Finite Group Databasebeta

← #25063444

Subgroups — #25063444

Order 11008.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148026C211yesmaximal, characteristic
2#19143714C211yesmaximal, characteristic, complemented
3#19143556C211yesmaximal, characteristic, complemented
4#19133061C211yesmaximal, characteristic, complemented
5#19133053C211yesmaximal, characteristic, complemented
6#19133050C211yesmaximal, characteristic, complemented
7#19133040C211yesmaximal, characteristic, complemented
8#19133033C211yesmaximal, characteristic, complemented
9#19133028C211yesmaximal, characteristic, complemented
10#19133022C211yesmaximal, characteristic, complemented
11#19133014C211yesmaximal, characteristic, complemented
12#19133007C211yesmaximal, characteristic, complemented
13#19133002C211yesmaximal, characteristic, complemented
14#19132996C211yesmaximal, characteristic, complemented
15C43×#1497C211yesmaximal, characteristic, complemented
16#14583526C411yescharacteristic
17#14583523C411yescharacteristic
18#14583522C411yescharacteristic
19#14583519—21no—
20#14583510C411yescharacteristic
21#14583509C411yescharacteristic
22#14583508—21no—
23#14583497—21no—
24#14583495—21no—
25#14583479C411yescharacteristic
26#14583474C411yescharacteristic
27#14583472C411yescharacteristic
28#14583453—21no—
29#14583453C2211yescharacteristic
30#14583436—21no—
31#14583436C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583427—21no—
34#14583427—21no—
35C4×#10621902C2211yescharacteristic
36C4×#10621898C2211yescharacteristic
37C4×Q8×D43C2211yescharacteristic
38#14583027—21no—
39#14583026—21no—
40#14582976—21no—
41#14582974—21no—
42#14582973—21no—
43#14582972—21no—
44#14582967—21no—
45#14582967—21no—
46#14582955C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49#14582950C2211yescharacteristic
50#14582923C2211yescharacteristic
51#14582921C2211yescharacteristic
52C4⋊C8×D43C2211yescharacteristic
53C4×#10621872C2211yescharacteristic
54C4×#10621872C2211yescharacteristic
55C2×C4×C43⋊C8C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58Q8⋊(C43⋊C8)C2211yescharacteristic
59Q8⋊(C43⋊C8)C2211yescharacteristic
60Q8⋊(C43⋊C8)C2211yescharacteristic
61Q8⋊(C43⋊C8)C2211yescharacteristic
62#14582629C2211yescharacteristic
63#14582629C2211yescharacteristic
64#14582628C2211yescharacteristic
65#14582628C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C43×#533C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×Q8⋊C8C2211yescharacteristic
74C43×Q8⋊C8C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×Q8×D43C2×C411yescharacteristic
78C2×#10621877—21no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C2×#10621872—21no—
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84#13063324—21no—
85#13063324C2×C411yescharacteristic
86#13063323—21no—
87#13063323C2×C411yescharacteristic
88#13063320—21no—
89#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063319—21no—
94#13063318—21no—
95#13063318—21no—
96#13063317C2×C411yescharacteristic
97#13063316—21no—
98#13063316C2×C411yescharacteristic
99#13063315—21no—
100#13063315—21no—
101#13063315—21no—
102#13063315—21no—
103#13063315—21no—
104#13063314—21no—
105#13063314C2×C411yescharacteristic
106#13063313C2×C411yescharacteristic
107#13063311—21no—
108#13063311—21no—
109#13063310—21no—
110#13063310—21no—
111#13063310—21no—
112#13063310—21no—
113#13063310—21no—
114#13063308—21no—
115#13063307—21no—
116#13063307—21no—
117#13063305—21no—
118#13063305C2×C411yescharacteristic
119#13063304C2×C411yescharacteristic
120#13063303—21no—
121#13063303—21no—
122#13063303—21no—
123#13063303—21no—
124#13063303—21no—
125#13063301—21no—
126#13063301—21no—
127#13063301C2×C411yescharacteristic
128#13063301C2×C411yescharacteristic
129#13063300—21no—
130#13063300C2×C411yescharacteristic
131#13063299C2×C411yescharacteristic
132#13063298—21no—
133#13063298—21no—
134Q8×Dic43C2×C411yescharacteristic
135Q8×Dic43C2×C411yescharacteristic
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86D411yescharacteristic
139C4×Dic86D411yescharacteristic
140C4×Dic86C2311yescharacteristic
141#13063290—21no—
142#13063290C2×C411yescharacteristic
143C4×D172—21no—
144C4×D172—21no—
145C4×D172D411yescharacteristic
146C4×D172D411yescharacteristic
147C4×D172C2311yescharacteristic
148#13063287—21no—
149#13063287C2×C411yescharacteristic
150C4×C22⋊D43—21no—
151C4×C22⋊D43D411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155#13063284C2×C411yescharacteristic
156#13063283—21no—
157#13063283C2×C411yescharacteristic
158#13063282—21no—
159#13063282—21no—
160#13063282—21no—
161#13063282C2×C411yescharacteristic
162#13063282C2×C411yescharacteristic
163C4⋊C4×D43—21no—
164C4⋊C4×D43C2×C411yescharacteristic
165C42×D43—21no—
166C42×D43—21no—
167C42×D43C2311yescharacteristic
168C42×D43C2311yescharacteristic
169C4⋊(C43⋊C8)—21no—
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063235—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8—21no—
184C4×C43⋊C8C2311yescharacteristic
185C4×C43⋊C8C2311yescharacteristic
186C8×Dic43—21no—
187C4⋊Q8×C43C2×C411yescharacteristic
188C4⋊Q8×C43C2×C411yescharacteristic
189#125×C43—21no—
190C22⋊Q8×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192C22⋊Q8×C43C2×C411yescharacteristic
193C4×Q8×C43—21no—
194C4×Q8×C43C2311yescharacteristic
195C4×Q8×C43C2311yescharacteristic
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#97×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C2×Q8×C43—21no—
207C2×Q8×C43C22×C411yescharacteristic
208C2×Q8×C43C22×C411yescharacteristic
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C2×C22⋊D43—21no—
213C2×C22⋊D43C22⋊C411yescharacteristic
214C2×C22⋊D43C22⋊C411yescharacteristic
215#10621902—42no—
216Q8×D43—42no—
217#10621898—42no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22⋊C411yescharacteristic
221C2×D172C22×C411yescharacteristic
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43C22×C411yescharacteristic
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86C22⋊C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43C22×C411yescharacteristic
249C4⋊C4×C43C22×C411yescharacteristic
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C42×C43—21no—
253C42×C43—21no—
254C42×C43C22×C411yescharacteristic
255C42×C43C2×D411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C42×C43C2411yescharacteristic
258C22⋊Dic43—21no—
259C22⋊Dic43C22⋊C411yescharacteristic
260C22⋊Dic43C22⋊C411yescharacteristic
261(C2×D43)⋊C4—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4C22⋊C411yescharacteristic
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275(C2×D43)⋊C4C22⋊C411yescharacteristic
276(C2×D43)⋊C4C22⋊C411yescharacteristic
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43C22⋊C411yescharacteristic
282C4⋊Dic43C22⋊C411yescharacteristic
283C4⋊Dic43C22×C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4C22⋊C411yescharacteristic
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301C4×Dic43—21no—
302C4×Dic43—21no—
303C4×Dic43—21no—
304C4×Dic43—21no—
305C4×Dic43—21no—
306C4×Dic43C22×C411yescharacteristic
307C4×Dic43C22×C411yescharacteristic
308C4×Dic43C2×D411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312#10621877—81no—
313C2×C43⋊C8—21no—
314C2×C43⋊C8—21no—
315C2×C43⋊C8—21no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—42no—
318#10621872—42no—
319#10621872—42no—
320#10621872—81no—
321C8×D43—81no—
322C23×C43C2×C22⋊C411yescharacteristic
323C22×D43—21no—
324C22×D43C2×C22⋊C411yescharacteristic
325C22×D43C2×C22⋊C411yescharacteristic
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—81no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—41no—
337C2×C4×C43C2×C22⋊C411yescharacteristic
338C2×C4×C43C2×C22⋊C411yescharacteristic
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C23×C411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C22⋊D43—41no—
344C22⋊D43—41no—
345C22⋊D43—81no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43C2×C22⋊C411yescharacteristic
350C2×Dic43C2×C22⋊C411yescharacteristic
351C2×Dic43C2×C22⋊C411yescharacteristic
352C2×Dic43C2×C22⋊C411yescharacteristic
353C2×Dic43C2×C22⋊C411yescharacteristic
354C2×Dic43C2×C22⋊C411yescharacteristic
355D172—22no—
356D172—41no—
357D172—42no—
358D172—81no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—21no—
362C4×D43—21no—
363C4×D43—21no—
364C4×D43—21no—
365C4×D43—41no—
366C4×D43—41no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—41no—
370C4×D43—41no—
371C4×D43—81no—
372C4×D43—81no—
373Dic86—22no—
374Dic86—41no—
375Dic86—42no—
376Dic86—81no—
377C8×C43—41no—
378C8×C43—41no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—22no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385#17506—431nomaximal, Sylow
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43C22×C22⋊C411yescharacteristic
390C2×D43—21no—
391C2×D43—21no—
392C2×D43—21no—
393C2×D43—21no—
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43#56812yes—
408C4×C43#57711yescharacteristic
409C4×C43#57811yescharacteristic
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—21no—
414Dic43—21no—
415Dic43—21no—
416Dic43—41no—
417Dic43—41no—
418Dic43—41no—
419#3461—431no—
420#2989—431no—
421#2965—431no—
422#1497D4311yescharacteristic, complemented
423#1495—431no—
424#1494—431no—
425#1493—431no—
426#1491—431no—
427#1489—431no—
428#1488—431no—
429#1487—431no—
430#1485—431no—
431#1483—431no—
432#1482—431no—
433#1481—431no—
434C2×C43—41no—
435C2×C43#287911yescharacteristic
436C2×C43#289811yescharacteristic
437C2×C43#290111yescharacteristic
438D43—41no—
439D43—41no—
440D43—81no—
441#544—431no—
442#542—431no—
443#542—431no—
444#542—861no—
445#541—431no—
446#541—431no—
447#541—861no—
448#539—861no—
449#539—861no—
450#537—431no—
451#536—431no—
452#536—431no—
453#533—431no—
454#533—861no—
455#533C2×D4311yescharacteristic
456#529—431no—
457#529—431no—
458#529—861no—
459#529—861no—
460#529—861no—
461C4×#41—431no—
462C4×#41—431no—
463C2×C4×Q8—431no—
464#446—861no—
465#446—861no—
466#436—861no—
467#436—861no—
468#435—861no—
469#435—861no—
470#435—861no—
471#435—861no—
472#432—431no—
473#432C2×D4311yescharacteristic
474#431—431no—
475#431—431no—
476#431—431no—
477#431C2×D4311yescharacteristic
478#423—431no—
479#423—431no—
480C2×C4⋊C8—431no—
481C4×M16—431no—
482C4×M16—431no—
483C2×C4×C8—431no—
484Q8⋊C8—431no—
485Q8⋊C8—431no—
486Q8⋊C8—431no—
487Q8⋊C8—431no—
488Q8⋊C8—431no—
489Q8⋊C8—431no—
490Q8⋊C8—431no—
491Q8⋊C8—431no—
492Q8⋊C8C2×D4311yescharacteristic
493Q8⋊C8C2×D4311yescharacteristic
494Q8⋊C8C2×D4311yescharacteristic
495Q8⋊C8C2×D4311yescharacteristic
496D4⋊C8—431no—
497D4⋊C8—431no—
498D4⋊C8—431no—
499D4⋊C8—431no—
500C43#1750611yescharacteristic, complemented, Sylow
501C2×#41—431no—
502C2×#41—431no—
503C22×Q8—431no—
504C2×M16—861no—
505C2×M16—861no—
506C2×M16—861no—
507C2×M16—861no—
508C22×C8—861no—
509C22×C8—861no—
510C4⋊Q8—431no—
511C4⋊Q8—431no—
512C4⋊Q8—861no—
513C4⋊Q8—861no—
514C4⋊Q8C4×D4311yescharacteristic
515C4⋊Q8C4×D4311yescharacteristic
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#126—861no—
521#126—861no—
522#126—861no—
523#126—861no—
524#125—21no—
525#125—431no—
526#125—431no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#124—431no—
534#124—431no—
535#124—861no—
536#124—861no—
537#124—861no—
538#123—861no—
539#123—861no—
540#123—861no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545#123—861no—
546C22⋊Q8—21no—
547C22⋊Q8—431no—
548C22⋊Q8—431no—
549C22⋊Q8—431no—
550C22⋊Q8—431no—
551C22⋊Q8—861no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8C4×D4311yescharacteristic
560C22⋊Q8C4×D4311yescharacteristic
561#121—431no—
562#121—431no—
563#121—861no—
564#121—861no—
565#121—861no—
566C4×Q8—21no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—431no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8C22×D4311yescharacteristic
577C4×Q8C22×D4311yescharacteristic
578C4×D4—431no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—431no—
582C4×D4—431no—
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590#117—21no—
591#117—431no—
592#117—431no—
593#117—431no—
594#117—431no—
595#117—861no—
596#117—861no—
597#117—861no—
598#117—861no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C42—431no—
602C2×C42—431no—
603C2×C42—861no—
604C2×C42—861no—
605C2×C42C22×D4311yescharacteristic
606C4⋊C8—21no—
607C4⋊C8—431no—
608C4⋊C8—431no—
609C4⋊C8—861no—
610C4⋊C8—861no—
611C4⋊C8—861no—
612C4⋊C8—861no—
613C4⋊C8—861no—
614C4⋊C8C22×D4311yescharacteristic
615C4⋊C8C22×D4311yescharacteristic
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622#97—21no—
623#97—861no—
624#97—861no—
625#97—861no—
626C4×C8—431no—
627C4×C8—431no—
628C4×C8—861no—
629C4×C8—861no—
630C4×C8C22×D4311yescharacteristic
631C4×C8C22×D4311yescharacteristic
632#41—1722no—
633#41—1722no—
634C2×Q8—21no—
635C2×Q8—431no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—1722no—
640C2×Q8C2×C4×D4311yescharacteristic
641C2×Q8C2×C4×D4311yescharacteristic
642C2×D4—431no—
643C2×D4—431no—
644C2×D4—431no—
645C2×D4—431no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4C2×C4×D4311yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663M16—3441no—
664M16—3441no—
665M16—1722no—
666M16—1722no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—3441no—
676C2×C8—1722no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—431no—
685C4⋊C4—431no—
686C4⋊C4—431no—
687C4⋊C4—431no—
688C4⋊C4—431no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—431no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4C2×C4×D4311yescharacteristic
709C4⋊C4C2×C4×D4311yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—431no—
713C22⋊C4—431no—
714C22⋊C4—431no—
715C22⋊C4—431no—
716C22⋊C4—431no—
717C22⋊C4—431no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C42—21no—
732C42—21no—
733C42—431no—
734C42—431no—
735C42—431no—
736C42—431no—
737C42—431no—
738C42—431no—
739C42—861no—
740C42—861no—
741C42—861no—
742C42—861no—
743C42—861no—
744C42C2×C4×D4311yescharacteristic
745C42D4×D4311yescharacteristic
746C42D4×D4311yescharacteristic
747C42C23×D4311yescharacteristic
748C23—431no—
749C23—431no—
750C23—861no—
751C23C22⋊C4×D4311yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—81no—
755Q8—862no—
756Q8—3441no—
757Q8—1721no—
758Q8—1722no—
759D4—862no—
760D4—3441no—
761D4—3441no—
762D4—1721no—
763D4—1722no—
764D4—1721no—
765D4—1721no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—41no—
774C2×C4—431no—
775C2×C4—431no—
776C2×C4—431no—
777C2×C4—431no—
778C2×C4—431no—
779C2×C4—431no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—3441no—
790C2×C4—3441no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4C22⋊C4×D4311yescharacteristic
798C2×C4C22⋊C4×D4311yescharacteristic
799C2×C4C22⋊C4×D4311yescharacteristic
800C2×C4C22×C4×D4311yescharacteristic
801C2×C4C2×D4×D4311yescharacteristic
802C2×C4C2×D4×D4311yescharacteristic
803C8—41no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—862no—
808C8—1721no—
809C8—1721no—
810C8—1721no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—861no—
815C22—861no—
816C22—861no—
817C22—861no—
818C22—861no—
819C22—861no—
820C22—1721no—
821C22—1721no—
822C22—1721no—
823C22C2×C22⋊C4×D4311yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—861no—
838C4—1721no—
839C4—1721no—
840C4—1721no—
841C4#1458366412yes—
842C4#1458370811yescharacteristic
843C4#1458371511yescharacteristic
844C2—41no—
845C2—3441no—
846C2—1721no—
847C2—1721no—
848C2#1914303711yescharacteristic
849C2#1914312711yescharacteristic
850C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1497C2
socleC22×C43C22×C22⋊C4
prime radical#14583479C4
cosocleC42×C43C24
hypercenter#1497D43
hypocenterC43#17506
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #19143714C2semidirect
3. #19143556C2semidirect
4. #19133061C2semidirect
5. #19133053C2semidirect
6. #19133050C2semidirect
7. #19133040C2semidirect
8. #19133033C2semidirect
9. #19133028C2semidirect
10. #19133022C2semidirect
11. #19133014C2semidirect
12. #19133007C2semidirect
13. #19133002C2semidirect
14. #19132996C2semidirect
15. C43×#1497C2semidirect
422. #1497D43semidirect
500. C43#17506semidirect

Maximal subgroups

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

subgroupindex
#191480262
#191437142
#191435562
#191330612
#191330532
#191330502
#191330402
#191330332
#191330282
#191330222
#191330142
#191330072
#191330022
#191329962
C43×#14972
#1750643