Finite Group Databasebeta

← #25117342

Subgroups — #25117342

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143817C211yesmaximal, characteristic
2C2×#14583020C211yesmaximal, characteristic, complemented
3#19143320C211yesmaximal, characteristic, complemented
4C2×#14582915C211yesmaximal, characteristic, complemented
5#19143045C211yesmaximal, characteristic, complemented
6#19135481C211yesmaximal, characteristic, complemented
7#19135304C211yesmaximal, characteristic, complemented
8#19135242C211yesmaximal, characteristic, complemented
9#19135041C211yesmaximal, characteristic, complemented
10#19134923C211yesmaximal, characteristic, complemented
11#19134923C211yesmaximal, characteristic, complemented
12#19134867C211yesmaximal, characteristic, complemented
13#19134431C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1855C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063347C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C2×#13063333C2211yescharacteristic, complemented
22#14583410C2211yescharacteristic
23C2×#13063284C2211yescharacteristic
24#14583063C411yescharacteristic, complemented
25#14583063C411yescharacteristic, complemented
26#14583057C411yescharacteristic, complemented
27#14583052C411yescharacteristic, complemented
28#14583046C411yescharacteristic, complemented
29#14583046C411yescharacteristic, complemented
30#14583040C411yescharacteristic, complemented
31#14583035C411yescharacteristic, complemented
32#14583020—24no—
33#14582975—21no—
34#14582970—21no—
35#14582968—21no—
36C8×C22⋊D43—21no—
37#14582927C2211yescharacteristic, complemented
38#14582915—24no—
39C2×#13063251C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic, complemented
44C2×#13063251C2211yescharacteristic, complemented
45#14582896C2211yescharacteristic
46#14582896C2211yescharacteristic
47#14582867C2211yescharacteristic
48#14582867C2211yescharacteristic
49#14582867C2211yescharacteristic, complemented
50#14582864—21no—
51#14582864—21no—
52#14582861—21no—
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C22⋊C8×D43—21no—
55#14582857C2211yescharacteristic, complemented
56C2×#13063235C2211yescharacteristic, complemented
57C2×C8×Dic43C2211yescharacteristic, complemented
58#14582660C2211yescharacteristic, complemented
59#14582660C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C22×M16×C43C2211yescharacteristic
63C2×#108×C43C2211yescharacteristic, complemented
64C2×#108×C43C2211yescharacteristic, complemented
65C43×#407C2211yescharacteristic
66C2×C22⋊C8×C43C2211yescharacteristic
67C43×#341C2211yescharacteristic, complemented
68C43×#341C2211yescharacteristic, complemented
69C2×#10621898—21no—
70C2×#10621898—21no—
71C2×#10621898—22no—
72C2×#10621898—22no—
73C2×#10621898—41no—
74C2×#10621898—41no—
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898C2311yescharacteristic
78C2×#10621898C2311yescharacteristic
79C2×#10621898C2311yescharacteristic
80C22×Dic86C2×C411yescharacteristic
81C22×D172C2×C411yescharacteristic
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84#13063347—22no—
85#13063347—22no—
86#13063347—41no—
87#13063347—41no—
88C2×Dic172C2×C411yescharacteristic
89C2×Dic172C2×C411yescharacteristic
90C2×#10621873C2×C411yescharacteristic
91C2×#10621873C2×C411yescharacteristic
92C2×#10621873C2×C411yescharacteristic
93C2×#10621873C2×C411yescharacteristic
94C2×D344C2×C411yescharacteristic
95C2×D344C2×C411yescharacteristic
96#13063333—22no—
97#13063333—22no—
98#13063333—22no—
99#13063333—41no—
100#13063333—41no—
101#13063333—41no—
102C2×#10621872—21no—
103C2×#10621872—21no—
104C2×#10621872—21no—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C2×C8×D43—21no—
108C2×C8×D43—21no—
109C2×C8×D43—21no—
110#13063308—21no—
111#13063304C2×C411yescharacteristic
112#13063304C2×C411yescharacteristic
113#13063299C2×C411yescharacteristic
114#13063299C2×C411yescharacteristic
115#13063294—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118#13063284—22no—
119#13063284—41no—
120#13063284C2311yescharacteristic
121C2×C4⋊Dic43—21no—
122C2×C22⋊Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124C2×C4×Dic43C2311yescharacteristic
125Dic43⋊C8—21no—
126Dic43⋊C8—21no—
127#13063251—22no—
128#13063251—22no—
129#13063251—22no—
130#13063251—22no—
131#13063251—41no—
132#13063251D414yescomplemented
133#13063250C2×C411yescharacteristic
134#13063250C2×C411yescharacteristic
135#13063250C2×C411yescharacteristic
136#13063250C2×C411yescharacteristic
137#13063247C2×C411yescharacteristic
138#13063247C2×C411yescharacteristic
139#13063247C2×C411yescharacteristic
140#13063247C2×C411yescharacteristic
141C22⋊(C43⋊C8)D411yescharacteristic
142C22⋊(C43⋊C8)D411yescharacteristic
143C22⋊(C43⋊C8)D411yescharacteristic
144C22⋊(C43⋊C8)D411yescharacteristic
145(C2×D43)⋊C8—21no—
146(C2×D43)⋊C8—21no—
147(C2×D43)⋊C8—21no—
148(C2×D43)⋊C8—21no—
149(C2×D43)⋊C8—21no—
150(C2×D43)⋊C8—21no—
151#13063235—22no—
152#13063235—21no—
153C8×Dic43—21no—
154C8×Dic43—41no—
155C23×C4×C43C2311yescharacteristic
156C2×M16×C43—21no—
157C2×M16×C43—22no—
158C2×M16×C43—41no—
159C2×M16×C43C2311yescharacteristic
160C2×M16×C43C2311yescharacteristic
161C2×M16×C43C2311yescharacteristic
162C2×M16×C43C2311yescharacteristic
163C22×C8×C43—21no—
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166#108×C43—22no—
167#108×C43—41no—
168C22⋊C8×C43—21no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43C2×C411yescharacteristic
171C22⋊C8×C43C2×C411yescharacteristic
172C22⋊C8×C43C2×C411yescharacteristic
173C22⋊C8×C43C2×C411yescharacteristic
174C24×C43#4111yescharacteristic
175C23×D43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C22×C411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—42no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198#10621898—21no—
199#10621898—21no—
200#10621898—21no—
201#10621898—21no—
202#10621898—21no—
203#10621898—21no—
204#10621898—21no—
205#10621898—21no—
206#10621898—21no—
207#10621898—21no—
208#10621898—22no—
209#10621898—22no—
210#10621898—41no—
211#10621898—41no—
212#10621898—42no—
213#10621898—42no—
214#10621898—42no—
215#10621898—42no—
216#10621898C2×D412yes—
217#10621898#4112yes—
218C2×D172—21no—
219C2×D172—22no—
220C2×D172—41no—
221C2×D172C22×C411yescharacteristic
222C2×D172C22×C411yescharacteristic
223C2×D172C22×C411yescharacteristic
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×Dic86—22no—
232C2×Dic86—21no—
233C2×Dic86—41no—
234C2×Dic86C22×C411yescharacteristic
235C2×Dic86C22×C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—42no—
245M16×C43C2×D412yes—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—42no—
255C2×C8×C43C22×C411yescharacteristic
256C2×C8×C43C22×C411yescharacteristic
257C2×C8×C43C22×C411yescharacteristic
258C2×C8×C43C22×C411yescharacteristic
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43—21no—
262C22⋊Dic43—42no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265C4⋊Dic43—42no—
266C4⋊Dic43C22×C411yescharacteristic
267C4⋊Dic43C22×C411yescharacteristic
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43C2×D412yes—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8C2×D411yescharacteristic
280C2×C43⋊C8C2×D411yescharacteristic
281C2×C43⋊C8C2×D411yescharacteristic
282C2×C43⋊C8C2×D411yescharacteristic
283Dic172—22no—
284Dic172—41no—
285D344—22no—
286D344—41no—
287#10621873—22no—
288#10621873—22no—
289#10621873—41no—
290#10621873—41no—
291#10621872—42no—
292#10621872—42no—
293#10621872—42no—
294C8×D43—42no—
295C8×D43—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43C4×D411yescharacteristic
302C23×C43C4×D411yescharacteristic
303C23×C43C2×#4111yescharacteristic
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43C4×D411yescharacteristic
321C2×C4×C43C4×D411yescharacteristic
322C2×C4×C43C23×C411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C2×C4×C43H(5,𝔽2)11yescharacteristic
328C22⋊D43—22no—
329C22⋊D43—22no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C22⋊D43—41no—
334C22⋊D43—41no—
335C22⋊D43—41no—
336C22⋊D43—41no—
337C22⋊D43—81no—
338C2×Dic43—21no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—22no—
344C2×Dic43—42no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350D172—21no—
351D172—21no—
352D172—21no—
353D172—21no—
354D172—21no—
355D172—42no—
356D172C4×D412yes—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365Dic86—21no—
366Dic86—21no—
367Dic86—21no—
368Dic86—21no—
369Dic86—21no—
370Dic86—42no—
371Dic86C4×D412yes—
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—21no—
375C8×C43—21no—
376C8×C43—22no—
377C8×C43—41no—
378C8×C43—41no—
379C8×C43—41no—
380C43⋊C8—21no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—21no—
384#22887—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43C2×C4×D411yescharacteristic
396C22×C43#54611yescharacteristic
397C22×C43#55111yescharacteristic
398C2×D43—22no—
399C2×D43—41no—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—41no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—84no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43C2×C4×D411yescharacteristic
411C4×C43#51811yescharacteristic
412C4×C43D4211yescharacteristic
413C4×C43#54611yescharacteristic
414Dic43—22no—
415Dic43—42no—
416Dic43—41no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43—81no—
421#3002—431no—
422C2×#444—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1974—431no—
427#1938—431no—
428#1929—431no—
429#1897—431no—
430#1876—431no—
431#1876—431no—
432#1866—431no—
433#1855D4311yescharacteristic, complemented
434#1764—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43#235811yescharacteristic
441C2×C43#295511yescharacteristic
442C2×C43#295711yescharacteristic
443D43—42no—
444D43—81no—
445D43—81no—
446C22×#41—431no—
447C2×#135—431no—
448C2×#135—431no—
449C2×#131—431no—
450C2×#131—431no—
451C2×#131—431no—
452C22×M16C2×D4311yescharacteristic
453#525—431no—
454C2×#117—431no—
455#452—431no—
456#452—431no—
457#451—431no—
458#450—431no—
459#449—431no—
460#449—431no—
461#448—431no—
462#447—431no—
463#444—864no—
464#436—861no—
465#435—861no—
466#435—861no—
467C8×D4—861no—
468C2×#108C2×D4311yescharacteristic, complemented
469C2×#108C2×D4311yescharacteristic, complemented
470#424—431no—
471#421—864no—
472C2×#104—431no—
473C2×#104—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478#416—431no—
479#416—431no—
480#408—431no—
481#408—431no—
482#408—431no—
483#408—861no—
484#408—861no—
485#407—861no—
486#407C2×D4311yescharacteristic
487C2×C22⋊C8—431no—
488C2×C22⋊C8—861no—
489C2×C22⋊C8C2×D4311yescharacteristic
490#405—431no—
491C2×#97—431no—
492C2×C4×C8—431no—
493#341C2×D4311yescharacteristic, complemented
494#341C2×D4311yescharacteristic, complemented
495#339—431no—
496#339—431no—
497#336—431no—
498#336—431no—
499C43#2288711yescharacteristic, complemented, Sylow
500C2×#41—431no—
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—862no—
506C2×#41—862no—
507C2×#41—861no—
508C2×#41—861no—
509C2×#41—1721no—
510C2×#41—1721no—
511C22×Q8—431no—
512C22×D4—431no—
513C22×D4—861no—
514C23×C4—861no—
515C23×C4C22×D4311yescharacteristic
516#135—862no—
517#135—862no—
518#135—1721no—
519#135—1721no—
520C2×Q16—431no—
521C2×Q16—431no—
522C2×SD16—431no—
523C2×SD16—431no—
524C2×SD16—431no—
525C2×SD16—431no—
526C2×D8—431no—
527C2×D8—431no—
528#131—862no—
529#131—862no—
530#131—862no—
531#131—1721no—
532#131—1721no—
533#131—1721no—
534C2×M16—21no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16C22×D4311yescharacteristic
541C2×M16C22×D4311yescharacteristic
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—21no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—861no—
548C22×C8—861no—
549C22×C8—861no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#123—861no—
553C22⋊Q8—431no—
554C22⋊Q8—431no—
555#121—431no—
556#121—431no—
557#120—861no—
558C4×D4—861no—
559C4×D4—861no—
560#117—431no—
561#117—862no—
562#117—1721no—
563C2×C4⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—431no—
566C2×C42—431no—
567#108—22no—
568#108—41no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—434no—
572#104—862no—
573#104—862no—
574#104—862no—
575#104—862no—
576#104—1721no—
577#103—431no—
578#103—431no—
579#103—431no—
580#103—431no—
581#102—431no—
582#102—431no—
583#102—431no—
584#102—431no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—431no—
588C22⋊C8—431no—
589C22⋊C8—431no—
590C22⋊C8—431no—
591C22⋊C8—861no—
592C22⋊C8—861no—
593C22⋊C8—861no—
594C22⋊C8—861no—
595C22⋊C8—861no—
596C22⋊C8—861no—
597C22⋊C8C4×D4311yescharacteristic
598C22⋊C8C4×D4311yescharacteristic
599C22⋊C8C4×D4311yescharacteristic
600C22⋊C8C4×D4311yescharacteristic
601#97—862no—
602#97—861no—
603C4×C8—861no—
604C4×C8—1721no—
605C24—861no—
606C24#1062190211yescharacteristic
607#41—432no—
608#41—432no—
609#41—862no—
610#41—862no—
611#41—861no—
612#41—861no—
613#41—861no—
614#41—861no—
615#41—861no—
616#41—861no—
617#41—861no—
618#41—861no—
619#41—861no—
620#41—861no—
621#41—1722no—
622#41—1722no—
623#41—1721no—
624#41—1721no—
625#41—1722no—
626#41—1722no—
627C2×Q8—431no—
628C2×Q8—431no—
629C2×Q8—431no—
630C2×Q8—862no—
631C2×Q8—861no—
632C2×Q8—1721no—
633C2×D4—431no—
634C2×D4—431no—
635C2×D4—431no—
636C2×D4—862no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—1721no—
646C2×D4—1722no—
647C2×D4—1722no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—861no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—1722no—
661C22×C4—1722no—
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×C4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4#1062190211yescharacteristic
667C22×C4C23×D4311yescharacteristic
668Q16—862no—
669Q16—1721no—
670SD16—862no—
671SD16—862no—
672SD16—1721no—
673SD16—1721no—
674D8—862no—
675D8—1721no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—42no—
684M16—1722no—
685M16—1722no—
686M16—1722no—
687M16D4×D4312yes—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—431no—
698C2×C8—431no—
699C2×C8—431no—
700C2×C8—431no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—1722no—
706C2×C8—1722no—
707C2×C8—1722no—
708C2×C8C2×C4×D4311yescharacteristic
709C2×C8C2×C4×D4311yescharacteristic
710C2×C8C2×C4×D4311yescharacteristic
711C2×C8C2×C4×D4311yescharacteristic
712C4⋊C4—431no—
713C4⋊C4—431no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—1722no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—1722no—
723C42—432no—
724C42—861no—
725C42—861no—
726C42—861no—
727C42—861no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—3441no—
736C23—1722no—
737C23—1722no—
738C23#1306328711yescharacteristic
739C23#1306328711yescharacteristic
740C23C2×#1062190211yescharacteristic
741Q8—432no—
742Q8—861no—
743Q8—861no—
744Q8—861no—
745Q8—861no—
746Q8—861no—
747Q8—1722no—
748D4—432no—
749D4—862no—
750D4—862no—
751D4—861no—
752D4—861no—
753D4—861no—
754D4—861no—
755D4—861no—
756D4—3441no—
757D4—1722no—
758D4—1722no—
759D4—1722no—
760D4—1722no—
761D4—1721no—
762D4—1721no—
763D4—1721no—
764D4—1721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—861no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—862no—
783C2×C4—1722no—
784C2×C4—1722no—
785C2×C4—1722no—
786C2×C4—1721no—
787C2×C4—1721no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4#1306328711yescharacteristic
796C2×C4#1306328711yescharacteristic
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4#41×D4311yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—861no—
812C8—861no—
813C8—861no—
814C8—861no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—81no—
824C22—81no—
825C22—862no—
826C22—3444no—
827C22—1721no—
828C22—1721no—
829C22—1721no—
830C22—1721no—
831C22—1721no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C2×#1306328711yescharacteristic
836C22#1458354011yescharacteristic
837C22#1458357611yescharacteristic
838C4—21no—
839C4—21no—
840C4—862no—
841C4—3441no—
842C4—1722no—
843C4—1721no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4C4×D4×D4311yescharacteristic
848C4#1458337111yescharacteristic
849C4#1458353111yescharacteristic
850C4#1458354111yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—3441no—
856C2—3441no—
857C2—1722no—
858C2#1913757111yescharacteristic
859C2#1914349711yescharacteristic
860C2#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#22887
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
2. C2×#14583020C2semidirect
3. #19143320C2semidirect
4. C2×#14582915C2semidirect
5. #19143045C2semidirect
6. #19135481C2semidirect
7. #19135304C2semidirect
8. #19135242C2semidirect
9. #19135041C2semidirect
10. #19134923C2semidirect
11. #19134923C2semidirect
12. #19134867C2semidirect
13. #19134431C2semidirect
14. #19134363C2semidirect
15. C43×#1855C2semidirect
21. C2×#13063333C22semidirect
24. #14583063C4semidirect
25. #14583063C4semidirect
26. #14583057C4semidirect
27. #14583052C4semidirect
28. #14583046C4semidirect
29. #14583046C4semidirect
30. #14583040C4semidirect
31. #14583035C4semidirect
37. #14582927C22semidirect
43. C2×#13063251C22semidirect
44. C2×#13063251C22semidirect
49. #14582867C22semidirect
55. #14582857C22semidirect
56. C2×#13063235C22semidirect
57. C2×C8×Dic43C22semidirect
58. #14582660C22semidirect
59. #14582660C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
63. C2×#108×C43C22semidirect
64. C2×#108×C43C22semidirect
67. C43×#341C22semidirect
68. C43×#341C22semidirect
132. #13063251D4semidirect
433. #1855D43semidirect
468. C2×#108C2×D43semidirect
469. C2×#108C2×D43semidirect
493. #341C2×D43semidirect
494. #341C2×D43semidirect
499. C43#22887semidirect

Maximal subgroups

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

subgroupindex
#191438172
C2×#145830202
#191433202
C2×#145829152
#191430452
#191354812
#191353042
#191352422
#191350412
#191349232
#191348672
#191344312
#191343632
C43×#18552
#2288743