Finite Group Databasebeta

← #25117384

Subgroups — #25117384

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×#14583017C211yesmaximal, characteristic, complemented
3#19143316C211yesmaximal, characteristic, complemented
4C2×#14582917C211yesmaximal, characteristic, complemented
5#19143041C211yesmaximal, characteristic, complemented
6#19135488C211yesmaximal, characteristic, complemented
7#19135299C211yesmaximal, characteristic, complemented
8#19135244C211yesmaximal, characteristic, complemented
9#19135043C211yesmaximal, characteristic, complemented
10#19134921C211yesmaximal, characteristic, complemented
11#19134921C211yesmaximal, characteristic, complemented
12#19134873C211yesmaximal, characteristic, complemented
13#19134802C211yesmaximal, characteristic, complemented
14#19134439C211yesmaximal, characteristic, complemented
15C43×#1750C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063347C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21C2×#13063331C2211yescharacteristic, complemented
22C22×#10621877C2211yescharacteristic
23#14583410C2211yescharacteristic
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#14583017—24no—
33#14582974—21no—
34#14582973—21no—
35#14582967—21no—
36(C22⋊D43)⋊C8—21no—
37C2×#13063261C2211yescharacteristic, complemented
38C2×#13063261C2211yescharacteristic, complemented
39#14582925C2211yescharacteristic, complemented
40#14582917—24no—
41C2×#13063253C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43C2×#13063253C2211yescharacteristic
44C2×#13063253C2211yescharacteristic
45C2×#13063253C2211yescharacteristic, complemented
46C2×#13063253C2211yescharacteristic, complemented
47#14582896C2211yescharacteristic
48#14582896C2211yescharacteristic
49#14582865C2211yescharacteristic
50#14582865C2211yescharacteristic
51#14582865C2211yescharacteristic, complemented
52#14582864—21no—
53#14582864—21no—
54#14582863C2211yescharacteristic
55#14582861—21no—
56C22⋊C8×D43—21no—
57#14582854C2211yescharacteristic, complemented
58#14582664C2211yescharacteristic, complemented
59#14582664C2211yescharacteristic, complemented
60#14582659C2211yescharacteristic, complemented
61#14582659C2211yescharacteristic, complemented
62C2×#117×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic
64C2×C22⋊C8×C43C2211yescharacteristic
65C2×#97×C43C2211yescharacteristic, complemented
66C2×C4×C8×C43C2211yescharacteristic, complemented
67C43×#336C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, 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#13063331—22no—
97#13063331—22no—
98#13063331—22no—
99#13063331—41no—
100#13063331—41no—
101#13063331—41no—
102C2×#10621877—21no—
103C2×#10621877—22no—
104C2×#10621877—41no—
105C2×#10621877C2311yescharacteristic
106C2×#10621877C2311yescharacteristic
107C2×#10621877C2311yescharacteristic
108C2×#10621877C2311yescharacteristic
109C2×#10621872—21no—
110C2×#10621872—21no—
111C2×#10621872—21no—
112C22×C43⋊C8—21no—
113C2×C8×D43—21no—
114C2×C8×D43—21no—
115C2×C8×D43—21no—
116#13063308—21no—
117#13063304C2×C411yescharacteristic
118#13063304C2×C411yescharacteristic
119#13063299C2×C411yescharacteristic
120#13063299C2×C411yescharacteristic
121#13063294—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124#13063284C2311yescharacteristic
125#13063261—22no—
126#13063261—41no—
127Dic43⋊C8—21no—
128Dic43⋊C8—21no—
129#13063253—22no—
130#13063253—22no—
131#13063253—22no—
132#13063253—22no—
133#13063253—41no—
134#13063253D414yescomplemented
135#13063250C2×C411yescharacteristic
136#13063250C2×C411yescharacteristic
137#13063250C2×C411yescharacteristic
138#13063250C2×C411yescharacteristic
139#13063247C2×C411yescharacteristic
140#13063247C2×C411yescharacteristic
141#13063247C2×C411yescharacteristic
142#13063247C2×C411yescharacteristic
143C22⋊(C43⋊C8)—21no—
144C22⋊(C43⋊C8)—21no—
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—21no—
152C8×Dic43—21no—
153C23×C4×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158#117×C43—22no—
159#117×C43—41no—
160C2×C4⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C42×C43C2311yescharacteristic
163C2×C42×C43C2311yescharacteristic
164C22⋊C8×C43C2×C411yescharacteristic
165C22⋊C8×C43C2×C411yescharacteristic
166C22⋊C8×C43C2×C411yescharacteristic
167C22⋊C8×C43C2×C411yescharacteristic
168C22⋊C8×C43D411yescharacteristic
169C22⋊C8×C43D411yescharacteristic
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172#97×C43—41no—
173C4×C8×C43—22no—
174C24×C43#4111yescharacteristic
175C23×D43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43#4111yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—21no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
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
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43C22×C411yescharacteristic
246C2×C8×C43C22×C411yescharacteristic
247C2×C8×C43C22×C411yescharacteristic
248C2×C8×C43C22×C411yescharacteristic
249C2×C8×C43C2×D411yescharacteristic
250C2×C8×C43C2×D411yescharacteristic
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C4⋊C4×C43—42no—
254C22⋊C4×C43—42no—
255C42×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43C2×D412yes—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264C4⋊Dic43C22×C411yescharacteristic
265C4⋊Dic43C22×C411yescharacteristic
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268C4×Dic43—21no—
269#10621877—21no—
270#10621877—21no—
271#10621877—21no—
272#10621877—21no—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877—42no—
277#10621877C2×D412yes—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—42no—
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×C43—22no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C4×D411yescharacteristic
328C2×C4×C43C23×C411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C2×#4111yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C22⋊D43—22no—
335C22⋊D43—22no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—41no—
340C22⋊D43—41no—
341C22⋊D43—41no—
342C22⋊D43—41no—
343C22⋊D43—81no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—42no—
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—21no—
377C8×C43—21no—
378C8×C43—21no—
379C8×C43—21no—
380C43⋊C8—22no—
381C43⋊C8—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22889—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×C43—42no—
411C4×C43—81no—
412C4×C43C2×C4×D411yescharacteristic
413C4×C43#51811yescharacteristic
414C4×C43D4211yescharacteristic
415C4×C43#54611yescharacteristic
416Dic43—22no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43—41no—
421#3002—431no—
422C2×#443—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1975—431no—
427#1937—431no—
428#1929—431no—
429#1897—431no—
430#1876—431no—
431#1876—431no—
432#1866—431no—
433#1855—431no—
434#1765—431no—
435#1750D4311yescharacteristic, complemented
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×M16—431no—
453#525—431no—
454C2×#117C2×D4311yescharacteristic
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#443—864no—
464#436—861no—
465#435—861no—
466#435—861no—
467C8×D4—861no—
468C2×#108—431no—
469C2×#108—431no—
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—431no—
486#407—861no—
487C2×C22⋊C8—861no—
488C2×C22⋊C8C2×D4311yescharacteristic
489C2×C22⋊C8C2×D4311yescharacteristic
490#405—431no—
491C2×#97C2×D4311yescharacteristic, complemented
492C2×C4×C8C2×D4311yescharacteristic, complemented
493#341—431no—
494#341—431no—
495#339—431no—
496#339—431no—
497#336C2×D4311yescharacteristic, complemented
498#336C2×D4311yescharacteristic, complemented
499C43#2288911yescharacteristic, 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—431no—
535C2×M16—431no—
536C2×M16—431no—
537C2×M16—431no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16—862no—
543C2×M16—1721no—
544C22×C8—861no—
545C22×C8—861no—
546C22×C8—861no—
547C22×C8—861no—
548C22×C8C22×D4311yescharacteristic
549C22×C8C22×D4311yescharacteristic
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—22no—
561#117—41no—
562#117—431no—
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D4311yescharacteristic
566C2×C42C22×D4311yescharacteristic
567#108—862no—
568#108—1721no—
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—861no—
586C22⋊C8—861no—
587C22⋊C8—861no—
588C22⋊C8—861no—
589C22⋊C8—861no—
590C22⋊C8—861no—
591C22⋊C8—861no—
592C22⋊C8—861no—
593C22⋊C8C4×D4311yescharacteristic
594C22⋊C8C4×D4311yescharacteristic
595C22⋊C8C4×D4311yescharacteristic
596C22⋊C8C4×D4311yescharacteristic
597C22⋊C8D17211yescharacteristic
598C22⋊C8D17211yescharacteristic
599C22⋊C8D17211yescharacteristic
600C22⋊C8D17211yescharacteristic
601#97—41no—
602#97—861no—
603C4×C8—22no—
604C4×C8—861no—
605C24—861no—
606C24#1062189811yescharacteristic
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—21no—
653C22×C4—21no—
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×C4C2×D17211yescharacteristic
665C22×C4C2×D17211yescharacteristic
666C22×C4#1062189811yescharacteristic
667C22×C4C23×D4311yescharacteristic
668Q16—862no—
669Q16—1721no—
670SD16—862no—
671SD16—862no—
672SD16—1721no—
673SD16—1721no—
674D8—862no—
675D8—1721no—
676M16—432no—
677M16—861no—
678M16—861no—
679M16—861no—
680M16—861no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—1722no—
685M16—1722no—
686M16—1722no—
687M16—1722no—
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—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—1722no—
701C2×C8—1722no—
702C2×C8—1722no—
703C2×C8—1722no—
704C2×C8C2×C4×D4311yescharacteristic
705C2×C8C2×C4×D4311yescharacteristic
706C2×C8C2×C4×D4311yescharacteristic
707C2×C8C2×C4×D4311yescharacteristic
708C2×C8C2×D17211yescharacteristic
709C2×C8C2×D17211yescharacteristic
710C2×C8C2×D17211yescharacteristic
711C2×C8C2×D17211yescharacteristic
712C4⋊C4—42no—
713C4⋊C4—431no—
714C4⋊C4—431no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C22⋊C4—42no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—861no—
727C42D4×D4312yes—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—861no—
733C23—861no—
734C23—861no—
735C23—3441no—
736C23—1722no—
737C23—1722no—
738C23C4×D17211yescharacteristic
739C23C4×D17211yescharacteristic
740C23C2×#1062189811yescharacteristic
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—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—861no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1722no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4C4×D17211yescharacteristic
796C2×C4C4×D17211yescharacteristic
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C22×D17211yescharacteristic
800C2×C4#41×D4311yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C8—862no—
812C8—1721no—
813C8—1721no—
814C8—1721no—
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×C4×D17211yescharacteristic
836C22#1458353911yescharacteristic
837C22#1458357311yescharacteristic
838C4—21no—
839C4—21no—
840C4—42no—
841C4—81no—
842C4—862no—
843C4—1721no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4C4×D4×D4311yescharacteristic
848C4#1458337111yescharacteristic
849C4D4×D17211yescharacteristic
850C4#1458354411yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—3441no—
856C2—3441no—
857C2—1722no—
858C2#1913757711yescharacteristic
859C2#1914349911yescharacteristic
860C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1750C2
socleC22×C43C2×C4×D4
prime radical#19143817C2
cosocleC22×C4×C43C24
hypercenter#1750D43
hypocenterC43#22889
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#14583017C2semidirect
3. #19143316C2semidirect
4. C2×#14582917C2semidirect
5. #19143041C2semidirect
6. #19135488C2semidirect
7. #19135299C2semidirect
8. #19135244C2semidirect
9. #19135043C2semidirect
10. #19134921C2semidirect
11. #19134921C2semidirect
12. #19134873C2semidirect
13. #19134802C2semidirect
14. #19134439C2semidirect
15. C43×#1750C2semidirect
21. C2×#13063331C22semidirect
24. #14583063C4semidirect
25. #14583063C4semidirect
26. #14583057C4semidirect
27. #14583052C4semidirect
28. #14583046C4semidirect
29. #14583046C4semidirect
30. #14583040C4semidirect
31. #14583035C4semidirect
37. C2×#13063261C22semidirect
38. C2×#13063261C22semidirect
39. #14582925C22semidirect
45. C2×#13063253C22semidirect
46. C2×#13063253C22semidirect
51. #14582865C22semidirect
57. #14582854C22semidirect
58. #14582664C22semidirect
59. #14582664C22semidirect
60. #14582659C22semidirect
61. #14582659C22semidirect
65. C2×#97×C43C22semidirect
66. C2×C4×C8×C43C22semidirect
67. C43×#336C22semidirect
68. C43×#336C22semidirect
134. #13063253D4semidirect
435. #1750D43semidirect
491. C2×#97C2×D43semidirect
492. C2×C4×C8C2×D43semidirect
497. #336C2×D43semidirect
498. #336C2×D43semidirect
499. C43#22889semidirect

Maximal subgroups

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

subgroupindex
#191438172
C2×#145830172
#191433162
C2×#145829172
#191430412
#191354882
#191352992
#191352442
#191350432
#191349212
#191348732
#191348022
#191344392
C43×#17502
#2288943