Finite Group Databasebeta

← C2×#19144897 #25964955

Subgroups — C2×#19144897 #25964955

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×#14583512C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic
3#19144897C2116yesmaximal, direct product factor
4C2×#14583243C211yesmaximal, characteristic
5C2×#14583242C211yesmaximal, characteristic
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583110C211yesmaximal, characteristic, complemented
8C2×#14583109C211yesmaximal, characteristic, complemented
9C2×#14583056C211yesmaximal, characteristic
10C2×#14583056C211yesmaximal, characteristic
11C2×#14583005C211yesmaximal, characteristic, complemented
12C2×#14583003C211yesmaximal, characteristic, complemented
13C2×#14582993C211yesmaximal, characteristic, complemented
14C2×#14582991C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621885C2211yescharacteristic
22#14583512—24no—
23#14583512C2218yes—
24C2×#13063325C2211yescharacteristic
25C2×#13063320—21no—
26C2×#13063320—21no—
27C2×#13063316—21no—
28C2×#13063316—21no—
29C2×#13063305C2211yescharacteristic
30C2×#13063305C2211yescharacteristic
31#14583375—24no—
32#14583375C2218yes—
33C2×Q8×Dic43C2211yescharacteristic
34C2×C4×Dic86—21no—
35C2×C4×Dic86C2211yescharacteristic
36C2×#13063290—21no—
37C2×#13063290C2211yescharacteristic
38C2×#13063290C2211yescharacteristic
39C2×#13063290C2211yescharacteristic
40C2×#13063283—21no—
41C2×#13063283C2211yescharacteristic
42C2×#13063282—21no—
43C2×#13063282C2211yescharacteristic
44#14583243C2218yes—
45#14583242C2218yes—
46#14583203C2218yescomplemented
47#14583110C2218yescomplemented
48#14583109C2218yescomplemented
49#14583056C2218yes—
50#14583056C2218yes—
51#14583005C2218yescomplemented
52#14583003C2218yescomplemented
53#14582993C2218yescomplemented
54#14582991C2218yescomplemented
55#14582959C2218yes—
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C2×Q8×D43—24no—
82C2×Q8×D43—22no—
83C2×Q8×D43—24no—
84C2×Q8×D43C2314yes—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C2×Dic172—24no—
88C2×Dic172—24no—
89C2×Dic172C2314yes—
90C2×Dic172C2314yes—
91C2×#10621885—24no—
92C2×#10621885—24no—
93C2×#10621885C2314yes—
94C2×#10621885C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063325—22no—
98#13063325C2314yes—
99#13063320—28no—
100#13063320—28no—
101#13063316—28no—
102#13063316—28no—
103#13063305—22no—
104#13063305—22no—
105#13063305C2314yes—
106#13063305C2314yes—
107Q8×Dic43—22no—
108Q8×Dic43C2314yes—
109C4×Dic86—22no—
110C4×Dic86—28no—
111C4×Dic86C2314yes—
112#13063290—28no—
113#13063290—22no—
114#13063290—22no—
115#13063290—22no—
116#13063290C2314yes—
117#13063290C2314yes—
118#13063290C2314yes—
119#13063283—22no—
120#13063283—28no—
121#13063283C2314yes—
122#13063282—28no—
123#13063282D414yes—
124#13063282C2314yes—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4D411yescharacteristic
136C2×Dic43⋊C4D411yescharacteristic
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063248C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158(C2×D43)⋊C8C2314yes—
159(C2×D43)⋊C8C2314yes—
160#13063235C2314yes—
161C8×Dic43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#125×C43—22no—
166#125×C43C2314yes—
167C4×Q8×C43—22no—
168C4×Q8×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43C2×D411yescharacteristic
183C2×Q8×C43—21no—
184C2×Q8×C43—22no—
185C2×Q8×C43#4114yes—
186C2×Q8×C43C2412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201Q8×D43—216no—
202Q8×D43—28no—
203Q8×D43—28no—
204C2×C4×D43—28no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—24no—
208C2×C4×D43C2×D412yes—
209C2×C4×D43C2412yes—
210C2×Dic86—28no—
211C2×Dic86—21no—
212C2×Dic86—22no—
213C2×Dic86—24no—
214C2×Dic86—22no—
215C2×Dic86—22no—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—21no—
219C2×Dic86—21no—
220C2×Dic86#4114yes—
221C2×Dic86C2412yes—
222C2×Dic86C2412yes—
223C2×Dic86C2412yes—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43C2412yes—
227C2×C8×C43C2412yes—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2412yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C42×C43—24no—
238C42×C43C2×D412yes—
239C42×C43C2412yes—
240#10621885—28no—
241#10621885—28no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4C2×D414yes—
246(C2×D43)⋊C4C2×D414yes—
247C4⋊Dic43—24no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—24no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2412yes—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4C2×D414yes—
259Dic43⋊C4C2×D414yes—
260C4×Dic43—24no—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43—24no—
265C4×Dic43—24no—
266C4×Dic43C2×D412yes—
267C4×Dic43C2412yes—
268C2×C43⋊C8—22no—
269C2×C43⋊C8—22no—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272Dic172—28no—
273Dic172—28no—
274C23×C43C22×D411yescharacteristic
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43C22×D412yes—
279Q8×C43—24no—
280Q8×C43—22no—
281Q8×C43C2×#4114yes—
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×C43C22×D412yes—
293C2×C4×C43C22×D412yes—
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4112yes—
296C2×C4×C43C2×#4112yes—
297C2×C4×C43C2511yescharacteristic
298C2×Dic43—22no—
299C2×Dic43—24no—
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×Dic43C22×D412yes—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312C4×D43—216no—
313C4×D43—24no—
314C4×D43—22no—
315C4×D43—22no—
316Dic86—216no—
317Dic86—24no—
318Dic86—22no—
319Dic86—22no—
320Dic86—22no—
321Dic86—22no—
322Dic86—22no—
323Dic86—42no—
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×#479D4311yescharacteristic, complemented
362C2×#462—431no—
363C2×#462—431no—
364C2×#451—431no—
365C2×#451—431no—
366C2×#441—431no—
367C2×#441—431no—
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×Q16—431no—
381#541—438no—
382#541—864no—
383C2×C4⋊Q8—431no—
384C2×#126—861no—
385C2×#126—861no—
386C2×#125—861no—
387C2×#125—861no—
388C2×#125C2×D4311yescharacteristic
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—431no—
398C2×C4×Q8—861no—
399C2×C4×Q8—861no—
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#479C2×D4318yescomplemented
409#462—438no—
410#462—438no—
411#451—438no—
412#451—438no—
413#441—438no—
414#441—438no—
415C4×Q16—438no—
416C4×Q16—438no—
417#433—438no—
418C2×#107—431no—
419C2×#107C2×D4311yescharacteristic
420C2×#106—431no—
421C2×#106C2×D4311yescharacteristic
422C2×C4⋊C8—431no—
423C2×C4⋊C8C2×D4311yescharacteristic
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×#97—431no—
435C2×C4×C8—431no—
436C43C2×#312711yescharacteristic, complemented, Sylow
437C22×Q8—434no—
438C22×Q8—431no—
439C22×Q8—431no—
440C22×Q8—431no—
441C22×Q8—861no—
442C22×Q8—862no—
443C22×Q8—864no—
444C22×Q8—864no—
445C22×Q8C22×D4311yescharacteristic
446C23×C4—431no—
447C23×C4—861no—
448C2×Q16—434no—
449C2×Q16—434no—
450C2×Q16—434no—
451C2×Q16—434no—
452C2×Q16—864no—
453C2×Q16—864no—
454C2×Q16—864no—
455C2×Q16—864no—
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—22no—
465#125—868no—
466#125—868no—
467#125C22×D4314yes—
468C22⋊Q8—434no—
469C22⋊Q8—434no—
470C22⋊Q8—862no—
471C22⋊Q8—862no—
472C4×Q8—22no—
473C4×Q8—434no—
474C4×Q8—434no—
475C4×Q8—434no—
476C4×Q8—434no—
477C4×Q8—434no—
478C4×Q8—868no—
479C4×Q8—862no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—868no—
484C4×Q8—862no—
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—21no—
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⋊C4C22×D4311yescharacteristic
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—431no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107C22×D4314yes—
526#106—434no—
527#106C22×D4314yes—
528C4⋊C8—434no—
529C4⋊C8C22×D4314yes—
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#97—434no—
541C4×C8—434no—
542C24—431no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—434no—
546C2×Q8—432no—
547C2×Q8—432no—
548C2×Q8—432no—
549C2×Q8—864no—
550C2×Q8—868no—
551C2×Q8—868no—
552C2×Q8—8616no—
553C2×Q8—868no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—862no—
558C2×Q8—862no—
559C2×Q8—862no—
560C2×Q8—862no—
561C2×Q8—862no—
562C2×Q8#1062190214yes—
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—868no—
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—24no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—434no—
603C4⋊C4—434no—
604C4⋊C4—432no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—861no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4C23×D4312yes—
616C4⋊C4C23×D4312yes—
617C4⋊C4C23×D4312yes—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—24no—
624C42—432no—
625C42—432no—
626C42—864no—
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—434no—
642Q8—8616no—
643Q8—864no—
644Q8—862no—
645Q8—862no—
646Q8—862no—
647Q8—862no—
648Q8—862no—
649Q8—1722no—
650Q8—1722no—
651Q8C2×#1062190214yes—
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×#1062190212yes—
685C2×C4C24×D4311yescharacteristic
686C8—22no—
687C8—22no—
688C8—862no—
689C8—862no—
690C22—862no—
691C22—862no—
692C22—862no—
693C22—1724no—
694C22#1458341212yes—
695C22#1458371312yes—
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#1458341212yes—
712C4C2×#41×D4311yescharacteristic
713C4C22×#1062190211yescharacteristic
714C2—1722no—
715C2#1914489714yesdirect product factor
716C2C2×#1458341211yescharacteristic
717C2C2×#1458371311yescharacteristic
718C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#479D43
hypocenterC43C2×#3127
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #19144897C2direct (N × H)
6. C2×#14583203C2semidirect
7. C2×#14583110C2semidirect
8. C2×#14583109C2semidirect
11. C2×#14583005C2semidirect
12. C2×#14583003C2semidirect
13. C2×#14582993C2semidirect
14. C2×#14582991C2semidirect
16. C2×C43×#479C2semidirect
46. #14583203C22semidirect
47. #14583110C22semidirect
48. #14583109C22semidirect
51. #14583005C22semidirect
52. #14583003C22semidirect
53. #14582993C22semidirect
54. #14582991C22semidirect
71. C43×#479C22semidirect
361. C2×#479D43semidirect
371. C2×C43#3127semidirect
408. #479C2×D43semidirect
436. C43C2×#3127semidirect
715. C2#19144897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835122
C2×#145833752
#191448972
C2×#145832432
C2×#145832422
C2×#145832032
C2×#145831102
C2×#145831092
C2×#145830562
C2×#145830052
C2×#145830032
C2×#145829932
C2×#145829912
C2×#145829592
C2×C43×#4792
C2×#312743