Finite Group Databasebeta

← #25117350

Subgroups — #25117350

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#19143811C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4#19143041C211yesmaximal, characteristic, complemented
5#19135482C211yesmaximal, characteristic, complemented
6#19135305C211yesmaximal, characteristic, complemented
7#19135243C211yesmaximal, characteristic, complemented
8#19135044C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134869C211yesmaximal, characteristic, complemented
12#19134800C211yesmaximal, characteristic, complemented
13#19134434C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#2933C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20C2×#13063331C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583059C411yescharacteristic, complemented
23#14583059C411yescharacteristic, complemented
24#14583054C411yescharacteristic, complemented
25#14583049C411yescharacteristic, complemented
26#14583042C411yescharacteristic, complemented
27#14583042C411yescharacteristic, complemented
28#14583037C411yescharacteristic, complemented
29#14583032C411yescharacteristic, complemented
30#14583019—24no—
31C2×#13063260C2211yescharacteristic, complemented
32C2×#13063260C2211yescharacteristic, complemented
33#14582915—24no—
34C2×#13063252C2211yescharacteristic, complemented
35C2×#13063252C2211yescharacteristic, complemented
36C2×#13063251C2211yescharacteristic
37C2×#13063251C2211yescharacteristic
38C2×#13063251C2211yescharacteristic
39C2×#13063251C2211yescharacteristic
40#14582893C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582865C2211yescharacteristic
43#14582865C2211yescharacteristic
44#14582864—21no—
45#14582864—21no—
46#14582863C2211yescharacteristic
47#14582861—21no—
48C2×C22⋊(C43⋊C8)C2211yescharacteristic
49C22⋊C8×D43—21no—
50C2×#13063235C2211yescharacteristic, complemented
51C2×C8×Dic43C2211yescharacteristic, complemented
52#14582663C2211yescharacteristic, complemented
53#14582663C2211yescharacteristic, complemented
54#14582658C2211yescharacteristic, complemented
55#14582658C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58C2×#131×C43C2211yescharacteristic, complemented
59C22×M16×C43C2211yescharacteristic
60C43×#525C2211yescharacteristic
61C43×#436—21no—
62C43×#435—21no—
63C43×#435—21no—
64C8×D4×C43—21no—
65C43×#424C2211yescharacteristic, complemented
66C43×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C43C2211yescharacteristic
68C43×#405C2211yescharacteristic, 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
79C22×Dic86C2×C411yescharacteristic
80C22×D172C2×C411yescharacteristic
81C22×C22⋊D43—21no—
82C22×C4×D43—21no—
83#13063345—22no—
84#13063345—22no—
85#13063345—41no—
86#13063345—41no—
87C2×#10621885C2×C411yescharacteristic
88C2×#10621885C2×C411yescharacteristic
89C2×#10621883C2×C411yescharacteristic
90C2×#10621883C2×C411yescharacteristic
91C2×#10621884C2×C411yescharacteristic
92C2×#10621884C2×C411yescharacteristic
93C2×#10621882C2×C411yescharacteristic
94C2×#10621882C2×C411yescharacteristic
95#13063331—22no—
96#13063331—22no—
97#13063331—41no—
98#13063331—41no—
99C2×#10621877C2311yescharacteristic
100C2×#10621877C2311yescharacteristic
101C2×#10621872—21no—
102C2×#10621872—21no—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105C2×C8×D43—21no—
106C2×C8×D43—21no—
107#13063284—22no—
108#13063284—41no—
109C2×C4⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113#13063260—22no—
114#13063260—41no—
115#13063252—22no—
116#13063252—41no—
117#13063251—22no—
118#13063251—22no—
119#13063251—22no—
120#13063251D414yescomplemented
121#13063248C2×C411yescharacteristic
122#13063248C2×C411yescharacteristic
123#13063248C2×C411yescharacteristic
124#13063248C2×C411yescharacteristic
125#13063245C2×C411yescharacteristic
126#13063245C2×C411yescharacteristic
127#13063245C2×C411yescharacteristic
128#13063245C2×C411yescharacteristic
129C22⋊(C43⋊C8)—21no—
130C22⋊(C43⋊C8)—21no—
131C22⋊(C43⋊C8)C2×C411yescharacteristic
132C22⋊(C43⋊C8)C2×C411yescharacteristic
133C22⋊(C43⋊C8)C2×C411yescharacteristic
134C22⋊(C43⋊C8)C2×C411yescharacteristic
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139#13063235—22no—
140C8×Dic43—41no—
141C2×#41×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143#131×C43—22no—
144#131×C43—41no—
145C2×M16×C43—21no—
146C2×M16×C43—21no—
147C2×M16×C43—22no—
148C2×M16×C43—41no—
149C2×M16×C43C2311yescharacteristic
150C2×M16×C43C2311yescharacteristic
151C22×C8×C43—21no—
152C22×C8×C43—21no—
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155#123×C43—21no—
156C22⋊Q8×C43C2×C411yescharacteristic
157C22⋊Q8×C43C2×C411yescharacteristic
158#121×C43C2×C411yescharacteristic
159#121×C43C2×C411yescharacteristic
160#120×C43—21no—
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163#117×C43C2311yescharacteristic
164C4⋊C8×C43—21no—
165C4⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43D411yescharacteristic
169C22⋊C8×C43D411yescharacteristic
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172#97×C43—21no—
173C4×C8×C43—21no—
174C24×C43#4111yescharacteristic
175C23×D43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—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—21no—
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205#10621898—21no—
206#10621898—21no—
207#10621898—21no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—22no—
212#10621898—22no—
213#10621898—41no—
214#10621898—41no—
215#10621898—42no—
216#10621898—42no—
217#10621898—42no—
218#10621898—42no—
219#10621898C2×D412yes—
220#10621898#4112yes—
221C2×D172—21no—
222C2×D172—22no—
223C2×D172—41no—
224C2×D172C22×C411yescharacteristic
225C2×D172C22×C411yescharacteristic
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×Dic86—22no—
233C2×Dic86—21no—
234C2×Dic86—41no—
235C2×Dic86C22×C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—42no—
241M16×C43—42no—
242M16×C43C2×D412yes—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—42no—
250C2×C8×C43—42no—
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C2×C8×C43C2×D411yescharacteristic
254C2×C8×C43C2×D411yescharacteristic
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C22×C411yescharacteristic
258C4⋊C4×C43C22×C411yescharacteristic
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C42×C43—21no—
265C22⋊Dic43—42no—
266#10621885—22no—
267#10621885—41no—
268#10621884—22no—
269#10621884—41no—
270#10621883—22no—
271#10621883—41no—
272#10621882—22no—
273#10621882—41no—
274C4⋊Dic43—42no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43C2×D412yes—
279#10621877—21no—
280#10621877—21no—
281#10621877—21no—
282#10621877—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8C22×C411yescharacteristic
290C2×C43⋊C8C22×C411yescharacteristic
291C2×C43⋊C8C22×C411yescharacteristic
292C2×C43⋊C8C22×C411yescharacteristic
293#10621872—42no—
294#10621872—42no—
295C8×D43—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43C4×D411yescharacteristic
303C23×C43C4×D411yescharacteristic
304C23×C43C2×#4111yescharacteristic
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310Q8×C43—21no—
311Q8×C43—21no—
312D4×C43—21no—
313D4×C43—21no—
314D4×C43—42no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—81no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43C4×D411yescharacteristic
334C2×C4×C43C4×D411yescharacteristic
335C2×C4×C43C23×C411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C2×C4×C43H(5,𝔽2)11yescharacteristic
340C2×C4×C43H(5,𝔽2)11yescharacteristic
341C22⋊D43—22no—
342C22⋊D43—22no—
343C22⋊D43—42no—
344C22⋊D43—42no—
345C22⋊D43—41no—
346C22⋊D43—41no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—42no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356D172—21no—
357D172—21no—
358D172—21no—
359D172—42no—
360D172C4×D412yes—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—41no—
366C4×D43—41no—
367Dic86—21no—
368Dic86—21no—
369Dic86—21no—
370Dic86—42no—
371Dic86C4×D412yes—
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—22no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—41no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—21no—
381C43⋊C8—21no—
382C43⋊C8—41no—
383C43⋊C8—41no—
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—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C2×C4×D411yescharacteristic
399C22×C43#54611yescharacteristic
400C22×C43#55111yescharacteristic
401C2×D43—22no—
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—41no—
411C4×C43—41no—
412C4×C43—41no—
413C4×C43C2×C4×D411yescharacteristic
414C4×C43#51811yescharacteristic
415C4×C43D4211yescharacteristic
416C4×C43#54611yescharacteristic
417Dic43—22no—
418Dic43—42no—
419Dic43—41no—
420Dic43—81no—
421#3002—431no—
422C2×#444—431no—
423#2933D4311yescharacteristic, complemented
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#1855—431no—
434#1764—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43—81no—
441C2×C43#235811yescharacteristic
442C2×C43#295511yescharacteristic
443C2×C43#295711yescharacteristic
444D43—42no—
445D43—81no—
446C22×#41—431no—
447C2×#135—431no—
448C2×#135—431no—
449C2×#131—431no—
450C2×#131—431no—
451C2×#131C2×D4311yescharacteristic, complemented
452C22×M16C2×D4311yescharacteristic
453#525C2×D4311yescharacteristic
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—21no—
465#435—21no—
466#435—21no—
467C8×D4—21no—
468C2×#108—431no—
469C2×#108—431no—
470#424C2×D4311yescharacteristic, complemented
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—861no—
483#408—861no—
484#408C2×D4311yescharacteristic, complemented
485#407—431no—
486#407—861no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—861no—
489C2×C22⋊C8C2×D4311yescharacteristic
490#405C2×D4311yescharacteristic, complemented
491C2×#97—431no—
492C2×C4×C8—431no—
493#341—431no—
494#341—431no—
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—862no—
505C2×#41—862no—
506C2×#41—861no—
507C2×#41—861no—
508C2×#41—1721no—
509C2×#41—1721no—
510C2×#41C22×D4311yescharacteristic
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—22no—
529#131—41no—
530#131—862no—
531#131—862no—
532#131—1721no—
533#131—1721no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—431no—
539C2×M16—431no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—861no—
549C22×C8—861no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#123—21no—
553C22⋊Q8C4×D4311yescharacteristic
554C22⋊Q8C4×D4311yescharacteristic
555#121C4×D4311yescharacteristic
556#121C4×D4311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—862no—
561#117—1721no—
562#117C22×D4311yescharacteristic
563C2×C4⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C42—431no—
566C2×C42—431no—
567#108—862no—
568#108—1721no—
569C4⋊C8—21no—
570C4⋊C8—21no—
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⋊C8C22⋊D4311yescharacteristic
598C22⋊C8C22⋊D4311yescharacteristic
599C22⋊C8C22⋊D4311yescharacteristic
600C22⋊C8C22⋊D4311yescharacteristic
601#97—21no—
602#97—862no—
603C4×C8—21no—
604C4×C8—1721no—
605C24—861no—
606C24#1062189811yescharacteristic
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—432no—
612#41—432no—
613#41—862no—
614#41—862no—
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—862no—
630C2×Q8—861no—
631C2×Q8—1721no—
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—431no—
637C2×D4—431no—
638C2×D4—862no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—1721no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4C2×C4×D4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
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×C4#1062189811yescharacteristic
665C22×C4C2×C22⋊D4311yescharacteristic
666C22×C4C2×C22⋊D4311yescharacteristic
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—42no—
680M16—42no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—861no—
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—42no—
695C2×C8—42no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—431no—
699C2×C8—431no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—1722no—
707C2×C8—1722no—
708C2×C8C2×C22⋊D4311yescharacteristic
709C2×C8C2×C22⋊D4311yescharacteristic
710C2×C8C2×C22⋊D4311yescharacteristic
711C2×C8C2×C22⋊D4311yescharacteristic
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—1722no—
715C4⋊C4C2×C4×D4311yescharacteristic
716C4⋊C4C2×C4×D4311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—1722no—
723C42—21no—
724C42—432no—
725C42—861no—
726C42—861no—
727C42—861no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—861no—
734C23—861no—
735C23—3441no—
736C23—1722no—
737C23—1722no—
738C23C4×C22⋊D4311yescharacteristic
739C23C4×C22⋊D4311yescharacteristic
740C23C2×#1062189811yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—432no—
744Q8—861no—
745Q8—861no—
746Q8—861no—
747Q8—1722no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—432no—
755D4—862no—
756D4—862no—
757D4—861no—
758D4—861no—
759D4—861no—
760D4—1722no—
761D4—1722no—
762D4—1722no—
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—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—861no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—861no—
784C2×C4—862no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1721no—
789C2×C4—1721no—
790C2×C4—1721no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4C4×C22⋊D4311yescharacteristic
796C2×C4C4×C22⋊D4311yescharacteristic
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C22×C22⋊D4311yescharacteristic
800C2×C4#41×D4311yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—21no—
804C8—21no—
805C8—22no—
806C8—21no—
807C8—21no—
808C8—41no—
809C8—861no—
810C8—861no—
811C8—861no—
812C8—861no—
813C8—1721no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—81no—
827C22—81no—
828C22—862no—
829C22—3444no—
830C22—1721no—
831C22—1721no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C2×C4×C22⋊D4311yescharacteristic
836C22#1458354511yescharacteristic
837C22#1458357811yescharacteristic
838C4—21no—
839C4—21no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—862no—
844C4—3441no—
845C4—1722no—
846C4—1721no—
847C4C4×D4×D4311yescharacteristic
848C4#1458337111yescharacteristic
849C4D4×C22⋊D4311yescharacteristic
850C4#1458353711yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—3441no—
857C2—1722no—
858C2#1913757211yescharacteristic
859C2#1914349611yescharacteristic
860C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2933C2
socleC22×C43C2×C4×D4
prime radical#19143811C2
cosocleC22×C4×C43C24
hypercenter#2933D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. C2×#14582915C2semidirect
4. #19143041C2semidirect
5. #19135482C2semidirect
6. #19135305C2semidirect
7. #19135243C2semidirect
8. #19135044C2semidirect
9. #19134925C2semidirect
10. #19134922C2semidirect
11. #19134869C2semidirect
12. #19134800C2semidirect
13. #19134434C2semidirect
14. #19134363C2semidirect
15. C43×#2933C2semidirect
22. #14583059C4semidirect
23. #14583059C4semidirect
24. #14583054C4semidirect
25. #14583049C4semidirect
26. #14583042C4semidirect
27. #14583042C4semidirect
28. #14583037C4semidirect
29. #14583032C4semidirect
31. C2×#13063260C22semidirect
32. C2×#13063260C22semidirect
34. C2×#13063252C22semidirect
35. C2×#13063252C22semidirect
50. C2×#13063235C22semidirect
51. C2×C8×Dic43C22semidirect
52. #14582663C22semidirect
53. #14582663C22semidirect
54. #14582658C22semidirect
55. #14582658C22semidirect
56. #14582653C22semidirect
57. #14582653C22semidirect
58. C2×#131×C43C22semidirect
65. C43×#424C22semidirect
66. C43×#408C22semidirect
68. C43×#405C22semidirect
120. #13063251D4semidirect
423. #2933D43semidirect
451. C2×#131C2×D43semidirect
470. #424C2×D43semidirect
484. #408C2×D43semidirect
490. #405C2×D43semidirect
499. C43#22887semidirect

Maximal subgroups

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

subgroupindex
#191438112
C2×#145830192
C2×#145829152
#191430412
#191354822
#191353052
#191352432
#191350442
#191349252
#191349222
#191348692
#191348002
#191344342
#191343632
C43×#29332
#2288743