Finite Group Databasebeta

← #25101760

Subgroups — #25101760

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583503C211yesmaximal, characteristic
2C2×#14582959C211yesmaximal, characteristic, complemented
3#19136949C211yesmaximal, characteristic, complemented
4#19135552C211yesmaximal, characteristic, complemented
5#19135550C211yesmaximal, characteristic, complemented
6#19135523C211yesmaximal, characteristic, complemented
7#19134914C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134422C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1982C211yesmaximal, characteristic, complemented
16#14583503—24no—
17#14583503C418yescomplemented
18C2×#13063317C2211yescharacteristic
19C2×#13063306—21no—
20C2×#13063306—21no—
21C2×#13063297—21no—
22C2×#13063297—21no—
23C2×#13063296C2211yescharacteristic
24C2×#13063296C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063282C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14582959—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×(C2×D43)⋊C8C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39C2×C8×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582750—21no—
45C4×(C2×D43)⋊C4—21no—
46#14582746—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#127×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063317—22no—
71#13063317C2×C414yescomplemented
72#13063306—28no—
73#13063306—28no—
74#13063297—28no—
75#13063297—28no—
76#13063296—22no—
77#13063296—22no—
78#13063296C2×C414yes—
79#13063296C2×C414yes—
80D4×Dic43—22no—
81D4×Dic43—22no—
82D4×Dic43C2×C414yescomplemented
83D4×Dic43C2×C414yescomplemented
84#13063283—22no—
85#13063283—22no—
86#13063282C2×C414yes—
87#13063282D414yes—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4D411yescharacteristic
96C2×Dic43⋊C4D411yescharacteristic
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C4⋊(C43⋊C8)—22no—
112#13063246—22no—
113#13063246—22no—
114#13063246—22no—
115#13063246—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063235—22no—
119C8×Dic43—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43—21no—
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#127×C43—22no—
130#127×C43C2×C414yescomplemented
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C23×D43C2×D411yescharacteristic
144C2×D4×C43—24no—
145C2×D4×C43—24no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C22×C412yes—
161C2×D4×C43C22×C412yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—81no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C2×C22⋊D43—81no—
173C22×Dic43—24no—
174C22×Dic43—24no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—24no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C4×D43C22×C412yes—
194C2×C4×D43C2×D412yes—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43#4112yes—
204C4⋊C4×C43#4112yes—
205C42×C43—81no—
206C42×C43C22×C412yes—
207C42×C43C2×D412yes—
208C22⋊Dic43—24no—
209C22⋊Dic43—24no—
210C22⋊Dic43—24no—
211C22⋊Dic43—24no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4C22⋊C414yes—
214(C2×D43)⋊C4C22⋊C414yes—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22×C412yes—
220C4⋊Dic43C22×C412yes—
221C4⋊Dic43#4112yes—
222C4⋊Dic43#4112yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—24no—
225Dic43⋊C4—24no—
226Dic43⋊C4C22⋊C414yes—
227Dic43⋊C4C22⋊C414yes—
228C4×Dic43—24no—
229C4×Dic43—81no—
230C4×Dic43—81no—
231C4×Dic43—81no—
232C4×Dic43C22×C412yes—
233C4×Dic43C2×D412yes—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43C22×D411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43C2×C22⋊C412yes—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271D4×C43—84no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43C2×C22⋊C412yes—
283C2×C4×C43C2×C22⋊C412yes—
284C2×C4×C43C23×C411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C22⋊D43—84no—
291C22⋊D43—84no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—84no—
311C2×Dic43—84no—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43C2×C22⋊C412yes—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—84no—
320C8×C43—41no—
321C8×C43—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#21399—431nomaximal, Sylow
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43C22×C22⋊C411yescharacteristic
340C22×C43#52511yescharacteristic
341C22×C43#52511yescharacteristic
342C22×C43#57611yescharacteristic
343C22×C43#57611yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57711yescharacteristic
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43C4×#4111yescharacteristic
358C4×C43C4×#4111yescharacteristic
359C4×C43#53211yescharacteristic
360C4×C43#53211yescharacteristic
361Dic43—22no—
362Dic43—22no—
363Dic43—22no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367Dic43—42no—
368C2×#540—431no—
369C2×#433—431no—
370#2274—431no—
371#1989—431no—
372#1989—431no—
373#1982—431no—
374#1982D4311yescharacteristic, complemented
375#1875—431no—
376#1875—431no—
377#1874—431no—
378#1874—431no—
379#1762—431no—
380#1762—431no—
381C4×#102—431no—
382C4×#102—431no—
383C2×C43—82no—
384C2×C43—82no—
385C2×C43#229711yescharacteristic
386C2×C43#289711yescharacteristic
387C2×C43#289711yescharacteristic
388C2×C43#311911yescharacteristic
389C2×C43#311911yescharacteristic
390C2×C43#312211yescharacteristic
391C2×C43#312611yescharacteristic
392D43—42no—
393#540—438no—
394#540—864no—
395C2×#127C2×D4311yescharacteristic
396C2×#125—431no—
397C2×#123—861no—
398C2×#123—861no—
399C2×#121—431no—
400C2×#121—431no—
401C2×#121—861no—
402C2×#121—861no—
403C2×C4×D4—431no—
404C2×C4×D4—431no—
405C2×#117—431no—
406C2×#117—431no—
407C22×C4⋊C4—431no—
408#433—864no—
409C2×C4⋊C8—431no—
410C2×C4⋊C8C2×D4311yescharacteristic
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102C2×D4311yescharacteristic
416C2×#102C2×D4311yescharacteristic
417C2×#102C2×D4311yescharacteristic
418C2×#102C2×D4311yescharacteristic
419C2×C22⋊C8—431no—
420C2×C22⋊C8—431no—
421C2×#97—431no—
422C2×C4×C8—431no—
423C4×C4⋊C4—431no—
424C4×C4⋊C4—431no—
425C4×C4⋊C4—431no—
426C4×C4⋊C4—861no—
427C4×C4⋊C4—861no—
428C4×C4⋊C4C2×D4311yescharacteristic
429C4×C22⋊C4—861no—
430C4×C22⋊C4—861no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439C43#2139911yescharacteristic, complemented, Sylow
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—861no—
443C22×D4—861no—
444C22×D4C22×D4311yescharacteristic
445C22×D4C22×D4311yescharacteristic
446C23×C4—431no—
447C23×C4—861no—
448C23×C4—861no—
449C23×C4—861no—
450C22×C8—431no—
451C22×C8—431no—
452C22×C8C22×D4311yescharacteristic
453C22×C8C22×D4311yescharacteristic
454#127—22no—
455#127C4×D4314yescomplemented
456#125—434no—
457#125—862no—
458#123—868no—
459#123—868no—
460#121—434no—
461#121—434no—
462#121—868no—
463#121—868no—
464#121—862no—
465#121—862no—
466C4×D4—434no—
467C4×D4—434no—
468C4×D4—862no—
469C4×D4—862no—
470#117—434no—
471#117—434no—
472#117—862no—
473#117—862no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C22⋊C4—431no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C42—21no—
495C2×C42—431no—
496C2×C42—861no—
497C2×C42—861no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501C4⋊C8—22no—
502C4⋊C8—862no—
503#102—22no—
504#102—22no—
505#102—22no—
506#102—22no—
507#102—862no—
508#102—862no—
509#102—862no—
510#102—862no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513#97—862no—
514C4×C8—862no—
515#95—21no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—21no—
520C24—21no—
521C24—431no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4—864no—
539C2×D4—864no—
540C2×D4—3441no—
541C2×D4—3441no—
542C2×D4—3441no—
543C2×D4—3441no—
544C2×D4C2×C4×D4312yes—
545C2×D4C2×C4×D4312yes—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—431no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—432no—
552C22×C4—432no—
553C22×C4—864no—
554C22×C4—864no—
555C22×C4—864no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—3441no—
569C22×C4—3441no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—434no—
588C4⋊C4—434no—
589C4⋊C4—432no—
590C4⋊C4—432no—
591C4⋊C4—432no—
592C4⋊C4—432no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—864no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4#1062190012yes—
601C4⋊C4#1062190012yes—
602C22⋊C4—434no—
603C22⋊C4—434no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—864no—
608C22⋊C4—864no—
609C42—81no—
610C42—432no—
611C42—432no—
612C42—864no—
613C42—3441no—
614C42—3441no—
615C42—3441no—
616C42C2×C4×D4312yes—
617C42D4×D4312yes—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—432no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23C2×D4×D4311yescharacteristic
640D4—22no—
641D4—22no—
642D4—22no—
643D4—22no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—84no—
649D4—84no—
650D4—3444no—
651D4—3444no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—432no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—3444no—
680C2×C4—3444no—
681C2×C4—3444no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C22⋊C4×D4312yes—
691C2×C4C22⋊C4×D4312yes—
692C2×C4C22×C4×D4311yescharacteristic
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4#41×D4311yescharacteristic
695C2×C4#41×D4311yescharacteristic
696C2×C4C2×#1062190011yescharacteristic
697C2×C4C2×#1062190011yescharacteristic
698C8—41no—
699C8—41no—
700C8—1721no—
701C8—1721no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—1721no—
720C22—1721no—
721C22—1721no—
722C22—1721no—
723C22C2×C22⋊C4×D4311yescharacteristic
724C22#1458340911yescharacteristic
725C22#1458340911yescharacteristic
726C22#1458370011yescharacteristic
727C22#1458370311yescharacteristic
728C22#1458370511yescharacteristic
729C22#1458370911yescharacteristic
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—862no—
735C4—862no—
736C4—862no—
737C4—1722no—
738C4—1722no—
739C4—1722no—
740C4—1722no—
741C4C4×#1062190011yescharacteristic
742C4C4×#1062190011yescharacteristic
743C4#1458344711yescharacteristic
744C4#1458344811yescharacteristic
745C2—82no—
746C2—82no—
747C2—1722no—
748C2#1913708211yescharacteristic
749C2#1914311611yescharacteristic
750C2#1914312011yescharacteristic
751C2#1914479111yescharacteristic
752C2#1914479311yescharacteristic
753C2#1914483611yescharacteristic
754C2#1914488411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1982C2
socleC23×C43C22×D4
prime radicalC2×#14583503C2
cosocleC22×C4×C43C24
hypercenter#1982D43
hypocenterC43#21399
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#14582959C2semidirect
3. #19136949C2semidirect
4. #19135552C2semidirect
5. #19135550C2semidirect
6. #19135523C2semidirect
7. #19134914C2semidirect
8. #19134914C2semidirect
9. #19134909C2semidirect
10. #19134909C2semidirect
11. #19134422C2semidirect
12. #19134422C2semidirect
13. #102×Dic43C2semidirect
14. #102×Dic43C2semidirect
15. C43×#1982C2semidirect
17. #14583503C4semidirect
71. #13063317C2×C4semidirect
82. D4×Dic43C2×C4semidirect
83. D4×Dic43C2×C4semidirect
130. #127×C43C2×C4semidirect
374. #1982D43semidirect
439. C43#21399semidirect
455. #127C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835032
C2×#145829592
#191369492
#191355522
#191355502
#191355232
#191349142
#191349092
#191344222
#102×Dic432
C43×#19822
#2139943