Finite Group Databasebeta

← #25117345

Subgroups — #25117345

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#19143813C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3#19143316C211yesmaximal, characteristic, complemented
4C2×#14582916C211yesmaximal, characteristic, complemented
5#19135482C211yesmaximal, characteristic, complemented
6#19135309C211yesmaximal, characteristic, complemented
7#19135240C211yesmaximal, characteristic, complemented
8#19135041C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134870C211yesmaximal, characteristic, complemented
12#19134799C211yesmaximal, characteristic, complemented
13#19134430C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063331C2211yescharacteristic, complemented
19C22×#10621877C2211yescharacteristic
20#14583410C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583061C411yescharacteristic, complemented
23#14583061C411yescharacteristic, complemented
24#14583055C411yescharacteristic, complemented
25#14583050C411yescharacteristic, complemented
26#14583044C411yescharacteristic, complemented
27#14583044C411yescharacteristic, complemented
28#14583038C411yescharacteristic, complemented
29#14583033C411yescharacteristic, complemented
30#14583019—24no—
31#14582974—21no—
32#14582973—21no—
33#14582967—21no—
34(C22⋊D43)⋊C8—21no—
35C2×#13063260C2211yescharacteristic, complemented
36C2×#13063260C2211yescharacteristic, complemented
37#14582925C2211yescharacteristic, complemented
38#14582916—24no—
39C2×#13063252C2211yescharacteristic
40C2×#13063252C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43C2×#13063251C2211yescharacteristic, complemented
44C2×#13063251C2211yescharacteristic, complemented
45#14582895C2211yescharacteristic
46#14582895C2211yescharacteristic
47#14582865C2211yescharacteristic, complemented
48C2×C22⋊(C43⋊C8)C2211yescharacteristic
49#14582854C2211yescharacteristic, complemented
50C2×#13063235C2211yescharacteristic, complemented
51C2×C8×Dic43C2211yescharacteristic, complemented
52#14582663C2211yescharacteristic, complemented
53#14582663C2211yescharacteristic, complemented
54#14582660C2211yescharacteristic, complemented
55#14582660C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58C22×#41×C43C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C43×#408—21no—
62C43×#408—21no—
63C43×#408C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#407—21no—
66C43×#407C2211yescharacteristic
67C2×C22⋊C8×C43—21no—
68C2×C22⋊C8×C43C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70#13063345—22no—
71#13063345—22no—
72#13063345—41no—
73#13063345—41no—
74C2×#10621885C2×C411yescharacteristic
75C2×#10621885C2×C411yescharacteristic
76C2×#10621883C2×C411yescharacteristic
77C2×#10621883C2×C411yescharacteristic
78C2×#10621884C2×C411yescharacteristic
79C2×#10621884C2×C411yescharacteristic
80C2×#10621882C2×C411yescharacteristic
81C2×#10621882C2×C411yescharacteristic
82#13063331—22no—
83#13063331—41no—
84C2×#10621877—21no—
85C2×#10621877—22no—
86C2×#10621877—41no—
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C22×C43⋊C8—21no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94#13063308—21no—
95#13063304C2×C411yescharacteristic
96#13063304C2×C411yescharacteristic
97#13063299C2×C411yescharacteristic
98#13063299C2×C411yescharacteristic
99#13063294—21no—
100C4×C22⋊D43—21no—
101C4×C22⋊D43—21no—
102#13063284—22no—
103#13063284—41no—
104#13063284C2311yescharacteristic
105C2×C4⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063260—22no—
110#13063260—41no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063252—22no—
114#13063252—22no—
115#13063252—22no—
116#13063252D414yescomplemented
117#13063251—22no—
118#13063251—41no—
119#13063249C2×C411yescharacteristic
120#13063249C2×C411yescharacteristic
121#13063249C2×C411yescharacteristic
122#13063249C2×C411yescharacteristic
123#13063246C2×C411yescharacteristic
124#13063246C2×C411yescharacteristic
125#13063246C2×C411yescharacteristic
126#13063246C2×C411yescharacteristic
127C22⋊(C43⋊C8)C2×C411yescharacteristic
128C22⋊(C43⋊C8)C2×C411yescharacteristic
129C22⋊(C43⋊C8)C2×C411yescharacteristic
130C22⋊(C43⋊C8)C2×C411yescharacteristic
131(C2×D43)⋊C8—21no—
132(C2×D43)⋊C8—21no—
133#13063235—21no—
134#13063235—22no—
135C8×Dic43—21no—
136C8×Dic43—41no—
137C2×#41×C43—21no—
138C2×#41×C43—21no—
139C2×#41×C43—22no—
140C2×#41×C43—22no—
141C2×#41×C43—41no—
142C2×#41×C43—41no—
143C2×#41×C43C2×C411yescharacteristic
144C2×#41×C43C2×C411yescharacteristic
145C2×#41×C43C2311yescharacteristic
146C2×#41×C43C2311yescharacteristic
147C22×Q8×C43C2×C411yescharacteristic
148C22×D4×C43—21no—
149C22×D4×C43C2×C411yescharacteristic
150C23×C4×C43—21no—
151C23×C4×C43C2311yescharacteristic
152#131×C43—22no—
153#131×C43—22no—
154#131×C43—41no—
155#131×C43—41no—
156C2×M16×C43—21no—
157C2×M16×C43—21no—
158C2×M16×C43C2311yescharacteristic
159C2×M16×C43C2311yescharacteristic
160C22×C8×C43—21no—
161C22×C8×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43—21no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172C22⋊C8×C43D411yescharacteristic
173C22⋊C8×C43D411yescharacteristic
174C24×C43—21no—
175C24×C43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—22no—
179#41×C43—22no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—42no—
185#41×C43—42no—
186#41×C43—41no—
187#41×C43—41no—
188#41×C43—42no—
189#41×C43—42no—
190#41×C43C2×D412yes—
191#41×C43#4112yes—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—41no—
195C2×Q8×C43C22×C411yescharacteristic
196C2×Q8×C43C22×C411yescharacteristic
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—22no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—41no—
206C2×D4×C43C22×C411yescharacteristic
207C2×D4×C43C22×C411yescharacteristic
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—42no—
218C22×C4×C43—42no—
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43#4111yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230#10621898—21no—
231#10621898—21no—
232#10621898—21no—
233#10621898—21no—
234C2×D172C22×C411yescharacteristic
235C2×C4×D43—21no—
236C2×Dic86C22×C411yescharacteristic
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241M16×C43—42no—
242M16×C43—42no—
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
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—42no—
259#10621885—22no—
260#10621885—41no—
261#10621884—22no—
262#10621884—41no—
263#10621883—22no—
264#10621883—41no—
265#10621882—22no—
266#10621882—41no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269C4⋊Dic43—42no—
270C4⋊Dic43C22×C411yescharacteristic
271C4⋊Dic43C22×C411yescharacteristic
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43C2×D412yes—
279#10621877—21no—
280#10621877—21no—
281#10621877—21no—
282#10621877—42no—
283#10621877C2×D412yes—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—42no—
291C2×C43⋊C8C22×C411yescharacteristic
292C2×C43⋊C8C22×C411yescharacteristic
293C2×C43⋊C8C22×C411yescharacteristic
294C2×C43⋊C8C22×C411yescharacteristic
295#10621872—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43—81no—
306C23×C43C4×D411yescharacteristic
307C23×C43C4×D411yescharacteristic
308C23×C43C2×#4111yescharacteristic
309C22×D43—21no—
310Q8×C43—21no—
311Q8×C43—21no—
312Q8×C43—21no—
313Q8×C43—42no—
314Q8×C43C4×D412yes—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—21no—
318D4×C43—21no—
319D4×C43—21no—
320D4×C43—42no—
321D4×C43—42no—
322D4×C43—42no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43C4×D412yes—
326C2×C4×C43—21no—
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—22no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43C4×D411yescharacteristic
346C2×C4×C43C4×D411yescharacteristic
347C2×C4×C43C23×C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C22⋊D43—42no—
354C22⋊D43—41no—
355C22⋊D43—41no—
356C22⋊D43—81no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—22no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366D172—21no—
367D172—21no—
368C4×D43—41no—
369C4×D43—41no—
370Dic86—21no—
371Dic86—21no—
372C8×C43—21no—
373C8×C43—21no—
374C8×C43—21no—
375C8×C43—21no—
376C8×C43—41no—
377C8×C43—41no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—21no—
381C43⋊C8—21no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#22887—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—22no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—84no—
402C22×C43C2×C4×D411yescharacteristic
403C22×C43#54611yescharacteristic
404C22×C43#55111yescharacteristic
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—22no—
411C4×C43—41no—
412C4×C43C2×C4×D411yescharacteristic
413C4×C43#51811yescharacteristic
414C4×C43D4211yescharacteristic
415C4×C43#54611yescharacteristic
416Dic43—42no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43—81no—
421#3002—431no—
422C2×#444—431no—
423#2933—431no—
424C2×#421—431no—
425#2880D4311yescharacteristic, complemented
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—42no—
441C2×C43—81no—
442C2×C43#235811yescharacteristic
443C2×C43#295511yescharacteristic
444C2×C43#295711yescharacteristic
445D43—81no—
446C22×#41C2×D4311yescharacteristic
447C2×#135—431no—
448C2×#135—431no—
449C2×#131—431no—
450C2×#131C2×D4311yescharacteristic
451C2×#131C2×D4311yescharacteristic
452C22×M16—431no—
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×#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—21no—
481#408—21no—
482#408—431no—
483#408C2×D4311yescharacteristic
484#408C2×D4311yescharacteristic
485#407—21no—
486#407C2×D4311yescharacteristic
487C2×C22⋊C8—21no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8C2×D4311yescharacteristic
490#405—431no—
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—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—431no—
507C2×#41C4×D4311yescharacteristic
508C2×#41C4×D4311yescharacteristic
509C2×#41C22×D4311yescharacteristic
510C2×#41C22×D4311yescharacteristic
511C22×Q8C4×D4311yescharacteristic
512C22×D4—21no—
513C22×D4C4×D4311yescharacteristic
514C23×C4—21no—
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—22no—
530#131—41no—
531#131—41no—
532#131—862no—
533#131—1721no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—431no—
537C2×M16—431no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—862no—
541C2×M16—1721no—
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—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—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—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—861no—
596C22⋊C8—861no—
597C22⋊C8C22⋊D4311yescharacteristic
598C22⋊C8C22⋊D4311yescharacteristic
599C22⋊C8C22⋊D4311yescharacteristic
600C22⋊C8C22⋊D4311yescharacteristic
601#97—862no—
602#97—861no—
603C4×C8—861no—
604C4×C8—1721no—
605C24—21no—
606C24#1062189811yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—861no—
622#41—861no—
623#41—861no—
624#41—861no—
625#41D4×D4312yes—
626#41#1062190012yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—431no—
631C2×Q8C2×C4×D4311yescharacteristic
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—431no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4C2×C4×D4311yescharacteristic
647C2×D4C2×C4×D4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
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—21no—
680M16—42no—
681M16—42no—
682M16—432no—
683M16—861no—
684M16—861no—
685M16—861no—
686M16—1722no—
687M16—1722no—
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—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—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—861no—
738C23C4×C22⋊D4311yescharacteristic
739C23C4×C22⋊D4311yescharacteristic
740C23C2×#1062189811yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—861no—
746Q8—861no—
747Q8(C22⋊D43)⋊C412yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—861no—
759D4—861no—
760D4—3441no—
761D4—1722no—
762D4—1721no—
763D4—1721no—
764D4(C22⋊D43)⋊C412yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—862no—
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×C4C2×#1062190011yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337011yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—861no—
810C8—861no—
811C8—861no—
812C8—861no—
813C8—862no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C2×C4×C22⋊D4311yescharacteristic
836C22#1458353911yescharacteristic
837C22#1458357511yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—3441no—
843C4—1722no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4C2×(C22⋊D43)⋊C411yescharacteristic
848C4#1458337211yescharacteristic
849C4D4×C22⋊D4311yescharacteristic
850C4#1458354311yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—3441no—
858C2#1913757411yescharacteristic
859C2#1914349611yescharacteristic
860C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2880C2
socleC22×C43C2×C4×D4
prime radical#19143813C2
cosocleC22×C4×C43C24
hypercenter#2880D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. #19143316C2semidirect
4. C2×#14582916C2semidirect
5. #19135482C2semidirect
6. #19135309C2semidirect
7. #19135240C2semidirect
8. #19135041C2semidirect
9. #19134925C2semidirect
10. #19134922C2semidirect
11. #19134870C2semidirect
12. #19134799C2semidirect
13. #19134430C2semidirect
14. #19134363C2semidirect
15. C43×#2880C2semidirect
18. C2×#13063331C22semidirect
22. #14583061C4semidirect
23. #14583061C4semidirect
24. #14583055C4semidirect
25. #14583050C4semidirect
26. #14583044C4semidirect
27. #14583044C4semidirect
28. #14583038C4semidirect
29. #14583033C4semidirect
35. C2×#13063260C22semidirect
36. C2×#13063260C22semidirect
37. #14582925C22semidirect
43. C2×#13063251C22semidirect
44. C2×#13063251C22semidirect
47. #14582865C22semidirect
49. #14582854C22semidirect
50. C2×#13063235C22semidirect
51. C2×C8×Dic43C22semidirect
52. #14582663C22semidirect
53. #14582663C22semidirect
54. #14582660C22semidirect
55. #14582660C22semidirect
56. #14582653C22semidirect
57. #14582653C22semidirect
116. #13063252D4semidirect
425. #2880D43semidirect
499. C43#22887semidirect

Maximal subgroups

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

subgroupindex
#191438132
C2×#145830192
#191433162
C2×#145829162
#191354822
#191353092
#191352402
#191350412
#191349252
#191349222
#191348702
#191347992
#191344302
#191343632
C43×#28802
#2288743