Finite Group Databasebeta

← #25064091

Subgroups — #25064091

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#383×D43C211yesmaximal, characteristic, complemented
4#19133173C211yesmaximal, characteristic, complemented
5#19133172C211yesmaximal, characteristic, complemented
6#19133170C211yesmaximal, characteristic, complemented
7#19133144C212yesmaximal, complemented
8#19133140C212yesmaximal, complemented
9#19133098C212yesmaximal, complemented
10#19133096C212yesmaximal, complemented
11C43×#1521C211yesmaximal, characteristic, complemented
12#14583455C411yescharacteristic, complemented
13#14583453C411yescharacteristic, complemented
14#14583451C2211yescharacteristic
15#14583448C411yescharacteristic, complemented
16#14583446C411yescharacteristic, complemented
17#14583444C2211yescharacteristic
18#14583434C411yescharacteristic, complemented
19#14583433C2211yescharacteristic
20#14583432—21no—
21#14583432—21no—
22#14583428C411yescharacteristic, complemented
23#14583427—21no—
24#14583426—21no—
25#14583412C2211yescharacteristic
26#14583409C2211yescharacteristic
27#14583408—21no—
28#14583407—21no—
29C4×#10621902C411yescharacteristic, complemented
30#14583367—21no—
31C4×#10621900—21no—
32C4×#10621900C411yescharacteristic, complemented
33C2×C42×D43C2211yescharacteristic
34#14582955—21no—
35#14582953C2212yes—
36#14582952C2211yescharacteristic
37#14582950—21no—
38#14582921—21no—
39#14582861C2212yes—
40C4×#10621872—21no—
41#14582767C2211yescharacteristic
42#14582766—21no—
43#14582766—21no—
44#14582766C2212yes—
45#95×D43—21no—
46#95×D43—21no—
47#95×D43C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C43×#383C2211yescharacteristic
57C43×#328C2212yes—
58C43×#327C2212yes—
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43—22no—
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68#13063324C2×C411yescharacteristic, complemented
69#13063324C2×C411yescharacteristic, complemented
70#13063323C2×C411yescharacteristic, complemented
71#13063321C2×C411yescharacteristic, complemented
72#13063320—21no—
73#13063319—21no—
74#13063318—21no—
75#13063317C2×C411yescharacteristic, complemented
76#13063315—21no—
77#13063315—21no—
78#13063313C2×C411yescharacteristic, complemented
79#13063311—21no—
80#13063311—21no—
81#13063310—21no—
82#13063310—21no—
83#13063308—21no—
84#13063307—21no—
85#13063307—21no—
86#13063305C2×C411yescharacteristic
87#13063304C2311yescharacteristic
88#13063303—21no—
89#13063303—21no—
90#13063303—21no—
91#13063302—21no—
92#13063301C2×C411yescharacteristic
93#13063300C2×C411yescharacteristic
94#13063299C2311yescharacteristic
95#13063298—21no—
96#13063298—21no—
97#13063298—21no—
98#13063297—21no—
99#13063296C2×C411yescharacteristic
100#13063295—21no—
101#13063293—21no—
102Q8×Dic43C2×C411yescharacteristic, complemented
103C4×Dic86—21no—
104C4×Dic86C2×C411yescharacteristic, complemented
105#13063290—21no—
106#13063290—21no—
107#13063290—21no—
108#13063290C2×C411yescharacteristic, complemented
109C4×D172—21no—
110C4×D172C2×C411yescharacteristic, complemented
111D4×Dic43—21no—
112D4×Dic43C2×C411yescharacteristic, complemented
113#13063287—21no—
114#13063287—21no—
115#13063287—21no—
116#13063287C2×C411yescharacteristic, complemented
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122(C22⋊D43)⋊C4—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127#13063283—21no—
128#13063283—21no—
129#13063283C2×C411yescharacteristic
130#13063283C2×C411yescharacteristic
131#13063282—21no—
132#13063282—21no—
133#13063281—21no—
134#13063281—21no—
135#13063281—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43D411yescharacteristic
138C2×C4×Dic43D411yescharacteristic
139C2×C4×Dic43C2311yescharacteristic
140C42×D43—21no—
141C42×D43C2×C411yescharacteristic
142C42×D43C2×C411yescharacteristic
143C42×D43C2×C411yescharacteristic
144C42×D43C2×C411yescharacteristic
145C42×D43D411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C4⋊(C43⋊C8)—21no—
150Dic43⋊C8—22no—
151C22⋊(C43⋊C8)C2312yes—
152(C2×D43)⋊C8—22no—
153#13063235—22no—
154C4×C43⋊C8—21no—
155C43⋊#95—21no—
156C43⋊#95—21no—
157C43⋊#95—22no—
158C43⋊#95—22no—
159C43⋊#95—22no—
160C43⋊#95C2312yes—
161#126×C43—21no—
162#125×C43C2×C411yescharacteristic, complemented
163#124×C43C2×C411yescharacteristic, complemented
164#123×C43—21no—
165C22⋊Q8×C43C2311yescharacteristic
166#121×C43C2311yescharacteristic
167C4×Q8×C43C2×C411yescharacteristic, complemented
168C4×D4×C43—21no—
169C4×D4×C43C2×C411yescharacteristic, complemented
170#117×C43—21no—
171C2×C42×C43C2311yescharacteristic
172C4⋊C8×C43—21no—
173C22⋊C8×C43C2312yes—
174C4×C8×C43—21no—
175#95×C43—21no—
176#95×C43—21no—
177#95×C43C2312yes—
178C23×D43C2×D411yescharacteristic
179C2×Q8×C43C22×C411yescharacteristic
180C2×D4×C43—21no—
181C2×D4×C43C22×C411yescharacteristic
182C22×C4×C43—21no—
183C22×C4×C43—22no—
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2411yescharacteristic
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—22no—
195C22×Dic43C2×D411yescharacteristic
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198#10621902—42no—
199#10621900—42no—
200#10621900—44no—
201#10621898—44no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172C22×C411yescharacteristic
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43—44no—
212C2×C4×D43—44no—
213C2×C4×D43—44no—
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22⋊C411yescharacteristic
219C2×C4×D43C22⋊C411yescharacteristic
220C2×C4×D43C22⋊C411yescharacteristic
221C2×C4×D43C22⋊C411yescharacteristic
222C2×C4×D43C22×C411yescharacteristic
223C2×C4×D43C22×C411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86C22×C411yescharacteristic
229C2×C8×C43—22no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C22×C411yescharacteristic
235C4⋊C4×C43C22×C411yescharacteristic
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C42×C43—21no—
242C42×C43C22×C411yescharacteristic
243C42×C43C22×C411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C42×C43C2×D411yescharacteristic
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43C22×C411yescharacteristic
262C4⋊Dic43C22×C411yescharacteristic
263Dic43⋊C4—21no—
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273C4×Dic43—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22×C411yescharacteristic
287C4×Dic43C22×C411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C2×C43⋊C8—22no—
291#10621872—44no—
292C23×C43—21no—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—21no—
298C22×D43C2×C22⋊C411yescharacteristic
299C22×D43C2×C22⋊C411yescharacteristic
300Q8×C43—41no—
301D4×C43—41no—
302D4×C43—42no—
303C2×C4×C43—22no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43C2×C22⋊C411yescharacteristic
314C2×C4×C43C2×C22⋊C411yescharacteristic
315C2×C4×C43C2×C22⋊C411yescharacteristic
316C2×C4×C43C2×C22⋊C411yescharacteristic
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C22⋊D43—42no—
320C22⋊D43—42no—
321C22⋊D43—42no—
322C22⋊D43—42no—
323C22⋊D43—42no—
324C2×Dic43—22no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341D172—41no—
342D172—42no—
343D172—42no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—41no—
349C4×D43—41no—
350C4×D43—41no—
351C4×D43—41no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—42no—
357C4×D43—42no—
358C4×D43—42no—
359C4×D43—88no—
360Dic86—42no—
361Dic86—42no—
362Dic86—41no—
363C8×C43—42no—
364C43⋊C8—42no—
365#17593—431nomaximal, Sylow
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43C22×C22⋊C411yescharacteristic
372C22×C43#57512yes—
373C2×D43—28no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C2×D43#41012yes—
382C2×D43#42112yes—
383C4×C43—21no—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—41no—
390C4×C43—41no—
391C4×C43—41no—
392C4×C43—82no—
393Dic43—21no—
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398Dic43—21no—
399Dic43—41no—
400Dic43—41no—
401Dic43—41no—
402Dic43—82no—
403#3444—431no—
404#2920—431no—
405C2×#383—431no—
406#1521—431no—
407#1521—431no—
408#1521—431no—
409#1521D4311yescharacteristic, complemented
410#1515—432no—
411#1514—432no—
412#1504—432no—
413#1504—432no—
414C2×C43—22no—
415C2×C43—81no—
416C2×C43C2×#41011yescharacteristic
417C2×C43#289611yescharacteristic
418C2×C43C2×#42111yescharacteristic
419D43—22no—
420D43—22no—
421D43—81no—
422#533—431no—
423#533—431no—
424#533—431no—
425#532—431no—
426#532—431no—
427#532—431no—
428#529—431no—
429#529—431no—
430#529—431no—
431#529—861no—
432#529—861no—
433#529—861no—
434#529—861no—
435#529C2×D4311yescharacteristic
436#525—431no—
437#525—431no—
438#525—861no—
439#525—861no—
440C4×#41—431no—
441C4×#41—431no—
442C4×#41—861no—
443C4×#41—861no—
444C22×C42—431no—
445#432—432no—
446#432—861no—
447#431—431no—
448#431—861no—
449#431C2×D4311yescharacteristic
450#423—861no—
451#407—432no—
452C4×M16—861no—
453#383—431no—
454#383—432no—
455#383—861no—
456#383—861no—
457#383C2×D4311yescharacteristic
458C2×#95—432no—
459C2×#95—861no—
460C2×#95—861no—
461#328—432no—
462#328—432no—
463#328—432no—
464#328C2×D4312yes—
465#327—432no—
466#327—432no—
467#327—432no—
468#327C2×D4312yes—
469C43#1759311yescharacteristic, complemented, Sylow
470C2×#41—431no—
471C2×#41—431no—
472C2×#41—861no—
473C2×#41—861no—
474C23×C4—431no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—862no—
478C2×M16—862no—
479C4⋊Q8—431no—
480C4⋊Q8—431no—
481C4⋊Q8—431no—
482#127—431no—
483#126—21no—
484#126—861no—
485#126—861no—
486#126—861no—
487#125—431no—
488#125—861no—
489#125—861no—
490#125C4×D4311yescharacteristic, complemented
491#124—431no—
492#124—861no—
493#124—861no—
494#124C4×D4311yescharacteristic, complemented
495#123—21no—
496#123—861no—
497#123—861no—
498#123—861no—
499#123—861no—
500#123—861no—
501C22⋊Q8—431no—
502C22⋊Q8—431no—
503C22⋊Q8—431no—
504C22⋊Q8—861no—
505C22⋊Q8—861no—
506C22⋊Q8—861no—
507C22⋊Q8—861no—
508C22⋊Q8C22×D4311yescharacteristic
509#121—431no—
510#121—431no—
511#121—431no—
512#121—861no—
513#121—861no—
514#121—861no—
515#121—861no—
516#121C22×D4311yescharacteristic
517#120—861no—
518#120—861no—
519C4×Q8—431no—
520C4×Q8—431no—
521C4×Q8—431no—
522C4×Q8—861no—
523C4×Q8—861no—
524C4×Q8—861no—
525C4×Q8—861no—
526C4×Q8C4×D4311yescharacteristic, complemented
527C4×D4—21no—
528C4×D4—431no—
529C4×D4—431no—
530C4×D4—431no—
531C4×D4—861no—
532C4×D4—861no—
533C4×D4—861no—
534C4×D4—861no—
535C4×D4—861no—
536C4×D4—861no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4C4×D4311yescharacteristic, complemented
547#117—21no—
548#117—431no—
549#117—431no—
550#117—861no—
551#117—861no—
552#117—861no—
553#117—861no—
554#117—861no—
555#117—861no—
556#117—861no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—861no—
569C2×C42—861no—
570C2×C42C22×D4311yescharacteristic
571C4⋊C8—21no—
572C4⋊C8—862no—
573C4⋊C8—861no—
574C22⋊C8—432no—
575C22⋊C8—862no—
576C22⋊C8C22×D4312yes—
577#97—862no—
578C4×C8—21no—
579C4×C8—861no—
580#95—21no—
581#95—21no—
582#95—432no—
583#95—862no—
584#95—862no—
585#95—862no—
586#95—861no—
587#95—861no—
588#95C22×D4312yes—
589C24—431no—
590#41—1724no—
591#41—1724no—
592#41—1722no—
593#41—1722no—
594C2×Q8—431no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8C2×C4×D4311yescharacteristic
598C2×D4—21no—
599C2×D4—431no—
600C2×D4—861no—
601C2×D4—861no—
602C2×D4—861no—
603C2×D4—861no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4C2×C4×D4311yescharacteristic
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—862no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4—1722no—
634C22×C4—1724no—
635C22×C4—1724no—
636C22×C4—1724no—
637C22×C4D4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4C23×D4311yescharacteristic
640M16—1724no—
641C2×C8—22no—
642C2×C8—862no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—431no—
648C4⋊C4—431no—
649C4⋊C4—861no—
650C4⋊C4—861no—
651C4⋊C4—861no—
652C4⋊C4—861no—
653C4⋊C4—861no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4C2×C4×D4311yescharacteristic
662C4⋊C4C2×C4×D4311yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C22⋊C4—861no—
671C22⋊C4—861no—
672C22⋊C4—861no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C42—21no—
682C42—431no—
683C42—431no—
684C42—431no—
685C42—431no—
686C42—431no—
687C42—431no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—861no—
695C42—861no—
696C42—861no—
697C42—861no—
698C42—861no—
699C42C2×C4×D4311yescharacteristic
700C42C2×C4×D4311yescharacteristic
701C42D4×D4311yescharacteristic
702C42D4×D4311yescharacteristic
703C23—21no—
704C23—431no—
705C23—431no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—861no—
710C23C2×D4×D4311yescharacteristic
711Q8—41no—
712Q8—1721no—
713Q8—1722no—
714Q8—1722no—
715D4—41no—
716D4—42no—
717D4—1721no—
718D4—1722no—
719D4—1722no—
720D4—1722no—
721D4—1722no—
722D4—1722no—
723D4—1722no—
724D4—1722no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—431no—
736C2×C4—431no—
737C2×C4—431no—
738C2×C4—431no—
739C2×C4—431no—
740C2×C4—431no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—861no—
747C2×C4—861no—
748C2×C4—861no—
749C2×C4—3448no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4—1721no—
757C2×C4—1721no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4C22⋊C4×D4311yescharacteristic
769C2×C4C22⋊C4×D4311yescharacteristic
770C2×C4C22⋊C4×D4311yescharacteristic
771C2×C4C22⋊C4×D4311yescharacteristic
772C2×C4C22×C4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C8—42no—
775C8—1722no—
776C22—21no—
777C22—21no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—432no—
782C22—432no—
783C22—868no—
784C22—861no—
785C22—861no—
786C22—861no—
787C22—861no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22C2×C22⋊C4×D4311yescharacteristic
792C22#1458369612yes—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—82no—
803C4—861no—
804C4—861no—
805C4—861no—
806C4—861no—
807C4—861no—
808C4—861no—
809C4—3442no—
810C4—1721no—
811C4—1721no—
812C4—1721no—
813C2—22no—
814C2—81no—
815C2—862no—
816C2—862no—
817C2—3441no—
818C2#410×D4311yescharacteristic
819C2#1914311011yescharacteristic
820C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1521C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC22×C4×C43C24
hypercenter#1521D43
hypocenterC43#17593
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #383×D43C2semidirect
4. #19133173C2semidirect
5. #19133172C2semidirect
6. #19133170C2semidirect
7. #19133144C2semidirect
8. #19133140C2semidirect
9. #19133098C2semidirect
10. #19133096C2semidirect
11. C43×#1521C2semidirect
12. #14583455C4semidirect
13. #14583453C4semidirect
15. #14583448C4semidirect
16. #14583446C4semidirect
18. #14583434C4semidirect
22. #14583428C4semidirect
29. C4×#10621902C4semidirect
32. C4×#10621900C4semidirect
68. #13063324C2×C4semidirect
69. #13063324C2×C4semidirect
70. #13063323C2×C4semidirect
71. #13063321C2×C4semidirect
75. #13063317C2×C4semidirect
78. #13063313C2×C4semidirect
102. Q8×Dic43C2×C4semidirect
104. C4×Dic86C2×C4semidirect
108. #13063290C2×C4semidirect
110. C4×D172C2×C4semidirect
112. D4×Dic43C2×C4semidirect
116. #13063287C2×C4semidirect
162. #125×C43C2×C4semidirect
163. #124×C43C2×C4semidirect
167. C4×Q8×C43C2×C4semidirect
169. C4×D4×C43C2×C4semidirect
409. #1521D43semidirect
469. C43#17593semidirect
490. #125C4×D43semidirect
494. #124C4×D43semidirect
526. C4×Q8C4×D43semidirect
546. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191478892
#191432232
#383×D432
#191331732
#191331722
#191331702
#191331442
#191331402
#191330982
#191330962
C43×#15212
#1759343