Finite Group Databasebeta

← #25096704

Subgroups — #25096704

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×#14583378C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic, complemented
3#19137203C211yesmaximal, characteristic, complemented
4#19134684C211yesmaximal, characteristic, complemented
5#19134680C211yesmaximal, characteristic, complemented
6#19134611C211yesmaximal, characteristic, complemented
7#19134605C211yesmaximal, characteristic, complemented
8#19134597C211yesmaximal, characteristic, complemented
9#19134532C211yesmaximal, characteristic
10#19134532C211yesmaximal, characteristic
11#19134424C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17#14583378—24no—
18#14583378C418yescomplemented
19C2×C4×Dic86C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23C2×(C22⋊D43)⋊C4—21no—
24C2×#13063282C2211yescharacteristic
25C2×#13063281—21no—
26C22×Dic43⋊C4—21no—
27C2×C4⋊C4×D43C2211yescharacteristic
28#14582959—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40#14582789—21no—
41#14582789—21no—
42#14582780—21no—
43#14582780—21no—
44#14582765C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#384C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900C2×C414yes—
68C22×Dic86C2311yescharacteristic
69C22×C22⋊D43—21no—
70C23×Dic43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C4×Dic86—22no—
77C4×Dic86C2×C414yes—
78#13063290—22no—
79#13063290C2×C414yes—
80D4×Dic43—22no—
81D4×Dic43C2×C414yes—
82C4×C22⋊D43—28no—
83(C22⋊D43)⋊C4—28no—
84#13063282C2×C414yes—
85#13063282D414yes—
86#13063281—28no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—28no—
94C2×Dic43⋊C4D411yescharacteristic
95C2×Dic43⋊C4D411yescharacteristic
96C4⋊C4×D43—22no—
97C4⋊C4×D43C2×C414yes—
98C2×C22⋊Dic43—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×(C2×D43)⋊C4D411yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C4⋊(C43⋊C8)—22no—
109#13063250—22no—
110#13063250—22no—
111#13063248—22no—
112#13063248—22no—
113#13063246—22no—
114#13063246—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117#13063235—22no—
118C8×Dic43—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4×D4×C43—22no—
130C4×D4×C43C2×C414yes—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141C24×C43—21no—
142C23×D43C2×D411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43C22×C412yes—
147C2×D4×C43#4112yes—
148C2×D4×C43#4112yes—
149C22×C4×C43—24no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—81no—
154C22×C4×C43—81no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—24no—
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C22×Dic43—24no—
162C22×Dic43—24no—
163C22×Dic43—24no—
164C22×Dic43—24no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—81no—
170C22×Dic43—81no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174#10621900—28no—
175#10621900—28no—
176#10621900—28no—
177#10621900—28no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—24no—
183C2×C4×D43—81no—
184C2×C4×D43—81no—
185C2×C4×D43C22×C412yes—
186C2×C4×D43C2×D412yes—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86C22×C412yes—
191C2×Dic86#4112yes—
192C2×Dic86#4112yes—
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—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—81no—
205C4⋊C4×C43—81no—
206C4⋊C4×C43C22×C412yes—
207C22⋊C4×C43—24no—
208C42×C43C22×C412yes—
209C42×C43C2×D412yes—
210C22⋊Dic43—24no—
211(C2×D43)⋊C4—81no—
212(C2×D43)⋊C4—81no—
213(C2×D43)⋊C4C22⋊C414yes—
214(C2×D43)⋊C4C22⋊C414yes—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C22×C412yes—
221Dic43⋊C4—24no—
222Dic43⋊C4—24no—
223Dic43⋊C4—24no—
224Dic43⋊C4C22⋊C414yes—
225Dic43⋊C4C22⋊C414yes—
226C4×Dic43—24no—
227C4×Dic43—24no—
228C4×Dic43—81no—
229C4×Dic43—81no—
230C4×Dic43C22×C412yes—
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—22no—
240C23×C43—22no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43C22×D411yescharacteristic
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43C2×C22⋊C412yes—
253D4×C43—22no—
254D4×C43—22no—
255D4×C43—22no—
256D4×C43#11714yes—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—84no—
271C2×C4×C43C2×C22⋊C412yes—
272C2×C4×C43C2×C22⋊C412yes—
273C2×C4×C43C23×C411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C22⋊D43—216no—
280C2×Dic43—216no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—22no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—84no—
300C2×Dic43C2×C22⋊C412yes—
301C2×Dic43C2×C22⋊C412yes—
302C2×Dic43C2×C22⋊C412yes—
303C4×D43—22no—
304C4×D43—22no—
305C4×D43—22no—
306C4×D43—22no—
307C4×D43—84no—
308Dic86—22no—
309Dic86—22no—
310Dic86—22no—
311Dic86#11714yes—
312C8×C43—41no—
313C8×C43—41no—
314C43⋊C8—41no—
315C43⋊C8—41no—
316#20746—431nomaximal, Sylow
317C22×C43—24no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43C22×C22⋊C411yescharacteristic
325C22×C43#52511yescharacteristic
326C22×C43#52511yescharacteristic
327C22×C43#57611yescharacteristic
328C22×C43#57711yescharacteristic
329C22×C43#57711yescharacteristic
330C22×C43#57811yescharacteristic
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—41no—
335C2×D43—41no—
336C2×D43—41no—
337C2×D43—41no—
338C4×C43—22no—
339C4×C43—22no—
340C4×C43—42no—
341C4×C43—81no—
342C4×C43—81no—
343C4×C43C2×#11711yescharacteristic
344C4×C43C2×#11711yescharacteristic
345C4×C43#52511yescharacteristic
346C4×C43#52511yescharacteristic
347Dic43—22no—
348Dic43—22no—
349Dic43—24no—
350Dic43—22no—
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#1802D4311yescharacteristic, complemented
363#1788—431no—
364#1788—431no—
365#1763—431no—
366#1762—431no—
367C4×#103—431no—
368C4×#102—431no—
369C2×C43—44no—
370C2×C43#228011yescharacteristic
371C2×C43#289711yescharacteristic
372C2×C43#289811yescharacteristic
373C2×C43#311911yescharacteristic
374C2×C43#312011yescharacteristic
375C2×C43#312411yescharacteristic
376C2×C43#312511yescharacteristic
377D43—42no—
378C22×#41—431no—
379#520—438no—
380#520—864no—
381C2×C4×Q8—431no—
382C2×C4×Q8—431no—
383C2×C4×D4—431no—
384C2×C4×D4—861no—
385C2×C4×D4—861no—
386C2×C4×D4C2×D4311yescharacteristic
387C2×#117—431no—
388C2×#117—861no—
389C22×C4⋊C4—431no—
390C22×C4⋊C4—861no—
391#433—864no—
392C2×C4⋊C8—431no—
393C2×C4⋊C8C2×D4311yescharacteristic
394C2×#103—431no—
395C2×#103—431no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#102—431no—
399C2×#102—431no—
400C2×#102C2×D4311yescharacteristic
401C2×#102C2×D4311yescharacteristic
402C2×C22⋊C8—431no—
403C2×C22⋊C8—431no—
404C2×#97—431no—
405C2×C4×C8—431no—
406#388—861no—
407#388—861no—
408#387—861no—
409#387—861no—
410#384C2×D4311yescharacteristic
411#382—431no—
412#380—431no—
413#380—431no—
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#340C2×D4311yescharacteristic
423#340C2×D4311yescharacteristic
424C43#2074611yescharacteristic, complemented, Sylow
425C2×#41—434no—
426C2×#41—862no—
427C2×#41—862no—
428C2×#41—862no—
429C2×#41—862no—
430C2×#41—862no—
431C22×Q8—431no—
432C22×D4—861no—
433C22×D4C22×D4311yescharacteristic
434C23×C4—21no—
435C23×C4—431no—
436C23×C4—861no—
437C23×C4—861no—
438C23×C4—861no—
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—22no—
448C4×D4—434no—
449C4×D4—862no—
450C4×D4—868no—
451C4×D4—868no—
452C4×D4C4×D4314yes—
453#117—434no—
454#117—434no—
455#117—868no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—434no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—862no—
465C2×C4⋊C4—868no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4C22×D4311yescharacteristic
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—861no—
480C2×C42—861no—
481C2×C42—861no—
482C2×C42—861no—
483C2×C42C22×D4311yescharacteristic
484C4⋊C8—22no—
485C4⋊C8—862no—
486#103—862no—
487#103—862no—
488#103—862no—
489#103—862no—
490#102—22no—
491#102—22no—
492#102—862no—
493#102—862no—
494C22⋊C8—862no—
495C22⋊C8—862no—
496#97—862no—
497C4×C8—862no—
498#95—861no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24—21no—
505C24—431no—
506#41—868no—
507#41—868no—
508#41—868no—
509#41—868no—
510C2×Q8—432no—
511C2×Q8—432no—
512C2×Q8—432no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—864no—
520C2×D4—864no—
521C2×D4—864no—
522C2×D4C2×C4×D4312yes—
523C2×D4#1062190012yes—
524C2×D4#1062190212yes—
525C22×C4—21no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—431no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—864no—
537C22×C4—864no—
538C22×C4—864no—
539C22×C4—864no—
540C22×C4—864no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—3441no—
550C22×C4—3441no—
551C22×C4—3441no—
552C22×C4—3441no—
553C22×C4D4×D4311yescharacteristic
554C22×C4D4×D4311yescharacteristic
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—21no—
573C4⋊C4—81no—
574C4⋊C4—81no—
575C4⋊C4—434no—
576C4⋊C4—434no—
577C4⋊C4—432no—
578C4⋊C4—864no—
579C4⋊C4—864no—
580C4⋊C4—864no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C4⋊C4C2×C4×D4312yes—
587C22⋊C4—24no—
588C22⋊C4—434no—
589C22⋊C4—434no—
590C22⋊C4—864no—
591C22⋊C4—3441no—
592C22⋊C4—3441no—
593C42—432no—
594C42—432no—
595C42—864no—
596C42—864no—
597C42—3441no—
598C42—3441no—
599C42C2×C4×D4312yes—
600C42D4×D4312yes—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—432no—
609C23—861no—
610C23—861no—
611C23—861no—
612C23—861no—
613C23—861no—
614C23—861no—
615C23C2×D4×D4311yescharacteristic
616Q8—434no—
617Q8—862no—
618Q8—862no—
619Q8—862no—
620D4—22no—
621D4—22no—
622D4—22no—
623D4—8616no—
624D4#1306328314yes—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—84no—
639C2×C4—432no—
640C2×C4—432no—
641C2×C4—432no—
642C2×C4—8616no—
643C2×C4—862no—
644C2×C4—861no—
645C2×C4—862no—
646C2×C4—861no—
647C2×C4—862no—
648C2×C4—861no—
649C2×C4—861no—
650C2×C4—861no—
651C2×C4—861no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—3444no—
658C2×C4—3444no—
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×C4C22⋊C4×D4312yes—
668C2×C4C22⋊C4×D4312yes—
669C2×C4C22×C4×D4311yescharacteristic
670C2×C4C2×D4×D4311yescharacteristic
671C2×C4#41×D4311yescharacteristic
672C2×C4#41×D4311yescharacteristic
673C2×C4C2×#1062190011yescharacteristic
674C2×C4C2×#1062190211yescharacteristic
675C8—41no—
676C8—41no—
677C8—1721no—
678C8—1721no—
679C22—24no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—862no—
687C22—862no—
688C22—862no—
689C22—1721no—
690C22—1721no—
691C22—1721no—
692C22—1721no—
693C22C2×C22⋊C4×D4311yescharacteristic
694C22#1458340911yescharacteristic
695C22#1458341211yescharacteristic
696C22#1458370011yescharacteristic
697C22#1458370511yescharacteristic
698C22#1458370911yescharacteristic
699C22#1458371511yescharacteristic
700C4—22no—
701C4—22no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—862no—
706C4—862no—
707C4—864no—
708C4—862no—
709C4—3441no—
710C4—3441no—
711C4—1722no—
712C4#117×D4311yescharacteristic
713C4C2×#1306328311yescharacteristic
714C4#1458340911yescharacteristic
715C4#1458341211yescharacteristic
716C2—44no—
717C2—1722no—
718C2#1913697711yescharacteristic
719C2#1914311611yescharacteristic
720C2#1914312611yescharacteristic
721C2#1914479111yescharacteristic
722C2#1914480611yescharacteristic
723C2#1914486211yescharacteristic
724C2#1914487711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1802D43
hypocenterC43#20746
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#14582959C2semidirect
3. #19137203C2semidirect
4. #19134684C2semidirect
5. #19134680C2semidirect
6. #19134611C2semidirect
7. #19134605C2semidirect
8. #19134597C2semidirect
11. #19134424C2semidirect
12. #19134422C2semidirect
13. #19134414C2semidirect
14. #102×Dic43C2semidirect
15. C43×#1802C2semidirect
18. #14583378C4semidirect
362. #1802D43semidirect
424. C43#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#145833782
C2×#145829592
#191372032
#191346842
#191346802
#191346112
#191346052
#191345972
#191345322
#191344242
#191344222
#191344142
#102×Dic432
C43×#18022
#2074643