Finite Group Databasebeta

← #25106614

Subgroups — #25106614

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147980C211yesmaximal, characteristic
2#19143232C211yesmaximal, characteristic, complemented
3#19137075C211yesmaximal, characteristic, complemented
4#19135537C211yesmaximal, characteristic, complemented
5#19135537C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135512C211yesmaximal, characteristic, complemented
8#19135042C211yesmaximal, characteristic, complemented
9#19135040C211yesmaximal, characteristic, complemented
10#19135037C211yesmaximal, characteristic, complemented
11#19135035C211yesmaximal, characteristic, complemented
12#19134616C211yesmaximal, characteristic, complemented
13#19134615C211yesmaximal, characteristic, complemented
14#19134612C211yesmaximal, characteristic, complemented
15C43×#1806C211yesmaximal, characteristic, complemented
16#14583521C411yescharacteristic, complemented
17#14583521C411yescharacteristic, complemented
18#14583514C411yescharacteristic, complemented
19#14583514C411yescharacteristic, complemented
20#14583507C411yescharacteristic, complemented
21#14583507C411yescharacteristic, complemented
22#14583500C411yescharacteristic, complemented
23#14583500C411yescharacteristic, complemented
24#14583491—21no—
25#14583491—21no—
26#14583482—21no—
27#14583482—21no—
28#14583452C2211yescharacteristic
29#14583445C2211yescharacteristic
30#14583433—21no—
31#14583433—21no—
32#14583427—21no—
33#14583427—21no—
34#14583411C2211yescharacteristic
35#14583406C2211yescharacteristic
36C4×#10621898C2211yescharacteristic
37C2×#13063282C2211yescharacteristic
38C2×#13063282C2211yescharacteristic
39C2×C42×D43C2211yescharacteristic
40#14582959—21no—
41#14582959—21no—
42#14582959—21no—
43#14582959—21no—
44#14582923C2211yescharacteristic
45C2×#13063253C2211yescharacteristic
46C2×#13063253C2211yescharacteristic
47C2×#13063252C2211yescharacteristic
48C2×#13063252C2211yescharacteristic
49C2×#13063251C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51#14582862C2211yescharacteristic
52#14582862C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55#14582796—21no—
56#14582794—21no—
57#14582773—21no—
58#14582770—21no—
59C4×Dic43⋊C4C2211yescharacteristic
60C4×Dic43⋊C4C2211yescharacteristic
61C4×C4⋊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×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80#13063324C2×C411yescharacteristic, complemented
81#13063324C2×C411yescharacteristic, complemented
82#13063323C2×C411yescharacteristic, complemented
83#13063321C2×C411yescharacteristic, complemented
84#13063320—21no—
85#13063320—21no—
86#13063319—21no—
87#13063319—21no—
88#13063319—21no—
89#13063319—21no—
90#13063318—21no—
91#13063318—21no—
92#13063317—21no—
93#13063317—21no—
94#13063316C2×C411yescharacteristic, complemented
95#13063316C2×C411yescharacteristic, complemented
96#13063315—21no—
97#13063315—21no—
98#13063314C2×C411yescharacteristic, complemented
99#13063313—21no—
100#13063313—21no—
101#13063312C2×C411yescharacteristic, complemented
102#13063311—21no—
103#13063311—21no—
104#13063310—21no—
105#13063310—21no—
106#13063309—21no—
107#13063308—21no—
108#13063308—21no—
109#13063308—21no—
110#13063308—21no—
111#13063307—21no—
112#13063307—21no—
113#13063306—21no—
114#13063305C2×C411yescharacteristic
115#13063305C2×C411yescharacteristic
116#13063304—21no—
117#13063304—21no—
118#13063303—21no—
119#13063303—21no—
120#13063302—21no—
121#13063302—21no—
122#13063301C2×C411yescharacteristic
123#13063301C2×C411yescharacteristic
124#13063300C2×C411yescharacteristic
125#13063300C2×C411yescharacteristic
126#13063299—21no—
127#13063299—21no—
128#13063298—21no—
129#13063298—21no—
130#13063297—21no—
131#13063297—21no—
132#13063296C2×C411yescharacteristic
133#13063296C2×C411yescharacteristic
134#13063295—21no—
135#13063293—21no—
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86C2×C411yescharacteristic, complemented
139C4×Dic86C2×C411yescharacteristic, complemented
140C4×D172—21no—
141C4×D172—21no—
142C4×D172C2×C411yescharacteristic, complemented
143C4×D172C2×C411yescharacteristic, complemented
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150#13063284C2311yescharacteristic
151#13063282—21no—
152#13063282—41no—
153#13063282—41no—
154#13063282C2×C411yescharacteristic
155#13063282C2×C411yescharacteristic
156#13063282C2×C411yescharacteristic
157#13063282C2×C411yescharacteristic
158#13063282D411yescharacteristic
159#13063282D411yescharacteristic
160#13063282D411yescharacteristic
161#13063282D411yescharacteristic
162C2×C4⋊Dic43—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C2×Dic43⋊C4—21no—
166C2×Dic43⋊C4D411yescharacteristic
167C2×Dic43⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4D411yescharacteristic
170C2×(C2×D43)⋊C4D411yescharacteristic
171C2×C4×Dic43—21no—
172C2×C4×Dic43C2311yescharacteristic
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2311yescharacteristic
175C42×D43—21no—
176C42×D43—41no—
177C42×D43—41no—
178C4⋊(C43⋊C8)—21no—
179C4⋊(C43⋊C8)—21no—
180#13063253—41no—
181#13063253—41no—
182#13063252—41no—
183#13063252—41no—
184#13063251—41no—
185#13063251—41no—
186(C2×D43)⋊C8—21no—
187(C2×D43)⋊C8—21no—
188(C2×D43)⋊C8—21no—
189(C2×D43)⋊C8—21no—
190#13063235—21no—
191#13063235—21no—
192C8×Dic43—21no—
193C8×Dic43—21no—
194C43⋊#95—21no—
195C43⋊#95—21no—
196C43⋊#95—21no—
197C2×#41×C43C2311yescharacteristic
198C2×M16×C43C2311yescharacteristic
199C2×M16×C43C2311yescharacteristic
200C4×Q8×C43C2×C411yescharacteristic, complemented
201C4×Q8×C43C2×C411yescharacteristic, complemented
202C4×D4×C43—21no—
203C4×D4×C43—21no—
204C4×D4×C43C2×C411yescharacteristic, complemented
205C4×D4×C43C2×C411yescharacteristic, complemented
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×D43—42no—
259C2×C4×D43—42no—
260C2×C4×D43—42no—
261C2×C4×D43C22×C411yescharacteristic
262C2×C4×D43C22×C411yescharacteristic
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×Dic86—21no—
266C2×Dic86—21no—
267C2×Dic86C22×C411yescharacteristic
268M16×C43—21no—
269M16×C43—21no—
270M16×C43—21no—
271M16×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—42no—
277C4⋊C4×C43C22×C411yescharacteristic
278C4⋊C4×C43C22×C411yescharacteristic
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43—21no—
285C42×C43—21no—
286C42×C43—21no—
287C42×C43—21no—
288C42×C43—21no—
289C42×C43C22×C411yescharacteristic
290C42×C43C22×C411yescharacteristic
291C42×C43C2×D411yescharacteristic
292C42×C43C2×D411yescharacteristic
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—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—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—42no—
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
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316(C2×D43)⋊C4C22⋊C411yescharacteristic
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43—21no—
320C4⋊Dic43—21no—
321C4⋊Dic43—42no—
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—
336Dic43⋊C4—42no—
337Dic43⋊C4C22⋊C411yescharacteristic
338Dic43⋊C4C22⋊C411yescharacteristic
339Dic43⋊C4C22⋊C411yescharacteristic
340Dic43⋊C4C22⋊C411yescharacteristic
341Dic43⋊C4C22⋊C411yescharacteristic
342Dic43⋊C4C22⋊C411yescharacteristic
343Dic43⋊C4C22⋊C411yescharacteristic
344Dic43⋊C4C22⋊C411yescharacteristic
345C4×Dic43—21no—
346C4×Dic43—21no—
347C4×Dic43—21no—
348C4×Dic43—21no—
349C4×Dic43—21no—
350C4×Dic43—21no—
351C4×Dic43—21no—
352C4×Dic43—42no—
353C4×Dic43C22×C411yescharacteristic
354C4×Dic43C22×C411yescharacteristic
355C4×Dic43C2×D411yescharacteristic
356C4×Dic43C2×D411yescharacteristic
357#10621877—21no—
358#10621877—21no—
359#10621877—21no—
360#10621877—21no—
361C2×C43⋊C8—21no—
362C2×C43⋊C8—21no—
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—48no—
441C4×D43—41no—
442C4×D43—41no—
443C4×D43—81no—
444C4×D43—81no—
445Dic86—21no—
446Dic86—21no—
447Dic86—81no—
448Dic86—81no—
449C8×C43—41no—
450C8×C43—41no—
451C43⋊C8—41no—
452C43⋊C8—41no—
453#21901—431nomaximal, Sylow
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43C22×C22⋊C411yescharacteristic
460C22×C43#53511yescharacteristic
461C22×C43#53611yescharacteristic
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—42no—
469C2×D43—42no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—41no—
473C4×C43—21no—
474C4×C43—21no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—42no—
478C4×C43—41no—
479C4×C43—41no—
480C4×C43—41no—
481C4×C43—81no—
482C4×C43#52011yescharacteristic
483C4×C43#52011yescharacteristic
484C4×C43#53711yescharacteristic
485C4×C43#53711yescharacteristic
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—21no—
490Dic43—21no—
491Dic43—21no—
492Dic43—42no—
493Dic43—41no—
494Dic43—41no—
495Dic43—41no—
496Dic43—81no—
497#3455—431no—
498#2921—431no—
499#2296—431no—
500#1986—431no—
501#1986—431no—
502#1980—431no—
503#1980—431no—
504#1897—431no—
505#1897—431no—
506#1896—431no—
507#1896—431no—
508#1806—431no—
509#1806—431no—
510#1806—431no—
511#1806D4311yescharacteristic, complemented
512C2×C43—21no—
513C2×C43—21no—
514C2×C43—81no—
515C2×C43#231111yescharacteristic
516C2×C43#290111yescharacteristic
517C2×C43#290111yescharacteristic
518D43—41no—
519D43—41no—
520D43—81no—
521#542—431no—
522#542—431no—
523#542—431no—
524#542—431no—
525#541—431no—
526#541—431no—
527#540—431no—
528#540—431no—
529#539—861no—
530#539—861no—
531#538—861no—
532#538—861no—
533#533—431no—
534#532—431no—
535#529—861no—
536#529—861no—
537#529—861no—
538#529—861no—
539#525—431no—
540#525—431no—
541C4×#41—431no—
542C4×#41C2×D4311yescharacteristic
543C2×#117—431no—
544C2×#117—431no—
545C22×C42—431no—
546#433—861no—
547#433—861no—
548#433—861no—
549#433—861no—
550#423—431no—
551#423C2×D4311yescharacteristic
552C2×#104—431no—
553C2×#104—431no—
554C2×#104—431no—
555C2×#104—431no—
556C2×#104—431no—
557C2×#104—431no—
558C2×#104C2×D4311yescharacteristic
559C2×#104C2×D4311yescharacteristic
560#407—431no—
561#407—431no—
562C4×M16—431no—
563C4×M16—431no—
564#389—861no—
565#389—861no—
566#385—861no—
567#385—861no—
568C4×C4⋊C4—431no—
569C4×C4⋊C4—431no—
570C4×C4⋊C4—431no—
571C4×C4⋊C4C2×D4311yescharacteristic
572#339—431no—
573#339—431no—
574#339—431no—
575#339—431no—
576#339—431no—
577#339—431no—
578#339C2×D4311yescharacteristic
579#339C2×D4311yescharacteristic
580C43#2190111yescharacteristic, complemented, Sylow
581C2×#41—431no—
582C2×#41C22×D4311yescharacteristic
583C23×C4—431no—
584C23×C4—861no—
585C2×M16—431no—
586C2×M16—431no—
587C2×M16C22×D4311yescharacteristic
588C2×M16C22×D4311yescharacteristic
589C4⋊Q8—431no—
590C4⋊Q8—431no—
591C4⋊Q8—431no—
592#127—431no—
593#126—861no—
594#126—861no—
595#126—861no—
596#126—861no—
597#126—861no—
598#126—861no—
599#126—861no—
600#126—861no—
601#125—431no—
602#125—431no—
603#125—861no—
604#125—861no—
605#125—861no—
606#125—861no—
607#124—431no—
608#124—431no—
609#124—861no—
610#124—861no—
611#124—861no—
612#124—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616#123—861no—
617#123—861no—
618#123—861no—
619#123—861no—
620#123—861no—
621#123—861no—
622#123—861no—
623C22⋊Q8—431no—
624C22⋊Q8—431no—
625C22⋊Q8—431no—
626C22⋊Q8—431no—
627C22⋊Q8—861no—
628C22⋊Q8—861no—
629C22⋊Q8—861no—
630C22⋊Q8—861no—
631C22⋊Q8—861no—
632C22⋊Q8—861no—
633#121—431no—
634#121—431no—
635#121—431no—
636#121—431no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#120—861no—
644#120—861no—
645C4×Q8—431no—
646C4×Q8—431no—
647C4×Q8—861no—
648C4×Q8—861no—
649C4×Q8C4×D4311yescharacteristic, complemented
650C4×Q8C4×D4311yescharacteristic, complemented
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—431no—
654C4×D4—431no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659C4×D4—861no—
660C4×D4—861no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4C4×D4311yescharacteristic, complemented
664C4×D4C4×D4311yescharacteristic, complemented
665#117—21no—
666#117—431no—
667#117—431no—
668#117—431no—
669#117—431no—
670#117—431no—
671#117—431no—
672#117—431no—
673#117—431no—
674#117—431no—
675#117—861no—
676#117—1721no—
677#117—1721no—
678#117C22×D4311yescharacteristic
679C2×C4⋊C4—21no—
680C2×C4⋊C4—431no—
681C2×C4⋊C4—431no—
682C2×C4⋊C4—861no—
683C2×C4⋊C4—861no—
684C2×C4⋊C4—861no—
685C2×C4⋊C4—861no—
686C2×C22⋊C4—431no—
687C2×C22⋊C4—431no—
688C2×C22⋊C4—861no—
689C2×C42—21no—
690C2×C42—431no—
691C2×C42—431no—
692C2×C42—431no—
693C2×C42—861no—
694C2×C42—861no—
695C2×C42—1721no—
696C2×C42—1721no—
697C2×C42C22×D4311yescharacteristic
698C2×C42C22×D4311yescharacteristic
699C2×C42C22×D4311yescharacteristic
700C4⋊C8—21no—
701C4⋊C8—21no—
702C4⋊C8—861no—
703C4⋊C8—861no—
704#104—41no—
705#104—41no—
706#104—1721no—
707#104—1721no—
708#104—1721no—
709#104—1721no—
710#104—1721no—
711#104—1721no—
712C22⋊C8—861no—
713C22⋊C8—861no—
714C22⋊C8—861no—
715C22⋊C8—861no—
716#97—861no—
717#97—861no—
718C4×C8—861no—
719C4×C8—861no—
720#95—21no—
721#95—861no—
722#95—861no—
723#95—861no—
724C24—431no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—861no—
730#41—861no—
731#41—861no—
732#41—861no—
733C2×Q8—431no—
734C2×Q8—861no—
735C2×Q8—861no—
736C2×Q8C2×C4×D4311yescharacteristic
737C2×D4—21no—
738C2×D4—431no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4C2×C4×D4311yescharacteristic
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—431no—
753C22×C4—431no—
754C22×C4—431no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
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×C4—861no—
768C22×C4—1722no—
769C22×C4—1722no—
770C22×C4—1722no—
771C22×C4D4×D4311yescharacteristic
772C22×C4D4×D4311yescharacteristic
773C22×C4C23×D4311yescharacteristic
774M16—21no—
775M16—21no—
776M16—21no—
777M16—21no—
778M16—861no—
779M16—861no—
780M16—861no—
781M16—861no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—861no—
785C2×C8—861no—
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⋊C4—1722no—
815C4⋊C4—1722no—
816C4⋊C4—1722no—
817C4⋊C4C2×C4×D4311yescharacteristic
818C4⋊C4C2×C4×D4311yescharacteristic
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
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—861no—
844C22⋊C4—861no—
845C22⋊C4—1722no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—21no—
850C42—21no—
851C42—21no—
852C42—21no—
853C42—431no—
854C42—431no—
855C42—431no—
856C42—431no—
857C42—861no—
858C42—861no—
859C42—861no—
860C42—861no—
861C42—861no—
862C42—861no—
863C42—861no—
864C42—1722no—
865C42C2×C4×D4311yescharacteristic
866C42C2×C4×D4311yescharacteristic
867C42D4×D4311yescharacteristic
868C42D4×D4311yescharacteristic
869C23—21no—
870C23—431no—
871C23—431no—
872C23—861no—
873C23—861no—
874C23—861no—
875C23—1721no—
876C23—1721no—
877C23C2×D4×D4311yescharacteristic
878Q8—21no—
879Q8—21no—
880Q8—861no—
881Q8—861no—
882Q8—3441no—
883Q8—3441no—
884D4—21no—
885D4—21no—
886D4—41no—
887D4—41no—
888D4—861no—
889D4—861no—
890D4—3441no—
891D4—3441no—
892D4—3441no—
893D4—3441no—
894D4—3441no—
895D4—3441no—
896D4—1721no—
897D4—1721no—
898C2×C4—22no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
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—41no—
911C2×C4—81no—
912C2×C4—81no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—431no—
918C2×C4—431no—
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—861no—
929C2×C4—862no—
930C2×C4—861no—
931C2×C4—861no—
932C2×C4—861no—
933C2×C4—3441no—
934C2×C4—3441no—
935C2×C4—1728no—
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×C4C22⋊C4×D4311yescharacteristic
949C2×C4C22×C4×D4311yescharacteristic
950C2×C4C2×D4×D4311yescharacteristic
951C2×C4#1306337011yescharacteristic
952C2×C4#1306337111yescharacteristic
953C2×C4#1306337211yescharacteristic
954C2×C4#1306337311yescharacteristic
955C8—41no—
956C8—41no—
957C8—1721no—
958C8—1721no—
959C22—21no—
960C22—21no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—861no—
969C22—861no—
970C22—1722no—
971C22—1722no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22C2×C22⋊C4×D4311yescharacteristic
976C22#1458346511yescharacteristic
977C22#1458347211yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—42no—
983C4—41no—
984C4—41no—
985C4—41no—
986C4—81no—
987C4—861no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—861no—
992C4—861no—
993C4—3441no—
994C4—1722no—
995C4—1721no—
996C4—1721no—
997C4—1721no—
998C4#1458337911yescharacteristic
999C4#1458338011yescharacteristic
1000C4#1458347811yescharacteristic
1001C4#1458347911yescharacteristic
1002C2—21no—
1003C2—21no—
1004C2—81no—
1005C2—3441no—
1006C2—1721no—
1007C2—1721no—
1008C2#1913718411yescharacteristic
1009C2#1914313911yescharacteristic
1010C2#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#21901
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. #19143232C2semidirect
3. #19137075C2semidirect
4. #19135537C2semidirect
5. #19135537C2semidirect
6. #19135512C2semidirect
7. #19135512C2semidirect
8. #19135042C2semidirect
9. #19135040C2semidirect
10. #19135037C2semidirect
11. #19135035C2semidirect
12. #19134616C2semidirect
13. #19134615C2semidirect
14. #19134612C2semidirect
15. C43×#1806C2semidirect
16. #14583521C4semidirect
17. #14583521C4semidirect
18. #14583514C4semidirect
19. #14583514C4semidirect
20. #14583507C4semidirect
21. #14583507C4semidirect
22. #14583500C4semidirect
23. #14583500C4semidirect
80. #13063324C2×C4semidirect
81. #13063324C2×C4semidirect
82. #13063323C2×C4semidirect
83. #13063321C2×C4semidirect
94. #13063316C2×C4semidirect
95. #13063316C2×C4semidirect
98. #13063314C2×C4semidirect
101. #13063312C2×C4semidirect
138. C4×Dic86C2×C4semidirect
139. C4×Dic86C2×C4semidirect
142. C4×D172C2×C4semidirect
143. C4×D172C2×C4semidirect
200. C4×Q8×C43C2×C4semidirect
201. C4×Q8×C43C2×C4semidirect
204. C4×D4×C43C2×C4semidirect
205. C4×D4×C43C2×C4semidirect
511. #1806D43semidirect
580. C43#21901semidirect
649. C4×Q8C4×D43semidirect
650. C4×Q8C4×D43semidirect
663. C4×D4C4×D43semidirect
664. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191479802
#191432322
#191370752
#191355372
#191355122
#191350422
#191350402
#191350372
#191350352
#191346162
#191346152
#191346122
C43×#18062
#2190143