Finite Group Databasebeta

← C2×#19147245 #25976170

Subgroups — C2×#19147245 #25976170

Order 11008.

1906 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×#14583621C211yesmaximal, characteristic, complemented
2C2×#14583608C211yesmaximal, characteristic, complemented
3#19147245C2116yesmaximal, direct product factor
4C2×#14583255C211yesmaximal, characteristic, complemented
5C2×#14583254C211yesmaximal, characteristic, complemented
6C2×#14583248C211yesmaximal, characteristic, complemented
7C2×#14583209C211yesmaximal, characteristic, complemented
8C2×#14583206C211yesmaximal, characteristic, complemented
9C2×#14583188C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic
11C2×#14583114C211yesmaximal, characteristic
12C2×#14583102C211yesmaximal, characteristic, complemented
13C2×C8×Dic86C211yesmaximal, characteristic, complemented
14C2×#14582990C211yesmaximal, characteristic, complemented
15C2×#14582979C211yesmaximal, characteristic
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19#14583621—24no—
20#14583621C2218yescomplemented
21#14583608—24no—
22#14583608C2218yescomplemented
23C2×#13063324C2211yescharacteristic
24C2×#13063323C2211yescharacteristic
25C2×#13063320—21no—
26C2×#13063319—21no—
27C2×#13063317C2211yescharacteristic
28C2×#13063316C2211yescharacteristic
29C2×#13063314C2211yescharacteristic
30C2×#13063313C2211yescharacteristic
31C2×#13063304—21no—
32C2×#13063303—21no—
33C2×#13063302—21no—
34C2×#13063302—21no—
35C2×C4×Dic86C2211yescharacteristic
36C2×#13063290C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×D4×Dic43C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×#13063282—21no—
41C22×Dic43⋊C4—21no—
42#14583255C2218yescomplemented
43#14583254C2218yescomplemented
44#14583248C2218yescomplemented
45#14583209C2218yescomplemented
46#14583206C2218yescomplemented
47#14583188C2218yescomplemented
48#14583116C2218yes—
49#14583114C2218yes—
50#14583102C2218yescomplemented
51C8×Dic86C2218yescomplemented
52#14582990C2218yescomplemented
53#14582979C2218yes—
54C2×#13063258C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57C2×Dic43⋊C8C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×C8×Dic43C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×SD16×C43C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86D411yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C23×Dic43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C2×#10621883—24no—
85C2×#10621883C2314yes—
86C2×#10621882—24no—
87C2×#10621882C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90#13063324—22no—
91#13063324C2314yes—
92#13063323—22no—
93#13063323C2314yes—
94#13063320—28no—
95#13063319—28no—
96#13063317—22no—
97#13063317C2314yes—
98#13063316—22no—
99#13063316C2314yes—
100#13063314—22no—
101#13063314C2314yes—
102#13063313—22no—
103#13063313C2314yes—
104#13063304—28no—
105#13063303—28no—
106#13063302—28no—
107#13063302—28no—
108C4×Dic86D414yes—
109C4×Dic86C2314yes—
110#13063290—22no—
111#13063290C2314yes—
112D4×Dic43—22no—
113D4×Dic43—22no—
114D4×Dic43C2314yes—
115D4×Dic43C2314yes—
116#13063287—22no—
117#13063287C2314yes—
118#13063282—28no—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43D411yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—28no—
131C2×Dic43⋊C4D411yescharacteristic
132C2×Dic43⋊C4D411yescharacteristic
133C2×C22⋊Dic43—21no—
134C2×C22⋊Dic43—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×C4×Dic43—21no—
141C2×C4×Dic43C2311yescharacteristic
142C2×C4×Dic43C2311yescharacteristic
143#13063258C2314yes—
144#13063256C2314yes—
145C4⋊(C43⋊C8)C2314yes—
146Dic43⋊C8C2314yes—
147Dic43⋊C8C2314yes—
148#13063250C2314yes—
149#13063250C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063248C2314yes—
153#13063247C2314yes—
154#13063247C2314yes—
155#13063245C2314yes—
156C8×Dic43C2314yes—
157C8×Dic43C2314yes—
158C22×Q8×C43C2311yescharacteristic
159C22×D4×C43C2311yescharacteristic
160C23×C4×C43—21no—
161C2×SD16×C43—24no—
162C2×SD16×C43C2314yes—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C4×Q8×C43—22no—
166C4×Q8×C43C2314yes—
167C4×D4×C43—22no—
168C4×D4×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C42×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#106×C43C2314yes—
176#103×C43C2314yes—
177#102×C43C2314yes—
178C4×C8×C43C2314yes—
179C24×C43—21no—
180C23×D43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—22no—
183C2×Q8×C43—22no—
184C2×Q8×C43C2412yes—
185C2×D4×C43—21no—
186C2×D4×C43—22no—
187C2×D4×C43#4114yes—
188C2×D4×C43C2412yes—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—82no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—24no—
198C22×Dic43—24no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—44no—
203C22×Dic43—82no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C2×D172—21no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172C2412yes—
212C2×C4×D43—24no—
213C2×C4×D43—44no—
214C2×Dic86—24no—
215C2×Dic86—22no—
216C2×Dic86—22no—
217C2×Dic86—21no—
218C2×Dic86—24no—
219C2×Dic86—82no—
220C2×Dic86C2×D414yes—
221C2×Dic86C2412yes—
222SD16×C43—28no—
223C2×C8×C43—22no—
224C2×C8×C43—22no—
225C2×C8×C43C2412yes—
226C2×C8×C43C2412yes—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43C2412yes—
231C4⋊C4×C43C2412yes—
232C22⋊C4×C43—24no—
233C42×C43—24no—
234C42×C43C2×D412yes—
235C42×C43C2412yes—
236C22⋊Dic43—24no—
237C22⋊Dic43—24no—
238#10621883—28no—
239#10621882—28no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—24no—
248C4⋊Dic43C2×D414yes—
249C4⋊Dic43C2412yes—
250C4⋊Dic43C2412yes—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4C2×D414yes—
259Dic43⋊C4C2×D414yes—
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—24no—
270C23×C43—22no—
271C23×C43—42no—
272C23×C43—42no—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278Q8×C43—22no—
279Q8×C43—22no—
280Q8×C43—42no—
281D4×C43—24no—
282D4×C43—22no—
283D4×C43C2×#4114yes—
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—84no—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4112yes—
297C2×C4×C432−1+412yes—
298C2×C4×C43C2511yescharacteristic
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—48no—
309C2×Dic43—84no—
310C2×Dic43#13514yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314C2×Dic43C22×D412yes—
315D172—22no—
316D172—22no—
317D172—42no—
318C4×D43—48no—
319Dic86—28no—
320Dic86—22no—
321Dic86—22no—
322Dic86—42no—
323Dic86—84no—
324C8×C43—22no—
325C8×C43—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328C2×#3360—431nomaximal, Sylow
329C22×C43—24no—
330C22×C43—48no—
331C22×C43—42no—
332C22×C43—42no—
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—22no—
342C4×C43—22no—
343C4×C43—42no—
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×#556—431no—
357C2×#554—431no—
358#3360—4316no—
359C2×#488—431no—
360C2×#488—431no—
361C2×#487—431no—
362C2×#479—431no—
363C2×#479—431no—
364C2×#476—431no—
365C2×#463—431no—
366C2×#463—431no—
367C2×#461—431no—
368C2×C8×Q8—431no—
369C2×C4×SD16—431no—
370C2×C4×SD16D4311yescharacteristic, complemented
371C2×C4×D8—431no—
372C2×C43—44no—
373C2×C43#336014yescomplemented
374C2×C43C2×#54811yescharacteristic
375C2×C43C22×#13511yescharacteristic
376C2×C43C2×#57711yescharacteristic
377D43—82no—
378C22×SD16—431no—
379C22×SD16C2×D4311yescharacteristic
380C22×D8—431no—
381#556—438no—
382#556—864no—
383#554—438no—
384#554—864no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8—431no—
387C2×#126—861no—
388C2×#126—861no—
389C2×#125—431no—
390C2×#125—431no—
391C2×#124—431no—
392C2×#124—431no—
393C2×C22⋊Q8—861no—
394C2×C22⋊Q8—861no—
395C2×C22⋊Q8—861no—
396C2×C22⋊Q8—861no—
397C2×C4×Q8—431no—
398C2×C4×Q8—431no—
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×D4—431no—
401C2×C4×D4—431no—
402C2×C4×D4—431no—
403C2×C4×D4C2×D4311yescharacteristic
404C2×#117—861no—
405C22×C4⋊C4—861no—
406#488—438no—
407#488—438no—
408#487—438no—
409#479—438no—
410#479—438no—
411#476—438no—
412#463—438no—
413#463—438no—
414#461—438no—
415C8×Q8—438no—
416C4×SD16—438no—
417C4×SD16C2×D4318yescomplemented
418C4×D8—438no—
419C2×#107—431no—
420C2×#106—431no—
421C2×#106C2×D4311yescharacteristic
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×C4⋊C8—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103C2×D4311yescharacteristic
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×#102C2×D4311yescharacteristic
435C2×C4×C8—431no—
436C2×C4×C8—431no—
437C2×C4×C8C2×D4311yescharacteristic
438C43C2×#336011yescharacteristic, complemented, Sylow
439C22×Q8—431no—
440C22×Q8—431no—
441C22×Q8—861no—
442C22×Q8C22×D4311yescharacteristic
443C22×D4—431no—
444C22×D4C22×D4311yescharacteristic
445C23×C4—21no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C2×SD16—24no—
450C2×SD16—434no—
451C2×SD16—864no—
452C2×SD16C22×D4314yes—
453C2×D8—434no—
454C2×D8—864no—
455C22×C8—431no—
456C22×C8—431no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C4⋊Q8—434no—
460C4⋊Q8—434no—
461C4⋊Q8—862no—
462C4⋊Q8—862no—
463#126—868no—
464#126—868no—
465#125—434no—
466#125—434no—
467#125—862no—
468#125—862no—
469#124—434no—
470#124—434no—
471#124—862no—
472#124—862no—
473C22⋊Q8—868no—
474C22⋊Q8—868no—
475C22⋊Q8—868no—
476C22⋊Q8—868no—
477C4×Q8—22no—
478C4×Q8—434no—
479C4×Q8—434no—
480C4×Q8—434no—
481C4×Q8—862no—
482C4×Q8C22×D4314yes—
483C4×D4—22no—
484C4×D4—434no—
485C4×D4—434no—
486C4×D4—434no—
487C4×D4—862no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4C22×D4314yes—
491#117—868no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—868no—
499C2×C4⋊C4—861no—
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⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C42—21no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42C22×D4311yescharacteristic
522#107—434no—
523#106—434no—
524#106C22×D4314yes—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8—434no—
528#103—434no—
529#103—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103C22×D4314yes—
534#102—434no—
535#102—434no—
536#102—434no—
537#102C22×D4314yes—
538C4×C8—434no—
539C4×C8—434no—
540C4×C8C22×D4314yes—
541C24—21no—
542C24—861no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—434no—
547C2×Q8—432no—
548C2×Q8—864no—
549C2×Q8—864no—
550C2×Q8—861no—
551C2×Q8—862no—
552C2×Q8—862no—
553C2×Q8—3442no—
554C2×Q8C23×D4312yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—432no—
558C2×D4—861no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4#1062189814yes—
562C2×D4C23×D4312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—864no—
573C22×C4—864no—
574C22×C4—864no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—3442no—
579C22×C4—1724no—
580C22×C4—1724no—
581C22×C4D4×D4311yescharacteristic
582C22×C4D4×D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584SD16—28no—
585SD16—868no—
586D8—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—21no—
598C4⋊C4—434no—
599C4⋊C4—434no—
600C4⋊C4—434no—
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—864no—
612C4⋊C4—864no—
613C4⋊C4C23×D4312yes—
614C4⋊C4C23×D4312yes—
615C22⋊C4—24no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—864no—
619C22⋊C4—864no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—24no—
624C42—432no—
625C42—432no—
626C42—432no—
627C42—432no—
628C42—864no—
629C42D4×D4312yes—
630C42C23×D4312yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—862no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23C2×D4×D4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—868no—
644Q8—862no—
645Q8—862no—
646Q8—3444no—
647Q8—1722no—
648D4—24no—
649D4—22no—
650D4—862no—
651D4—862no—
652D4—1722no—
653D4C2×#1062189814yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—434no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—432no—
667C2×C4—432no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—3444no—
675C2×C4—1728no—
676C2×C4—1728no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4C2×D4×D4312yes—
681C2×C4C2×D4×D4312yes—
682C2×C4C2×D4×D4311yescharacteristic
683C2×C4C2×#1062189812yes—
684C2×C4#1306337212yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—862no—
689C8—862no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—3444no—
695C22—1722no—
696C22—1722no—
697C22—1722no—
698C22#1458355812yes—
699C22#135×D4312yes—
700C22#1458370512yes—
701C22C22×D4×D4311yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—434no—
708C4—862no—
709C4—862no—
710C4—862no—
711C4—1722no—
712C4—1722no—
713C4—1722no—
714C4#1458355812yes—
715C4C22×#1062189811yescharacteristic
716C4C2×#1306337211yescharacteristic
717C2—44no—
718C2—3442no—
719C2#1914724514yesdirect product factor
720C2C2×#1458355811yescharacteristic
721C2C2×#135×D4311yescharacteristic
722C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×C4×SD16D43
hypocenterC43C2×#3360
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14583621C2semidirect
2. C2×#14583608C2semidirect
3. #19147245C2direct (N × H)
4. C2×#14583255C2semidirect
5. C2×#14583254C2semidirect
6. C2×#14583248C2semidirect
7. C2×#14583209C2semidirect
8. C2×#14583206C2semidirect
9. C2×#14583188C2semidirect
12. C2×#14583102C2semidirect
13. C2×C8×Dic86C2semidirect
14. C2×#14582990C2semidirect
16. C2×C4×SD16×C43C2semidirect
20. #14583621C22semidirect
22. #14583608C22semidirect
42. #14583255C22semidirect
43. #14583254C22semidirect
44. #14583248C22semidirect
45. #14583209C22semidirect
46. #14583206C22semidirect
47. #14583188C22semidirect
50. #14583102C22semidirect
51. C8×Dic86C22semidirect
52. #14582990C22semidirect
72. C4×SD16×C43C22semidirect
370. C2×C4×SD16D43semidirect
373. C2×C43#3360semidirect
417. C4×SD16C2×D43semidirect
438. C43C2×#3360semidirect
719. C2#19147245direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836212
C2×#145836082
#191472452
C2×#145832552
C2×#145832542
C2×#145832482
C2×#145832092
C2×#145832062
C2×#145831882
C2×#145831162
C2×#145831142
C2×#145831022
C2×C8×Dic862
C2×#145829902
C2×#145829792
C2×C4×SD16×C432
C2×#336043