Finite Group Databasebeta

← #25063750

Subgroups — #25063750

Order 11008.

1150 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic, complemented
3#376×D43C211yesmaximal, characteristic, complemented
4#19133105C212yesmaximal, complemented
5#19133101C212yesmaximal, complemented
6#19133098C212yesmaximal, complemented
7#19133096C212yesmaximal, complemented
8#19133082C211yesmaximal, characteristic, complemented
9#19133081C211yesmaximal, characteristic, complemented
10#19133079C211yesmaximal, characteristic, complemented
11C43×#1500C211yesmaximal, 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×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582955—21no—
36#14582953C2212yes—
37#14582952C2211yescharacteristic
38#14582950—21no—
39#14582921—21no—
40#14582861C2212yes—
41C4×#10621872—21no—
42#14582745—21no—
43#14582745C2211yescharacteristic
44#14582744—21no—
45#14582744C2212yes—
46#95×D43—21no—
47#95×D43C2212yes—
48#14582637C2212yes—
49#14582636C2212yes—
50#14582635C2212yes—
51#14582634C2212yes—
52#14582633C2212yes—
53#14582632C2212yes—
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic
56C43×#376C2211yescharacteristic
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×Dic43—22no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C42×D43—28no—
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43C2×C411yescharacteristic
147C42×D43C2×C411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C4⋊(C43⋊C8)—21no—
153Dic43⋊C8—22no—
154C22⋊(C43⋊C8)C2312yes—
155(C2×D43)⋊C8—22no—
156#13063235—22no—
157C4×C43⋊C8—21no—
158C43⋊#95—21no—
159C43⋊#95—22no—
160C43⋊#95—22no—
161C43⋊#95C2312yes—
162#126×C43—21no—
163#125×C43C2×C411yescharacteristic, complemented
164#124×C43C2×C411yescharacteristic, complemented
165#123×C43—21no—
166C22⋊Q8×C43C2311yescharacteristic
167#121×C43C2311yescharacteristic
168C4×Q8×C43C2×C411yescharacteristic, complemented
169C4×D4×C43—21no—
170C4×D4×C43C2×C411yescharacteristic, complemented
171#117×C43—21no—
172C2×C42×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C22⋊C8×C43C2312yes—
176C4×C8×C43—21no—
177#95×C43—21no—
178#95×C43C2312yes—
179C23×D43C2×D411yescharacteristic
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43—22no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—22no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621902—42no—
200#10621900—42no—
201#10621900—44no—
202#10621898—44no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—24no—
207C2×C4×D43—28no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—44no—
214C2×C4×D43—44no—
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×D43C22×C411yescharacteristic
225C2×C4×D43C2×D411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86C22×C411yescharacteristic
230C2×C8×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C22×C411yescharacteristic
236C4⋊C4×C43C22×C411yescharacteristic
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C42×C43—24no—
243C42×C43—21no—
244C42×C43C22×C411yescharacteristic
245C42×C43C22×C411yescharacteristic
246C42×C43C2×D411yescharacteristic
247C42×C43C2×D411yescharacteristic
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—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—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C22×C411yescharacteristic
264C4⋊Dic43C22×C411yescharacteristic
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—28no—
276C4×Dic43—24no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43—21no—
281C4×Dic43—21no—
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22⋊C411yescharacteristic
287C4×Dic43C22⋊C411yescharacteristic
288C4×Dic43C22⋊C411yescharacteristic
289C4×Dic43C22⋊C411yescharacteristic
290C4×Dic43C22×C411yescharacteristic
291C4×Dic43C22×C411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C2×C43⋊C8—22no—
295#10621872—44no—
296C23×C43—21no—
297C23×C43C22×D411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—21no—
302C22×D43C2×C22⋊C411yescharacteristic
303C22×D43C2×C22⋊C411yescharacteristic
304Q8×C43—41no—
305D4×C43—41no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—41no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C23×C411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—24no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—41no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343C2×Dic43C2×C22⋊C411yescharacteristic
344C2×Dic43C2×C22⋊C411yescharacteristic
345D172—41no—
346D172—42no—
347D172—42no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—41no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—416no—
362C4×D43—42no—
363C4×D43#10414yes—
364Dic86—42no—
365Dic86—42no—
366Dic86—41no—
367C8×C43—42no—
368C43⋊C8—42no—
369#17541—431nomaximal, Sylow
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43C22×C22⋊C411yescharacteristic
376C22×C43#57512yes—
377C2×D43—28no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—21no—
381C2×D43—21no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43#41012yes—
386C2×D43C2×#10412yes—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—44no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43C2×#10412yes—
397Dic43—21no—
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—44no—
403Dic43—41no—
404Dic43—41no—
405Dic43—41no—
406Dic43C2×#10412yes—
407#3444—431no—
408#2920—431no—
409C2×#376—431no—
410#1506—432no—
411#1505—432no—
412#1504—432no—
413#1504—432no—
414#1500—431no—
415#1500—431no—
416#1500—431no—
417#1500D4311yescharacteristic, complemented
418C2×C43—22no—
419C2×C43—81no—
420C2×C43C2×#41011yescharacteristic
421C2×C43#289611yescharacteristic
422C2×C43C22×#10411yescharacteristic
423D43—22no—
424D43—22no—
425D43—81no—
426#533—431no—
427#533—431no—
428#533—431no—
429#532—431no—
430#532—431no—
431#532—431no—
432#529—431no—
433#529—431no—
434#529—431no—
435#529—861no—
436#529—861no—
437#529—861no—
438#529—861no—
439#529C2×D4311yescharacteristic
440#525—431no—
441#525—431no—
442#525—861no—
443#525—861no—
444C4×#41—431no—
445C4×#41—431no—
446C4×#41—861no—
447C4×#41—861no—
448C22×C42—431no—
449C22×C42—861no—
450#432—432no—
451#432—861no—
452#431—431no—
453#431—861no—
454#431C2×D4311yescharacteristic
455#423—861no—
456#407—432no—
457C4×M16—861no—
458#376—431no—
459#376—432no—
460#376—861no—
461#376—861no—
462#376C2×D4311yescharacteristic
463C2×#95—432no—
464C2×#95—861no—
465#328—432no—
466#328—432no—
467#328—432no—
468#328C2×D4312yes—
469#327—432no—
470#327—432no—
471#327—432no—
472#327C2×D4312yes—
473C43#1754111yescharacteristic, complemented, Sylow
474C2×#41—431no—
475C2×#41—431no—
476C2×#41—861no—
477C2×#41—861no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—862no—
482C2×M16—862no—
483C4⋊Q8—431no—
484C4⋊Q8—431no—
485C4⋊Q8—431no—
486#127—431no—
487#126—21no—
488#126—861no—
489#126—861no—
490#126—861no—
491#125—431no—
492#125—861no—
493#125—861no—
494#125C4×D4311yescharacteristic, complemented
495#124—431no—
496#124—861no—
497#124—861no—
498#124C4×D4311yescharacteristic, complemented
499#123—21no—
500#123—861no—
501#123—861no—
502#123—861no—
503#123—861no—
504#123—861no—
505C22⋊Q8—431no—
506C22⋊Q8—431no—
507C22⋊Q8—431no—
508C22⋊Q8—861no—
509C22⋊Q8—861no—
510C22⋊Q8—861no—
511C22⋊Q8—861no—
512C22⋊Q8C22×D4311yescharacteristic
513#121—431no—
514#121—431no—
515#121—431no—
516#121—861no—
517#121—861no—
518#121—861no—
519#121—861no—
520#121C22×D4311yescharacteristic
521#120—861no—
522#120—861no—
523C4×Q8—431no—
524C4×Q8—431no—
525C4×Q8—431no—
526C4×Q8—861no—
527C4×Q8—861no—
528C4×Q8—861no—
529C4×Q8—861no—
530C4×Q8C4×D4311yescharacteristic, complemented
531C4×D4—21no—
532C4×D4—431no—
533C4×D4—431no—
534C4×D4—431no—
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×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4C4×D4311yescharacteristic, complemented
551#117—21no—
552#117—431no—
553#117—431no—
554#117—861no—
555#117—861no—
556#117—861no—
557#117—861no—
558#117—861no—
559#117—861no—
560#117—861no—
561C2×C42—21no—
562C2×C42—431no—
563C2×C42—431no—
564C2×C42—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—861no—
574C2×C42—868no—
575C2×C42—861no—
576C2×C42—862no—
577C2×C42—861no—
578C2×C42C22×D4311yescharacteristic
579C4⋊C8—21no—
580C4⋊C8—862no—
581C4⋊C8—861no—
582C22⋊C8—432no—
583C22⋊C8—862no—
584C22⋊C8C22×D4312yes—
585#97—862no—
586C4×C8—21no—
587C4×C8—861no—
588#95—21no—
589#95—432no—
590#95—862no—
591#95—862no—
592#95—861no—
593#95C22×D4312yes—
594C24—431no—
595#41—1724no—
596#41—1724no—
597#41—1722no—
598#41—1722no—
599C2×Q8—431no—
600C2×Q8—861no—
601C2×Q8—861no—
602C2×Q8C2×C4×D4311yescharacteristic
603C2×D4—21no—
604C2×D4—431no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4C2×C4×D4311yescharacteristic
613C22×C4—22no—
614C22×C4—21no—
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—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—864no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—868no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—862no—
637C22×C4—861no—
638C22×C4—1722no—
639C22×C4—1722no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4311yescharacteristic
645M16—1724no—
646C2×C8—22no—
647C2×C8—862no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—431no—
653C4⋊C4—431no—
654C4⋊C4—861no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4C2×C4×D4311yescharacteristic
667C4⋊C4C2×C4×D4311yescharacteristic
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—861no—
674C22⋊C4—861no—
675C22⋊C4—861no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C42—24no—
687C42—21no—
688C42—431no—
689C42—431no—
690C42—431no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—861no—
701C42—861no—
702C42—861no—
703C42—861no—
704C42—864no—
705C42—868no—
706C42—861no—
707C42C2×C4×D4311yescharacteristic
708C42C2×C4×D4311yescharacteristic
709C42D4×D4311yescharacteristic
710C42D4×D4311yescharacteristic
711C23—21no—
712C23—431no—
713C23—431no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—861no—
718C23C2×D4×D4311yescharacteristic
719Q8—41no—
720Q8—1721no—
721Q8—1722no—
722Q8—1722no—
723D4—41no—
724D4—42no—
725D4—1721no—
726D4—1722no—
727D4—1722no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732D4—1722no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—431no—
744C2×C4—434no—
745C2×C4—431no—
746C2×C4—431no—
747C2×C4—431no—
748C2×C4—431no—
749C2×C4—431no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—864no—
758C2×C4—861no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—1721no—
762C2×C4—1721no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—17216no—
770C2×C4—1721no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1722no—
774C2×C4—1722no—
775C2×C4—1722no—
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22⋊C4×D4311yescharacteristic
779C2×C4C22⋊C4×D4311yescharacteristic
780C2×C4C22×C4×D4311yescharacteristic
781C2×C4C2×D4×D4311yescharacteristic
782C8—42no—
783C8—1722no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—432no—
790C22—432no—
791C22—868no—
792C22—861no—
793C22—861no—
794C22—861no—
795C22—861no—
796C22—1721no—
797C22—1721no—
798C22—1721no—
799C22C2×C22⋊C4×D4311yescharacteristic
800C22#1458369612yes—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—432no—
811C4—861no—
812C4—861no—
813C4—861no—
814C4—861no—
815C4—861no—
816C4—1724no—
817C4—1721no—
818C4—1721no—
819C4—1721no—
820C4#104×D4312yes—
821C2—22no—
822C2—81no—
823C2—862no—
824C2—862no—
825C2—3441no—
826C2#410×D4311yescharacteristic
827C2#1914311011yescharacteristic
828C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1500C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC22×C4×C43C24
hypercenter#1500D43
hypocenterC43#17541
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #19143223C2semidirect
3. #376×D43C2semidirect
4. #19133105C2semidirect
5. #19133101C2semidirect
6. #19133098C2semidirect
7. #19133096C2semidirect
8. #19133082C2semidirect
9. #19133081C2semidirect
10. #19133079C2semidirect
11. C43×#1500C2semidirect
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
163. #125×C43C2×C4semidirect
164. #124×C43C2×C4semidirect
168. C4×Q8×C43C2×C4semidirect
170. C4×D4×C43C2×C4semidirect
417. #1500D43semidirect
473. C43#17541semidirect
494. #125C4×D43semidirect
498. #124C4×D43semidirect
530. C4×Q8C4×D43semidirect
550. 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
#376×D432
#191331052
#191331012
#191330982
#191330962
#191330822
#191330812
#191330792
C43×#15002
#1754143