Finite Group Databasebeta

← #25112976

Subgroups — #25112976

Order 11008.

1174 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×#14583604C211yesmaximal, characteristic
2C2×#14582968C211yesmaximal, characteristic
3#19137525C211yesmaximal, characteristic
4#19135566C211yesmaximal, characteristic, complemented
5#19135545C211yesmaximal, characteristic, complemented
6#19135028C211yesmaximal, characteristic, complemented
7#19135017C211yesmaximal, characteristic, complemented
8#19134907C211yesmaximal, characteristic, complemented
9#19134901C211yesmaximal, characteristic, complemented
10#19134684C211yesmaximal, characteristic, complemented
11#19134681C211yesmaximal, characteristic, complemented
12#19134609C211yesmaximal, characteristic, complemented
13#19134424C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×C8×D43C2211yescharacteristic
17#14583604—24no—
18#14583604C418yescomplemented
19C2×#13063324C2211yescharacteristic
20C2×#13063315—21no—
21C2×#13063305C2211yescharacteristic
22C2×#13063304—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063303—21no—
25C2×#13063290C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×C4⋊C4×D43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14582968—24no—
31C2×Dic43⋊C8C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic
39#14582793—21no—
40#14582783—21no—
41#14582775—21no—
42#14582764C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×(C2×D43)⋊C4—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C2×#117×C43C2211yescharacteristic
57C22×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86C2311yescharacteristic
64C22×C22⋊D43D411yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C8×D43—22no—
71C2×C8×D43—22no—
72C2×C8×D43—41no—
73#13063324—22no—
74#13063324C2×C414yescomplemented
75#13063315—28no—
76#13063305—22no—
77#13063305C2×C414yes—
78#13063304—22no—
79#13063304—28no—
80#13063304C2×C414yescomplemented
81#13063303—28no—
82#13063290—22no—
83#13063290C2×C414yescomplemented
84C4×C22⋊D43—28no—
85C4×C22⋊D43C2×C414yes—
86C4×C22⋊D43D414yes—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4D411yescharacteristic
97C4⋊C4×D43—22no—
98C4⋊C4×D43—22no—
99C4⋊C4×D43—41no—
100C4⋊C4×D43C2×C414yes—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110Dic43⋊C8—22no—
111#13063250—22no—
112#13063250—41no—
113#13063248—22no—
114#13063248—41no—
115C22⋊(C43⋊C8)—22no—
116(C2×D43)⋊C8—22no—
117#13063235—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C23×C4×C43—21no—
124C23×C4×C43C2311yescharacteristic
125C2×M16×C43—22no—
126C2×M16×C43—22no—
127C2×M16×C43—41no—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#117×C43—22no—
131#117×C43—41no—
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C414yescomplemented
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43—21no—
140C2×C42×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43C2×D411yescharacteristic
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—81no—
153C22×C4×C43—81no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43C22⋊C414yes—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—24no—
173C2×C4×D43—42no—
174C2×C4×D43—42no—
175C2×C4×D43—81no—
176C2×C4×D43—81no—
177C2×C4×D43—81no—
178C2×C4×D43C22×C412yes—
179C2×C4×D43C2×D412yes—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—24no—
186C2×Dic86—81no—
187C2×Dic86—81no—
188C2×Dic86C22×C412yes—
189M16×C43—44no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43#4112yes—
196C4⋊C4×C43—24no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C22×C412yes—
203C4⋊C4×C43C22×C412yes—
204C4⋊C4×C43#4112yes—
205C22⋊C4×C43—42no—
206C42×C43—42no—
207C22⋊Dic43—24no—
208C22⋊Dic43—81no—
209C22⋊Dic43C22⋊C414yes—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4C22⋊C414yes—
213C4⋊Dic43—21no—
214C4⋊Dic43—24no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22×C412yes—
220Dic43⋊C4—24no—
221Dic43⋊C4—24no—
222Dic43⋊C4—24no—
223Dic43⋊C4—24no—
224Dic43⋊C4—42no—
225Dic43⋊C4C22⋊C414yes—
226C4×Dic43—24no—
227C4×Dic43—81no—
228C4×Dic43C22×C412yes—
229C4×Dic43C2×D412yes—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C8×D43—44no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43C2×C22⋊C412yes—
244C23×C43C22×D411yescharacteristic
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43C2×C22⋊C412yes—
250C22×D43#13712yes—
251C22×D43#13712yes—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—22no—
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×C43—41no—
270C2×C4×C43—84no—
271C2×C4×C43C2×C22⋊C412yes—
272C2×C4×C43C23×C411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43H(5,𝔽2)11yescharacteristic
277C2×C4×C432−1+411yescharacteristic
278C22⋊D43—28no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43C2×C22⋊C412yes—
298C2×Dic43C2×C22⋊C412yes—
299C2×Dic43C2×C22⋊C412yes—
300C4×D43—22no—
301C4×D43—22no—
302C4×D43—22no—
303C4×D43—22no—
304C4×D43—84no—
305C4×D43—84no—
306Dic86—22no—
307Dic86—22no—
308Dic86—41no—
309Dic86—41no—
310Dic86—84no—
311C8×C43—22no—
312C8×C43—41no—
313C43⋊C8—41no—
314C43⋊C8—41no—
315#22497—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×#13711yescharacteristic
327C22×C43C2×#13711yescharacteristic
328C22×C43#57611yescharacteristic
329C22×C43#57711yescharacteristic
330C2×D43—22no—
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—22no—
335C2×D43—22no—
336C2×D43#41914yes—
337C4×C43—22no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43—81no—
342C4×C43C4×#4111yescharacteristic
343C4×C43#52011yescharacteristic
344C4×C43#54611yescharacteristic
345C4×C43#54711yescharacteristic
346Dic43—22no—
347Dic43—22no—
348Dic43—22no—
349Dic43—42no—
350Dic43—42no—
351Dic43—81no—
352Dic43—81no—
353C2×#554—431no—
354C2×#435—431no—
355#2352—431no—
356#1993—431no—
357#1988—431no—
358#1894—431no—
359#1892—431no—
360#1873—431no—
361#1872—431no—
362#1824—431no—
363#1823—431no—
364#1805—431no—
365#1763—431no—
366#1736D4311yescharacteristic, complemented
367C2×#340—431no—
368C2×C43—42no—
369C2×C43#233911yescharacteristic
370C2×C43C2×#41911yescharacteristic
371C2×C43#289711yescharacteristic
372C2×C43#331411yescharacteristic
373C2×C43#331611yescharacteristic
374C2×C43#334411yescharacteristic
375C2×C43#334611yescharacteristic
376D43—24no—
377C22×M16C2×D4311yescharacteristic
378C23×C8—431no—
379#554—438no—
380#554—864no—
381C2×C4⋊Q8—431no—
382C2×#125—861no—
383C2×C22⋊Q8—431no—
384C2×C22⋊Q8—431no—
385C2×C22⋊Q8—861no—
386C2×C22⋊Q8—861no—
387C2×C4×Q8—431no—
388C2×C4×D4—431no—
389C2×C4×D4—861no—
390C2×#117C2×D4311yescharacteristic
391C22×C4⋊C4—431no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4C2×D4311yescharacteristic
394#435—864no—
395C2×C4⋊C8—431no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#103—431no—
399C2×#103—431no—
400C2×C22⋊C8—431no—
401C2×C22⋊C8—431no—
402C2×#97—431no—
403#388—861no—
404#387—861no—
405#386—861no—
406#382—431no—
407#380—431no—
408#380—431no—
409C4×C4⋊C4—431no—
410C4×C22⋊C4—861no—
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#2249711yescharacteristic, complemented, Sylow
424C22×Q8—431no—
425C22×Q8—861no—
426C22×D4—431no—
427C23×C4—21no—
428C23×C4—431no—
429C23×C4—861no—
430C23×C4—861no—
431C23×C4C22×D4311yescharacteristic
432C2×M16—22no—
433C2×M16—22no—
434C2×M16—41no—
435C22×C8—431no—
436C22×C8—431no—
437C22×C8—862no—
438C22×C8—862no—
439C22×C8—1721no—
440C22×C8C22×D4311yescharacteristic
441C22×C8C22×D4311yescharacteristic
442C4⋊Q8—434no—
443C4⋊Q8—862no—
444#125—868no—
445C22⋊Q8—434no—
446C22⋊Q8—434no—
447C22⋊Q8—868no—
448C22⋊Q8—868no—
449C22⋊Q8—862no—
450C22⋊Q8—862no—
451C4×Q8—434no—
452C4×Q8—862no—
453C4×D4—434no—
454C4×D4—434no—
455C4×D4—868no—
456#117—22no—
457#117—41no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—434no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—862no—
466C2×C4⋊C4—861no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4—861no—
471C2×C4⋊C4—862no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4—1721no—
474C2×C4⋊C4C4×D4314yescomplemented
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—431no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—21no—
487C2×C42—431no—
488C2×C42—861no—
489C2×C42—861no—
490C4⋊C8—862no—
491#103—862no—
492#103—862no—
493#103—1721no—
494#103—1721no—
495C22⋊C8—862no—
496C22⋊C8—862no—
497#97—862no—
498#95—861no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503C24—431no—
504C24D4×D4311yescharacteristic
505C2×Q8—432no—
506C2×Q8—864no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—3441no—
513C2×Q8—3441no—
514C2×D4—434no—
515C2×D4—862no—
516C2×D4—862no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—431no—
529C22×C4—431no—
530C22×C4—431no—
531C22×C4—432no—
532C22×C4—432no—
533C22×C4—864no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—3441no—
543C22×C4—3441no—
544C22×C4—3441no—
545C22×C4—1722no—
546C22×C4—1722no—
547C22×C4C2×C4×D4312yes—
548C22×C4D4×D4311yescharacteristic
549C22×C4D4×D4312yes—
550C22×C4C23×D4311yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—1724no—
564C2×C8#1062189812yes—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—434no—
572C4⋊C4—432no—
573C4⋊C4—864no—
574C4⋊C4—864no—
575C4⋊C4—864no—
576C4⋊C4—864no—
577C4⋊C4—864no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—1722no—
584C4⋊C4C2×C4×D4312yes—
585C4⋊C4C2×C4×D4312yes—
586C4⋊C4#1062189812yes—
587C22⋊C4—42no—
588C22⋊C4—434no—
589C22⋊C4—434no—
590C22⋊C4—864no—
591C22⋊C4—864no—
592C22⋊C4—3441no—
593C22⋊C4—1722no—
594C42—42no—
595C42—432no—
596C42—432no—
597C42—864no—
598C42—3441no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—432no—
606C23—432no—
607C23—432no—
608C23—861no—
609C23—861no—
610C23—861no—
611C23—861no—
612C23C22⋊C4×D4312yes—
613C23C2×D4×D4311yescharacteristic
614Q8—862no—
615Q8—862no—
616Q8—3444no—
617Q8—1721no—
618Q8—1721no—
619D4—868no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
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—84no—
639C2×C4—432no—
640C2×C4—432no—
641C2×C4—432no—
642C2×C4—861no—
643C2×C4—861no—
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—3444no—
655C2×C4—3444no—
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×C4—1721no—
666C2×C4C22⋊C4×D4312yes—
667C2×C4C22×C4×D4311yescharacteristic
668C2×C4C2×D4×D4311yescharacteristic
669C2×C4C2×#1062189811yescharacteristic
670C2×C4C2×#1062189811yescharacteristic
671C2×C4#1306337011yescharacteristic
672C2×C4#1306337311yescharacteristic
673C8—22no—
674C8—41no—
675C8—1721no—
676C8—1721no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—434no—
685C22—862no—
686C22—862no—
687C22—862no—
688C22—862no—
689C22—862no—
690C22—862no—
691C22C2×C22⋊C4×D4311yescharacteristic
692C22#1458353911yescharacteristic
693C22#1458355011yescharacteristic
694C22#137×D4311yescharacteristic
695C22#137×D4311yescharacteristic
696C22#1458370311yescharacteristic
697C22#1458370911yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—81no—
703C4—862no—
704C4—862no—
705C4—862no—
706C4—3441no—
707C4—3441no—
708C4—1722no—
709C4—1722no—
710C4C4×#1062189811yescharacteristic
711C4#1458338011yescharacteristic
712C4#1458353911yescharacteristic
713C4#1458355011yescharacteristic
714C2—42no—
715C2—864no—
716C2#1913742211yescharacteristic
717C2#419×D4311yescharacteristic
718C2#1914312011yescharacteristic
719C2#1914667711yescharacteristic
720C2#1914670711yescharacteristic
721C2#1914705111yescharacteristic
722C2#1914708111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#22497
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #19135566C2semidirect
5. #19135545C2semidirect
6. #19135028C2semidirect
7. #19135017C2semidirect
8. #19134907C2semidirect
9. #19134901C2semidirect
10. #19134684C2semidirect
11. #19134681C2semidirect
12. #19134609C2semidirect
13. #19134424C2semidirect
14. #340×D43C2semidirect
15. C43×#1736C2semidirect
18. #14583604C4semidirect
74. #13063324C2×C4semidirect
80. #13063304C2×C4semidirect
83. #13063290C2×C4semidirect
134. C2×C4⋊C4×C43C2×C4semidirect
366. #1736D43semidirect
423. C43#22497semidirect
474. 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×#145836042
C2×#145829682
#191375252
#191355662
#191355452
#191350282
#191350172
#191349072
#191349012
#191346842
#191346812
#191346092
#191344242
#340×D432
C43×#17362
#2249743