Finite Group Databasebeta

← #25147282

Subgroups — #25147282

Order 11008.

980 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583294C211yesmaximal, characteristic
2C2×#14583118C211yesmaximal, characteristic
3C2×#14583109C211yesmaximal, characteristic, complemented
4C2×#14583104C211yesmaximal, characteristic
5#19139583C211yesmaximal, characteristic, complemented
6#19135917C211yesmaximal, characteristic, complemented
7#19135912C211yesmaximal, characteristic
8#19135694C211yesmaximal, characteristic, complemented
9#19135677C211yesmaximal, characteristic
10#19135518C211yesmaximal, characteristic, complemented
11#19135319C211yesmaximal, characteristic, complemented
12#19134936C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic
14#19134428C211yesmaximal, characteristic, complemented
15C43×#2367C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C2×#13063325C2211yescharacteristic
23C2×#13063325C2211yescharacteristic
24C2×#13063325C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26#14583294—24no—
27#14583118—24no—
28#14583109—24no—
29#14583104—24no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582831—21no—
43#14582831—21no—
44#14582805C2211yescharacteristic
45#14582805C2211yescharacteristic
46#14582798—21no—
47#14582798—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#388—21no—
58C43×#388—21no—
59C43×#385—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C4×C22⋊C4×C43—21no—
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C22×Dic86C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—41no—
73C2×#10621885—41no—
74C2×#10621885—41no—
75C2×#10621883—22no—
76C2×#10621883—22no—
77C2×#10621883—22no—
78C2×#10621883—22no—
79C2×#10621883—22no—
80C2×#10621883—22no—
81C2×#10621883—41no—
82C2×#10621883—41no—
83C2×#10621883—41no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063325—22no—
89#13063325—22no—
90#13063325—22no—
91#13063325—22no—
92#13063325—41no—
93#13063325—41no—
94C4×Dic86—22no—
95C4×Dic86—22no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×C4×Dic43—21no—
105C4⋊(C43⋊C8)—22no—
106C4⋊(C43⋊C8)—22no—
107C4⋊(C43⋊C8)—22no—
108#13063249—22no—
109#13063248—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—41no—
113#13063248—41no—
114#13063248D414yes—
115#13063246—22no—
116#13063236—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43—21no—
124#124×C43—22no—
125#124×C43D414yes—
126C4×Q8×C43—22no—
127C4×Q8×C43—41no—
128C4×D4×C43—22no—
129C4×D4×C43—41no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C4⋊C4×C43D411yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43—21no—
142C2×C42×C43C2311yescharacteristic
143C2×C42×C43C2311yescharacteristic
144C2×C42×C43C2311yescharacteristic
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43C2×D412yes—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—42no—
167C22×C4×C43—42no—
168C22×C4×C43—81no—
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86C2×D412yes—
198C4⋊C4×C43—22no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—42no—
204C4⋊C4×C43C2×D412yes—
205C22⋊C4×C43—24no—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—42no—
208C22⋊C4×C43—42no—
209C22⋊C4×C43—81no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—42no—
215C42×C43—81no—
216C42×C43C2×D412yes—
217C42×C43#4112yes—
218#10621885—44no—
219#10621885—44no—
220#10621885—44no—
221#10621883—44no—
222#10621883—44no—
223#10621883—44no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—42no—
227C4⋊Dic43—42no—
228C4⋊Dic43—42no—
229C4⋊Dic43—42no—
230C4⋊Dic43—42no—
231C4⋊Dic43—42no—
232Dic43⋊C4—42no—
233C4×Dic43—42no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8C2×D412yes—
245C2×C43⋊C8#4112yes—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43C22×D411yescharacteristic
254Q8×C43—22no—
255Q8×C43—22no—
256Q8×C43—41no—
257Q8×C43—41no—
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—41no—
261D4×C43—41no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—84no—
286C2×C4×C43#12112yes—
287C2×C4×C43#12112yes—
288C2×C4×C43#13712yes—
289C2×C4×C43#13712yes—
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×Dic43—22no—
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—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308Dic86—22no—
309Dic86—22no—
310Dic86—41no—
311Dic86—41no—
312Dic86—41no—
313Dic86—41no—
314Dic86—41no—
315Dic86—41no—
316Dic86—41no—
317Dic86—41no—
318Dic86—41no—
319Dic86—41no—
320C43⋊C8—22no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#25382—431nomaximal, Sylow
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43C2×#12111yescharacteristic
333C22×C43D4211yescharacteristic
334C22×C43#55011yescharacteristic
335C22×C43C2×#13711yescharacteristic
336C22×C43C2×#13711yescharacteristic
337C22×C43#57711yescharacteristic
338C22×C43#57811yescharacteristic
339C4×C43—22no—
340C4×C43—22no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43—42no—
344C4×C43—41no—
345C4×C43—42no—
346C4×C43—41no—
347C4×C43—81no—
348C4×C43#53211yescharacteristic
349C4×C43#54011yescharacteristic
350C4×C43D4211yescharacteristic
351C4×C43#54611yescharacteristic
352Dic43—42no—
353Dic43—81no—
354Dic43—81no—
355Dic43—81no—
356C2×#497—431no—
357C2×#464—431no—
358C2×#462—431no—
359C2×#461—431no—
360#2546—431no—
361#2367D4311yescharacteristic
362#2056—431no—
363#2055—431no—
364#2016—431no—
365#2013—431no—
366#1981—431no—
367#1940—431no—
368#1878—431no—
369#1877—431no—
370#1763—431no—
371C2×C43—82no—
372C2×C43#242811yescharacteristic
373C2×C43#303911yescharacteristic
374C2×C43#304611yescharacteristic
375C2×C43#326611yescharacteristic
376C2×C43#327011yescharacteristic
377C2×C43#339811yescharacteristic
378C2×C43#340011yescharacteristic
379C22×Q16—431no—
380C22×Q16—431no—
381C22×Q16—431no—
382C22×SD16—431no—
383C22×SD16—431no—
384C22×SD16—431no—
385C2×C4⋊Q8—431no—
386C2×C4⋊Q8—431no—
387C2×C4⋊Q8—431no—
388C2×#124C2×D4311yescharacteristic
389C2×C4×Q8—431no—
390C2×C4×Q8C2×D4311yescharacteristic
391C2×C4×D4C2×D4311yescharacteristic
392#497—864no—
393#464—864no—
394#462—864no—
395#461—864no—
396C2×C4⋊C8—431no—
397C2×C4⋊C8—431no—
398C2×C4⋊C8—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×#103—431no—
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#102—431no—
407C2×#97—431no—
408#398—861no—
409#398—861no—
410#391—431no—
411#391—431no—
412#391C2×D4311yescharacteristic
413#390C2×D4311yescharacteristic
414#389—861no—
415#389—861no—
416#388—21no—
417#388—21no—
418#385—21no—
419C4×C4⋊C4C2×D4311yescharacteristic
420C4×C4⋊C4C2×D4311yescharacteristic
421C4×C22⋊C4—21no—
422#340—431no—
423#340—431no—
424#336—431no—
425#336—431no—
426C43#2538211yescharacteristic, complemented, Sylow
427C22×Q8—431no—
428C22×Q8—431no—
429C22×Q8—431no—
430C22×Q8C22×D4311yescharacteristic
431C22×D4C22×D4311yescharacteristic
432C23×C4—21no—
433C2×Q16—862no—
434C2×Q16—862no—
435C2×Q16—862no—
436C2×Q16—862no—
437C2×Q16—862no—
438C2×Q16—862no—
439C2×Q16—1721no—
440C2×Q16—1721no—
441C2×Q16—1721no—
442C2×SD16—862no—
443C2×SD16—862no—
444C2×SD16—862no—
445C2×SD16—862no—
446C2×SD16—862no—
447C2×SD16—862no—
448C2×SD16—1721no—
449C2×SD16—1721no—
450C2×SD16—1721no—
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C4⋊Q8—862no—
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458C4⋊Q8—862no—
459C4⋊Q8—1721no—
460C4⋊Q8—1721no—
461#124—22no—
462#124D17214yes—
463C4×Q8—22no—
464C4×Q8—41no—
465C4×Q8—862no—
466C4×Q8—862no—
467C4×D4—22no—
468C4×D4—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4C22⋊D4311yescharacteristic
479C2×C4⋊C4C22⋊D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—861no—
490C2×C42C22×D4311yescharacteristic
491C2×C42C22×D4311yescharacteristic
492C2×C42C22×D4311yescharacteristic
493C4⋊C8—862no—
494C4⋊C8—862no—
495C4⋊C8—862no—
496#103—434no—
497#103—862no—
498#103—862no—
499#103—862no—
500#103—862no—
501#103—1721no—
502#103—1721no—
503#102—862no—
504#97—862no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95C22⋊D4311yescharacteristic
513#95C22⋊D4311yescharacteristic
514C24—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—432no—
521C2×Q8—861no—
522C2×Q8—861no—
523C2×Q8—861no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8C2×D17212yes—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4C2×D17212yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4C2×C22⋊D4311yescharacteristic
556C22×C4C2×C22⋊D4311yescharacteristic
557C22×C4C2×C22⋊D4311yescharacteristic
558C22×C4C2×C22⋊D4311yescharacteristic
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C23×D4311yescharacteristic
562Q16—1724no—
563Q16—1724no—
564Q16—1724no—
565SD16—1724no—
566SD16—1724no—
567SD16—1724no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—42no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—1722no—
589C4⋊C4—1722no—
590C4⋊C4—1722no—
591C4⋊C4—1722no—
592C4⋊C4—1722no—
593C4⋊C4—1722no—
594C4⋊C4—1722no—
595C4⋊C4D4×D4312yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—42no—
606C42—81no—
607C42—1722no—
608C42C2×D17212yes—
609C42#1062189812yes—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×C22⋊D4311yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—41no—
621Q8—41no—
622Q8—862no—
623Q8—862no—
624Q8—1721no—
625Q8—1721no—
626Q8—1721no—
627Q8—1721no—
628Q8—1721no—
629Q8—1721no—
630Q8—1721no—
631Q8—1721no—
632Q8—1721no—
633Q8—1721no—
634D4—22no—
635D4—22no—
636D4—41no—
637D4—41no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—862no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4#1306329912yes—
675C2×C4#1306329912yes—
676C2×C4#1306335512yes—
677C2×C4#1306335512yes—
678C2×C4C2×D4×D4311yescharacteristic
679C2×C4C22×D17211yescharacteristic
680C2×C4#41×D4311yescharacteristic
681C2×C4C2×#1062189811yescharacteristic
682C2×C4#1306337011yescharacteristic
683C2×C4#1306337111yescharacteristic
684C8—862no—
685C8—862no—
686C8—1721no—
687C8—1721no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22C2×#1306329911yescharacteristic
696C22D4×C22⋊D4311yescharacteristic
697C22#1458356811yescharacteristic
698C22C2×#1306335511yescharacteristic
699C22C2×#1306335511yescharacteristic
700C22#1458371011yescharacteristic
701C22#1458371411yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—41no—
707C4—42no—
708C4—42no—
709C4—41no—
710C4—81no—
711C4—3441no—
712C4—3441no—
713C4—3441no—
714C4—1722no—
715C4#1458344611yescharacteristic
716C4#1458350011yescharacteristic
717C4D4×D17211yescharacteristic
718C4#1458354411yescharacteristic
719C2—82no—
720C2#1913817711yescharacteristic
721C2#1914408211yescharacteristic
722C2#1914414511yescharacteristic
723C2#1914610111yescharacteristic
724C2#1914616111yescharacteristic
725C2#1914762611yescharacteristic
726C2#1914764811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2367C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2367D43
hypocenterC43#25382
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
3. C2×#14583109C2semidirect
5. #19139583C2semidirect
6. #19135917C2semidirect
8. #19135694C2semidirect
10. #19135518C2semidirect
11. #19135319C2semidirect
12. #19134936C2semidirect
14. #19134428C2semidirect
426. C43#25382semidirect

Maximal subgroups

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

subgroupindex
C2×#145832942
C2×#145831182
C2×#145831092
C2×#145831042
#191395832
#191359172
#191359122
#191356942
#191356772
#191355182
#191353192
#191349362
#191349292
#191344282
C43×#23672
#2538243