Finite Group Databasebeta

← #26005051

Subgroups — #26005051

Order 11008.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148686C212yesmaximal, complemented
2#19148635C216yesmaximal, complemented
3#19148607C212yesmaximal, complemented
4#19148564C216yesmaximal, complemented
5#19148502C213yesmaximal, complemented
6#19148479C213yesmaximal, complemented
7#19148414C211yesmaximal, characteristic, complemented
8#19148344C216yesmaximal, complemented
9#19148268C212yesmaximal, complemented
10#19148216C212yesmaximal, complemented
11#19148207C216yesmaximal, complemented
12Q8×#10621900C212yesmaximal, complemented
13#19148158C216yesmaximal, complemented
14#19148019C216yesmaximal, complemented
15#19147890C213yesmaximal, complemented
16C2×#14583454C213yesmaximal, complemented
172−1+4×Dic43C212yesmaximal, complemented
18C4×#41×D43C211yesmaximal, characteristic, complemented
19C43×#3499C211yesmaximal, characteristic, complemented
20C2×#41×D43C2211yescharacteristic
21Q8×Dic86C2212yescomplemented
22#14583628C2212yescomplemented
23#14583624C2216yescomplemented
24#14583624C2216yescomplemented
25#14583623C2216yescomplemented
26#14583623C2216yescomplemented
27#14583620C22112yescomplemented
28#14583619C2216yescomplemented
29#14583614C2216yescomplemented
30#14583607C22112yes—
31#14583606C2216yescomplemented
32#14583606C2216yescomplemented
33#14583601C22112yescomplemented
34#14583591C22112yescomplemented
35#14583586C22124yescomplemented
36#14583584C22112yescomplemented
37#14583584C22112yescomplemented
38#14583583C22112yes—
39#14583572C22124yes—
40D4×Dic86C2216yescomplemented
41Q8×C22⋊D43C2214yes—
42#14583560C2214yes—
43#14583555C22112yescomplemented
44#14583553C2216yescomplemented
45#14583548C22112yes—
46#14583537C22112yes—
47#14583527C2216yescomplemented
48#14583522C22112yescomplemented
49#14583518C22112yescomplemented
50#14583510C22112yescomplemented
51#14583509C22112yescomplemented
52#14583493C22124yescomplemented
53#14583477C2216yes—
54#14583473C2216yes—
55#14583456C2213yescomplemented
56#14583454C2216yes—
57#14583454C2216yes—
58#14583454C2213yes—
59#14583454C2216yes—
60#14583454C2216yescomplemented
61#14583454C2216yescomplemented
62#14583454C2216yescomplemented
63#14583454C2216yescomplemented
64#14583454C2213yescomplemented
65#14583451C22112yescomplemented
66#14583447C2211yescharacteristic
67#14583447C2213yescomplemented
68C2×#13063325C2213yescomplemented
69#14583435C22112yescomplemented
70#14583431C2216yes—
71#14583431C2216yescomplemented
72#14583430C2216yescomplemented
73#14583430C2216yescomplemented
74#14583428C2216yes—
75#14583428C2216yescomplemented
76#14583426C22124yescomplemented
77C2×#13063316C2216yescomplemented
78#14583409C2216yes—
79#14583409C2216yes—
80#14583406C2216yes—
81C2×#13063305C2216yes—
82C2×#13063301C2216yes—
83#14583382C2212yes—
84#14583382C22112yescomplemented
85#14583382C2216yescomplemented
86#14583377C2216yescomplemented
87#14583377C2214yescomplemented
88#41×Dic43C2211yescharacteristic
89#41×Dic43C2216yescomplemented
90#41×Dic43C22112yescomplemented
91C4×#10621902C2211yescharacteristic
92C4×#10621902C2211yescharacteristic
93C4×#10621898C2213yes—
94#14583367C2213yes—
95C4×#10621900C2213yes—
96C4×#10621900C2216yes—
97C4×#10621900C2213yes—
98C4×#10621900C2216yescomplemented
99C2×Q8×Dic43C2216yescomplemented
100C2×Q8×Dic43C2214yescomplemented
101C2×#13063290C2216yescomplemented
102C4×Q8×D43C2211yescharacteristic
103C4×Q8×D43C2211yescharacteristic
104C4×D4×D43C2213yes—
105C4×D4×D43C2213yes—
106C2×#13063283C2216yes—
107#117×D43C2213yes—
108C2×C42×D43C2213yes—
109C2×2−1+4×C43C2212yes—
110D4×Q8×C43C2212yescomplemented
111D4×Q8×C43C2212yescomplemented
112C43×#547C2216yescomplemented
113C43×#547C2216yescomplemented
114C43×#536C2216yescomplemented
115C43×#532C2213yescomplemented
116C2×C4⋊Q8×C43C2213yescomplemented
117C4×#41×C43C2211yescharacteristic
118C2×#10621902C2311yescharacteristic
119C2×#10621898C2313yes—
120C2×#10621900C2312yes—
121C2×#10621900C2313yes—
122C2×#10621900C2316yes—
123#41×D43—28no—
124C22×Dic86C2316yes—
125C2×Q8×D43C2311yescharacteristic
126C2×D4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129C22×C4×D43C2313yes—
130#13063325C2316yes—
131#13063325C2316yes—
132#13063325C2313yes—
133#13063325C2316yes—
134#13063325C2311yescharacteristic
135#13063324C23112yes—
136#13063323C23112yes—
137#13063320C23124yes—
138#13063320C23124yes—
139#13063318C23124yes—
140#13063318C23112yes—
141#13063318C23112yes—
142#13063317C2316yes—
143#13063316C23112yes—
144#13063316C2316yes—
145#13063316C23112yes—
146#13063316C23112yes—
147#13063316C2316yes—
148#13063316C23112yes—
149#13063315C23124yes—
150#13063315C23124yes—
151#13063314C23112yes—
152#13063312C2316yes—
153#13063312C2312yes—
154#13063311C23124yes—
155#13063309C23124yes—
156#13063308C23124yes—
157#13063307C23112yes—
158#13063307C23112yes—
159#13063306C23112yes—
160#13063305C23112yes—
161#13063305C23112yes—
162#13063305C2316yes—
163#13063305C2316yes—
164#13063305C23112yes—
165#13063304C23112yes—
166#13063304C2316yes—
167#13063304C2316yes—
168#13063302C23124yes—
169#13063302C23124yes—
170#13063301C23112yes—
171#13063301C23112yes—
172#13063301C2316yes—
173#13063301C23112yes—
174#13063301C2316yes—
175#13063299C23112yes—
176#13063297C23124yes—
177#13063296C2316yes—
178#13063296C2312yes—
179#13063296C2316yes—
180#13063296C2312yes—
181#13063293C23112yes—
182Q8×Dic43C2314yes—
183Q8×Dic43C23112yes—
184Q8×Dic43C23112yes—
185Q8×Dic43C2311yescharacteristic
186Q8×Dic43C2311yescharacteristic
187Q8×Dic43C2316yes—
188Q8×Dic43C23112yes—
189Q8×Dic43C23112yes—
190Q8×Dic43C23112yes—
191Q8×Dic43C2316yes—
192C4×Dic86C2316yes—
193C4×Dic86C2313yes—
194C4×Dic86C2316yes—
195C4×Dic86C2313yes—
196#13063290C23112yes—
197#13063290C2316yes—
198#13063290C23112yes—
199#13063290C2313yes—
200#13063290C2313yes—
201#13063290C2316yes—
202#13063290C23112yes—
203C4×D172C2313yes—
204C4×D172C2313yes—
205D4×Dic43C23124yes—
206D4×Dic43C23112yes—
207D4×Dic43C2316yes—
208D4×Dic43C2313yes—
209D4×Dic43C2313yes—
210D4×Dic43C2312yes—
211D4×Dic43C23112yes—
212D4×Dic43C2312yes—
213D4×Dic43C23112yes—
214D4×Dic43C2316yes—
215#13063287C2313yes—
216#13063287C2313yes—
217C4×C22⋊D43C2316yes—
218C4×C22⋊D43C23112yes—
219C4×C22⋊D43C23112yes—
220C4×C22⋊D43C2316yes—
221(C22⋊D43)⋊C4C23112yes—
222(C22⋊D43)⋊C4C2316yes—
223(C22⋊D43)⋊C4C2316yes—
224(C22⋊D43)⋊C4C23112yes—
225#13063284C23124yes—
226#13063284C23112yes—
227#13063284C2313yes—
228#13063284C2316yes—
229#13063284C23112yes—
230#13063283C23112yes—
231#13063283C2316yes—
232#13063283C23112yes—
233#13063283C2313yes—
234#13063283C2313yes—
235#13063283C2316yes—
236#13063283C23112yes—
237#13063282C2316yes—
238#13063281C2316yes—
239#13063281C23112yes—
240#13063281C23112yes—
241C2×C4⋊Dic43C23112yes—
242C2×C4⋊Dic43C2316yes—
243C2×C4⋊Dic43C2316yes—
244C2×C4⋊Dic43C23112yes—
245C2×Dic43⋊C4C23112yes—
246C4⋊C4×D43C2313yes—
247C4⋊C4×D43C2313yes—
248C2×(C2×D43)⋊C4C23112yes—
249C22⋊C4×D43C2316yes—
250C2×C4×Dic43C2313yes—
251C2×C4×Dic43C2313yes—
252C2×C4×Dic43C2313yes—
253C2×C4×Dic43C23112yes—
254C2×C4×Dic43C23112yes—
255C42×D43C2311yescharacteristic
256C42×D43C2313yes—
257C42×D43C2313yes—
258C42×D43C2313yes—
259C42×D43C2313yes—
260C42×D43C2313yes—
261C42×D43C2313yes—
262C42×D43C2313yes—
2632−1+4×C43—216no—
264C2×#41×C43C2316yes—
265C2×#41×C43C23112yes—
266C2×#41×C43C2311yescharacteristic
267C22×Q8×C43C2314yes—
268C22×Q8×C43C2316yes—
269C4⋊Q8×C43C2313yes—
270C4⋊Q8×C43C2316yes—
271C4⋊Q8×C43C2316yes—
272C4⋊Q8×C43C2316yes—
273#127×C43C2311yescharacteristic
274#124×C43C2316yes—
275#123×C43C23124yes—
276C22⋊Q8×C43C23112yes—
277C22⋊Q8×C43C23112yes—
278#121×C43C2316yes—
279#121×C43C2316yes—
280C4×Q8×C43C2311yescharacteristic
281C4×Q8×C43C2311yescharacteristic
282C4×D4×C43C2316yes—
283C4×D4×C43C2313yes—
284C4×D4×C43C2313yes—
285C4×D4×C43C2316yes—
286#117×C43C2313yes—
287C2×C4⋊C4×C43C2316yes—
288C2×C4⋊C4×C43C2316yes—
289C2×C42×C43C2313yes—
290C23×D43C2413yes—
291#41×C43—248no—
292#41×C43—224no—
293#41×C43#4118yescomplemented
294C2×Q8×C43—216no—
295C2×Q8×C43—224no—
296C2×Q8×C43C24112yes—
297C2×Q8×C43C2416yes—
298C2×Q8×C43C2411yescharacteristic
299C2×D4×C43C2412yes—
300C2×D4×C43C2412yes—
301C2×D4×C43C24112yes—
302C2×D4×C43C2412yes—
303C2×D4×C43C2413yes—
304C22×C4×C43C2413yes—
305C22×C4×C43C2413yes—
306C22×C4×C43C24112yes—
307C22×C4×C43C24112yes—
308C22×C4×C43C2413yes—
309C2×C22⋊D43C2414yes—
310C2×C22⋊D43C2416yes—
311C2×C22⋊D43C24112yes—
312C22×Dic43C2413yes—
313C22×Dic43C2414yes—
314C22×Dic43C2413yes—
315C22×Dic43C2413yes—
316C22×Dic43C24112yes—
317C22×Dic43C24112yes—
318#10621902—24no—
319Q8×D43—24no—
320#10621900—212no—
321#10621900—28no—
322#10621900—412no—
323D4×D43—212no—
324#10621898—212no—
325C2×D172C2413yes—
326C2×C4×D43—212no—
327C2×C4×D43—212no—
328C2×C4×D43—46no—
329C2×C4×D43C2411yescharacteristic
330C2×C4×D43C2411yescharacteristic
331C2×C4×D43C2413yes—
332C2×C4×D43C2413yes—
333C2×C4×D43C2413yes—
334C2×C4×D43C2413yes—
335C2×C4×D43C2413yes—
336C2×C4×D43C2413yes—
337C2×C4×D43C2413yes—
338C2×C4×D43C2413yes—
339C2×C4×D43C2413yes—
340C2×C4×D43C2411yescharacteristic
341C2×Dic86—412no—
342C2×Dic86C2412yes—
343C2×Dic86C2416yes—
344C2×Dic86C2413yes—
345C2×Dic86C24112yes—
346C4⋊C4×C43C2416yes—
347C4⋊C4×C43C2416yes—
348C4⋊C4×C43C24112yes—
349C4⋊C4×C43C24112yes—
350C4⋊C4×C43C2413yes—
351C4⋊C4×C43C2413yes—
352C22⋊C4×C43C2416yes—
353C22⋊C4×C43C24112yes—
354C22⋊C4×C43C24112yes—
355C42×C43C2411yescharacteristic
356C42×C43C2413yes—
357C42×C43C2413yes—
358C42×C43C2413yes—
359C22⋊Dic43C2416yes—
360C22⋊Dic43C2414yes—
361C22⋊Dic43C24112yes—
362C22⋊Dic43C24112yes—
363C22⋊Dic43C2414yes—
364C22⋊Dic43C24112yes—
365(C2×D43)⋊C4C2416yes—
366(C2×D43)⋊C4C2416yes—
367(C2×D43)⋊C4C24112yes—
368(C2×D43)⋊C4C24124yes—
369(C2×D43)⋊C4C24112yes—
370C4⋊Dic43C2413yes—
371C4⋊Dic43C2413yes—
372C4⋊Dic43C2416yes—
373C4⋊Dic43C2416yes—
374C4⋊Dic43C24112yes—
375C4⋊Dic43C24124yes—
376C4⋊Dic43C24112yes—
377C4⋊Dic43C24112yes—
378C4⋊Dic43C2412yes—
379C4⋊Dic43C2412yes—
380C4⋊Dic43C24112yes—
381Dic43⋊C4C2416yes—
382Dic43⋊C4C2416yes—
383Dic43⋊C4C24112yes—
384Dic43⋊C4C24124yes—
385Dic43⋊C4C24112yes—
386Dic43⋊C4C24112yes—
387Dic43⋊C4C24112yes—
388C4×Dic43C2411yescharacteristic
389C4×Dic43C2411yescharacteristic
390C4×Dic43C2411yescharacteristic
391C4×Dic43C2413yes—
392C4×Dic43C2413yes—
393C4×Dic43C2413yes—
394C4×Dic43C2413yes—
395C4×Dic43C2413yes—
396C4×Dic43C2413yes—
397C4×Dic43C2413yes—
398C4×Dic43C2413yes—
399C4×Dic43C2413yes—
400C4×Dic43C24112yes—
401C4×Dic43C24112yes—
402C4×Dic43C24124yes—
403C4×Dic43C24112yes—
404C23×C43C2514yes—
405C23×C43C2513yes—
406C22×D43—26no—
407C22×D43—26no—
408C22×D43—43no—
409C22×D43C2513yes—
410C22×D43C2511yescharacteristic
411Q8×C43—224no—
412Q8×C43—212no—
413Q8×C43C2×#4114yes—
414D4×C43—224no—
415D4×C43—24no—
416D4×C43—24no—
417D4×C43—24no—
418D4×C43C2×#41112yes—
419C2×C4×C43—224no—
420C2×C4×C43—224no—
421C2×C4×C43—26no—
422C2×C4×C43—26no—
423C2×C4×C43C2×#41112yes—
424C2×C4×C43C25112yes—
425C2×C4×C43C2513yes—
426C2×C4×C43C2513yes—
427C2×C4×C43C2513yes—
428C2×C4×C43C2511yescharacteristic
429C2×C4×C43C2511yescharacteristic
430C2×C4×C43C2511yescharacteristic
431C22⋊D43—212no—
432C22⋊D43—28no—
433C22⋊D43—412no—
434C2×Dic43—26no—
435C2×Dic43—26no—
436C2×Dic43—28no—
437C2×Dic43—412no—
438C2×Dic43—43no—
439C2×Dic43—412no—
440C2×Dic43C2513yes—
441C2×Dic43C2511yescharacteristic
442C2×Dic43C2513yes—
443C2×Dic43C2511yescharacteristic
444C2×Dic43C2514yes—
445C2×Dic43C2513yes—
446C2×Dic43C25112yes—
447C2×Dic43C2511yescharacteristic
448D172—26no—
449C4×D43—26no—
450C4×D43—22no—
451C4×D43—26no—
452C4×D43—26no—
453C4×D43—26no—
454C4×D43—26no—
455C4×D43—22no—
456C4×D43—26no—
457C4×D43—26no—
458C4×D43—43no—
459C4×D43—43no—
460C4×D432−1+414yescomplemented
461Dic86—26no—
462Dic86—24no—
463Dic86—212no—
464Dic86—412no—
465#62805—431nomaximal, Sylow
466C22×C43—23no—
467C22×C43—23no—
468C22×C43—24no—
469C22×C43—24no—
470C22×C43—24no—
471C22×C43C22×#4116yes—
472C22×C43C2611yescharacteristic
473C2×D43—21no—
474C2×D43—21no—
475C2×D43—23no—
476C2×D43—23no—
477C2×D43—23no—
478C2×D43—412no—
479C2×D43C2×2−1+412yes—
480C4×C43—212no—
481C4×C43—23no—
482C4×C43—23no—
483C4×C43C22×#4116yes—
484C4×C43C22×#4112yes—
485C4×C43C2×2−1+412yes—
486C4×C43#58512yes—
487Dic43—23no—
488Dic43—21no—
489Dic43—24no—
490Dic43—23no—
491Dic43—212no—
492Dic43—21no—
493Dic43—23no—
494Dic43C2×2−1+412yes—
495#3523—432no—
496#3520—436no—
497#3518—432no—
498#3515—436no—
499#3511—433no—
500#3509—433no—
501#3503—431no—
502#3499D4311yescharacteristic, complemented
503#3495—436no—
504#3489—432no—
505#3482—432no—
506#3482—436no—
507Q8×#41—432no—
508#3475—436no—
509#3461—436no—
510#3444—433no—
511C2×#533—433no—
512C4×2−1+4—432no—
513C2×C4×#41—431no—
514C2×C43—26no—
515C2×C43—44no—
516C2×C43C23×#4111yescharacteristic
517C2×C43C22×2−1+411yescharacteristic
518C2×C43C2×#58511yescharacteristic
519D43—22no—
520D43—43no—
521C2×2−1+4C2×D4312yes—
522C22×#41—431no—
523Q82—432no—
524#557—436no—
525#557—436no—
526#557—432no—
527#556—436no—
528#556—436no—
529#556—4312no—
530#556—436no—
531#555—436no—
532#554—4312no—
533#554—436no—
534#554—436no—
535#553—4312no—
536#552—4324no—
537#552—4312no—
538#552—4312no—
539#552—4312no—
540#552—4312no—
541#551—4324no—
542D4×Q8—434no—
543D4×Q8—436no—
544D4×Q8C2×D4312yescomplemented
545D4×Q8C2×D4312yescomplemented
546#548—434no—
547#548—4312no—
548#547—4312no—
549#547—436no—
550#547C2×D4316yescomplemented
551#547C2×D4316yescomplemented
552#546—4312no—
553#544—436no—
554#542—4312no—
555#542—4312no—
556#541—4312no—
557#541—4312no—
558#539—4324no—
559#537—436no—
560#536—436no—
561#536C2×D4316yescomplemented
562#533—433no—
563#533—436no—
564#533—436no—
565#533—436no—
566#533—436no—
567#533—436no—
568#533—436no—
569#533—436no—
570#533—433no—
571#533—4312no—
572#533—433no—
573#532—431no—
574#532—433no—
575#532C2×D4313yescomplemented
576C2×C4⋊Q8—433no—
577C2×C4⋊Q8C2×D4313yescomplemented
578#529—436no—
579#529—436no—
580#529—4324no—
581#529—4312no—
582#529—436no—
583#529—436no—
584#529—436no—
585#529—436no—
586C2×#125—436no—
587#525—436no—
588#525—436no—
589#525—436no—
590C2×C22⋊Q8—436no—
591C2×C22⋊Q8—436no—
592#520—432no—
593#520—436no—
594#520—4312no—
595#519—436no—
596#519—434no—
597C4×#41—431no—
598C4×#41—436no—
599C4×#41—4312no—
600C4×#41—431no—
601C4×#41—431no—
602C4×#41—433no—
603C4×#41—433no—
604C4×#41—436no—
605C4×#41—436no—
606C4×#41—433no—
607C4×#41—433no—
608C4×#41C2×D4311yescharacteristic
609C2×C4×Q8—436no—
610C2×C4×Q8—434no—
611C2×C4×Q8—431no—
612C2×C4×Q8—431no—
613C2×C4×Q8—436no—
614C2×C4×D4—433no—
615C2×C4×D4—433no—
616C2×#117—433no—
617C2×#117—436no—
618C22×C42—433no—
619C43#6280511yescharacteristic, complemented, Sylow
6202−1+4—216no—
621C2×#41—431no—
622C2×#41—432no—
623C2×#41—433no—
624C2×#41—436no—
625C2×#41—433no—
626C2×#41—868no—
627C2×#41C22×D4316yes—
628C2×#41C22×D43112yes—
629C2×#41C22×D4311yescharacteristic
630C22×Q8—431no—
631C22×Q8—436no—
632C22×Q8C22×D4316yes—
633C22×Q8C22×D4314yes—
634C22×D4—433no—
635C23×C4—433no—
636C23×C4—433no—
637C23×C4—433no—
638C4⋊Q8—4312no—
639C4⋊Q8—4312no—
640C4⋊Q8—433no—
641C4⋊Q8—436no—
642C4⋊Q8—436no—
643C4⋊Q8—436no—
644C4⋊Q8—431no—
645C4⋊Q8C22×D4313yes—
646C4⋊Q8C22×D4316yes—
647C4⋊Q8C22×D4316yes—
648C4⋊Q8C22×D4316yes—
649#127C22×D4311yescharacteristic
650#126—4324no—
651#126—4324no—
652#126—4312no—
653#126—4312no—
654#126—4324no—
655#125—436no—
656#125—4312no—
657#125—4312no—
658#125—4312no—
659#125—436no—
660#125—4324no—
661#125—4312no—
662#125—4324no—
663#125—436no—
664#124—4312no—
665#124—432no—
666#124—436no—
667#124—4324no—
668#124C22×D4316yes—
669#123—4312no—
670#123—4324no—
671#123—4312no—
672#123—4312no—
673#123—4324no—
674#123C22×D43124yes—
675C22⋊Q8—436no—
676C22⋊Q8—4312no—
677C22⋊Q8—4312no—
678C22⋊Q8—4312no—
679C22⋊Q8—436no—
680C22⋊Q8—436no—
681C22⋊Q8—436no—
682C22⋊Q8—4312no—
683C22⋊Q8—436no—
684C22⋊Q8—4312no—
685C22⋊Q8—4312no—
686C22⋊Q8—4312no—
687C22⋊Q8—436no—
688C22⋊Q8—4324no—
689C22⋊Q8—4324no—
690C22⋊Q8C22×D43112yes—
691C22⋊Q8C22×D43112yes—
692#121—432no—
693#121—432no—
694#121—436no—
695#121—436no—
696#121—4324no—
697#121—4312no—
698#121C22×D4316yes—
699#121C22×D4316yes—
700#120—4312no—
701C4×Q8—431no—
702C4×Q8—436no—
703C4×Q8—4312no—
704C4×Q8—431no—
705C4×Q8—4312no—
706C4×Q8—4312no—
707C4×Q8—434no—
708C4×Q8—4312no—
709C4×Q8—436no—
710C4×Q8—4312no—
711C4×Q8—436no—
712C4×Q8—433no—
713C4×Q8—433no—
714C4×Q8—4312no—
715C4×Q8—4312no—
716C4×Q8—4312no—
717C4×Q8—436no—
718C4×Q8—433no—
719C4×Q8—433no—
720C4×Q8—436no—
721C4×Q8—436no—
722C4×Q8C22×D4311yescharacteristic
723C4×Q8C22×D4311yescharacteristic
724C4×D4—433no—
725C4×D4—433no—
726C4×D4—4312no—
727C4×D4—432no—
728C4×D4—432no—
729C4×D4—4312no—
730C4×D4—436no—
731C4×D4—4312no—
732C4×D4—4324no—
733C4×D4—436no—
734C4×D4—436no—
735C4×D4—436no—
736C4×D4—4312no—
737C4×D4—4312no—
738C4×D4—433no—
739C4×D4—433no—
740C4×D4—436no—
741C4×D4—436no—
742C4×D4—4312no—
743C4×D4—4312no—
744C4×D4—433no—
745C4×D4—433no—
746C4×D4C22×D4313yes—
747C4×D4C22×D4313yes—
748C4×D4C22×D4316yes—
749C4×D4C22×D4316yes—
750#117—433no—
751#117—436no—
752#117—4312no—
753#117—4324no—
754#117—4312no—
755#117—436no—
756#117—433no—
757#117—433no—
758#117—4312no—
759#117—4312no—
760#117—4312no—
761#117—436no—
762#117—436no—
763#117—4312no—
764#117—4312no—
765#117—436no—
766#117C22×D4313yes—
767C2×C4⋊C4—436no—
768C2×C4⋊C4—4312no—
769C2×C4⋊C4—436no—
770C2×C4⋊C4—4312no—
771C2×C4⋊C4—4312no—
772C2×C4⋊C4—433no—
773C2×C4⋊C4—433no—
774C2×C4⋊C4C22×D4316yes—
775C2×C4⋊C4C22×D4316yes—
776C2×C22⋊C4—4312no—
777C2×C22⋊C4—436no—
778C2×C42—4312no—
779C2×C42—433no—
780C2×C42—433no—
781C2×C42—4312no—
782C2×C42—433no—
783C2×C42—433no—
784C2×C42—433no—
785C2×C42—433no—
786C2×C42—433no—
787C2×C42—433no—
788C2×C42—433no—
789C2×C42—433no—
790C2×C42—431no—
791C2×C42C22×D4313yes—
792C24—433no—
793#41—248no—
794#41—224no—
795#41—868no—
796#41—864no—
797#41—8612no—
798#41—8612no—
799#41—17212no—
800#41#1062190018yescomplemented
801C2×Q8—216no—
802C2×Q8—224no—
803C2×Q8—432no—
804C2×Q8—436no—
805C2×Q8—433no—
806C2×Q8—4312no—
807C2×Q8—864no—
808C2×Q8—17212no—
809C2×Q8C23×D4316yes—
810C2×Q8C23×D43112yes—
811C2×Q8C23×D4311yescharacteristic
812C2×D4—434no—
813C2×D4—436no—
814C2×D4—4312no—
815C2×D4—433no—
816C2×D4—8612no—
817C2×D4C23×D43112yes—
818C2×D4C23×D4312yes—
819C2×D4C23×D4312yes—
820C2×D4C23×D4312yes—
821C2×D4C23×D4313yes—
822C22×C4—431no—
823C22×C4—433no—
824C22×C4—434no—
825C22×C4—433no—
826C22×C4—433no—
827C22×C4—4312no—
828C22×C4—4312no—
829C22×C4—431no—
830C22×C4—431no—
831C22×C4—433no—
832C22×C4—433no—
833C22×C4—433no—
834C22×C4—433no—
835C22×C4—433no—
836C22×C4—433no—
837C22×C4—433no—
838C22×C4—433no—
839C22×C4—433no—
840C22×C4—8612no—
841C22×C4—8612no—
842C22×C4—1726no—
843C22×C4C23×D4313yes—
844C22×C4C23×D4313yes—
845C22×C4C23×D43112yes—
846C22×C4C23×D43112yes—
847C22×C4C23×D4313yes—
848C4⋊C4—433no—
849C4⋊C4—436no—
850C4⋊C4—4312no—
851C4⋊C4—436no—
852C4⋊C4—4312no—
853C4⋊C4—4312no—
854C4⋊C4—4324no—
855C4⋊C4—433no—
856C4⋊C4—436no—
857C4⋊C4—436no—
858C4⋊C4—4312no—
859C4⋊C4—4324no—
860C4⋊C4—432no—
861C4⋊C4—432no—
862C4⋊C4—4312no—
863C4⋊C4—4312no—
864C4⋊C4—4312no—
865C4⋊C4—4312no—
866C4⋊C4C23×D4313yes—
867C4⋊C4C23×D4313yes—
868C4⋊C4C23×D4316yes—
869C4⋊C4C23×D4316yes—
870C4⋊C4C23×D43112yes—
871C4⋊C4C23×D43112yes—
872C22⋊C4—436no—
873C22⋊C4—4312no—
874C22⋊C4—434no—
875C22⋊C4—434no—
876C22⋊C4—4312no—
877C22⋊C4—4312no—
878C22⋊C4—4312no—
879C22⋊C4—436no—
880C22⋊C4—436no—
881C22⋊C4—4324no—
882C22⋊C4—4312no—
883C22⋊C4C23×D4316yes—
884C22⋊C4C23×D43112yes—
885C22⋊C4C23×D43112yes—
886C42—433no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—433no—
891C42—4312no—
892C42—433no—
893C42—433no—
894C42—433no—
895C42—433no—
896C42—433no—
897C42—433no—
898C42—433no—
899C42—4312no—
900C42—4324no—
901C42—4312no—
902C42C23×D4311yescharacteristic
903C42C23×D4313yes—
904C42C23×D4313yes—
905C42C23×D4313yes—
906C23—431no—
907C23—433no—
908C23—866no—
909C23—866no—
910C23—1723no—
911C23C24×D4314yes—
912C23C24×D4313yes—
913Q8—224no—
914Q8—212no—
915Q8—866no—
916Q8—864no—
917Q8—8612no—
918Q8—17212no—
919Q8C2×#1062190014yes—
920D4—224no—
921D4—24no—
922D4—24no—
923D4—24no—
924D4—868no—
925D4—8612no—
926D4—866no—
927D4—17212no—
928D4C2×#10621900112yes—
929C2×C4—224no—
930C2×C4—224no—
931C2×C4—26no—
932C2×C4—26no—
933C2×C4—431no—
934C2×C4—434no—
935C2×C4—433no—
936C2×C4—431no—
937C2×C4—431no—
938C2×C4—433no—
939C2×C4—434no—
940C2×C4—4312no—
941C2×C4—433no—
942C2×C4—866no—
943C2×C4—866no—
944C2×C4—866no—
945C2×C4—868no—
946C2×C4—866no—
947C2×C4—862no—
948C2×C4—866no—
949C2×C4—866no—
950C2×C4—866no—
951C2×C4—866no—
952C2×C4—862no—
953C2×C4—866no—
954C2×C4—1723no—
955C2×C4—1723no—
956C2×C4—1723no—
957C2×C4—17212no—
958C2×C4—17212no—
959C2×C4C2×#10621900112yes—
960C2×C4C24×D43112yes—
961C2×C4C24×D4313yes—
962C2×C4C24×D4313yes—
963C2×C4C24×D4313yes—
964C2×C4C24×D4311yescharacteristic
965C2×C4C24×D4311yescharacteristic
966C2×C4C24×D4311yescharacteristic
967C22—23no—
968C22—23no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—432no—
973C22—861no—
974C22—861no—
975C22—863no—
976C22—863no—
977C22—863no—
978C22—17212no—
979C22C22×#1062190016yes—
980C22C25×D4311yescharacteristic
981C4—212no—
982C4—23no—
983C4—23no—
984C4—432no—
985C4—861no—
986C4—863no—
987C4—863no—
988C4—864no—
989C4—861no—
990C4—863no—
991C4—8612no—
992C4C22×#1062190016yes—
993C4C22×#1062190012yes—
994C42−1+4×D4312yes—
995C4#1458373612yes—
996C2—26no—
997C2—44no—
998C2—862no—
999C2—1723no—
1000C2C23×#1062190011yescharacteristic
1001C2C2×2−1+4×D4311yescharacteristic
1002C2C2×#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3499C2
hypercenter#3499D43
hypocenterC43#62805
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #19148686C2semidirect
2. #19148635C2semidirect
3. #19148607C2semidirect
4. #19148564C2semidirect
5. #19148502C2semidirect
6. #19148479C2semidirect
7. #19148414C2semidirect
8. #19148344C2semidirect
9. #19148268C2semidirect
10. #19148216C2semidirect
11. #19148207C2semidirect
12. Q8×#10621900C2semidirect
13. #19148158C2semidirect
14. #19148019C2semidirect
15. #19147890C2semidirect
16. C2×#14583454C2semidirect
17. 2−1+4×Dic43C2semidirect
18. C4×#41×D43C2semidirect
19. C43×#3499C2semidirect
21. Q8×Dic86C22semidirect
22. #14583628C22semidirect
23. #14583624C22semidirect
24. #14583624C22semidirect
25. #14583623C22semidirect
26. #14583623C22semidirect
27. #14583620C22semidirect
28. #14583619C22semidirect
29. #14583614C22semidirect
31. #14583606C22semidirect
32. #14583606C22semidirect
33. #14583601C22semidirect
34. #14583591C22semidirect
35. #14583586C22semidirect
36. #14583584C22semidirect
37. #14583584C22semidirect
40. D4×Dic86C22semidirect
43. #14583555C22semidirect
44. #14583553C22semidirect
47. #14583527C22semidirect
48. #14583522C22semidirect
49. #14583518C22semidirect
50. #14583510C22semidirect
51. #14583509C22semidirect
52. #14583493C22semidirect
55. #14583456C22semidirect
60. #14583454C22semidirect
61. #14583454C22semidirect
62. #14583454C22semidirect
63. #14583454C22semidirect
64. #14583454C22semidirect
65. #14583451C22semidirect
67. #14583447C22semidirect
68. C2×#13063325C22semidirect
69. #14583435C22semidirect
71. #14583431C22semidirect
72. #14583430C22semidirect
73. #14583430C22semidirect
75. #14583428C22semidirect
76. #14583426C22semidirect
77. C2×#13063316C22semidirect
84. #14583382C22semidirect
85. #14583382C22semidirect
86. #14583377C22semidirect
87. #14583377C22semidirect
89. #41×Dic43C22semidirect
90. #41×Dic43C22semidirect
98. C4×#10621900C22semidirect
99. C2×Q8×Dic43C22semidirect
100. C2×Q8×Dic43C22semidirect
101. C2×#13063290C22semidirect
110. D4×Q8×C43C22semidirect
111. D4×Q8×C43C22semidirect
112. C43×#547C22semidirect
113. C43×#547C22semidirect
114. C43×#536C22semidirect
115. C43×#532C22semidirect
116. C2×C4⋊Q8×C43C22semidirect
293. #41×C43#41semidirect
460. C4×D432−1+4semidirect
502. #3499D43semidirect
544. D4×Q8C2×D43semidirect
545. D4×Q8C2×D43semidirect
550. #547C2×D43semidirect
551. #547C2×D43semidirect
561. #536C2×D43semidirect
575. #532C2×D43semidirect
577. C2×C4⋊Q8C2×D43semidirect
619. C43#62805semidirect
800. #41#10621900semidirect

Maximal subgroups

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

subgroupindex
#191486862
#191486352
#191486072
#191485642
#191485022
#191484792
#191484142
#191483442
#191482682
#191482162
#191482072
Q8×#106219002
#191481582
#191480192
#191478902
C2×#145834542
2−1+4×Dic432
C4×#41×D432
C43×#34992
#6280543