Finite Group Databasebeta

← #25969363

Subgroups — #25969363

Order 11008.

1672 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148414C211yesmaximal, characteristic, complemented
2#19148022C211yesmaximal, characteristic
3#19145880C214yesmaximal, complemented
4#19145865C214yesmaximal, complemented
5#19145818C212yesmaximal, complemented
6#19145811C212yesmaximal, complemented
7#19145776C212yesmaximal, complemented
8#19145748C212yesmaximal, complemented
9#19145134C212yesmaximal, complemented
10#19144962C212yesmaximal, complemented
11#19144575C212yesmaximal
12#19144565C212yesmaximal, complemented
13#19144411C211yesmaximal, characteristic, complemented
14#19144402C211yesmaximal, characteristic, complemented
15#19144385C211yesmaximal, characteristic, complemented
16C2×#14583195C211yesmaximal, characteristic, complemented
17C43×#2925C211yesmaximal, characteristic, complemented
18Q8×Dic86—21no—
19#14583628—21no—
20#14583606—22no—
21#14583606—21no—
22D4×Dic86—22no—
23D4×Dic86—21no—
24#14583527C2212yes—
25#14583527C2214yes—
26#14583527C2211yescharacteristic
27#14583520C2212yes—
28#14583514—21no—
29#14583511C2212yes—
30#14583507—21no—
31#14583491—22no—
32#14583477C2211yescharacteristic
33#14583475C2211yescharacteristic
34#14583470C2211yescharacteristic
35#14583456C2212yes—
36#14583456C2212yes—
37#14583456C2211yescharacteristic
38#14583453—21no—
39C2×#13063325C2212yes—
40C2×#13063325C2211yescharacteristic
41#14583433C2212yes—
42#14583431—21no—
43#14583429—22no—
44#14583382C2212yes—
45C4×#10621898C2211yescharacteristic
46C2×C4×Dic86C2211yescharacteristic
47#14583308C2214yes—
48#14583308C2214yes—
49#14583304C2214yes—
50#14583301C2214yes—
51#14583268C2214yes—
52#14583259C2214yes—
53#14583254C2214yes—
54#14583250C2214yes—
55#14583241C2214yes—
56#14583241C2214yes—
57#14583241C2214yes—
58#14583235C2214yes—
59#14583235C2214yes—
60#14583230C2214yes—
61#14583224C2214yes—
62#14583213C2214yes—
63#14583207C2212yes—
64#14583207C2214yes—
65#14583200C2212yes—
66#14583195C2211yescharacteristic
67#14583195C2212yes—
68#14583195C2212yes—
69#14583195C2212yes—
70#14583195C2212yes—
71#14583195C2214yes—
72#14583190C2212yes—
73#14583190C2211yescharacteristic
74#14583185C2212yes—
75#14583185C2211yescharacteristic
76#14583185C2212yes—
77#14583180C2211yescharacteristic
78#14583180C2212yes—
79#14582941C2212yes—
80#14582941C2212yes—
81#14582937C2212yes—
82C2×#13063259C2212yes—
83#14582909C2212yes—
84#14582901C2212yes—
85#14582896C2212yes—
86C2×#13063250C2212yes—
87C4×#41×C43C2211yescharacteristic
88C43×#433C2214yes—
89C43×#432C2212yes—
90C43×#431C2212yes—
91C43×#423C2211yescharacteristic
92C2×C4⋊C8×C43C2211yescharacteristic
93C43×#408C2212yes—
94C43×#405C2212yes—
95C2×#10621898C2311yescharacteristic
96C22×Dic86—21no—
97C22×Dic86—22no—
98C22×Dic86C2311yescharacteristic
99#13063325—21no—
100#13063325—22no—
101#13063325—21no—
102#13063325—22no—
103#13063325C2312yes—
104#13063325C2312yes—
105#13063325C2314yes—
106#13063325C2311yescharacteristic
107#13063325C2312yes—
108#13063325C2311yescharacteristic
109#13063325C2312yes—
110#13063324—24no—
111#13063324—22no—
112#13063324—21no—
113#13063323—21no—
114#13063320—22no—
115#13063319—22no—
116#13063318—22no—
117#13063318—22no—
118#13063317—22no—
119#13063317C2312yes—
120#13063317C2314yes—
121#13063317C2312yes—
122#13063316—22no—
123#13063316—24no—
124#13063316—21no—
125#13063315—22no—
126#13063315—22no—
127#13063313C2312yes—
128#13063312—21no—
129#13063311—22no—
130#13063309—22no—
131#13063308—22no—
132#13063307—22no—
133#13063306—22no—
134#13063305—21no—
135#13063305—21no—
136#13063304—21no—
137#13063304—22no—
138#13063304—21no—
139#13063304—22no—
140#13063304—22no—
141#13063304C2312yes—
142#13063304C2312yes—
143#13063304C2312yes—
144#13063303—22no—
145#13063302—24no—
146#13063302—24no—
147#13063302—24no—
148#13063302—22no—
149#13063301—21no—
150#13063299C2312yes—
151#13063297—22no—
152#13063296—21no—
153Q8×Dic43—22no—
154C4×Dic86—21no—
155C4×Dic86—22no—
156C4×Dic86—21no—
157C4×Dic86—22no—
158C4×Dic86—21no—
159C4×Dic86—21no—
160C4×Dic86—22no—
161C4×Dic86C2312yes—
162C4×Dic86C2312yes—
163C4×Dic86C2311yescharacteristic
164C4×Dic86C2311yescharacteristic
165C4×D172C2311yescharacteristic
166C4×D172C2311yescharacteristic
167D4×Dic43—22no—
168D4×Dic43—24no—
169C4×C22⋊D43—21no—
170C4×C22⋊D43—21no—
171C4×C22⋊D43—22no—
172#13063284—22no—
173#13063284C2311yescharacteristic
174#13063284C2312yes—
175#13063284C2314yes—
176#13063282—21no—
177#13063282—22no—
178C2×C4⋊Dic43—21no—
179C2×C4⋊Dic43—22no—
180C2×C4⋊Dic43C2311yescharacteristic
181C2×C4⋊Dic43C2312yes—
182C2×C4⋊Dic43C2314yes—
183C2×Dic43⋊C4—21no—
184C2×C4×Dic43—21no—
185C42×D43—21no—
186#13063259C2312yes—
187#13063259C2314yes—
188#13063259C2312yes—
189#13063259C2314yes—
190#13063259C2314yes—
191#13063259C2314yes—
192#13063257C2314yes—
193#13063257C2314yes—
194#13063257C2312yes—
195#13063257C2312yes—
196#13063250C2314yes—
197#13063250C2314yes—
198#13063250C2312yes—
199#13063250C2312yes—
200#13063250C2314yes—
201#13063250C2314yes—
202#13063250C2314yes—
203#13063247C2312yes—
204#13063247C2312yes—
205#13063247C2314yes—
206C2×#41×C43C2311yescharacteristic
207C2×M16×C43C2312yes—
208C22×C8×C43C2312yes—
209C4×Q8×C43D411yescharacteristic
210C4×Q8×C43D411yescharacteristic
211C4×D4×C43D412yes—
212C4×D4×C43D411yescharacteristic
213C4×D4×C43D412yes—
214C4×D4×C43D411yescharacteristic
215#117×C43C2311yescharacteristic
216#117×C43C2312yes—
217C2×C42×C43C2311yescharacteristic
218C2×C42×C43C2312yes—
219C4⋊C8×C43C2312yes—
220C4⋊C8×C43C2311yescharacteristic
221C4⋊C8×C43C2311yescharacteristic
222C4⋊C8×C43C2312yes—
223C4⋊C8×C43C2312yes—
224C22⋊C8×C43C2314yes—
225C22⋊C8×C43C2314yes—
226#97×C43C2314yes—
227C4×C8×C43C2314yes—
228#41×C43—22no—
229#41×C43—22no—
230C2×Q8×C43C2×D411yescharacteristic
231C2×D4×C43C2×D411yescharacteristic
232C2×D4×C43C2×D412yes—
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D412yes—
237C22×C4×C43C2412yes—
238C22×C4×C43C2411yescharacteristic
239C2×C22⋊D43—21no—
240C2×C22⋊D43—22no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—24no—
244C22×Dic43—22no—
245#10621898—22no—
246#10621898—22no—
247C2×D172C2411yescharacteristic
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×Dic86—22no—
252C2×Dic86—22no—
253C2×Dic86—21no—
254C2×Dic86—21no—
255C2×Dic86—21no—
256C2×Dic86—22no—
257C2×Dic86—22no—
258C2×Dic86—22no—
259C2×Dic86—24no—
260C2×Dic86—84no—
261C2×Dic86—82no—
262C2×Dic86C2412yes—
263C2×Dic86C2411yescharacteristic
264M16×C43—24no—
265C2×C8×C43—24no—
266C2×C8×C43C2412yes—
267C2×C8×C43C2414yes—
268C2×C8×C43C2412yes—
269C4⋊C4×C43C2×D412yes—
270C4⋊C4×C43C2×D411yescharacteristic
271C4⋊C4×C43C2×D411yescharacteristic
272C4⋊C4×C43C2×D412yes—
273C22⋊C4×C43C2×D412yes—
274C22⋊C4×C43C2×D412yes—
275C22⋊C4×C43C2×D412yes—
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D412yes—
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D412yes—
280C42×C43C2412yes—
281C42×C43C2411yescharacteristic
282C42×C43C2411yescharacteristic
283C22⋊Dic43—22no—
284C22⋊Dic43—22no—
285C22⋊Dic43—21no—
286C22⋊Dic43—24no—
287C22⋊Dic43—22no—
288C22⋊Dic43—22no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—22no—
294C4⋊Dic43—22no—
295C4⋊Dic43—21no—
296C4⋊Dic43—22no—
297C4⋊Dic43—24no—
298C4⋊Dic43—24no—
299C4⋊Dic43—22no—
300C4⋊Dic43—21no—
301C4⋊Dic43—22no—
302C4⋊Dic43—22no—
303C4⋊Dic43—21no—
304C4⋊Dic43—22no—
305C4⋊Dic43C2412yes—
306C4⋊Dic43C2412yes—
307C4⋊Dic43C2414yes—
308C4⋊Dic43C2411yescharacteristic
309C4⋊Dic43C2412yes—
310C4⋊Dic43C2411yescharacteristic
311Dic43⋊C4—22no—
312Dic43⋊C4—22no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320Dic43⋊C4—24no—
321Dic43⋊C4—22no—
322Dic43⋊C4—24no—
323Dic43⋊C4—22no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—22no—
328C4×Dic43—22no—
329C4×Dic43—24no—
330C4×Dic43—22no—
331C23×C43C22×D412yes—
332C23×C43C22×D411yescharacteristic
333C22×D43—21no—
334Q8×C43—22no—
335D4×C43—24no—
336D4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—24no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—42no—
342C2×C4×C43—41no—
343C2×C4×C43C22×D412yes—
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D412yes—
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D412yes—
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C432−1+412yes—
352C2×C4×C432−1+412yes—
353C2×C4×C43C2511yescharacteristic
354C22⋊D43—42no—
355C22⋊D43—82no—
356C2×Dic43—22no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—21no—
360C2×Dic43—22no—
361C2×Dic43—21no—
362C2×Dic43—24no—
363C2×Dic43—22no—
364C2×Dic43—42no—
365C2×Dic43—82no—
366C2×Dic43—84no—
367C2×Dic43—81no—
368D172—21no—
369D172—21no—
370C4×D43—42no—
371C4×D43—42no—
372C4×D43—81no—
373Dic86—22no—
374Dic86—22no—
375Dic86—21no—
376Dic86—21no—
377Dic86—42no—
378Dic86—44no—
379Dic86—42no—
380Dic86—42no—
381Dic86—82no—
382Dic86—84no—
383Dic86—82no—
384C8×C43—22no—
385C8×C43—22no—
386C8×C43—24no—
387#60893—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
393C22×C43#53612yes—
394C22×C43C23×D411yescharacteristic
395C2×D43—41no—
396C2×D43—41no—
397C2×D43—41no—
398C4×C43—21no—
399C4×C43—22no—
400C4×C43—21no—
401C4×C43—22no—
402C4×C43—21no—
403C4×C43—22no—
404C4×C43#53612yes—
405C4×C43#57812yes—
406C4×C43C2×2−1+411yescharacteristic
407C4×C43C2×2−1+411yescharacteristic
408Dic43—42no—
409Dic43—44no—
410Dic43—41no—
411Dic43—42no—
412Dic43—42no—
413Dic43—41no—
414Dic43—42no—
415Dic43—41no—
416#3503—431no—
417#3461—431no—
418#3243—434no—
419#3242—434no—
420#3238—432no—
421#3237—432no—
422#3233—432no—
423#3230—432no—
424#3164—432no—
425#3137—432no—
426#3098—432no—
427#3097—432no—
428#3079—431no—
429#3078—431no—
430#3076—431no—
431C2×#477—431no—
432#2925D4311yescharacteristic, complemented
433C2×C43—22no—
434C2×C43—42no—
435C2×C43C2×#53611yescharacteristic
436C2×C43C2×#57811yescharacteristic
437C2×C43#358511yescharacteristic
438D43—81no—
439Q82—861no—
440#557—861no—
441#554—862no—
442#554—861no—
443D4×Q8—862no—
444D4×Q8—861no—
445#544—432no—
446#544—431no—
447#544—434no—
448#542—432no—
449#542—861no—
450#541—432no—
451#541—861no—
452#539—862no—
453#537—431no—
454#536—431no—
455#536—431no—
456#533—431no—
457#533—432no—
458#533—432no—
459#533—861no—
460C2×C4⋊Q8—431no—
461C2×C4⋊Q8—432no—
462#529—432no—
463#529—862no—
464#529—861no—
465#520—432no—
466C4×#41—431no—
467C4×#41C2×D4311yescharacteristic
468C2×C4×Q8—431no—
469#501—434no—
470#501—434no—
471#500—434no—
472#499—434no—
473#491—434no—
474#489—434no—
475#488—434no—
476#487—434no—
477#485—434no—
478#485—434no—
479#485—434no—
480#484—434no—
481#484—434no—
482#483—434no—
483#482—434no—
484#480—434no—
485#479—432no—
486#479—434no—
487#478—432no—
488#477—432no—
489#477—432no—
490#477—434no—
491#477—431no—
492#477—432no—
493#477—432no—
494#476—431no—
495#476—432no—
496#475—431no—
497#475—432no—
498#475—432no—
499#474—431no—
500#474—432no—
501#433C2×D4314yes—
502#432C2×D4312yes—
503#431C2×D4312yes—
504#428—432no—
505#428—432no—
506#427—432no—
507C2×#107—432no—
508#423C2×D4311yescharacteristic
509C2×C4⋊C8C2×D4311yescharacteristic
510#419—432no—
511#417—432no—
512#416—432no—
513C2×#103—432no—
514#408C2×D4312yes—
515#405C2×D4312yes—
516C43#6089311yescharacteristic, complemented, Sylow
517C2×#41—431no—
518C2×#41C22×D4311yescharacteristic
519C22×Q8—431no—
520C22×Q8—861no—
521C22×Q8—862no—
522C2×M16C22×D4312yes—
523C22×C8C22×D4312yes—
524C4⋊Q8—432no—
525C4⋊Q8—431no—
526C4⋊Q8—432no—
527C4⋊Q8—434no—
528C4⋊Q8—431no—
529C4⋊Q8—432no—
530C4⋊Q8—432no—
531C4⋊Q8—861no—
532C4⋊Q8—861no—
533C4⋊Q8—864no—
534C4⋊Q8—862no—
535C4⋊Q8—861no—
536C4⋊Q8—862no—
537C4⋊Q8—861no—
538C4⋊Q8—862no—
539#126—862no—
540#126—862no—
541#126—862no—
542#126—862no—
543#125—432no—
544#125—432no—
545#125—434no—
546#125—862no—
547#125—861no—
548#125—862no—
549#125—862no—
550#125—864no—
551#125—862no—
552#124—432no—
553#124—861no—
554#124—862no—
555#123—862no—
556#123—862no—
557#123—862no—
558#123—862no—
559C22⋊Q8—432no—
560C22⋊Q8—432no—
561C22⋊Q8—432no—
562C22⋊Q8—861no—
563C22⋊Q8—862no—
564C22⋊Q8—861no—
565C22⋊Q8—862no—
566C22⋊Q8—861no—
567C22⋊Q8—862no—
568C22⋊Q8—861no—
569C22⋊Q8—861no—
570C22⋊Q8—862no—
571C22⋊Q8—862no—
572C22⋊Q8—864no—
573C22⋊Q8—864no—
574C22⋊Q8—864no—
575#121—432no—
576#121—862no—
577#121—861no—
578C4×Q8—432no—
579C4×Q8—432no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—862no—
583C4×Q8—861no—
584C4×Q8—861no—
585C4×Q8—862no—
586C4×Q8—861no—
587C4×Q8—862no—
588C4×Q8—861no—
589C4×Q8—862no—
590C4×Q8D17211yescharacteristic
591C4×Q8D17211yescharacteristic
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—864no—
595C4×D4—862no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—862no—
599C4×D4D17211yescharacteristic
600C4×D4D17212yes—
601C4×D4D17212yes—
602C4×D4D17211yescharacteristic
603#117—431no—
604#117—432no—
605#117—434no—
606#117—862no—
607#117—861no—
608#117—862no—
609#117C22×D4311yescharacteristic
610#117C22×D4312yes—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—432no—
613C2×C4⋊C4—434no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—862no—
617C2×C42—861no—
618C2×C42—861no—
619C2×C42C22×D4311yescharacteristic
620C2×C42C22×D4312yes—
621#107—434no—
622#107—434no—
623#107—432no—
624#107—432no—
625#107—434no—
626#107—434no—
627#106—432no—
628#106—432no—
629#106—434no—
630#106—434no—
631C4⋊C8C22×D4311yescharacteristic
632C4⋊C8C22×D4311yescharacteristic
633C4⋊C8C22×D4312yes—
634C4⋊C8C22×D4312yes—
635C4⋊C8C22×D4312yes—
636#103—434no—
637#103—434no—
638#103—432no—
639#103—432no—
640#103—434no—
641#103—434no—
642#103—434no—
643#102—432no—
644#102—432no—
645#102—434no—
646C22⋊C8C22×D4314yes—
647C22⋊C8C22×D4314yes—
648#97C22×D4314yes—
649C4×C8C22×D4314yes—
650#41—22no—
651#41—22no—
652#41—862no—
653#41—862no—
654C2×Q8—432no—
655C2×Q8—431no—
656C2×Q8—862no—
657C2×Q8—862no—
658C2×Q8—864no—
659C2×Q8—861no—
660C2×Q8—861no—
661C2×Q8—861no—
662C2×Q8—862no—
663C2×Q8—862no—
664C2×Q8—862no—
665C2×Q8—3442no—
666C2×Q8—3444no—
667C2×Q8C2×D17211yescharacteristic
668C2×D4—431no—
669C2×D4—862no—
670C2×D4—861no—
671C2×D4C2×D17212yes—
672C2×D4C2×D17211yescharacteristic
673C22×C4—861no—
674C22×C4—864no—
675C22×C4—862no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4C2×D17211yescharacteristic
681C22×C4C2×D17212yes—
682C22×C4C2×D17211yescharacteristic
683C22×C4C2×D17212yes—
684C22×C4C23×D4312yes—
685C22×C4C23×D4311yescharacteristic
686M16—24no—
687C2×C8—24no—
688C2×C8C23×D4312yes—
689C2×C8C23×D4314yes—
690C2×C8C23×D4312yes—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—434no—
694C4⋊C4—431no—
695C4⋊C4—432no—
696C4⋊C4—431no—
697C4⋊C4—864no—
698C4⋊C4—862no—
699C4⋊C4—861no—
700C4⋊C4—862no—
701C4⋊C4—861no—
702C4⋊C4—862no—
703C4⋊C4—862no—
704C4⋊C4—862no—
705C4⋊C4—864no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—862no—
709C4⋊C4—862no—
710C4⋊C4—862no—
711C4⋊C4—862no—
712C4⋊C4—862no—
713C4⋊C4—861no—
714C4⋊C4—862no—
715C4⋊C4—862no—
716C4⋊C4—862no—
717C4⋊C4—864no—
718C4⋊C4—862no—
719C4⋊C4—864no—
720C4⋊C4—862no—
721C4⋊C4C2×D17211yescharacteristic
722C4⋊C4C2×D17212yes—
723C4⋊C4C2×D17211yescharacteristic
724C4⋊C4C2×D17212yes—
725C22⋊C4—864no—
726C22⋊C4—862no—
727C22⋊C4—861no—
728C22⋊C4—862no—
729C22⋊C4—862no—
730C22⋊C4—862no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—862no—
734C22⋊C4—862no—
735C22⋊C4—862no—
736C22⋊C4C2×D17212yes—
737C22⋊C4C2×D17212yes—
738C22⋊C4C2×D17212yes—
739C42—861no—
740C42—861no—
741C42—862no—
742C42—861no—
743C42—862no—
744C42—864no—
745C42—862no—
746C42C2×D17211yescharacteristic
747C42C2×D17212yes—
748C42C2×D17211yescharacteristic
749C42C2×D17212yes—
750C42C23×D4312yes—
751C42C23×D4311yescharacteristic
752C42C23×D4311yescharacteristic
753C23—861no—
754C23C22×D17212yes—
755C23C22×D17211yescharacteristic
756Q8—22no—
757Q8—862no—
758Q8—862no—
759Q8—861no—
760Q8—861no—
761Q8—3442no—
762Q8—3444no—
763Q8—3442no—
764Q8—1724no—
765Q8—1722no—
766Q8—1722no—
767Q8—1722no—
768D4—24no—
769D4—22no—
770D4—861no—
771D4—861no—
772D4—3442no—
773D4—1722no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—862no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—861no—
786C2×C4—864no—
787C2×C4—862no—
788C2×C4—3441no—
789C2×C4—3442no—
790C2×C4—3444no—
791C2×C4—3441no—
792C2×C4—1722no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4C22×D17212yes—
796C2×C4C22×D17211yescharacteristic
797C2×C4C22×D17211yescharacteristic
798C2×C4C22×D17211yescharacteristic
799C2×C4C22×D17212yes—
800C2×C4C22×D17212yes—
801C2×C4C22×D17211yescharacteristic
802C2×C4C22×D17211yescharacteristic
803C2×C4#1306337212yes—
804C2×C4#1306337212yes—
805C2×C4C24×D4311yescharacteristic
806C8—22no—
807C8—22no—
808C8—24no—
809C22—21no—
810C22—21no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—1721no—
815C22—1721no—
816C22—1721no—
817C22#1458347512yes—
818C22C23×D17211yescharacteristic
819C4—21no—
820C4—22no—
821C4—21no—
822C4—21no—
823C4—22no—
824C4—22no—
825C4—1721no—
826C4—1722no—
827C4—1724no—
828C4—1722no—
829C4—1722no—
830C4—1721no—
831C4—1721no—
832C4—1722no—
833C4#1458347512yes—
834C4#1458371612yes—
835C4C2×#1306337211yescharacteristic
836C4C2×#1306337211yescharacteristic
837C2—22no—
838C2—42no—
839C2—3441no—
840C2C2×#1458347511yescharacteristic
841C2C2×#1458371611yescharacteristic
842C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2925C2
socleC22×C43C23×D4
prime radical#14583477C22
hypercenter#2925D43
hypocenterC43#60893
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. #19148414C2semidirect
3. #19145880C2semidirect
4. #19145865C2semidirect
5. #19145818C2semidirect
6. #19145811C2semidirect
7. #19145776C2semidirect
8. #19145748C2semidirect
9. #19145134C2semidirect
10. #19144962C2semidirect
12. #19144565C2semidirect
13. #19144411C2semidirect
14. #19144402C2semidirect
15. #19144385C2semidirect
16. C2×#14583195C2semidirect
17. C43×#2925C2semidirect
432. #2925D43semidirect
516. C43#60893semidirect

Maximal subgroups

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

subgroupindex
#191484142
#191480222
#191458802
#191458652
#191458182
#191458112
#191457762
#191457482
#191451342
#191449622
#191445752
#191445652
#191444112
#191444022
#191443852
C2×#145831952
C43×#29252
#6089343