Finite Group Databasebeta

← #25960587

Subgroups — #25960587

Order 11008.

2742 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×#14583664C211yesmaximal, characteristic, complemented
2#41×C22⋊D43C211yesmaximal, characteristic
3#19143337C213yesmaximal, complemented
4M16×C22⋊D43C213yesmaximal, complemented
5#19143320C213yesmaximal, complemented
6#19143317C213yesmaximal, complemented
7#19143305C213yesmaximal, complemented
8#19143298C213yesmaximal, complemented
9#19143296C213yesmaximal, complemented
10C2×#14582975C213yesmaximal, complemented
11#19143161C211yesmaximal, characteristic, complemented
12#19143044C211yesmaximal, characteristic, complemented
13#19143042C211yesmaximal, characteristic, complemented
14#131×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#568C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17#14583664—28no—
18C2×#13063333C2213yescomplemented
19C2×#13063332C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21C2×#13063331C2213yescomplemented
22C22×#10621872C2213yescomplemented
23C2×M16×D43C2213yescomplemented
24#14583568C411yescharacteristic
25Q8×C22⋊D43C411yescharacteristic
26#14583560C411yescharacteristic
27#14583556C411yescharacteristic
28#14583548C413yes—
29#14583543C413yes—
30#14583537C413yes—
31D4×C22⋊D43C413yes—
32#14583445C2213yes—
33#14583410C2213yes—
34#14583406C2213yes—
35#41×Dic43C2211yescharacteristic
36C2×C4×C22⋊D43C2213yes—
37#14582975C2211yescharacteristic
38#14582975C2213yes—
39#14582975C2213yescomplemented
40#14582975C2213yescomplemented
41#14582975C2213yescomplemented
42#14582975C2213yescomplemented
43#14582975C2213yescomplemented
44#14582975C2213yescomplemented
45#14582975C2216yescomplemented
46#14582970C2216yescomplemented
47#14582970C2216yescomplemented
48#14582968C2216yescomplemented
49#14582968C2216yescomplemented
50C8×C22⋊D43C2216yescomplemented
51C8×C22⋊D43C2216yescomplemented
52#14582927C2213yescomplemented
53#14582925C2213yescomplemented
54#14582922C2213yescomplemented
55C2×Dic43⋊C8C2213yescomplemented
56#14582867C2213yescomplemented
57#14582866C2213yescomplemented
58#14582866C2213yescomplemented
59#14582865C2213yescomplemented
60#14582863C2213yescomplemented
61#14582862C2213yescomplemented
62C2×C22⋊(C43⋊C8)C2213yescomplemented
63C2×(C2×D43)⋊C8C2213yescomplemented
64#14582857C2213yescomplemented
65#14582854C2213yescomplemented
66M16×Dic43C2213yescomplemented
67C2×C8×Dic43C2213yescomplemented
68C22×#41×C43C2211yescharacteristic
69C43×#568—28no—
70C2×#131×C43C2211yescharacteristic
71C2×#131×C43C2211yescharacteristic
72C2×#131×C43C2213yescomplemented
73C2×#131×C43C2213yescomplemented
74C22×M16×C43C2213yescomplemented
75C22×M16×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—24no—
88#13063331—212no—
89C2×#10621877C2313yes—
90C2×#10621877C2313yes—
91C2×#10621872—212no—
92C2×#10621872C2313yes—
93C2×#10621872C2311yescharacteristic
94C2×#10621872C2313yes—
95C2×#10621872C2313yes—
96M16×D43—212no—
97C22×C43⋊C8C2313yes—
98C22×C43⋊C8C2313yes—
99C2×C8×D43C2316yes—
100#13063323C2×C413yes—
101#13063321C2×C413yes—
102#13063314C2×C413yes—
103#13063312C2×C413yes—
104#13063308C2×C416yes—
105#13063306C2×C416yes—
106#13063304C2×C413yes—
107#13063304C2×C413yes—
108#13063301C2×C413yes—
109#13063301C2×C413yes—
110#13063299C2×C413yes—
111#13063299C2×C413yes—
112#13063297C2×C416yes—
113#13063297C2×C416yes—
114#13063296C2×C413yes—
115#13063296C2×C413yes—
116#13063294C2×C416yes—
117#13063293C2×C416yes—
118Q8×Dic43C2×C411yescharacteristic
119Q8×Dic43C2×C411yescharacteristic
120D4×Dic43C2×C413yes—
121D4×Dic43C2×C413yes—
122C4×C22⋊D43C2×C413yes—
123C4×C22⋊D43C2×C413yes—
124C4×C22⋊D43C2×C413yes—
125C4×C22⋊D43C2×C413yes—
126C4×C22⋊D43C2311yescharacteristic
127C4×C22⋊D43C2313yes—
128C4×C22⋊D43C2313yes—
129C4×C22⋊D43C2313yes—
130C4×C22⋊D43C2316yes—
131#13063284C2313yes—
132C2×Dic43⋊C4C2×C413yes—
133C2×C22⋊Dic43C2×C413yes—
134C2×(C2×D43)⋊C4C2×C413yes—
135C2×C4×Dic43C2313yes—
136Dic43⋊C8C2311yescharacteristic
137Dic43⋊C8C2313yes—
138Dic43⋊C8C2313yes—
139Dic43⋊C8C2313yes—
140Dic43⋊C8C2316yes—
141C22⋊(C43⋊C8)C2311yescharacteristic
142C22⋊(C43⋊C8)C2313yes—
143C22⋊(C43⋊C8)C2313yes—
144C22⋊(C43⋊C8)C2313yes—
145C22⋊(C43⋊C8)C2316yes—
146(C2×D43)⋊C8C2311yescharacteristic
147(C2×D43)⋊C8C2313yes—
148(C2×D43)⋊C8C2313yes—
149(C2×D43)⋊C8C2313yes—
150(C2×D43)⋊C8C2316yes—
151#13063235C2316yes—
152C8×Dic43C2311yescharacteristic
153C8×Dic43C2313yes—
154C8×Dic43C2313yes—
155C8×Dic43C2313yes—
156C2×#41×C43—24no—
157C2×#41×C43—24no—
158C2×#41×C43C2×C411yescharacteristic
159C2×#41×C43C2×C413yes—
160C2×#41×C43C2313yes—
161C2×#41×C43C2311yescharacteristic
162C22×Q8×C43C2×C411yescharacteristic
163C22×D4×C43C2×C413yes—
164C23×C4×C43C2313yes—
165#131×C43—24no—
166#131×C43—212no—
167#131×C43—212no—
168#131×C43D418yescomplemented
169C2×M16×C43—212no—
170C2×M16×C43—212no—
171C2×M16×C43C2313yes—
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2313yes—
174C2×M16×C43C2313yes—
175C2×M16×C43C2313yes—
176C2×M16×C43C2313yes—
177C22×C8×C43C2313yes—
178C22×C8×C43C2316yes—
179C22×C8×C43C2313yes—
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×C43C2413yes—
201C22×C4×C43C2411yescharacteristic
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×D43C2413yes—
225C2×C4×D43C2411yescharacteristic
226C2×Dic86C22×C413yes—
227M16×C43—26no—
228M16×C43—26no—
229M16×C43—22no—
230M16×C43—26no—
231M16×C43—26no—
232M16×C43C2×D4112yescomplemented
233C2×C8×C43—26no—
234C2×C8×C43—212no—
235C2×C8×C43C2×D4112yescomplemented
236C2×C8×C43C2411yescharacteristic
237C2×C8×C43C2413yes—
238C2×C8×C43C2411yescharacteristic
239C2×C8×C43C2413yes—
240C22⋊Dic43C22×C411yescharacteristic
241C22⋊Dic43C22×C413yes—
242C22⋊Dic43C22×C413yes—
243C22⋊Dic43C22×C413yes—
244C22⋊Dic43C22×C416yes—
245C22⋊Dic43C22×C416yes—
246(C2×D43)⋊C4C22×C411yescharacteristic
247(C2×D43)⋊C4C22×C413yes—
248(C2×D43)⋊C4C22×C413yes—
249(C2×D43)⋊C4C22×C413yes—
250(C2×D43)⋊C4C22×C416yes—
251C4⋊Dic43C22×C413yes—
252C4⋊Dic43C22×C413yes—
253Dic43⋊C4C22×C411yescharacteristic
254Dic43⋊C4C22×C413yes—
255Dic43⋊C4C22×C413yes—
256Dic43⋊C4C22×C413yes—
257Dic43⋊C4C22×C416yes—
258C4×Dic43C22×C413yes—
259C4×Dic43C22×C413yes—
260C4×Dic43C2411yescharacteristic
261C4×Dic43C2413yes—
262#10621877—26no—
263#10621877—26no—
264C2×C43⋊C8—26no—
265C2×C43⋊C8—26no—
266C2×C43⋊C8C2411yescharacteristic
267C2×C43⋊C8C2413yes—
268C2×C43⋊C8C2413yes—
269C2×C43⋊C8C2411yescharacteristic
270#10621872—26no—
271#10621872—22no—
272#10621872—26no—
273#10621872—26no—
274C8×D43—212no—
275C23×C43—26no—
276C23×C43—43no—
277C23×C43—43no—
278C23×C43C23×C411yescharacteristic
279C23×C43C23×C413yes—
280C23×C43C23×C413yes—
281C22×D43—26no—
282C22×D43—43no—
283C22×D43—43no—
284C22×D43C23×C411yescharacteristic
285C22×D43C23×C413yes—
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—26no—
312C2×Dic43—43no—
313C2×Dic43C23×C411yescharacteristic
314C2×Dic43C23×C413yes—
315C2×Dic43C23×C413yes—
316C2×Dic43C23×C413yes—
317C2×Dic43C23×C411yescharacteristic
318C2×Dic43C23×C411yescharacteristic
319D172—26no—
320C4×D43—26no—
321C4×D43—26no—
322C4×D43—23no—
323C4×D43—21no—
324C4×D43—21no—
325C4×D43—23no—
326Dic86—26no—
327C8×C43—21no—
328C8×C43—23no—
329C8×C43C22×D416yes—
330C8×C43C22×D412yes—
331C43⋊C8—23no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—23no—
335#60147—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—23no—
349C2×D43—21no—
350C2×D43—23no—
351C2×D43—21no—
352C2×D43—23no—
353C2×D43—86no—
354C4×C43—21no—
355C4×C43—23no—
356C4×C43C2×C4×D416yes—
357C4×C43C23×D411yescharacteristic
358C4×C43C22×#4111yescharacteristic
359Dic43—23no—
360Dic43—21no—
361Dic43—23no—
362Dic43—21no—
363Dic43—23no—
364Dic43#56812yescomplemented
365C2×#568—431no—
366C2×#568D4311yescharacteristic, complemented
367D4×#41—431no—
368#2935—433no—
369D4×M16—433no—
370#2933—433no—
371#2933—433no—
372#2931—433no—
373#2930—433no—
374#2930—433no—
375C2×#436—433no—
376#2906—431no—
377#2880—431no—
378#2880—431no—
379C4×#131—431no—
380C2×C43—26no—
381C2×C43—43no—
382C2×C43—41no—
383C2×C43C22×C4×D411yescharacteristic
384C2×C43C2×#56811yescharacteristic
385C2×C43#357311yescharacteristic
386D43—43no—
387D43—41no—
388C22×#41—431no—
389C22×#41C2×D4311yescharacteristic
390#568—28no—
391#568—868no—
392C2×#131—431no—
393C2×#131—431no—
394C2×#131—433no—
395C2×#131—433no—
396C2×#131C2×D4311yescharacteristic
397C2×#131C2×D4311yescharacteristic
398C2×#131C2×D4313yescomplemented
399C2×#131C2×D4313yescomplemented
400C22×M16—433no—
401C22×M16—433no—
402C22×M16C2×D4313yescomplemented
403C22×M16C2×D4313yescomplemented
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—431no—
418#436—433no—
419#436—433no—
420#436—433no—
421#436—433no—
422#436—433no—
423#436—433no—
424#436—433no—
425#436—436no—
426#435—436no—
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#408—433no—
439#408—433no—
440#407—433no—
441#407—433no—
442C2×C22⋊C8—433no—
443C2×C22⋊C8—433no—
444#405—433no—
445#405—433no—
446C4×M16—433no—
447C2×C4×C8—433no—
448C43#6014711yescharacteristic, 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—212no—
469#131—212no—
470#131—864no—
471#131—864no—
472#131—8612no—
473#131—8612no—
474#131C22⋊D4318yescomplemented
475C2×M16—212no—
476C2×M16—212no—
477C2×M16—433no—
478C2×M16—433no—
479C2×M16—433no—
480C2×M16—431no—
481C2×M16—433no—
482C2×M16—433no—
483C2×M16—8612no—
484C2×M16—8612no—
485C2×M16C22×D4313yes—
486C2×M16C22×D4311yescharacteristic
487C2×M16C22×D4313yes—
488C2×M16C22×D4313yes—
489C2×M16C22×D4313yes—
490C2×M16C22×D4313yes—
491C22×C8—433no—
492C22×C8—433no—
493C22×C8—436no—
494C22×C8C22×D4313yes—
495C22×C8C22×D4316yes—
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⋊C8—431no—
544C22⋊C8—433no—
545C22⋊C8—433no—
546C22⋊C8—433no—
547C22⋊C8—436no—
548#97—436no—
549C4×C8—431no—
550C4×C8—433no—
551C4×C8—433no—
552C4×C8—433no—
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#41#1062189814yes—
564#41C2×C22⋊D4314yes—
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—433no—
591C22×C4—431no—
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—22no—
603M16—26no—
604M16—26no—
605M16—866no—
606M16—866no—
607M16—866no—
608M16—862no—
609M16—866no—
610M16—866no—
611M16C2×C22⋊D43112yescomplemented
612C2×C8—26no—
613C2×C8—212no—
614C2×C8—431no—
615C2×C8—433no—
616C2×C8—431no—
617C2×C8—433no—
618C2×C8—866no—
619C2×C8—866no—
620C2×C8—8612no—
621C2×C8C2×C22⋊D43112yescomplemented
622C2×C8C23×D4311yescharacteristic
623C2×C8C23×D4313yes—
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—431no—
647C42—433no—
648C23—26no—
649C23—43no—
650C23—43no—
651C23—431no—
652C23—433no—
653C23—866no—
654C23—1723no—
655C23—1723no—
656C23C22×C4×D4311yescharacteristic
657C23C22×C4×D4313yes—
658C23C22×C4×D4313yes—
659Q8—26no—
660Q8—866no—
661Q8C4×C22⋊D4314yes—
662D4—212no—
663D4—26no—
664D4—862no—
665D4—866no—
666D4—8612no—
667D4—866no—
668D4—1723no—
669D4—1723no—
670D4—1726no—
671D4C4×C22⋊D43112yes—
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—866no—
689C2×C4—863no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—863no—
693C2×C4—1723no—
694C2×C4C22×C4×D4311yescharacteristic
695C2×C4C22×C4×D4313yes—
696C2×C4C22×C4×D4313yes—
697C2×C4C22×C22⋊D4316yes—
698C2×C4C2×#1062189816yes—
699C2×C4C24×D4311yescharacteristic
700C8—21no—
701C8—23no—
702C8—861no—
703C8—863no—
704C8—861no—
705C8—863no—
706C8C22×C22⋊D4316yes—
707C8C22×C22⋊D4312yes—
708C22—23no—
709C22—23no—
710C22—21no—
711C22—23no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—86no—
717C22—861no—
718C22—863no—
719C22—861no—
720C22—863no—
721C22—863no—
722C22—861no—
723C22—3446no—
724C22C2×C4×C22⋊D4316yes—
725C22C23×C4×D4311yescharacteristic
726C4—21no—
727C4—23no—
728C4—432no—
729C4—861no—
730C4—863no—
731C4—863no—
732C4—861no—
733C4—863no—
734C4C2×C4×C22⋊D4316yes—
735C4C23×C22⋊D4311yescharacteristic
736C4C22×#1062189811yescharacteristic
737C2—26no—
738C2—41no—
739C2—43no—
740C2—1721no—
741C2—1723no—
742C2C22×C4×C22⋊D4311yescharacteristic
743C2#568×D4311yescharacteristic
744C2#1914930811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC2×C43×#568C2
prime radical#41×C22⋊D43C2
cosocleC2×C4×C43C25
hypercenterC2×#568D43
hypocenterC43#60147
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×#14583664C2semidirect
3. #19143337C2semidirect
4. M16×C22⋊D43C2semidirect
5. #19143320C2semidirect
6. #19143317C2semidirect
7. #19143305C2semidirect
8. #19143298C2semidirect
9. #19143296C2semidirect
10. C2×#14582975C2semidirect
11. #19143161C2semidirect
12. #19143044C2semidirect
13. #19143042C2semidirect
14. #131×Dic43C2semidirect
15. C2×C43×#568C2semidirect
18. C2×#13063333C22semidirect
21. C2×#13063331C22semidirect
22. C22×#10621872C22semidirect
23. C2×M16×D43C22semidirect
39. #14582975C22semidirect
40. #14582975C22semidirect
41. #14582975C22semidirect
42. #14582975C22semidirect
43. #14582975C22semidirect
44. #14582975C22semidirect
45. #14582975C22semidirect
46. #14582970C22semidirect
47. #14582970C22semidirect
48. #14582968C22semidirect
49. #14582968C22semidirect
50. C8×C22⋊D43C22semidirect
51. C8×C22⋊D43C22semidirect
52. #14582927C22semidirect
53. #14582925C22semidirect
54. #14582922C22semidirect
55. C2×Dic43⋊C8C22semidirect
56. #14582867C22semidirect
57. #14582866C22semidirect
58. #14582866C22semidirect
59. #14582865C22semidirect
60. #14582863C22semidirect
61. #14582862C22semidirect
62. C2×C22⋊(C43⋊C8)C22semidirect
63. C2×(C2×D43)⋊C8C22semidirect
64. #14582857C22semidirect
65. #14582854C22semidirect
66. M16×Dic43C22semidirect
67. C2×C8×Dic43C22semidirect
72. C2×#131×C43C22semidirect
73. C2×#131×C43C22semidirect
74. C22×M16×C43C22semidirect
75. C22×M16×C43C22semidirect
168. #131×C43D4semidirect
232. M16×C43C2×D4semidirect
235. C2×C8×C43C2×D4semidirect
364. Dic43#568semidirect
366. C2×#568D43semidirect
398. C2×#131C2×D43semidirect
399. C2×#131C2×D43semidirect
402. C22×M16C2×D43semidirect
403. C22×M16C2×D43semidirect
448. C43#60147semidirect
474. #131C22⋊D43semidirect
611. M16C2×C22⋊D43semidirect
621. C2×C8C2×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836642
#41×C22⋊D432
#191433372
M16×C22⋊D432
#191433202
#191433172
#191433052
#191432982
#191432962
C2×#145829752
#191431612
#191430442
#191430422
#131×Dic432
C2×C43×#5682
#6014743