Finite Group Databasebeta

← #25112884

Subgroups — #25112884

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583587C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic
3#19137495C211yesmaximal, characteristic
4#19135553C211yesmaximal, characteristic, complemented
5#19135027C211yesmaximal, characteristic, complemented
6#19135017C211yesmaximal, characteristic, complemented
7#19134901C211yesmaximal, characteristic, complemented
8#19134901C211yesmaximal, characteristic, complemented
9#19134688C211yesmaximal, characteristic, complemented
10#19134680C211yesmaximal, characteristic, complemented
11#19134597C211yesmaximal, characteristic, complemented
12#19134426C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1992C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583587—24no—
19#14583587C418yescomplemented
20C2×#13063320—21no—
21C2×#13063316—21no—
22C2×#13063310—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×#13063287—21no—
28C2×#13063283—21no—
29C2×#13063283C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×C4⋊C4×D43C2211yescharacteristic
33#14582972—24no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41#14582795—21no—
42#14582770—21no—
43#14582770—21no—
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172D411yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43—41no—
77#13063320—28no—
78#13063316—28no—
79#13063310—28no—
80#13063305—22no—
81#13063305—22no—
82#13063305C2×C414yescomplemented
83#13063305C2×C414yescomplemented
84C4×Dic86—22no—
85C4×Dic86C2×C414yescomplemented
86C4×D172C2×C414yes—
87C4×D172D414yes—
88#13063287—44no—
89#13063283—22no—
90#13063283—28no—
91#13063283C2×C414yescomplemented
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C4⋊C4×D43—22no—
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—41no—
106C4⋊C4×D43—41no—
107C4⋊C4×D43C2×C414yescomplemented
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×(C2×D43)⋊C4D411yescharacteristic
115C2×C4×Dic43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43—21no—
118C4⋊(C43⋊C8)—22no—
119#13063250—22no—
120#13063250—22no—
121#13063248—41no—
122#13063248—41no—
123(C2×D43)⋊C8—22no—
124(C2×D43)⋊C8—22no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#125×C43—22no—
131#125×C43C2×C414yescomplemented
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141#97×C43—22no—
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C2×D172—22no—
158C2×D172—22no—
159C2×D172C22⋊C414yes—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—24no—
169C2×C4×D43—42no—
170C2×C4×D43—42no—
171C2×C4×D43—42no—
172C2×C4×D43—42no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×C4×D43C22×C412yes—
178C2×C4×D43C22×C412yes—
179C2×C4×D43C2×D412yes—
180C2×C4×D43C2×D412yes—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86C22×C412yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43#4112yes—
193C4⋊C4×C43—24no—
194C4⋊C4×C43—24no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—42no—
202C4⋊C4×C43—81no—
203C4⋊C4×C43C22×C412yes—
204C4⋊C4×C43C22×C412yes—
205C42×C43C22×C412yes—
206C42×C43C2×D412yes—
207(C2×D43)⋊C4—24no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—24no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4C22⋊C414yes—
213(C2×D43)⋊C4C22⋊C414yes—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—24no—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C22⋊C414yes—
221C4⋊Dic43C22×C412yes—
222C4⋊Dic43#4112yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—24no—
225Dic43⋊C4—42no—
226Dic43⋊C4—42no—
227C4×Dic43—24no—
228C4×Dic43—24no—
229C4×Dic43—42no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236#10621872—44no—
237C8×D43—44no—
238C23×C43C22×D411yescharacteristic
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43C2×C22⋊C412yes—
250C22×D43C2×C22⋊C412yes—
251C22×D43AGL(1,ℤ/8)12yes—
252C22×D43#13712yes—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
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×C43C2×C22⋊C412yes—
270C2×C4×C43C2×C22⋊C412yes—
271C2×C4×C43C23×C411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43C2×C22⋊C412yes—
294C2×Dic43C2×C22⋊C412yes—
295D172—28no—
296C4×D43—22no—
297C4×D43—22no—
298C4×D43—22no—
299C4×D43—22no—
300C4×D43—22no—
301C4×D43—22no—
302C4×D43—22no—
303C4×D43—22no—
304C4×D43—48no—
305C4×D43—84no—
306C4×D43—84no—
307Dic86—22no—
308Dic86—22no—
309Dic86—41no—
310Dic86—41no—
311C8×C43—22no—
312C8×C43—41no—
313C43⋊C8—41no—
314C43⋊C8—41no—
315#22491—431nomaximal, Sylow
316C22×C43C22×C22⋊C411yescharacteristic
317C22×C43#54611yescharacteristic
318C22×C43#54711yescharacteristic
319C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C43C2×#13711yescharacteristic
321C22×C43#57711yescharacteristic
322C22×C43#57811yescharacteristic
323C2×D43—22no—
324C2×D43—22no—
325C2×D43—22no—
326C2×D43—22no—
327C2×D43—22no—
328C2×D43—22no—
329C2×D43—22no—
330C2×D43—22no—
331C2×D43—22no—
332C2×D43—41no—
333C2×D43—41no—
334C2×D43—41no—
335C2×D43—41no—
336C2×D43#41714yes—
337C4×C43—22no—
338C4×C43—22no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—81no—
342C4×C43—81no—
343C4×C43C4×#4111yescharacteristic
344C4×C43#52011yescharacteristic
345C4×C43#54611yescharacteristic
346C4×C43#54711yescharacteristic
347Dic43—22no—
348Dic43—22no—
349Dic43—42no—
350Dic43—42no—
351Dic43—42no—
352Dic43—81no—
353C2×#552—431no—
354C2×#435—431no—
355D4×C4⋊C4—431no—
356#1992D4311yescharacteristic, complemented
357#1989—431no—
358#1894—431no—
359#1892—431no—
360#1872—431no—
361#1872—431no—
362#1825—431no—
363#1823—431no—
364#1803—431no—
365#1763—431no—
366#1736—431no—
367C2×#340—431no—
368C2×C43#233911yescharacteristic
369C2×C43C2×#41711yescharacteristic
370C2×C43#289811yescharacteristic
371C2×C43#331011yescharacteristic
372C2×C43#331211yescharacteristic
373C2×C43#334311yescharacteristic
374C2×C43#334411yescharacteristic
375D43—24no—
376D43—42no—
377C22×M16—431no—
378C23×C8—431no—
379#552—438no—
380#552—864no—
381C2×#126—861no—
382C2×#125—861no—
383C2×#125C2×D4311yescharacteristic
384C2×#123—861no—
385C2×C22⋊Q8—431no—
386C2×C22⋊Q8—431no—
387C2×C4×Q8—431no—
388C2×C4×D4—431no—
389C2×C4×D4—861no—
390C2×#117—431no—
391C2×#117—861no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4—431no—
395#435—864no—
396C2×C4⋊C8—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×#103—431no—
401C2×C22⋊C8—431no—
402C2×C22⋊C8—431no—
403C2×#97C2×D4311yescharacteristic
404#389—861no—
405#385—861no—
406#385—861no—
407#384C2×D4311yescharacteristic
408#380—431no—
409#380—431no—
410C4×C4⋊C4—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416#340—431no—
417#340—431no—
418#340—431no—
419#340C2×D4311yescharacteristic
420#340C2×D4311yescharacteristic
421#340C2×D4311yescharacteristic
422#340C2×D4311yescharacteristic
423C43#2249111yescharacteristic, complemented, Sylow
424C22×Q8—431no—
425C22×D4—431no—
426C23×C4—431no—
427C23×C4—431no—
428C23×C4—861no—
429C23×C4—861no—
430C23×C4—861no—
431C2×M16—862no—
432C2×M16—862no—
433C2×M16—1721no—
434C22×C8—431no—
435C22×C8—431no—
436C22×C8—862no—
437C22×C8—862no—
438C22×C8—1721no—
439C22×C8C22×D4311yescharacteristic
440C22×C8C22×D4311yescharacteristic
441#126—868no—
442#125—22no—
443#125—868no—
444#125C4×D4314yescomplemented
445#123—868no—
446C22⋊Q8—434no—
447C22⋊Q8—434no—
448C22⋊Q8—862no—
449C22⋊Q8—862no—
450C4×Q8—434no—
451C4×Q8—862no—
452C4×D4—434no—
453C4×D4—434no—
454C4×D4—1724no—
455#117—434no—
456#117—868no—
457#117—862no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—434no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—862no—
469C2×C4⋊C4—862no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—1721no—
477C2×C4⋊C4—1721no—
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C42—861no—
490C2×C42—861no—
491C2×C42—861no—
492C2×C42C22×D4311yescharacteristic
493C4⋊C8—862no—
494#103—862no—
495#103—862no—
496#103—1721no—
497#103—1721no—
498C22⋊C8—862no—
499C22⋊C8—862no—
500#97—22no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24—431no—
505C24—431no—
506C2×Q8—432no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×D4—434no—
513C2×D4—862no—
514C2×D4—862no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—432no—
522C22×C4—432no—
523C22×C4—432no—
524C22×C4—432no—
525C22×C4—864no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—3441no—
539C22×C4—3441no—
540C22×C4—1722no—
541C22×C4—1722no—
542C22×C4—1722no—
543C22×C4—1722no—
544C22×C4—1722no—
545C22×C4—1722no—
546C22×C4D4×D4311yescharacteristic
547C22×C4D4×D4311yescharacteristic
548C22×C4C23×D4311yescharacteristic
549M16—1724no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—1724no—
562C2×C8#1062190212yes—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4—434no—
574C4⋊C4—432no—
575C4⋊C4—432no—
576C4⋊C4—864no—
577C4⋊C4—864no—
578C4⋊C4—864no—
579C4⋊C4—864no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—1722no—
585C4⋊C4—1722no—
586C4⋊C4C2×C4×D4312yes—
587C4⋊C4C2×C4×D4312yes—
588C22⋊C4—434no—
589C22⋊C4—434no—
590C22⋊C4—864no—
591C22⋊C4—864no—
592C22⋊C4—864no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C42—864no—
596C42—864no—
597C42—1722no—
598C42C2×C4×D4312yes—
599C42D4×D4312yes—
600C23—432no—
601C23—432no—
602C23—432no—
603C23—432no—
604C23—861no—
605C23—861no—
606C23—861no—
607C23—861no—
608C23—861no—
609C23—861no—
610C23—861no—
611C23—861no—
612C23—861no—
613C23—861no—
614C23C2×D4×D4311yescharacteristic
615Q8—862no—
616Q8—862no—
617Q8—1721no—
618Q8—1721no—
619D4—868no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—432no—
637C2×C4—432no—
638C2×C4—861no—
639C2×C4—861no—
640C2×C4—861no—
641C2×C4—861no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—862no—
646C2×C4—862no—
647C2×C4—862no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—3444no—
654C2×C4—3444no—
655C2×C4—1728no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4C22⋊C4×D4312yes—
666C2×C4C22⋊C4×D4312yes—
667C2×C4C22×C4×D4311yescharacteristic
668C2×C4C2×D4×D4311yescharacteristic
669C2×C4#41×D4311yescharacteristic
670C2×C4C2×#1062190211yescharacteristic
671C2×C4#1306337111yescharacteristic
672C2×C4#1306337311yescharacteristic
673C8—22no—
674C8—41no—
675C8—1721no—
676C8—1721no—
677C22—434no—
678C22—862no—
679C22—862no—
680C22—862no—
681C22—862no—
682C22—862no—
683C22—862no—
684C22—862no—
685C22—862no—
686C22—862no—
687C22—1721no—
688C22—1721no—
689C22—1721no—
690C22—1721no—
691C22C2×C22⋊C4×D4311yescharacteristic
692C22#1458354211yescharacteristic
693C22#1458355211yescharacteristic
694C22AGL(1,ℤ/8)×D4311yescharacteristic
695C22#137×D4311yescharacteristic
696C22#1458370911yescharacteristic
697C22#1458371511yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—81no—
704C4—862no—
705C4—862no—
706C4—3441no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C4C4×#1062190211yescharacteristic
711C4#1458338111yescharacteristic
712C4#1458354011yescharacteristic
713C4#1458355111yescharacteristic
714C2—864no—
715C2—1722no—
716C2#1913742411yescharacteristic
717C2#417×D4311yescharacteristic
718C2#1914312611yescharacteristic
719C2#1914661511yescharacteristic
720C2#1914664511yescharacteristic
721C2#1914703411yescharacteristic
722C2#1914704911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1992C2
socleC23×C43C22×D4
prime radicalC22×D172D4
cosocleC22×C4×C43C24
hypercenter#1992D43
hypocenterC43#22491
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
4. #19135553C2semidirect
5. #19135027C2semidirect
6. #19135017C2semidirect
7. #19134901C2semidirect
8. #19134901C2semidirect
9. #19134688C2semidirect
10. #19134680C2semidirect
11. #19134597C2semidirect
12. #19134426C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C43×#1992C2semidirect
19. #14583587C4semidirect
82. #13063305C2×C4semidirect
83. #13063305C2×C4semidirect
85. C4×Dic86C2×C4semidirect
91. #13063283C2×C4semidirect
107. C4⋊C4×D43C2×C4semidirect
131. #125×C43C2×C4semidirect
356. #1992D43semidirect
423. C43#22491semidirect
444. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835872
C2×#145829722
#191374952
#191355532
#191350272
#191350172
#191349012
#191346882
#191346802
#191345972
#191344262
#191343132
#340×D432
C43×#19922
#2249143