Finite Group Databasebeta

← C2×#19144894 #25964952

Subgroups — C2×#19144894 #25964952

Order 11008.

1994 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583507C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic
3#19144894C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic
5C2×#14583238C211yesmaximal, characteristic
6C2×#14583209C211yesmaximal, characteristic, complemented
7C2×#14583204C211yesmaximal, characteristic, complemented
8C2×#14583108C211yesmaximal, characteristic, complemented
9C2×#14583107C211yesmaximal, characteristic, complemented
10C2×#14583056C211yesmaximal, characteristic
11C2×#14583053C211yesmaximal, characteristic
12C2×#14583007C211yesmaximal, characteristic, complemented
13C2×C4×#10621885C211yesmaximal, characteristic, complemented
14C2×C4×#10621885C211yesmaximal, characteristic, complemented
15C2×#14582961C211yesmaximal, characteristic
16C2×C43×#441C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21#14583507—24no—
22#14583507C2218yes—
23C2×#13063323C2211yescharacteristic
24C2×#13063320—21no—
25C2×#13063319—21no—
26C2×#13063317—21no—
27C2×#13063316C2211yescharacteristic
28C2×#13063315—21no—
29C2×#13063305C2211yescharacteristic
30C2×#13063301C2211yescharacteristic
31#14583375—24no—
32#14583375C2218yes—
33C2×Q8×Dic43C2211yescharacteristic
34C2×C4×Dic86—21no—
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×Dic86C2211yescharacteristic
37C2×#13063290—21no—
38C2×#13063290C2211yescharacteristic
39C2×#13063283—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C2×#13063282C2211yescharacteristic
43#14583243C2218yes—
44#14583238C2218yes—
45#14583209C2218yescomplemented
46#14583204C2218yescomplemented
47#14583108C2218yescomplemented
48#14583107C2218yescomplemented
49#14583056C2218yes—
50#14583053C2218yes—
51#14583007C2218yescomplemented
52C4×#10621885C2218yescomplemented
53C4×#10621885C2218yescomplemented
54#14582961C2218yes—
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C43×#441C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C2×Q8×D43—24no—
81C2×Q8×D43—22no—
82C2×Q8×D43—24no—
83C2×Q8×D43C2314yes—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×Dic172—24no—
87C2×Dic172C2314yes—
88C2×#10621885—24no—
89C2×#10621885—24no—
90C2×#10621885C2314yes—
91C2×#10621885C2314yes—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063323—22no—
95#13063323C2314yes—
96#13063320—28no—
97#13063319—28no—
98#13063317—28no—
99#13063316—22no—
100#13063316C2314yes—
101#13063315—28no—
102#13063305—22no—
103#13063305C2314yes—
104#13063301—22no—
105#13063301C2314yes—
106Q8×Dic43—22no—
107Q8×Dic43C2314yes—
108C4×Dic86—22no—
109C4×Dic86—22no—
110C4×Dic86—28no—
111C4×Dic86C2314yes—
112C4×Dic86C2314yes—
113#13063290—28no—
114#13063290—22no—
115#13063290C2314yes—
116#13063283—22no—
117#13063283—28no—
118#13063283C2314yes—
119#13063282—28no—
120#13063282D414yes—
121#13063282C2314yes—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43—21no—
125C2×C4⋊Dic43C2311yescharacteristic
126C2×C4⋊Dic43C2311yescharacteristic
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4D411yescharacteristic
135C2×Dic43⋊C4D411yescharacteristic
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×C4×Dic43—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063258C2314yes—
148#13063258C2314yes—
149#13063257C2314yes—
150Dic43⋊C8C2314yes—
151Dic43⋊C8C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160C4×C43⋊C8C2314yes—
161C22×Q8×C43C2311yescharacteristic
162C22×Q8×C43C2311yescharacteristic
163C2×Q16×C43—24no—
164C2×Q16×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C4×Q8×C43—22no—
168C4×Q8×C43—22no—
169C4×Q8×C43C2314yes—
170C4×Q8×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178#106×C43C2314yes—
179#103×C43C2314yes—
180#103×C43C2314yes—
181#97×C43C2314yes—
182C23×D43C2×D411yescharacteristic
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—22no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43#4114yes—
189C2×Q8×C43C2412yes—
190C2×Q8×C43C2412yes—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205Q8×D43—216no—
206Q8×D43—28no—
207Q8×D43—28no—
208C2×C4×D43—28no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—24no—
212C2×C4×D43C2×D412yes—
213C2×C4×D43C2412yes—
214C2×Dic86—28no—
215C2×Dic86—21no—
216C2×Dic86—22no—
217C2×Dic86—24no—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—21no—
221C2×Dic86#4114yes—
222C2×Dic86C2412yes—
223C2×Dic86C2412yes—
224Q16×C43—28no—
225C2×C8×C43—22no—
226C2×C8×C43—22no—
227C2×C8×C43C2412yes—
228C2×C8×C43C2412yes—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43C2412yes—
234C4⋊C4×C43C2412yes—
235C42×C43—24no—
236C42×C43—24no—
237C42×C43C2×D412yes—
238C42×C43C2412yes—
239#10621885—28no—
240#10621885—28no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4C2×D414yes—
245(C2×D43)⋊C4C2×D414yes—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—24no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43C2412yes—
252C4⋊Dic43C2412yes—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261Dic43⋊C4C2×D414yes—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43—24no—
267C4×Dic43C2×D412yes—
268C4×Dic43C2412yes—
269C2×C43⋊C8—22no—
270C2×C43⋊C8—22no—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273Dic172—28no—
274C23×C43C22×D411yescharacteristic
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43C22×D412yes—
279Q8×C43—24no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43—22no—
283Q8×C43—42no—
284Q8×C43C2×#4114yes—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—42no—
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×C43C2×#4112yes—
300C2×C4×C43C2511yescharacteristic
301C2×Dic43—22no—
302C2×Dic43—24no—
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×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314C2×Dic43C22×D412yes—
315C4×D43—216no—
316C4×D43—24no—
317C4×D43—22no—
318C4×D43—22no—
319Dic86—216no—
320Dic86—24no—
321Dic86—22no—
322Dic86—22no—
323Dic86—22no—
324Dic86—42no—
325Dic86C2×#4114yes—
326C8×C43—22no—
327C8×C43—22no—
328C43⋊C8—22no—
329C43⋊C8—22no—
330C2×#3127—431nomaximal, Sylow
331C22×C43#52512yes—
332C22×C43#57812yes—
333C22×C43#57812yes—
334C22×C43C23×D411yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—44no—
339C4×C43—24no—
340C4×C43—22no—
341C4×C43—22no—
342C4×C43—42no—
343C4×C43—42no—
344C4×C43—42no—
345C4×C43#52512yes—
346C4×C43C22×#4111yescharacteristic
347C4×C43C22×#4111yescharacteristic
348Dic43—22no—
349Dic43—24no—
350Dic43—22no—
351Dic43—22no—
352Dic43—42no—
353Dic43—42no—
354Dic43—42no—
355C2×#541—431no—
356C2×#519—431no—
357#3127—4316no—
358C2×#485—431no—
359C2×#485—431no—
360C2×#479—431no—
361C2×#479—431no—
362C2×#462—431no—
363C2×#462—431no—
364C2×#451—431no—
365C2×#451—431no—
366C2×#441—431no—
367C2×#441D4311yescharacteristic, complemented
368C2×C4×Q16—431no—
369C2×C4×Q16—431no—
370C2×#433—431no—
371C2×C43#312714yescomplemented
372C2×C43C2×#52511yescharacteristic
373C2×C43C2×#57811yescharacteristic
374C2×C43C2×#57811yescharacteristic
375D43—42no—
376C23×Q8—431no—
377C22×Q16—431no—
378C22×Q16—431no—
379C22×Q16—431no—
380C22×Q16C2×D4311yescharacteristic
381#541—438no—
382#541—864no—
383C2×C4⋊Q8—431no—
384C2×#126—861no—
385C2×#126—861no—
386C2×#125—431no—
387C2×#125—861no—
388C2×#125—861no—
389C2×C22⋊Q8—431no—
390C2×C22⋊Q8—431no—
391#519—438no—
392#519—864no—
393C2×C4×Q8—431no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×Q8—861no—
398C2×C4×Q8—861no—
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×Q8C2×D4311yescharacteristic
401C2×#117—431no—
402C2×#117—431no—
403C2×#117—861no—
404C2×#117—861no—
405#485—438no—
406#485—438no—
407#479—438no—
408#479—438no—
409#462—438no—
410#462—438no—
411#451—438no—
412#451—438no—
413#441—438no—
414#441C2×D4318yescomplemented
415C4×Q16—438no—
416C4×Q16—438no—
417#433—438no—
418C2×#107—431no—
419C2×#107—431no—
420C2×#106—431no—
421C2×#106C2×D4311yescharacteristic
422C2×C4⋊C8—431no—
423C2×C4⋊C8—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103—431no—
430C2×#103C2×D4311yescharacteristic
431C2×#103C2×D4311yescharacteristic
432C2×C22⋊C8—431no—
433C2×C22⋊C8—431no—
434C2×#97C2×D4311yescharacteristic
435C2×C4×C8—431no—
436C43C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—434no—
438C22×Q8—431no—
439C22×Q8—431no—
440C22×Q8—861no—
441C22×Q8—862no—
442C22×Q8—864no—
443C22×Q8—864no—
444C22×Q8C22×D4311yescharacteristic
445C22×Q8C22×D4311yescharacteristic
446C23×C4—431no—
447C23×C4—861no—
448C2×Q16—24no—
449C2×Q16—434no—
450C2×Q16—434no—
451C2×Q16—434no—
452C2×Q16—864no—
453C2×Q16—864no—
454C2×Q16—864no—
455C2×Q16C22×D4314yes—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8C22×D4311yescharacteristic
459C22×C8C22×D4311yescharacteristic
460C4⋊Q8—434no—
461C4⋊Q8—862no—
462#126—868no—
463#126—868no—
464#125—434no—
465#125—868no—
466#125—862no—
467#125—868no—
468C22⋊Q8—434no—
469C22⋊Q8—434no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—434no—
475C4×Q8—434no—
476C4×Q8—434no—
477C4×Q8—434no—
478C4×Q8—868no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—868no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8C22×D4314yes—
485C4×Q8C22×D4314yes—
486#117—434no—
487#117—434no—
488#117—434no—
489#117—868no—
490#117—868no—
491#117—862no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—861no—
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⋊C4—861no—
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—431no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—431no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107—434no—
526#106—434no—
527#106C22×D4314yes—
528C4⋊C8—434no—
529C4⋊C8—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103—434no—
535#103—434no—
536#103C22×D4314yes—
537#103C22×D4314yes—
538C22⋊C8—434no—
539C22⋊C8—434no—
540#97C22×D4314yes—
541C4×C8—434no—
542C24—431no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—434no—
549C2×Q8—432no—
550C2×Q8—432no—
551C2×Q8—864no—
552C2×Q8—868no—
553C2×Q8—868no—
554C2×Q8—8616no—
555C2×Q8—868no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×Q8—862no—
561C2×Q8#1062189814yes—
562C2×Q8C23×D4312yes—
563C2×Q8C23×D4312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—864no—
574C22×C4—868no—
575C22×C4—861no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4D4×D4311yescharacteristic
582C22×C4D4×D4311yescharacteristic
583C22×C4C23×D4311yescharacteristic
584Q16—28no—
585Q16—868no—
586Q16—868no—
587Q16—868no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—432no—
591C2×C8—432no—
592C2×C8—862no—
593C2×C8—862no—
594C2×C8C23×D4312yes—
595C2×C8C23×D4312yes—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—434no—
601C4⋊C4—434no—
602C4⋊C4—432no—
603C4⋊C4—432no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4C23×D4312yes—
617C4⋊C4C23×D4312yes—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—24no—
624C42—24no—
625C42—432no—
626C42—432no—
627C42—864no—
628C42—864no—
629C42—864no—
630C42—864no—
631C42—864no—
632C42D4×D4312yes—
633C42C23×D4312yes—
634C23—432no—
635C23—862no—
636C23—862no—
637C23—862no—
638C23C2×D4×D4311yescharacteristic
639Q8—24no—
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—42no—
644Q8—434no—
645Q8—8616no—
646Q8—864no—
647Q8—862no—
648Q8—862no—
649Q8—862no—
650Q8—1722no—
651Q8C2×#1062189814yes—
652C2×C4—24no—
653C2×C4—22no—
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—432no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—8616no—
666C2×C4—862no—
667C2×C4—864no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—864no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—1722no—
678C2×C4—1722no—
679C2×C4—1722no—
680C2×C4C2×D4×D4312yes—
681C2×C4C2×D4×D4312yes—
682C2×C4C2×D4×D4311yescharacteristic
683C2×C4#41×D4312yes—
684C2×C4C2×#1062189812yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—862no—
689C8—862no—
690C22—862no—
691C22—862no—
692C22—862no—
693C22—1724no—
694C22#1458340812yes—
695C22#1458371512yes—
696C22#1458371512yes—
697C22C22×D4×D4311yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—862no—
705C4—862no—
706C4—862no—
707C4—864no—
708C4—1722no—
709C4—1722no—
710C4—1722no—
711C4#1458340812yes—
712C4C2×#41×D4311yescharacteristic
713C4C22×#1062189811yescharacteristic
714C2—1722no—
715C2#1914489414yesdirect product factor
716C2C2×#1458340811yescharacteristic
717C2C2×#1458371511yescharacteristic
718C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#441D43
hypocenterC43C2×#3127
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #19144894C2direct (N × H)
6. C2×#14583209C2semidirect
7. C2×#14583204C2semidirect
8. C2×#14583108C2semidirect
9. C2×#14583107C2semidirect
12. C2×#14583007C2semidirect
13. C2×C4×#10621885C2semidirect
14. C2×C4×#10621885C2semidirect
16. C2×C43×#441C2semidirect
45. #14583209C22semidirect
46. #14583204C22semidirect
47. #14583108C22semidirect
48. #14583107C22semidirect
51. #14583007C22semidirect
52. C4×#10621885C22semidirect
53. C4×#10621885C22semidirect
72. C43×#441C22semidirect
367. C2×#441D43semidirect
371. C2×C43#3127semidirect
414. #441C2×D43semidirect
436. C43C2×#3127semidirect
715. C2#19144894direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835072
C2×#145833752
#191448942
C2×#145832432
C2×#145832382
C2×#145832092
C2×#145832042
C2×#145831082
C2×#145831072
C2×#145830562
C2×#145830532
C2×#145830072
C2×C4×#106218852
C2×#145829612
C2×C43×#4412
C2×#312743