Finite Group Databasebeta

← #25105692

Subgroups — #25105692

Order 11008.

1518 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583466C211yesmaximal, characteristic
2C2×#14582864C211yesmaximal, characteristic, complemented
3#19137184C211yesmaximal, characteristic, complemented
4#19135030C211yesmaximal, characteristic, complemented
5#19135030C211yesmaximal, characteristic, complemented
6#19135020C211yesmaximal, characteristic, complemented
7#19135020C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic, complemented
9#19134914C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134691C211yesmaximal, characteristic, complemented
13#19134687C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621872C2211yescharacteristic, complemented
18C22×C8×D43C2211yescharacteristic, complemented
19#14583466—24no—
20#14583466C418yescomplemented
21C2×#13063321—21no—
22C2×#13063312—21no—
23C2×#13063296C2211yescharacteristic
24C2×#13063296C2211yescharacteristic
25C2×#13063296C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×#13063294—21no—
28C2×#13063294—21no—
29C2×#13063284C2211yescharacteristic
30C2×#13063283C2211yescharacteristic, complemented
31C2×C4⋊C4×D43C2211yescharacteristic, complemented
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36#14582864—24no—
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
40#14582803—21no—
41#14582799—21no—
42#14582777—21no—
43#14582775—21no—
44#14582759C2211yescharacteristic
45#14582756C2211yescharacteristic, complemented
46#14582756C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582662C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55C23×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898C2×C414yes—
67C2×#10621898D414yes—
68C22×Dic86D411yescharacteristic
69C22×D172D411yescharacteristic
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43D411yescharacteristic
75C22×C22⋊D43D411yescharacteristic
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C2×#10621872—22no—
80C2×#10621872—41no—
81C2×#10621872—41no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C2×C8×D43—22no—
85C2×C8×D43—41no—
86C2×C8×D43—41no—
87#13063321—28no—
88#13063312—28no—
89#13063296—22no—
90#13063296—22no—
91#13063296—22no—
92#13063296—22no—
93#13063296C2×C414yes—
94#13063296C2×C414yes—
95#13063296C2×C414yescomplemented
96#13063296C2×C414yescomplemented
97#13063294—28no—
98#13063294—28no—
99#13063284—22no—
100#13063284C2×C414yescomplemented
101#13063283—41no—
102#13063283—41no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C4⋊C4×D43—41no—
109C4⋊C4×D43—41no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121#13063246—41no—
122#13063246—41no—
123#13063246—41no—
124#13063246—41no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C25×C43—21no—
132C22×D4×C43—21no—
133C22×D4×C43—22no—
134C22×D4×C43—41no—
135C22×D4×C43—41no—
136C22×D4×C43—41no—
137C22×D4×C43—41no—
138C22×D4×C43C2×C414yescomplemented
139C22×D4×C43C2311yescharacteristic
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#102×C43—41no—
148#102×C43—41no—
149#102×C43—41no—
150#102×C43—41no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—24no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43C2×D411yescharacteristic
163C23×D43C2×D411yescharacteristic
164C23×D43C2×D411yescharacteristic
165C2×D4×C43—24no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—44no—
177C2×D4×C43—44no—
178C2×D4×C43—44no—
179C2×D4×C43—44no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43C22×C412yes—
183C2×D4×C43C22×C412yes—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C22×C412yes—
191C22×C4×C43C2×D412yes—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C2×C22⋊D43—41no—
202C2×C22⋊D43—81no—
203C2×C22⋊D43—81no—
204C2×C22⋊D43—81no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43C22⋊C414yes—
211C2×C22⋊D43C22⋊C414yes—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218#10621898—44no—
219#10621898—44no—
220#10621898—44no—
221#10621898—44no—
222C2×D172—41no—
223C2×D172—41no—
224C2×D172C22⋊C414yes—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—42no—
234C2×C4×D43—81no—
235C2×C4×D43—81no—
236C2×C4×D43C22×C412yes—
237C2×C4×D43C22×C412yes—
238C2×C4×D43C2×D412yes—
239C2×C4×D43C2×D412yes—
240C2×Dic86—41no—
241C2×Dic86—41no—
242C2×Dic86C22⋊C414yes—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C22⋊C4×C43—81no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43—81no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—81no—
262(C2×D43)⋊C4—81no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43C22×C412yes—
270C4⋊Dic43C22×C412yes—
271Dic43⋊C4—42no—
272C4×Dic43—24no—
273C4×Dic43—42no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280#10621872—44no—
281C8×D43—44no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—48no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43—84no—
307C23×C43—84no—
308C23×C43—84no—
309C23×C43C2×C22⋊C412yes—
310C23×C43C22×D411yescharacteristic
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43—21no—
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—21no—
322C22×D43—21no—
323C22×D43C2×C22⋊C412yes—
324C22×D43C2×C22⋊C412yes—
325D4×C43—22no—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—22no—
329D4×C43—48no—
330D4×C43—41no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—41no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43C2×C22⋊C412yes—
347C2×C4×C43C23×C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C2×C4×C43H(5,𝔽2)11yescharacteristic
352C2×C4×C43H(5,𝔽2)11yescharacteristic
353C22⋊D43—44no—
354C22⋊D43—44no—
355C22⋊D43—84no—
356C22⋊D43—84no—
357C22⋊D43—84no—
358C22⋊D43—84no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43C2×C22⋊C412yes—
376C2×Dic43C2×C22⋊C412yes—
377D172—44no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—84no—
387Dic86—44no—
388C8×C43—41no—
389C8×C43—41no—
390C43⋊C8—41no—
391C43⋊C8—41no—
392#21770—431nomaximal, Sylow
393C22×C43—22no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—816no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43C22×C22⋊C411yescharacteristic
416C22×C43#53411yescharacteristic
417C22×C43#53411yescharacteristic
418C22×C43#57611yescharacteristic
419C22×C43#57611yescharacteristic
420C22×C43#57711yescharacteristic
421C22×C43#57711yescharacteristic
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—22no—
428C2×D43—41no—
429C2×D43—41no—
430C2×D43—41no—
431C2×D43—41no—
432C2×D43—41no—
433C2×D43—41no—
434C2×D43—41no—
435C2×D43—41no—
436C4×C43—22no—
437C4×C43—81no—
438C4×C43—81no—
439C4×C43#51811yescharacteristic
440C4×C43#51811yescharacteristic
441C4×C43#53411yescharacteristic
442C4×C43#53411yescharacteristic
443Dic43—22no—
444Dic43—22no—
445Dic43—42no—
446Dic43—42no—
447Dic43—81no—
448Dic43—81no—
449C2×#535—431no—
450C2×#408—431no—
451#2311—431no—
452#1895—431no—
453#1895—431no—
454#1893—431no—
455#1893—431no—
456#1875—431no—
457#1875—431no—
458#1874—431no—
459#1874—431no—
460#1825—431no—
461#1825—431no—
462#1786—431no—
463#1786D4311yescharacteristic, complemented
464C2×C43—42no—
465C2×C43—82no—
466C2×C43—82no—
467C2×C43#230811yescharacteristic
468C2×C43#289711yescharacteristic
469C2×C43#289711yescharacteristic
470C2×C43#319811yescharacteristic
471C2×C43#319811yescharacteristic
472C2×C43#319911yescharacteristic
473C2×C43#320011yescharacteristic
474D43—42no—
475D43—42no—
476C22×#41—431no—
477C23×D4C2×D4311yescharacteristic
478C22×M16—431no—
479C23×C8—431no—
480#535—438no—
481#535—864no—
482C2×#127—861no—
483C2×#124—861no—
484C2×#121—431no—
485C2×#121—431no—
486C2×#121—431no—
487C2×#121—431no—
488C2×#120—861no—
489C2×#120—861no—
490C2×#117—431no—
491C2×#117—431no—
492C22×C4⋊C4—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—431no—
497C2×#102C2×D4311yescharacteristic
498C2×#102C2×D4311yescharacteristic
499C2×#102C2×D4311yescharacteristic
500C2×#102C2×D4311yescharacteristic
501#408—864no—
502C2×C22⋊C8—431no—
503C2×C22⋊C8—431no—
504C2×C22⋊C8—431no—
505C2×C22⋊C8C2×D4311yescharacteristic
506#391—861no—
507#390—861no—
508#386—861no—
509#386—861no—
510#380—431no—
511#380—431no—
512#380—431no—
513#380C2×D4311yescharacteristic
514#340—431no—
515#340—431no—
516#340—431no—
517#340—431no—
518#340—431no—
519#340—431no—
520#340—431no—
521#340—431no—
522C43#2177011yescharacteristic, complemented, Sylow
523C25—21no—
524C2×#41—434no—
525C2×#41—434no—
526C2×#41—1721no—
527C2×#41—1721no—
528C2×#41—1721no—
529C2×#41—1721no—
530C22×Q8—431no—
531C22×D4—21no—
532C22×D4—22no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—431no—
538C22×D4—431no—
539C22×D4—431no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4C4×D4314yescomplemented
545C22×D4C22×D4311yescharacteristic
546C22×D4C22×D4311yescharacteristic
547C23×C4—431no—
548C23×C4—431no—
549C23×C4—861no—
550C23×C4C22×D4311yescharacteristic
551C2×M16—862no—
552C2×M16—1721no—
553C2×M16—1721no—
554C22×C8—431no—
555C22×C8—431no—
556C22×C8—862no—
557C22×C8—1721no—
558C22×C8—1721no—
559C22×C8C22×D4311yescharacteristic
560C22×C8C22×D4311yescharacteristic
561#127—868no—
562#124—868no—
563#121—434no—
564#121—434no—
565#121—434no—
566#121—434no—
567#121—862no—
568#121—862no—
569#121—862no—
570#121—862no—
571#120—868no—
572#120—868no—
573#117—434no—
574#117—862no—
575#117—1721no—
576#117—1721no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—431no—
579C2×C4⋊C4—431no—
580C2×C4⋊C4—431no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—1721no—
583C2×C4⋊C4—1721no—
584C2×C4⋊C4C22×D4311yescharacteristic
585C2×C4⋊C4C22×D4311yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C22⋊C4—861no—
595C2×C22⋊C4—861no—
596C2×C42—861no—
597C2×C42—861no—
598#102—41no—
599#102—41no—
600#102—41no—
601#102—41no—
602#102—1721no—
603#102—1721no—
604#102—1721no—
605#102—1721no—
606C22⋊C8—22no—
607C22⋊C8—862no—
608C22⋊C8—862no—
609C22⋊C8—862no—
610#95—21no—
611#95—861no—
612#95—861no—
613#95—861no—
614C24—21no—
615C24—21no—
616C24—24no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24—81no—
622C24—81no—
623C24—431no—
624C24—431no—
625C24D4×D4311yescharacteristic
626#41—1724no—
627#41—1724no—
628#41—1724no—
629#41—1724no—
630C2×Q8—434no—
631C2×Q8—1721no—
632C2×Q8—1721no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—434no—
651C2×D4—434no—
652C2×D4—434no—
653C2×D4—864no—
654C2×D4—864no—
655C2×D4—864no—
656C2×D4—864no—
657C2×D4—3441no—
658C2×D4—3441no—
659C2×D4—3441no—
660C2×D4—3441no—
661C2×D4—3441no—
662C2×D4—3441no—
663C2×D4—3441no—
664C2×D4—3441no—
665C2×D4—1721no—
666C2×D4—1721no—
667C2×D4—1721no—
668C2×D4—1721no—
669C2×D4—1721no—
670C2×D4—1721no—
671C2×D4C2×C4×D4312yes—
672C2×D4C2×C4×D4312yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—432no—
682C22×C4—432no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—3441no—
698C22×C4—3441no—
699C22×C4—1722no—
700C22×C4C2×C4×D4312yes—
701C22×C4D4×D4311yescharacteristic
702C22×C4D4×D4312yes—
703C22×C4C23×D4311yescharacteristic
704M16—1724no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—861no—
714C2×C8—861no—
715C2×C8—861no—
716C2×C8—861no—
717C2×C8—1724no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—432no—
723C4⋊C4—432no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—1722no—
731C22⋊C4—81no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—3441no—
738C22⋊C4—3441no—
739C22⋊C4—3441no—
740C22⋊C4—1722no—
741C42—864no—
742C42—1722no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—22no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—432no—
771C23—432no—
772C23—861no—
773C23—861no—
774C23—861no—
775C23—861no—
776C23—861no—
777C23—861no—
778C23—861no—
779C23—861no—
780C23—861no—
781C23—861no—
782C23—861no—
783C23—861no—
784C23C22⋊C4×D4312yes—
785C23C2×D4×D4311yescharacteristic
786Q8—1724no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—1724no—
801D4—1724no—
802D4—1724no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—432no—
816C2×C4—432no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—862no—
831C2×C4—3444no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4C22⋊C4×D4312yes—
843C2×C4C22×C4×D4311yescharacteristic
844C2×C4C2×D4×D4311yescharacteristic
845C2×C4#1306337011yescharacteristic
846C2×C4#1306337011yescharacteristic
847C2×C4#1306337011yescharacteristic
848C2×C4#1306337011yescharacteristic
849C8—41no—
850C8—41no—
851C8—1721no—
852C8—1721no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—816no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—862no—
876C22—862no—
877C22—862no—
878C22—862no—
879C22—862no—
880C22—862no—
881C22—1721no—
882C22—1721no—
883C22—1721no—
884C22—1721no—
885C22—1721no—
886C22—1721no—
887C22—1721no—
888C22—1721no—
889C22C2×C22⋊C4×D4311yescharacteristic
890C22#1458345911yescharacteristic
891C22#1458345911yescharacteristic
892C22#1458370011yescharacteristic
893C22#1458370311yescharacteristic
894C22#1458370511yescharacteristic
895C22#1458370911yescharacteristic
896C4—22no—
897C4—81no—
898C4—81no—
899C4—862no—
900C4—862no—
901C4—3441no—
902C4—3441no—
903C4—1722no—
904C4—1722no—
905C4#1458337211yescharacteristic
906C4#1458337211yescharacteristic
907C4#1458345911yescharacteristic
908C4#1458345911yescharacteristic
909C2—42no—
910C2—82no—
911C2—82no—
912C2—1722no—
913C2—1722no—
914C2#1913717111yescharacteristic
915C2#1914311611yescharacteristic
916C2#1914312011yescharacteristic
917C2#1914544311yescharacteristic
918C2#1914545111yescharacteristic
919C2#1914545811yescharacteristic
920C2#1914546411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583466C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#21770
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14582864C2semidirect
3. #19137184C2semidirect
4. #19135030C2semidirect
5. #19135030C2semidirect
6. #19135020C2semidirect
7. #19135020C2semidirect
8. #19134914C2semidirect
9. #19134914C2semidirect
10. #19134909C2semidirect
11. #19134909C2semidirect
12. #19134691C2semidirect
13. #19134687C2semidirect
14. #19134526C2semidirect
15. C43×#1786C2semidirect
17. C22×#10621872C22semidirect
18. C22×C8×D43C22semidirect
20. #14583466C4semidirect
30. C2×#13063283C22semidirect
31. C2×C4⋊C4×D43C22semidirect
38. C2×(C2×D43)⋊C8C22semidirect
39. C2×(C2×D43)⋊C8C22semidirect
45. #14582756C22semidirect
46. #14582756C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582662C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
95. #13063296C2×C4semidirect
96. #13063296C2×C4semidirect
100. #13063284C2×C4semidirect
138. C22×D4×C43C2×C4semidirect
463. #1786D43semidirect
522. C43#21770semidirect
544. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834662
C2×#145828642
#191371842
#191350302
#191350202
#191349142
#191349092
#191346912
#191346872
#191345262
C43×#17862
#2177043