Finite Group Databasebeta

← #25117324

Subgroups — #25117324

Order 11008.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583040C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic, complemented
3C2×#14582909C211yesmaximal, characteristic, complemented
4#19137631C211yesmaximal, characteristic
5C22⋊C4×Dic86C211yesmaximal, characteristic, complemented
6#19135476C211yesmaximal, characteristic, complemented
7#19135271C211yesmaximal, characteristic, complemented
8#19135230C211yesmaximal, characteristic, complemented
9#19135033C211yesmaximal, characteristic
10#19134949C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134852C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134426C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C23×Dic86C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×#13063284C2211yescharacteristic
24#14583040C418yescomplemented
25C4×#10621873—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28#14582909—24no—
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582803—21no—
40#14582803—21no—
41#14582801C2211yescharacteristic
42#14582799—21no—
43#14582797C2211yescharacteristic
44#14582788—21no—
45#14582775—21no—
46#14582759C2211yescharacteristic
47#14582757—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C22⋊C4×C43C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—21no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2×C414yescomplemented
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C2×#10621873—22no—
76C2×#10621873—22no—
77C2×#10621873—41no—
78C2×#10621873—41no—
79C2×#10621873C2×C414yes—
80C2×#10621873C2×C414yes—
81#13063299—22no—
82#13063299C2×C414yes—
83C4×Dic86—22no—
84C4×Dic86—22no—
85C4×Dic86—41no—
86C4×Dic86—41no—
87C4×D172—22no—
88C4×D172—41no—
89#13063284—22no—
90#13063284—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109#13063259—41no—
110#13063257—22no—
111#13063250—22no—
112#13063250—22no—
113#13063250—22no—
114#13063250C2×C414yescomplemented
115#13063250C2×C414yescomplemented
116#13063250D414yescomplemented
117#13063247—22no—
118#13063247—41no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—22no—
128C2×M16×C43—22no—
129C2×M16×C43—41no—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C2×C22⋊C4×C43D411yescharacteristic
135C2×C22⋊C4×C43D411yescharacteristic
136C2×C42×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138C22⋊C8×C43C2×C414yescomplemented
139#97×C43—41no—
140C4×C8×C43—22no—
141#95×C43D411yescharacteristic
142#95×C43D411yescharacteristic
143C24×C43C2×D411yescharacteristic
144C23×D43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43C22×C412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4112yes—
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—24no—
158C2×C22⋊D43—81no—
159C2×C22⋊D43—81no—
160C22×Dic43—24no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—42no—
169C22×Dic43—42no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22×C412yes—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—81no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—28no—
187C2×Dic86—24no—
188C2×Dic86—21no—
189C2×Dic86—44no—
190C2×Dic86—44no—
191C2×Dic86—44no—
192C2×Dic86—42no—
193C2×Dic86—42no—
194C2×Dic86C22×C412yes—
195C2×Dic86C22×C412yes—
196C2×Dic86C2×D412yes—
197C2×Dic86#4112yes—
198M16×C43—44no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C22×C412yes—
209C2×C8×C43C22×C412yes—
210C2×C8×C43C2×D412yes—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—41no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—81no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C2×D412yes—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235Dic43⋊C4—81no—
236C4×Dic43—42no—
237C4×Dic43—42no—
238C4×Dic43—42no—
239C4×Dic43—81no—
240#10621873—28no—
241#10621873—44no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43C4×D412yes—
249C23×C43C22×D411yescharacteristic
250C22×D43—22no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43C4×D412yes—
275C2×C4×C43#13712yes—
276C2×C4×C43C23×C411yescharacteristic
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43H(5,𝔽2)11yescharacteristic
281C2×C4×C43H(5,𝔽2)11yescharacteristic
282C22⋊D43—84no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—48no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305D172—22no—
306D172—22no—
307D172—41no—
308D172—41no—
309C4×D43—84no—
310Dic86—22no—
311Dic86—22no—
312Dic86—22no—
313Dic86—22no—
314Dic86—22no—
315Dic86—48no—
316Dic86—41no—
317Dic86—41no—
318Dic86C4×D414yes—
319C8×C43—22no—
320C8×C43—22no—
321C8×C43—22no—
322C8×C43—41no—
323#22885—431nomaximal, Sylow
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43C2×C4×D411yescharacteristic
332C22×C43D4211yescharacteristic
333C22×C43#54611yescharacteristic
334C22×C43C2×#13711yescharacteristic
335C22×C43#57511yescharacteristic
336C22×C43#57711yescharacteristic
337C22×C43#57711yescharacteristic
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—42no—
341C2×D43—81no—
342C2×D43—81no—
343C2×D43—81no—
344C2×D43—81no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—41no—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43C2×C4×D411yescharacteristic
351C4×C43#51811yescharacteristic
352C4×C43#54611yescharacteristic
353C4×C43#55111yescharacteristic
354Dic43—24no—
355Dic43—42no—
356Dic43—42no—
357Dic43—42no—
358Dic43—81no—
359Dic43—81no—
360Dic43—81no—
361C2×#448—431no—
362C2×C4×SD16—431no—
363C2×#419—431no—
364#2363—431no—
365Q8×C22⋊C4—431no—
366#1973—431no—
367#1933—431no—
368#1927—431no—
369#1895—431no—
370#1880—431no—
371#1877—431no—
372#1863—431no—
373#1854—431no—
374#1763—431no—
375#1753D4311yescharacteristic, complemented
376C2×C43—42no—
377C2×C43#235811yescharacteristic
378C2×C43C4×#13711yescharacteristic
379C2×C43#294911yescharacteristic
380C2×C43#326611yescharacteristic
381C2×C43#327111yescharacteristic
382C2×C43#332611yescharacteristic
383C2×C43#332911yescharacteristic
384D43—82no—
385C23×Q8—431no—
386C22×SD16—431no—
387C22×SD16—431no—
388C22×M16C2×D4311yescharacteristic
389C2×#121—431no—
390C2×C4×Q8—431no—
391C2×C4×Q8—431no—
392C2×C4×D4—431no—
393C2×#117—431no—
394#448—438no—
395C4×SD16—864no—
396C2×#107—431no—
397C2×#106—431no—
398#419—864no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×C22⋊C8C2×D4311yescharacteristic
408C2×#97C2×D4311yescharacteristic
409C2×C4×C8C2×D4311yescharacteristic
410#391—431no—
411#391—431no—
412#391—861no—
413#391—861no—
414#390—431no—
415#390—861no—
416#389—431no—
417#388—861no—
418#386—861no—
419#380—431no—
420#380—861no—
421C4×C4⋊C4—431no—
422C4×C22⋊C4—861no—
423C4×C22⋊C4—861no—
424C4×C22⋊C4C2×D4311yescharacteristic
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#336C2×D4311yescharacteristic
430#336C2×D4311yescharacteristic
431C43#2288511yescharacteristic, complemented, Sylow
432C22×Q8—434no—
433C22×Q8—431no—
434C22×Q8—431no—
435C22×Q8—862no—
436C22×Q8—862no—
437C22×Q8—861no—
438C22×Q8—862no—
439C22×Q8—1721no—
440C22×Q8—1721no—
441C22×D4—431no—
442C22×D4—861no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4C22×D4311yescharacteristic
446C2×SD16—434no—
447C2×SD16—434no—
448C2×SD16—862no—
449C2×SD16—862no—
450C2×SD16—1721no—
451C2×SD16—1721no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—41no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459#121—434no—
460#121—862no—
461C4×Q8—862no—
462C4×Q8—862no—
463C4×Q8—1721no—
464C4×Q8—1721no—
465C4×D4—862no—
466C4×D4—1721no—
467#117—862no—
468#117—1721no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4D17211yescharacteristic
484C2×C22⋊C4D17211yescharacteristic
485C2×C42—861no—
486C2×C42—861no—
487C2×C42—861no—
488C2×C42—861no—
489C2×C42C22×D4311yescharacteristic
490C2×C42C22×D4311yescharacteristic
491#107—1721no—
492#106—862no—
493#103—434no—
494#103—434no—
495#103—434no—
496#103—862no—
497#103—862no—
498#103—862no—
499#102—862no—
500#102—1721no—
501C22⋊C8C4×D4314yescomplemented
502#97—41no—
503C4×C8—22no—
504#95—861no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95D17211yescharacteristic
512#95D17211yescharacteristic
513C24—861no—
514C24C2×D17211yescharacteristic
515C2×Q8—432no—
516C2×Q8—432no—
517C2×Q8—432no—
518C2×Q8—432no—
519C2×Q8—868no—
520C2×Q8—864no—
521C2×Q8—861no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—1722no—
530C2×Q8—1722no—
531C2×Q8—1724no—
532C2×Q8—1724no—
533C2×Q8—1724no—
534C2×D4—432no—
535C2×D4—864no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—3441no—
542C2×D4—3441no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—861no—
548C22×C4—864no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—3441no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4C2×C4×D4312yes—
561C22×C4C2×D17211yescharacteristic
562C22×C4C2×D17211yescharacteristic
563C22×C4C2×D17211yescharacteristic
564C22×C4C2×D17211yescharacteristic
565C22×C4C2×D17211yescharacteristic
566C22×C4#1062189812yes—
567C22×C4C23×D4311yescharacteristic
568SD16—868no—
569SD16—1724no—
570M16—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8C2×C4×D4312yes—
581C2×C8C2×C4×D4312yes—
582C2×C8D4×D4312yes—
583C4⋊C4—432no—
584C4⋊C4—432no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—3441no—
594C4⋊C4—1722no—
595C4⋊C4—1722no—
596C22⋊C4—22no—
597C22⋊C4—41no—
598C22⋊C4—864no—
599C22⋊C4—3441no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C22⋊C4—1722no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—3441no—
609C42—1722no—
610C42—1722no—
611C42—1722no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—862no—
619C23—1721no—
620C23—1721no—
621C23—1721no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23C4×D17212yes—
626C23C22×D17211yescharacteristic
627Q8—434no—
628Q8—862no—
629Q8—862no—
630Q8—862no—
631Q8—862no—
632Q8—862no—
633Q8—1728no—
634Q8—1721no—
635Q8—1721no—
636D4—862no—
637D4—862no—
638D4—3444no—
639D4—1721no—
640D4—1721no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—3444no—
665C2×C4—1728no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4C4×D17212yes—
682C2×C4#1306335812yes—
683C2×C4C22×C4×D4311yescharacteristic
684C2×C4C2×D4×D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4C2×#1062189811yescharacteristic
687C2×C4#1306337011yescharacteristic
688C2×C4#1306337111yescharacteristic
689C8—22no—
690C8—22no—
691C8—22no—
692C8—41no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—3441no—
701C22—3441no—
702C22—3441no—
703C22—3441no—
704C22—1722no—
705C22—1722no—
706C22—1722no—
707C22C2×C4×D17211yescharacteristic
708C22D4×D17211yescharacteristic
709C22#1458354411yescharacteristic
710C22C2×#1306335811yescharacteristic
711C22#1458369911yescharacteristic
712C22#1458371111yescharacteristic
713C22#1458371111yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—864no—
720C4—3441no—
721C4—3441no—
722C4—3441no—
723C4—1722no—
724C4—1722no—
725C4—1722no—
726C4C4×D4×D4311yescharacteristic
727C4#1458337111yescharacteristic
728C4#1458353911yescharacteristic
729C4#1458357311yescharacteristic
730C2—42no—
731C2—3442no—
732C2#1913757711yescharacteristic
733C2C4×#1306335811yescharacteristic
734C2#1914345611yescharacteristic
735C2#1914611011yescharacteristic
736C2#1914618511yescharacteristic
737C2#1914685011yescharacteristic
738C2#1914689011yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22885
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621873C2semidirect
3. C2×#14582909C2semidirect
5. C22⋊C4×Dic86C2semidirect
6. #19135476C2semidirect
7. #19135271C2semidirect
8. #19135230C2semidirect
10. #19134949C2semidirect
11. #19134928C2semidirect
12. #19134852C2semidirect
13. #19134796C2semidirect
14. #19134426C2semidirect
15. C43×#1753C2semidirect
24. #14583040C4semidirect
68. C22×Dic86C2×C4semidirect
114. #13063250C2×C4semidirect
115. #13063250C2×C4semidirect
116. #13063250D4semidirect
138. C22⋊C8×C43C2×C4semidirect
375. #1753D43semidirect
431. C43#22885semidirect
501. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830402
C2×C4×#106218732
C2×#145829092
#191376312
C22⋊C4×Dic862
#191354762
#191352712
#191352302
#191350332
#191349492
#191349282
#191348522
#191347962
#191344262
C43×#17532
#2288543