Finite Group Databasebeta

← C2×#19147131 #25975230

Subgroups — C2×#19147131 #25975230

Order 11008.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583620C211yesmaximal, characteristic
2C2×#14583583C211yesmaximal, characteristic
3#19147131C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583239C211yesmaximal, characteristic, complemented
7C2×#14583237C211yesmaximal, characteristic, complemented
8C2×#14583237C211yesmaximal, characteristic, complemented
9C2×#14583208C211yesmaximal, characteristic, complemented
10C2×#14583192C211yesmaximal, characteristic, complemented
11C2×#14583154C211yesmaximal, characteristic, complemented
12C2×#14583006C211yesmaximal, characteristic, complemented
13C2×#14582970C211yesmaximal, characteristic
14C2×#14582940C211yesmaximal, characteristic, complemented
15C2×#14582937C211yesmaximal, characteristic, complemented
16C2×C43×#467C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18#14583620—24no—
19#14583620C2218yes—
20#14583583—24no—
21#14583583C2218yes—
22C2×#13063324C2211yescharacteristic
23C2×#13063320—21no—
24C2×#13063318—21no—
25C2×#13063318—21no—
26C2×#13063316C2211yescharacteristic
27C2×#13063315—21no—
28C2×#13063311—21no—
29C2×#13063307—21no—
30C2×#13063301C2211yescharacteristic
31C2×#13063301C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×Q8×Dic43C2211yescharacteristic
34C2×#13063290—21no—
35C2×C4×C22⋊D43C2211yescharacteristic
36C2×#13063284C2211yescharacteristic
37C2×#13063284C2211yescharacteristic
38C2×#13063283—21no—
39C2×#13063283C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41#14583307C2218yescomplemented
42#14583239C2218yescomplemented
43#14583237C2218yescomplemented
44#14583237C2218yescomplemented
45#14583233C2218yescomplemented
46#14583208C2218yescomplemented
47#14583192C2218yescomplemented
48#14583154C2218yescomplemented
49#14583006C2218yescomplemented
50#14582970C2218yes—
51#14582940C2218yescomplemented
52#14582937C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063249C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#467C2218yescomplemented
74C2×#107×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×C22⋊D43D411yescharacteristic
79C22×C4×D43—21no—
80C22×C4×D43C2311yescharacteristic
81C2×#10621872—24no—
82C2×#10621872C2314yes—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063324—22no—
86#13063324C2314yes—
87#13063320—28no—
88#13063318—28no—
89#13063318—28no—
90#13063316—22no—
91#13063316C2314yes—
92#13063315—28no—
93#13063311—28no—
94#13063307—28no—
95#13063301—22no—
96#13063301—22no—
97#13063301C2314yes—
98#13063301C2314yes—
99Q8×Dic43—22no—
100Q8×Dic43—22no—
101Q8×Dic43C2314yes—
102Q8×Dic43C2314yes—
103#13063290—28no—
104C4×C22⋊D43D414yes—
105C4×C22⋊D43C2314yes—
106#13063284—22no—
107#13063284—22no—
108#13063284C2314yes—
109#13063284C2314yes—
110#13063283—22no—
111#13063283—28no—
112#13063283C2314yes—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43—21no—
116C2×C4⋊Dic43C2311yescharacteristic
117C2×C4⋊Dic43C2311yescharacteristic
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2311yescharacteristic
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4D411yescharacteristic
126C4⋊C4×D43—22no—
127C4⋊C4×D43C2314yes—
128C2×C22⋊Dic43—21no—
129C2×C22⋊Dic43—21no—
130C2×C22⋊Dic43D411yescharacteristic
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4D411yescharacteristic
135C2×C4×Dic43—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43C2311yescharacteristic
141#13063259C2314yes—
142#13063259C2314yes—
143#13063258C2314yes—
144#13063258C2314yes—
145#13063257C2314yes—
146#13063257C2314yes—
147#13063256C2314yes—
148#13063256C2314yes—
149Dic43⋊C8C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154C22⋊(C43⋊C8)C2314yes—
155(C2×D43)⋊C8C2314yes—
156#13063235C2314yes—
157C22×Q8×C43C2311yescharacteristic
158C22×Q8×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C2×Q16×C43—24no—
161C2×Q16×C43C2314yes—
162C22×C8×C43—24no—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22⋊Q8×C43—22no—
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43C2314yes—
169C22⋊Q8×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176#107×C43C2314yes—
177#103×C43C2314yes—
178#103×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C23×D43C2×D411yescharacteristic
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43C2412yes—
188C2×Q8×C43C2412yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—42no—
200C2×C22⋊D43C2×D414yes—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—24no—
211C2×C4×D43—44no—
212C2×C4×D43C2×D412yes—
213C2×C4×D43C2412yes—
214C2×Dic86—24no—
215C2×Dic86—44no—
216Q16×C43—28no—
217C2×C8×C43—22no—
218C2×C8×C43—28no—
219C2×C8×C43#4114yes—
220C2×C8×C43C2412yes—
221C2×C8×C43C2412yes—
222C4⋊C4×C43—24no—
223C4⋊C4×C43—24no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43C2412yes—
227C4⋊C4×C43C2412yes—
228C22⋊C4×C43—24no—
229C22⋊C4×C43—24no—
230C22⋊Dic43—24no—
231C22⋊Dic43—24no—
232C22⋊Dic43C2×D414yes—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4C2×D414yes—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—24no—
242C4⋊Dic43—24no—
243C4⋊Dic43—24no—
244C4⋊Dic43C2412yes—
245C4⋊Dic43C2412yes—
246C4⋊Dic43C2412yes—
247C4⋊Dic43C2412yes—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4C2×D414yes—
254C4×Dic43—24no—
255C4×Dic43—24no—
256C4×Dic43—24no—
257C4×Dic43—24no—
258C4×Dic43—24no—
259C4×Dic43C2×D412yes—
260C4×Dic43C2412yes—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8C2412yes—
264C2×C43⋊C8C2412yes—
265#10621872—28no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43C22×D412yes—
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43C22×D412yes—
275Q8×C43—22no—
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—42no—
280Q8×C43—42no—
281C2×C4×C43—22no—
282C2×C4×C43—24no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4112yes—
296C2×C4×C432−1+412yes—
297C2×C4×C43C2511yescharacteristic
298C22⋊D43—44no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313C4×D43—24no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—48no—
317Dic86—48no—
318C8×C43—22no—
319C8×C43C2×#4114yes—
320C43⋊C8—22no—
321C43⋊C8—22no—
322C2×#3349—431nomaximal, Sylow
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—44no—
327C22×C43#54712yes—
328C22×C43#57512yes—
329C22×C43#57812yes—
330C22×C43C23×D411yescharacteristic
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—44no—
335C4×C43—22no—
336C4×C43—42no—
337C4×C43—42no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43#54712yes—
341C4×C43C22×#4111yescharacteristic
342C4×C43C2×2−1+411yescharacteristic
343Dic43—22no—
344Dic43—22no—
345Dic43—22no—
346Dic43—42no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350C2×#556—431no—
351C2×#552—431no—
352#3349—4316no—
353C2×#501—431no—
354C2×#484—431no—
355C2×#485—431no—
356C2×#485—431no—
357C2×#485—431no—
358C2×#479—431no—
359C2×#477—431no—
360C2×#470—431no—
361C2×#467D4311yescharacteristic, complemented
362C2×#441—431no—
363C2×#435—431no—
364C2×#428—431no—
365C2×#427—431no—
366C2×C43—42no—
367C2×C43#334914yescomplemented
368C2×C43C2×#54711yescharacteristic
369C2×C43C2×#57511yescharacteristic
370C2×C43C2×#57811yescharacteristic
371D43—42no—
372C22×Q16C2×D4311yescharacteristic
373C22×M16—431no—
374C23×C8C2×D4311yescharacteristic
375#556—438no—
376#556—864no—
377#552—438no—
378#552—864no—
379C2×C4⋊Q8—431no—
380C2×#126—861no—
381C2×#126—861no—
382C2×#126—861no—
383C2×#125—431no—
384C2×#125—861no—
385C2×#124—861no—
386C2×#123—861no—
387C2×C22⋊Q8—431no—
388C2×C22⋊Q8—431no—
389C2×C22⋊Q8C2×D4311yescharacteristic
390C2×C22⋊Q8C2×D4311yescharacteristic
391C2×C4×Q8—431no—
392C2×C4×Q8—431no—
393C2×C4×Q8—861no—
394C2×C4×D4—431no—
395C2×#117—431no—
396C2×#117—431no—
397C2×#117—431no—
398C2×#117—861no—
399C22×C4⋊C4—431no—
400#501—438no—
401#485—438no—
402#485—438no—
403#485—438no—
404#484—438no—
405#479—438no—
406#477—438no—
407#470—438no—
408#467C2×D4318yescomplemented
409#441—438no—
410#435—438no—
411#428—438no—
412#427—438no—
413C2×#107—431no—
414C2×#107—431no—
415C2×#107—431no—
416C2×#107—431no—
417C2×#107C2×D4311yescharacteristic
418C2×#106—431no—
419C2×#106—431no—
420C2×#106—431no—
421C2×#106—431no—
422C2×C4⋊C8—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103C2×D4311yescharacteristic
428C2×#103C2×D4311yescharacteristic
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×#97—431no—
432C43C2×#334911yescharacteristic, complemented, Sylow
433C22×Q8—861no—
434C22×Q8C22×D4311yescharacteristic
435C22×Q8C22×D4311yescharacteristic
436C22×D4—431no—
437C23×C4—431no—
438C23×C4—861no—
439C23×C4C22×D4311yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D4314yes—
442C2×M16—434no—
443C2×M16—864no—
444C22×C8—24no—
445C22×C8—431no—
446C22×C8—431no—
447C22×C8C22×D4311yescharacteristic
448C22×C8C22×D4314yes—
449C22×C8C22×D4311yescharacteristic
450C4⋊Q8—434no—
451C4⋊Q8—862no—
452#126—868no—
453#126—868no—
454#126—868no—
455#125—434no—
456#125—862no—
457#125—868no—
458#124—868no—
459#123—868no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—434no—
463C22⋊Q8—434no—
464C22⋊Q8—862no—
465C22⋊Q8—862no—
466C22⋊Q8C22×D4314yes—
467C22⋊Q8C22×D4314yes—
468C4×Q8—434no—
469C4×Q8—434no—
470C4×Q8—862no—
471C4×Q8—862no—
472C4×Q8—868no—
473C4×D4—434no—
474C4×D4—434no—
475#117—434no—
476#117—434no—
477#117—434no—
478#117—868no—
479#117—862no—
480#117—862no—
481#117—862no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—434no—
490C2×C4⋊C4—862no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C42—431no—
511C2×C42—861no—
512C2×C42—861no—
513C2×C42—861no—
514C2×C42—861no—
515C2×C42—861no—
516#107—434no—
517#107—434no—
518#107—434no—
519#107—434no—
520#107C22×D4314yes—
521#106—434no—
522#106—434no—
523#106—434no—
524#106—434no—
525C4⋊C8—434no—
526#103—434no—
527#103—434no—
528#103—434no—
529#103—434no—
530#103C22×D4314yes—
531#103C22×D4314yes—
532C22⋊C8—434no—
533C22⋊C8—434no—
534#97—434no—
535C24—431no—
536C24D4×D4311yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—864no—
544C2×Q8—1724no—
545C2×Q8C23×D4312yes—
546C2×Q8C23×D4312yes—
547C2×D4—434no—
548C2×D4—1722no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—864no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—1724no—
568C22×C4D4×D4312yes—
569C22×C4D4×D4311yescharacteristic
570C22×C4C23×D4312yes—
571C22×C4C23×D4311yescharacteristic
572Q16—28no—
573M16—868no—
574C2×C8—22no—
575C2×C8—28no—
576C2×C8—432no—
577C2×C8—432no—
578C2×C8—862no—
579C2×C8—862no—
580C2×C8#1062190014yes—
581C2×C8C23×D4312yes—
582C2×C8C23×D4312yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—434no—
588C4⋊C4—432no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—864no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4C23×D4312yes—
605C4⋊C4C23×D4312yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—434no—
609C22⋊C4—434no—
610C22⋊C4—864no—
611C22⋊C4—864no—
612C22⋊C4—864no—
613C22⋊C4—864no—
614C22⋊C4—864no—
615C42—432no—
616C42—432no—
617C42—864no—
618C42—864no—
619C42—864no—
620C42—864no—
621C42—864no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—432no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23C2×D4×D4312yes—
630C23C2×D4×D4311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637Q8—1728no—
638D4—1724no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—432no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—864no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—1728no—
665C2×C4—1722no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1722no—
669C2×C4C2×D4×D4312yes—
670C2×C4C2×D4×D4311yescharacteristic
671C2×C4C2×#1062190012yes—
672C2×C4#1306337212yes—
673C2×C4C24×D4311yescharacteristic
674C8—22no—
675C8—862no—
676C8—862no—
677C8C2×#1062190014yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—862no—
683C22—862no—
684C22—862no—
685C22—1724no—
686C22#1458354912yes—
687C22#1458369612yes—
688C22#1458371212yes—
689C22C22×D4×D4311yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—862no—
696C4—862no—
697C4—862no—
698C4—1722no—
699C4—1722no—
700C4—1722no—
701C4—1722no—
702C4#1458354912yes—
703C4C22×#1062190011yescharacteristic
704C4C2×#1306337211yescharacteristic
705C2—42no—
706C2—1722no—
707C2#1914713114yesdirect product factor
708C2C2×#1458354911yescharacteristic
709C2C2×#1458369611yescharacteristic
710C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#467D43
hypocenterC43C2×#3349
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #19147131C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583239C2semidirect
7. C2×#14583237C2semidirect
8. C2×#14583237C2semidirect
9. C2×#14583208C2semidirect
10. C2×#14583192C2semidirect
11. C2×#14583154C2semidirect
12. C2×#14583006C2semidirect
14. C2×#14582940C2semidirect
15. C2×#14582937C2semidirect
16. C2×C43×#467C2semidirect
41. #14583307C22semidirect
42. #14583239C22semidirect
43. #14583237C22semidirect
44. #14583237C22semidirect
45. #14583233C22semidirect
46. #14583208C22semidirect
47. #14583192C22semidirect
48. #14583154C22semidirect
49. #14583006C22semidirect
51. #14582940C22semidirect
52. #14582937C22semidirect
73. C43×#467C22semidirect
361. C2×#467D43semidirect
367. C2×C43#3349semidirect
408. #467C2×D43semidirect
432. C43C2×#3349semidirect
707. C2#19147131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836202
C2×#145835832
#191471312
C2×#145833072
C2×#145832332
C2×#145832392
C2×#145832372
C2×#145832082
C2×#145831922
C2×#145831542
C2×#145830062
C2×#145829702
C2×#145829402
C2×#145829372
C2×C43×#4672
C2×#334943