Finite Group Databasebeta

← #25106565

Subgroups — #25106565

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2C2×#14582926C211yesmaximal, characteristic, complemented
3#19135547C211yesmaximal, characteristic, complemented
4#19135543C211yesmaximal, characteristic, complemented
5#19135527C211yesmaximal, characteristic, complemented
6#19135527C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic
8#19135026C211yesmaximal, characteristic, complemented
9#19135021C211yesmaximal, characteristic
10#19135016C211yesmaximal, characteristic, complemented
11#19134607C211yesmaximal, characteristic, complemented
12#19134602C211yesmaximal, characteristic, complemented
13#19134597C211yesmaximal, characteristic, complemented
14#19134592C211yesmaximal, characteristic, complemented
15C43×#2314C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18#14583520—24no—
19#14583520C418yescomplemented
20C2×#13063325C2211yescharacteristic
21C2×#13063320—21no—
22C2×#13063313C2211yescharacteristic
23C2×#13063311—21no—
24C2×#13063307—21no—
25C2×#13063304C2211yescharacteristic
26C2×#13063303—21no—
27C2×#13063299C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30#14582926—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#388—21no—
53C43×#388—21no—
54C43×#387—21no—
55C43×#387—21no—
56C43×#384C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621877—22no—
68C2×#10621877—41no—
69C2×#10621877—41no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—41no—
72C22×C43⋊C8—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063325—22no—
78#13063325C2×C414yes—
79#13063320—28no—
80#13063313—22no—
81#13063313C2×C414yes—
82#13063311—28no—
83#13063307—28no—
84#13063304—22no—
85#13063304C2×C414yes—
86#13063303—28no—
87#13063299—22no—
88#13063299C2×C414yes—
89C4×Dic86—22no—
90C4×Dic86C2×C414yes—
91C4×D172—22no—
92C4×D172C2×C414yes—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C4⋊(C43⋊C8)—22no—
105C4⋊(C43⋊C8)—22no—
106C4⋊(C43⋊C8)—22no—
107C4⋊(C43⋊C8)—22no—
108#13063248—41no—
109#13063248—41no—
110#13063248—41no—
111#13063248—41no—
112#13063245—41no—
113#13063245—41no—
114#13063245—41no—
115#13063245—41no—
116C23×C4×C43C2311yescharacteristic
117#117×C43C2×C414yes—
118#117×C43D414yes—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—81no—
161C2×C22⋊D43—81no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172C22×C412yes—
171C2×C4×D43—24no—
172C2×C4×D43—81no—
173C2×C4×D43—81no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—24no—
180C2×Dic86—81no—
181C2×Dic86—81no—
182C2×Dic86C22×C412yes—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—81no—
192C4⋊C4×C43—81no—
193C4⋊C4×C43C22⋊C414yes—
194C4⋊C4×C43C22⋊C414yes—
195C22⋊C4×C43—81no—
196C22⋊C4×C43—81no—
197C22⋊C4×C43C22⋊C414yes—
198C22⋊C4×C43C22⋊C414yes—
199C42×C43—81no—
200C42×C43—81no—
201C42×C43C22×C412yes—
202C42×C43C22×C412yes—
203C42×C43C2×D412yes—
204C42×C43C2×D412yes—
205C22⋊Dic43—24no—
206(C2×D43)⋊C4—24no—
207(C2×D43)⋊C4—24no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—24no—
210C4⋊Dic43—24no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43C22×C412yes—
214C4⋊Dic43C22×C412yes—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217C4×Dic43—24no—
218#10621877—44no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—44no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43C2×C22⋊C412yes—
239C23×C43C22×D411yescharacteristic
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
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—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43C2×C22⋊C412yes—
274C2×C4×C43C2×C22⋊C412yes—
275C2×C4×C43C2×C22⋊C412yes—
276C2×C4×C43C2×C22⋊C412yes—
277C2×C4×C43C2×C22⋊C412yes—
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43H(5,𝔽2)11yescharacteristic
281C2×C4×C43H(5,𝔽2)11yescharacteristic
282C2×C4×C432−1+411yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C22⋊D43—84no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294D172—22no—
295D172—22no—
296D172—41no—
297D172—41no—
298C4×D43—84no—
299Dic86—22no—
300Dic86—22no—
301Dic86—41no—
302Dic86—41no—
303Dic86—84no—
304C43⋊C8—41no—
305C43⋊C8—41no—
306C43⋊C8—41no—
307C43⋊C8—41no—
308#21896—431nomaximal, Sylow
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43C22×C22⋊C411yescharacteristic
317C22×C43#53711yescharacteristic
318C22×C43#53711yescharacteristic
319C22×C43#57611yescharacteristic
320C22×C43#57711yescharacteristic
321C22×C43#57711yescharacteristic
322C22×C43#57811yescharacteristic
323C2×D43—42no—
324C2×D43—42no—
325C2×D43—42no—
326C2×D43—81no—
327C2×D43—81no—
328C2×D43—81no—
329C2×D43—81no—
330C4×C43—22no—
331C4×C43—22no—
332C4×C43—22no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43—81no—
339C4×C43#52011yescharacteristic
340C4×C43#52011yescharacteristic
341C4×C43#53511yescharacteristic
342C4×C43#53611yescharacteristic
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346C2×#542—431no—
347C2×#424—431no—
348#2314D4311yescharacteristic, complemented
349#1988—431no—
350#1987—431no—
351#1983—431no—
352#1983—431no—
353#1895—431no—
354#1894—431no—
355#1893—431no—
356#1892—431no—
357#1805—431no—
358#1804—431no—
359#1803—431no—
360#1802—431no—
361C2×C43—42no—
362C2×C43#231111yescharacteristic
363C2×C43#289711yescharacteristic
364C2×C43#289811yescharacteristic
365C2×C43#325711yescharacteristic
366C2×C43#325811yescharacteristic
367C2×C43#326211yescharacteristic
368C2×C43#326311yescharacteristic
369D43—82no—
370C22×M16—431no—
371C23×C8—431no—
372#542—438no—
373#542—864no—
374C2×C4⋊Q8—431no—
375C2×#126—861no—
376C2×#124—431no—
377C2×#124—861no—
378C2×#123—861no—
379C2×C22⋊Q8—431no—
380C2×C22⋊Q8—861no—
381C2×#121—431no—
382C2×C4×Q8—431no—
383C2×C4×D4—431no—
384C2×#117C2×D4311yescharacteristic
385#424—864no—
386C2×C4⋊C8—431no—
387C2×C4⋊C8—431no—
388C2×C4⋊C8—431no—
389C2×C4⋊C8—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#103—431no—
393C2×#103—431no—
394C2×#102—431no—
395C2×#102—431no—
396C2×#102—431no—
397C2×#102—431no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#384C2×D4311yescharacteristic
403#382C2×D4311yescharacteristic
404#380C2×D4311yescharacteristic
405#380C2×D4311yescharacteristic
406C4×C4⋊C4C2×D4311yescharacteristic
407C4×C4⋊C4C2×D4311yescharacteristic
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416C43#2189611yescharacteristic, complemented, Sylow
417C22×Q8—431no—
418C22×Q8—861no—
419C22×D4—431no—
420C22×D4—861no—
421C23×C4—861no—
422C23×C4C22×D4311yescharacteristic
423C2×M16—862no—
424C2×M16—1721no—
425C2×M16—1721no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8—431no—
430C22×C8—862no—
431C22×C8—1721no—
432C22×C8—1721no—
433C4⋊Q8—434no—
434C4⋊Q8—862no—
435#126—868no—
436#124—434no—
437#124—868no—
438#124—862no—
439#123—868no—
440C22⋊Q8—434no—
441C22⋊Q8—862no—
442C22⋊Q8—868no—
443#121—434no—
444#121—862no—
445C4×Q8—434no—
446C4×Q8—862no—
447C4×D4—434no—
448C4×D4—862no—
449#117C4×D4314yes—
450#117D17214yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4C22⋊D4311yescharacteristic
459C2×C4⋊C4C22⋊D4311yescharacteristic
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4C22⋊D4311yescharacteristic
472C2×C22⋊C4C22⋊D4311yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—861no—
476C2×C42C22×D4311yescharacteristic
477C2×C42C22×D4311yescharacteristic
478C4⋊C8—862no—
479C4⋊C8—862no—
480C4⋊C8—862no—
481C4⋊C8—862no—
482#103—1721no—
483#103—1721no—
484#103—1721no—
485#103—1721no—
486#102—1721no—
487#102—1721no—
488#102—1721no—
489#102—1721no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496C24—861no—
497C24C2×C22⋊D4311yescharacteristic
498C2×Q8—432no—
499C2×Q8—864no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—3441no—
506C2×Q8—3441no—
507C2×D4—432no—
508C2×D4—864no—
509C2×D4—861no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—3441no—
515C2×D4—3441no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—864no—
528C22×C4—3441no—
529C22×C4—3441no—
530C22×C4C2×C4×D4312yes—
531C22×C4C2×D17212yes—
532C22×C4C2×C22⋊D4311yescharacteristic
533C22×C4C2×C22⋊D4311yescharacteristic
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C2×C22⋊D4311yescharacteristic
536C22×C4C2×C22⋊D4311yescharacteristic
537C22×C4C23×D4311yescharacteristic
538M16—1724no—
539C2×C8—861no—
540C2×C8—861no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—1724no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—432no—
563C4⋊C4—432no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—864no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4(C2×D43)⋊C414yes—
570C4⋊C4(C2×D43)⋊C414yes—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—864no—
574C22⋊C4—864no—
575C22⋊C4—864no—
576C22⋊C4—864no—
577C22⋊C4—864no—
578C22⋊C4(C2×D43)⋊C414yes—
579C22⋊C4(C2×D43)⋊C414yes—
580C42—81no—
581C42—81no—
582C42—864no—
583C42C2×C4×D4312yes—
584C42C2×C4×D4312yes—
585C42C2×D17212yes—
586C42C2×D17212yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—862no—
594C23—1721no—
595C23—1721no—
596C23—1721no—
597C23—1721no—
598C23—1721no—
599C23—1721no—
600C23C2×(C2×D43)⋊C412yes—
601C23C22×C22⋊D4311yescharacteristic
602Q8—862no—
603Q8—862no—
604Q8—3444no—
605Q8—1721no—
606Q8—1721no—
607D4—862no—
608D4—862no—
609D4—3444no—
610D4—1721no—
611D4—1721no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—3444no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4C2×(C2×D43)⋊C412yes—
649C2×C4C2×(C2×D43)⋊C412yes—
650C2×C4C2×(C2×D43)⋊C412yes—
651C2×C4C2×(C2×D43)⋊C412yes—
652C2×C4C2×(C2×D43)⋊C412yes—
653C2×C4C22×C4×D4311yescharacteristic
654C2×C4C22×D17211yescharacteristic
655C2×C4#1306337111yescharacteristic
656C2×C4#1306337111yescharacteristic
657C2×C4#1306337211yescharacteristic
658C2×C4#1306337211yescharacteristic
659C8—1721no—
660C8—1721no—
661C8—1721no—
662C8—1721no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—3441no—
671C22—3441no—
672C22—3441no—
673C22—3441no—
674C22—1722no—
675C22—1722no—
676C22—1722no—
677C22C22×(C2×D43)⋊C411yescharacteristic
678C22#1458347711yescharacteristic
679C22#1458347711yescharacteristic
680C22#1458370211yescharacteristic
681C22#1458370711yescharacteristic
682C22#1458371011yescharacteristic
683C22#1458371411yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—1722no—
694C4—1722no—
695C4—1722no—
696C4#1458337911yescharacteristic
697C4#1458337911yescharacteristic
698C4#1458346811yescharacteristic
699C4#1458347511yescharacteristic
700C2—42no—
701C2—3442no—
702C2#1913718311yescharacteristic
703C2#1914311811yescharacteristic
704C2#1914312511yescharacteristic
705C2#1914600011yescharacteristic
706C2#1914601511yescharacteristic
707C2#1914605111yescharacteristic
708C2#1914606011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2314C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
cosocleC22×C4×C43C24
hypercenter#2314D43
hypocenterC43#21896
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#14582926C2semidirect
3. #19135547C2semidirect
4. #19135543C2semidirect
5. #19135527C2semidirect
6. #19135527C2semidirect
8. #19135026C2semidirect
10. #19135016C2semidirect
11. #19134607C2semidirect
12. #19134602C2semidirect
13. #19134597C2semidirect
14. #19134592C2semidirect
15. C43×#2314C2semidirect
19. #14583520C4semidirect
348. #2314D43semidirect
416. C43#21896semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145829262
#191355472
#191355432
#191355272
#191350312
#191350262
#191350212
#191350162
#191346072
#191346022
#191345972
#191345922
C43×#23142
#2189643