Finite Group Databasebeta

← #25112906

Subgroups — #25112906

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic
2C2×#14582970C211yesmaximal, characteristic, complemented
3#19137517C211yesmaximal, characteristic, complemented
4#19135566C211yesmaximal, characteristic, complemented
5#19135545C211yesmaximal, characteristic, complemented
6#19135030C211yesmaximal, characteristic, complemented
7#19134918C211yesmaximal, characteristic, complemented
8#19134909C211yesmaximal, characteristic, complemented
9#19134688C211yesmaximal, characteristic, complemented
10#19134687C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134312C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17#14583613—24no—
18#14583613C418yescomplemented
19C2×#13063324C2211yescharacteristic
20C2×#13063312—21no—
21C2×#13063311—21no—
22C2×#13063297—21no—
23C2×#13063296C2211yescharacteristic
24C2×D4×Dic43C2211yescharacteristic
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063284C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×#13063281—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31#14582970—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×#13063235C2211yescharacteristic
38#14582787—21no—
39#14582781—21no—
40#14582775—21no—
41#14582764C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44#14582746—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×C22⋊D43—21no—
64C22×C22⋊D43D411yescharacteristic
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C2×#10621872—22no—
69C2×#10621872—22no—
70C2×#10621872—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—22no—
74#13063324C2×C414yescomplemented
75#13063312—28no—
76#13063311—28no—
77#13063297—28no—
78#13063296—22no—
79#13063296C2×C414yes—
80D4×Dic43—22no—
81D4×Dic43C2×C414yescomplemented
82C4×C22⋊D43C2×C414yes—
83C4×C22⋊D43D414yes—
84#13063284—22no—
85#13063284—22no—
86#13063284—41no—
87#13063284C2×C414yescomplemented
88#13063283—22no—
89#13063283C2×C414yes—
90#13063281—28no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C4⋊C4×D43—22no—
99C4⋊C4×D43—41no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43D411yescharacteristic
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113Dic43⋊C8—22no—
114#13063246—22no—
115#13063246—41no—
116C22⋊(C43⋊C8)—22no—
117(C2×D43)⋊C8—22no—
118#13063235—22no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43—21no—
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43—22no—
127C22×C8×C43—22no—
128C22×C8×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#121×C43—22no—
132#121×C43C2×C414yescomplemented
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138#102×C43—22no—
139#102×C43—41no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—24no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—81no—
151C2×D4×C43—81no—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43—81no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43C22⋊C414yes—
170C22×Dic43—24no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C22×Dic43C2×D411yescharacteristic
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—42no—
185C2×C4×D43—42no—
186C2×C4×D43—81no—
187C2×C4×D43C22×C412yes—
188C2×C4×D43C2×D412yes—
189C2×Dic86—24no—
190C2×Dic86—81no—
191C2×Dic86—81no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—44no—
198C2×C8×C43#4112yes—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43C22×C412yes—
205C22⋊C4×C43—24no—
206C22⋊C4×C43—81no—
207C22⋊Dic43—24no—
208C22⋊Dic43—24no—
209C22⋊Dic43—24no—
210C22⋊Dic43—42no—
211C22⋊Dic43C22⋊C414yes—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4C22⋊C414yes—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C22×C412yes—
221C4⋊Dic43C22×C412yes—
222C4⋊Dic43#4112yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—42no—
225Dic43⋊C4C22⋊C414yes—
226C4×Dic43—24no—
227C4×Dic43—24no—
228C4×Dic43—42no—
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—
238#10621872—44no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43C2×C22⋊C412yes—
253C23×C43C22×D411yescharacteristic
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43C2×C22⋊C412yes—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—41no—
264D4×C43—41no—
265D4×C43—84no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C22⋊D43—44no—
289C22⋊D43—84no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—48no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43C2×C22⋊C412yes—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—84no—
317Dic86—84no—
318C8×C43—22no—
319C8×C43—41no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322#22492—431nomaximal, Sylow
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43C22×C22⋊C411yescharacteristic
338C22×C43#54611yescharacteristic
339C22×C43#54711yescharacteristic
340C22×C43#57511yescharacteristic
341C22×C43#57511yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57711yescharacteristic
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43C4×#4111yescharacteristic
356C4×C43#52011yescharacteristic
357C4×C43#54611yescharacteristic
358C4×C43#54711yescharacteristic
359Dic43—22no—
360Dic43—22no—
361Dic43—22no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365Dic43—81no—
366C2×#555—431no—
367C2×#435—431no—
368#2352—431no—
369#1993—431no—
370#1988—431no—
371#1895—431no—
372#1893D4311yescharacteristic, complemented
373#1875—431no—
374#1874—431no—
375#1825—431no—
376#1825—431no—
377#1804—431no—
378#1762—431no—
379#1736—431no—
380#1735—431no—
381C2×C43—42no—
382C2×C43—82no—
383C2×C43#233911yescharacteristic
384C2×C43#289611yescharacteristic
385C2×C43#289711yescharacteristic
386C2×C43#331911yescharacteristic
387C2×C43#332111yescharacteristic
388C2×C43#334711yescharacteristic
389C2×C43#334811yescharacteristic
390D43—42no—
391C22×M16—431no—
392C23×C8C2×D4311yescharacteristic
393#555—438no—
394#555—864no—
395C2×C4⋊Q8—431no—
396C2×#124—861no—
397C2×#124—861no—
398C2×#121—431no—
399C2×#121—861no—
400C2×#121C2×D4311yescharacteristic
401C2×C4×D4—431no—
402C2×C4×D4—431no—
403C2×#117—431no—
404C2×#117—431no—
405C2×#117—431no—
406C2×#117—861no—
407C22×C4⋊C4—431no—
408#435—864no—
409C2×C4⋊C8—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102C2×D4311yescharacteristic
413C2×#102C2×D4311yescharacteristic
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×#97—431no—
417#388—861no—
418#387—861no—
419#386—861no—
420#382—431no—
421#380—431no—
422#380C2×D4311yescharacteristic
423C4×C4⋊C4—431no—
424C4×C22⋊C4—861no—
425#340—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340C2×D4311yescharacteristic
436#340C2×D4311yescharacteristic
437C43#2249211yescharacteristic, complemented, Sylow
438C22×Q8—861no—
439C22×D4—21no—
440C22×D4—431no—
441C22×D4—861no—
442C22×D4C22×D4311yescharacteristic
443C23×C4—431no—
444C23×C4—861no—
445C23×C4—861no—
446C23×C4C22×D4311yescharacteristic
447C2×M16—862no—
448C2×M16—862no—
449C2×M16—1721no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C4⋊Q8—434no—
458C4⋊Q8—862no—
459#124—868no—
460#124—868no—
461#121—22no—
462#121—434no—
463#121—862no—
464#121—868no—
465#121C4×D4314yescomplemented
466C4×D4—434no—
467C4×D4—434no—
468C4×D4—434no—
469C4×D4—862no—
470#117—434no—
471#117—434no—
472#117—868no—
473#117—862no—
474#117—862no—
475#117—862no—
476#117—1721no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—1721no—
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C42—431no—
500C2×C42—861no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42—861no—
504C4⋊C8—862no—
505#102—22no—
506#102—41no—
507#102—862no—
508#102—1721no—
509C22⋊C8—862no—
510C22⋊C8—862no—
511#97—862no—
512#95—21no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—21no—
518C24—431no—
519C24D4×D4311yescharacteristic
520C2×Q8—864no—
521C2×Q8—3441no—
522C2×Q8—3441no—
523C2×D4—24no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4—434no—
532C2×D4—864no—
533C2×D4—3441no—
534C2×D4—3441no—
535C2×D4—1721no—
536C2×D4—1721no—
537C2×D4C2×C4×D4312yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—864no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—3441no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4C2×C4×D4312yes—
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4312yes—
567C22×C4C23×D4311yescharacteristic
568M16—1724no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—44no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8#1062190012yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—434no—
588C4⋊C4—432no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—864no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—1722no—
598C4⋊C4C2×C4×D4312yes—
599C22⋊C4—24no—
600C22⋊C4—81no—
601C22⋊C4—434no—
602C22⋊C4—434no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—432no—
610C42—432no—
611C42—864no—
612C42—864no—
613C42—3441no—
614C42—1722no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—432no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23C22⋊C4×D4312yes—
636C23C2×D4×D4311yescharacteristic
637Q8—3444no—
638D4—22no—
639D4—22no—
640D4—41no—
641D4—41no—
642D4—84no—
643D4—3444no—
644D4—1724no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—3444no—
677C2×C4—1728no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4C22⋊C4×D4312yes—
688C2×C4C22×C4×D4311yescharacteristic
689C2×C4C2×D4×D4311yescharacteristic
690C2×C4#41×D4311yescharacteristic
691C2×C4C2×#1062190011yescharacteristic
692C2×C4#1306337011yescharacteristic
693C2×C4#1306337211yescharacteristic
694C8—22no—
695C8—41no—
696C8—1721no—
697C8—1721no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—1721no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22C2×C22⋊C4×D4311yescharacteristic
720C22#1458353811yescharacteristic
721C22#1458354911yescharacteristic
722C22#1458369611yescharacteristic
723C22#1458369611yescharacteristic
724C22#1458370011yescharacteristic
725C22#1458370511yescharacteristic
726C4—22no—
727C4—42no—
728C4—81no—
729C4—81no—
730C4—862no—
731C4—862no—
732C4—862no—
733C4—3441no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4C4×#1062190011yescharacteristic
738C4#1458337811yescharacteristic
739C4#1458353611yescharacteristic
740C4#1458354711yescharacteristic
741C2—42no—
742C2—82no—
743C2—1722no—
744C2#1913742111yescharacteristic
745C2#1914311011yescharacteristic
746C2#1914311611yescharacteristic
747C2#1914675711yescharacteristic
748C2#1914678711yescharacteristic
749C2#1914710111yescharacteristic
750C2#1914711611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583613C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#22492
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#14582970C2semidirect
3. #19137517C2semidirect
4. #19135566C2semidirect
5. #19135545C2semidirect
6. #19135030C2semidirect
7. #19134918C2semidirect
8. #19134909C2semidirect
9. #19134688C2semidirect
10. #19134687C2semidirect
11. #19134603C2semidirect
12. #19134422C2semidirect
13. #19134313C2semidirect
14. #19134312C2semidirect
15. C43×#1893C2semidirect
18. #14583613C4semidirect
74. #13063324C2×C4semidirect
81. D4×Dic43C2×C4semidirect
87. #13063284C2×C4semidirect
132. #121×C43C2×C4semidirect
372. #1893D43semidirect
437. C43#22492semidirect
465. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145829702
#191375172
#191355662
#191355452
#191350302
#191349182
#191349092
#191346882
#191346872
#191346032
#191344222
#191343132
#191343122
C43×#18932
#2249243