Finite Group Databasebeta

← #25113035

Subgroups — #25113035

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×#14583597C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic, complemented
3#19137517C211yesmaximal, characteristic, complemented
4#19135558C211yesmaximal, characteristic, complemented
5#19135549C211yesmaximal, characteristic, complemented
6#19135032C211yesmaximal, characteristic, complemented
7#19135031C211yesmaximal, characteristic, complemented
8#19134915C211yesmaximal, characteristic, complemented
9#19134911C211yesmaximal, characteristic, complemented
10#19134688C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134409C211yesmaximal, characteristic, complemented
13#19134314C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1823C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583597—24no—
19#14583597C418yescomplemented
20C2×#13063320—21no—
21C2×#13063316C2211yescharacteristic
22C2×#13063310—21no—
23C2×#13063300C2211yescharacteristic
24C2×#13063299—21no—
25C2×#13063299C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×C4×C22⋊D43—21no—
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582974—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40#14582787—21no—
41#14582781—21no—
42#14582775—21no—
43#14582764C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46#14582746—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43C2311yescharacteristic
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—41no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063320—28no—
78#13063316—22no—
79#13063316C2×C414yescomplemented
80#13063310—28no—
81#13063300—22no—
82#13063300C2×C414yes—
83#13063299—22no—
84#13063299—28no—
85#13063299C2×C414yescomplemented
86#13063287—22no—
87#13063287C2×C414yescomplemented
88C4×C22⋊D43—28no—
89C4×C22⋊D43C2×C414yes—
90C4×C22⋊D43D414yes—
91#13063284—22no—
92#13063284—41no—
93#13063283—22no—
94#13063283C2×C414yes—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C4⋊C4×D43—22no—
103C4⋊C4×D43—41no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43D411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4D411yescharacteristic
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063247—22no—
118#13063247—41no—
119#13063245—22no—
120#13063245—41no—
121(C2×D43)⋊C8—22no—
122C8×Dic43—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C23×C4×C43—21no—
128C23×C4×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2×C414yescomplemented
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C22⋊C8×C43—22no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—24no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—81no—
154C22×C4×C43—81no—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—41no—
161C2×C22⋊D43—41no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43C22⋊C414yes—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C2×D172—21no—
172C2×D172—24no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—81no—
178C2×D172—81no—
179C2×D172C22×C412yes—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—24no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×C4×D43C22×C412yes—
191C2×C4×D43C2×D412yes—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C4⋊C4×C43—24no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C22×C412yes—
206C4⋊C4×C43C22×C412yes—
207C22⋊C4×C43—81no—
208C22⋊Dic43—42no—
209C22⋊Dic43C22⋊C414yes—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4C22⋊C414yes—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—24no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43C22×C412yes—
222C4⋊Dic43#4112yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—42no—
225Dic43⋊C4C22⋊C414yes—
226C4×Dic43—24no—
227C4×Dic43—42no—
228C4×Dic43—81no—
229C4×Dic43C22×C412yes—
230C4×Dic43C2×D412yes—
231#10621877—44no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8#4112yes—
238#10621872—44no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43C2×C22⋊C412yes—
246C23×C43C22×D411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—22no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43C2×C22⋊C412yes—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
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×C43—41no—
279C2×C4×C43—84no—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C432−1+411yescharacteristic
287C22⋊D43—44no—
288C22⋊D43—48no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—22no—
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×Dic43C2×C22⋊C412yes—
305C2×Dic43C2×C22⋊C412yes—
306C2×Dic43C2×C22⋊C412yes—
307D172—22no—
308D172—22no—
309D172—41no—
310D172—41no—
311D172—84no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—84no—
317C4×D43—84no—
318C8×C43—41no—
319C8×C43—41no—
320C43⋊C8—22no—
321C43⋊C8—41no—
322#22501—431nomaximal, Sylow
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43C22×C22⋊C411yescharacteristic
331C22×C43#54611yescharacteristic
332C22×C43#54711yescharacteristic
333C22×C43#57511yescharacteristic
334C22×C43#57511yescharacteristic
335C22×C43#57611yescharacteristic
336C22×C43#57711yescharacteristic
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C2×D43—81no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43C4×#4111yescharacteristic
357C4×C43#52011yescharacteristic
358C4×C43#54611yescharacteristic
359C4×C43#54711yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—22no—
363Dic43—42no—
364Dic43—42no—
365Dic43—81no—
366C2×#553—431no—
367C2×#436—431no—
368#2352—431no—
369#1991—431no—
370#1989—431no—
371#1895—431no—
372#1895—431no—
373#1875—431no—
374#1874—431no—
375#1825—431no—
376#1823D4311yescharacteristic, complemented
377#1804—431no—
378C4×#102—431no—
379#1736—431no—
380#1736—431no—
381C2×C43—42no—
382C2×C43#233911yescharacteristic
383C2×C43#289611yescharacteristic
384C2×C43#289711yescharacteristic
385C2×C43#332211yescharacteristic
386C2×C43#332611yescharacteristic
387C2×C43#335111yescharacteristic
388C2×C43#335511yescharacteristic
389D43—42no—
390D43—82no—
391C22×M16—431no—
392C22×M16—431no—
393#553—438no—
394#553—864no—
395C2×#126—861no—
396C2×#125—431no—
397C2×#123—861no—
398C2×#121—431no—
399C2×#121—431no—
400C2×#121—861no—
401C2×C4×D4—431no—
402C2×C4×D4—431no—
403C2×C4×D4—861no—
404C2×#117—431no—
405C2×#117—431no—
406C22×C4⋊C4—431no—
407C22×C4⋊C4C2×D4311yescharacteristic
408#436—864no—
409C2×C4⋊C8—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8C2×D4311yescharacteristic
416C2×C4×C8—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#340C2×D4311yescharacteristic
434#340C2×D4311yescharacteristic
435#340C2×D4311yescharacteristic
436#340C2×D4311yescharacteristic
437C43#2250111yescharacteristic, complemented, Sylow
438C22×D4—431no—
439C22×D4—431no—
440C22×D4—861no—
441C22×D4—861no—
442C23×C4—21no—
443C23×C4—431no—
444C23×C4—861no—
445C23×C4—861no—
446C23×C4C22×D4311yescharacteristic
447C2×M16—862no—
448C2×M16—862no—
449C2×M16—862no—
450C2×M16—862no—
451C2×M16—1721no—
452C2×M16—1721no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457#126—868no—
458#125—434no—
459#125—862no—
460#123—868no—
461#121—434no—
462#121—434no—
463#121—862no—
464#121—868no—
465#121—862no—
466C4×D4—434no—
467C4×D4—434no—
468C4×D4—434no—
469C4×D4—862no—
470C4×D4—868no—
471#117—434no—
472#117—862no—
473#117—862no—
474#117—1721no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—1721no—
486C2×C4⋊C4C4×D4314yescomplemented
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C42—431no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42—861no—
504C4⋊C8—862no—
505#102—862no—
506#102—862no—
507#102—1721no—
508#102—1721no—
509C22⋊C8—22no—
510C22⋊C8—862no—
511C4×C8—862no—
512#95—21no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517C24—431no—
518C24—861no—
519C24D4×D4311yescharacteristic
520C2×D4—434no—
521C2×D4—432no—
522C2×D4—864no—
523C2×D4—864no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—3441no—
530C2×D4—3441no—
531C2×D4—1721no—
532C2×D4—1721no—
533C2×D4—1722no—
534C2×D4—1722no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—432no—
550C22×C4—432no—
551C22×C4—864no—
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—3441no—
561C22×C4—3441no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4C2×C4×D4312yes—
565C22×C4D4×D4311yescharacteristic
566C22×C4D4×D4312yes—
567C22×C4C23×D4311yescharacteristic
568M16—1724no—
569M16—1724no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—432no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—434no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—864no—
593C4⋊C4—864no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—1722no—
599C4⋊C4C2×C4×D4312yes—
600C4⋊C4C2×C4×D4312yes—
601C22⋊C4—81no—
602C22⋊C4—434no—
603C22⋊C4—434no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—864no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C42—432no—
611C42—432no—
612C42—864no—
613C42—3441no—
614C42—1722no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—432no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—862no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23C22⋊C4×D4312yes—
636C23C2×D4×D4311yescharacteristic
637D4—862no—
638D4—862no—
639D4—3444no—
640D4—1724no—
641D4—1728no—
642D4—1721no—
643D4—1721no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
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—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—3444no—
679C2×C4—3444no—
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×C4#41×D4311yescharacteristic
692C2×C4#1306337111yescharacteristic
693C2×C4#1306337211yescharacteristic
694C8—41no—
695C8—41no—
696C8—862no—
697C8—1721no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—3441no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22—1721no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22C2×C22⋊C4×D4311yescharacteristic
720C22#1458354111yescharacteristic
721C22#1458354711yescharacteristic
722C22#1458369811yescharacteristic
723C22#1458369811yescharacteristic
724C22#1458370011yescharacteristic
725C22#1458370511yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—862no—
732C4—862no—
733C4—862no—
734C4—3441no—
735C4—1722no—
736C4—1722no—
737C4#1458336711yescharacteristic
738C4#1458337911yescharacteristic
739C4#1458354111yescharacteristic
740C4#1458354711yescharacteristic
741C2—42no—
742C2—3442no—
743C2—1722no—
744C2#1913741911yescharacteristic
745C2#1914311311yescharacteristic
746C2#1914311611yescharacteristic
747C2#1914679911yescharacteristic
748C2#1914685111yescharacteristic
749C2#1914715811yescharacteristic
750C2#1914720111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1823C2
socleC23×C43C22×D4
prime radicalC2×#14583597C2
cosocleC22×C4×C43C24
hypercenter#1823D43
hypocenterC43#22501
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. #19137517C2semidirect
4. #19135558C2semidirect
5. #19135549C2semidirect
6. #19135032C2semidirect
7. #19135031C2semidirect
8. #19134915C2semidirect
9. #19134911C2semidirect
10. #19134688C2semidirect
11. #19134604C2semidirect
12. #19134409C2semidirect
13. #19134314C2semidirect
14. #19134313C2semidirect
15. C43×#1823C2semidirect
19. #14583597C4semidirect
79. #13063316C2×C4semidirect
85. #13063299C2×C4semidirect
87. #13063287C2×C4semidirect
133. C2×C4⋊C4×C43C2×C4semidirect
376. #1823D43semidirect
437. C43#22501semidirect
486. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835972
C2×#145829742
#191375172
#191355582
#191355492
#191350322
#191350312
#191349152
#191349112
#191346882
#191346042
#191344092
#191343142
#191343132
C43×#18232
#2250143