yes—
579C2×C4×C43C2512yes—
580C2×C4×C43C2513yes—
581C2×C4×C43C2511yescharacteristic
582C2×C4×C43C2511yescharacteristic
583C22⋊D43—24no—
584C22⋊D43—212no—
585C22⋊D43—212no—
586C22⋊D43—212no—
587C22⋊D43—46no—
588C2×Dic43—22no—
589C2×Dic43—26no—
590C2×Dic43—224no—
591C2×Dic43—43no—
592C2×Dic43—412no—
593C2×Dic43C2511yescharacteristic
594C2×Dic43C2511yescharacteristic
595C2×Dic43C2513yes—
596C2×Dic43C2512yes—
597C2×Dic43C2513yes—
598C2×Dic43C2516yes—
599C2×Dic43C2516yes—
600C2×Dic43C2513yes—
601C2×Dic43C2513yes—
602D172—24no—
603D172—24no—
604D172—22no—
605C4×D43—26no—
606C4×D43—26no—
607C4×D43—26no—
608C4×D43—26no—
609C4×D43—212no—
610C4×D43—22no—
611C4×D43—22no—
612C4×D43—22no—
613C4×D43—22no—
614C4×D43—24no—
615C4×D43—26no—
616C4×D43—43no—
617C4×D43—43no—
618C4×D43—46no—
619C4×D43C2×#41112yes—
620Dic86—212no—
621Dic86—26no—
622Dic86—22no—
623Dic86—212no—
624Dic86—212no—
625Dic86—46no—
626Dic86—46no—
627Dic86C2×#41112yes—
628#62788—431nomaximal, Sylow
629C22×C43—21no—
630C22×C43—21no—
631C22×C43—26no—
632C22×C43—26no—
633C22×C43—26no—
634C22×C43C2×2−1+412yes—
635C22×C43C2611yescharacteristic
636C2×D43—28no—
637C2×D43—21no—
638C2×D43—21no—
639C2×D43—21no—
640C2×D43—21no—
641C2×D43—22no—
642C2×D43—22no—
643C2×D43—22no—
644C2×D43C22×#4112yes—
645C2×D43#58512yes—
646C4×C43—22no—
647C4×C43—23no—
648C4×C43—26no—
649C4×C43—22no—
650C4×C43—23no—
651C4×C43—23no—
652C4×C43C22×#4116yes—
653C4×C43C2×2−1+412yes—
654C4×C43C2×2−1+412yes—
655Dic43—23no—
656Dic43—26no—
657Dic43—22no—
658Dic43—21no—
659Dic43—21no—
660Dic43—26no—
661Dic43—23no—
662Dic43—23no—
663Dic43C22×#4116yes—
664#3523—431no—
665#3523—433no—
666#3522—433no—
667#3522—431no—
668#3516—436no—
669#3516—432no—
670#3507—433no—
671#3507—433no—
672#3502—431no—
673#3497—431no—
674#3492—436no—
675#3486—432no—
676#3482—436no—
677#3482—432no—
678#3480—433no—
679#3480D4311yescharacteristic, complemented
680Q8×#41—433no—
681Q8×#41—431no—
682#3461—436no—
683#3444—433no—
684#3444—433no—
685C4×2−1+4—432no—
686C22×C4×Q8—431no—
687C2×C43—22no—
688C2×C43—46no—
689C2×C43C23×#4111yescharacteristic
690C2×C43C22×2−1+411yescharacteristic
691C2×C43C2×#58511yescharacteristic
692D43—22no—
693D43—22no—
694D43—42no—
695C2×2−1+4—432no—
696C23×Q8—431no—
697#559—433no—
698#559—436no—
699#559C2×D4313yescomplemented
700Q82—431no—
701Q82—433no—
702#557—433no—
703#557—436no—
704#557—436no—
705#557—433no—
706#557—433no—
707#557—432no—
708#557C2×D4311yescharacteristic, complemented
709#556—433no—
710#556—4312no—
711#556—436no—
712#556—436no—
713#556—436no—
714#556C2×D4313yescomplemented
715#554—433no—
716#554—436no—
717#554—433no—
718#554—4312no—
719#554—436no—
720#554—436no—
721#553—4312no—
722#553—436no—
723#553C2×D4316yes—
724#552—4312no—
725#552—436no—
726#552—4312no—
727#552—436no—
728#552—436no—
729#552—436no—
730#550—433no—
731#550C2×D4311yescharacteristic, complemented
732D4×Q8—432no—
733D4×Q8—436no—
734D4×Q8—432no—
735D4×Q8—431no—
736D4×Q8—436no—
737D4×Q8—433no—
738#548—432no—
739#548—432no—
740#548—436no—
741#548—436no—
742#548—436no—
743#548C2×D4312yes—
744#547—4312no—
745#547—436no—
746#547—436no—
747#544—436no—
748#542—436no—
749#542—4312no—
750#542—436no—
751#541—4312no—
752#541—436no—
753#541—436no—
754#539—4312no—
755#539—4312no—
756#537—436no—
757#536—436no—
758#536—436no—
759#533—433no—
760#533—433no—
761#533—433no—
762#533—433no—
763#533—436no—
764#533—433no—
765#533—4312no—
766#533—433no—
767#533—436no—
768#532—433no—
769#532—433no—
770#532—433no—
771#532—433no—
772#532—433no—
773#532C2×D4313yes—
774#529—436no—
775#529—436no—
776#529—436no—
777#529—436no—
778#529—433no—
779#529—433no—
780#529—436no—
781#529—436no—
782#529—436no—
783#529—436no—
784#529—433no—
785#529—433no—
786#529—4312no—
787#529—436no—
788#529—436no—
789#529—436no—
790#529C2×D4316yescomplemented
791#525—433no—
792#525—436no—
793#525—436no—
794#525—436no—
795#525—436no—
796#525—431no—
797#520—432no—
798#520—436no—
799#520—436no—
800#520—436no—
801#519—432no—
802#519—432no—
803#519—436no—
804C4×#41—436no—
805C4×#41—436no—
806C4×#41—436no—
807C4×#41—436no—
808C4×#41—436no—
809C4×#41—433no—
810C4×#41—436no—
811C4×#41C2×D4313yes—
812C4×#41C2×D4312yescomplemented
813C2×C4×Q8—431no—
814C2×C4×Q8—431no—
815C2×C4×Q8—433no—
816C2×C4×Q8—431no—
817C2×C4×Q8—433no—
818C2×C4×Q8—431no—
819C2×C4×Q8—433no—
820C2×C4×Q8—431no—
821C2×C4×Q8—433no—
822C2×C4×Q8—432no—
823C2×C4×Q8—433no—
824C2×C4×Q8—433no—
825C2×C4×Q8—436no—
826C2×C4×Q8C2×D4311yescharacteristic
827C22×C4⋊C4—433no—
828C22×C42—433no—
829C43#6278811yescharacteristic, complemented, Sylow
8302−1+4—8616no—
831C2×#41—436no—
832C2×#41—436no—
833C2×#41—436no—
834C2×#41—431no—
835C2×#41—436no—
836C2×#41—436no—
837C2×#41C22×D4313yes—
838C2×#41C22×D4312yes—
839C22×Q8—431no—
840C22×Q8—433no—
841C22×Q8—433no—
842C22×Q8—431no—
843C22×Q8—432no—
844C22×Q8—433no—
845C22×Q8—436no—
846C22×Q8—868no—
847C22×Q8C22×D4311yescharacteristic
848C23×C4—433no—
849C23×C4—431no—
850C23×C4—433no—
851C4⋊Q8—433no—
852C4⋊Q8—436no—
853C4⋊Q8—433no—
854C4⋊Q8—433no—
855C4⋊Q8—4312no—
856C4⋊Q8—4312no—
857C4⋊Q8—436no—
858C4⋊Q8—433no—
859C4⋊Q8—433no—
860C4⋊Q8—436no—
861C4⋊Q8—436no—
862C4⋊Q8C22×D4313yes—
863#127—433no—
864#127C22×D4313yes—
865#126—436no—
866#126—436no—
867#126—4312no—
868#126—4312no—
869#126—436no—
870#126—436no—
871#126—4312no—
872#126—4312no—
873#126—4312no—
874#126C22×D43112yes—
875#125—436no—
876#125—436no—
877#125—436no—
878#125—436no—
879#125—433no—
880#125—433no—
881#125—4312no—
882#125—436no—
883#125—4312no—
884#125—4312no—
885#125—4312no—
886#125—436no—
887#125—4312no—
888#125C22×D4316yes—
889#124—433no—
890#124—436no—
891#124—436no—
892#124—433no—
893#124—436no—
894#124—436no—
895#124—436no—
896#124—4312no—
897#124C22×D4316yes—
898#124C22×D4316yes—
899#123—436no—
900#123—4312no—
901#123—436no—
902#123—436no—
903#123—432no—
904#123—4312no—
905#123—436no—
906#123—436no—
907#123—4312no—
908#123—4312no—
909#123—4312no—
910#123C22×D43112yes—
911C22⋊Q8—433no—
912C22⋊Q8—433no—
913C22⋊Q8—436no—
914C22⋊Q8—436no—
915C22⋊Q8—436no—
916C22⋊Q8—436no—
917C22⋊Q8—436no—
918C22⋊Q8—4312no—
919C22⋊Q8—431no—
920C22⋊Q8—431no—
921C22⋊Q8—436no—
922C22⋊Q8—436no—
923C22⋊Q8—436no—
924C22⋊Q8—436no—
925C22⋊Q8—436no—
926C22⋊Q8—436no—
927C22⋊Q8—4312no—
928C22⋊Q8—436no—
929C22⋊Q8—436no—
930C22⋊Q8—4312no—
931C22⋊Q8—4312no—
932C22⋊Q8—4312no—
933C22⋊Q8—4312no—
934C22⋊Q8—4312no—
935C22⋊Q8C22×D4316yes—
936#121—433no—
937#121—433no—
938#121—436no—
939#121—436no—
940#121—436no—
941#121—436no—
942#121—436no—
943#121—4312no—
944#121—431no—
945#121—431no—
946#121—436no—
947#121—436no—
948#121C22×D4316yes—
949#121C22×D4316yes—
950#121C22×D4316yes—
951#120—436no—
952#120—432no—
953C4×Q8—431no—
954C4×Q8—433no—
955C4×Q8—431no—
956C4×Q8—433no—
957C4×Q8—432no—
958C4×Q8—436no—
959C4×Q8—436no—
960C4×Q8—433no—
961C4×Q8—436no—
962C4×Q8—433no—
963C4×Q8—433no—
964C4×Q8—436no—
965C4×Q8—433no—
966C4×Q8—436no—
967C4×Q8—436no—
968C4×Q8—436no—
969C4×Q8—436no—
970C4×Q8—433no—
971C4×Q8—436no—
972C4×Q8—433no—
973C4×Q8—433no—
974C4×Q8—433no—
975C4×Q8—436no—
976C4×Q8—436no—
977C4×Q8—436no—
978C4×Q8—436no—
979C4×Q8—436no—
980C4×Q8—4312no—
981C4×Q8—436no—
982C4×Q8—436no—
983C4×Q8—436no—
984C4×Q8—436no—
985C4×Q8—433no—
986C4×Q8—433no—
987C4×Q8C22×D4311yescharacteristic
988C4×Q8C22×D4313yes—
989C4×Q8C22×D4311yescharacteristic
990C4×Q8C22×D4313yes—
991C4×Q8C22×D4313yes—
992C4×Q8C22×D4313yes—
993C4×Q8C22×D4312yes—
994C4×D4—436no—
995C4×D4—436no—
996C4×D4—4312no—
997C4×D4—4312no—
998C4×D4—436no—
999C4×D4—436no—
1000C4×D4—436no—
1001C4×D4—436no—
1002C4×D4—436no—
1003C4×D4—436no—
1004C4×D4—436no—
1005C4×D4—436no—
1006C4×D4—436no—
1007C4×D4—436no—
1008C4×D4—436no—
1009C4×D4—436no—
1010C4×D4—436no—
1011C4×D4—4312no—
1012C4×D4—4312no—
1013C4×D4—4312no—
1014C4×D4—432no—
1015C4×D4—432no—
1016C4×D4—436no—
1017C4×D4—436no—
1018C4×D4—433no—
1019C4×D4—433no—
1020C4×D4C22×D4316yes—
1021C4×D4C22×D4316yes—
1022C4×D4C22×D4316yes—
1023C4×D4C22×D4316yes—
1024C4×D4C22×D4313yes—
1025C4×D4C22×D4313yes—
1026C4×D4C22×D4316yes—
1027#117—433no—
1028#117—436no—
1029#117—4312no—
1030#117—436no—
1031#117—436no—
1032#117—436no—
1033#117—436no—
1034#117—4312no—
1035#117—4312no—
1036#117—4312no—
1037#117—436no—
1038#117—436no—
1039#117—436no—
1040#117—436no—
1041#117—436no—
1042#117C22×D4311yescharacteristic
1043#117C22×D4316yes—
1044#117C22×D4316yes—
1045C2×C4⋊C4—436no—
1046C2×C4⋊C4—433no—
1047C2×C4⋊C4—4312no—
1048C2×C4⋊C4—436no—
1049C2×C4⋊C4—433no—
1050C2×C4⋊C4—433no—
1051C2×C4⋊C4—436no—
1052C2×C4⋊C4—436no—
1053C2×C4⋊C4—433no—
1054C2×C4⋊C4—433no—
1055C2×C4⋊C4—436no—
1056C2×C4⋊C4C22×D4313yes—
1057C2×C42—433no—
1058C2×C42—433no—
1059C2×C42—433no—
1060C2×C42—4312no—
1061C2×C42—433no—
1062C2×C42—433no—
1063C2×C42—433no—
1064C2×C42—433no—
1065C2×C42—433no—
1066C2×C42—433no—
1067C2×C42—433no—
1068C2×C42—433no—
1069C2×C42—436no—
1070C2×C42C22×D4313yes—
1071C2×C42C22×D4316yes—
1072C24—431no—
1073#41—28no—
1074#41—212no—
1075#41—8624no—
1076#41—8624no—
1077#41—8624no—
1078#41—864no—
1079#41—17212no—
1080#41—17212no—
1081C2×Q8—24no—
1082C2×Q8—438no—
1083C2×Q8—433no—
1084C2×Q8—431no—
1085C2×Q8—436no—
1086C2×Q8—433no—
1087C2×Q8—436no—
1088C2×Q8—436no—
1089C2×Q8—436no—
1090C2×Q8—436no—
1091C2×Q8—8612no—
1092C2×Q8—8624no—
1093C2×Q8—8612no—
1094C2×Q8—8612no—
1095C2×Q8—864no—
1096C2×Q8—868no—
1097C2×Q8C23×D4313yes—
1098C2×Q8C23×D4313yes—
1099C2×Q8C23×D4311yescharacteristic
1100C2×D4—432no—
1101C2×D4—436no—
1102C2×D4—436no—
1103C2×D4—436no—
1104C2×D4—436no—
1105C2×D4—431no—
1106C2×D4—432no—
1107C2×D4—432no—
1108C2×D4C23×D4316yes—
1109C2×D4C23×D4313yes—
1110C2×D4C23×D4316yes—
1111C2×D4C23×D4316yes—
1112C22×C4—433no—
1113C22×C4—431no—
1114C22×C4—433no—
1115C22×C4—4312no—
1116C22×C4—433no—
1117C22×C4—4312no—
1118C22×C4—431no—
1119C22×C4—431no—
1120C22×C4—433no—
1121C22×C4—433no—
1122C22×C4—433no—
1123C22×C4—433no—
1124C22×C4—433no—
1125C22×C4—436no—
1126C22×C4—431no—
1127C22×C4—431no—
1128C22×C4—432no—
1129C22×C4—433no—
1130C22×C4—433no—
1131C22×C4—436no—
1132C22×C4—8612no—
1133C22×C4—864no—
1134C22×C4—1726no—
1135C22×C4C23×D4313yes—
1136C22×C4C23×D4316yes—
1137C22×C4C23×D4316yes—
1138C22×C4C23×D4313yes—
1139C22×C4C23×D4316yes—
1140C22×C4C23×D4311yescharacteristic
1141C4⋊C4—436no—
1142C4⋊C4—433no—
1143C4⋊C4—436no—
1144C4⋊C4—433no—
1145C4⋊C4—436no—
1146C4⋊C4—436no—
1147C4⋊C4—436no—
1148C4⋊C4—436no—
1149C4⋊C4—436no—
1150C4⋊C4—436no—
1151C4⋊C4—4312no—
1152C4⋊C4—436no—
1153C4⋊C4—436no—
1154C4⋊C4—436no—
1155C4⋊C4—436no—
1156C4⋊C4—432no—
1157C4⋊C4—432no—
1158C4⋊C4—433no—
1159C4⋊C4—433no—
1160C4⋊C4—436no—
1161C4⋊C4—436no—
1162C4⋊C4—436no—
1163C4⋊C4—436no—
1164C4⋊C4—4312no—
1165C4⋊C4—436no—
1166C4⋊C4—436no—
1167C4⋊C4—4312no—
1168C4⋊C4—436no—
1169C4⋊C4—4312no—
1170C4⋊C4C23×D4313yes—
1171C4⋊C4C23×D4313yes—
1172C4⋊C4C23×D4316yes—
1173C4⋊C4C23×D4316yes—
1174C4⋊C4C23×D4316yes—
1175C4⋊C4C23×D4311yescharacteristic
1176C4⋊C4C23×D4311yescharacteristic
1177C4⋊C4C23×D4316yes—
1178C4⋊C4C23×D4316yes—
1179C22⋊C4—436no—
1180C22⋊C4—436no—
1181C22⋊C4—436no—
1182C22⋊C4—436no—
1183C22⋊C4—4312no—
1184C22⋊C4—4312no—
1185C22⋊C4—436no—
1186C22⋊C4—432no—
1187C22⋊C4—432no—
1188C22⋊C4—436no—
1189C22⋊C4—436no—
1190C22⋊C4—436no—
1191C22⋊C4—432no—
1192C22⋊C4—432no—
1193C22⋊C4—436no—
1194C22⋊C4—436no—
1195C22⋊C4—436no—
1196C22⋊C4C23×D43112yes—
1197C22⋊C4C23×D43112yes—
1198C22⋊C4C23×D4312yes—
1199C22⋊C4C23×D4316yes—
1200C22⋊C4C23×D4316yes—
1201C42—433no—
1202C42—433no—
1203C42—433no—
1204C42—433no—
1205C42—433no—
1206C42—433no—
1207C42—433no—
1208C42—433no—
1209C42—433no—
1210C42—433no—
1211C42—4312no—
1212C42—436no—
1213C42—4312no—
1214C42—436no—
1215C42—433no—
1216C42—433no—
1217C42—436no—
1218C42C23×D4313yes—
1219C42C23×D4313yes—
1220C42C23×D4316yes—
1221C42C23×D4316yes—
1222C42C23×D4313yes—
1223C42C23×D4313yes—
1224C42C23×D4312yes—
1225C23—431no—
1226C23—431no—
1227C23—432no—
1228C23—862no—
1229C23—862no—
1230C23—862no—
1231C23C24×D4316yes—
1232C23C24×D4311yescharacteristic
1233Q8—26no—
1234Q8—26no—
1235Q8—4312no—
1236Q8—8612no—
1237Q8—8612no—
1238Q8—866no—
1239Q8—8612no—
1240Q8—862no—
1241Q8—1726no—
1242Q8—1726no—
1243Q8#41×D4314yes—
1244D4—212no—
1245D4—212no—
1246D4—26no—
1247D4—46no—
1248D4—864no—
1249D4—864no—
1250D4—8612no—
1251D4—8612no—
1252D4—8612no—
1253D4—864no—
1254D4—862no—
1255D4—1726no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—212no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—433no—
1262C2×C4—4312no—
1263C2×C4—431no—
1264C2×C4—431no—
1265C2×C4—433no—
1266C2×C4—432no—
1267C2×C4—433no—
1268C2×C4—436no—
1269C2×C4—436no—
1270C2×C4—433no—
1271C2×C4—866no—
1272C2×C4—866no—
1273C2×C4—866no—
1274C2×C4—866no—
1275C2×C4—866no—
1276C2×C4—8624no—
1277C2×C4—862no—
1278C2×C4—866no—
1279C2×C4—8612no—
1280C2×C4—862no—
1281C2×C4—862no—
1282C2×C4—862no—
1283C2×C4—862no—
1284C2×C4—864no—
1285C2×C4—1723no—
1286C2×C4—1723no—
1287C2×C4—1726no—
1288C2×C4—1723no—
1289C2×C4—17212no—
1290C2×C4#1306337214yescomplemented
1291C2×C4C24×D4313yes—
1292C2×C4C24×D4316yes—
1293C2×C4C24×D4313yes—
1294C2×C4C24×D4313yes—
1295C2×C4C24×D4312yes—
1296C2×C4C24×D4312yes—
1297C2×C4C24×D4313yes—
1298C2×C4C24×D4311yescharacteristic
1299C2×C4C24×D4311yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—26no—
1303C22—26no—
1304C22—26no—
1305C22—432no—
1306C22—432no—
1307C22—868no—
1308C22—861no—
1309C22—861no—
1310C22—861no—
1311C22—861no—
1312C22—862no—
1313C22—862no—
1314C22—862no—
1315C22C2×#1306337212yes—
1316C22C25×D4311yescharacteristic
1317C4—22no—
1318C4—23no—
1319C4—26no—
1320C4—23no—
1321C4—22no—
1322C4—23no—
1323C4—436no—
1324C4—866no—
1325C4—863no—
1326C4—861no—
1327C4—861no—
1328C4—862no—
1329C4—863no—
1330C4—863no—
1331C4—866no—
1332C4C2×#41×D4316yes—
1333C4C2×#1306337212yes—
1334C4C2×#1306337212yes—
1335C2—22no—
1336C2—46no—
1337C2—862no—
1338C2—862no—
1339C2—1722no—
1340C2C22×#41×D4311yescharacteristic
1341C2C22×#1306337211yescharacteristic
1342C2#585×D4311yescharacteristic
subgroupG/H
centerC2×C4C24×D43
commutator, socle, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC43×#3480C2
hypercenter#3480D43
hypocenterC43#62788
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #19148692C2semidirect
2. #19148690C2semidirect
3. #19148677C2semidirect
4. #19148675C2semidirect
5. #19148579C2semidirect
6. #19148577C2semidirect
7. #19148452C2semidirect
8. #19148450C2semidirect
9. #19148399C2semidirect
10. #19148360C2semidirect
11. #19148299C2semidirect
12. #19148241C2semidirect
13. #19148217C2semidirect
14. #19148208C2semidirect
15. #19148192C2semidirect
16. Q8×#10621898C2semidirect
17. #41×Dic86C2semidirect
18. #19148020C2semidirect
19. #19147890C2semidirect
20. #19147888C2semidirect
21. C4×#13063372C2semidirect
22. C2×C4×Q8×D43C2semidirect
23. C43×#3480C2semidirect
26. #14583635C22semidirect
27. #14583631C22semidirect
28. Q8×Dic86C22semidirect
29. Q8×Dic86C22semidirect
30. #14583628C22semidirect
31. #14583628C22semidirect
32. #14583627C22semidirect
33. #14583626C22semidirect
34. #14583625C22semidirect
35. #14583624C22semidirect
36. #14583623C22semidirect
37. #14583619C22semidirect
38. #14583618C22semidirect
39. #14583618C22semidirect
40. #14583616C22semidirect
41. #14583609C22semidirect
43. #14583608C22semidirect
45. #14583606C22semidirect
49. #14583591C22semidirect
51. #14583588C22semidirect
53. #14583586C22semidirect
55. #14583569C22semidirect
57. Q8×D172C22semidirect
59. D4×Dic86C22semidirect
64. #14583556C22semidirect
66. #14583555C22semidirect
71. #14583518C22semidirect
72. #14583517C22semidirect
73. #14583516C22semidirect
74. #14583512C22semidirect
75. #14583509C22semidirect
76. #14583506C22semidirect
83. #14583456C22semidirect
88. #14583453C22semidirect
90. #14583452C22semidirect
102. #14583431C22semidirect
107. #14583429C22semidirect
118. #14583382C22semidirect
121. #14583378C22semidirect
122. #14583376C22semidirect
124. #14583375C22semidirect
131. C4×#10621900C22semidirect
134. C2×C4×Dic86C22semidirect
144. C4×Q8×D43C22semidirect
147. C43×#559C22semidirect
148. C43×#557C22semidirect
149. C43×#556C22semidirect
151. C43×#550C22semidirect
154. C43×#529C22semidirect
156. C4×#41×C43C22semidirect
431. Q8×D43#41semidirect
573. C2×C4×C432−1+4semidirect
679. #3480D43semidirect
699. #559C2×D43semidirect
708. #557C2×D43semidirect
714. #556C2×D43semidirect
731. #550C2×D43semidirect
790. #529C2×D43semidirect
812. C4×#41C2×D43semidirect
829. C43#62788semidirect
1290. C2×C4#13063372semidirect

Maximal subgroups

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

subgroupindex
#191486922
#191486902
#191486772
#191486752
#191485792
#191485772
#191484522
#191484502
#191483992
#191483602
#191482992
#191482412
#191482172
#191482082
#191481922
Q8×#106218982
#41×Dic862
#191480202
#191478902
#191478882
C4×#130633722
C2×C4×Q8×D432
C43×#34802
#6278843