Finite Group Databasebeta

← #25096708

Subgroups — #25096708

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583382C211yesmaximal, characteristic
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19137202C211yesmaximal, characteristic, complemented
4#19134686C211yesmaximal, characteristic, complemented
5#19134679C211yesmaximal, characteristic, complemented
6#19134608C211yesmaximal, characteristic, complemented
7#19134603C211yesmaximal, characteristic, complemented
8#19134598C211yesmaximal, characteristic, complemented
9#19134593C211yesmaximal, characteristic, complemented
10#19134535C211yesmaximal, characteristic
11#19134427C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic
16#14583382—24no—
17#14583382C418yescomplemented
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×D4×Dic43—21no—
21C2×D4×Dic43—21no—
22C2×D4×Dic43C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×#13063284—21no—
25C2×#13063284C2211yescharacteristic
26C22×C4⋊Dic43—21no—
27C22×C4⋊Dic43C2211yescharacteristic
28#14582957—24no—
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582793—21no—
39#14582787—21no—
40#14582784—21no—
41#14582782—21no—
42#14582768C2211yescharacteristic
43#14582764C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C23×Dic43—21no—
63C23×Dic43—21no—
64C23×Dic43—21no—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69Q8×Dic43C2×C414yes—
70Q8×Dic43C2×C414yes—
71D4×Dic43—28no—
72D4×Dic43—28no—
73D4×Dic43—22no—
74D4×Dic43—22no—
75D4×Dic43C2×C414yes—
76D4×Dic43C2×C414yes—
77#13063284—28no—
78#13063284C2×C414yes—
79#13063284D414yes—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—28no—
85C2×C4⋊Dic43C2×C414yes—
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43D411yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43D411yescharacteristic
98C2×C22⋊Dic43D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105Dic43⋊C8—22no—
106Dic43⋊C8—22no—
107#13063249—22no—
108#13063249—22no—
109#13063246—22no—
110#13063246—22no—
111C22⋊(C43⋊C8)—22no—
112#13063235—22no—
113C8×Dic43—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43C2×C414yes—
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43—21no—
127C22×D4×C43C2311yescharacteristic
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135#103×C43—22no—
136#103×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139C22⋊C8×C43—22no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143#41×C43—28no—
144#41×C43—28no—
145#41×C43—28no—
146#41×C43—28no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22×C412yes—
151C2×Q8×C43#4112yes—
152C2×Q8×C43#4112yes—
153C2×D4×C43—24no—
154C2×D4×C43—24no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—24no—
159C2×D4×C43C22×C412yes—
160C2×D4×C43#4112yes—
161C2×D4×C43#4112yes—
162C22×C4×C43—24no—
163C22×C4×C43—24no—
164C22×C4×C43—24no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—24no—
177C22×Dic43—24no—
178C22×Dic43—24no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—81no—
184C22×Dic43—81no—
185C22×Dic43—81no—
186C22×Dic43—81no—
187C22×Dic43—81no—
188C22×Dic43—81no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C22⋊C4×C43—81no—
204C22⋊Dic43—24no—
205C22⋊Dic43—24no—
206C22⋊Dic43—81no—
207C22⋊Dic43C22⋊C414yes—
208C22⋊Dic43C22⋊C414yes—
209C4⋊Dic43—24no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—24no—
213C4⋊Dic43—24no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43C22⋊C414yes—
219C4⋊Dic43C22⋊C414yes—
220C4⋊Dic43C22×C412yes—
221C4⋊Dic43C22×C412yes—
222Dic43⋊C4—81no—
223Dic43⋊C4—81no—
224C4×Dic43—24no—
225C4×Dic43—24no—
226C4×Dic43—81no—
227C4×Dic43—81no—
228C4×Dic43C22×C412yes—
229C4×Dic43C22×C412yes—
230C4×Dic43C2×D412yes—
231C4×Dic43C2×D412yes—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C23×C43—22no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C2×C22⋊C412yes—
252C23×C43C22×D411yescharacteristic
253Q8×C43—22no—
254Q8×C43—22no—
255Q8×C43—22no—
256Q8×C43#11714yes—
257D4×C43—216no—
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43#11714yes—
262C2×C4×C43—216no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43C2×C22⋊C412yes—
279C2×C4×C43C23×C411yescharacteristic
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—84no—
306C2×Dic43—84no—
307C2×Dic43—84no—
308C2×Dic43C2×C22⋊C412yes—
309C2×Dic43C2×C22⋊C412yes—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C8×C43—41no—
313C8×C43—41no—
314C43⋊C8—41no—
315C43⋊C8—41no—
316#20746—431nomaximal, Sylow
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—24no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—42no—
323C22×C43—41no—
324C22×C43—42no—
325C22×C43—41no—
326C22×C43—42no—
327C22×C43—41no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43C22×C22⋊C411yescharacteristic
332C22×C43#52511yescharacteristic
333C22×C43#52511yescharacteristic
334C22×C43#57611yescharacteristic
335C22×C43#57711yescharacteristic
336C22×C43#57711yescharacteristic
337C22×C43#57811yescharacteristic
338C4×C43—22no—
339C4×C43—24no—
340C4×C43—81no—
341C4×C43—81no—
342C4×C43C2×#11711yescharacteristic
343C4×C43C2×#11711yescharacteristic
344C4×C43#52511yescharacteristic
345C4×C43#52511yescharacteristic
346Dic43—22no—
347Dic43—22no—
348Dic43—22no—
349Dic43—22no—
350Dic43—42no—
351Dic43—42no—
352Dic43—81no—
353Dic43—81no—
354C2×#520—431no—
355C2×#433—431no—
356#2314—431no—
357#1824—431no—
358#1823—431no—
359#1805—431no—
360#1804—431no—
361#1803—431no—
362#1802—431no—
363#1788—431no—
364#1788D4311yescharacteristic
365#1763—431no—
366#1762—431no—
367C4×#103—431no—
368C4×#102—431no—
369C2×C43—42no—
370C2×C43—44no—
371C2×C43#228011yescharacteristic
372C2×C43#289711yescharacteristic
373C2×C43#289811yescharacteristic
374C2×C43#311911yescharacteristic
375C2×C43#312011yescharacteristic
376C2×C43#312411yescharacteristic
377C2×C43#312511yescharacteristic
378C22×#41C2×D4311yescharacteristic
379#520—438no—
380#520—864no—
381C2×C4×Q8—431no—
382C2×C4×Q8—431no—
383C2×C4×D4—431no—
384C2×C4×D4—431no—
385C2×C4×D4—861no—
386C2×C4×D4—861no—
387C2×#117—431no—
388C2×#117—861no—
389C22×C4⋊C4—431no—
390C22×C4⋊C4—861no—
391#433—864no—
392C2×C4⋊C8—431no—
393C2×C4⋊C8—431no—
394C2×#103—431no—
395C2×#103—431no—
396C2×#103C2×D4311yescharacteristic
397C2×#103C2×D4311yescharacteristic
398C2×#102—431no—
399C2×#102—431no—
400C2×#102C2×D4311yescharacteristic
401C2×#102C2×D4311yescharacteristic
402C2×C22⋊C8—431no—
403C2×C22⋊C8C2×D4311yescharacteristic
404C2×#97—431no—
405C2×C4×C8—431no—
406#388—861no—
407#388—861no—
408#387—861no—
409#387—861no—
410#384—431no—
411#382—431no—
412#380—431no—
413#380C2×D4311yescharacteristic
414C4×C4⋊C4—431no—
415C4×C4⋊C4—431no—
416#340—431no—
417#340—431no—
418#340—431no—
419#340—431no—
420#340—431no—
421#340—431no—
422#340—431no—
423#340—431no—
424C43#2074611yescharacteristic, complemented, Sylow
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41C4×D4314yes—
431C22×Q8C22×D4311yescharacteristic
432C22×D4—21no—
433C22×D4C22×D4311yescharacteristic
434C23×C4—21no—
435C23×C4—861no—
436C23×C4—861no—
437C23×C4—861no—
438C23×C4C22×D4311yescharacteristic
439C22×C8—431no—
440C22×C8—431no—
441C22×C8C22×D4311yescharacteristic
442C22×C8C22×D4311yescharacteristic
443C4×Q8—434no—
444C4×Q8—434no—
445C4×Q8—862no—
446C4×Q8—862no—
447C4×D4—434no—
448C4×D4—434no—
449C4×D4—862no—
450C4×D4—862no—
451C4×D4—868no—
452C4×D4—868no—
453#117—434no—
454#117—434no—
455#117—868no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—868no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—861no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—431no—
474C2×C22⋊C4—431no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C42—431no—
479C2×C42—431no—
480C2×C42—861no—
481C2×C42—861no—
482C2×C42—861no—
483C2×C42—861no—
484C4⋊C8—862no—
485C4⋊C8—862no—
486#103—22no—
487#103—22no—
488#103—862no—
489#103—862no—
490#102—22no—
491#102—22no—
492#102—862no—
493#102—862no—
494C22⋊C8—22no—
495C22⋊C8—862no—
496#97—862no—
497C4×C8—862no—
498#95—21no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24—21no—
505C24D4×D4311yescharacteristic
506#41—28no—
507#41—28no—
508#41—28no—
509#41—28no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C2×C4×D4312yes—
514C2×Q8#1062190012yes—
515C2×Q8#1062190012yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4C2×C4×D4312yes—
523C2×D4#1062190012yes—
524C2×D4#1062190012yes—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—431no—
536C22×C4—431no—
537C22×C4—431no—
538C22×C4—431no—
539C22×C4—864no—
540C22×C4—864no—
541C22×C4—864no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—3441no—
547C22×C4—3441no—
548C22×C4—3441no—
549C22×C4—3441no—
550C22×C4—3441no—
551C22×C4—3441no—
552C22×C4C2×C4×D4312yes—
553C22×C4D4×D4311yescharacteristic
554C22×C4D4×D4312yes—
555C22×C4C23×D4311yescharacteristic
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—434no—
573C4⋊C4—434no—
574C4⋊C4—432no—
575C4⋊C4—432no—
576C4⋊C4—864no—
577C4⋊C4—864no—
578C4⋊C4—864no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—3441no—
586C4⋊C4—3441no—
587C22⋊C4—81no—
588C22⋊C4—434no—
589C22⋊C4—434no—
590C22⋊C4—864no—
591C22⋊C4—864no—
592C22⋊C4—3441no—
593C42—432no—
594C42—432no—
595C42—432no—
596C42—432no—
597C42—864no—
598C42—864no—
599C42—3441no—
600C42—3441no—
601C23—22no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C22⋊C4×D4312yes—
615C23C2×D4×D4311yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8#1306328114yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4#1306328114yes—
625C2×C4—216no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—432no—
642C2×C4—432no—
643C2×C4—432no—
644C2×C4—432no—
645C2×C4—861no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—861no—
651C2×C4—861no—
652C2×C4—861no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—3444no—
656C2×C4—3444no—
657C2×C4—3444no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4C22⋊C4×D4312yes—
669C2×C4C22×C4×D4311yescharacteristic
670C2×C4C2×D4×D4311yescharacteristic
671C2×C4C2×#1062190011yescharacteristic
672C2×C4C2×#1062190011yescharacteristic
673C2×C4C2×#1062190011yescharacteristic
674C2×C4C2×#1062190011yescharacteristic
675C8—41no—
676C8—41no—
677C8—1721no—
678C8—1721no—
679C22—22no—
680C22—24no—
681C22—22no—
682C22—22no—
683C22—41no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22C2×C22⋊C4×D4311yescharacteristic
694C22#1458340511yescharacteristic
695C22#1458340511yescharacteristic
696C22#1458370311yescharacteristic
697C22#1458370611yescharacteristic
698C22#1458370811yescharacteristic
699C22#1458371311yescharacteristic
700C4—22no—
701C4—24no—
702C4—81no—
703C4—81no—
704C4—862no—
705C4—862no—
706C4—862no—
707C4—862no—
708C4—3441no—
709C4—3441no—
710C4—1722no—
711C4—1722no—
712C4C2×#1306328111yescharacteristic
713C4C2×#1306328111yescharacteristic
714C4#1458340511yescharacteristic
715C4#1458340511yescharacteristic
716C2—42no—
717C2—44no—
718C2#1913697311yescharacteristic
719C2#1914311911yescharacteristic
720C2#1914312411yescharacteristic
721C2#1914479511yescharacteristic
722C2#1914481011yescharacteristic
723C2#1914485011yescharacteristic
724C2#1914486511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#20746
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582957C2semidirect
3. #19137202C2semidirect
4. #19134686C2semidirect
5. #19134679C2semidirect
6. #19134608C2semidirect
7. #19134603C2semidirect
8. #19134598C2semidirect
9. #19134593C2semidirect
11. #19134427C2semidirect
12. #19134422C2semidirect
13. #103×Dic43C2semidirect
14. #102×Dic43C2semidirect
17. #14583382C4semidirect
424. C43#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#145833822
C2×#145829572
#191372022
#191346862
#191346792
#191346082
#191346032
#191345982
#191345932
#191345352
#191344272
#191344222
#103×Dic432
#102×Dic432
C43×#17882
#2074643