Finite Group Databasebeta

← #25960582

Subgroups — #25960582

Order 11008.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583666C211yesmaximal, characteristic, complemented
2C2×#131×D43C211yesmaximal, characteristic, complemented
3#41×C22⋊D43C211yesmaximal, characteristic
4#19143335C213yesmaximal, complemented
5#19143327C213yesmaximal, complemented
6#19143325C213yesmaximal, complemented
7#19143316C213yesmaximal, complemented
8#19143310C213yesmaximal, complemented
9#19143294C213yesmaximal, complemented
10#19143292C213yesmaximal, complemented
11C2×#14582973C213yesmaximal, complemented
12#19143161C211yesmaximal, characteristic, complemented
13#19143042C211yesmaximal, characteristic, complemented
14#19143021C211yesmaximal, characteristic, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583666—28no—
18C2×#13063333C2213yescomplemented
19C2×#13063332C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21C2×#13063332C2213yescomplemented
22C2×#13063332C2213yescomplemented
23C2×#13063331C2213yescomplemented
24#131×D43—28no—
25C22×#10621877C2213yescomplemented
26C22×#10621877C2213yescomplemented
27C2×M16×D43C2213yescomplemented
28C22×C8×D43C2213yescomplemented
29#14583568C411yescharacteristic
30Q8×C22⋊D43C411yescharacteristic
31#14583560C411yescharacteristic
32#14583556C411yescharacteristic
33#14583548C413yes—
34#14583543C413yes—
35#14583537C413yes—
36D4×C22⋊D43C413yes—
37#14583445C2213yes—
38#14583410C2213yes—
39#14583406C2213yes—
40#41×Dic43C2211yescharacteristic
41C2×C4×C22⋊D43C2213yes—
42#14582974C2216yescomplemented
43#14582974C2216yescomplemented
44#14582973C2211yescharacteristic
45#14582973C2213yes—
46#14582973C2213yescomplemented
47#14582973C2213yescomplemented
48#14582973C2213yescomplemented
49#14582973C2213yescomplemented
50#14582973C2213yescomplemented
51#14582973C2213yescomplemented
52#14582973C2216yescomplemented
53#14582967C2216yescomplemented
54#14582967C2216yescomplemented
55(C22⋊D43)⋊C8C2216yescomplemented
56(C22⋊D43)⋊C8C2216yescomplemented
57#14582927C2213yescomplemented
58#14582925C2213yescomplemented
59#14582922C2213yescomplemented
60C2×Dic43⋊C8C2213yescomplemented
61#14582867C2213yescomplemented
62#14582865C2213yescomplemented
63#14582862C2213yescomplemented
64C2×(C2×D43)⋊C8C2213yescomplemented
65#14582857C2213yescomplemented
66#14582854C2213yescomplemented
67M16×Dic43C2213yescomplemented
68C2×#13063235C2213yescomplemented
69C22×#41×C43C2211yescharacteristic
70C2×#131×C43C2211yescharacteristic
71C2×#131×C43C2211yescharacteristic
72C43×#408C2213yescomplemented
73C43×#408C2213yescomplemented
74C43×#407C2213yescomplemented
75C2×C22⋊C8×C43C2213yescomplemented
76C2×#10621902C2×C411yescharacteristic
77C2×#10621898C2313yes—
78C2×#10621900C2×C413yes—
79#41×D43—24no—
80#41×D43—24no—
81C2×Q8×D43C2×C411yescharacteristic
82C22×C22⋊D43C2×C413yes—
83C2×D4×D43C2×C413yes—
84C22×C4×D43C2313yes—
85#13063333—212no—
86#13063332—24no—
87#13063332—212no—
88#13063332—212no—
89#13063332D418yescomplemented
90#13063331—212no—
91C2×#10621877—212no—
92C2×#10621877—212no—
93C2×#10621877C2313yes—
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2313yes—
96C2×#10621877C2313yes—
97C2×#10621877C2313yes—
98C2×#10621877C2313yes—
99C2×#10621872C2316yes—
100M16×D43—212no—
101C22×C43⋊C8C2313yes—
102C22×C43⋊C8C2316yes—
103C22×C43⋊C8C2313yes—
104C2×C8×D43—212no—
105C2×C8×D43C2311yescharacteristic
106C2×C8×D43C2313yes—
107C2×C8×D43C2313yes—
108C2×C8×D43C2313yes—
109#13063323C2×C413yes—
110#13063321C2×C413yes—
111#13063314C2×C413yes—
112#13063312C2×C413yes—
113#13063308C2×C416yes—
114#13063306C2×C416yes—
115#13063304C2×C413yes—
116#13063304C2×C413yes—
117#13063301C2×C413yes—
118#13063301C2×C413yes—
119#13063299C2×C413yes—
120#13063299C2×C413yes—
121#13063297C2×C416yes—
122#13063297C2×C416yes—
123#13063296C2×C413yes—
124#13063296C2×C413yes—
125#13063294C2×C416yes—
126#13063293C2×C416yes—
127Q8×Dic43C2×C411yescharacteristic
128Q8×Dic43C2×C411yescharacteristic
129D4×Dic43C2×C413yes—
130D4×Dic43C2×C413yes—
131C4×C22⋊D43C2×C413yes—
132C4×C22⋊D43C2×C413yes—
133C4×C22⋊D43C2×C413yes—
134C4×C22⋊D43C2×C413yes—
135C4×C22⋊D43C2311yescharacteristic
136C4×C22⋊D43C2313yes—
137C4×C22⋊D43C2313yes—
138C4×C22⋊D43C2313yes—
139C4×C22⋊D43C2316yes—
140#13063284C2313yes—
141C2×Dic43⋊C4C2×C413yes—
142C2×C22⋊Dic43C2×C413yes—
143C2×(C2×D43)⋊C4C2×C413yes—
144C2×C4×Dic43C2313yes—
145Dic43⋊C8C2311yescharacteristic
146Dic43⋊C8C2313yes—
147Dic43⋊C8C2313yes—
148Dic43⋊C8C2313yes—
149Dic43⋊C8C2316yes—
150(C2×D43)⋊C8C2311yescharacteristic
151(C2×D43)⋊C8C2313yes—
152(C2×D43)⋊C8C2313yes—
153(C2×D43)⋊C8C2313yes—
154(C2×D43)⋊C8C2316yes—
155#13063235C2311yescharacteristic
156#13063235C2313yes—
157#13063235C2313yes—
158#13063235C2313yes—
159C8×Dic43C2316yes—
160C2×#41×C43—24no—
161C2×#41×C43—24no—
162C2×#41×C43C2×C411yescharacteristic
163C2×#41×C43C2×C413yes—
164C2×#41×C43C2313yes—
165C2×#41×C43C2311yescharacteristic
166C22×Q8×C43C2×C411yescharacteristic
167C22×D4×C43C2×C413yes—
168C23×C4×C43C2313yes—
169#131×C43—24no—
170#131×C43—24no—
171C2×M16×C43C2313yes—
172C2×M16×C43C2313yes—
173C22×C8×C43C2313yes—
174C22×C8×C43C2313yes—
175C22⋊C8×C43C2311yescharacteristic
176C22⋊C8×C43C2313yes—
177C22⋊C8×C43C2313yes—
178C22⋊C8×C43C2313yes—
179C22⋊C8×C43C2316yes—
180C24×C43C22×C413yes—
181C23×D43C22×C413yes—
182#41×C43—24no—
183#41×C43—212no—
184#41×C43—26no—
185#41×C43—26no—
186#41×C43C2×D414yes—
187#41×C43#4114yes—
188C2×Q8×C43—24no—
189C2×Q8×C43C22×C413yes—
190C2×Q8×C43C22×C411yescharacteristic
191C2×D4×C43—212no—
192C2×D4×C43C22×C416yes—
193C2×D4×C43C22×C413yes—
194C2×D4×C43C22×C413yes—
195C22×C4×C43—26no—
196C22×C4×C43—26no—
197C22×C4×C43C22×C413yes—
198C22×C4×C43C22×C413yes—
199C22×C4×C43C22×C413yes—
200C22×C4×C43C2411yescharacteristic
201C22×C4×C43C2413yes—
202C22×C4×C43C2413yes—
203C2×C22⋊D43—46no—
204C2×C22⋊D43C22×C411yescharacteristic
205C2×C22⋊D43C22×C413yes—
206C2×C22⋊D43C22×C416yes—
207C2×C22⋊D43C22×C413yes—
208C2×C22⋊D43C22×C413yes—
209C2×C22⋊D43C22×C416yes—
210C22×Dic43C22×C413yes—
211C22×Dic43C22×C413yes—
212C22×Dic43C22×C413yes—
213#10621902—24no—
214Q8×D43—24no—
215#10621900—212no—
216D4×D43—212no—
217#10621898—26no—
218#10621898—26no—
219C2×D172C22×C413yes—
220C2×C4×D43—26no—
221C2×C4×D43—26no—
222C2×C4×D43C22×C413yes—
223C2×C4×D43C22×C413yes—
224C2×C4×D43C2411yescharacteristic
225C2×C4×D43C2413yes—
226C2×Dic86C22×C413yes—
227M16×C43—26no—
228M16×C43—26no—
229C2×C8×C43—26no—
230C2×C8×C43—26no—
231C2×C8×C43C2411yescharacteristic
232C2×C8×C43C2411yescharacteristic
233C2×C8×C43C2413yes—
234C2×C8×C43C2413yes—
235C22⋊Dic43C22×C411yescharacteristic
236C22⋊Dic43C22×C413yes—
237C22⋊Dic43C22×C413yes—
238C22⋊Dic43C22×C413yes—
239C22⋊Dic43C22×C416yes—
240C22⋊Dic43C22×C416yes—
241(C2×D43)⋊C4C22×C411yescharacteristic
242(C2×D43)⋊C4C22×C413yes—
243(C2×D43)⋊C4C22×C413yes—
244(C2×D43)⋊C4C22×C413yes—
245(C2×D43)⋊C4C22×C416yes—
246C4⋊Dic43C22×C413yes—
247C4⋊Dic43C22×C413yes—
248Dic43⋊C4C22×C411yescharacteristic
249Dic43⋊C4C22×C413yes—
250Dic43⋊C4C22×C413yes—
251Dic43⋊C4C22×C413yes—
252Dic43⋊C4C22×C416yes—
253C4×Dic43C22×C413yes—
254C4×Dic43C22×C413yes—
255C4×Dic43C2413yes—
256C4×Dic43C2411yescharacteristic
257#10621877—26no—
258#10621877—22no—
259#10621877—26no—
260#10621877—26no—
261#10621877—26no—
262#10621877C2×D4112yescomplemented
263C2×C43⋊C8—26no—
264C2×C43⋊C8—212no—
265C2×C43⋊C8C2×D4112yescomplemented
266C2×C43⋊C8C2411yescharacteristic
267C2×C43⋊C8C2413yes—
268C2×C43⋊C8C2413yes—
269C2×C43⋊C8C2411yescharacteristic
270#10621872—212no—
271C8×D43—22no—
272C8×D43—26no—
273C8×D43—26no—
274C8×D43—26no—
275C23×C43—26no—
276C23×C43—43no—
277C23×C43—43no—
278C23×C43C23×C411yescharacteristic
279C23×C43C23×C413yes—
280C23×C43C23×C413yes—
281C22×D43—26no—
282C22×D43—26no—
283C22×D43—43no—
284C22×D43C23×C413yes—
285C22×D43C23×C411yescharacteristic
286Q8×C43—26no—
287Q8×C43C4×D414yes—
288D4×C43—212no—
289D4×C43—26no—
290D4×C43C4×D4112yes—
291C2×C4×C43—26no—
292C2×C4×C43—26no—
293C2×C4×C43—26no—
294C2×C4×C43—23no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—23no—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C23×C413yes—
300C2×C4×C43C23×C413yes—
301C2×C4×C43C22×D416yes—
302C2×C4×C43C2×#4116yes—
303C2×C4×C43C2511yescharacteristic
304C22⋊D43—212no—
305C22⋊D43—22no—
306C22⋊D43—26no—
307C22⋊D43—43no—
308C22⋊D43—43no—
309C22⋊D43—46no—
310C2×Dic43—26no—
311C2×Dic43—43no—
312C2×Dic43—43no—
313C2×Dic43C23×C411yescharacteristic
314C2×Dic43C23×C411yescharacteristic
315C2×Dic43C23×C413yes—
316C2×Dic43C23×C413yes—
317C2×Dic43C23×C413yes—
318C2×Dic43C23×C411yescharacteristic
319D172—26no—
320C4×D43—26no—
321C4×D43—26no—
322C4×D43—21no—
323C4×D43—23no—
324C4×D43—21no—
325C4×D43—23no—
326Dic86—26no—
327C8×C43—21no—
328C8×C43—23no—
329C8×C43—21no—
330C8×C43—23no—
331C43⋊C8—21no—
332C43⋊C8—23no—
333C43⋊C8C22×D412yes—
334C43⋊C8C22×D416yes—
335#60146—431nomaximal, Sylow
336C22×C43—23no—
337C22×C43—23no—
338C22×C43—21no—
339C22×C43—23no—
340C22×C43—21no—
341C22×C43—23no—
342C22×C43—21no—
343C22×C43—23no—
344C22×C43—86no—
345C22×C43C2×C4×D416yes—
346C22×C43C24×C411yescharacteristic
347C2×D43—21no—
348C2×D43—21no—
349C2×D43—23no—
350C2×D43—23no—
351C2×D43—23no—
352C2×D43—412no—
353C2×D43#56812yescomplemented
354C4×C43—21no—
355C4×C43—23no—
356C4×C43C2×C4×D416yes—
357C4×C43C23×D411yescharacteristic
358C4×C43C22×#4111yescharacteristic
359Dic43—23no—
360Dic43—21no—
361Dic43—21no—
362Dic43—23no—
363Dic43—21no—
364Dic43—23no—
365C2×#568—431no—
366C22×#131—431no—
367D4×#41—431no—
368#2935—433no—
369D4×M16—433no—
370#2933—433no—
371#2933—433no—
372#2932—433no—
373#2930—433no—
374#2929—433no—
375C2×#435—433no—
376#2906—431no—
377#2880—431no—
378#2880D4311yescharacteristic, complemented
379#2875—431no—
380C2×C43—26no—
381C2×C43—43no—
382C2×C43—41no—
383C2×C43C22×C4×D411yescharacteristic
384C2×C43C2×#56811yescharacteristic
385C2×C43#357311yescharacteristic
386D43—22no—
387D43—43no—
388C22×#41—431no—
389C22×#41C2×D4311yescharacteristic
390#568—868no—
391C2×#131—431no—
392C2×#131—431no—
393C2×#131—433no—
394C2×#131—433no—
395C2×#131—433no—
396C2×#131—433no—
397C2×#131—868no—
398C2×#131C2×D4311yescharacteristic
399C2×#131C2×D4311yescharacteristic
400C22×M16—433no—
401C22×M16—433no—
402C22×M16—433no—
403C23×C8—433no—
404#550—431no—
405D4×Q8—431no—
406#548—431no—
407#548—431no—
408#547—433no—
409#546—433no—
410#546—433no—
411D42—433no—
412#532—433no—
413#525—433no—
414#525—433no—
415C4×#41—431no—
416C2×C4×D4—433no—
417#436—436no—
418#436—436no—
419#435—431no—
420#435—433no—
421#435—433no—
422#435—433no—
423#435—433no—
424#435—433no—
425#435—433no—
426#435—433no—
427#435—436no—
428#435—436no—
429#435—436no—
430C8×D4—436no—
431C8×D4—436no—
432#424—433no—
433#424—433no—
434#423—433no—
435C2×C4⋊C8—433no—
436#408—433no—
437#408—433no—
438#408C2×D4313yescomplemented
439#408C2×D4313yescomplemented
440#407—433no—
441#407C2×D4313yescomplemented
442C2×C22⋊C8—433no—
443C2×C22⋊C8C2×D4313yescomplemented
444#405—433no—
445#405—433no—
446C4×M16—433no—
447C2×#97—433no—
448C43#6014611yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—431no—
452C2×#41—433no—
453C2×#41—433no—
454C2×#41—864no—
455C2×#41—864no—
456C2×#41C4×D4313yes—
457C2×#41C4×D4311yescharacteristic
458C2×#41C22×D4313yes—
459C2×#41C22×D4311yescharacteristic
460C22×Q8—431no—
461C22×Q8C4×D4311yescharacteristic
462C22×D4—433no—
463C22×D4—433no—
464C22×D4C4×D4313yes—
465C23×C4—433no—
466C23×C4C22×D4313yes—
467#131—24no—
468#131—24no—
469#131—438no—
470#131—8612no—
471#131—8612no—
472#131—8612no—
473#131—8612no—
474#131—864no—
475C2×M16—433no—
476C2×M16—431no—
477C2×M16—433no—
478C2×M16—433no—
479C2×M16—433no—
480C2×M16—433no—
481C2×M16—436no—
482C2×M16—8612no—
483C2×M16—8612no—
484C2×M16—8612no—
485C2×M16C22×D4313yes—
486C2×M16C22×D4313yes—
487C22×C8—433no—
488C22×C8—433no—
489C22×C8—436no—
490C22×C8—431no—
491C22×C8—433no—
492C22×C8—433no—
493C22×C8—433no—
494C22×C8—8612no—
495C22×C8C22×D4313yes—
496C22×C8C22×D4313yes—
497C4⋊Q8—433no—
498#127—433no—
499#124—433no—
500#124—433no—
501#123—436no—
502#123—436no—
503C22⋊Q8—433no—
504C22⋊Q8—433no—
505C22⋊Q8—433no—
506C22⋊Q8—433no—
507#121—433no—
508#121—433no—
509#121—436no—
510#121—436no—
511#121—433no—
512#121—433no—
513#120—436no—
514#120—436no—
515C4×Q8—431no—
516C4×Q8—431no—
517C4×D4—433no—
518C4×D4—433no—
519C4×D4—433no—
520C4×D4—433no—
521C4×D4—433no—
522C4×D4—433no—
523C4×D4—431no—
524C4×D4—433no—
525C4×D4—433no—
526C4×D4—433no—
527C4×D4—436no—
528#117—433no—
529C2×C4⋊C4—433no—
530C2×C22⋊C4—433no—
531C2×C22⋊C4—433no—
532C2×C42—433no—
533C4⋊C8—431no—
534C4⋊C8—433no—
535C4⋊C8—433no—
536C4⋊C8—433no—
537C4⋊C8—436no—
538C22⋊C8—431no—
539C22⋊C8—433no—
540C22⋊C8—433no—
541C22⋊C8—433no—
542C22⋊C8—436no—
543C22⋊C8C22×D4311yescharacteristic
544C22⋊C8C22×D4313yes—
545C22⋊C8C22×D4313yes—
546C22⋊C8C22×D4313yes—
547C22⋊C8C22×D4316yes—
548#97—431no—
549#97—433no—
550#97—433no—
551#97—433no—
552C4×C8—436no—
553C24—433no—
554C24C2×C4×D4313yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—864no—
560#41—8612no—
561#41—866no—
562#41—866no—
563#41D4×D4314yes—
564#41#1062190014yes—
565C2×Q8—24no—
566C2×Q8—433no—
567C2×Q8—864no—
568C2×Q8C2×C4×D4313yes—
569C2×Q8C2×C4×D4311yescharacteristic
570C2×D4—212no—
571C2×D4—431no—
572C2×D4—433no—
573C2×D4—436no—
574C2×D4—433no—
575C2×D4—433no—
576C2×D4—436no—
577C2×D4—433no—
578C2×D4—8612no—
579C2×D4—1726no—
580C2×D4C2×C4×D4316yes—
581C2×D4C2×C4×D4313yes—
582C2×D4C2×C4×D4313yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—433no—
586C22×C4—433no—
587C22×C4—433no—
588C22×C4—433no—
589C22×C4—433no—
590C22×C4—431no—
591C22×C4—433no—
592C22×C4—866no—
593C22×C4—866no—
594C22×C4C2×C4×D4313yes—
595C22×C4C2×C4×D4313yes—
596C22×C4C2×C4×D4313yes—
597C22×C4C23×D4313yes—
598C22×C4C23×D4311yescharacteristic
599C22×C4C23×D4313yes—
600M16—26no—
601M16—26no—
602M16—4312no—
603M16—8612no—
604M16—862no—
605M16—866no—
606M16—866no—
607M16—866no—
608M16—866no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—4312no—
612C2×C8—433no—
613C2×C8—431no—
614C2×C8—431no—
615C2×C8—433no—
616C2×C8—862no—
617C2×C8—866no—
618C2×C8—866no—
619C2×C8—866no—
620C2×C8—8612no—
621C2×C8—866no—
622C2×C8C23×D4313yes—
623C2×C8C23×D4311yescharacteristic
624C2×C8C23×D4311yescharacteristic
625C2×C8C23×D4313yes—
626C4⋊C4—431no—
627C4⋊C4—433no—
628C4⋊C4—433no—
629C4⋊C4—433no—
630C4⋊C4—433no—
631C4⋊C4—433no—
632C4⋊C4—436no—
633C22⋊C4—431no—
634C22⋊C4—433no—
635C22⋊C4—433no—
636C22⋊C4—433no—
637C22⋊C4—436no—
638C22⋊C4—436no—
639C22⋊C4—431no—
640C22⋊C4—433no—
641C22⋊C4—433no—
642C22⋊C4—433no—
643C22⋊C4—436no—
644C42—433no—
645C42—433no—
646C42—433no—
647C42—431no—
648C23—26no—
649C23—43no—
650C23—43no—
651C23—431no—
652C23—433no—
653C23—866no—
654C23—866no—
655C23—1723no—
656C23C22×C4×D4311yescharacteristic
657C23C22×C4×D4313yes—
658C23C22×C4×D4313yes—
659Q8—26no—
660Q8—866no—
661Q8(C22⋊D43)⋊C414yes—
662D4—212no—
663D4—26no—
664D4—862no—
665D4—866no—
666D4—8612no—
667D4—866no—
668D4—1723no—
669D4—1723no—
670D4—1726no—
671D4(C22⋊D43)⋊C4112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—23no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—23no—
679C2×C4—431no—
680C2×C4—431no—
681C2×C4—433no—
682C2×C4—433no—
683C2×C4—431no—
684C2×C4—433no—
685C2×C4—866no—
686C2×C4—866no—
687C2×C4—866no—
688C2×C4—861no—
689C2×C4—863no—
690C2×C4—861no—
691C2×C4—863no—
692C2×C4—1723no—
693C2×C4—1723no—
694C2×C4C22×C4×D4311yescharacteristic
695C2×C4C22×C4×D4313yes—
696C2×C4C22×C4×D4313yes—
697C2×C4C2×D4×D4316yes—
698C2×C4C2×#1062190016yes—
699C2×C4C24×D4311yescharacteristic
700C8—21no—
701C8—23no—
702C8—21no—
703C8—23no—
704C8—432no—
705C8—436no—
706C8—863no—
707C8—861no—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—432no—
718C22—861no—
719C22—861no—
720C22—863no—
721C22—863no—
722C22—863no—
723C22—17212no—
724C22C2×(C22⋊D43)⋊C416yes—
725C22C23×C4×D4311yescharacteristic
726C4—21no—
727C4—23no—
728C4—861no—
729C4—863no—
730C4—861no—
731C4—863no—
732C4—861no—
733C4—863no—
734C4C2×(C22⋊D43)⋊C416yes—
735C4C22×D4×D4311yescharacteristic
736C4C22×#1062190011yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—862no—
741C2—1723no—
742C2C22×(C22⋊D43)⋊C411yescharacteristic
743C2#568×D4311yescharacteristic
744C2#1914930611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2880C2
prime radical#41×C22⋊D43C2
cosocleC2×C4×C43C25
hypercenter#2880D43
hypocenterC43#60146
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. C2×#14583666C2semidirect
2. C2×#131×D43C2semidirect
4. #19143335C2semidirect
5. #19143327C2semidirect
6. #19143325C2semidirect
7. #19143316C2semidirect
8. #19143310C2semidirect
9. #19143294C2semidirect
10. #19143292C2semidirect
11. C2×#14582973C2semidirect
12. #19143161C2semidirect
13. #19143042C2semidirect
14. #19143021C2semidirect
15. C43×#2880C2semidirect
18. C2×#13063333C22semidirect
21. C2×#13063332C22semidirect
22. C2×#13063332C22semidirect
23. C2×#13063331C22semidirect
25. C22×#10621877C22semidirect
26. C22×#10621877C22semidirect
27. C2×M16×D43C22semidirect
28. C22×C8×D43C22semidirect
42. #14582974C22semidirect
43. #14582974C22semidirect
46. #14582973C22semidirect
47. #14582973C22semidirect
48. #14582973C22semidirect
49. #14582973C22semidirect
50. #14582973C22semidirect
51. #14582973C22semidirect
52. #14582973C22semidirect
53. #14582967C22semidirect
54. #14582967C22semidirect
55. (C22⋊D43)⋊C8C22semidirect
56. (C22⋊D43)⋊C8C22semidirect
57. #14582927C22semidirect
58. #14582925C22semidirect
59. #14582922C22semidirect
60. C2×Dic43⋊C8C22semidirect
61. #14582867C22semidirect
62. #14582865C22semidirect
63. #14582862C22semidirect
64. C2×(C2×D43)⋊C8C22semidirect
65. #14582857C22semidirect
66. #14582854C22semidirect
67. M16×Dic43C22semidirect
68. C2×#13063235C22semidirect
72. C43×#408C22semidirect
73. C43×#408C22semidirect
74. C43×#407C22semidirect
75. C2×C22⋊C8×C43C22semidirect
89. #13063332D4semidirect
262. #10621877C2×D4semidirect
265. C2×C43⋊C8C2×D4semidirect
353. C2×D43#568semidirect
378. #2880D43semidirect
438. #408C2×D43semidirect
439. #408C2×D43semidirect
441. #407C2×D43semidirect
443. C2×C22⋊C8C2×D43semidirect
448. C43#60146semidirect

Maximal subgroups

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

subgroupindex
C2×#145836662
C2×#131×D432
#41×C22⋊D432
#191433352
#191433272
#191433252
#191433162
#191433102
#191432942
#191432922
C2×#145829732
#191431612
#191430422
#191430212
C43×#28802
#6014643