Finite Group Databasebeta

← #25113500

Subgroups — #25113500

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148192C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3#19137067C211yesmaximal, characteristic, complemented
4#19135515C211yesmaximal, characteristic, complemented
5#19135512C211yesmaximal, characteristic, complemented
6#19135512C211yesmaximal, characteristic, complemented
7#19135425C211yesmaximal, characteristic, complemented
8#19135421C211yesmaximal, characteristic, complemented
9#19134613C211yesmaximal, characteristic, complemented
10#19134613C211yesmaximal, characteristic, complemented
11#19134612C211yesmaximal, characteristic, complemented
12#19134407C211yesmaximal, characteristic, complemented
13#19134406C211yesmaximal, characteristic, complemented
14#104×Dic43C211yesmaximal, characteristic, complemented
15C43×#1963C211yesmaximal, characteristic, complemented
16#14583635C411yescharacteristic, complemented
17#14583631C411yescharacteristic, complemented
18#14583631C411yescharacteristic, complemented
19#14583624C411yescharacteristic, complemented
20#14583623C411yescharacteristic, complemented
21#14583618C411yescharacteristic, complemented
22#14583618C411yescharacteristic, complemented
23#14583601—21no—
24#14583592—21no—
25#14583592—21no—
26#14583569C411yescharacteristic, complemented
27#14583555—21no—
28#14583445C2211yescharacteristic
29#14583445C2211yescharacteristic
30#14583431—21no—
31#14583429—21no—
32#14583429—21no—
33#41×Dic43C2211yescharacteristic
34#41×Dic43C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36C4×#10621900—21no—
37C2×C4×Dic86C2211yescharacteristic
38#14583028—21no—
39#14583028—21no—
40#14583026—21no—
41#14583023—21no—
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×#13063253C2211yescharacteristic
45C2×#13063253C2211yescharacteristic
46C2×#13063252C2211yescharacteristic
47C2×#13063252C2211yescharacteristic
48C2×#13063252C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063251C2211yescharacteristic
51C2×#13063251C2211yescharacteristic
52C4×#10621877C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55#14582803—21no—
56#14582796—21no—
57#14582786—21no—
58#14582782—21no—
59C4×Dic43⋊C4C2211yescharacteristic
60C4×Dic43⋊C4C2211yescharacteristic
61C4×C4⋊Dic43C2211yescharacteristic
62#14582745C2211yescharacteristic
63C42×Dic43C2211yescharacteristic
64#14582660C2211yescharacteristic
65#14582660C2211yescharacteristic
66#14582659C2211yescharacteristic
67#14582659C2211yescharacteristic
68C43×#532C2211yescharacteristic
69C43×#423C2211yescharacteristic
70C2×#104×C43C2211yescharacteristic
71C2×#104×C43C2211yescharacteristic
72C2×#104×C43C2211yescharacteristic
73C2×#104×C43C2211yescharacteristic
74C43×#376C2211yescharacteristic
75C2×#10621898C2311yescharacteristic
76C2×#10621900—21no—
77C22×Dic86D411yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80#13063323C2×C411yescharacteristic
81#13063323C2×C411yescharacteristic
82#13063321C2×C411yescharacteristic
83#13063321C2×C411yescharacteristic
84#13063320—21no—
85#13063320—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063316—21no—
91#13063315—21no—
92#13063315—21no—
93#13063314C2×C411yescharacteristic
94#13063314C2×C411yescharacteristic
95#13063312—21no—
96#13063312C2×C411yescharacteristic
97#13063312C2×C411yescharacteristic
98#13063311—21no—
99#13063311—21no—
100#13063309—21no—
101#13063309—21no—
102#13063307—21no—
103#13063307—21no—
104#13063306—21no—
105#13063306—21no—
106#13063305—21no—
107#13063302—21no—
108#13063302—21no—
109#13063297—21no—
110#13063297—21no—
111#13063297—21no—
112#13063297—21no—
113#13063297—21no—
114#13063297—21no—
115#13063296—21no—
116Q8×Dic43C2×C411yescharacteristic
117Q8×Dic43C2×C411yescharacteristic
118Q8×Dic43C2×C411yescharacteristic
119Q8×Dic43C2×C411yescharacteristic
120C4×Dic86C2×C411yescharacteristic
121C4×Dic86C2×C411yescharacteristic
122C4×Dic86C2×C411yescharacteristic
123C4×Dic86C2×C411yescharacteristic
124C4×Dic86C2×C411yescharacteristic
125C4×Dic86C2×C411yescharacteristic
126C4×Dic86D411yescharacteristic
127C4×Dic86D411yescharacteristic
128C4×Dic86D411yescharacteristic
129C4×Dic86D411yescharacteristic
130#13063290—21no—
131C4×D172C2×C411yescharacteristic
132C4×D172C2×C411yescharacteristic
133D4×Dic43—21no—
134D4×Dic43—21no—
135D4×Dic43—21no—
136D4×Dic43—21no—
137D4×Dic43—21no—
138D4×Dic43C2×C411yescharacteristic
139D4×Dic43C2×C411yescharacteristic
140D4×Dic43C2×C411yescharacteristic
141D4×Dic43C2×C411yescharacteristic
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
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#13063284—21no—
152#13063284C2311yescharacteristic
153#13063283—21no—
154#13063282—21no—
155#13063281—21no—
156#13063281—21no—
157C2×C4⋊Dic43—21no—
158C2×C4⋊Dic43D411yescharacteristic
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C2×Dic43⋊C4D411yescharacteristic
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169C2×C4×Dic43C2311yescharacteristic
170C2×C4×Dic43C2311yescharacteristic
171C42×D43—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176#13063253—22no—
177#13063253—22no—
178#13063252—22no—
179#13063252—22no—
180#13063252—41no—
181#13063252—41no—
182#13063251—41no—
183#13063251—41no—
184#13063236—21no—
185#13063235—21no—
186#13063235—21no—
187C4×C43⋊C8—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
196C2×#41×C43C2311yescharacteristic
197C2×M16×C43C2311yescharacteristic
198C2×M16×C43C2311yescharacteristic
199C4⋊Q8×C43C2×C411yescharacteristic
200#127×C43C2×C411yescharacteristic
201#124×C43C2×C411yescharacteristic
202#124×C43C2×C411yescharacteristic
203#121×C43—21no—
204#121×C43—21no—
205C4×D4×C43—21no—
206C4×D4×C43—21no—
207C2×C42×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209C2×C42×C43C2311yescharacteristic
210C4⋊C8×C43—21no—
211C4⋊C8×C43—21no—
212#104×C43—22no—
213#104×C43—22no—
214#104×C43—41no—
215#104×C43—41no—
216#95×C43—21no—
217#95×C43—21no—
218#41×C43—21no—
219#41×C43—21no—
220#41×C43—21no—
221#41×C43—21no—
222#41×C43—21no—
223#41×C43—21no—
224#41×C43—21no—
225#41×C43—21no—
226C2×Q8×C43C22×C411yescharacteristic
227C2×Q8×C43C22×C411yescharacteristic
228C2×D4×C43—21no—
229C2×D4×C43—21no—
230C2×D4×C43—21no—
231C2×D4×C43—21no—
232C2×D4×C43C22×C411yescharacteristic
233C2×D4×C43C22×C411yescharacteristic
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
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×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43C2×D411yescharacteristic
253C22×Dic43C2×D411yescharacteristic
254C22×Dic43C2×D411yescharacteristic
255C22×Dic43C2×D411yescharacteristic
256#10621900—44no—
257#10621898—21no—
258#10621898—21no—
259#10621898—21no—
260#10621898—21no—
261C2×D172C22×C411yescharacteristic
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×Dic86—42no—
266C2×Dic86C22⋊C411yescharacteristic
267C2×Dic86C22⋊C411yescharacteristic
268C2×Dic86C22⋊C411yescharacteristic
269C2×Dic86C22⋊C411yescharacteristic
270C2×Dic86C22×C411yescharacteristic
271M16×C43—21no—
272M16×C43—21no—
273M16×C43—21no—
274M16×C43—21no—
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C42×C43—21no—
284C42×C43—21no—
285C42×C43—21no—
286C42×C43C22×C411yescharacteristic
287C42×C43C22×C411yescharacteristic
288C42×C43C2×D411yescharacteristic
289C42×C43C2×D411yescharacteristic
290C42×C43#4112yescomplemented
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43—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—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—42no—
311C4⋊Dic43C22⋊C411yescharacteristic
312C4⋊Dic43C22⋊C411yescharacteristic
313C4⋊Dic43C22⋊C411yescharacteristic
314C4⋊Dic43C22⋊C411yescharacteristic
315C4⋊Dic43C22×C411yescharacteristic
316C4⋊Dic43C22×C411yescharacteristic
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—42no—
324Dic43⋊C4—42no—
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328Dic43⋊C4C22⋊C411yescharacteristic
329Dic43⋊C4C22⋊C411yescharacteristic
330Dic43⋊C4C22⋊C411yescharacteristic
331Dic43⋊C4C22⋊C411yescharacteristic
332Dic43⋊C4C22⋊C411yescharacteristic
333C4×Dic43—21no—
334C4×Dic43—21no—
335C4×Dic43—21no—
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—42no—
345C4×Dic43—42no—
346C4×Dic43C22×C411yescharacteristic
347C4×Dic43C22×C411yescharacteristic
348C4×Dic43C22×C411yescharacteristic
349C4×Dic43C22×C411yescharacteristic
350C4×Dic43C2×D411yescharacteristic
351C4×Dic43C2×D411yescharacteristic
352C4×Dic43C2×D411yescharacteristic
353C4×Dic43C2×D411yescharacteristic
354#10621877—21no—
355#10621877—21no—
356#10621877—21no—
357#10621877#4112yescomplemented
358C2×C43⋊C8—21no—
359C2×C43⋊C8—21no—
360C23×C43—21no—
361C23×C43—21no—
362C23×C43C22×D411yescharacteristic
363C22×D43—21no—
364Q8×C43—21no—
365Q8×C43—21no—
366Q8×C43—21no—
367Q8×C43—21no—
368D4×C43—21no—
369D4×C43—21no—
370D4×C43—21no—
371D4×C43—21no—
372D4×C43—42no—
373D4×C43—41no—
374D4×C43—41no—
375D4×C43—41no—
376D4×C43—41no—
377D4×C43—81no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—22no—
381C2×C4×C43—41no—
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—41no—
392C2×C4×C43C2×C22⋊C411yescharacteristic
393C2×C4×C43C2×C22⋊C411yescharacteristic
394C2×C4×C43C2×C22⋊C411yescharacteristic
395C2×C4×C43C2×C22⋊C411yescharacteristic
396C2×C4×C43C23×C411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C2×#4111yescharacteristic
399C2×C4×C43C2×#4111yescharacteristic
400C2×C4×C43H(5,𝔽2)11yescharacteristic
401C2×C4×C432−1+411yescharacteristic
402C22⋊D43—42no—
403C22⋊D43—41no—
404C22⋊D43—41no—
405C22⋊D43—42no—
406C22⋊D43—81no—
407C22⋊D43—81no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—21no—
411C2×Dic43—21no—
412C2×Dic43—21no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—42no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—42no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—81no—
424C2×Dic43—81no—
425C2×Dic43C2×C22⋊C411yescharacteristic
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428C2×Dic43C2×C22⋊C411yescharacteristic
429C2×Dic43C2×C22⋊C411yescharacteristic
430C2×Dic43C2×C22⋊C411yescharacteristic
431C2×Dic43C2×C22⋊C411yescharacteristic
432C2×Dic43C2×C22⋊C411yescharacteristic
433D172—21no—
434D172—21no—
435C4×D43—42no—
436C4×D43—41no—
437C4×D43—41no—
438C4×D43—81no—
439Dic86—22no—
440Dic86—22no—
441Dic86—21no—
442Dic86—21no—
443Dic86—41no—
444Dic86—41no—
445C8×C43—41no—
446C8×C43—41no—
447C43⋊C8—22no—
448C43⋊C8—41no—
449#22551—431nomaximal, Sylow
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43C22×C22⋊C411yescharacteristic
459C22×C43#54811yescharacteristic
460C22×C43#55011yescharacteristic
461C2×D43—41no—
462C2×D43—41no—
463C2×D43—41no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—21no—
468C4×C43—42no—
469C4×C43—41no—
470C4×C43—41no—
471C4×C43—81no—
472C4×C43C4×#4111yescharacteristic
473C4×C43#52011yescharacteristic
474C4×C43#54811yescharacteristic
475C4×C43#55011yescharacteristic
476Dic43—21no—
477Dic43—21no—
478Dic43—21no—
479Dic43—21no—
480Dic43—21no—
481Dic43—21no—
482Dic43—21no—
483Dic43—42no—
484Dic43—41no—
485Dic43—41no—
486Dic43—41no—
487Dic43—81no—
488Dic43#42112yes—
489#3480—431no—
490Q8×M16—431no—
491#2295—431no—
492#1980—431no—
493#1980—431no—
494#1980—431no—
495#1963—431no—
496#1963D4311yescharacteristic, complemented
497#1962—431no—
498#1806—431no—
499#1806—431no—
500#1806—431no—
501#1759—431no—
502#1759—431no—
503C4×#104—431no—
504C2×C43—21no—
505C2×C43—21no—
506C2×C43—81no—
507C2×C43—81no—
508C2×C43#234111yescharacteristic
509C2×C43C2×#42111yescharacteristic
510C2×C43#290111yescharacteristic
511D43—81no—
512#559—431no—
513#559—431no—
514#559—431no—
515#557—431no—
516#556—431no—
517#556—431no—
518#556—431no—
519#553—861no—
520#553—861no—
521#553—861no—
522#550—431no—
523#548—861no—
524#532—431no—
525#532—431no—
526#532C2×D4311yescharacteristic
527#529—861no—
528#529—861no—
529#529—861no—
530C4×#41—431no—
531C4×#41—431no—
532C4×#41—431no—
533C4×#41—861no—
534C2×C4×Q8—431no—
535#446—861no—
536#446—861no—
537#446—861no—
538C8×Q8—861no—
539#423—431no—
540#423—431no—
541#423C2×D4311yescharacteristic
542C2×#104—431no—
543C2×#104—431no—
544C2×#104—431no—
545C2×#104—431no—
546C2×#104—431no—
547C2×#104—431no—
548C2×#104—431no—
549C2×#104—431no—
550C2×#104C2×D4311yescharacteristic
551C2×#104C2×D4311yescharacteristic
552C2×#104C2×D4311yescharacteristic
553C2×#104C2×D4311yescharacteristic
554C4×M16—431no—
555C4×M16—431no—
556C4×M16—431no—
557#391—861no—
558#389—861no—
559#387—861no—
560#387—861no—
561C4×C4⋊C4—431no—
562C4×C4⋊C4—431no—
563C4×C4⋊C4—431no—
564#376—431no—
565#376C2×D4311yescharacteristic
566C43—431no—
567#339—431no—
568#339—431no—
569#339—431no—
570#339—431no—
571C43#2255111yescharacteristic, complemented, Sylow
572C2×#41—431no—
573C2×#41—861no—
574C2×#41C22×D4311yescharacteristic
575C2×#41C22×D4311yescharacteristic
576C22×Q8—431no—
577C2×M16—431no—
578C2×M16—431no—
579C2×M16C22×D4311yescharacteristic
580C2×M16C22×D4311yescharacteristic
581C4⋊Q8—431no—
582C4⋊Q8—431no—
583C4⋊Q8C4×D4311yescharacteristic
584#127—431no—
585#127—431no—
586#127C4×D4311yescharacteristic
587#126—861no—
588#126—861no—
589#126—861no—
590#126—861no—
591#126—861no—
592#126—861no—
593#125—861no—
594#125—861no—
595#125—861no—
596#124—431no—
597#124—431no—
598#124—431no—
599#124—431no—
600#124—861no—
601#124—861no—
602#124—861no—
603#124C4×D4311yescharacteristic
604#124C4×D4311yescharacteristic
605#123—861no—
606#123—861no—
607#123—861no—
608#123—861no—
609#123—861no—
610#123—861no—
611C22⋊Q8—861no—
612C22⋊Q8—861no—
613C22⋊Q8—861no—
614#121—21no—
615#121—21no—
616#121—861no—
617#121—861no—
618#121—861no—
619#121—861no—
620#121—861no—
621#121—861no—
622#121—861no—
623C4×Q8—431no—
624C4×Q8—431no—
625C4×Q8—431no—
626C4×Q8—431no—
627C4×Q8—431no—
628C4×Q8—431no—
629C4×Q8—431no—
630C4×Q8—431no—
631C4×Q8—431no—
632C4×Q8—431no—
633C4×Q8—431no—
634C4×Q8—431no—
635C4×Q8—431no—
636C4×Q8—431no—
637C4×Q8—861no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—431no—
641C4×D4—431no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—431no—
645C4×D4—431no—
646C4×D4—861no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652C4×D4—861no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659#117—431no—
660#117—861no—
661#117—861no—
662#117—861no—
663#117—861no—
664#117—861no—
665#117—861no—
666C2×C4⋊C4—431no—
667C2×C4⋊C4—431no—
668C2×C4⋊C4—431no—
669C2×C4⋊C4—861no—
670C2×C4⋊C4—861no—
671C2×C4⋊C4—861no—
672C2×C42—431no—
673C2×C42—431no—
674C2×C42—431no—
675C2×C42—431no—
676C2×C42—861no—
677C2×C42—861no—
678C2×C42—861no—
679C2×C42—861no—
680C2×C42—861no—
681C2×C42C22×D4311yescharacteristic
682C2×C42C22×D4311yescharacteristic
683C2×C42C22×D4311yescharacteristic
684C4⋊C8—21no—
685C4⋊C8—21no—
686C4⋊C8—861no—
687C4⋊C8—861no—
688C4⋊C8—861no—
689C4⋊C8—861no—
690#104—22no—
691#104—22no—
692#104—41no—
693#104—41no—
694#104—862no—
695#104—862no—
696#104—862no—
697#104—862no—
698#104—1721no—
699#104—1721no—
700#104—1721no—
701#104—1721no—
702#97—861no—
703#97—861no—
704#97—861no—
705C4×C8—861no—
706C4×C8—861no—
707C4×C8—861no—
708#95—21no—
709#95—21no—
710#95—861no—
711#95—861no—
712#95—861no—
713#95—861no—
714#95—861no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—861no—
724#41—861no—
725#41—861no—
726#41—861no—
727#41—1724no—
728C2×Q8—431no—
729C2×Q8—431no—
730C2×Q8—431no—
731C2×Q8—431no—
732C2×Q8—431no—
733C2×Q8—1722no—
734C2×Q8C2×C4×D4311yescharacteristic
735C2×Q8C2×C4×D4311yescharacteristic
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—431no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4C2×C4×D4311yescharacteristic
747C2×D4C2×C4×D4311yescharacteristic
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—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4D4×D4311yescharacteristic
766C22×C4D4×D4311yescharacteristic
767C22×C4C23×D4311yescharacteristic
768M16—21no—
769M16—21no—
770M16—21no—
771M16—21no—
772M16—432no—
773M16—861no—
774M16—861no—
775M16—861no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—861no—
779C2×C8—861no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—431no—
783C4⋊C4—431no—
784C4⋊C4—431no—
785C4⋊C4—431no—
786C4⋊C4—431no—
787C4⋊C4—431no—
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—861no—
797C4⋊C4—861no—
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—1722no—
807C4⋊C4—1722no—
808C4⋊C4—1722no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C22⋊C4—861no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C42—21no—
829C42—21no—
830C42—21no—
831C42—431no—
832C42—431no—
833C42—431no—
834C42—431no—
835C42—431no—
836C42—431no—
837C42—431no—
838C42—431no—
839C42—861no—
840C42—861no—
841C42—861no—
842C42—861no—
843C42—861no—
844C42—861no—
845C42—861no—
846C42—861no—
847C42—861no—
848C42—861no—
849C42—861no—
850C42—1722no—
851C42—1722no—
852C42C2×C4×D4311yescharacteristic
853C42C2×C4×D4311yescharacteristic
854C42D4×D4311yescharacteristic
855C42D4×D4311yescharacteristic
856C42#1062190012yescomplemented
857C23—21no—
858C23—21no—
859C23—861no—
860C23C2×D4×D4311yescharacteristic
861Q8—21no—
862Q8—21no—
863Q8—21no—
864Q8—21no—
865Q8—862no—
866Q8—862no—
867Q8—861no—
868Q8—861no—
869Q8—1721no—
870Q8—1721no—
871D4—21no—
872D4—21no—
873D4—21no—
874D4—21no—
875D4—42no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—81no—
881D4—861no—
882D4—861no—
883D4—3441no—
884D4—3441no—
885D4—1722no—
886D4—1722no—
887D4—1721no—
888D4—1721no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—431no—
904C2×C4—431no—
905C2×C4—431no—
906C2×C4—431no—
907C2×C4—431no—
908C2×C4—431no—
909C2×C4—431no—
910C2×C4—431no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—861no—
914C2×C4—861no—
915C2×C4—861no—
916C2×C4—3441no—
917C2×C4—3441no—
918C2×C4—3441no—
919C2×C4—1722no—
920C2×C4—1722no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1722no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4C22⋊C4×D4311yescharacteristic
933C2×C4C22⋊C4×D4311yescharacteristic
934C2×C4C22⋊C4×D4311yescharacteristic
935C2×C4C22⋊C4×D4311yescharacteristic
936C2×C4C22×C4×D4311yescharacteristic
937C2×C4C2×D4×D4311yescharacteristic
938C2×C4#41×D4311yescharacteristic
939C2×C4C2×#1062190011yescharacteristic
940C2×C4#1306337011yescharacteristic
941C2×C4#1306337211yescharacteristic
942C8—41no—
943C8—41no—
944C8—862no—
945C8—1721no—
946C22—21no—
947C22—21no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—1721no—
955C22—1721no—
956C22—1721no—
957C22C2×C22⋊C4×D4311yescharacteristic
958C22#1458355511yescharacteristic
959C22#1458356711yescharacteristic
960C4—21no—
961C4—21no—
962C4—21no—
963C4—21no—
964C4—42no—
965C4—41no—
966C4—41no—
967C4—81no—
968C4—432no—
969C4—861no—
970C4—861no—
971C4—861no—
972C4—861no—
973C4—861no—
974C4—861no—
975C4—861no—
976C4—3441no—
977C4—1722no—
978C4—1721no—
979C4—1721no—
980C4—1721no—
981C4C4×#1062190011yescharacteristic
982C4#1458337811yescharacteristic
983C4#1458355711yescharacteristic
984C4#1458356911yescharacteristic
985C2—21no—
986C2—21no—
987C2—81no—
988C2—81no—
989C2—3441no—
990C2#1913743411yescharacteristic
991C2#421×D4311yescharacteristic
992C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1963C2
socleC22×C43C22×C22⋊C4
prime radical#19148192C2
cosocleC22×C4×C43C24
hypercenter#1963D43
hypocenterC43#22551
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
3. #19137067C2semidirect
4. #19135515C2semidirect
5. #19135512C2semidirect
6. #19135512C2semidirect
7. #19135425C2semidirect
8. #19135421C2semidirect
9. #19134613C2semidirect
10. #19134613C2semidirect
11. #19134612C2semidirect
12. #19134407C2semidirect
13. #19134406C2semidirect
14. #104×Dic43C2semidirect
15. C43×#1963C2semidirect
16. #14583635C4semidirect
17. #14583631C4semidirect
18. #14583631C4semidirect
19. #14583624C4semidirect
20. #14583623C4semidirect
21. #14583618C4semidirect
22. #14583618C4semidirect
26. #14583569C4semidirect
290. C42×C43#41semidirect
357. #10621877#41semidirect
496. #1963D43semidirect
571. C43#22551semidirect
856. C42#10621900semidirect

Maximal subgroups

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

subgroupindex
#191481922
#191435462
#191370672
#191355152
#191355122
#191354252
#191354212
#191346132
#191346122
#191344072
#191344062
#104×Dic432
C43×#19632
#2255143