Finite Group Databasebeta

← #25063516

Subgroups — #25063516

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148151C211yesmaximal, characteristic
2#19143556C211yesmaximal, characteristic, complemented
3#19143256C211yesmaximal, characteristic, complemented
4#19133066C211yesmaximal, characteristic, complemented
5#19133057C211yesmaximal, characteristic, complemented
6#19133055C211yesmaximal, characteristic, complemented
7#19133036C211yesmaximal, characteristic, complemented
8#19133033C211yesmaximal, characteristic, complemented
9#19133030C211yesmaximal, characteristic, complemented
10#19133014C211yesmaximal, characteristic, complemented
11#19133005C211yesmaximal, characteristic, complemented
12#19132984C211yesmaximal, characteristic, complemented
13#19132981C211yesmaximal, characteristic, complemented
14#19132975C211yesmaximal, characteristic, complemented
15C43×#1482C211yesmaximal, characteristic, complemented
16#14583618C411yescharacteristic
17#14583613C411yescharacteristic
18#14583605C411yescharacteristic
19#14583594—21no—
20#14583587C411yescharacteristic
21#14583585—21no—
22#14583583C411yescharacteristic
23#14583577—21no—
24#14583574—21no—
25#14583551C411yescharacteristic
26#14583546C411yescharacteristic
27#14583542C411yescharacteristic
28#14583453C2211yescharacteristic
29#14583431—21no—
30#14583431C2211yescharacteristic
31#14583427—21no—
32#14583408—21no—
33C4×#10621902C2211yescharacteristic
34C4×#10621898C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36C4×D4×D43C2211yescharacteristic
37#117×D43—21no—
38#14583026—21no—
39#14582976—21no—
40#14582967—21no—
41#14582967—21no—
42#14582958—21no—
43#14582957—21no—
44#14582956C2211yescharacteristic, complemented
45#14582955C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582950C2211yescharacteristic, complemented
49#14582921C2211yescharacteristic, complemented
50C4⋊C8×D43C2211yescharacteristic, complemented
51#14582864—21no—
52#14582853—21no—
53C4×#10621872C2211yescharacteristic
54C4×#10621872C2211yescharacteristic, complemented
55C2×C4×C43⋊C8C2211yescharacteristic, complemented
56#14582631C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
60#14582629C2211yescharacteristic, complemented
61#14582629C2211yescharacteristic, complemented
62#14582628C2211yescharacteristic
63#14582628C2211yescharacteristic
64D4⋊(C43⋊C8)C2211yescharacteristic
65D4⋊(C43⋊C8)C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, complemented
71C43×Q8⋊C8C2211yescharacteristic, complemented
72C43×Q8⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898D411yescharacteristic
78C2×D4×D43C2×C411yescharacteristic
79C22×C4×D43—21no—
80C2×#10621872—21no—
81C2×#10621872—21no—
82C2×#10621872—21no—
83C22×C43⋊C8—21no—
84C2×C8×D43—21no—
85#13063324C2×C411yescharacteristic
86#13063323C2×C411yescharacteristic
87#13063320—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063316—21no—
93#13063316C2×C411yescharacteristic
94#13063315—21no—
95#13063315—21no—
96#13063312—21no—
97#13063312C2×C411yescharacteristic
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063307—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063305—21no—
107#13063305C2×C411yescharacteristic
108#13063305C2×C411yescharacteristic
109#13063303—21no—
110#13063303—21no—
111#13063303—21no—
112#13063302—21no—
113#13063301C2×C411yescharacteristic
114#13063298—21no—
115#13063298—21no—
116#13063297—21no—
117#13063296—21no—
118#13063296C2×C411yescharacteristic
119#13063295—21no—
120#13063293—21no—
121Q8×Dic43C2×C411yescharacteristic
122C4×Dic86—21no—
123C4×Dic86C2×C411yescharacteristic
124C4×Dic86C2×C411yescharacteristic
125C4×Dic86D411yescharacteristic
126C4×Dic86C2311yescharacteristic
127C4×D172—21no—
128C4×D172C2×C411yescharacteristic
129C4×D172C2×C411yescharacteristic
130C4×D172D411yescharacteristic
131C4×D172C2311yescharacteristic
132D4×Dic43C2×C411yescharacteristic
133#13063287—21no—
134#13063287C2×C411yescharacteristic
135#13063287C2×C411yescharacteristic
136C4×C22⋊D43—21no—
137C4×C22⋊D43—21no—
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43C2×C411yescharacteristic
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143C4×C22⋊D43D411yescharacteristic
144(C22⋊D43)⋊C4—21no—
145#13063284—21no—
146#13063284C2×C411yescharacteristic
147#13063284D411yescharacteristic
148#13063283—21no—
149#13063283—21no—
150#13063283—21no—
151#13063283C2×C411yescharacteristic
152#13063282—21no—
153#13063282—21no—
154#13063282D411yescharacteristic
155#13063282D411yescharacteristic
156#13063281—21no—
157#13063281—21no—
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43C2×C411yescharacteristic
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C42×D43—21no—
165C42×D43—21no—
166C42×D43C2311yescharacteristic
167C42×D43C2311yescharacteristic
168C4⋊(C43⋊C8)C2311yescharacteristic
169C4⋊(C43⋊C8)C2311yescharacteristic
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063236—21no—
180#13063235—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8—21no—
184C4×C43⋊C8C2311yescharacteristic
185C4×C43⋊C8C2311yescharacteristic
186C8×Dic43—21no—
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic
189#124×C43C2×C411yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192#121×C43C2×C411yescharacteristic
193C4×Q8×C43C2311yescharacteristic
194C4×D4×C43—21no—
195C4×D4×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—
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⋊D43C22⋊C411yescharacteristic
218C2×C22⋊D43C22⋊C411yescharacteristic
219C22×Dic43—21no—
220#10621902—22no—
221#10621902—41no—
222D4×D43—22no—
223D4×D43—41no—
224#10621898—22no—
225#10621898—41no—
226#10621898—41no—
227#10621898—41no—
228C2×D172—21no—
229C2×D172C22⋊C411yescharacteristic
230C2×D172C22×C411yescharacteristic
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—42no—
239C2×C4×D43—42no—
240C2×C4×D43C22×C411yescharacteristic
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C2×D411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×Dic86—21no—
247C2×Dic86C22⋊C411yescharacteristic
248C2×Dic86C22×C411yescharacteristic
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C22×C411yescharacteristic
258C4⋊C4×C43C22×C411yescharacteristic
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C42×C43—21no—
265C42×C43C22×C411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2411yescharacteristic
269C22⋊Dic43—21no—
270C22⋊Dic43—21no—
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43C22⋊C411yescharacteristic
275C22⋊Dic43C22⋊C411yescharacteristic
276(C2×D43)⋊C4—21no—
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)⋊C4C22⋊C411yescharacteristic
285(C2×D43)⋊C4C22⋊C411yescharacteristic
286(C2×D43)⋊C4C22⋊C411yescharacteristic
287(C2×D43)⋊C4C22⋊C411yescharacteristic
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43C22⋊C411yescharacteristic
293C4⋊Dic43C22⋊C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295C4⋊Dic43C22×C411yescharacteristic
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—42no—
324#10621872—42no—
325#10621872—42no—
326#10621872—42no—
327C8×D43—42no—
328C23×C43—21no—
329C23×C43C2×C22⋊C411yescharacteristic
330C22×D43—21no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—81no—
334C22×D43C2×C22⋊C411yescharacteristic
335C22×D43C2×C22⋊C411yescharacteristic
336Q8×C43—21no—
337Q8×C43—21no—
338D4×C43—21no—
339D4×C43—21no—
340D4×C43—81no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C23×C411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C22⋊D43—41no—
358C22⋊D43—41no—
359C22⋊D43—42no—
360C22⋊D43—42no—
361C22⋊D43—81no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—42no—
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—41no—
374D172—42no—
375D172#13112yes—
376C4×D43—21no—
377C4×D43—21no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—21no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—41no—
385C4×D43—41no—
386C4×D43—42no—
387C4×D43—42no—
388C4×D43—42no—
389C4×D43—42no—
390C4×D43—41no—
391C4×D43—41no—
392C4×D43—81no—
393C4×D43—81no—
394Dic86—21no—
395Dic86—21no—
396Dic86—41no—
397Dic86—81no—
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#17513—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—22no—
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—21no—
419C2×D43—21no—
420C2×D43—21no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—84no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43C2×#13111yescharacteristic
432C4×C43#56811yescharacteristic
433C4×C43#57511yescharacteristic
434C4×C43#57511yescharacteristic
435Dic43—21no—
436Dic43—21no—
437Dic43—21no—
438Dic43—21no—
439Dic43—21no—
440Dic43—21no—
441Dic43—41no—
442Dic43—41no—
443Dic43—41no—
444#3475—431no—
445#2965—431no—
446#2925—431no—
447#1497—431no—
448#1495—431no—
449#1494—431no—
450#1490—431no—
451#1489—431no—
452#1488—431no—
453#1485—431no—
454#1483—431no—
455#1482D4311yescharacteristic, complemented
456#1478—431no—
457#1477—431no—
458#1476—431no—
459C2×C43—41no—
460C2×C43—81no—
461C2×C43#288011yescharacteristic
462C2×C43#289611yescharacteristic
463C2×C43#290111yescharacteristic
464D43—41no—
465D43—41no—
466D43—42no—
467#556—431no—
468#555—431no—
469#554—431no—
470#553—861no—
471#552—431no—
472#552—431no—
473#552—861no—
474#551—861no—
475#551—861no—
476#547—431no—
477#546—431no—
478#546—431no—
479#533—431no—
480#529—431no—
481#529—861no—
482#529—861no—
483#529C2×D4311yescharacteristic
484#525—861no—
485C4×#41—431no—
486C4×#41—431no—
487C4×#41—431no—
488C2×C4×D4—431no—
489C2×#117—861no—
490#446—861no—
491#436—861no—
492#435—861no—
493#435—861no—
494#433—861no—
495#433—861no—
496#432—431no—
497#432—431no—
498#431—431no—
499#431—431no—
500#431—431no—
501#431C2×D4311yescharacteristic, complemented
502#431C2×D4311yescharacteristic, complemented
503#423—431no—
504C2×C4⋊C8—431no—
505#408—861no—
506#405—861no—
507C4×M16—431no—
508C4×M16—431no—
509C2×C4×C8—431no—
510Q8⋊C8—431no—
511Q8⋊C8—431no—
512Q8⋊C8—431no—
513Q8⋊C8—431no—
514Q8⋊C8—431no—
515Q8⋊C8—431no—
516Q8⋊C8C2×D4311yescharacteristic, complemented
517Q8⋊C8C2×D4311yescharacteristic, complemented
518D4⋊C8—431no—
519D4⋊C8—431no—
520D4⋊C8—431no—
521D4⋊C8—431no—
522D4⋊C8—431no—
523D4⋊C8—431no—
524D4⋊C8C2×D4311yescharacteristic
525D4⋊C8C2×D4311yescharacteristic
526C43#1751311yescharacteristic, complemented, Sylow
527C2×#41—431no—
528C2×#41—431no—
529C2×#41—431no—
530C22×D4—431no—
531C23×C4—861no—
532C2×M16—861no—
533C2×M16—861no—
534C2×M16—861no—
535C22×C8—861no—
536C22×C8—861no—
537C4⋊Q8—431no—
538C4⋊Q8—431no—
539#126—21no—
540#126—861no—
541#126—861no—
542#126—861no—
543#126—861no—
544#126—861no—
545#125—431no—
546#125—861no—
547#125—861no—
548#125—861no—
549#125C4×D4311yescharacteristic
550#124—431no—
551#124—861no—
552#124—861no—
553#124C4×D4311yescharacteristic
554#123—21no—
555#123—861no—
556#123—861no—
557#123—861no—
558#123—861no—
559#123—861no—
560#123—861no—
561#123—861no—
562C22⋊Q8—431no—
563C22⋊Q8—431no—
564C22⋊Q8—431no—
565C22⋊Q8—861no—
566C22⋊Q8—861no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8—861no—
570C22⋊Q8C4×D4311yescharacteristic
571#121—431no—
572#121—861no—
573#121—861no—
574#121—861no—
575#121—861no—
576#121C4×D4311yescharacteristic
577#120—861no—
578#120—861no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—431no—
584C4×Q8—861no—
585C4×Q8C22×D4311yescharacteristic
586C4×D4—21no—
587C4×D4—431no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—431no—
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—431no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4—861no—
601C4×D4—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4C22×D4311yescharacteristic
606#117—21no—
607#117—431no—
608#117—431no—
609#117—431no—
610#117—431no—
611#117—431no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117—861no—
616#117—861no—
617#117—861no—
618#117—861no—
619#117—861no—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C42—431no—
627C2×C42—431no—
628C2×C42—861no—
629C2×C42—861no—
630C2×C42C22×D4311yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—431no—
633C4⋊C8—431no—
634C4⋊C8—861no—
635C4⋊C8—861no—
636C4⋊C8—861no—
637C4⋊C8—861no—
638C4⋊C8C22×D4311yescharacteristic
639C4⋊C8C22×D4311yescharacteristic
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—861no—
643C22⋊C8—861no—
644C22⋊C8—861no—
645C22⋊C8—861no—
646C22⋊C8—861no—
647#97—861no—
648#97—861no—
649#97—861no—
650#97—861no—
651C4×C8—21no—
652C4×C8—431no—
653C4×C8—431no—
654C4×C8—861no—
655C4×C8—861no—
656C4×C8C22×D4311yescharacteristic
657C4×C8C22×D4311yescharacteristic
658C24—861no—
659#41—862no—
660#41—862no—
661#41—1721no—
662#41—1721no—
663#41—1721no—
664#41—1721no—
665C2×Q8—431no—
666C2×Q8—431no—
667C2×Q8—861no—
668C2×Q8C2×C4×D4311yescharacteristic
669C2×D4—21no—
670C2×D4—431no—
671C2×D4—431no—
672C2×D4—431no—
673C2×D4—431no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—862no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—1721no—
680C2×D4C2×C4×D4311yescharacteristic
681C22×C4—21no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—431no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—1722no—
697C22×C4—1722no—
698C22×C4C2×C4×D4311yescharacteristic
699C22×C4D4×D4311yescharacteristic
700C22×C4D4×D4311yescharacteristic
701M16—1722no—
702M16—1722no—
703M16—1722no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—1722no—
713C2×C8—1722no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—431no—
722C4⋊C4—431no—
723C4⋊C4—431no—
724C4⋊C4—431no—
725C4⋊C4—431no—
726C4⋊C4—861no—
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⋊C4—861no—
738C4⋊C4C2×C4×D4311yescharacteristic
739C4⋊C4C2×C4×D4311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—431no—
746C22⋊C4—431no—
747C22⋊C4—431no—
748C22⋊C4—431no—
749C22⋊C4—431no—
750C22⋊C4—431no—
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—
761C22⋊C4—861no—
762C22⋊C4—861no—
763C22⋊C4—861no—
764C42—21no—
765C42—431no—
766C42—431no—
767C42—431no—
768C42—431no—
769C42—431no—
770C42—431no—
771C42—861no—
772C42—861no—
773C42—861no—
774C42—861no—
775C42—861no—
776C42C2×C4×D4311yescharacteristic
777C42D4×D4311yescharacteristic
778C42D4×D4311yescharacteristic
779C42C23×D4311yescharacteristic
780C23—21no—
781C23—431no—
782C23—431no—
783C23—861no—
784C23—3441no—
785C23—1722no—
786C23—1722no—
787C23C22⋊C4×D4311yescharacteristic
788Q8—21no—
789Q8—21no—
790Q8—861no—
791Q8—861no—
792Q8—3441no—
793Q8—1721no—
794D4—21no—
795D4—21no—
796D4—81no—
797D4—432no—
798D4—861no—
799D4—3441no—
800D4—1721no—
801D4—1722no—
802D4—1721no—
803D4—1721no—
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—1721no—
836C2×C4—1721no—
837C2×C4—1722no—
838C2×C4—1722no—
839C2×C4—1722no—
840C2×C4—1722no—
841C2×C4—1722no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4C22⋊C4×D4311yescharacteristic
845C2×C4C22⋊C4×D4311yescharacteristic
846C2×C4C22⋊C4×D4311yescharacteristic
847C2×C4C22×C4×D4311yescharacteristic
848C2×C4C2×D4×D4311yescharacteristic
849C2×C4C2×D4×D4311yescharacteristic
850C8—41no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—862no—
855C8—1721no—
856C8—1721no—
857C8—1721no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—861no—
865C22—861no—
866C22—862no—
867C22—861no—
868C22—861no—
869C22—861no—
870C22—861no—
871C22—3444no—
872C22—1721no—
873C22—1721no—
874C22C2×C22⋊C4×D4311yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—861no—
883C4—861no—
884C4—861no—
885C4—861no—
886C4—861no—
887C4—861no—
888C4—1721no—
889C4—1721no—
890C4—1721no—
891C4#131×D4311yescharacteristic
892C4#1458366411yescharacteristic
893C4#1458369611yescharacteristic
894C4#1458369611yescharacteristic
895C2—41no—
896C2—81no—
897C2—1721no—
898C2—1721no—
899C2—1722no—
900C2#1914304311yescharacteristic
901C2#1914311011yescharacteristic
902C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1482C2
socleC22×C43C22×C22⋊C4
prime radical#19148151C2
cosocleC42×C43C24
hypercenter#1482D43
hypocenterC43#17513
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #19143556C2semidirect
3. #19143256C2semidirect
4. #19133066C2semidirect
5. #19133057C2semidirect
6. #19133055C2semidirect
7. #19133036C2semidirect
8. #19133033C2semidirect
9. #19133030C2semidirect
10. #19133014C2semidirect
11. #19133005C2semidirect
12. #19132984C2semidirect
13. #19132981C2semidirect
14. #19132975C2semidirect
15. C43×#1482C2semidirect
44. #14582956C22semidirect
48. #14582950C22semidirect
49. #14582921C22semidirect
50. C4⋊C8×D43C22semidirect
54. C4×#10621872C22semidirect
55. C2×C4×C43⋊C8C22semidirect
56. #14582631C22semidirect
57. #14582631C22semidirect
58. Q8⋊(C43⋊C8)C22semidirect
59. Q8⋊(C43⋊C8)C22semidirect
60. #14582629C22semidirect
61. #14582629C22semidirect
69. C43×#431C22semidirect
70. C43×#431C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
455. #1482D43semidirect
501. #431C2×D43semidirect
502. #431C2×D43semidirect
516. Q8⋊C8C2×D43semidirect
517. Q8⋊C8C2×D43semidirect
526. C43#17513semidirect

Maximal subgroups

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

subgroupindex
#191481512
#191435562
#191432562
#191330662
#191330572
#191330552
#191330362
#191330332
#191330302
#191330142
#191330052
#191329842
#191329812
#191329752
C43×#14822
#1751343