Finite Group Databasebeta

← C2×#19147286 #25976216

Subgroups — C2×#19147286 #25976216

Order 11008.

1894 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583631C211yesmaximal, characteristic
2C2×#14583625C211yesmaximal, characteristic, complemented
3#19147286C2116yesmaximal, direct product factor
4C2×#14583255C211yesmaximal, characteristic, complemented
5C2×#14583253C211yesmaximal, characteristic, complemented
6C2×#14583244C211yesmaximal, characteristic
7C2×#14583182C211yesmaximal, characteristic, complemented
8C2×#14583200C211yesmaximal, characteristic, complemented
9C2×#14583197C211yesmaximal, characteristic, complemented
10C2×#14583123C211yesmaximal, characteristic, complemented
11C2×#14583097C211yesmaximal, characteristic
12C2×#14583023C211yesmaximal, characteristic, complemented
13C2×Q16×Dic43C211yesmaximal, characteristic, complemented
14C2×SD16×Dic43C211yesmaximal, characteristic, complemented
15C2×C4×#10621884C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18#14583631—24no—
19#14583631C2218yes—
20#14583625—24no—
21#14583625C2218yescomplemented
22C2×#13063324—21no—
23C2×#13063324C2211yescharacteristic
24C2×#13063321C2211yescharacteristic
25C2×#13063317—21no—
26C2×#13063317C2211yescharacteristic
27C2×#13063316—21no—
28C2×#13063316C2211yescharacteristic
29C2×#13063314C2211yescharacteristic
30C2×#13063311—21no—
31C2×#13063309—21no—
32C2×#13063307—21no—
33C2×Q8×Dic43C2211yescharacteristic
34C2×Q8×Dic43C2211yescharacteristic
35C2×Q8×Dic43C2211yescharacteristic
36C2×C4×Dic86—21no—
37C2×C4×Dic86C2211yescharacteristic
38C2×C4×D172C2211yescharacteristic
39C2×D4×Dic43C2211yescharacteristic
40C2×(C22⋊D43)⋊C4—21no—
41#14583255C2218yescomplemented
42#14583253C2218yescomplemented
43#14583244C2218yes—
44#14583200C2218yescomplemented
45#14583197C2218yescomplemented
46#14583182C2218yescomplemented
47#14583123C2218yescomplemented
48#14583097C2218yes—
49#14583023C2218yescomplemented
50Q16×Dic43C2218yescomplemented
51SD16×Dic43C2218yescomplemented
52C4×#10621884C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063249C2211yescharacteristic
60C2×#13063249C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C4×C43⋊C8C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#464C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86D411yescharacteristic
79C22×D172C2311yescharacteristic
80C22×C22⋊D43—21no—
81C22×C22⋊D43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C2×#10621884—24no—
85C2×#10621884C2314yes—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063324—28no—
89#13063324—22no—
90#13063324C2314yes—
91#13063321—22no—
92#13063321C2314yes—
93#13063317—22no—
94#13063317—28no—
95#13063317C2314yes—
96#13063316—28no—
97#13063316—22no—
98#13063316C2314yes—
99#13063314—22no—
100#13063314C2314yes—
101#13063311—28no—
102#13063309—28no—
103#13063307—28no—
104Q8×Dic43—22no—
105Q8×Dic43—22no—
106Q8×Dic43—22no—
107Q8×Dic43C2314yes—
108Q8×Dic43C2314yes—
109Q8×Dic43C2314yes—
110C4×Dic86—28no—
111C4×Dic86D414yes—
112C4×Dic86C2314yes—
113C4×D172—22no—
114C4×D172C2314yes—
115D4×Dic43—22no—
116D4×Dic43C2314yes—
117(C22⋊D43)⋊C4—28no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43D411yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C2×Dic43⋊C4D411yescharacteristic
132C2×C22⋊Dic43—21no—
133C2×(C2×D43)⋊C4—21no—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×C4×Dic43—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141#13063259C2314yes—
142#13063257C2314yes—
143#13063256C2314yes—
144Dic43⋊C8C2314yes—
145Dic43⋊C8C2314yes—
146#13063249C2314yes—
147#13063249C2314yes—
148#13063249C2314yes—
149#13063247C2314yes—
150#13063247C2314yes—
151#13063246C2314yes—
152#13063246C2314yes—
153#13063245C2314yes—
154C4×C43⋊C8C2314yes—
155C8×Dic43C2314yes—
156C8×Dic43C2314yes—
157C22×Q8×C43C2311yescharacteristic
158C22×Q8×C43C2311yescharacteristic
159C22×D4×C43C2311yescharacteristic
160C2×Q16×C43—24no—
161C2×Q16×C43C2314yes—
162C2×SD16×C43—24no—
163C2×SD16×C43C2314yes—
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166#124×C43—22no—
167#124×C43C2314yes—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C42×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43C2314yes—
177#103×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C23×D43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43#4114yes—
187C2×Q8×C43C2412yes—
188C2×Q8×C43C2412yes—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43C2412yes—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—44no—
202C2×C22⋊D43—82no—
203C22×Dic43—24no—
204C22×Dic43—21no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—82no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C2×D172—21no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172C2412yes—
216C2×C4×D43—24no—
217C2×C4×D43—82no—
218C2×Dic86—24no—
219C2×Dic86—24no—
220C2×Dic86—44no—
221C2×Dic86C2×D414yes—
222Q16×C43—28no—
223SD16×C43—28no—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43C2412yes—
227C2×C8×C43C2412yes—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43C2412yes—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—24no—
233C42×C43—24no—
234C42×C43C2×D412yes—
235C42×C43C2412yes—
236C22⋊Dic43—24no—
237#10621884—28no—
238(C2×D43)⋊C4—24no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—21no—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43—24no—
247C4⋊Dic43—24no—
248C4⋊Dic43C2×D414yes—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251C4⋊Dic43C2412yes—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4C2×D414yes—
257Dic43⋊C4C2×D414yes—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—24no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2×D412yes—
263C4×Dic43C2412yes—
264C4×Dic43C2412yes—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269C23×C43—22no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43—42no—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278Q8×C43—24no—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—42no—
283Q8×C43C2×#4114yes—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—42no—
287C2×C4×C43—24no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D412yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C2×#4112yes—
299C2×C4×C432−1+412yes—
300C2×C4×C43C2511yescharacteristic
301C22⋊D43—48no—
302C22⋊D43—84no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—84no—
313C2×Dic43#13514yes—
314C2×Dic43C22×D412yes—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318D172—22no—
319D172—22no—
320D172—42no—
321C4×D43—84no—
322Dic86—28no—
323Dic86—48no—
324C8×C43—22no—
325C8×C43—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C2×#3365—431nomaximal, Sylow
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—84no—
333C22×C43#54812yes—
334C22×C43C2×#13512yes—
335C22×C43#57712yes—
336C22×C43C23×D411yescharacteristic
337C2×D43—42no—
338C2×D43—42no—
339C2×D43—42no—
340C2×D43—84no—
341C4×C43—24no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—42no—
346C4×C43#54812yes—
347C4×C43C22×#4111yescharacteristic
348C4×C43C2×2−1+411yescharacteristic
349Dic43—22no—
350Dic43—22no—
351Dic43—22no—
352Dic43—42no—
353Dic43—42no—
354Dic43—42no—
355Dic43C2×#13514yes—
356C2×#559—431no—
357C2×#557—431no—
358#3365—4316no—
359C2×#488—431no—
360C2×#488—431no—
361C2×#486—431no—
362C2×#475—431no—
363C2×#478—431no—
364C2×#478—431no—
365C2×#464—431no—
366C2×#464D4311yescharacteristic, complemented
367C2×#460—431no—
368C2×C8×Q8—431no—
369C2×C4×Q16—431no—
370C2×C4×SD16—431no—
371C2×C4×SD16—431no—
372C2×C43—82no—
373C2×C43#336514yescomplemented
374C2×C43C2×#54811yescharacteristic
375C2×C43C22×#13511yescharacteristic
376C2×C43C2×#57711yescharacteristic
377D43—82no—
378C22×Q16C2×D4311yescharacteristic
379C22×SD16—431no—
380C22×SD16C2×D4311yescharacteristic
381#559—438no—
382#559—864no—
383#557—438no—
384#557—864no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8—861no—
387C2×#127—431no—
388C2×#125—431no—
389C2×#125—431no—
390C2×#125—861no—
391C2×#125—861no—
392C2×#124—431no—
393C2×#124—861no—
394C2×#124C2×D4311yescharacteristic
395C2×#123—861no—
396C2×#123—861no—
397C2×C4×Q8—431no—
398C2×C4×Q8—431no—
399C2×C4×Q8—431no—
400C2×C4×Q8—431no—
401C2×C4×Q8—861no—
402C2×C4×Q8C2×D4311yescharacteristic
403C2×C4×D4—431no—
404C2×C4×D4—431no—
405C2×C4×D4—861no—
406#488—438no—
407#488—438no—
408#486—438no—
409#478—438no—
410#478—438no—
411#475—438no—
412#464—438no—
413#464C2×D4318yescomplemented
414#460—438no—
415C8×Q8—438no—
416C4×Q16—438no—
417C4×SD16—438no—
418C4×SD16—438no—
419C2×#107—431no—
420C2×#106—431no—
421C2×#106—431no—
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8C2×D4311yescharacteristic
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103C2×D4311yescharacteristic
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102C2×D4311yescharacteristic
435C2×C4×C8—431no—
436C2×C4×C8—431no—
437C2×C4×C8—431no—
438C43C2×#336511yescharacteristic, complemented, Sylow
439C22×Q8—431no—
440C22×Q8—861no—
441C22×Q8C22×D4311yescharacteristic
442C22×Q8C22×D4311yescharacteristic
443C22×D4—431no—
444C22×D4—861no—
445C22×D4—861no—
446C22×D4C22×D4311yescharacteristic
447C23×C4—861no—
448C23×C4—861no—
449C2×Q16—24no—
450C2×Q16C22×D4314yes—
451C2×SD16—24no—
452C2×SD16—434no—
453C2×SD16—864no—
454C2×SD16C22×D4314yes—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C4⋊Q8—434no—
460C4⋊Q8—862no—
461C4⋊Q8—868no—
462#127—434no—
463#127—862no—
464#125—434no—
465#125—434no—
466#125—868no—
467#125—862no—
468#125—868no—
469#125—862no—
470#124—22no—
471#124—434no—
472#124—862no—
473#124—868no—
474#124C22×D4314yes—
475#123—868no—
476#123—868no—
477C4×Q8—22no—
478C4×Q8—434no—
479C4×Q8—434no—
480C4×Q8—434no—
481C4×Q8—434no—
482C4×Q8—434no—
483C4×Q8—868no—
484C4×Q8—862no—
485C4×Q8—862no—
486C4×Q8—862no—
487C4×Q8C22×D4314yes—
488C4×D4—434no—
489C4×D4—434no—
490C4×D4—862no—
491C4×D4—868no—
492C4×D4—862no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C42—21no—
516C2×C42—431no—
517C2×C42—431no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521C2×C42C22×D4311yescharacteristic
522#107—434no—
523#106—434no—
524#106—434no—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8C22×D4314yes—
528#103—434no—
529#103—434no—
530#103—434no—
531#103C22×D4314yes—
532#102—434no—
533#102—434no—
534#102—434no—
535#102—434no—
536#102—434no—
537#102C22×D4314yes—
538C4×C8—434no—
539C4×C8—434no—
540C4×C8—434no—
541C24—21no—
542C24—861no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—434no—
549C2×Q8—864no—
550C2×Q8—864no—
551C2×Q8—1724no—
552C2×Q8#1062190014yes—
553C2×Q8C23×D4312yes—
554C2×Q8C23×D4312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—432no—
559C2×D4—864no—
560C2×D4—864no—
561C2×D4—861no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—3442no—
565C2×D4—1724no—
566C2×D4C23×D4312yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—864no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—864no—
579C22×C4—3442no—
580C22×C4—3442no—
581C22×C4D4×D4311yescharacteristic
582C22×C4D4×D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584Q16—28no—
585SD16—28no—
586SD16—868no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—432no—
590C2×C8—432no—
591C2×C8—862no—
592C2×C8—862no—
593C2×C8C23×D4312yes—
594C2×C8C23×D4312yes—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—434no—
598C4⋊C4—434no—
599C4⋊C4—434no—
600C4⋊C4—432no—
601C4⋊C4—432no—
602C4⋊C4—432no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4C23×D4312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C42—24no—
622C42—432no—
623C42—432no—
624C42—432no—
625C42—432no—
626C42—864no—
627C42—864no—
628C42—864no—
629C42D4×D4312yes—
630C42C23×D4312yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—862no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23C2×D4×D4311yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—868no—
646Q8—1728no—
647Q8C2×#1062190014yes—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—862no—
652D4—862no—
653D4—3444no—
654D4—1728no—
655D4—1722no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—434no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—432no—
668C2×C4—432no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—3444no—
676C2×C4—3444no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4C2×D4×D4312yes—
681C2×C4C2×D4×D4312yes—
682C2×C4C2×D4×D4311yescharacteristic
683C2×C4C2×#1062190012yes—
684C2×C4#1306337212yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—862no—
689C8—862no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—3444no—
695C22—1722no—
696C22—1722no—
697C22—1722no—
698C22#1458355512yes—
699C22#135×D4312yes—
700C22#1458370812yes—
701C22C22×D4×D4311yescharacteristic
702C4—22no—
703C4—24no—
704C4—22no—
705C4—42no—
706C4—42no—
707C4—434no—
708C4—862no—
709C4—862no—
710C4—862no—
711C4—1722no—
712C4—1722no—
713C4—1722no—
714C4#1458355512yes—
715C4C22×#1062190011yescharacteristic
716C4C2×#1306337211yescharacteristic
717C2—82no—
718C2—3442no—
719C2#1914728614yesdirect product factor
720C2C2×#1458355511yescharacteristic
721C2C2×#135×D4311yescharacteristic
722C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenterC2×#464D43
hypocenterC43C2×#3365
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#14583625C2semidirect
3. #19147286C2direct (N × H)
4. C2×#14583255C2semidirect
5. C2×#14583253C2semidirect
7. C2×#14583182C2semidirect
8. C2×#14583200C2semidirect
9. C2×#14583197C2semidirect
10. C2×#14583123C2semidirect
12. C2×#14583023C2semidirect
13. C2×Q16×Dic43C2semidirect
14. C2×SD16×Dic43C2semidirect
15. C2×C4×#10621884C2semidirect
16. C2×C43×#464C2semidirect
21. #14583625C22semidirect
41. #14583255C22semidirect
42. #14583253C22semidirect
44. #14583200C22semidirect
45. #14583197C22semidirect
46. #14583182C22semidirect
47. #14583123C22semidirect
49. #14583023C22semidirect
50. Q16×Dic43C22semidirect
51. SD16×Dic43C22semidirect
52. C4×#10621884C22semidirect
73. C43×#464C22semidirect
366. C2×#464D43semidirect
373. C2×C43#3365semidirect
413. #464C2×D43semidirect
438. C43C2×#3365semidirect
719. C2#19147286direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836312
C2×#145836252
#191472862
C2×#145832552
C2×#145832532
C2×#145832442
C2×#145831822
C2×#145832002
C2×#145831972
C2×#145831232
C2×#145830972
C2×#145830232
C2×Q16×Dic432
C2×SD16×Dic432
C2×C4×#106218842
C2×C43×#4642
C2×#336543