Finite Group Databasebeta

← #25101634

Subgroups — #25101634

Order 11008.

1094 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147983C211yesmaximal, characteristic
2#19143013C211yesmaximal, characteristic, complemented
3#19137091C211yesmaximal, characteristic, complemented
4#19135537C211yesmaximal, characteristic, complemented
5#19135537C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135512C211yesmaximal, characteristic, complemented
8#19134898C211yesmaximal, characteristic, complemented
9#19134897C211yesmaximal, characteristic, complemented
10#19134895C211yesmaximal, characteristic, complemented
11#19134407C211yesmaximal, characteristic, complemented
12#19134404C211yesmaximal, characteristic, complemented
13#104×Dic43C211yesmaximal, characteristic, complemented
14#19134399C211yesmaximal, characteristic, complemented
15C43×#1871C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17#14583522C411yescharacteristic, complemented
18#14583522C411yescharacteristic, complemented
19#14583516C411yescharacteristic, complemented
20#14583516C411yescharacteristic, complemented
21#14583509C411yescharacteristic, complemented
22#14583509C411yescharacteristic, complemented
23#14583502C411yescharacteristic, complemented
24#14583502C411yescharacteristic, complemented
25#14583493—21no—
26#14583493—21no—
27#14583484—21no—
28#14583484—21no—
29#14583452C2211yescharacteristic
30#14583445C2211yescharacteristic
31#14583431—21no—
32#14583431—21no—
33#14583429—21no—
34#14583429—21no—
35#14583410C2211yescharacteristic
36#41×Dic43C2211yescharacteristic
37#14583367C2211yescharacteristic
38C2×#13063284C2211yescharacteristic
39C2×#13063253C2211yescharacteristic
40C2×#13063253C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45#14582857—21no—
46#14582857—21no—
47#14582854—21no—
48#14582854—21no—
49M16×Dic43C2211yescharacteristic
50M16×Dic43C2211yescharacteristic
51M16×Dic43C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53#14582793—21no—
54#14582787—21no—
55#14582784—21no—
56#14582782—21no—
57C4×Dic43⋊C4C2211yescharacteristic
58C4×Dic43⋊C4C2211yescharacteristic
59C4×C22⋊Dic43C2211yescharacteristic
60#14582745C2211yescharacteristic
61C42×Dic43C2211yescharacteristic
62#14582660C2211yescharacteristic
63#14582660C2211yescharacteristic
64#14582659C2211yescharacteristic
65#14582659C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C22×M16×C43C2211yescharacteristic
69C43×#525C2211yescharacteristic
70C2×#104×C43C2211yescharacteristic
71C2×#104×C43C2211yescharacteristic
72C4×C22⋊C4×C43C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C2×#10621898C2311yescharacteristic
76C2×#10621877—21no—
77C2×#10621877—22no—
78C2×#10621877—22no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C22×C43⋊C8—21no—
82#13063324C2×C411yescharacteristic
83#13063324C2×C411yescharacteristic
84#13063323C2×C411yescharacteristic
85#13063321C2×C411yescharacteristic
86#13063320—21no—
87#13063320—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063316—21no—
95#13063316—21no—
96#13063316C2×C411yescharacteristic
97#13063316C2×C411yescharacteristic
98#13063315—21no—
99#13063315—21no—
100#13063314C2×C411yescharacteristic
101#13063312—21no—
102#13063312—21no—
103#13063312C2×C411yescharacteristic
104#13063311—21no—
105#13063311—21no—
106#13063309—21no—
107#13063309—21no—
108#13063308—21no—
109#13063307—21no—
110#13063307—21no—
111#13063307—21no—
112#13063307—21no—
113#13063306—21no—
114#13063306—21no—
115#13063305—21no—
116#13063305—21no—
117#13063304C2×C411yescharacteristic
118#13063304C2×C411yescharacteristic
119#13063302—21no—
120#13063302—21no—
121#13063302—21no—
122#13063302—21no—
123#13063299C2×C411yescharacteristic
124#13063299C2×C411yescharacteristic
125#13063297—21no—
126#13063297—21no—
127#13063297—21no—
128#13063297—21no—
129#13063296—21no—
130#13063296—21no—
131#13063294—21no—
132Q8×Dic43C2×C411yescharacteristic
133Q8×Dic43C2×C411yescharacteristic
134C4×Dic86—21no—
135C4×Dic86—21no—
136#13063290C2×C411yescharacteristic
137#13063290C2×C411yescharacteristic
138D4×Dic43—21no—
139D4×Dic43—21no—
140D4×Dic43C2×C411yescharacteristic
141D4×Dic43C2×C411yescharacteristic
142#13063287C2×C411yescharacteristic
143#13063287C2×C411yescharacteristic
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063284—21no—
151#13063284C2×C411yescharacteristic
152#13063284C2×C411yescharacteristic
153#13063284C2×C411yescharacteristic
154#13063284C2×C411yescharacteristic
155#13063284D411yescharacteristic
156#13063284D411yescharacteristic
157#13063284D411yescharacteristic
158#13063284D411yescharacteristic
159#13063284C2311yescharacteristic
160#13063282—21no—
161C2×C4⋊Dic43D411yescharacteristic
162C2×C4⋊Dic43D411yescharacteristic
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×C22⋊Dic43—21no—
166C2×C22⋊Dic43D411yescharacteristic
167C2×C22⋊Dic43D411yescharacteristic
168C2×C4×Dic43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43C2311yescharacteristic
172C2×C4×Dic43C2311yescharacteristic
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2311yescharacteristic
175C42×D43—21no—
176#13063253—22no—
177#13063253—22no—
178#13063252—22no—
179#13063252—22no—
180#13063251—22no—
181#13063251—22no—
182#13063235—21no—
183#13063235—21no—
184#13063235—21no—
185#13063235—21no—
186C8×Dic43—21no—
187C8×Dic43—21no—
188C8×Dic43—21no—
189C8×Dic43—21no—
190C43⋊#95—21no—
191C43⋊#95—21no—
192C43⋊#95—21no—
193C43⋊#95—21no—
194C43⋊#95—21no—
195C2×#41×C43C2311yescharacteristic
196C23×C4×C43C2311yescharacteristic
197C2×M16×C43—21no—
198C2×M16×C43—22no—
199C2×M16×C43—22no—
200C2×M16×C43C2311yescharacteristic
201C2×M16×C43C2311yescharacteristic
202C22×C8×C43—21no—
203#123×C43—21no—
204C22⋊Q8×C43C2×C411yescharacteristic
205C22⋊Q8×C43C2×C411yescharacteristic
206#121×C43C2×C411yescharacteristic
207#121×C43C2×C411yescharacteristic
208#120×C43—21no—
209C4×D4×C43—21no—
210C4×D4×C43—21no—
211#117×C43C2311yescharacteristic
212C2×C22⋊C4×C43—21no—
213C2×C42×C43C2311yescharacteristic
214C2×C42×C43C2311yescharacteristic
215#104×C43—22no—
216#104×C43—22no—
217#95×C43—21no—
218C24×C43C2×D411yescharacteristic
219#41×C43—21no—
220#41×C43—21no—
221#41×C43—21no—
222#41×C43—21no—
223C2×Q8×C43C22×C411yescharacteristic
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43C22×C411yescharacteristic
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43—21no—
232C22×C4×C43—21no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43C22×C411yescharacteristic
236C22×C4×C43C22×C411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2411yescharacteristic
241C2×C22⋊D43—21no—
242C2×C22⋊D43—21no—
243C2×C22⋊D43—21no—
244C2×C22⋊D43—21no—
245C2×C22⋊D43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252C22×Dic43C2×D411yescharacteristic
253C22×Dic43C2×D411yescharacteristic
254#10621898—21no—
255#10621898—21no—
256#10621898—21no—
257#10621898—21no—
258C2×D172C22×C411yescharacteristic
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×Dic86—21no—
263C2×Dic86—21no—
264C2×Dic86C22×C411yescharacteristic
265M16×C43—24no—
266M16×C43—21no—
267M16×C43—21no—
268M16×C43#4112yes—
269M16×C43#4112yes—
270C2×C8×C43—24no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43C22×C411yescharacteristic
276C4⋊C4×C43C22×C411yescharacteristic
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—42no—
283C42×C43—21no—
284C42×C43—21no—
285C42×C43—21no—
286C42×C43—21no—
287C42×C43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—42no—
296C22⋊Dic43C22⋊C411yescharacteristic
297C22⋊Dic43C22⋊C411yescharacteristic
298C22⋊Dic43C22⋊C411yescharacteristic
299C22⋊Dic43C22⋊C411yescharacteristic
300C22⋊Dic43C22⋊C411yescharacteristic
301C22⋊Dic43C22⋊C411yescharacteristic
302C22⋊Dic43C22⋊C411yescharacteristic
303C22⋊Dic43C22⋊C411yescharacteristic
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314C4⋊Dic43C22⋊C411yescharacteristic
315C4⋊Dic43C22⋊C411yescharacteristic
316C4⋊Dic43C22⋊C411yescharacteristic
317C4⋊Dic43C22⋊C411yescharacteristic
318C4⋊Dic43C22⋊C411yescharacteristic
319C4⋊Dic43C22⋊C411yescharacteristic
320C4⋊Dic43C22⋊C411yescharacteristic
321C4⋊Dic43C22⋊C411yescharacteristic
322C4⋊Dic43C22×C411yescharacteristic
323C4⋊Dic43C22×C411yescharacteristic
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328Dic43⋊C4—21no—
329Dic43⋊C4—21no—
330Dic43⋊C4—21no—
331Dic43⋊C4—21no—
332Dic43⋊C4—21no—
333Dic43⋊C4—21no—
334Dic43⋊C4—42no—
335Dic43⋊C4—42no—
336C4×Dic43—21no—
337C4×Dic43—21no—
338C4×Dic43—21no—
339C4×Dic43—21no—
340C4×Dic43—21no—
341C4×Dic43—21no—
342C4×Dic43—21no—
343C4×Dic43—21no—
344C4×Dic43—21no—
345C4×Dic43—42no—
346C4×Dic43—42no—
347C4×Dic43C22×C411yescharacteristic
348C4×Dic43C22×C411yescharacteristic
349C4×Dic43C22×C411yescharacteristic
350C4×Dic43C22×C411yescharacteristic
351C4×Dic43C2×D411yescharacteristic
352C4×Dic43C2×D411yescharacteristic
353C4×Dic43C2×D411yescharacteristic
354C4×Dic43C2×D411yescharacteristic
355#10621877—24no—
356#10621877—21no—
357#10621877—21no—
358#10621877#4112yes—
359#10621877#4112yes—
360C2×C43⋊C8—24no—
361C2×C43⋊C8—21no—
362C2×C43⋊C8—21no—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—21no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43C2×C22⋊C411yescharacteristic
369C23×C43C2×C22⋊C411yescharacteristic
370C23×C43C22×D411yescharacteristic
371C22×D43—21no—
372Q8×C43—21no—
373Q8×C43—21no—
374D4×C43—21no—
375D4×C43—21no—
376D4×C43—41no—
377D4×C43—41no—
378D4×C43—81no—
379D4×C43—81no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—22no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43—41no—
400C2×C4×C43—41no—
401C2×C4×C43C2×C22⋊C411yescharacteristic
402C2×C4×C43C2×C22⋊C411yescharacteristic
403C2×C4×C43C23×C411yescharacteristic
404C2×C4×C43C22×D411yescharacteristic
405C2×C4×C43C2×#4111yescharacteristic
406C2×C4×C43C2×#4111yescharacteristic
407C2×C4×C43C2×#4111yescharacteristic
408C2×C4×C43C2×#4111yescharacteristic
409C22⋊D43—41no—
410C22⋊D43—41no—
411C22⋊D43—81no—
412C22⋊D43—81no—
413C22⋊D43—81no—
414C22⋊D43—81no—
415C2×Dic43—22no—
416C2×Dic43—21no—
417C2×Dic43—21no—
418C2×Dic43—21no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—81no—
429C2×Dic43—81no—
430C2×Dic43C2×C22⋊C411yescharacteristic
431C2×Dic43C2×C22⋊C411yescharacteristic
432C2×Dic43C2×C22⋊C411yescharacteristic
433C2×Dic43C2×C22⋊C411yescharacteristic
434C2×Dic43C2×C22⋊C411yescharacteristic
435C2×Dic43C2×C22⋊C411yescharacteristic
436C2×Dic43C2×C22⋊C411yescharacteristic
437C2×Dic43C2×C22⋊C411yescharacteristic
438D172—21no—
439D172—21no—
440C4×D43—41no—
441C4×D43—41no—
442C4×D43—81no—
443C4×D43—81no—
444Dic86—21no—
445Dic86—21no—
446Dic86—81no—
447Dic86—81no—
448C8×C43—22no—
449C8×C43—22no—
450C43⋊C8—22no—
451C43⋊C8—22no—
452#21384—431nomaximal, Sylow
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—21no—
457C22×C43—21no—
458C22×C43—21no—
459C22×C43—21no—
460C22×C43—21no—
461C22×C43—41no—
462C22×C43—41no—
463C22×C43—41no—
464C22×C43—81no—
465C22×C43—81no—
466C22×C43C22×C22⋊C411yescharacteristic
467C22×C43#53211yescharacteristic
468C22×C43#53211yescharacteristic
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C4×C43—21no—
473C4×C43—21no—
474C4×C43—42no—
475C4×C43—41no—
476C4×C43—41no—
477C4×C43—41no—
478C4×C43—81no—
479C4×C43C4×#4111yescharacteristic
480C4×C43C4×#4111yescharacteristic
481C4×C43#52511yescharacteristic
482C4×C43#52511yescharacteristic
483Dic43—21no—
484Dic43—21no—
485Dic43—21no—
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—21no—
490Dic43—21no—
491Dic43—42no—
492Dic43—41no—
493Dic43—41no—
494Dic43—41no—
495Dic43—81no—
496#3455—431no—
497#2873—431no—
498#2298—431no—
499#1986—431no—
500#1986—431no—
501#1980—431no—
502#1980—431no—
503#1871—431no—
504#1871—431no—
505#1871—431no—
506#1871D4311yescharacteristic, complemented
507#1759—431no—
508#1759—431no—
509C4×#104—431no—
510C4×#104—431no—
511C2×C43—21no—
512C2×C43—21no—
513C2×C43—41no—
514C2×C43—41no—
515C2×C43—81no—
516C2×C43#229711yescharacteristic
517C2×C43#290111yescharacteristic
518C2×C43#290111yescharacteristic
519D43—81no—
520C22×M16—431no—
521C22×M16C2×D4311yescharacteristic
522#542—431no—
523#542—431no—
524#542—431no—
525#542—431no—
526#541—431no—
527#541—431no—
528#540—431no—
529#540—431no—
530#539—861no—
531#539—861no—
532#538—861no—
533#538—861no—
534#533—431no—
535#532—431no—
536#529—861no—
537#529—861no—
538#529—861no—
539#529—861no—
540#525—431no—
541#525C2×D4311yescharacteristic
542C4×#41—431no—
543C4×#41—431no—
544C2×#117—431no—
545C2×#104—431no—
546C2×#104—431no—
547C2×#104—431no—
548C2×#104—431no—
549C2×#104—431no—
550C2×#104—431no—
551C2×#104C2×D4311yescharacteristic
552C2×#104C2×D4311yescharacteristic
553#405—861no—
554#405—861no—
555#405—861no—
556#405—861no—
557C4×M16—431no—
558C4×M16—431no—
559C4×M16—431no—
560C4×M16—431no—
561#388—861no—
562#388—861no—
563#387—861no—
564#387—861no—
565C4×C4⋊C4—431no—
566C4×C4⋊C4—431no—
567C4×C22⋊C4—431no—
568C4×C22⋊C4C2×D4311yescharacteristic
569#376—431no—
570C43—431no—
571#339—431no—
572#339—431no—
573#339—431no—
574#339—431no—
575#339—431no—
576#339—431no—
577#339C2×D4311yescharacteristic
578#339C2×D4311yescharacteristic
579C43#2138411yescharacteristic, complemented, Sylow
580C2×#41—431no—
581C2×#41C22×D4311yescharacteristic
582C23×C4C22×D4311yescharacteristic
583C2×M16—21no—
584C2×M16—22no—
585C2×M16—22no—
586C2×M16—431no—
587C2×M16—431no—
588C2×M16—862no—
589C2×M16—862no—
590C2×M16—861no—
591C2×M16C22×D4311yescharacteristic
592C2×M16C22×D4311yescharacteristic
593C22×C8—21no—
594C22×C8—861no—
595C4⋊Q8—431no—
596C4⋊Q8—431no—
597C4⋊Q8—431no—
598#127—431no—
599#126—861no—
600#126—861no—
601#126—861no—
602#126—861no—
603#126—861no—
604#126—861no—
605#126—861no—
606#126—861no—
607#125—431no—
608#125—431no—
609#125—861no—
610#125—861no—
611#125—861no—
612#125—861no—
613#124—431no—
614#124—431no—
615#124—861no—
616#124—861no—
617#124—861no—
618#124—861no—
619#123—21no—
620#123—861no—
621#123—861no—
622#123—861no—
623#123—861no—
624#123—861no—
625#123—861no—
626#123—861no—
627#123—861no—
628#123—861no—
629C22⋊Q8—431no—
630C22⋊Q8—431no—
631C22⋊Q8—861no—
632C22⋊Q8—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8C4×D4311yescharacteristic
638C22⋊Q8C4×D4311yescharacteristic
639#121—431no—
640#121—431no—
641#121—861no—
642#121—861no—
643#121—861no—
644#121—861no—
645#121—861no—
646#121—861no—
647#121C4×D4311yescharacteristic
648#121C4×D4311yescharacteristic
649#120—21no—
650#120—861no—
651C4×Q8—431no—
652C4×Q8—431no—
653C4×Q8—431no—
654C4×Q8—431no—
655C4×Q8—861no—
656C4×Q8—861no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4—861no—
670C4×D4—861no—
671#117—431no—
672#117—431no—
673#117—431no—
674#117—431no—
675#117—431no—
676#117—431no—
677#117—431no—
678#117—431no—
679#117—431no—
680#117—861no—
681#117—861no—
682#117C22×D4311yescharacteristic
683C2×C4⋊C4—431no—
684C2×C4⋊C4—431no—
685C2×C4⋊C4—861no—
686C2×C4⋊C4—861no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—431no—
689C2×C22⋊C4—431no—
690C2×C22⋊C4—861no—
691C2×C42—431no—
692C2×C42—431no—
693C2×C42—431no—
694C2×C42—431no—
695C2×C42—861no—
696C2×C42—861no—
697C2×C42—861no—
698C2×C42—861no—
699C2×C42C22×D4311yescharacteristic
700C2×C42C22×D4311yescharacteristic
701#104—22no—
702#104—22no—
703#104—862no—
704#104—862no—
705#104—862no—
706#104—862no—
707#104—862no—
708#104—862no—
709#97—861no—
710#97—861no—
711#97—861no—
712#97—861no—
713C4×C8—861no—
714C4×C8—861no—
715C4×C8—861no—
716C4×C8—861no—
717#95—21no—
718#95—861no—
719#95—861no—
720#95—861no—
721#95—861no—
722#95—861no—
723C24D4×D4311yescharacteristic
724#41—21no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—861no—
729#41—861no—
730#41—861no—
731#41—861no—
732C2×Q8—431no—
733C2×Q8—861no—
734C2×Q8—861no—
735C2×Q8C2×C4×D4311yescharacteristic
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—431no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4C2×C4×D4311yescharacteristic
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4C2×C4×D4311yescharacteristic
765C22×C4C2×C4×D4311yescharacteristic
766C22×C4D4×D4311yescharacteristic
767C22×C4D4×D4311yescharacteristic
768C22×C4D4×D4311yescharacteristic
769C22×C4C23×D4311yescharacteristic
770M16—24no—
771M16—21no—
772M16—21no—
773M16—432no—
774M16—432no—
775M16—864no—
776M16—861no—
777M16—861no—
778M16#1062190012yes—
779M16#1062190012yes—
780C2×C8—24no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—864no—
784C2×C8—861no—
785C2×C8—861no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—431no—
789C4⋊C4—431no—
790C4⋊C4—431no—
791C4⋊C4—431no—
792C4⋊C4—431no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—431no—
796C4⋊C4—431no—
797C4⋊C4—431no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—861no—
803C4⋊C4—861no—
804C4⋊C4—861no—
805C4⋊C4—861no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—1722no—
813C4⋊C4—1722no—
814C4⋊C4C2×C4×D4311yescharacteristic
815C4⋊C4C2×C4×D4311yescharacteristic
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—42no—
822C22⋊C4—431no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—431no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—861no—
840C22⋊C4—861no—
841C22⋊C4—861no—
842C22⋊C4—861no—
843C22⋊C4—1722no—
844C42—21no—
845C42—21no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—431no—
850C42—431no—
851C42—431no—
852C42—431no—
853C42—431no—
854C42—431no—
855C42—431no—
856C42—431no—
857C42—861no—
858C42—861no—
859C42—861no—
860C42—861no—
861C42—861no—
862C42—861no—
863C42—861no—
864C42—861no—
865C42—861no—
866C42—1722no—
867C42—1722no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—41no—
872C23—41no—
873C23—861no—
874C23C22⋊C4×D4311yescharacteristic
875C23C22⋊C4×D4311yescharacteristic
876C23C2×D4×D4311yescharacteristic
877Q8—21no—
878Q8—21no—
879Q8—861no—
880Q8—861no—
881Q8—3441no—
882Q8—3441no—
883D4—21no—
884D4—21no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—861no—
890D4—861no—
891D4—3441no—
892D4—3441no—
893D4—3441no—
894D4—3441no—
895D4—1721no—
896D4—1721no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—431no—
919C2×C4—431no—
920C2×C4—431no—
921C2×C4—431no—
922C2×C4—431no—
923C2×C4—431no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—862no—
927C2×C4—861no—
928C2×C4—861no—
929C2×C4—861no—
930C2×C4—3441no—
931C2×C4—3441no—
932C2×C4—3441no—
933C2×C4—3441no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4C22⋊C4×D4311yescharacteristic
946C2×C4C22⋊C4×D4311yescharacteristic
947C2×C4C22×C4×D4311yescharacteristic
948C2×C4C2×D4×D4311yescharacteristic
949C2×C4#41×D4311yescharacteristic
950C2×C4#41×D4311yescharacteristic
951C2×C4C2×#1062190011yescharacteristic
952C2×C4C2×#1062190011yescharacteristic
953C8—22no—
954C8—22no—
955C8—862no—
956C8—862no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—81no—
969C22—81no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22C2×C22⋊C4×D4311yescharacteristic
974C22#1458344411yescharacteristic
975C22#1458344411yescharacteristic
976C4—21no—
977C4—21no—
978C4—42no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—81no—
983C4—861no—
984C4—861no—
985C4—861no—
986C4—861no—
987C4—861no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—3441no—
992C4—1722no—
993C4—1721no—
994C4—1721no—
995C4—1721no—
996C4C4×#1062190011yescharacteristic
997C4C4×#1062190011yescharacteristic
998C4#1458340511yescharacteristic
999C4#1458340711yescharacteristic
1000C2—21no—
1001C2—21no—
1002C2—41no—
1003C2—41no—
1004C2—81no—
1005C2—3441no—
1006C2#1913708011yescharacteristic
1007C2#1914313911yescharacteristic
1008C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C22×C22⋊C4
prime radical#19147983C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#21384
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #19143013C2semidirect
3. #19137091C2semidirect
4. #19135537C2semidirect
5. #19135537C2semidirect
6. #19135512C2semidirect
7. #19135512C2semidirect
8. #19134898C2semidirect
9. #19134897C2semidirect
10. #19134895C2semidirect
11. #19134407C2semidirect
12. #19134404C2semidirect
13. #104×Dic43C2semidirect
14. #19134399C2semidirect
15. C43×#1871C2semidirect
17. #14583522C4semidirect
18. #14583522C4semidirect
19. #14583516C4semidirect
20. #14583516C4semidirect
21. #14583509C4semidirect
22. #14583509C4semidirect
23. #14583502C4semidirect
24. #14583502C4semidirect
506. #1871D43semidirect
579. C43#21384semidirect

Maximal subgroups

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

subgroupindex
#191479832
#191430132
#191370912
#191355372
#191355122
#191348982
#191348972
#191348952
#191344072
#191344042
#104×Dic432
#191343992
C43×#18712
#2138443