Finite Group Databasebeta

← #25117279

Subgroups — #25117279

Order 11008.

1134 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583063C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic
4#19137598C211yesmaximal, characteristic, complemented
5#19137426C211yesmaximal, characteristic
6#19135466C211yesmaximal, characteristic, complemented
7#19135271C211yesmaximal, characteristic, complemented
8#19135230C211yesmaximal, characteristic, complemented
9#19135028C211yesmaximal, characteristic, complemented
10#19134935C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134859C211yesmaximal, characteristic, complemented
13#19134790C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24#14583063C418yescomplemented
25C4×#10621873—24no—
26C2×#13063257C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28#14582901—24no—
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582796—21no—
42#14582786—21no—
43#14582775—21no—
44#14582775—21no—
45#14582771—21no—
46#14582761—21no—
47#14582759C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50#95×D43—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
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yes—
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C23×Dic43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C2×Dic172—41no—
77C2×Dic172—41no—
78C2×Dic172C2×C414yescomplemented
79C2×#10621873—22no—
80C2×#10621873—22no—
81C2×#10621873C2×C414yescomplemented
82#13063304—22no—
83#13063304C2×C414yescomplemented
84C4×Dic86—22no—
85C4×Dic86—41no—
86C4×D172—22no—
87C4×D172—22no—
88C4×D172—41no—
89C4×D172—41no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107#13063257—22no—
108#13063257—41no—
109#13063250—22no—
110#13063250—22no—
111#13063250—22no—
112#13063250—41no—
113#13063250C2×C414yescomplemented
114#13063247—22no—
115#13063247C2×C414yescomplemented
116#13063247D414yes—
117C43⋊#95—21no—
118C43⋊#95—21no—
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—42no—
159C2×C22⋊D43—42no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—42no—
168C22×Dic43—42no—
169C22×Dic43—81no—
170#10621898—28no—
171#10621898—44no—
172#10621898—44no—
173#10621898—44no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172C22×C412yes—
178C2×D172C2×D412yes—
179C2×D172#4112yes—
180C2×C4×D43—24no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86C22×C412yes—
200C2×Dic86C22×C412yes—
201M16×C43—44no—
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×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C22×C412yes—
212C2×C8×C43C22×C412yes—
213C2×C8×C43C2×D412yes—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—41no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C22⋊Dic43—24no—
221C22⋊Dic43—81no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233C4⋊Dic43C22×C412yes—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—42no—
237Dic43⋊C4—81no—
238C4×Dic43—42no—
239C4×Dic43—81no—
240Dic172—44no—
241#10621873—28no—
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—22no—
252C22×D43—22no—
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—48no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
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—84no—
305D172—22no—
306D172—22no—
307D172—22no—
308D172C4×D414yes—
309C4×D43—48no—
310C4×D43—84no—
311C4×D43—84no—
312Dic86—22no—
313Dic86—22no—
314Dic86—22no—
315Dic86—22no—
316Dic86—41no—
317Dic86—41no—
318Dic86—41no—
319Dic86—41no—
320C8×C43—22no—
321C8×C43—22no—
322C8×C43—22no—
323C8×C43—41no—
324#22882—431nomaximal, Sylow
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43C2×C4×D411yescharacteristic
333C22×C43D4211yescharacteristic
334C22×C43#54611yescharacteristic
335C22×C43C2×#13711yescharacteristic
336C22×C43#57511yescharacteristic
337C22×C43#57711yescharacteristic
338C22×C43#57711yescharacteristic
339C2×D43—24no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C4×C43—22no—
347C4×C43—22no—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43C2×C4×D411yescharacteristic
352C4×C43#51811yescharacteristic
353C4×C43#54611yescharacteristic
354C4×C43#55111yescharacteristic
355Dic43—42no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359Dic43—81no—
360Dic43—81no—
361Dic43—81no—
362C2×#452—431no—
363C2×C4×SD16—431no—
364C2×#417—431no—
365#2360—431no—
366#2339—431no—
367#1971—431no—
368#1933—431no—
369#1927—431no—
370#1894—431no—
371#1878—431no—
372#1877—431no—
373#1864—431no—
374#1853—431no—
375#1762—431no—
376#1753D4311yescharacteristic, complemented
377C2×C43—42no—
378C2×C43#235811yescharacteristic
379C2×C43C4×#13711yescharacteristic
380C2×C43#295211yescharacteristic
381C2×C43#326611yescharacteristic
382C2×C43#326711yescharacteristic
383C2×C43#332311yescharacteristic
384C2×C43#333111yescharacteristic
385D43—44no—
386C22×#41—431no—
387C22×Q16—431no—
388C22×SD16—431no—
389C22×M16C2×D4311yescharacteristic
390C2×C22⋊Q8—431no—
391C2×C4×Q8—431no—
392C2×C4×D4—431no—
393C2×C4×D4—431no—
394C22×C4⋊C4—431no—
395#452—438no—
396C4×SD16—864no—
397C2×#106—431no—
398C2×#106—431no—
399#417—864no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×C22⋊C8C2×D4311yescharacteristic
409C2×#97C2×D4311yescharacteristic
410C2×C4×C8C2×D4311yescharacteristic
411#391—431no—
412#391—431no—
413#391—431no—
414#389—431no—
415#389—861no—
416#387—861no—
417#386—861no—
418#386—861no—
419#385—861no—
420#381—861no—
421#380—431no—
422C4×C4⋊C4—431no—
423C4×C22⋊C4—861no—
424C4×C22⋊C4C2×D4311yescharacteristic
425C2×#95—861no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#336C2×D4311yescharacteristic
431#336C2×D4311yescharacteristic
432C43#2288211yescharacteristic, complemented, Sylow
433C2×#41—434no—
434C2×#41—862no—
435C2×#41—862no—
436C2×#41—862no—
437C2×#41—1721no—
438C2×#41—1721no—
439C22×Q8—431no—
440C22×Q8—431no—
441C22×D4—431no—
442C22×D4—861no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4C22×D4311yescharacteristic
448C2×Q16—434no—
449C2×Q16—1721no—
450C2×Q16—1721no—
451C2×SD16—434no—
452C2×SD16—862no—
453C2×SD16—862no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C22×C8C22×D4311yescharacteristic
460C22×C8C22×D4311yescharacteristic
461C22⋊Q8—434no—
462C22⋊Q8—862no—
463C4×Q8—862no—
464C4×Q8—1721no—
465C4×D4—862no—
466C4×D4—862no—
467C4×D4—1721no—
468C4×D4—1721no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—1721no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4D17211yescharacteristic
485C2×C22⋊C4D17211yescharacteristic
486C2×C42—861no—
487C2×C42—861no—
488C2×C42C22×D4311yescharacteristic
489C2×C42C22×D4311yescharacteristic
490#106—862no—
491#106—1721no—
492#103—434no—
493#103—862no—
494#103—862no—
495#103—862no—
496#103—1721no—
497#102—434no—
498#102—434no—
499#102—862no—
500C22⋊C8C4×D4314yescomplemented
501#97—41no—
502C4×C8—22no—
503#95—861no—
504#95—861no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95D17211yescharacteristic
513#95D17211yescharacteristic
514C24—861no—
515C24C2×D17211yescharacteristic
516#41—868no—
517#41—1724no—
518#41—1724no—
519#41—1724no—
520C2×Q8—432no—
521C2×Q8—432no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×D4—432no—
533C2×D4—432no—
534C2×D4—432no—
535C2×D4—864no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—861no—
539C2×D4—1722no—
540C2×D4—1722no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—864no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—3441no—
554C22×C4—3441no—
555C22×C4—3441no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4C2×C4×D4312yes—
565C22×C4C2×D17211yescharacteristic
566C22×C4C2×D17211yescharacteristic
567C22×C4C2×D17211yescharacteristic
568C22×C4C2×D17211yescharacteristic
569C22×C4C2×D17211yescharacteristic
570C22×C4#1062189812yes—
571C22×C4C23×D4311yescharacteristic
572Q16—1724no—
573SD16—868no—
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8C2×C4×D4312yes—
585C2×C8C2×C4×D4312yes—
586C2×C8D4×D4312yes—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—864no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—3441no—
599C4⋊C4—1722no—
600C4⋊C4—1722no—
601C22⋊C4—22no—
602C22⋊C4—41no—
603C22⋊C4—864no—
604C22⋊C4—3441no—
605C22⋊C4—1722no—
606C22⋊C4—1722no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—3441no—
612C42—1722no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—862no—
620C23—862no—
621C23—862no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23—1721no—
626C23C4×D17212yes—
627C23C22×D17211yescharacteristic
628Q8—862no—
629Q8—862no—
630Q8—862no—
631Q8—862no—
632Q8—1721no—
633Q8—1721no—
634Q8—1721no—
635Q8—1721no—
636D4—434no—
637D4—862no—
638D4—862no—
639D4—862no—
640D4—1728no—
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—3444no—
663C2×C4—3444no—
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×C4—1721no—
682C2×C4—1721no—
683C2×C4C4×D17212yes—
684C2×C4#1306335812yes—
685C2×C4C22×C4×D4311yescharacteristic
686C2×C4C2×D4×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337111yescharacteristic
691C8—22no—
692C8—22no—
693C8—22no—
694C8—41no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—864no—
703C22—1722no—
704C22—1722no—
705C22—1722no—
706C22—1722no—
707C22—1722no—
708C22—1722no—
709C22C2×C4×D17211yescharacteristic
710C22D4×D17211yescharacteristic
711C22#1458354411yescharacteristic
712C22C2×#1306335811yescharacteristic
713C22#1458369911yescharacteristic
714C22#1458371111yescharacteristic
715C22#1458371111yescharacteristic
716C4—22no—
717C4—22no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—3441no—
722C4—3441no—
723C4—3441no—
724C4—1722no—
725C4—1722no—
726C4—1722no—
727C4—1722no—
728C4C4×D4×D4311yescharacteristic
729C4#1458337111yescharacteristic
730C4#1458353911yescharacteristic
731C4#1458357311yescharacteristic
732C2—42no—
733C2—1724no—
734C2#1913757711yescharacteristic
735C2C4×#1306335811yescharacteristic
736C2#1914348011yescharacteristic
737C2#1914611011yescharacteristic
738C2#1914612511yescharacteristic
739C2#1914681311yescharacteristic
740C2#1914691211yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#22882
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
4. #19137598C2semidirect
6. #19135466C2semidirect
7. #19135271C2semidirect
8. #19135230C2semidirect
9. #19135028C2semidirect
10. #19134935C2semidirect
11. #19134928C2semidirect
12. #19134859C2semidirect
13. #19134790C2semidirect
14. #19134421C2semidirect
15. C43×#1753C2semidirect
24. #14583063C4semidirect
78. C2×Dic172C2×C4semidirect
81. C2×#10621873C2×C4semidirect
83. #13063304C2×C4semidirect
113. #13063250C2×C4semidirect
115. #13063247C2×C4semidirect
138. C22⋊C8×C43C2×C4semidirect
376. #1753D43semidirect
432. C43#22882semidirect
500. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830632
C2×C4×#106218732
C2×#145829012
#191375982
#191374262
#191354662
#191352712
#191352302
#191350282
#191349352
#191349282
#191348592
#191347902
#191344212
C43×#17532
#2288243