Finite Group Databasebeta

← #25063562

Subgroups — #25063562

Order 11008.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148186C211yesmaximal, characteristic
2#19143559C211yesmaximal, characteristic, complemented
3#19143263C211yesmaximal, characteristic, complemented
4#19133062C211yesmaximal, characteristic, complemented
5#19133054C211yesmaximal, characteristic, complemented
6#19133040C211yesmaximal, characteristic, complemented
7#19133032C211yesmaximal, characteristic, complemented
8#19133026C211yesmaximal, characteristic, complemented
9#19133010C211yesmaximal, characteristic, complemented
10#19133008C211yesmaximal, characteristic, complemented
11#19133002C211yesmaximal, characteristic, complemented
12#19132988C211yesmaximal, characteristic, complemented
13#19132983C211yesmaximal, characteristic, complemented
14#19132974C211yesmaximal, characteristic, complemented
15C43×#1495C211yesmaximal, characteristic, complemented
16#14583633—21no—
17#14583631C411yescharacteristic
18#14583626C411yescharacteristic
19#14583620C411yescharacteristic
20#14583616—21no—
21#14583602C411yescharacteristic
22#14583600—21no—
23#14583596C411yescharacteristic
24#14583594—21no—
25#14583567C411yescharacteristic
26#14583559C411yescharacteristic
27#14583557C411yescharacteristic
28#14583446—21no—
29#14583446C2211yescharacteristic
30#14583436C2211yescharacteristic
31#14583429—21no—
32#14583427—21no—
33C4×#10621898C2211yescharacteristic
34C4×#10621898C2211yescharacteristic
35#14583367—21no—
36C4×#10621900C2211yescharacteristic
37C4×Q8×D43C2211yescharacteristic
38#14583028—21no—
39#14582974—21no—
40#14582973—21no—
41#14582969—21no—
42#14582959—21no—
43#14582959—21no—
44#14582955C2211yescharacteristic
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49#14582950C2211yescharacteristic
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51#14582867—21no—
52#14582857—21no—
53C4×#10621877C2211yescharacteristic
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58Q8⋊(C43⋊C8)C2211yescharacteristic
59Q8⋊(C43⋊C8)C2211yescharacteristic
60#14582629C2211yescharacteristic
61#14582629C2211yescharacteristic
62#14582628C2211yescharacteristic
63#14582628C2211yescharacteristic
64D4⋊(C43⋊C8)C2211yescharacteristic
65D4⋊(C43⋊C8)C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#431C2211yescharacteristic
70C43×#423C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898D411yescharacteristic
78C2×#10621900C2×C411yescharacteristic
79C2×Q8×D43C2×C411yescharacteristic
80C2×#10621877—21no—
81C2×#10621872—21no—
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84#13063324—21no—
85#13063324C2×C411yescharacteristic
86#13063321—21no—
87#13063321C2×C411yescharacteristic
88#13063320—21no—
89#13063320—21no—
90#13063320—21no—
91#13063318—21no—
92#13063318—21no—
93#13063316C2×C411yescharacteristic
94#13063315—21no—
95#13063315—21no—
96#13063314C2×C411yescharacteristic
97#13063311—21no—
98#13063311—21no—
99#13063311—21no—
100#13063311—21no—
101#13063311—21no—
102#13063310—21no—
103#13063310—21no—
104#13063309—21no—
105#13063307—21no—
106#13063306—21no—
107#13063303—21no—
108#13063302—21no—
109#13063301C2×C411yescharacteristic
110#13063300—21no—
111#13063300C2×C411yescharacteristic
112#13063300C2×C411yescharacteristic
113#13063298—21no—
114#13063298—21no—
115#13063298—21no—
116#13063298—21no—
117#13063297—21no—
118#13063296—21no—
119#13063296C2×C411yescharacteristic
120Q8×Dic43C2×C411yescharacteristic
121C4×Dic86—21no—
122C4×Dic86C2×C411yescharacteristic
123C4×Dic86C2×C411yescharacteristic
124C4×Dic86D411yescharacteristic
125C4×Dic86C2311yescharacteristic
126#13063290—21no—
127#13063290—21no—
128#13063290—21no—
129#13063290C2×C411yescharacteristic
130#13063290C2×C411yescharacteristic
131C4×D172—21no—
132C4×D172C2×C411yescharacteristic
133C4×D172C2×C411yescharacteristic
134C4×D172D411yescharacteristic
135C4×D172C2311yescharacteristic
136D4×Dic43C2×C411yescharacteristic
137#13063287—21no—
138#13063287—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152#13063284C2×C411yescharacteristic
153#13063284D411yescharacteristic
154#13063283C2×C411yescharacteristic
155#13063282—21no—
156#13063282—21no—
157#13063282D411yescharacteristic
158#13063282D411yescharacteristic
159#13063281—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43C2×C411yescharacteristic
162C2×C4×Dic43—21no—
163C42×D43—21no—
164C42×D43—21no—
165C42×D43C2311yescharacteristic
166C42×D43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)C2311yescharacteristic
169C4⋊(C43⋊C8)C2311yescharacteristic
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172(C2×D43)⋊C8—21no—
173(C2×D43)⋊C8—21no—
174(C2×D43)⋊C8—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063236—21no—
179#13063235—21no—
180#13063235—21no—
181#13063235—21no—
182C4×C43⋊C8C2311yescharacteristic
183C4×C43⋊C8C2311yescharacteristic
184C8×Dic43—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C2×M16×C43—21no—
188#126×C43—21no—
189#125×C43C2×C411yescharacteristic
190#124×C43C2×C411yescharacteristic
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic
193#121×C43C2×C411yescharacteristic
194C4×Q8×C43C2311yescharacteristic
195C4×D4×C43—21no—
196C4×D4×C43C2311yescharacteristic
197#117×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C4⋊C8×C43—21no—
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C2×C22⋊D43—21no—
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43C22⋊C411yescharacteristic
219C2×C22⋊D43C22⋊C411yescharacteristic
220C22×Dic43—21no—
221C22×Dic43—21no—
222Q8×D43—22no—
223Q8×D43—41no—
224#10621900—22no—
225#10621900—41no—
226#10621898—22no—
227#10621898—41no—
228#10621898—41no—
229#10621898—41no—
230#10621898—42no—
231#10621898—42no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172C22⋊C411yescharacteristic
235C2×D172C22×C411yescharacteristic
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86C22⋊C411yescharacteristic
250C2×Dic86C22×C411yescharacteristic
251M16×C43—42no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43C22×C411yescharacteristic
261C4⋊C4×C43C22×C411yescharacteristic
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C42×C43—21no—
268C42×C43C22×C411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2411yescharacteristic
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43C22⋊C411yescharacteristic
276C22⋊Dic43C22⋊C411yescharacteristic
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4C22⋊C411yescharacteristic
286(C2×D43)⋊C4C22⋊C411yescharacteristic
287(C2×D43)⋊C4C22⋊C411yescharacteristic
288(C2×D43)⋊C4C22⋊C411yescharacteristic
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43C22⋊C411yescharacteristic
292C4⋊Dic43C22⋊C411yescharacteristic
293C4⋊Dic43C22×C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307C4×Dic43—21no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C22×C411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320#10621877—42no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—42no—
326#10621872—42no—
327C8×D43—42no—
328C23×C43—21no—
329C23×C43C2×C22⋊C411yescharacteristic
330C22×D43—21no—
331C22×D43C2×C22⋊C411yescharacteristic
332C22×D43C2×C22⋊C411yescharacteristic
333Q8×C43—21no—
334Q8×C43—21no—
335D4×C43—21no—
336D4×C43—21no—
337D4×C43—81no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C23×C411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C22⋊D43—41no—
355C22⋊D43—41no—
356C22⋊D43—42no—
357C22⋊D43—42no—
358C22⋊D43—42no—
359C22⋊D43—42no—
360C22⋊D43—81no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—42no—
365C2×Dic43—81no—
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368C2×Dic43C2×C22⋊C411yescharacteristic
369C2×Dic43C2×C22⋊C411yescharacteristic
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372D172—21no—
373D172—21no—
374D172—41no—
375D172—42no—
376D172—81no—
377C4×D43—21no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—21no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—41no—
386C4×D43—41no—
387C4×D43—42no—
388C4×D43—42no—
389C4×D43—41no—
390C4×D43—41no—
391C4×D43—81no—
392C4×D43—81no—
393Dic86—21no—
394Dic86—41no—
395Dic86—42no—
396Dic86—42no—
397Dic86#13112yes—
398C8×C43—41no—
399C8×C43—41no—
400C8×C43—41no—
401C8×C43—41no—
402C43⋊C8—22no—
403C43⋊C8—41no—
404C43⋊C8—41no—
405C43⋊C8—41no—
406#17516—431nomaximal, Sylow
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43C22×C22⋊C411yescharacteristic
414C2×D43—21no—
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—21no—
419C2×D43—21no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—41no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43C2×#13111yescharacteristic
431C4×C43#56811yescharacteristic
432C4×C43#57511yescharacteristic
433C4×C43#57511yescharacteristic
434Dic43—22no—
435Dic43—21no—
436Dic43—21no—
437Dic43—21no—
438Dic43—21no—
439Dic43—21no—
440Dic43—21no—
441Dic43—41no—
442Dic43—41no—
443#3480—431no—
444#2965—431no—
445#2925—431no—
446#1496—431no—
447#1495D4311yescharacteristic, complemented
448#1494—431no—
449#1491—431no—
450#1489—431no—
451#1488—431no—
452#1484—431no—
453#1483—431no—
454#1482—431no—
455#1479—431no—
456#1477—431no—
457#1476—431no—
458C2×C43—41no—
459C2×C43—81no—
460C2×C43#288011yescharacteristic
461C2×C43#289611yescharacteristic
462C2×C43#290111yescharacteristic
463D43—41no—
464D43—41no—
465D43—81no—
466#559—431no—
467#559—861no—
468#557—431no—
469#556—431no—
470#556—861no—
471#553—431no—
472#553—431no—
473#553—861no—
474#553—861no—
475#550—431no—
476#548—431no—
477#548—431no—
478#532—431no—
479#532—861no—
480#529—431no—
481#529—861no—
482#529—861no—
483#529C2×D4311yescharacteristic
484C4×#41—431no—
485C4×#41—431no—
486C4×#41—431no—
487C4×#41—861no—
488C2×C4×Q8—431no—
489#446—861no—
490#436—861no—
491#435—861no—
492#435—861no—
493#433—861no—
494#433—861no—
495#432—431no—
496#432—431no—
497#431—431no—
498#431—431no—
499#431—431no—
500#431—431no—
501#431C2×D4311yescharacteristic
502#423C2×D4311yescharacteristic
503C2×C4⋊C8—431no—
504#408—861no—
505#405—861no—
506C4×M16—431no—
507C4×M16—431no—
508C2×C4×C8—431no—
509Q8⋊C8—431no—
510Q8⋊C8—431no—
511Q8⋊C8—431no—
512Q8⋊C8—431no—
513Q8⋊C8—431no—
514Q8⋊C8—431no—
515Q8⋊C8C2×D4311yescharacteristic
516Q8⋊C8C2×D4311yescharacteristic
517D4⋊C8—431no—
518D4⋊C8—431no—
519D4⋊C8—431no—
520D4⋊C8—431no—
521D4⋊C8—431no—
522D4⋊C8—431no—
523D4⋊C8C2×D4311yescharacteristic
524D4⋊C8C2×D4311yescharacteristic
525C43#1751611yescharacteristic, complemented, Sylow
526C2×#41—431no—
527C2×#41—431no—
528C2×#41—431no—
529C2×#41—861no—
530C22×Q8—431no—
531C2×M16—21no—
532C2×M16—861no—
533C2×M16—861no—
534C22×C8—861no—
535C22×C8—861no—
536C4⋊Q8—431no—
537C4⋊Q8—861no—
538#127—431no—
539#127—861no—
540#126—21no—
541#126—861no—
542#126—861no—
543#126—861no—
544#126—861no—
545#126—861no—
546#125—431no—
547#125—861no—
548#125—861no—
549#125C4×D4311yescharacteristic
550#124—431no—
551#124—861no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124—861no—
556#124C4×D4311yescharacteristic
557#123—21no—
558#123—861no—
559#123—861no—
560#123—861no—
561#123—861no—
562#123—861no—
563C22⋊Q8—431no—
564C22⋊Q8—861no—
565C22⋊Q8—861no—
566C22⋊Q8C4×D4311yescharacteristic
567#121—431no—
568#121—431no—
569#121—431no—
570#121—861no—
571#121—861no—
572#121—861no—
573#121—861no—
574#121—861no—
575#121—861no—
576#121—861no—
577#121C4×D4311yescharacteristic
578C4×Q8—431no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—431no—
584C4×Q8—431no—
585C4×Q8—861no—
586C4×Q8—861no—
587C4×Q8—861no—
588C4×Q8—861no—
589C4×Q8C22×D4311yescharacteristic
590C4×D4—21no—
591C4×D4—431no—
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—431no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—861no—
601C4×D4—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4C22×D4311yescharacteristic
613#117—21no—
614#117—431no—
615#117—431no—
616#117—431no—
617#117—431no—
618#117—431no—
619#117—861no—
620#117—861no—
621#117—861no—
622C2×C4⋊C4—431no—
623C2×C4⋊C4—861no—
624C2×C42—431no—
625C2×C42—431no—
626C2×C42—861no—
627C2×C42—861no—
628C2×C42—861no—
629C2×C42C22×D4311yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—431no—
633C4⋊C8—431no—
634C4⋊C8—861no—
635C4⋊C8—861no—
636C4⋊C8—861no—
637C4⋊C8C22×D4311yescharacteristic
638C4⋊C8C22×D4311yescharacteristic
639C22⋊C8—21no—
640C22⋊C8—861no—
641C22⋊C8—861no—
642C22⋊C8—861no—
643C22⋊C8—861no—
644C22⋊C8—861no—
645C22⋊C8—861no—
646#97—861no—
647#97—861no—
648#97—861no—
649#97—861no—
650C4×C8—431no—
651C4×C8—431no—
652C4×C8—861no—
653C4×C8—861no—
654C4×C8—861no—
655C4×C8C22×D4311yescharacteristic
656C4×C8C22×D4311yescharacteristic
657#41—862no—
658#41—862no—
659#41—1721no—
660#41—1721no—
661#41—1721no—
662#41—1722no—
663#41—1722no—
664#41—1721no—
665C2×Q8—431no—
666C2×Q8—431no—
667C2×Q8—861no—
668C2×Q8—861no—
669C2×Q8—862no—
670C2×Q8—1721no—
671C2×Q8C2×C4×D4311yescharacteristic
672C2×D4—21no—
673C2×D4—431no—
674C2×D4—431no—
675C2×D4—431no—
676C2×D4—431no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4C2×C4×D4311yescharacteristic
685C22×C4—21no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—431no—
689C22×C4—431no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4C2×C4×D4311yescharacteristic
700C22×C4D4×D4311yescharacteristic
701C22×C4D4×D4311yescharacteristic
702M16—42no—
703M16—1722no—
704M16—1722no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—1722no—
714C2×C8—1722no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—431no—
722C4⋊C4—431no—
723C4⋊C4—431no—
724C4⋊C4—431no—
725C4⋊C4—431no—
726C4⋊C4—431no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4C2×C4×D4311yescharacteristic
738C4⋊C4C2×C4×D4311yescharacteristic
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—431no—
745C22⋊C4—431no—
746C22⋊C4—431no—
747C22⋊C4—431no—
748C22⋊C4—431no—
749C22⋊C4—431no—
750C22⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C22⋊C4—861no—
758C22⋊C4—861no—
759C22⋊C4—861no—
760C22⋊C4—861no—
761C42—21no—
762C42—431no—
763C42—431no—
764C42—431no—
765C42—431no—
766C42—431no—
767C42—431no—
768C42—861no—
769C42—861no—
770C42—861no—
771C42—861no—
772C42—861no—
773C42—861no—
774C42—861no—
775C42C2×C4×D4311yescharacteristic
776C42D4×D4311yescharacteristic
777C42D4×D4311yescharacteristic
778C42C23×D4311yescharacteristic
779C23—21no—
780C23—431no—
781C23—431no—
782C23—861no—
783C23C22⋊C4×D4311yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—432no—
787Q8—861no—
788Q8—1721no—
789Q8—1722no—
790Q8—1722no—
791D4—21no—
792D4—21no—
793D4—81no—
794D4—861no—
795D4—861no—
796D4—3441no—
797D4—3441no—
798D4—1721no—
799D4—1722no—
800D4—1721no—
801D4—1721no—
802D4—1722no—
803D4—1722no—
804D4—1722no—
805D4—1722no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—431no—
817C2×C4—431no—
818C2×C4—431no—
819C2×C4—431no—
820C2×C4—431no—
821C2×C4—431no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—861no—
828C2×C4—861no—
829C2×C4—861no—
830C2×C4—861no—
831C2×C4—861no—
832C2×C4—861no—
833C2×C4—3441no—
834C2×C4—3441no—
835C2×C4—3441no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1722no—
839C2×C4—1722no—
840C2×C4—1722no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4C22⋊C4×D4311yescharacteristic
844C2×C4C22⋊C4×D4311yescharacteristic
845C2×C4C22⋊C4×D4311yescharacteristic
846C2×C4C22×C4×D4311yescharacteristic
847C2×C4C2×D4×D4311yescharacteristic
848C2×C4C2×D4×D4311yescharacteristic
849C8—41no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—862no—
854C8—1721no—
855C8—1721no—
856C8—1721no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—861no—
864C22—861no—
865C22—861no—
866C22—861no—
867C22—861no—
868C22—861no—
869C22—1721no—
870C22—1721no—
871C22—1721no—
872C22C2×C22⋊C4×D4311yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—861no—
881C4—861no—
882C4—862no—
883C4—861no—
884C4—861no—
885C4—861no—
886C4—861no—
887C4—1721no—
888C4—1721no—
889C4#131×D4311yescharacteristic
890C4#1458366411yescharacteristic
891C4#1458369511yescharacteristic
892C4#1458369811yescharacteristic
893C2—41no—
894C2—81no—
895C2—3441no—
896C2—1721no—
897C2—1721no—
898C2#1914304311yescharacteristic
899C2#1914311111yescharacteristic
900C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1495C2
socleC22×C43C22×C22⋊C4
prime radical#19148186C2
cosocleC42×C43C24
hypercenter#1495D43
hypocenterC43#17516
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #19143559C2semidirect
3. #19143263C2semidirect
4. #19133062C2semidirect
5. #19133054C2semidirect
6. #19133040C2semidirect
7. #19133032C2semidirect
8. #19133026C2semidirect
9. #19133010C2semidirect
10. #19133008C2semidirect
11. #19133002C2semidirect
12. #19132988C2semidirect
13. #19132983C2semidirect
14. #19132974C2semidirect
15. C43×#1495C2semidirect
447. #1495D43semidirect
525. C43#17516semidirect

Maximal subgroups

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

subgroupindex
#191481862
#191435592
#191432632
#191330622
#191330542
#191330402
#191330322
#191330262
#191330102
#191330082
#191330022
#191329882
#191329832
#191329742
C43×#14952
#1751643