Finite Group Databasebeta

← #25106262

Subgroups — #25106262

Order 11008.

1038 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#19147980C211yesmaximal, characteristic
2#19143157C211yesmaximal, characteristic, complemented
3#19137088C211yesmaximal, characteristic, complemented
4#19135574C211yesmaximal, characteristic, complemented
5#19135570C211yesmaximal, characteristic, complemented
6#19135425C211yesmaximal, characteristic, complemented
7#19135421C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic, complemented
9#19134896C211yesmaximal, characteristic, complemented
10#19134894C211yesmaximal, characteristic, complemented
11#19134894C211yesmaximal, characteristic, complemented
12#19134616C211yesmaximal, characteristic, complemented
13#19134615C211yesmaximal, characteristic, complemented
14#19134612C211yesmaximal, characteristic, complemented
15C43×#1806C211yesmaximal, characteristic, complemented
16C2×M16×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18#14583521C411yescharacteristic, complemented
19#14583521C411yescharacteristic, complemented
20#14583514C411yescharacteristic, complemented
21#14583514C411yescharacteristic, complemented
22#14583507C411yescharacteristic, complemented
23#14583507C411yescharacteristic, complemented
24#14583500C411yescharacteristic, complemented
25#14583500C411yescharacteristic, complemented
26#14583491—21no—
27#14583491—21no—
28#14583482—21no—
29#14583482—21no—
30#14583452C2211yescharacteristic
31#14583445C2211yescharacteristic
32#14583433—21no—
33#14583433—21no—
34#14583427—21no—
35#14583427—21no—
36#14583411C2211yescharacteristic
37#14583406C2211yescharacteristic
38C4×#10621898C2211yescharacteristic
39C2×#13063282C2211yescharacteristic
40#14582924—21no—
41#14582924—21no—
42#14582924—21no—
43#14582924—21no—
44#14582923C2211yescharacteristic
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063253C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063252C2211yescharacteristic
51C2×#13063251C2211yescharacteristic
52C2×#13063251C2211yescharacteristic
53#14582791—21no—
54#14582789—21no—
55#14582786—21no—
56#14582780—21no—
57C4×C4⋊Dic43C2211yescharacteristic
58C4×(C2×D43)⋊C4C2211yescharacteristic
59C4×(C2×D43)⋊C4C2211yescharacteristic
60#14582745C2211yescharacteristic
61C42×Dic43C2211yescharacteristic
62#14582660C2211yescharacteristic
63#14582660C2211yescharacteristic
64#14582659C2211yescharacteristic
65#14582659C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C43×#423C2211yescharacteristic
70C2×#104×C43C2211yescharacteristic
71C2×#104×C43C2211yescharacteristic
72C4×C4⋊C4×C43C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C2×#10621898C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621872—21no—
80C2×#10621872—21no—
81M16×D43—41no—
82M16×D43—41no—
83M16×D43—41no—
84M16×D43—41no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063324C2×C411yescharacteristic
88#13063324C2×C411yescharacteristic
89#13063323C2×C411yescharacteristic
90#13063321C2×C411yescharacteristic
91#13063320—21no—
92#13063320—21no—
93#13063319—21no—
94#13063319—21no—
95#13063319—21no—
96#13063319—21no—
97#13063318—21no—
98#13063318—21no—
99#13063317—21no—
100#13063317—21no—
101#13063316C2×C411yescharacteristic
102#13063316C2×C411yescharacteristic
103#13063315—21no—
104#13063315—21no—
105#13063314C2×C411yescharacteristic
106#13063313—21no—
107#13063313—21no—
108#13063312C2×C411yescharacteristic
109#13063311—21no—
110#13063311—21no—
111#13063310—21no—
112#13063310—21no—
113#13063309—21no—
114#13063308—21no—
115#13063308—21no—
116#13063308—21no—
117#13063308—21no—
118#13063307—21no—
119#13063307—21no—
120#13063306—21no—
121#13063305C2×C411yescharacteristic
122#13063305C2×C411yescharacteristic
123#13063304—21no—
124#13063304—21no—
125#13063303—21no—
126#13063303—21no—
127#13063302—21no—
128#13063302—21no—
129#13063301C2×C411yescharacteristic
130#13063301C2×C411yescharacteristic
131#13063300C2×C411yescharacteristic
132#13063300C2×C411yescharacteristic
133#13063299—21no—
134#13063299—21no—
135#13063298—21no—
136#13063298—21no—
137#13063297—21no—
138#13063297—21no—
139#13063296C2×C411yescharacteristic
140#13063296C2×C411yescharacteristic
141#13063295—21no—
142#13063293—21no—
143C4×Dic86—21no—
144C4×Dic86—21no—
145C4×Dic86C2×C411yescharacteristic
146C4×Dic86C2×C411yescharacteristic
147C4×D172—21no—
148C4×D172—21no—
149C4×D172C2×C411yescharacteristic
150C4×D172C2×C411yescharacteristic
151C4×C22⋊D43—21no—
152C4×C22⋊D43—21no—
153C4×C22⋊D43—21no—
154C4×C22⋊D43—21no—
155C4×C22⋊D43—21no—
156C4×C22⋊D43—21no—
157#13063284C2311yescharacteristic
158#13063282—21no—
159#13063282C2×C411yescharacteristic
160#13063282C2×C411yescharacteristic
161#13063282C2×C411yescharacteristic
162#13063282C2×C411yescharacteristic
163#13063282D411yescharacteristic
164#13063282D411yescharacteristic
165#13063282D411yescharacteristic
166#13063282D411yescharacteristic
167C2×C4⋊Dic43—21no—
168C2×Dic43⋊C4D411yescharacteristic
169C2×Dic43⋊C4D411yescharacteristic
170C2×(C2×D43)⋊C4—21no—
171C2×(C2×D43)⋊C4—21no—
172C2×(C2×D43)⋊C4D411yescharacteristic
173C2×(C2×D43)⋊C4D411yescharacteristic
174C2×C4×Dic43—21no—
175C2×C4×Dic43—21no—
176C2×C4×Dic43C2311yescharacteristic
177C2×C4×Dic43C2311yescharacteristic
178C2×C4×Dic43C2311yescharacteristic
179C42×D43—21no—
180C4⋊(C43⋊C8)—21no—
181C4⋊(C43⋊C8)—21no—
182Dic43⋊C8—21no—
183Dic43⋊C8—21no—
184Dic43⋊C8—21no—
185Dic43⋊C8—21no—
186#13063253—41no—
187#13063253—41no—
188#13063252—41no—
189#13063252—41no—
190#13063251—41no—
191#13063251—41no—
192C43⋊#95—21no—
193C43⋊#95—21no—
194C43⋊#95—21no—
195C43⋊#95—21no—
196C43⋊#95—21no—
197C2×#41×C43C2311yescharacteristic
198C2×M16×C43C2311yescharacteristic
199C2×M16×C43C2311yescharacteristic
200C4×Q8×C43C2×C411yescharacteristic
201C4×Q8×C43C2×C411yescharacteristic
202C4×D4×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43C2×C411yescharacteristic
205C4×D4×C43C2×C411yescharacteristic
206#117×C43—21no—
207#117×C43C2311yescharacteristic
208C2×C4⋊C4×C43—21no—
209C2×C42×C43—21no—
210C2×C42×C43C2311yescharacteristic
211C2×C42×C43C2311yescharacteristic
212C2×C42×C43C2311yescharacteristic
213C4⋊C8×C43—21no—
214C4⋊C8×C43—21no—
215#104×C43—41no—
216#104×C43—41no—
217#95×C43—21no—
218C23×D43C2×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×C43C22×C411yescharacteristic
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—21no—
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244#10621898—21no—
245#10621898—21no—
246#10621898—21no—
247#10621898—21no—
248C2×D172—21no—
249C2×D172—21no—
250C2×D172C22×C411yescharacteristic
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43C22×C411yescharacteristic
259C2×C4×D43C22×C411yescharacteristic
260C2×C4×D43C2×D411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
262C2×Dic86—21no—
263C2×Dic86—21no—
264C2×Dic86C22×C411yescharacteristic
265M16×C43—21no—
266M16×C43—21no—
267M16×C43—21no—
268M16×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—42no—
274C4⋊C4×C43C22×C411yescharacteristic
275C4⋊C4×C43C22×C411yescharacteristic
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C42×C43—21no—
280C42×C43—21no—
281C42×C43—21no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43—21no—
285C42×C43—21no—
286C42×C43C22×C411yescharacteristic
287C42×C43C22×C411yescharacteristic
288C42×C43C2×D411yescharacteristic
289C42×C43C2×D411yescharacteristic
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—42no—
306(C2×D43)⋊C4—42no—
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315C4⋊Dic43—21no—
316C4⋊Dic43—21no—
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43—42no—
320C4⋊Dic43C22×C411yescharacteristic
321C4⋊Dic43C22×C411yescharacteristic
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
333Dic43⋊C4C22⋊C411yescharacteristic
334Dic43⋊C4C22⋊C411yescharacteristic
335Dic43⋊C4C22⋊C411yescharacteristic
336Dic43⋊C4C22⋊C411yescharacteristic
337Dic43⋊C4C22⋊C411yescharacteristic
338Dic43⋊C4C22⋊C411yescharacteristic
339Dic43⋊C4C22⋊C411yescharacteristic
340C4×Dic43—21no—
341C4×Dic43—21no—
342C4×Dic43—21no—
343C4×Dic43—21no—
344C4×Dic43—21no—
345C4×Dic43—21no—
346C4×Dic43—21no—
347C4×Dic43—42no—
348C4×Dic43—42no—
349C4×Dic43C22×C411yescharacteristic
350C4×Dic43C22×C411yescharacteristic
351C4×Dic43C2×D411yescharacteristic
352C4×Dic43C2×D411yescharacteristic
353#10621877—21no—
354#10621877—21no—
355#10621877—21no—
356#10621877—21no—
357C2×C43⋊C8—21no—
358C2×C43⋊C8—21no—
359#10621872—42no—
360#10621872—42no—
361C8×D43—42no—
362C8×D43—42no—
363C23×C43—21no—
364C23×C43C22×D411yescharacteristic
365C22×D43—21no—
366C22×D43—21no—
367C22×D43—21no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43C2×C22⋊C411yescharacteristic
371C22×D43C2×C22⋊C411yescharacteristic
372Q8×C43—21no—
373Q8×C43—21no—
374D4×C43—21no—
375D4×C43—21no—
376D4×C43—41no—
377D4×C43—41no—
378C2×C4×C43—22no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—81no—
392C2×C4×C43—81no—
393C2×C4×C43C2×C22⋊C411yescharacteristic
394C2×C4×C43C2×C22⋊C411yescharacteristic
395C2×C4×C43C2×C22⋊C411yescharacteristic
396C2×C4×C43C2×C22⋊C411yescharacteristic
397C2×C4×C43C23×C411yescharacteristic
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C43H(5,𝔽2)11yescharacteristic
400C2×C4×C43H(5,𝔽2)11yescharacteristic
401C2×C4×C432−1+411yescharacteristic
402C2×C4×C432−1+411yescharacteristic
403C22⋊D43—41no—
404C22⋊D43—41no—
405C22⋊D43—81no—
406C22⋊D43—81no—
407C22⋊D43—81no—
408C22⋊D43—81no—
409C2×Dic43—21no—
410C2×Dic43—21no—
411C2×Dic43—22no—
412C2×Dic43—21no—
413C2×Dic43—21no—
414C2×Dic43—21no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43C2×C22⋊C411yescharacteristic
423C2×Dic43C2×C22⋊C411yescharacteristic
424C2×Dic43C2×C22⋊C411yescharacteristic
425C2×Dic43C2×C22⋊C411yescharacteristic
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428D172—21no—
429D172—21no—
430D172—81no—
431D172—81no—
432C4×D43—21no—
433C4×D43—21no—
434C4×D43—21no—
435C4×D43—21no—
436C4×D43—21no—
437C4×D43—21no—
438C4×D43—21no—
439C4×D43—21no—
440C4×D43—41no—
441C4×D43—41no—
442C4×D43—81no—
443C4×D43—81no—
444Dic86—21no—
445Dic86—21no—
446Dic86—81no—
447Dic86—81no—
448C8×C43—41no—
449C8×C43—41no—
450C43⋊C8—41no—
451C43⋊C8—41no—
452#21858—431nomaximal, Sylow
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43C22×C22⋊C411yescharacteristic
459C22×C43#53711yescharacteristic
460C22×C43#53711yescharacteristic
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—81no—
471C2×D43—81no—
472C4×C43—21no—
473C4×C43—21no—
474C4×C43—21no—
475C4×C43—21no—
476C4×C43—42no—
477C4×C43—41no—
478C4×C43—41no—
479C4×C43—41no—
480C4×C43—81no—
481C4×C43#52011yescharacteristic
482C4×C43#52011yescharacteristic
483C4×C43#53511yescharacteristic
484C4×C43#53611yescharacteristic
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#2905—431no—
498#2298—431no—
499#1995—431no—
500#1994—431no—
501#1963—431no—
502#1962—431no—
503#1871—431no—
504#1871—431no—
505#1871—431no—
506#1871—431no—
507#1806—431no—
508#1806—431no—
509#1806—431no—
510#1806D4311yescharacteristic, complemented
511C2×C43—21no—
512C2×C43—21no—
513C2×C43—81no—
514C2×C43#231111yescharacteristic
515C2×C43#290111yescharacteristic
516C2×C43#290111yescharacteristic
517D43—41no—
518D43—41no—
519D43—81no—
520C22×M16—431no—
521C22×M16—431no—
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#525—431no—
542C4×#41—431no—
543C4×#41C2×D4311yescharacteristic
544C2×#117—431no—
545#424—861no—
546#424—861no—
547#424—861no—
548#424—861no—
549#423—431no—
550#423—431no—
551#423—431no—
552#423C2×D4311yescharacteristic
553C2×#104—431no—
554C2×#104—431no—
555C2×#104—431no—
556C2×#104—431no—
557C2×#104—431no—
558C2×#104—431no—
559C2×#104C2×D4311yescharacteristic
560C2×#104C2×D4311yescharacteristic
561#388—861no—
562#388—861no—
563#387—861no—
564#387—861no—
565C4×C4⋊C4—431no—
566C4×C4⋊C4C2×D4311yescharacteristic
567C4×C22⋊C4—431no—
568C4×C22⋊C4—431no—
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#2185811yescharacteristic, complemented, Sylow
580C2×#41—431no—
581C2×#41C22×D4311yescharacteristic
582C23×C4—431no—
583C2×M16—431no—
584C2×M16—431no—
585C2×M16—861no—
586C2×M16—861no—
587C2×M16—1721no—
588C2×M16—1721no—
589C2×M16—1721no—
590C2×M16—1721no—
591C2×M16C22×D4311yescharacteristic
592C2×M16C22×D4311yescharacteristic
593C22×C8—861no—
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—861no—
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—431no—
632C22⋊Q8—431no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8—861no—
638C22⋊Q8—861no—
639#121—431no—
640#121—431no—
641#121—431no—
642#121—431no—
643#121—861no—
644#121—861no—
645#121—861no—
646#121—861no—
647#121—861no—
648#121—861no—
649#120—861no—
650#120—861no—
651C4×Q8—431no—
652C4×Q8—431no—
653C4×Q8—861no—
654C4×Q8—861no—
655C4×Q8C4×D4311yescharacteristic
656C4×Q8C4×D4311yescharacteristic
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4C4×D4311yescharacteristic
670C4×D4C4×D4311yescharacteristic
671#117—21no—
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—431no—
681#117—861no—
682#117C22×D4311yescharacteristic
683C2×C4⋊C4—21no—
684C2×C4⋊C4—431no—
685C2×C4⋊C4—431no—
686C2×C4⋊C4—861no—
687C2×C22⋊C4—431no—
688C2×C22⋊C4—431no—
689C2×C22⋊C4—861no—
690C2×C22⋊C4—861no—
691C2×C42—21no—
692C2×C42—431no—
693C2×C42—431no—
694C2×C42—431no—
695C2×C42—861no—
696C2×C42—861no—
697C2×C42—861no—
698C2×C42C22×D4311yescharacteristic
699C2×C42C22×D4311yescharacteristic
700C2×C42C22×D4311yescharacteristic
701C4⋊C8—21no—
702C4⋊C8—21no—
703C4⋊C8—861no—
704C4⋊C8—861no—
705C4⋊C8—861no—
706C4⋊C8—861no—
707C4⋊C8—861no—
708C4⋊C8—861no—
709#104—41no—
710#104—41no—
711#104—1721no—
712#104—1721no—
713#104—1721no—
714#104—1721no—
715#104—1721no—
716#104—1721no—
717#95—21no—
718#95—861no—
719#95—861no—
720#95—861no—
721#95—861no—
722#95—861no—
723C24—431no—
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—431no—
738C2×D4—861no—
739C2×D4—861no—
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—431no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4D4×D4311yescharacteristic
768C22×C4D4×D4311yescharacteristic
769C22×C4C23×D4311yescharacteristic
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—861no—
775M16—861no—
776M16—861no—
777M16—861no—
778M16—1722no—
779M16—1722no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—861no—
783C2×C8—861no—
784C2×C8—1722no—
785C2×C8—1722no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—42no—
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—431no—
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—861no—
813C4⋊C4—1722no—
814C4⋊C4C2×C4×D4311yescharacteristic
815C4⋊C4C2×C4×D4311yescharacteristic
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—431no—
820C22⋊C4—431no—
821C22⋊C4—431no—
822C22⋊C4—431no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
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—1722no—
843C22⋊C4—1722no—
844C42—21no—
845C42—21no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—21no—
850C42—21no—
851C42—431no—
852C42—431no—
853C42—431no—
854C42—431no—
855C42—861no—
856C42—861no—
857C42—861no—
858C42—861no—
859C42—861no—
860C42—861no—
861C42—861no—
862C42—1722no—
863C42—1722no—
864C42C2×C4×D4311yescharacteristic
865C42C2×C4×D4311yescharacteristic
866C42D4×D4311yescharacteristic
867C42D4×D4311yescharacteristic
868C23—21no—
869C23—431no—
870C23—431no—
871C23—861no—
872C23—861no—
873C23—861no—
874C23—1721no—
875C23—1721no—
876C23C2×D4×D4311yescharacteristic
877Q8—21no—
878Q8—21no—
879Q8—861no—
880Q8—861no—
881Q8—3441no—
882Q8—3441no—
883D4—21no—
884D4—21no—
885D4—41no—
886D4—41no—
887D4—861no—
888D4—861no—
889D4—3441no—
890D4—3441no—
891D4—3441no—
892D4—3441no—
893D4—3441no—
894D4—3441no—
895D4—1721no—
896D4—1721no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—431no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—861no—
922C2×C4—861no—
923C2×C4—861no—
924C2×C4—861no—
925C2×C4—861no—
926C2×C4—861no—
927C2×C4—861no—
928C2×C4—862no—
929C2×C4—861no—
930C2×C4—861no—
931C2×C4—861no—
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×C4C22⋊C4×D4311yescharacteristic
944C2×C4C22⋊C4×D4311yescharacteristic
945C2×C4C22⋊C4×D4311yescharacteristic
946C2×C4C22⋊C4×D4311yescharacteristic
947C2×C4C22×C4×D4311yescharacteristic
948C2×C4C2×D4×D4311yescharacteristic
949C2×C4#1306337011yescharacteristic
950C2×C4#1306337111yescharacteristic
951C2×C4#1306337211yescharacteristic
952C2×C4#1306337311yescharacteristic
953C8—41no—
954C8—41no—
955C8—1721no—
956C8—1721no—
957C22—21no—
958C22—21no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—3441no—
969C22—3441no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22C2×C22⋊C4×D4311yescharacteristic
974C22#1458347811yescharacteristic
975C22#1458347911yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—42no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—81no—
985C4—861no—
986C4—861no—
987C4—861no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—3441no—
992C4—1722no—
993C4—1721no—
994C4—1721no—
995C4—1721no—
996C4#1458337911yescharacteristic
997C4#1458338011yescharacteristic
998C4#1458346511yescharacteristic
999C4#1458347211yescharacteristic
1000C2—21no—
1001C2—21no—
1002C2—81no—
1003C2—3441no—
1004C2—1721no—
1005C2—1721no—
1006C2#1913718411yescharacteristic
1007C2#1914313911yescharacteristic
1008C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radical#19147980C2
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#21858
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143157C2semidirect
3. #19137088C2semidirect
4. #19135574C2semidirect
5. #19135570C2semidirect
6. #19135425C2semidirect
7. #19135421C2semidirect
8. #19134896C2semidirect
9. #19134896C2semidirect
10. #19134894C2semidirect
11. #19134894C2semidirect
12. #19134616C2semidirect
13. #19134615C2semidirect
14. #19134612C2semidirect
15. C43×#1806C2semidirect
18. #14583521C4semidirect
19. #14583521C4semidirect
20. #14583514C4semidirect
21. #14583514C4semidirect
22. #14583507C4semidirect
23. #14583507C4semidirect
24. #14583500C4semidirect
25. #14583500C4semidirect
510. #1806D43semidirect
579. C43#21858semidirect

Maximal subgroups

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

subgroupindex
#191479802
#191431572
#191370882
#191355742
#191355702
#191354252
#191354212
#191348962
#191348942
#191346162
#191346152
#191346122
C43×#18062
#2185843