Finite Group Databasebeta

← #25112018

Subgroups — #25112018

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×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4C22×#13063246C211yesmaximal, characteristic, complemented
5#19137526C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135405C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19135016C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134900C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic, complemented
19#14583543—24no—
20#14583543C418yescomplemented
21C2×#13063312C2211yescharacteristic
22C2×#13063306—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063294—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic, complemented
30C22×C4⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43—21no—
32(C22⋊D43)⋊C8—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34#14582892—24no—
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063246—24no—
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
45C2×C8×Dic43C2211yescharacteristic, complemented
46#14582791—21no—
47#14582786—21no—
48#14582776—21no—
49#14582764C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic, complemented
51C4⋊C4×Dic43C2211yescharacteristic, complemented
52C22⋊C4×Dic43—21no—
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C23×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
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—
76C23×Dic43—21no—
77C22×C4×D43C2311yescharacteristic
78C22×C43⋊C8—22no—
79C22×C43⋊C8—22no—
80C22×C43⋊C8—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85C2×C8×D43—41no—
86#13063312—22no—
87#13063312C2×C414yescomplemented
88#13063306—28no—
89#13063304—22no—
90#13063304C2×C414yes—
91#13063297—28no—
92#13063296—22no—
93#13063296C2×C414yescomplemented
94#13063294—28no—
95D4×Dic43—22no—
96D4×Dic43C2×C414yescomplemented
97C4×C22⋊D43C2×C414yes—
98C4×C22⋊D43D414yes—
99#13063283—22no—
100#13063283—41no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—41no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—28no—
115C2×C22⋊Dic43D411yescharacteristic
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43C2311yescharacteristic
122Dic43⋊C8—22no—
123#13063250—22no—
124#13063250—41no—
125#13063248—22no—
126#13063248—41no—
127#13063246—22no—
128#13063246—22no—
129#13063246—22no—
130#13063246D414yescomplemented
131(C2×D43)⋊C8—22no—
132C8×Dic43—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C25×C43—21no—
138C22×D4×C43—22no—
139C22×D4×C43—22no—
140C22×D4×C43—21no—
141C22×D4×C43—22no—
142C22×D4×C43—41no—
143C22×D4×C43—41no—
144C22×D4×C43C2×C414yes—
145C22×D4×C43C2311yescharacteristic
146C22×D4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153#102×C43—22no—
154#102×C43—22no—
155#102×C43—41no—
156#102×C43—41no—
157C22⋊C8×C43—22no—
158#95×C43—21no—
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×C43C22×C412yes—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—42no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43C22⋊C414yes—
208C22×Dic43—24no—
209C22×Dic43—24no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—42no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43—42no—
218C22×Dic43—81no—
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—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C22⋊C4×C43—42no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43C22⋊C414yes—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—81no—
259(C2×D43)⋊C4C22⋊C414yes—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—42no—
265C4⋊Dic43C22×C412yes—
266C4⋊Dic43C2×D412yes—
267Dic43⋊C4—24no—
268Dic43⋊C4C22⋊C414yes—
269C4×Dic43—42no—
270C4×Dic43—81no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—44no—
279C2×C43⋊C8C2×D412yes—
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—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43C2×C22⋊C412yes—
339C2×C4×C43C23×C411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C22⋊D43—28no—
346C22⋊D43—48no—
347C22⋊D43—84no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—22no—
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—84no—
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—41no—
381C8×C43—41no—
382C43⋊C8—22no—
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—81no—
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—42no—
434Dic43—81no—
435C2×#546—431no—
436C2×C8×D4—431no—
437C2×#416—431no—
438C22×#102—431no—
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#1786D4311yescharacteristic, complemented
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×C8—431no—
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⋊C4—431no—
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—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—864no—
490C2×#102C2×D4311yescharacteristic
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8C2×D4311yescharacteristic
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380C2×D4311yescharacteristic
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—431no—
531C23×C4—861no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—862no—
541C22×C8—1721no—
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—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—862no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—1721no—
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—868no—
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—41no—
592#102—41no—
593#102—434no—
594#102—862no—
595#102—862no—
596#102—862no—
597C22⋊C8—22no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—21no—
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×D4D4×D4312yes—
653C2×D4#1062190012yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—3441no—
676C22×C4—3441no—
677C22×C4—3441no—
678C22×C4—1722no—
679C22×C4—1722no—
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—21no—
692C2×C8—432no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—1724no—
699C2×C8—1724no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—434no—
705C4⋊C4—432no—
706C4⋊C4—432no—
707C4⋊C4—864no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—1722no—
713C22⋊C4—42no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—864no—
721C22⋊C4—3441no—
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—
778D4(C22⋊D43)⋊C414yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—432no—
792C2×C4—432no—
793C2×C4—432no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—3444no—
808C2×C4—3444no—
809C2×C4—1728no—
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×C4C2×D4×D4311yescharacteristic
823C2×C4C2×#1062190011yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337011yescharacteristic
826C8—41no—
827C8—41no—
828C8—862no—
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
860C22#1458353111yescharacteristic
861C22#1458353611yescharacteristic
862C22C2×#1306334411yescharacteristic
863C22C2×#1306334611yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370911yescharacteristic
866C4—22no—
867C4—81no—
868C4—81no—
869C4—862no—
870C4—862no—
871C4—862no—
872C4—3441no—
873C4—1722no—
874C4—1722no—
875C4—1722no—
876C4C2×(C22⋊D43)⋊C411yescharacteristic
877C4#1458337211yescharacteristic
878C4#1458353111yescharacteristic
879C4#1458353611yescharacteristic
880C2—24no—
881C2—44no—
882C2—82no—
883C2—1722no—
884C2#1913741111yescharacteristic
885C2C2×#1458289211yescharacteristic
886C2#1914312011yescharacteristic
887C2#1914627311yescharacteristic
888C2#1914630611yescharacteristic
889C2#1914643411yescharacteristic
890C2#1914644911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583543C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#22414
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×(C22⋊D43)⋊C8C2semidirect
3. C2×#14582892C2semidirect
4. C22×#13063246C2semidirect
5. #19137526C2semidirect
6. #19135526C2semidirect
7. #19135405C2semidirect
8. #19135020C2semidirect
9. #19135016C2semidirect
10. #19134914C2semidirect
11. #19134900C2semidirect
12. #19134603C2semidirect
13. #19134532C2semidirect
14. #102×Dic43C2semidirect
15. C43×#1786C2semidirect
18. C22×C8×D43C22semidirect
20. #14583543C4semidirect
29. C2×#13063283C22semidirect
33. C2×Dic43⋊C8C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063248C22semidirect
44. C2×(C2×D43)⋊C8C22semidirect
45. C2×C8×Dic43C22semidirect
49. #14582764C22semidirect
50. #14582756C22semidirect
51. C4⋊C4×Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
69. C2×#10621900C2×C4semidirect
87. #13063312C2×C4semidirect
93. #13063296C2×C4semidirect
96. D4×Dic43C2×C4semidirect
130. #13063246D4semidirect
406. C22×C43#416semidirect
448. #1786D43semidirect
509. C43#22414semidirect
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×(C22⋊D43)⋊C82
C2×#145828922
C22×#130632462
#191375262
#191355262
#191354052
#191350202
#191350162
#191349142
#191349002
#191346032
#191345322
#102×Dic432
C43×#17862
#2241443