Finite Group Databasebeta

← #26004442

Subgroups — #26004442

Order 11008.

6518 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149100C214yesmaximal, complemented
2#19149090C211yesmaximal, characteristic, complemented
3#19149086C214yesmaximal, complemented
4#19149062C214yesmaximal, complemented
5#19149050C214yesmaximal, complemented
6#19149033C214yesmaximal, complemented
7#19149009C212yesmaximal, complemented
8#19148876C218yesmaximal, complemented
9#19148739C214yesmaximal, complemented
10#19148207C214yesmaximal, complemented
11#19148194C214yesmaximal, complemented
12#19148174C214yesmaximal, complemented
13#19148023C218yesmaximal, complemented
14#19147979C214yesmaximal, complemented
15#19147890C212yesmaximal, complemented
16#533×D43C211yesmaximal, characteristic, complemented
17C43×#3548C211yesmaximal, characteristic, complemented
18C43⋊#564C2214yescomplemented
19#14583652C22116yescomplemented
20#14583650C22116yes—
21#14583649C2218yescomplemented
22#14583644C22116yes—
23#14583635C2218yescomplemented
24#14583635C2214yescomplemented
25#14583629C2214yescomplemented
26#14583628C2214yescomplemented
27#14583627C2214yescomplemented
28#14583626C2218yescomplemented
29#14583624C2214yescomplemented
30#14583620C2218yes—
31#14583619C2218yescomplemented
32#14583619C2214yescomplemented
33#14583619C2214yescomplemented
34#14583608C2218yescomplemented
35#14583604C2218yes—
36#14583603C22116yes—
37#14583596C2218yes—
38#14583596C22116yes—
39#14583586C22116yescomplemented
40#14583584C2218yes—
41D4×Dic86C2214yescomplemented
42D4×Dic86C2214yescomplemented
43#14583562C2218yes—
44#14583556C2218yes—
45#14583555C2218yes—
46#14583548C2218yes—
47#14583530C2218yescomplemented
48#14583516C22116yes—
49#14583516C2218yes—
50#14583516C2218yes—
51#14583516C2218yescomplemented
52#14583514C2218yes—
53#14583512C2214yes—
54#14583511C2214yes—
55#14583509C2218yes—
56#14583509C2218yescomplemented
57#14583509C22116yescomplemented
58#14583503C2214yes—
59#14583494C22116yes—
60#14583494C22116yescomplemented
61#14583492C22116yes—
62#14583481C22116yes—
63#14583470C2218yes—
64#14583470C2218yescomplemented
65#14583456C2212yes—
66#14583456C2211yescharacteristic
67#14583455C2212yes—
68#14583455C2214yes—
69#14583454C2212yes—
70#14583454C2212yes—
71#14583454C2212yes—
72#14583453C2214yes—
73#14583452C2212yes—
74#14583451C2214yes—
75#14583451C2218yescomplemented
76#14583451C22116yescomplemented
77#14583447C2212yes—
78#14583447C2212yes—
79#14583447C2214yes—
80C4⋊Q8×D43C2212yes—
81#14583431C2214yes—
82#14583431C2214yes—
83#14583430C2214yes—
84#14583430C2214yes—
85#14583430C22116yes—
86#14583430C2218yescomplemented
87#14583430C22116yescomplemented
88#14583428C2214yes—
89#14583428C2214yes—
90#14583426C22116yes—
91#125×D43C2212yes—
92#14583409C2214yes—
93#14583409C2214yes—
94#14583406C2214yes—
95C22⋊Q8×D43C2214yes—
96#41×Dic43C2214yes—
97#41×Dic43C2218yescomplemented
98C4×#10621900C2214yes—
99C4×#10621900C2214yes—
100C4×#10621900C2218yes—
101C2×#13063290C2218yescomplemented
102C4×Q8×D43C2214yes—
103#117×D43C2212yes—
104C2×C42×D43C2211yescharacteristic
105C43×#562C2214yescomplemented
106C43×#554C2214yescomplemented
107C43×#550C2214yescomplemented
108C43×#547C2214yescomplemented
109C43×#540C2214yes—
110C43×#537C2218yes—
111C43×#533C2211yescharacteristic
112C43×#532C2212yes—
113C2×#10621900C2314yes—
114C2×#10621900C2314yes—
115C22×Dic86C2318yes—
116C2×Q8×D43C2314yes—
117C22×C4×D43C2311yescharacteristic
118C22×C4×D43C2312yes—
119#13063325C2312yes—
120#13063325C2312yes—
121#13063325C2312yes—
122#13063325C2314yes—
123#13063324C23116yes—
124#13063324C2318yes—
125#13063324C2318yes—
126#13063324C2314yes—
127#13063324C2314yes—
128#13063323C2318yes—
129#13063323C23116yes—
130#13063323C2314yes—
131#13063320C23116yes—
132#13063318C23116yes—
133#13063318C23116yes—
134#13063318C23116yes—
135#13063318C23116yes—
136#13063318C2318yes—
137#13063318C2318yes—
138#13063318C23116yes—
139#13063318C23116yes—
140#13063317C2314yes—
141#13063317C2312yes—
142#13063317C2314yes—
143#13063316C2318yes—
144#13063316C2314yes—
145#13063316C23116yes—
146#13063316C2314yes—
147#13063316C2314yes—
148#13063316C23116yes—
149#13063315C23116yes—
150#13063315C23116yes—
151#13063315C23116yes—
152#13063315C23116yes—
153#13063315C2318yes—
154#13063312C2318yes—
155#13063312C23116yes—
156#13063312C2314yes—
157#13063312C2318yes—
158#13063312C2314yes—
159#13063312C23116yes—
160#13063311C23116yes—
161#13063308C23116yes—
162#13063307C2318yes—
163#13063307C2318yes—
164#13063306C23116yes—
165#13063306C23116yes—
166#13063306C23116yes—
167#13063306C2318yes—
168#13063306C23116yes—
169#13063306C23116yes—
170#13063305C2314yes—
171#13063305C2314yes—
172#13063305C2314yes—
173#13063304C2318yes—
174#13063304C23116yes—
175#13063304C2318yes—
176#13063304C23116yes—
177#13063304C2314yes—
178#13063304C2314yes—
179#13063304C2314yes—
180#13063304C23116yes—
181#13063303C23116yes—
182#13063303C2318yes—
183#13063302C23116yes—
184#13063302C23116yes—
185#13063302C23116yes—
186#13063302C23116yes—
187#13063302C2318yes—
188#13063301C2314yes—
189#13063301C2314yes—
190#13063301C2314yes—
191#13063297C23116yes—
192#13063296C2314yes—
193#13063296C23116yes—
194#13063296C2314yes—
195#13063296C2314yes—
196#13063296C2314yes—
197#13063293C2318yes—
198Q8×Dic43C2318yes—
199Q8×Dic43C2314yes—
200Q8×Dic43C2314yes—
201Q8×Dic43C2314yes—
202C4×Dic86C2314yes—
203C4×Dic86C2314yes—
204C4×Dic86C2318yes—
205C4×Dic86C2318yes—
206C4×Dic86C2314yes—
207#13063290C2318yes—
208#13063290C2318yes—
209#13063290C23116yes—
210#13063290C2314yes—
211#13063290C2318yes—
212#13063290C2314yes—
213#13063290C23116yes—
214#13063290C2314yes—
215#13063290C2318yes—
216D4×Dic43C23116yes—
217D4×Dic43C2318yes—
218D4×Dic43C2318yes—
219D4×Dic43C2314yes—
220D4×Dic43C2314yes—
221D4×Dic43C2318yes—
222D4×Dic43C2318yes—
223D4×Dic43C2314yes—
224D4×Dic43C2314yes—
225D4×Dic43C23116yes—
226C4×C22⋊D43C2318yes—
227C4×C22⋊D43C2318yes—
228C4×C22⋊D43C23116yes—
229(C22⋊D43)⋊C4C23116yes—
230(C22⋊D43)⋊C4C2318yes—
231(C22⋊D43)⋊C4C2318yes—
232#13063284C23116yes—
233#13063284C2318yes—
234#13063284C2312yes—
235#13063284C2314yes—
236#13063284C2318yes—
237#13063283C2314yes—
238#13063283C2314yes—
239#13063283C2314yes—
240#13063282C2314yes—
241#13063281C2318yes—
242#13063281C2314yes—
243#13063281C23116yes—
244#13063281C2318yes—
245C2×Dic43⋊C4C23116yes—
246C4⋊C4×D43C2318yes—
247C4⋊C4×D43C2314yes—
248C4⋊C4×D43C2314yes—
249C22⋊C4×D43C2314yes—
250C2×C4×Dic43C2312yes—
251C2×C4×Dic43C2311yescharacteristic
252C2×C4×Dic43C2318yes—
253C2×C4×Dic43C23116yes—
254C42×D43C2312yes—
255C42×D43C2311yescharacteristic
256C42×D43C2311yescharacteristic
257C42×D43C2311yescharacteristic
258C42×D43C2311yescharacteristic
259C42×D43C2312yes—
260C42×D43C2314yes—
261C2×#41×C43C2318yes—
262C2×#41×C43C2314yes—
263C4⋊Q8×C43C2312yes—
264C4⋊Q8×C43C2312yes—
265#127×C43C2312yes—
266#127×C43C2314yes—
267#125×C43C2312yes—
268#125×C43C2314yes—
269#124×C43C2314yes—
270#123×C43C23116yes—
271C22⋊Q8×C43C2318yes—
272C22⋊Q8×C43C2314yes—
273C22⋊Q8×C43C23116yes—
274#121×C43C2318yes—
275#121×C43C2314yes—
276#121×C43C2314yes—
277#121×C43C23116yes—
278#121×C43C23116yes—
279C4×Q8×C43C2314yes—
280C4×D4×C43C2314yes—
281C4×D4×C43C2314yes—
282C4×D4×C43C2318yes—
283#117×C43C2312yes—
284C2×C4⋊C4×C43C2318yes—
285C2×C42×C43C2311yescharacteristic
286C23×D43C2411yescharacteristic
287#41×C43—48no—
288#41×C43—416no—
289C2×Q8×C43C2414yes—
290C2×Q8×C43C2414yes—
291C2×D4×C43C2414yes—
292C2×D4×C43C2414yes—
293C2×D4×C43C2418yes—
294C2×D4×C43C24116yes—
295C2×D4×C43C2414yes—
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2412yes—
298C22×C4×C43C2418yes—
299C22×C4×C43C24116yes—
300C2×C22⋊D43C2418yes—
301C2×C22⋊D43C2418yes—
302C22×Dic43C2418yes—
303C22×Dic43C2411yescharacteristic
304C22×Dic43C2412yes—
305C22×Dic43C2418yes—
306C22×Dic43C24116yes—
307Q8×D43—48no—
308#10621900—216no—
309#10621900—48no—
310C2×C4×D43—24no—
311C2×C4×D43—44no—
312C2×C4×D43C2411yescharacteristic
313C2×C4×D43C2412yes—
314C2×C4×D43C2411yescharacteristic
315C2×C4×D43C2411yescharacteristic
316C2×C4×D43C2412yes—
317C2×C4×D43C2412yes—
318C2×C4×D43C2412yes—
319C2×C4×D43C2418yes—
320C2×C4×D43C2411yescharacteristic
321C2×Dic86—416no—
322C2×Dic86C2414yes—
323C2×Dic86C2414yes—
324C2×Dic86C2414yes—
325C2×Dic86C24116yes—
326C2×Dic86C2418yes—
327C4⋊C4×C43C2414yes—
328C4⋊C4×C43C2414yes—
329C4⋊C4×C43C24116yes—
330C4⋊C4×C43C2414yes—
331C4⋊C4×C43C2414yes—
332C4⋊C4×C43C2418yes—
333C22⋊C4×C43C2414yes—
334C22⋊C4×C43C24116yes—
335C22⋊C4×C43C2418yes—
336C22⋊C4×C43C2418yes—
337C42×C43C2411yescharacteristic
338C42×C43C2412yes—
339C42×C43C2411yescharacteristic
340C42×C43C2414yes—
341C22⋊Dic43C2414yes—
342C22⋊Dic43C2418yes—
343C22⋊Dic43C2418yes—
344C22⋊Dic43C24116yes—
345C22⋊Dic43C2418yes—
346C22⋊Dic43C24116yes—
347C22⋊Dic43C2418yes—
348C22⋊Dic43C24116yes—
349C22⋊Dic43C2418yes—
350(C2×D43)⋊C4C2418yes—
351(C2×D43)⋊C4C2418yes—
352(C2×D43)⋊C4C2418yes—
353C4⋊Dic43C2414yes—
354C4⋊Dic43C2414yes—
355C4⋊Dic43C2418yes—
356C4⋊Dic43C2414yes—
357C4⋊Dic43C2414yes—
358C4⋊Dic43C2414yes—
359C4⋊Dic43C2414yes—
360C4⋊Dic43C24116yes—
361C4⋊Dic43C2418yes—
362C4⋊Dic43C2418yes—
363Dic43⋊C4C2418yes—
364Dic43⋊C4C2418yes—
365Dic43⋊C4C2418yes—
366Dic43⋊C4C2418yes—
367Dic43⋊C4C2418yes—
368Dic43⋊C4C24116yes—
369Dic43⋊C4C24116yes—
370Dic43⋊C4C2418yes—
371Dic43⋊C4C2418yes—
372Dic43⋊C4C24116yes—
373Dic43⋊C4C2418yes—
374Dic43⋊C4C24116yes—
375C4×Dic43C2412yes—
376C4×Dic43C2411yescharacteristic
377C4×Dic43C2412yes—
378C4×Dic43C2412yes—
379C4×Dic43C2412yes—
380C4×Dic43C2412yes—
381C4×Dic43C2411yescharacteristic
382C4×Dic43C2418yes—
383C4×Dic43C2414yes—
384C4×Dic43C2418yes—
385C4×Dic43C2418yes—
386C4×Dic43C24116yes—
387C4×Dic43C2418yes—
388C4×Dic43C24116yes—
389C23×C43C2511yescharacteristic
390C23×C43C2518yes—
391C22×D43—22no—
392C22×D43—42no—
393C22×D43C2511yescharacteristic
394C22×D43C2511yescharacteristic
395Q8×C43—28no—
396Q8×C43—44no—
397D4×C43—28no—
398D4×C43—28no—
399D4×C43—48no—
400D4×C43—416no—
401D4×C43—44no—
402C2×C4×C43—22no—
403C2×C4×C43—216no—
404C2×C4×C43—24no—
405C2×C4×C43—416no—
406C2×C4×C43C2518yes—
407C2×C4×C43C2518yes—
408C2×C4×C43C2511yescharacteristic
409C2×C4×C43C2512yes—
410C2×C4×C43C2511yescharacteristic
411C2×C4×C43C2512yes—
412C22⋊D43—216no—
413C22⋊D43—48no—
414C2×Dic43—22no—
415C2×Dic43—216no—
416C2×Dic43—416no—
417C2×Dic43—42no—
418C2×Dic43—48no—
419C2×Dic43C2512yes—
420C2×Dic43C2518yes—
421C2×Dic43C2518yes—
422C2×Dic43C2518yes—
423C2×Dic43C2511yescharacteristic
424C2×Dic43C2512yes—
425C2×Dic43C2511yescharacteristic
426C4×D43—22no—
427C4×D43—22no—
428C4×D43—24no—
429C4×D43—24no—
430C4×D43—22no—
431C4×D43—42no—
432C4×D43—42no—
433C4×D43—48no—
434C4×D432−1+414yes—
435Dic86—28no—
436Dic86—28no—
437Dic86—28no—
438Dic86—416no—
439Dic86—48no—
440#62761—431nomaximal, Sylow
441C22×C43—21no—
442C22×C43—28no—
443C22×C43—22no—
444C22×C43—28no—
445C22×C43—28no—
446C22×C43C2611yescharacteristic
447C2×D43—22no—
448C2×D43—21no—
449C2×D43—22no—
450C2×D43—44no—
451C2×D43C2×2−1+412yes—
452C4×C43—21no—
453C4×C43—28no—
454C4×C43—28no—
455C4×C43—22no—
456C4×C43C2×2−1+412yes—
457C4×C43#58514yes—
458Dic43—28no—
459Dic43—21no—
460Dic43—28no—
461Dic43—28no—
462Dic43—22no—
463Dic43—22no—
464Dic43C2×2−1+412yes—
465#3557—434no—
466#3556—431no—
467#3555—434no—
468#3554—434no—
469#3553—434no—
470#3552—434no—
471#3550—432no—
472#3548D4311yescharacteristic, complemented
473#3541—438no—
474#3531—434no—
475#3482—434no—
476#3480—434no—
477Q8×#41—434no—
478#3461—438no—
479#3455—434no—
480#3444—432no—
481C2×#533—431no—
482C2×C43—41no—
483C2×C43—48no—
484C2×C43C22×2−1+411yescharacteristic
485C2×C43C2×#58512yes—
486D43—22no—
487D43—41no—
488#564—434no—
489#563—438no—
490#563—4316no—
491#563—4316no—
492#562—4316no—
493#562C2×D4314yescomplemented
494#559—434no—
495#559—438no—
496Q82—434no—
497#557—434no—
498#557—438no—
499#557—434no—
500#557—434no—
501#556—438no—
502#556—434no—
503#556—438no—
504#556—434no—
505#554—4316no—
506#554—438no—
507#554—438no—
508#554C2×D4314yescomplemented
509#553—438no—
510#553—4316no—
511#552—4316no—
512#552—438no—
513#550C2×D4314yescomplemented
514D4×Q8—438no—
515D4×Q8—434no—
516D4×Q8—434no—
517#548—438no—
518#548—438no—
519#547—438no—
520#547C2×D4314yescomplemented
521#544—438no—
522#542—438no—
523#542—438no—
524#542—4316no—
525#542—438no—
526#542—438no—
527#541—434no—
528#541—438no—
529#541—438no—
530#541—4316no—
531#541—434no—
532#540—434no—
533#540C2×D4314yes—
534#539—4316no—
535#539—4316no—
536#539—4316no—
537#538—4316no—
538#537C2×D4318yes—
539#536—438no—
540#536—438no—
541#533—432no—
542#533—432no—
543#533—432no—
544#533—432no—
545#533—434no—
546#533—434no—
547#533—438no—
548#533—4316no—
549#533—434no—
550#533—432no—
551#533—431no—
552#533—432no—
553#533C2×D4311yescharacteristic
554#532—432no—
555#532—432no—
556#532—434no—
557#532C2×D4312yes—
558C2×C4⋊Q8—432no—
559#529—434no—
560#529—434no—
561#529—4316no—
562#529—434no—
563#529—434no—
564#529—4316no—
565#529—438no—
566#529—4316no—
567#529—434no—
568#529—434no—
569C2×#125—432no—
570#525—434no—
571#525—434no—
572#525—434no—
573C2×C22⋊Q8—434no—
574C4×#41—434no—
575C4×#41—438no—
576C4×#41—434no—
577C4×#41—434no—
578C4×#41—438no—
579C2×C4×Q8—434no—
580C2×C4×Q8—438no—
581C2×#117—432no—
582C22×C42—431no—
583C43#6276111yescharacteristic, complemented, Sylow
584C2×#41—434no—
585C2×#41—434no—
586C2×#41C22×D4314yes—
587C2×#41C22×D4318yes—
588C22×Q8—434no—
589C22×Q8—438no—
590C23×C4—431no—
591C23×C4—432no—
592C4⋊Q8—434no—
593C4⋊Q8—438no—
594C4⋊Q8—4316no—
595C4⋊Q8—434no—
596C4⋊Q8—434no—
597C4⋊Q8—438no—
598C4⋊Q8—438no—
599C4⋊Q8—4316no—
600C4⋊Q8—432no—
601C4⋊Q8—432no—
602C4⋊Q8—432no—
603C4⋊Q8—434no—
604C4⋊Q8C22×D4312yes—
605C4⋊Q8C22×D4312yes—
606#127C22×D4312yes—
607#127C22×D4314yes—
608#126—4316no—
609#126—438no—
610#126—438no—
611#126—4316no—
612#126—4316no—
613#126—4316no—
614#126—4316no—
615#126—4316no—
616#126—4316no—
617#125—438no—
618#125—434no—
619#125—434no—
620#125—434no—
621#125—4316no—
622#125—4316no—
623#125—4316no—
624#125—438no—
625#125—4316no—
626#125—4316no—
627#125—4316no—
628#125—432no—
629#125—434no—
630#125—434no—
631#125C22×D4312yes—
632#125C22×D4314yes—
633#124—434no—
634#124—434no—
635#124—4316no—
636#124—438no—
637#124—4316no—
638#124—438no—
639#124—4316no—
640#124C22×D4314yes—
641#123—438no—
642#123—4316no—
643#123—4316no—
644#123—4316no—
645#123—4316no—
646#123—4316no—
647#123—4316no—
648#123—438no—
649#123—438no—
650#123C22×D43116yes—
651C22⋊Q8—434no—
652C22⋊Q8—434no—
653C22⋊Q8—434no—
654C22⋊Q8—434no—
655C22⋊Q8—434no—
656C22⋊Q8—434no—
657C22⋊Q8—4316no—
658C22⋊Q8—438no—
659C22⋊Q8—4316no—
660C22⋊Q8—438no—
661C22⋊Q8—4316no—
662C22⋊Q8—434no—
663C22⋊Q8—438no—
664C22⋊Q8—434no—
665C22⋊Q8—434no—
666C22⋊Q8—4316no—
667C22⋊Q8—438no—
668C22⋊Q8—4316no—
669C22⋊Q8—4316no—
670C22⋊Q8—4316no—
671C22⋊Q8—4316no—
672C22⋊Q8C22×D4314yes—
673C22⋊Q8C22×D4318yes—
674C22⋊Q8C22×D43116yes—
675#121—434no—
676#121—434no—
677#121—434no—
678#121—434no—
679#121—4316no—
680#121—4316no—
681#121C22×D4314yes—
682#121C22×D4314yes—
683#121C22×D43116yes—
684#121C22×D43116yes—
685#121C22×D4318yes—
686#120—438no—
687C4×Q8—434no—
688C4×Q8—434no—
689C4×Q8—434no—
690C4×Q8—438no—
691C4×Q8—434no—
692C4×Q8—434no—
693C4×Q8—4316no—
694C4×Q8—438no—
695C4×Q8—438no—
696C4×Q8—438no—
697C4×Q8—4316no—
698C4×Q8—434no—
699C4×Q8—438no—
700C4×Q8—434no—
701C4×Q8—438no—
702C4×Q8—434no—
703C4×Q8—434no—
704C4×Q8—438no—
705C4×Q8C22×D4314yes—
706C4×D4—434no—
707C4×D4—438no—
708C4×D4—438no—
709C4×D4—434no—
710C4×D4—4316no—
711C4×D4—434no—
712C4×D4—434no—
713C4×D4—4316no—
714C4×D4—438no—
715C4×D4—438no—
716C4×D4—438no—
717C4×D4—438no—
718C4×D4—4316no—
719C4×D4—438no—
720C4×D4—438no—
721C4×D4—4316no—
722C4×D4C22×D4314yes—
723C4×D4C22×D4314yes—
724C4×D4C22×D4318yes—
725#117—432no—
726#117—434no—
727#117—438no—
728#117—438no—
729#117—4316no—
730#117—434no—
731#117—434no—
732#117—434no—
733#117—434no—
734#117—438no—
735#117—4316no—
736#117—438no—
737#117—434no—
738#117C22×D4312yes—
739C2×C4⋊C4—4316no—
740C2×C4⋊C4—434no—
741C2×C4⋊C4—438no—
742C2×C4⋊C4—434no—
743C2×C4⋊C4C22×D4318yes—
744C2×C22⋊C4—434no—
745C2×C42—438no—
746C2×C42—4316no—
747C2×C42—432no—
748C2×C42—431no—
749C2×C42—434no—
750C2×C42—432no—
751C2×C42—431no—
752C2×C42—431no—
753C2×C42—431no—
754C2×C42—431no—
755C2×C42—432no—
756C2×C42C22×D4311yescharacteristic
757C24—431no—
758#41—48no—
759#41—416no—
760#41—8616no—
761#41—1728no—
762C2×Q8—434no—
763C2×Q8—434no—
764C2×Q8—434no—
765C2×Q8—438no—
766C2×Q8—4316no—
767C2×Q8—17216no—
768C2×Q8—1728no—
769C2×Q8C23×D4314yes—
770C2×Q8C23×D4314yes—
771C2×D4—438no—
772C2×D4—438no—
773C2×D4C23×D4314yes—
774C2×D4C23×D4314yes—
775C2×D4C23×D4318yes—
776C2×D4C23×D4314yes—
777C2×D4C23×D43116yes—
778C22×C4—431no—
779C22×C4—438no—
780C22×C4—431no—
781C22×C4—432no—
782C22×C4—438no—
783C22×C4—4316no—
784C22×C4—431no—
785C22×C4—432no—
786C22×C4—431no—
787C22×C4—431no—
788C22×C4—432no—
789C22×C4—432no—
790C22×C4—432no—
791C22×C4—438no—
792C22×C4—864no—
793C22×C4—1724no—
794C22×C4C23×D4311yescharacteristic
795C22×C4C23×D4312yes—
796C22×C4C23×D4318yes—
797C22×C4C23×D43116yes—
798C4⋊C4—438no—
799C4⋊C4—438no—
800C4⋊C4—438no—
801C4⋊C4—434no—
802C4⋊C4—434no—
803C4⋊C4—438no—
804C4⋊C4—4316no—
805C4⋊C4—438no—
806C4⋊C4—438no—
807C4⋊C4—4316no—
808C4⋊C4—434no—
809C4⋊C4—434no—
810C4⋊C4—434no—
811C4⋊C4—4316no—
812C4⋊C4—434no—
813C4⋊C4—438no—
814C4⋊C4—438no—
815C4⋊C4—438no—
816C4⋊C4—438no—
817C4⋊C4—4316no—
818C4⋊C4—4316no—
819C4⋊C4—438no—
820C4⋊C4C23×D4314yes—
821C4⋊C4C23×D4314yes—
822C4⋊C4C23×D4318yes—
823C4⋊C4C23×D4314yes—
824C4⋊C4C23×D43116yes—
825C4⋊C4C23×D4314yes—
826C22⋊C4—434no—
827C22⋊C4—438no—
828C22⋊C4—438no—
829C22⋊C4—438no—
830C22⋊C4—4316no—
831C22⋊C4—438no—
832C22⋊C4—438no—
833C22⋊C4—4316no—
834C22⋊C4—4316no—
835C22⋊C4—438no—
836C22⋊C4—438no—
837C22⋊C4—438no—
838C22⋊C4C23×D4314yes—
839C22⋊C4C23×D4318yes—
840C22⋊C4C23×D43116yes—
841C22⋊C4C23×D4318yes—
842C42—432no—
843C42—431no—
844C42—438no—
845C42—432no—
846C42—438no—
847C42—432no—
848C42—432no—
849C42—432no—
850C42—431no—
851C42—438no—
852C42—438no—
853C42—434no—
854C42—4316no—
855C42—4316no—
856C42C23×D4311yescharacteristic
857C42C23×D4312yes—
858C42C23×D4311yescharacteristic
859C42C23×D4314yes—
860C23—431no—
861C23—431no—
862C23—862no—
863C23—1722no—
864C23C24×D4311yescharacteristic
865C23C24×D4318yes—
866Q8—28no—
867Q8—44no—
868Q8—868no—
869Q8—868no—
870Q8—868no—
871Q8—17216no—
872Q8—1728no—
873D4—28no—
874D4—28no—
875D4—48no—
876D4—44no—
877D4—416no—
878D4—8616no—
879D4—1728no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—216no—
883C2×C4—416no—
884C2×C4—431no—
885C2×C4—434no—
886C2×C4—432no—
887C2×C4—438no—
888C2×C4—431no—
889C2×C4—432no—
890C2×C4—438no—
891C2×C4—438no—
892C2×C4—862no—
893C2×C4—862no—
894C2×C4—862no—
895C2×C4—8616no—
896C2×C4—862no—
897C2×C4—864no—
898C2×C4—864no—
899C2×C4—1722no—
900C2×C4—1722no—
901C2×C4—1728no—
902C2×C4—1722no—
903C2×C4—17216no—
904C2×C4—1728no—
905C2×C4C24×D4318yes—
906C2×C4C24×D4318yes—
907C2×C4C24×D4311yescharacteristic
908C2×C4C24×D4312yes—
909C2×C4C24×D4311yescharacteristic
910C2×C4C24×D4312yes—
911C22—21no—
912C22—28no—
913C22—28no—
914C22—22no—
915C22—28no—
916C22—432no—
917C22—862no—
918C22—861no—
919C22—862no—
920C22—1724no—
921C22C25×D4311yescharacteristic
922C4—21no—
923C4—28no—
924C4—22no—
925C4—28no—
926C4—432no—
927C4—861no—
928C4—868no—
929C4—862no—
930C4—862no—
931C4—868no—
932C4—868no—
933C42−1+4×D4312yes—
934C4#1458373414yes—
935C2—41no—
936C2—48no—
937C2—862no—
938C2—1721no—
939C2C2×2−1+4×D4311yescharacteristic
940C2C2×#1458373412yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3548C2
hypercenter#3548D43
hypocenterC43#62761
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #19149100C2semidirect
2. #19149090C2semidirect
3. #19149086C2semidirect
4. #19149062C2semidirect
5. #19149050C2semidirect
6. #19149033C2semidirect
7. #19149009C2semidirect
8. #19148876C2semidirect
9. #19148739C2semidirect
10. #19148207C2semidirect
11. #19148194C2semidirect
12. #19148174C2semidirect
13. #19148023C2semidirect
14. #19147979C2semidirect
15. #19147890C2semidirect
16. #533×D43C2semidirect
17. C43×#3548C2semidirect
18. C43⋊#564C22semidirect
19. #14583652C22semidirect
21. #14583649C22semidirect
23. #14583635C22semidirect
24. #14583635C22semidirect
25. #14583629C22semidirect
26. #14583628C22semidirect
27. #14583627C22semidirect
28. #14583626C22semidirect
29. #14583624C22semidirect
31. #14583619C22semidirect
32. #14583619C22semidirect
33. #14583619C22semidirect
34. #14583608C22semidirect
39. #14583586C22semidirect
41. D4×Dic86C22semidirect
42. D4×Dic86C22semidirect
47. #14583530C22semidirect
51. #14583516C22semidirect
56. #14583509C22semidirect
57. #14583509C22semidirect
60. #14583494C22semidirect
64. #14583470C22semidirect
75. #14583451C22semidirect
76. #14583451C22semidirect
86. #14583430C22semidirect
87. #14583430C22semidirect
97. #41×Dic43C22semidirect
101. C2×#13063290C22semidirect
105. C43×#562C22semidirect
106. C43×#554C22semidirect
107. C43×#550C22semidirect
108. C43×#547C22semidirect
472. #3548D43semidirect
493. #562C2×D43semidirect
508. #554C2×D43semidirect
513. #550C2×D43semidirect
520. #547C2×D43semidirect
583. C43#62761semidirect

Maximal subgroups

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

subgroupindex
#191491002
#191490902
#191490862
#191490622
#191490502
#191490332
#191490092
#191488762
#191487392
#191482072
#191481942
#191481742
#191480232
#191479792
#191478902
#533×D432
C43×#35482
#6276143