Finite Group Databasebeta

← #25106362

Subgroups — #25106362

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2#19137218C211yesmaximal, characteristic, complemented
3#19135568C211yesmaximal, characteristic, complemented
4#19135556C211yesmaximal, characteristic, complemented
5#19135411C211yesmaximal, characteristic, complemented
6#19135406C211yesmaximal, characteristic, complemented
7#19134915C211yesmaximal, characteristic
8#19134910C211yesmaximal, characteristic
9#19134905C211yesmaximal, characteristic, complemented
10#19134900C211yesmaximal, characteristic, complemented
11#19134611C211yesmaximal, characteristic, complemented
12#19134606C211yesmaximal, characteristic, complemented
13#19134601C211yesmaximal, characteristic, complemented
14#19134596C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic, complemented
16#14583520—24no—
17#14583520C418yescomplemented
18C2×#13063325C2211yescharacteristic
19C2×#13063320—21no—
20C2×#13063313C2211yescharacteristic
21C2×#13063311—21no—
22C2×#13063307—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063303—21no—
25C2×#13063299C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29C22×C4⋊Dic43C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38#14582798—21no—
39#14582798—21no—
40#14582774—21no—
41#14582774—21no—
42#14582769C2211yescharacteristic
43#14582769C2211yescharacteristic
44#14582765C2211yescharacteristic
45#14582765C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#433—24no—
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C2×C4×C8×C43C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68#13063325—22no—
69#13063325C2×C414yescomplemented
70#13063320—28no—
71#13063313—22no—
72#13063313C2×C414yescomplemented
73#13063311—28no—
74#13063307—28no—
75#13063304—22no—
76#13063304C2×C414yes—
77#13063303—28no—
78#13063299—22no—
79#13063299C2×C414yes—
80C4×Dic86—22no—
81C4×Dic86C2×C414yescomplemented
82C4×D172—22no—
83C4×D172C2×C414yescomplemented
84#13063284—41no—
85#13063284—41no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43—41no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110#13063250—41no—
111#13063250—41no—
112#13063250—41no—
113#13063250—41no—
114#13063247—41no—
115#13063247—41no—
116#13063247—41no—
117#13063247—41no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127#117×C43C2×C414yes—
128#117×C43D414yes—
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—22no—
136C4⋊C8×C43—22no—
137C22⋊C8×C43—22no—
138C22⋊C8×C43—22no—
139#97×C43—22no—
140C4×C8×C43—22no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—24no—
156C2×C22⋊D43—81no—
157C2×C22⋊D43—81no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—42no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172C22×C412yes—
174C2×C4×D43—24no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—24no—
183C2×Dic86—81no—
184C2×Dic86—81no—
185C2×Dic86C22×C412yes—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C4⋊C4×C43C22⋊C414yes—
199C4⋊C4×C43C22⋊C414yes—
200C22⋊C4×C43C22⋊C414yes—
201C22⋊C4×C43C22⋊C414yes—
202C42×C43C22×C412yes—
203C42×C43C22×C412yes—
204C42×C43C2×D412yes—
205C42×C43C2×D412yes—
206C22⋊Dic43—24no—
207C22⋊Dic43—42no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—24no—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—24no—
212C4⋊Dic43—24no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—42no—
224C4⋊Dic43—81no—
225C4⋊Dic43—81no—
226C4⋊Dic43—81no—
227C4⋊Dic43—81no—
228C4⋊Dic43C22×C412yes—
229C4⋊Dic43C22×C412yes—
230Dic43⋊C4—24no—
231Dic43⋊C4—24no—
232C4×Dic43—24no—
233C4×Dic43—42no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43C2×C22⋊C412yes—
241C23×C43C22×D411yescharacteristic
242C22×D43—22no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43C2×C22⋊C412yes—
264C2×C4×C43C2×C22⋊C412yes—
265C2×C4×C43C2×C22⋊C412yes—
266C2×C4×C43C2×C22⋊C412yes—
267C2×C4×C43C2×C22⋊C412yes—
268C2×C4×C43C23×C411yescharacteristic
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C2×C4×C432−1+411yescharacteristic
274C22⋊D43—84no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—22no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
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—84no—
297D172—22no—
298D172—22no—
299D172—41no—
300D172—41no—
301C4×D43—84no—
302Dic86—22no—
303Dic86—22no—
304Dic86—41no—
305Dic86—41no—
306Dic86—84no—
307C8×C43—41no—
308C8×C43—41no—
309C8×C43—41no—
310C8×C43—41no—
311#21871—431nomaximal, Sylow
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43C22×C22⋊C411yescharacteristic
320C22×C43#53511yescharacteristic
321C22×C43#53611yescharacteristic
322C22×C43#57611yescharacteristic
323C22×C43#57711yescharacteristic
324C22×C43#57711yescharacteristic
325C22×C43#57811yescharacteristic
326C2×D43—42no—
327C2×D43—42no—
328C2×D43—42no—
329C2×D43—81no—
330C2×D43—81no—
331C2×D43—81no—
332C2×D43—81no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—22no—
336C4×C43—22no—
337C4×C43—22no—
338C4×C43#52011yescharacteristic
339C4×C43#52011yescharacteristic
340C4×C43#53711yescharacteristic
341C4×C43#53711yescharacteristic
342Dic43—42no—
343Dic43—42no—
344Dic43—42no—
345Dic43—81no—
346Dic43—81no—
347Dic43—81no—
348Dic43—81no—
349C2×#542—431no—
350C2×#433D4311yescharacteristic, complemented
351#2317—431no—
352#1993—431no—
353#1990—431no—
354#1959—431no—
355#1958—431no—
356#1875—431no—
357#1874—431no—
358#1873—431no—
359#1872—431no—
360#1805—431no—
361#1804—431no—
362#1803—431no—
363#1802—431no—
364C2×C43—42no—
365C2×C43#231111yescharacteristic
366C2×C43#289711yescharacteristic
367C2×C43#289811yescharacteristic
368C2×C43#322411yescharacteristic
369C2×C43#322511yescharacteristic
370C2×C43#324311yescharacteristic
371C2×C43#324411yescharacteristic
372D43—82no—
373#542—438no—
374#542—864no—
375C2×C4⋊Q8—431no—
376C2×#126—861no—
377C2×#124—431no—
378C2×#124—861no—
379C2×#123—861no—
380C2×C22⋊Q8—431no—
381C2×C22⋊Q8—861no—
382C2×#121—431no—
383C2×C4×Q8—431no—
384C2×C4×D4—431no—
385C2×#117—431no—
386C2×#117C2×D4311yescharacteristic
387C22×C4⋊C4—431no—
388#433—24no—
389C2×C4⋊C8C2×D4311yescharacteristic
390C2×C4⋊C8C2×D4311yescharacteristic
391C2×#103—431no—
392C2×#103—431no—
393C2×#103—431no—
394C2×#103—431no—
395C2×#102—431no—
396C2×#102—431no—
397C2×#102—431no—
398C2×#102—431no—
399C2×C22⋊C8C2×D4311yescharacteristic
400C2×C22⋊C8C2×D4311yescharacteristic
401C2×#97C2×D4311yescharacteristic
402C2×C4×C8C2×D4311yescharacteristic
403#389—861no—
404#389—861no—
405#385—861no—
406#385—861no—
407#384—431no—
408#384—431no—
409#382—431no—
410#382—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416#340—431no—
417#340—431no—
418#340—431no—
419C43#2187111yescharacteristic, complemented, Sylow
420C22×Q8—431no—
421C22×Q8—861no—
422C22×D4—431no—
423C22×D4—861no—
424C23×C4—861no—
425C23×C4—861no—
426C23×C4C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4⋊Q8—434no—
432C4⋊Q8—862no—
433#126—868no—
434#124—434no—
435#124—868no—
436#124—862no—
437#123—868no—
438C22⋊Q8—434no—
439C22⋊Q8—862no—
440C22⋊Q8—868no—
441#121—434no—
442#121—862no—
443C4×Q8—434no—
444C4×Q8—862no—
445C4×D4—434no—
446C4×D4—862no—
447#117—1721no—
448#117—1721no—
449#117C4×D4314yes—
450#117C22⋊D4314yes—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4—861no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—1721no—
466C2×C4⋊C4—1721no—
467C2×C4⋊C4D17211yescharacteristic
468C2×C4⋊C4D17211yescharacteristic
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4D17211yescharacteristic
476C2×C22⋊C4D17211yescharacteristic
477C2×C42—861no—
478C2×C42—861no—
479C2×C42C22×D4311yescharacteristic
480C2×C42C22×D4311yescharacteristic
481C4⋊C8—22no—
482C4⋊C8—22no—
483#103—1721no—
484#103—1721no—
485#103—1721no—
486#103—1721no—
487#102—1721no—
488#102—1721no—
489#102—1721no—
490#102—1721no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493#97—22no—
494C4×C8—22no—
495#95—861no—
496#95—861no—
497#95—861no—
498#95—861no—
499C24—861no—
500C24C2×D17211yescharacteristic
501C2×Q8—432no—
502C2×Q8—864no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
507C2×Q8—861no—
508C2×Q8—3441no—
509C2×Q8—3441no—
510C2×D4—432no—
511C2×D4—864no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—861no—
517C2×D4—3441no—
518C2×D4—3441no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—864no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—3441no—
532C22×C4—3441no—
533C22×C4—3441no—
534C22×C4—3441no—
535C22×C4—1722no—
536C22×C4C2×C4×D4312yes—
537C22×C4C2×D17211yescharacteristic
538C22×C4C2×D17211yescharacteristic
539C22×C4C2×D17211yescharacteristic
540C22×C4C2×D17211yescharacteristic
541C22×C4C2×D17211yescharacteristic
542C22×C4C2×C22⋊D4312yes—
543C22×C4C23×D4311yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—432no—
557C4⋊C4—432no—
558C4⋊C4—864no—
559C4⋊C4—864no—
560C4⋊C4—864no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—3441no—
572C4⋊C4—3441no—
573C4⋊C4—3441no—
574C4⋊C4—3441no—
575C4⋊C4—1722no—
576C4⋊C4(C2×D43)⋊C414yes—
577C4⋊C4(C2×D43)⋊C414yes—
578C22⋊C4—864no—
579C22⋊C4—864no—
580C22⋊C4—864no—
581C22⋊C4—864no—
582C22⋊C4—864no—
583C22⋊C4—1722no—
584C22⋊C4(C2×D43)⋊C414yes—
585C22⋊C4(C2×D43)⋊C414yes—
586C42—864no—
587C42—1722no—
588C42C2×C4×D4312yes—
589C42C2×C4×D4312yes—
590C42C2×C22⋊D4312yes—
591C42C2×C22⋊D4312yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—862no—
599C23—1721no—
600C23—1721no—
601C23—1721no—
602C23—1721no—
603C23—1721no—
604C23—1721no—
605C23C2×(C2×D43)⋊C412yes—
606C23C22×D17211yescharacteristic
607Q8—862no—
608Q8—862no—
609Q8—3444no—
610Q8—1721no—
611Q8—1721no—
612D4—862no—
613D4—862no—
614D4—3444no—
615D4—1721no—
616D4—1721no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—3444no—
635C2×C4—3444no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4—1721no—
653C2×C4—1721no—
654C2×C4C2×(C2×D43)⋊C412yes—
655C2×C4C2×(C2×D43)⋊C412yes—
656C2×C4C2×(C2×D43)⋊C412yes—
657C2×C4C2×(C2×D43)⋊C412yes—
658C2×C4C2×(C2×D43)⋊C412yes—
659C2×C4C22×C4×D4311yescharacteristic
660C2×C4C22×C22⋊D4311yescharacteristic
661C2×C4#1306337111yescharacteristic
662C2×C4#1306337111yescharacteristic
663C2×C4#1306337211yescharacteristic
664C2×C4#1306337211yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—3441no—
677C22—3441no—
678C22—3441no—
679C22—3441no—
680C22—1722no—
681C22—1722no—
682C22—1722no—
683C22C22×(C2×D43)⋊C411yescharacteristic
684C22#1458346811yescharacteristic
685C22#1458347511yescharacteristic
686C22#1458370411yescharacteristic
687C22#1458371111yescharacteristic
688C22#1458371111yescharacteristic
689C22#1458371611yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—3441no—
696C4—3441no—
697C4—3441no—
698C4—3441no—
699C4—1722no—
700C4—1722no—
701C4—1722no—
702C4#1458337911yescharacteristic
703C4#1458337911yescharacteristic
704C4#1458347711yescharacteristic
705C4#1458347711yescharacteristic
706C2—42no—
707C2—3442no—
708C2#1913718311yescharacteristic
709C2#1914312211yescharacteristic
710C2#1914312911yescharacteristic
711C2#1914569111yescharacteristic
712C2#1914570611yescharacteristic
713C2#1914588011yescharacteristic
714C2#1914589511yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenterC2×#433D43
hypocenterC43#21871
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #19137218C2semidirect
3. #19135568C2semidirect
4. #19135556C2semidirect
5. #19135411C2semidirect
6. #19135406C2semidirect
9. #19134905C2semidirect
10. #19134900C2semidirect
11. #19134611C2semidirect
12. #19134606C2semidirect
13. #19134601C2semidirect
14. #19134596C2semidirect
15. C2×C43×#433C2semidirect
17. #14583520C4semidirect
69. #13063325C2×C4semidirect
72. #13063313C2×C4semidirect
81. C4×Dic86C2×C4semidirect
83. C4×D172C2×C4semidirect
350. C2×#433D43semidirect
419. C43#21871semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
#191372182
#191355682
#191355562
#191354112
#191354062
#191349152
#191349102
#191349052
#191349002
#191346112
#191346062
#191346012
#191345962
C2×C43×#4332
#2187143