Finite Group Databasebeta

← #25116925

Subgroups — #25116925

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583055C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3C22×#13063249C211yesmaximal, characteristic
4#19137598C211yesmaximal, characteristic
5#19135465C211yesmaximal, characteristic, complemented
6#19135288C211yesmaximal, characteristic, complemented
7#19135226C211yesmaximal, characteristic, complemented
8#19135016C211yesmaximal, characteristic
9#19134939C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134863C211yesmaximal, characteristic, complemented
12#19134787C211yesmaximal, characteristic
13#19134425C211yesmaximal, characteristic, complemented
14#19134373C211yesmaximal, characteristic
15Q8×C22⋊C4×C43C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22#14583055C418yescomplemented
23#14583004—24no—
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063249—24no—
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582796—21no—
41#14582786—21no—
42#14582771—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C23×Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#391—21no—
55C43×#391—21no—
56C43×#391C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#380—21no—
59C43×#380C2211yescharacteristic
60C4×C22⋊C4×C43—21no—
61C4×C22⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—41no—
67C2×#10621885—41no—
68C2×#10621885C2×C414yescomplemented
69C2×#10621885C2×C414yescomplemented
70C22×C43⋊C8—22no—
71C22×C43⋊C8—22no—
72C22×C43⋊C8—41no—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063304—22no—
78#13063304C2×C414yes—
79C4×Dic86—22no—
80C4×Dic86—41no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93#13063256—22no—
94#13063256—41no—
95#13063249—22no—
96#13063249—22no—
97#13063249—22no—
98#13063249C2×C414yescomplemented
99#13063249C2×C414yescomplemented
100#13063249D414yes—
101#13063248—22no—
102#13063248—41no—
103C22⋊(C43⋊C8)C2×C414yes—
104#13063236—22no—
105#13063236—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×Q8×C43—21no—
111C22×Q8×C43—22no—
112C22×Q8×C43—22no—
113C22×Q8×C43—22no—
114C22×Q8×C43—41no—
115C22×Q8×C43—41no—
116C22×Q8×C43C2×C414yes—
117C22×Q8×C43C2311yescharacteristic
118C22×Q8×C43C2311yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C4×Q8×C43—22no—
122C4×Q8×C43—22no—
123C4×Q8×C43—41no—
124C4×Q8×C43—41no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43D411yescharacteristic
142#95×C43D411yescharacteristic
143C24×C43C2×D411yescharacteristic
144C2×Q8×C43—24no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—28no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—42no—
155C2×Q8×C43—42no—
156C2×Q8×C43—44no—
157C2×Q8×C43—44no—
158C2×Q8×C43—44no—
159C2×Q8×C43C22×C412yes—
160C2×Q8×C43C22×C412yes—
161C2×Q8×C43C2×D412yes—
162C2×Q8×C43#4112yes—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—24no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—42no—
173C22×C4×C43—42no—
174C22×C4×C43C22×C412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43#4112yes—
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43—81no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86C22×C412yes—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—42no—
200C4⋊C4×C43—42no—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—22no—
203C22⋊C4×C43—42no—
204C42×C43—21no—
205C42×C43—21no—
206C42×C43—21no—
207C42×C43—21no—
208C42×C43—42no—
209C42×C43—42no—
210C22⋊Dic43—24no—
211#10621885—28no—
212#10621885—44no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—42no—
218C4⋊Dic43C22×C412yes—
219C4⋊Dic43C2×D412yes—
220Dic43⋊C4—24no—
221Dic43⋊C4—42no—
222Dic43⋊C4—81no—
223C4×Dic43—42no—
224C4×Dic43—81no—
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—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—44no—
235C2×C43⋊C8C22×C412yes—
236C2×C43⋊C8C22×C412yes—
237C2×C43⋊C8C2×D412yes—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43C4×D412yes—
243C23×C43#13712yes—
244C23×C43#13712yes—
245C23×C43C22×D411yescharacteristic
246Q8×C43—22no—
247Q8×C43—22no—
248Q8×C43—22no—
249Q8×C43—22no—
250Q8×C43—22no—
251Q8×C43—48no—
252Q8×C43—41no—
253Q8×C43—41no—
254Q8×C43C4×D414yes—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—21no—
260C2×C4×C43—22no—
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×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—48no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C4×D412yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
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—
305C2×Dic43—84no—
306Dic86—22no—
307Dic86—22no—
308Dic86—41no—
309Dic86—41no—
310C43⋊C8—22no—
311C43⋊C8—22no—
312C43⋊C8—22no—
313C43⋊C8—41no—
314#22859—431nomaximal, Sylow
315C22×C43—22no—
316C22×C43—22no—
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43#44114yescomplemented
322C22×C43C2×C4×D411yescharacteristic
323C22×C43D4211yescharacteristic
324C22×C43#54611yescharacteristic
325C22×C43C2×#13711yescharacteristic
326C22×C43C2×#13711yescharacteristic
327C22×C43#57711yescharacteristic
328C22×C43#57811yescharacteristic
329C4×C43—22no—
330C4×C43—24no—
331C4×C43—42no—
332C4×C43—41no—
333C4×C43—41no—
334C4×C43—41no—
335C4×C43—41no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43C2×C4×D411yescharacteristic
339C4×C43#51811yescharacteristic
340C4×C43#54611yescharacteristic
341C4×C43#55111yescharacteristic
342Dic43—42no—
343Dic43—42no—
344Dic43—42no—
345Dic43—81no—
346C2×#451—431no—
347C2×#441—431no—
348C22×#103—431no—
349#2360—431no—
350Q8×C22⋊C4D4311yescharacteristic
351#1971—431no—
352#1935—431no—
353#1927—431no—
354#1892—431no—
355#1878—431no—
356#1878—431no—
357#1865—431no—
358#1853—431no—
359#1763—431no—
360#1752—431no—
361C2×C43—24no—
362C2×C43#235811yescharacteristic
363C2×C43C2×#44111yescharacteristic
364C2×C43#294711yescharacteristic
365C2×C43#326611yescharacteristic
366C2×C43#327011yescharacteristic
367C2×C43#331211yescharacteristic
368C2×C43#331611yescharacteristic
369C23×Q8C2×D4311yescharacteristic
370C22×Q16—431no—
371C22×Q16—431no—
372C23×C8—431no—
373C2×C22⋊Q8—431no—
374C2×C4×Q8—431no—
375C2×C4×Q8C2×D4311yescharacteristic
376C2×C4×Q8C2×D4311yescharacteristic
377C22×C4⋊C4—431no—
378#451—438no—
379#441—864no—
380C2×#106—431no—
381C2×#106—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#103—431no—
389C2×#103—431no—
390C2×#103—864no—
391C2×C22⋊C8—431no—
392C2×#97—431no—
393C2×#97—431no—
394#391—21no—
395#391—21no—
396#391—431no—
397#391C2×D4311yescharacteristic
398#391C2×D4311yescharacteristic
399#389—431no—
400#389—861no—
401#387—861no—
402#385—861no—
403#380—21no—
404#380C2×D4311yescharacteristic
405C4×C4⋊C4—431no—
406C4×C22⋊C4—21no—
407C4×C22⋊C4—861no—
408C4×C22⋊C4C2×D4311yescharacteristic
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#336—431no—
414#336—431no—
415C43#2285911yescharacteristic, complemented, Sylow
416C22×Q8—22no—
417C22×Q8—21no—
418C22×Q8—22no—
419C22×Q8—22no—
420C22×Q8—41no—
421C22×Q8—41no—
422C22×Q8—431no—
423C22×Q8C4×D4314yes—
424C22×Q8C22×D4311yescharacteristic
425C22×Q8C22×D4311yescharacteristic
426C23×C4—21no—
427C23×C4—861no—
428C23×C4C22×D4311yescharacteristic
429C2×Q16—434no—
430C2×Q16—434no—
431C2×Q16—862no—
432C2×Q16—862no—
433C2×Q16—1721no—
434C2×Q16—1721no—
435C22×C8—431no—
436C22×C8—431no—
437C22×C8—431no—
438C22×C8—431no—
439C22×C8—862no—
440C22×C8—862no—
441C22×C8—1721no—
442C22⋊Q8—434no—
443C22⋊Q8—862no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—41no—
447C4×Q8—41no—
448C4×Q8—862no—
449C4×Q8—1721no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—862no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4—1721no—
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4C22⋊D4311yescharacteristic
466C2×C22⋊C4C22⋊D4311yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—861no—
470C2×C42—861no—
471C2×C42C22×D4311yescharacteristic
472C2×C42C22×D4311yescharacteristic
473#106—862no—
474#106—1721no—
475#103—434no—
476#103—434no—
477#103—434no—
478#103—862no—
479#103—862no—
480#103—862no—
481#103—862no—
482#103—1721no—
483C22⋊C8—434no—
484#97—862no—
485#97—1721no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—861no—
492#95—861no—
493#95—861no—
494#95—861no—
495#95C22⋊D4311yescharacteristic
496#95C22⋊D4311yescharacteristic
497C24C2×C22⋊D4311yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—28no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—432no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8—861no—
518C2×Q8—861no—
519C2×Q8C2×C4×D4312yes—
520C2×Q8C2×C4×D4312yes—
521C2×Q8D4×D4312yes—
522C2×Q8#1062190012yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—3441no—
539C22×C4—1722no—
540C22×C4—1722no—
541C22×C4C2×C4×D4312yes—
542C22×C4#1062189812yes—
543C22×C4C2×C22⋊D4311yescharacteristic
544C22×C4C2×C22⋊D4311yescharacteristic
545C22×C4C2×C22⋊D4311yescharacteristic
546C22×C4C2×C22⋊D4311yescharacteristic
547C22×C4C2×C22⋊D4311yescharacteristic
548C22×C4C23×D4311yescharacteristic
549Q16—868no—
550Q16—1724no—
551C2×C8—432no—
552C2×C8—432no—
553C2×C8—432no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—1724no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—432no—
571C4⋊C4—432no—
572C4⋊C4—864no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—3441no—
578C4⋊C4—1722no—
579C4⋊C4—1722no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—864no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C42—3441no—
591C42—1722no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C4×C22⋊D4312yes—
597C23#1306335512yes—
598C23#1306335612yes—
599C23C22×C22⋊D4311yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—48no—
606Q8—41no—
607Q8—41no—
608Q8—862no—
609Q8—862no—
610Q8—1721no—
611Q8—1721no—
612Q8(C22⋊D43)⋊C414yes—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—3444no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4—1721no—
653C2×C4—1721no—
654C2×C4—1721no—
655C2×C4—1721no—
656C2×C4—1721no—
657C2×C4C4×C22⋊D4312yes—
658C2×C4C22×C4×D4311yescharacteristic
659C2×C4C2×D4×D4311yescharacteristic
660C2×C4C2×#1062190011yescharacteristic
661C2×C4C2×#1062189811yescharacteristic
662C2×C4#1306337011yescharacteristic
663C2×C4#1306337011yescharacteristic
664C8—862no—
665C8—862no—
666C8—862no—
667C8—1721no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22#1458300414yescomplemented
675C22C2×C4×C22⋊D4311yescharacteristic
676C22D4×C22⋊D4311yescharacteristic
677C22#1458354311yescharacteristic
678C22C2×#1306335511yescharacteristic
679C22C2×#1306335611yescharacteristic
680C22#1458370711yescharacteristic
681C22#1458371411yescharacteristic
682C4—22no—
683C4—24no—
684C4—42no—
685C4—41no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—81no—
690C4—81no—
691C4—3441no—
692C4—1722no—
693C4—1722no—
694C4—1722no—
695C4C2×(C22⋊D43)⋊C411yescharacteristic
696C4#1458337211yescharacteristic
697C4#1458353911yescharacteristic
698C4#1458357511yescharacteristic
699C2—24no—
700C2#1913757411yescharacteristic
701C2C2×#1458300411yescharacteristic
702C2#1914343811yescharacteristic
703C2#1914610611yescharacteristic
704C2#1914616111yescharacteristic
705C2#1914664611yescharacteristic
706C2#1914670611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterQ8×C22⋊C4D43
hypocenterC43#22859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
5. #19135465C2semidirect
6. #19135288C2semidirect
7. #19135226C2semidirect
9. #19134939C2semidirect
10. #19134936C2semidirect
11. #19134863C2semidirect
13. #19134425C2semidirect
22. #14583055C4semidirect
68. C2×#10621885C2×C4semidirect
69. C2×#10621885C2×C4semidirect
98. #13063249C2×C4semidirect
99. #13063249C2×C4semidirect
321. C22×C43#441semidirect
415. C43#22859semidirect
674. C22#14583004semidirect

Maximal subgroups

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

subgroupindex
C2×#145830552
C2×#145830042
C22×#130632492
#191375982
#191354652
#191352882
#191352262
#191350162
#191349392
#191349362
#191348632
#191347872
#191344252
#191343732
Q8×C22⋊C4×C432
#2285943