Finite Group Databasebeta

← #25063271

Subgroups — #25063271

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148016C211yesmaximal, characteristic
2#19143714C211yesmaximal, characteristic, complemented
3C8×#10621898C211yesmaximal, characteristic, complemented
4#19133063C211yesmaximal, characteristic, complemented
5#19133062C211yesmaximal, characteristic, complemented
6#19133060C211yesmaximal, characteristic, complemented
7#19133059C211yesmaximal, characteristic, complemented
8#19133054C211yesmaximal, characteristic, complemented
9#19133047C211yesmaximal, characteristic, complemented
10#19133044C211yesmaximal, characteristic, complemented
11#19132984C211yesmaximal, characteristic, complemented
12#19132981C211yesmaximal, characteristic, complemented
13#19132976C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1494C211yesmaximal, characteristic, complemented
16#14583529C411yescharacteristic
17#14583522C411yescharacteristic
18#14583518C411yescharacteristic
19#14583515—21no—
20#14583505C411yescharacteristic
21#14583502C411yescharacteristic
22#14583501—21no—
23#14583488—21no—
24#14583485—21no—
25#14583479C411yescharacteristic
26#14583467C411yescharacteristic
27#14583465C411yescharacteristic
28#14583449C2211yescharacteristic
29#14583446—21no—
30#14583446C2211yescharacteristic
31#14583436C2211yescharacteristic
32#14583427—21no—
33#14583411—21no—
34#14583408—21no—
35C4×#10621902C2211yescharacteristic
36C4×#10621898C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38#14583027—21no—
39C8×Dic86—21no—
40#14582974—21no—
41#14582973—21no—
42#14582972—21no—
43C8×D172—21no—
44C8×C22⋊D43—21no—
45C8×C22⋊D43—21no—
46#14582955C2211yescharacteristic, complemented
47#14582952C2211yescharacteristic, complemented
48#14582951C2211yescharacteristic
49#14582950C2211yescharacteristic
50#14582950C2211yescharacteristic, complemented
51#14582923C2211yescharacteristic, complemented
52#14582921C2211yescharacteristic, complemented
53C4⋊C8×D43C2211yescharacteristic
54C4×C8×D43C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic, complemented
56Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
57Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60#14582628C2211yescharacteristic, complemented
61#14582628C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic
63D4⋊(C43⋊C8)C2211yescharacteristic
64#14582626C2211yescharacteristic
65#14582626C2211yescharacteristic
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C2×C4×C8×C43C2211yescharacteristic, complemented
71C43×Q8⋊C8C2211yescharacteristic, complemented
72C43×Q8⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898—21no—
77C2×#10621898—21no—
78C2×#10621898C2×C411yescharacteristic
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43—21no—
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86#13063325C2×C411yescharacteristic
87#13063324—21no—
88#13063324C2×C411yescharacteristic
89#13063322C2×C411yescharacteristic
90#13063321—21no—
91#13063321C2×C411yescharacteristic
92#13063320—21no—
93#13063320—21no—
94#13063318—21no—
95#13063316C2×C411yescharacteristic
96#13063315—21no—
97#13063314C2×C411yescharacteristic
98#13063313—21no—
99#13063311—21no—
100#13063311—21no—
101#13063311—21no—
102#13063311—21no—
103#13063310—21no—
104#13063310—21no—
105#13063310—21no—
106#13063309—21no—
107#13063309—21no—
108#13063307—21no—
109#13063307—21no—
110#13063305—21no—
111#13063305—21no—
112#13063303—21no—
113#13063303—21no—
114#13063302—21no—
115#13063301C2×C411yescharacteristic
116#13063300—21no—
117#13063300—21no—
118#13063300—21no—
119#13063300C2×C411yescharacteristic
120#13063300C2×C411yescharacteristic
121#13063299—21no—
122#13063299C2×C411yescharacteristic
123#13063299C2×C411yescharacteristic
124#13063298—21no—
125#13063298—21no—
126#13063298—21no—
127#13063298—21no—
128#13063298—21no—
129#13063297—21no—
130#13063296—21no—
131#13063296C2×C411yescharacteristic
132#13063295—21no—
133#13063295—21no—
134#13063295—21no—
135#13063293—21no—
136Q8×Dic43C2×C411yescharacteristic
137C4×Dic86D411yescharacteristic
138C4×Dic86D411yescharacteristic
139C4×D172—21no—
140C4×D172—21no—
141C4×D172—21no—
142C4×D172D411yescharacteristic
143C4×D172D411yescharacteristic
144C4×D172C2311yescharacteristic
145C4×D172C2311yescharacteristic
146D4×Dic43C2×C411yescharacteristic
147#13063287—21no—
148#13063287C2×C411yescharacteristic
149#13063287C2×C411yescharacteristic
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155C4×C22⋊D43D411yescharacteristic
156(C22⋊D43)⋊C4—21no—
157#13063284C2×C411yescharacteristic
158#13063283—21no—
159#13063283C2×C411yescharacteristic
160#13063282—21no—
161#13063282C2×C411yescharacteristic
162#13063282C2×C411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic
164C22⋊C4×D43—21no—
165C42×D43—21no—
166C42×D43C2311yescharacteristic
167C42×D43C2311yescharacteristic
168C4⋊(C43⋊C8)—21no—
169C4⋊(C43⋊C8)—21no—
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182C4×C43⋊C8C2311yescharacteristic
183C4×C43⋊C8C2311yescharacteristic
184C8×Dic43—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C22×C8×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×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43—21no—
202#97×C43—21no—
203C4×C8×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C23×D43—21no—
207C2×Q8×C43C22×C411yescharacteristic
208C2×D4×C43—21no—
209C2×D4×C43C22×C411yescharacteristic
210C22×C4×C43—21no—
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43C22⋊C411yescharacteristic
221C2×C22⋊D43C22⋊C411yescharacteristic
222C22×Dic43—21no—
223#10621902—24no—
224D4×D43—24no—
225#10621898—24no—
226#10621898—81no—
227#10621898—81no—
228#10621898—81no—
229#10621898—81no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172C22⋊C411yescharacteristic
236C2×D172C22×C411yescharacteristic
237C2×D172C22×C411yescharacteristic
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—81no—
245C2×C4×D43—81no—
246C2×C4×D43C22×C411yescharacteristic
247C2×C4×D43C22×C411yescharacteristic
248C2×C4×D43C2×D411yescharacteristic
249C2×C4×D43C2×D411yescharacteristic
250C2×C4×D43C2×D411yescharacteristic
251C2×C4×D43C2×D411yescharacteristic
252C2×Dic86—21no—
253C2×Dic86—21no—
254C2×Dic86C22⋊C411yescharacteristic
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—42no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C22×C411yescharacteristic
265C4⋊C4×C43C22×C411yescharacteristic
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C42×C43—21no—
272C42×C43C22×C411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2×D411yescharacteristic
275C42×C43C2411yescharacteristic
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C411yescharacteristic
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)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4C22⋊C411yescharacteristic
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43C22⋊C411yescharacteristic
300C4⋊Dic43C22⋊C411yescharacteristic
301C4⋊Dic43C22×C411yescharacteristic
302C4⋊Dic43C22×C411yescharacteristic
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319#10621877—81no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324#10621872—81no—
325C8×D43—42no—
326C8×D43—42no—
327C8×D43—81no—
328C23×C43—21no—
329C23×C43C2×C22⋊C411yescharacteristic
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—42no—
333C22×D43—81no—
334C22×D43—81no—
335C22×D43C2×C22⋊C411yescharacteristic
336C22×D43C2×C22⋊C411yescharacteristic
337Q8×C43—22no—
338D4×C43—22no—
339D4×C43—81no—
340C2×C4×C43—22no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C23×C411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C22×D411yescharacteristic
355C22⋊D43—22no—
356C22⋊D43—22no—
357C22⋊D43—42no—
358C22⋊D43—81no—
359C22⋊D43—81no—
360C22⋊D43—81no—
361C22⋊D43—81no—
362C22⋊D43—81no—
363C2×Dic43—21no—
364C2×Dic43—21no—
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—22no—
373D172—22no—
374D172—22no—
375D172—42no—
376D172—81no—
377D172—81no—
378D172—81no—
379D172—81no—
380C4×D43—22no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—41no—
386C4×D43—41no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—41no—
390C4×D43—41no—
391C4×D43—42no—
392C4×D43—81no—
393C4×D43—81no—
394C4×D43—81no—
395C4×D43#13114yes—
396Dic86—22no—
397Dic86—81no—
398Dic86—81no—
399C8×C43—22no—
400C8×C43—41no—
401C8×C43—41no—
402C8×C43—41no—
403C43⋊C8—41no—
404C43⋊C8—41no—
405C43⋊C8—41no—
406C43⋊C8—41no—
407#17483—431nomaximal, Sylow
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—41no—
414C22×C43C22×C22⋊C411yescharacteristic
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—21no—
419C2×D43—21no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43—84no—
427C2×D43#40812yes—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43C2×#13112yes—
436C4×C43#57611yescharacteristic
437C4×C43#57711yescharacteristic
438Dic43—21no—
439Dic43—21no—
440Dic43—21no—
441Dic43—21no—
442Dic43—21no—
443Dic43—41no—
444Dic43—41no—
445Dic43#40812yes—
446#3460—431no—
447#2989—431no—
448C8×#41—431no—
449#1496—431no—
450#1496—431no—
451#1495—431no—
452#1495—431no—
453#1494—431no—
454#1494D4311yescharacteristic, complemented
455#1492—431no—
456#1492—431no—
457#1478—431no—
458#1477—431no—
459#1476—431no—
460C2×D4⋊C8—431no—
461C2×C43—41no—
462C2×C43—81no—
463C2×C43C2×#40811yescharacteristic
464C2×C43#289711yescharacteristic
465C2×C43#290111yescharacteristic
466D43—22no—
467D43—41no—
468D43—81no—
469D43—81no—
470#544—431no—
471#542—431no—
472#542—431no—
473#542—861no—
474#540—431no—
475#540—431no—
476#540—861no—
477#538—861no—
478#538—861no—
479#537—431no—
480#535—431no—
481#535—431no—
482#532—431no—
483#532—431no—
484#532—861no—
485#529—431no—
486#529—861no—
487#529C2×D4311yescharacteristic
488#525—861no—
489#525—861no—
490C4×#41—431no—
491C4×#41—431no—
492C2×C4×D4—431no—
493#446—861no—
494C8×Q8—861no—
495#436—861no—
496#435—861no—
497#435—861no—
498C8×D4—861no—
499C8×D4—861no—
500C8×D4—861no—
501#432—431no—
502#432C2×D4311yescharacteristic, complemented
503#431—431no—
504#431—431no—
505#431—431no—
506#431—431no—
507#423—431no—
508#423—431no—
509C2×C4⋊C8—431no—
510C2×C4×C8—431no—
511C2×C4×C8—431no—
512C2×C4×C8C2×D4311yescharacteristic, complemented
513Q8⋊C8—431no—
514Q8⋊C8—431no—
515Q8⋊C8C2×D4311yescharacteristic, complemented
516Q8⋊C8C2×D4311yescharacteristic, complemented
517D4⋊C8—431no—
518D4⋊C8—431no—
519D4⋊C8—431no—
520D4⋊C8—431no—
521D4⋊C8—431no—
522D4⋊C8—431no—
523D4⋊C8—431no—
524D4⋊C8—431no—
525D4⋊C8—431no—
526D4⋊C8—431no—
527D4⋊C8C2×D4311yescharacteristic
528D4⋊C8C2×D4311yescharacteristic
529C43#1748311yescharacteristic, complemented, Sylow
530C2×#41—431no—
531C2×#41—431no—
532C2×#41—861no—
533C2×#41—861no—
534C22×D4—431no—
535C23×C4—861no—
536C2×M16—861no—
537C2×M16—861no—
538C22×C8—21no—
539C22×C8—861no—
540C22×C8—861no—
541C22×C8—861no—
542C4⋊Q8—431no—
543C4⋊Q8—431no—
544C4⋊Q8—861no—
545#127—431no—
546#127—431no—
547#127—861no—
548#126—21no—
549#126—861no—
550#126—861no—
551#126—861no—
552#125—431no—
553#125—861no—
554#125C4×D4311yescharacteristic
555#124—431no—
556#124—861no—
557#124—861no—
558#124—861no—
559#124—861no—
560#124—861no—
561#124C4×D4311yescharacteristic
562#123—21no—
563#123—861no—
564#123—861no—
565#123—861no—
566#123—861no—
567#123—861no—
568#123—861no—
569#123—861no—
570C22⋊Q8—431no—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573C22⋊Q8—861no—
574C22⋊Q8—861no—
575C22⋊Q8—861no—
576C22⋊Q8C4×D4311yescharacteristic
577#121—431no—
578#121—431no—
579#121—431no—
580#121—431no—
581#121—431no—
582#121—861no—
583#121—861no—
584#121—861no—
585#121—861no—
586#121—861no—
587#121—861no—
588#121—861no—
589#121—861no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121C4×D4311yescharacteristic
594#120—861no—
595#120—861no—
596#120—861no—
597#120—861no—
598C4×Q8—431no—
599C4×Q8—431no—
600C4×Q8—431no—
601C4×Q8C22×D4311yescharacteristic
602C4×D4—21no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—431no—
613C4×D4—431no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4C22×D4311yescharacteristic
622#117—21no—
623#117—431no—
624#117—431no—
625#117—431no—
626#117—431no—
627#117—861no—
628#117—861no—
629C2×C4⋊C4—431no—
630C2×C22⋊C4—861no—
631C2×C42—431no—
632C2×C42—431no—
633C2×C42—861no—
634C2×C42C22×D4311yescharacteristic
635C4⋊C8—431no—
636C4⋊C8—431no—
637C4⋊C8—861no—
638C4⋊C8—861no—
639C4⋊C8—861no—
640C4⋊C8—861no—
641C4⋊C8—861no—
642C4⋊C8—861no—
643C4⋊C8C22×D4311yescharacteristic
644C4⋊C8C22×D4311yescharacteristic
645C22⋊C8—21no—
646C22⋊C8—861no—
647C22⋊C8—861no—
648C22⋊C8—861no—
649C22⋊C8—861no—
650C22⋊C8—861no—
651#97—21no—
652#97—861no—
653C4×C8—21no—
654C4×C8—431no—
655C4×C8—431no—
656C4×C8—861no—
657C4×C8—861no—
658C4×C8—861no—
659C4×C8C22×D4311yescharacteristic
660C4×C8C22×D4311yescharacteristic
661C24—861no—
662#41—864no—
663#41—864no—
664#41—3441no—
665#41—3441no—
666#41—3441no—
667#41—3441no—
668C2×Q8—431no—
669C2×Q8—861no—
670C2×Q8—861no—
671C2×Q8C2×C4×D4311yescharacteristic
672C2×D4—21no—
673C2×D4—431no—
674C2×D4—431no—
675C2×D4—431no—
676C2×D4—431no—
677C2×D4—431no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—864no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—861no—
690C2×D4C2×C4×D4311yescharacteristic
691C22×C4—21no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—3441no—
706C22×C4—3441no—
707C22×C4C2×C4×D4311yescharacteristic
708C22×C4D4×D4311yescharacteristic
709C22×C4D4×D4311yescharacteristic
710M16—3441no—
711M16—3441no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—42no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—3441no—
722C2×C8—1722no—
723C2×C8—1722no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—431no—
729C4⋊C4—431no—
730C4⋊C4—431no—
731C4⋊C4—431no—
732C4⋊C4—431no—
733C4⋊C4—431no—
734C4⋊C4—431no—
735C4⋊C4—431no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4C2×C4×D4311yescharacteristic
744C4⋊C4C2×C4×D4311yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—431no—
751C22⋊C4—431no—
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⋊C4—861no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C42—21no—
771C42—431no—
772C42—431no—
773C42—431no—
774C42—431no—
775C42—431no—
776C42—431no—
777C42—861no—
778C42—861no—
779C42C2×C4×D4311yescharacteristic
780C42D4×D4311yescharacteristic
781C42D4×D4311yescharacteristic
782C42C23×D4311yescharacteristic
783C23—21no—
784C23—431no—
785C23—431no—
786C23—861no—
787C23—861no—
788C23—3441no—
789C23—3441no—
790C23—1722no—
791C23C22⋊C4×D4311yescharacteristic
792Q8—22no—
793Q8—862no—
794Q8—3441no—
795Q8—3441no—
796D4—22no—
797D4—81no—
798D4—862no—
799D4—862no—
800D4—862no—
801D4—862no—
802D4—862no—
803D4—3441no—
804D4—3441no—
805D4—3441no—
806D4—3441no—
807D4—3441no—
808D4—3441no—
809D4—3441no—
810D4—3441no—
811D4—3441no—
812D4—1722no—
813D4—1722no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—431no—
824C2×C4—434no—
825C2×C4—431no—
826C2×C4—431no—
827C2×C4—431no—
828C2×C4—431no—
829C2×C4—431no—
830C2×C4—862no—
831C2×C4—861no—
832C2×C4—861no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—3441no—
838C2×C4—3441no—
839C2×C4—3441no—
840C2×C4—3441no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1722no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4C22⋊C4×D4311yescharacteristic
849C2×C4C22⋊C4×D4311yescharacteristic
850C2×C4C22⋊C4×D4311yescharacteristic
851C2×C4C22×C4×D4311yescharacteristic
852C2×C4C2×D4×D4311yescharacteristic
853C2×C4C2×D4×D4311yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C8—1721no—
859C8—1721no—
860C8—1721no—
861C8—1721no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—432no—
869C22—861no—
870C22—861no—
871C22—861no—
872C22—861no—
873C22—861no—
874C22—3444no—
875C22—1721no—
876C22—1721no—
877C22—1721no—
878C22—1721no—
879C22—1721no—
880C22—1721no—
881C22C2×C22⋊C4×D4311yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—41no—
887C4—41no—
888C4—41no—
889C4—432no—
890C4—861no—
891C4—861no—
892C4—861no—
893C4—861no—
894C4—861no—
895C4—1721no—
896C4—1721no—
897C4#131×D4312yes—
898C4#1458370111yescharacteristic
899C4#1458370611yescharacteristic
900C2—41no—
901C2—81no—
902C2—862no—
903C2—3441no—
904C2—3441no—
905C2—1721no—
906C2#408×D4311yescharacteristic
907C2#1914311711yescharacteristic
908C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1494C2
socleC22×C43C22×C22⋊C4
prime radical#19148016C2
cosocleC42×C43C24
hypercenter#1494D43
hypocenterC43#17483
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #19143714C2semidirect
3. C8×#10621898C2semidirect
4. #19133063C2semidirect
5. #19133062C2semidirect
6. #19133060C2semidirect
7. #19133059C2semidirect
8. #19133054C2semidirect
9. #19133047C2semidirect
10. #19133044C2semidirect
11. #19132984C2semidirect
12. #19132981C2semidirect
13. #19132976C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1494C2semidirect
46. #14582955C22semidirect
47. #14582952C22semidirect
50. #14582950C22semidirect
51. #14582923C22semidirect
52. #14582921C22semidirect
55. C4×C8×D43C22semidirect
56. Q8⋊(C43⋊C8)C22semidirect
57. Q8⋊(C43⋊C8)C22semidirect
60. #14582628C22semidirect
61. #14582628C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#432C22semidirect
70. C2×C4×C8×C43C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
454. #1494D43semidirect
502. #432C2×D43semidirect
512. C2×C4×C8C2×D43semidirect
515. Q8⋊C8C2×D43semidirect
516. Q8⋊C8C2×D43semidirect
529. C43#17483semidirect

Maximal subgroups

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

subgroupindex
#191480162
#191437142
C8×#106218982
#191330632
#191330622
#191330602
#191330592
#191330542
#191330472
#191330442
#191329842
#191329812
#191329762
D4⋊C8×D432
C43×#14942
#1748343