Finite Group Databasebeta

← #25113063

Subgroups — #25113063

Order 11008.

1182 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×#14583620C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic
3#19137491C211yesmaximal, characteristic
4#19135554C211yesmaximal, characteristic, complemented
5#19135545C211yesmaximal, characteristic, complemented
6#19135025C211yesmaximal, characteristic, complemented
7#19134903C211yesmaximal, characteristic, complemented
8#19134899C211yesmaximal, characteristic, complemented
9#19134689C211yesmaximal, characteristic, complemented
10#19134687C211yesmaximal, characteristic, complemented
11#19134598C211yesmaximal, characteristic, complemented
12#103×Dic43C211yesmaximal, characteristic, complemented
13#19134315C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1894C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17#14583620—24no—
18#14583620C418yescomplemented
19C2×#13063324C2211yescharacteristic
20C2×#13063320—21no—
21C2×#13063318—21no—
22C2×#13063311—21no—
23C2×#13063301C2211yescharacteristic
24C2×Q8×Dic43C2211yescharacteristic
25C2×#13063290—21no—
26C2×C4×C22⋊D43C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063284C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582975—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582796—21no—
40#14582773—21no—
41#14582771—21no—
42#14582768C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×C22⋊D43D411yescharacteristic
64C23×Dic43—21no—
65C22×C4×D43—21no—
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68C2×#10621872—22no—
69C2×#10621872—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—22no—
73#13063324C2×C414yescomplemented
74#13063320—28no—
75#13063318—28no—
76#13063311—28no—
77#13063301—22no—
78#13063301C2×C414yescomplemented
79Q8×Dic43—22no—
80Q8×Dic43C2×C414yescomplemented
81#13063290—28no—
82C4×C22⋊D43C2×C414yes—
83C4×C22⋊D43D414yes—
84(C22⋊D43)⋊C4—44no—
85#13063284—22no—
86#13063284C2×C414yescomplemented
87#13063283—22no—
88#13063283C2×C414yescomplemented
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—41no—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C4⋊C4×D43—22no—
104C4⋊C4×D43—41no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43D411yescharacteristic
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063249—22no—
118#13063249—41no—
119C22⋊(C43⋊C8)—22no—
120(C2×D43)⋊C8—22no—
121C8×Dic43—22no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×Q8×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C2×M16×C43—22no—
127C2×M16×C43—22no—
128C2×M16×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C22⋊Q8×C43—22no—
132C22⋊Q8×C43C2×C414yescomplemented
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139#103×C43—22no—
140#103×C43—41no—
141#95×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C2×D412yes—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43C22⋊C414yes—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—42no—
170C22×Dic43—42no—
171C22×Dic43—81no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—81no—
182C2×C4×D43C22×C412yes—
183C2×C4×D43C2×D412yes—
184C2×Dic86—24no—
185C2×Dic86—42no—
186C2×Dic86—42no—
187M16×C43—44no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43#4112yes—
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×C43C22×C412yes—
201C22⋊C4×C43—24no—
202C22⋊C4×C43—42no—
203C22⋊Dic43—24no—
204C22⋊Dic43C22⋊C414yes—
205(C2×D43)⋊C4—24no—
206(C2×D43)⋊C4—24no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4C22⋊C414yes—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—24no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—42no—
216C4⋊Dic43C22×C412yes—
217C4⋊Dic43C22×C412yes—
218C4⋊Dic43#4112yes—
219Dic43⋊C4—24no—
220Dic43⋊C4—24no—
221Dic43⋊C4—42no—
222Dic43⋊C4—42no—
223Dic43⋊C4—81no—
224Dic43⋊C4C22⋊C414yes—
225C4×Dic43—24no—
226C4×Dic43—24no—
227C4×Dic43—24no—
228C4×Dic43—42no—
229C4×Dic43C22×C412yes—
230C4×Dic43C2×D412yes—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237#10621872—44no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43C2×C22⋊C412yes—
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—
253Q8×C43—22no—
254Q8×C43—22no—
255Q8×C43—41no—
256Q8×C43—41no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
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×C43C2×C22⋊C412yes—
276C2×C4×C43C23×C411yescharacteristic
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43H(5,𝔽2)11yescharacteristic
281C2×C4×C432−1+411yescharacteristic
282C22⋊D43—28no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—41no—
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—
303C2×Dic43AGL(1,ℤ/8)12yes—
304C2×Dic43#13712yes—
305C4×D43—22no—
306C4×D43—22no—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—84no—
310Dic86—48no—
311C8×C43—22no—
312C8×C43—41no—
313C43⋊C8—41no—
314C43⋊C8—41no—
315#22504—431nomaximal, Sylow
316C22×C43—22no—
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43C22×C22⋊C411yescharacteristic
324C22×C43#54611yescharacteristic
325C22×C43#54711yescharacteristic
326C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C43C2×#13711yescharacteristic
328C22×C43#57711yescharacteristic
329C22×C43#57811yescharacteristic
330C2×D43—22no—
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—41no—
334C2×D43—41no—
335C2×D43—41no—
336C2×D43—41no—
337C4×C43—22no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—81no—
341C4×C43—81no—
342C4×C43C4×#4111yescharacteristic
343C4×C43#52011yescharacteristic
344C4×C43#54611yescharacteristic
345C4×C43#54711yescharacteristic
346Dic43—22no—
347Dic43—22no—
348Dic43—42no—
349Dic43—42no—
350Dic43—42no—
351Dic43—81no—
352Dic43#41714yes—
353C2×#556—431no—
354C2×#436—431no—
355D4×C4⋊C4—431no—
356#1990—431no—
357#1988—431no—
358#1894—431no—
359#1894D4311yescharacteristic, complemented
360#1872—431no—
361#1872—431no—
362#1825—431no—
363#1825—431no—
364#1803—431no—
365C4×#103—431no—
366#1736—431no—
367#1736—431no—
368C2×C43—42no—
369C2×C43#233911yescharacteristic
370C2×C43C2×#41711yescharacteristic
371C2×C43#289811yescharacteristic
372C2×C43#332411yescharacteristic
373C2×C43#332811yescharacteristic
374C2×C43#335311yescharacteristic
375C2×C43#335611yescharacteristic
376D43—42no—
377C22×M16—431no—
378C22×M16C2×D4311yescharacteristic
379#556—438no—
380#556—864no—
381C2×C4⋊Q8—431no—
382C2×#126—861no—
383C2×#126—861no—
384C2×#124—861no—
385C2×C22⋊Q8—431no—
386C2×C22⋊Q8C2×D4311yescharacteristic
387C2×C4×Q8—431no—
388C2×C4×Q8—861no—
389C2×C4×D4—431no—
390C2×C4×D4—861no—
391C2×#117—431no—
392C2×#117—431no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4—431no—
395#436—864no—
396C2×C4⋊C8—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103C2×D4311yescharacteristic
400C2×#103C2×D4311yescharacteristic
401C2×C22⋊C8—431no—
402C2×C22⋊C8—431no—
403C2×C4×C8—431no—
404#389—861no—
405#385—861no—
406#385—861no—
407#384—431no—
408#380—431no—
409#380C2×D4311yescharacteristic
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#340—431no—
420#340—431no—
421#340C2×D4311yescharacteristic
422#340C2×D4311yescharacteristic
423C43#2250411yescharacteristic, complemented, Sylow
424C22×Q8—861no—
425C22×Q8C22×D4311yescharacteristic
426C22×D4—431no—
427C23×C4—431no—
428C23×C4—861no—
429C23×C4—861no—
430C23×C4C22×D4311yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C2×M16—862no—
435C2×M16—862no—
436C2×M16—1721no—
437C22×C8—431no—
438C22×C8—431no—
439C22×C8C22×D4311yescharacteristic
440C22×C8C22×D4311yescharacteristic
441C4⋊Q8—434no—
442C4⋊Q8—862no—
443#126—868no—
444#126—868no—
445#124—868no—
446C22⋊Q8—22no—
447C22⋊Q8—434no—
448C22⋊Q8—862no—
449C22⋊Q8C4×D4314yescomplemented
450C4×Q8—434no—
451C4×Q8—862no—
452C4×Q8—868no—
453C4×D4—434no—
454C4×D4—434no—
455C4×D4—1724no—
456#117—434no—
457#117—434no—
458#117—862no—
459#117—862no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—862no—
467C2×C4⋊C4—862no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—861no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—1721no—
476C2×C4⋊C4—1721no—
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
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×C42—431no—
489C2×C42—861no—
490C2×C42—861no—
491C2×C42—861no—
492C2×C42—861no—
493C4⋊C8—862no—
494#103—22no—
495#103—41no—
496#103—862no—
497#103—1721no—
498C22⋊C8—862no—
499C22⋊C8—862no—
500C4×C8—862no—
501#95—21no—
502#95—861no—
503#95—861no—
504C24—431no—
505C24D4×D4311yescharacteristic
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—864no—
512C2×Q8—1722no—
513C2×Q8—1722no—
514C2×Q8C2×C4×D4312yes—
515C2×D4—434no—
516C2×D4—862no—
517C2×D4—862no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—431no—
527C22×C4—431no—
528C22×C4—431no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—3441no—
540C22×C4—3441no—
541C22×C4—1722no—
542C22×C4—1722no—
543C22×C4—1722no—
544C22×C4—1722no—
545C22×C4C2×C4×D4312yes—
546C22×C4D4×D4311yescharacteristic
547C22×C4D4×D4312yes—
548C22×C4C23×D4311yescharacteristic
549M16—44no—
550M16—1724no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8#1062190012yes—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—434no—
570C4⋊C4—432no—
571C4⋊C4—432no—
572C4⋊C4—432no—
573C4⋊C4—864no—
574C4⋊C4—864no—
575C4⋊C4—864no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—3441no—
582C4⋊C4—1722no—
583C4⋊C4—1722no—
584C4⋊C4—1722no—
585C4⋊C4C2×C4×D4312yes—
586C22⋊C4—24no—
587C22⋊C4—42no—
588C22⋊C4—434no—
589C22⋊C4—434no—
590C22⋊C4—864no—
591C22⋊C4—864no—
592C22⋊C4—864no—
593C22⋊C4—1722no—
594C42—432no—
595C42—432no—
596C42—864no—
597C42—864no—
598C42—864no—
599C42—1722no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—432no—
607C23—861no—
608C23—861no—
609C23—861no—
610C23—861no—
611C23—861no—
612C23—861no—
613C23C22⋊C4×D4312yes—
614C23C2×D4×D4311yescharacteristic
615Q8—22no—
616Q8—22no—
617Q8—41no—
618Q8—41no—
619Q8—1728no—
620D4—868no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
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—41no—
639C2×C4—432no—
640C2×C4—432no—
641C2×C4—432no—
642C2×C4—432no—
643C2×C4—432no—
644C2×C4—861no—
645C2×C4—861no—
646C2×C4—861no—
647C2×C4—861no—
648C2×C4—862no—
649C2×C4—862no—
650C2×C4—862no—
651C2×C4—862no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—3444no—
656C2×C4—3444no—
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×C4—1721no—
666C2×C4C22⋊C4×D4312yes—
667C2×C4C22×C4×D4311yescharacteristic
668C2×C4C2×D4×D4311yescharacteristic
669C2×C4#41×D4311yescharacteristic
670C2×C4C2×#1062190011yescharacteristic
671C2×C4#1306337011yescharacteristic
672C2×C4#1306337211yescharacteristic
673C8—22no—
674C8—41no—
675C8—1721no—
676C8—1721no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—862no—
685C22—862no—
686C22—862no—
687C22—1721no—
688C22—1721no—
689C22—1721no—
690C22—1721no—
691C22C2×C22⋊C4×D4311yescharacteristic
692C22#1458353811yescharacteristic
693C22#1458354911yescharacteristic
694C22AGL(1,ℤ/8)×D4311yescharacteristic
695C22#137×D4311yescharacteristic
696C22#1458370811yescharacteristic
697C22#1458371511yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—81no—
702C4—81no—
703C4—434no—
704C4—862no—
705C4—862no—
706C4—3441no—
707C4—1722no—
708C4—1722no—
709C4—1722no—
710C4C4×#1062190011yescharacteristic
711C4#1458337811yescharacteristic
712C4#1458353611yescharacteristic
713C4#1458354711yescharacteristic
714C2—42no—
715C2—1722no—
716C2#1913742111yescharacteristic
717C2#417×D4311yescharacteristic
718C2#1914312711yescharacteristic
719C2#1914682111yescharacteristic
720C2#1914687311yescharacteristic
721C2#1914717411yescharacteristic
722C2#1914720511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1894C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1894D43
hypocenterC43#22504
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
4. #19135554C2semidirect
5. #19135545C2semidirect
6. #19135025C2semidirect
7. #19134903C2semidirect
8. #19134899C2semidirect
9. #19134689C2semidirect
10. #19134687C2semidirect
11. #19134598C2semidirect
12. #103×Dic43C2semidirect
13. #19134315C2semidirect
14. #19134313C2semidirect
15. C43×#1894C2semidirect
18. #14583620C4semidirect
73. #13063324C2×C4semidirect
78. #13063301C2×C4semidirect
80. Q8×Dic43C2×C4semidirect
86. #13063284C2×C4semidirect
88. #13063283C2×C4semidirect
132. C22⋊Q8×C43C2×C4semidirect
359. #1894D43semidirect
423. C43#22504semidirect
449. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836202
C2×#145829752
#191374912
#191355542
#191355452
#191350252
#191349032
#191348992
#191346892
#191346872
#191345982
#103×Dic432
#191343152
#191343132
C43×#18942
#2250443