Finite Group Databasebeta

← #25112010

Subgroups — #25112010

Order 11008.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583543C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4#19137520C211yesmaximal, characteristic, complemented
5#19135526C211yesmaximal, characteristic, complemented
6#19135405C211yesmaximal, characteristic, complemented
7#19135020C211yesmaximal, characteristic, complemented
8#19135018C211yesmaximal, characteristic, complemented
9#19134914C211yesmaximal, characteristic, complemented
10#19134902C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134532C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C22×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic, complemented
18#14583543—24no—
19#14583543C418yescomplemented
20C2×#13063312C2211yescharacteristic
21C2×#13063306—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063297—21no—
24C2×#13063296C2211yescharacteristic
25C2×#13063294—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic, complemented
29C22×C22⋊Dic43—21no—
30C8×C22⋊D43—24no—
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32#14582892—24no—
33C2×#13063250C2211yescharacteristic, complemented
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063248C2211yescharacteristic, complemented
36C2×#13063248C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
43C2×C8×Dic43C2211yescharacteristic, complemented
44#14582789—21no—
45#14582780—21no—
46#14582778—21no—
47#14582764C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic
49#14582756C2211yescharacteristic, complemented
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×C22⋊Dic43—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C23×D4×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic
59C2×#102×C43—24no—
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900—41no—
68C2×#10621900—41no—
69C2×#10621900C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43D411yescharacteristic
74C23×Dic43—21no—
75C23×Dic43—21no—
76C22×C4×D43C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—41no—
82#13063312—22no—
83#13063312C2×C414yescomplemented
84#13063306—28no—
85#13063304—22no—
86#13063304C2×C414yes—
87#13063297—28no—
88#13063296—22no—
89#13063296C2×C414yescomplemented
90#13063294—28no—
91D4×Dic43—22no—
92D4×Dic43C2×C414yescomplemented
93C4×C22⋊D43C2×C414yes—
94C4×C22⋊D43D414yes—
95#13063283—22no—
96#13063283—41no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—28no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116Dic43⋊C8—22no—
117#13063250—22no—
118#13063250—41no—
119#13063248—22no—
120#13063248—41no—
121#13063246—22no—
122#13063246—22no—
123#13063246—41no—
124#13063246—41no—
125C22⋊(C43⋊C8)—22no—
126(C2×D43)⋊C8—22no—
127C8×Dic43—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C25×C43—21no—
134C22×D4×C43—22no—
135C22×D4×C43—22no—
136C22×D4×C43—21no—
137C22×D4×C43—22no—
138C22×D4×C43—41no—
139C22×D4×C43—41no—
140C22×D4×C43C2×C414yes—
141C22×D4×C43C2311yescharacteristic
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C23×C4×C43C2311yescharacteristic
145C22×C8×C43—22no—
146C22×C8×C43—22no—
147C22×C8×C43—41no—
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C2×C4⋊C4×C43—22no—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43—41no—
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155#102×C43—22no—
156#102×C43—22no—
157#102×C43—22no—
158#102×C43D414yescomplemented
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—24no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—42no—
165C24×C43—42no—
166C24×C43—81no—
167C24×C43—81no—
168C24×C43C2×D411yescharacteristic
169C23×D43C2×D411yescharacteristic
170C2×D4×C43—24no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—28no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43—44no—
183C2×D4×C43—44no—
184C2×D4×C43—44no—
185C2×D4×C43C22×C412yes—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43—81no—
198C22×C4×C43C22×C412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43C22⋊C414yes—
211C22×Dic43—24no—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—42no—
218C22×Dic43—42no—
219C22×Dic43—81no—
220C22×Dic43—81no—
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224#10621900—28no—
225#10621900—44no—
226#10621900—44no—
227#10621900—44no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43C22×C412yes—
233C2×C4×D43C2×D412yes—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—44no—
246C2×C8×C43C2×D412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—42no—
251C4⋊C4×C43C2×D412yes—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—24no—
257C22⋊Dic43—42no—
258C22⋊Dic43C22⋊C414yes—
259(C2×D43)⋊C4—42no—
260(C2×D43)⋊C4—81no—
261(C2×D43)⋊C4C22⋊C414yes—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43C22×C412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4C22⋊C414yes—
270C4×Dic43—42no—
271C4×Dic43—81no—
272C4×Dic43C22×C412yes—
273C4×Dic43C2×D412yes—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C8×D43—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43—48no—
290C23×C43—41no—
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—48no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43C2×C22⋊C412yes—
307C23×C43#13512yes—
308C23×C43#13512yes—
309C23×C43C22×D411yescharacteristic
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—21no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43—21no—
316C22×D43C2×C22⋊C412yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43C4×D414yes—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—84no—
339C2×C4×C43C2×C22⋊C412yes—
340C2×C4×C43C23×C411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C2×#4111yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C22⋊D43—28no—
347C22⋊D43—48no—
348C22⋊D43—84no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—48no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—84no—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43C2×C22⋊C412yes—
371C2×Dic43C2×C22⋊C412yes—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22414—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—24no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—816no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43#41614yescomplemented
407C22×C43C22×C22⋊C411yescharacteristic
408C22×C43D4211yescharacteristic
409C22×C43#54611yescharacteristic
410C22×C43C2×#13511yescharacteristic
411C22×C43C2×#13511yescharacteristic
412C22×C43#57611yescharacteristic
413C22×C43#57711yescharacteristic
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—81no—
424C4×C43C2×C4×D411yescharacteristic
425C4×C43#51811yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—22no—
429Dic43—22no—
430Dic43—22no—
431Dic43—42no—
432Dic43—42no—
433Dic43—81no—
434Dic43—81no—
435C2×#546—431no—
436C2×C8×D4—431no—
437C2×#416—431no—
438C22×#102D4311yescharacteristic, complemented
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1893—431no—
443#1892—431no—
444#1875—431no—
445#1872—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—24no—
451C2×C43—44no—
452C2×C43—82no—
453C2×C43D4×C22⋊C411yescharacteristic
454C2×C43C2×#41611yescharacteristic
455C2×C43#289711yescharacteristic
456C2×C43#328011yescharacteristic
457C2×C43#328211yescharacteristic
458C2×C43#329611yescharacteristic
459C2×C43#329711yescharacteristic
460D43—42no—
461C22×#41—431no—
462C23×D4C2×D4311yescharacteristic
463C23×C8—431no—
464C23×C8C2×D4311yescharacteristic
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—431no—
471C2×#121—861no—
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4C2×D4311yescharacteristic
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#102—24no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102C2×D4311yescharacteristic
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8—431no—
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380—431no—
503C4×C4⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340—431no—
508#340—431no—
509C43#2241411yescharacteristic, complemented, Sylow
510C25—21no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—431no—
525C22×D4—861no—
526C22×D4—861no—
527C22×D4C4×D4314yes—
528C22×D4C22×D4311yescharacteristic
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8—431no—
539C22×C8—431no—
540C22×C8—862no—
541C22×C8—862no—
542C22×C8—1721no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—434no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—431no—
582C2×C42—861no—
583C2×C42—861no—
584C4⋊C8—862no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—862no—
593#102—862no—
594#102—1721no—
595#102—1721no—
596#102C22⋊D4314yescomplemented
597C22⋊C8—862no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—861no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24—431no—
615C24D4×D4311yescharacteristic
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—432no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—434no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—864no—
645C2×D4—864no—
646C2×D4—3441no—
647C2×D4—3441no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4C2×C4×D4312yes—
651C2×D4C2×C4×D4312yes—
652C2×D4#1062189812yes—
653C2×D4C2×C22⋊D4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—81no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—864no—
669C22×C4—864no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—3441no—
679C22×C4—3441no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4C2×C4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4312yes—
685C22×C4C23×D4311yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8C2×C22⋊D4312yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—42no—
704C4⋊C4—434no—
705C4⋊C4—432no—
706C4⋊C4—864no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4C2×C22⋊D4312yes—
713C22⋊C4—434no—
714C22⋊C4—434no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—3441no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—432no—
724C42—432no—
725C42—3441no—
726C42—1722no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—48no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—48no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—432no—
753C23—861no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—861no—
759C23C22⋊C4×D4312yes—
760C23#1306334412yes—
761C23#1306334612yes—
762C23C2×D4×D4311yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—868no—
776D4—3444no—
777D4—1728no—
778D4C4×C22⋊D4314yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—84no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—432no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—3444no—
808C2×C4—1728no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C22×C22⋊D4311yescharacteristic
823C2×C4C2×#1062189811yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337011yescharacteristic
826C8—22no—
827C8—41no—
828C8—1721no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—24no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—816no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—1721no—
855C22—1721no—
856C22—1721no—
857C22—1721no—
858C22#1458289214yescomplemented
859C22C2×C22⋊C4×D4311yescharacteristic
860C22D4×C22⋊D4311yescharacteristic
861C22#1458353911yescharacteristic
862C22C2×#1306334411yescharacteristic
863C22C2×#1306334611yescharacteristic
864C22#1458370011yescharacteristic
865C22#1458370511yescharacteristic
866C4—22no—
867C4—42no—
868C4—81no—
869C4—862no—
870C4—862no—
871C4—862no—
872C4—3441no—
873C4—3441no—
874C4—1722no—
875C4—1722no—
876C4C2×C4×C22⋊D4311yescharacteristic
877C4#1458337211yescharacteristic
878C4D4×C22⋊D4311yescharacteristic
879C4#1458353911yescharacteristic
880C2—24no—
881C2—44no—
882C2—82no—
883C2—1722no—
884C2C22⋊C4×C22⋊D4311yescharacteristic
885C2C2×#1458289211yescharacteristic
886C2#1914311611yescharacteristic
887C2#1914628011yescharacteristic
888C2#1914630211yescharacteristic
889C2#1914642611yescharacteristic
890C2#1914644111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
cosocleC22×C4×C43C24
hypercenterC22×#102D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D43C2semidirect
3. C2×#14582892C2semidirect
4. #19137520C2semidirect
5. #19135526C2semidirect
6. #19135405C2semidirect
7. #19135020C2semidirect
8. #19135018C2semidirect
9. #19134914C2semidirect
10. #19134902C2semidirect
11. #19134603C2semidirect
12. #19134532C2semidirect
13. #19134526C2semidirect
14. #102×Dic43C2semidirect
15. C22×#102×C43C2semidirect
17. C22×C8×D43C22semidirect
19. #14583543C4semidirect
28. C2×#13063283C22semidirect
31. C2×Dic43⋊C8C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063248C22semidirect
42. C2×(C2×D43)⋊C8C22semidirect
43. C2×C8×Dic43C22semidirect
47. #14582764C22semidirect
49. #14582756C22semidirect
50. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
69. C2×#10621900C2×C4semidirect
83. #13063312C2×C4semidirect
89. #13063296C2×C4semidirect
92. D4×Dic43C2×C4semidirect
158. #102×C43D4semidirect
406. C22×C43#416semidirect
438. C22×#102D43semidirect
509. C43#22414semidirect
596. #102C22⋊D43semidirect
858. C22#14582892semidirect

Maximal subgroups

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

subgroupindex
C2×#145835432
C2×C8×C22⋊D432
C2×#145828922
#191375202
#191355262
#191354052
#191350202
#191350182
#191349142
#191349022
#191346032
#191345322
#191345262
#102×Dic432
C22×#102×C432
#2241443