Finite Group Databasebeta

← #25102455

Subgroups — #25102455

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19143817C211yesmaximal, characteristic
3C2×#14583020C211yesmaximal, characteristic, complemented
4C2×#14583015C211yesmaximal, characteristic, complemented
5#19143294C211yesmaximal, characteristic, complemented
6#19134923C211yesmaximal, characteristic, complemented
7#19134923C211yesmaximal, characteristic, complemented
8#19134897C211yesmaximal, characteristic, complemented
9#19134867C211yesmaximal, characteristic, complemented
10#19134867C211yesmaximal, characteristic, complemented
11#19134538C211yesmaximal, characteristic, complemented
12#19134438C211yesmaximal, characteristic, complemented
13#19134431C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#1855C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063347C2211yescharacteristic
19#14583665—24no—
20#14583665—24no—
21C2×#13063333C2211yescharacteristic
22C2×#13063333C2211yescharacteristic
23C2×#13063333C2211yescharacteristic
24C2×#13063333C2211yescharacteristic
25C2×#13063333C2211yescharacteristic, complemented
26C2×#13063331—21no—
27C2×#13063331—21no—
28C22×#10621877C2211yescharacteristic
29C2×M16×D43—21no—
30C2×M16×D43—21no—
31#14583410C2211yescharacteristic
32#14583063C411yescharacteristic, complemented
33#14583063C411yescharacteristic, complemented
34#14583057C411yescharacteristic, complemented
35#14583052C411yescharacteristic, complemented
36#14583046C411yescharacteristic, complemented
37#14583046C411yescharacteristic, complemented
38#14583040C411yescharacteristic, complemented
39#14583035C411yescharacteristic, complemented
40#14583020—24no—
41#14583015—24no—
42#14582974—21no—
43#14582974—21no—
44#14582973—21no—
45#14582973—21no—
46#14582927C2211yescharacteristic, complemented
47C2×#13063251C2211yescharacteristic
48C2×#13063251C2211yescharacteristic
49C2×#13063251C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51C2×#13063251C2211yescharacteristic, complemented
52C2×#13063251C2211yescharacteristic, complemented
53#14582896C2211yescharacteristic
54#14582896C2211yescharacteristic
55#14582867C2211yescharacteristic, complemented
56#14582857C2211yescharacteristic, complemented
57C2×#13063235C2211yescharacteristic, complemented
58C2×C8×Dic43C2211yescharacteristic, complemented
59C4×C22⋊Dic43C2211yescharacteristic
60#14582660C2211yescharacteristic, complemented
61#14582660C2211yescharacteristic, complemented
62#14582653C2211yescharacteristic, complemented
63#14582653C2211yescharacteristic, complemented
64C22×M16×C43C2211yescharacteristic
65C2×#108×C43C2211yescharacteristic, complemented
66C2×#108×C43C2211yescharacteristic, complemented
67C43×#407C2211yescharacteristic
68C2×C22⋊C8×C43C2211yescharacteristic
69C43×#341C2211yescharacteristic, complemented
70C43×#341C2211yescharacteristic, complemented
71C2×#10621898—21no—
72C2×#10621898—21no—
73C2×#10621898—22no—
74C2×#10621898—22no—
75C2×#10621898—22no—
76C2×#10621898—22no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898C2×C411yescharacteristic
79C2×#10621898C2311yescharacteristic
80C2×#10621898C2311yescharacteristic
81C2×#10621898C2311yescharacteristic
82C22×Dic86C2×C411yescharacteristic
83C22×D172C2×C411yescharacteristic
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86#13063347—22no—
87#13063347—22no—
88#13063347—22no—
89#13063347—22no—
90C2×Dic172C2×C411yescharacteristic
91C2×Dic172C2×C411yescharacteristic
92C2×#10621873C2×C411yescharacteristic
93C2×#10621873C2×C411yescharacteristic
94C2×#10621873C2×C411yescharacteristic
95C2×#10621873C2×C411yescharacteristic
96C2×D344C2×C411yescharacteristic
97C2×D344C2×C411yescharacteristic
98#13063333—22no—
99#13063333—22no—
100#13063333—22no—
101#13063333—22no—
102#13063333—22no—
103#13063333—22no—
104#13063333—22no—
105#13063333—22no—
106#13063333D414yescomplemented
107#13063333D414yescomplemented
108#13063331—28no—
109#13063331—28no—
110C2×#10621877—22no—
111C2×#10621877—22no—
112C2×#10621877D411yescharacteristic
113C2×#10621877D411yescharacteristic
114C2×#10621877D411yescharacteristic
115C2×#10621877D411yescharacteristic
116C2×#10621872—21no—
117C2×#10621872—21no—
118C2×#10621872—21no—
119C2×#10621872—21no—
120C2×#10621872—21no—
121M16×D43—28no—
122M16×D43—28no—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2311yescharacteristic
125C2×C8×D43—21no—
126C2×C8×D43—21no—
127C2×C8×D43—21no—
128C2×C8×D43—21no—
129C2×C8×D43—21no—
130#13063308—21no—
131#13063304C2×C411yescharacteristic
132#13063304C2×C411yescharacteristic
133#13063299C2×C411yescharacteristic
134#13063299C2×C411yescharacteristic
135#13063294—21no—
136C4×C22⋊D43—21no—
137C4×C22⋊D43—21no—
138#13063284C2311yescharacteristic
139C2×C22⋊Dic43—21no—
140C2×C4×Dic43C2311yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142Dic43⋊C8—21no—
143Dic43⋊C8—21no—
144#13063251—22no—
145#13063251—22no—
146#13063251—22no—
147#13063251—22no—
148#13063251—22no—
149#13063251—22no—
150#13063250C2×C411yescharacteristic
151#13063250C2×C411yescharacteristic
152#13063250C2×C411yescharacteristic
153#13063250C2×C411yescharacteristic
154#13063247C2×C411yescharacteristic
155#13063247C2×C411yescharacteristic
156#13063247C2×C411yescharacteristic
157#13063247C2×C411yescharacteristic
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8—21no—
160#13063235—22no—
161#13063235—21no—
162C8×Dic43—22no—
163C8×Dic43—21no—
164C43⋊#95—21no—
165C23×C4×C43C2311yescharacteristic
166C2×M16×C43—21no—
167C2×M16×C43—22no—
168C2×M16×C43—22no—
169C2×M16×C43C2311yescharacteristic
170C2×M16×C43C2311yescharacteristic
171C2×M16×C43C2311yescharacteristic
172C2×M16×C43C2311yescharacteristic
173C22×C8×C43—21no—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176#108×C43—22no—
177#108×C43—22no—
178C22⋊C8×C43—21no—
179C22⋊C8×C43—21no—
180C22⋊C8×C43C2×C411yescharacteristic
181C22⋊C8×C43C2×C411yescharacteristic
182C22⋊C8×C43C2×C411yescharacteristic
183C22⋊C8×C43C2×C411yescharacteristic
184C24×C43#4111yescharacteristic
185C23×D43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C22×C411yescharacteristic
191C22×C4×C43C22×C411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43#4111yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208#10621898—24no—
209#10621898—24no—
210#10621898—24no—
211#10621898—24no—
212#10621898—21no—
213#10621898—21no—
214#10621898—21no—
215#10621898—21no—
216#10621898—22no—
217#10621898—22no—
218#10621898—21no—
219#10621898—21no—
220#10621898—21no—
221#10621898—21no—
222#10621898—22no—
223#10621898—22no—
224#10621898C2×D412yes—
225#10621898C2×D412yes—
226#10621898#4112yes—
227#10621898#4112yes—
228C2×D172—21no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172C22×C411yescharacteristic
232C2×D172C22×C411yescharacteristic
233C2×D172C22×C411yescharacteristic
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×Dic86—21no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86C22×C411yescharacteristic
245C2×Dic86C22×C411yescharacteristic
246C2×Dic86C22×C411yescharacteristic
247M16×C43—24no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—21no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43C2×D412yes—
255M16×C43C2×D412yes—
256C2×C8×C43—24no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43C22×C411yescharacteristic
266C2×C8×C43C22×C411yescharacteristic
267C2×C8×C43C22×C411yescharacteristic
268C2×C8×C43C22×C411yescharacteristic
269C22⋊Dic43—21no—
270C22⋊Dic43—21no—
271C22⋊Dic43—21no—
272C22⋊Dic43—42no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275C4⋊Dic43C22×C411yescharacteristic
276C4⋊Dic43C22×C411yescharacteristic
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282C4×Dic43—21no—
283C4×Dic43—21no—
284#10621877—22no—
285#10621877—22no—
286#10621877—22no—
287#10621877—22no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8C2×D411yescharacteristic
291C2×C43⋊C8C2×D411yescharacteristic
292C2×C43⋊C8C2×D411yescharacteristic
293C2×C43⋊C8C2×D412yes—
294C2×C43⋊C8C2×D411yescharacteristic
295C2×C43⋊C8C2×D412yes—
296Dic172—22no—
297Dic172—22no—
298D344—22no—
299D344—22no—
300#10621873—22no—
301#10621873—22no—
302#10621873—22no—
303#10621873—22no—
304#10621872—24no—
305#10621872—24no—
306#10621872—24no—
307#10621872—24no—
308#10621872—42no—
309C8×D43—24no—
310C8×D43—24no—
311C8×D43—24no—
312C8×D43—24no—
313C8×D43—42no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43C4×D411yescharacteristic
319C23×C43C4×D411yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—24no—
324C22×D43—21no—
325C22×D43—81no—
326C22×D43—81no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43C4×D411yescharacteristic
338C2×C4×C43C4×D411yescharacteristic
339C2×C4×C43C23×C411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C22⋊D43—24no—
346C22⋊D43—24no—
347C22⋊D43—22no—
348C22⋊D43—22no—
349C22⋊D43—22no—
350C22⋊D43—22no—
351C22⋊D43—41no—
352C22⋊D43—41no—
353C22⋊D43—81no—
354C22⋊D43—81no—
355C2×Dic43—24no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367D172—24no—
368D172—21no—
369D172—21no—
370D172—21no—
371D172—21no—
372D172C4×D412yes—
373D172C4×D412yes—
374C4×D43—24no—
375C4×D43—24no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—41no—
381C4×D43—41no—
382Dic86—24no—
383Dic86—21no—
384Dic86—21no—
385Dic86—21no—
386Dic86—21no—
387Dic86C4×D412yes—
388Dic86C4×D412yes—
389C8×C43—21no—
390C8×C43—21no—
391C8×C43—21no—
392C8×C43—21no—
393C8×C43—22no—
394C8×C43—22no—
395C8×C43—41no—
396C8×C43—41no—
397C43⋊C8—21no—
398C43⋊C8—21no—
399C43⋊C8#12012yes—
400C43⋊C8#12012yes—
401#21468—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43C2×C4×D411yescharacteristic
413C22×C43#52511yescharacteristic
414C22×C43#52511yescharacteristic
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—84no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43C2×C4×D411yescharacteristic
428C4×C43C2×C4×D411yescharacteristic
429C4×C43C2×#12011yescharacteristic
430C4×C43#52511yescharacteristic
431Dic43—22no—
432Dic43—22no—
433Dic43—42no—
434Dic43—41no—
435Dic43—41no—
436Dic43—41no—
437Dic43—81no—
438C2×#568—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#443—431no—
442#2930—431no—
443#1876—431no—
444#1876—431no—
445#1871—431no—
446#1866—431no—
447#1866—431no—
448#1855D4311yescharacteristic, complemented
449#1789—431no—
450#1765—431no—
451#1764—431no—
452#1753—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—41no—
456C2×C43—41no—
457C2×C43C4×#12011yescharacteristic
458C2×C43#295611yescharacteristic
459C2×C43#295711yescharacteristic
460D43—42no—
461D43—42no—
462D43—81no—
463C22×#41—431no—
464C2×#135—431no—
465C2×#135—431no—
466#568—864no—
467#568—864no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131—431no—
471C2×#131—431no—
472C2×#131—431no—
473C2×#131—861no—
474C2×#131—861no—
475C22×M16—431no—
476C22×M16—861no—
477C22×M16—861no—
478C22×M16C2×D4311yescharacteristic
479#525—431no—
480#452—431no—
481#452—431no—
482#451—431no—
483#450—431no—
484#449—431no—
485#449—431no—
486#448—431no—
487#447—431no—
488#444—864no—
489#443—864no—
490#436—861no—
491#436—861no—
492#435—861no—
493#435—861no—
494C2×#108C2×D4311yescharacteristic, complemented
495C2×#108C2×D4311yescharacteristic, complemented
496#424—431no—
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500C2×#104—431no—
501C2×#104—431no—
502C2×#104—431no—
503#416—431no—
504#416—431no—
505#408—431no—
506#407C2×D4311yescharacteristic
507C2×C22⋊C8C2×D4311yescharacteristic
508#405—431no—
509C2×#97—431no—
510C2×C4×C8—431no—
511C4×C22⋊C4—431no—
512#341C2×D4311yescharacteristic, complemented
513#341C2×D4311yescharacteristic, complemented
514#339—431no—
515#339—431no—
516#336—431no—
517#336—431no—
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—431no—
523C2×#41—431no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—861no—
529C2×#41—861no—
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535#135—862no—
536#135—862no—
537#135—862no—
538#135—862no—
539C2×Q16—431no—
540C2×Q16—431no—
541C2×SD16—431no—
542C2×SD16—431no—
543C2×SD16—431no—
544C2×SD16—431no—
545C2×D8—431no—
546C2×D8—431no—
547#131—434no—
548#131—434no—
549#131—868no—
550#131—868no—
551#131—862no—
552#131—862no—
553#131—862no—
554#131—862no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131—862no—
559C2×M16—21no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—431no—
566C2×M16—861no—
567C2×M16—861no—
568C2×M16—861no—
569C2×M16—861no—
570C2×M16—861no—
571C2×M16—862no—
572C2×M16—862no—
573C2×M16—868no—
574C2×M16—868no—
575C2×M16C22×D4311yescharacteristic
576C2×M16C22×D4311yescharacteristic
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—21no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—861no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8—861no—
586C22×C8—861no—
587C22×C8C22×D4311yescharacteristic
588C22×C8C22×D4311yescharacteristic
589#123—861no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592#121—431no—
593#121—431no—
594#120—861no—
595C4×D4—861no—
596C4×D4—861no—
597#117—431no—
598C2×C22⋊C4—861no—
599C2×C42—431no—
600C2×C42—431no—
601#108—22no—
602#108—22no—
603C4⋊C8—861no—
604C4⋊C8—861no—
605#104—862no—
606#104—862no—
607#104—862no—
608#104—862no—
609#104—862no—
610#104—862no—
611#103—431no—
612#103—431no—
613#103—431no—
614#103—431no—
615#102—431no—
616#102—431no—
617#102—431no—
618#102—431no—
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—861no—
622C22⋊C8—861no—
623C22⋊C8C4×D4311yescharacteristic
624C22⋊C8C4×D4311yescharacteristic
625C22⋊C8C4×D4311yescharacteristic
626C22⋊C8C4×D4311yescharacteristic
627#97—862no—
628#97—861no—
629C4×C8—862no—
630C4×C8—861no—
631#95—861no—
632C24—861no—
633C24#1062190211yescharacteristic
634#41—432no—
635#41—432no—
636#41—432no—
637#41—432no—
638#41—862no—
639#41—862no—
640#41—862no—
641#41—862no—
642#41—864no—
643#41—864no—
644#41—864no—
645#41—864no—
646#41—861no—
647#41—861no—
648#41—861no—
649#41—861no—
650#41—861no—
651#41—861no—
652#41—861no—
653#41—861no—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—431no—
657C2×Q8—862no—
658C2×Q8—862no—
659C2×Q8—861no—
660C2×D4—431no—
661C2×D4—431no—
662C2×D4—431no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—861no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—864no—
680C22×C4—864no—
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4C2×C4×D4311yescharacteristic
690C22×C4C2×C4×D4311yescharacteristic
691C22×C4D4×D4311yescharacteristic
692C22×C4D4×D4311yescharacteristic
693C22×C4#1062190211yescharacteristic
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—864no—
711M16—864no—
712M16—864no—
713M16—864no—
714M16—862no—
715M16—862no—
716M16—862no—
717M16—862no—
718M16—1722no—
719M16D4×D4312yes—
720M16D4×D4312yes—
721C2×C8—24no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—432no—
731C2×C8—432no—
732C2×C8—431no—
733C2×C8—431no—
734C2×C8—431no—
735C2×C8—431no—
736C2×C8—864no—
737C2×C8—864no—
738C2×C8—864no—
739C2×C8—864no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—1722no—
743C2×C8C2×C4×D4311yescharacteristic
744C2×C8C2×C4×D4311yescharacteristic
745C2×C8C2×C4×D4311yescharacteristic
746C2×C8C2×C4×D4311yescharacteristic
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—1722no—
757C42—861no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42—861no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—864no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—3441no—
771C23—3441no—
772C23#1306328711yescharacteristic
773C23#1306328711yescharacteristic
774C23C2×#1062190211yescharacteristic
775Q8—432no—
776Q8—432no—
777Q8—864no—
778Q8—861no—
779Q8—861no—
780Q8—861no—
781Q8—861no—
782D4—432no—
783D4—432no—
784D4—864no—
785D4—864no—
786D4—864no—
787D4—862no—
788D4—862no—
789D4—862no—
790D4—862no—
791D4—861no—
792D4—861no—
793D4—861no—
794D4—861no—
795D4—3441no—
796D4—3441no—
797D4—1721no—
798D4—1721no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—864no—
810C2×C4—864no—
811C2×C4—864no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4#1306328711yescharacteristic
830C2×C4#1306328711yescharacteristic
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#41×D4311yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—21no—
841C8—22no—
842C8—22no—
843C8—41no—
844C8—41no—
845C8—432no—
846C8—432no—
847C8—861no—
848C8—861no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—81no—
858C22—81no—
859C22—862no—
860C22—862no—
861C22—3444no—
862C22—1721no—
863C22—1721no—
864C22—1721no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C2×#1306328711yescharacteristic
870C22#1458341211yescharacteristic
871C22#1458341211yescharacteristic
872C4—21no—
873C4—21no—
874C4—862no—
875C4—862no—
876C4—3441no—
877C4—1722no—
878C4—1721no—
879C4—1721no—
880C4—1721no—
881C4C4×D4×D4311yescharacteristic
882C4C4×D4×D4311yescharacteristic
883C4#120×D4311yescharacteristic
884C4#1458340711yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—3441no—
890C2—1722no—
891C2—1722no—
892C2#1913709611yescharacteristic
893C2#1914350411yescharacteristic
894C2#1914351111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1855C2
socleC22×C43C2×C4×D4
prime radical#19143817C2
cosocleC22×C4×C43C24
hypercenter#1855D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14583020C2semidirect
4. C2×#14583015C2semidirect
5. #19143294C2semidirect
6. #19134923C2semidirect
7. #19134923C2semidirect
8. #19134897C2semidirect
9. #19134867C2semidirect
10. #19134867C2semidirect
11. #19134538C2semidirect
12. #19134438C2semidirect
13. #19134431C2semidirect
14. #19134381C2semidirect
15. C43×#1855C2semidirect
25. C2×#13063333C22semidirect
32. #14583063C4semidirect
33. #14583063C4semidirect
34. #14583057C4semidirect
35. #14583052C4semidirect
36. #14583046C4semidirect
37. #14583046C4semidirect
38. #14583040C4semidirect
39. #14583035C4semidirect
46. #14582927C22semidirect
51. C2×#13063251C22semidirect
52. C2×#13063251C22semidirect
55. #14582867C22semidirect
56. #14582857C22semidirect
57. C2×#13063235C22semidirect
58. C2×C8×Dic43C22semidirect
60. #14582660C22semidirect
61. #14582660C22semidirect
62. #14582653C22semidirect
63. #14582653C22semidirect
65. C2×#108×C43C22semidirect
66. C2×#108×C43C22semidirect
69. C43×#341C22semidirect
70. C43×#341C22semidirect
106. #13063333D4semidirect
107. #13063333D4semidirect
448. #1855D43semidirect
494. C2×#108C2×D43semidirect
495. C2×#108C2×D43semidirect
512. #341C2×D43semidirect
513. #341C2×D43semidirect
518. C43#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191438172
C2×#145830202
C2×#145830152
#191432942
#191349232
#191348972
#191348672
#191345382
#191344382
#191344312
#191343812
C43×#18552
#2146843