Finite Group Databasebeta

← #25112198

Subgroups — #25112198

Order 11008.

1606 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×#14583537C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4#19137520C211yesmaximal, characteristic, complemented
5#19135524C211yesmaximal, characteristic, complemented
6#19135403C211yesmaximal, characteristic, complemented
7#19135033C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19134912C211yesmaximal, characteristic, complemented
10#19134904C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18#14583537—24no—
19#14583537C418yescomplemented
20C2×#13063314C2211yescharacteristic
21C2×#13063308—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063293—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×C4×C22⋊D43C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C22×(C2×D43)⋊C4—21no—
30#14582975—24no—
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32#14582902—24no—
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063249C2211yescharacteristic, complemented
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic, complemented
44#14582789—21no—
45#14582780—21no—
46#14582778—21no—
47#14582764C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic, complemented
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×C22⋊Dic43—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C22×#41×C43C2211yescharacteristic
57C22×M16×C43C2211yescharacteristic, complemented
58C22×C4⋊C4×C43C2211yescharacteristic, complemented
59C43×#417—24no—
60C2×#103×C43C2211yescharacteristic, complemented
61C2×#103×C43C2211yescharacteristic, complemented
62C2×#102×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43D411yescharacteristic
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—41no—
73C2×D4×D43—41no—
74C2×D4×D43C2×C414yescomplemented
75C23×Dic43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063314—22no—
83#13063314C2×C414yescomplemented
84#13063308—28no—
85#13063301—22no—
86#13063301C2×C414yescomplemented
87#13063299—22no—
88#13063299C2×C414yes—
89#13063297—28no—
90#13063293—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⋊Dic43D411yescharacteristic
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—28no—
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#13063249—41no—
118#13063249—41no—
119#13063247—22no—
120#13063247—41no—
121#13063246—22no—
122#13063246—22no—
123#13063245—22no—
124#13063245—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—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—41no—
137C2×#41×C43—41no—
138C2×#41×C43C2×C414yes—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—21no—
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43—21no—
144C23×C4×C43C2311yescharacteristic
145C2×M16×C43—22no—
146C2×M16×C43—22no—
147C2×M16×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#103×C43—22no—
156#103×C43—22no—
157#102×C43—22no—
158#102×C43D414yescomplemented
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×D411yescharacteristic
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43C22×C412yes—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—24no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
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—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43—42no—
201C22×C4×C43—81no—
202C22×C4×C43C22×C412yes—
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—24no—
207C2×C22⋊D43—24no—
208C2×C22⋊D43—41no—
209C2×C22⋊D43—41no—
210C2×C22⋊D43—42no—
211C2×C22⋊D43—42no—
212C2×C22⋊D43—81no—
213C2×C22⋊D43—81no—
214C2×C22⋊D43C22⋊C414yes—
215C22×Dic43—24no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—81no—
220C22×Dic43—81no—
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224D4×D43—28no—
225D4×D43—44no—
226D4×D43—44no—
227D4×D43—44no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172C22×C412yes—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C2×D412yes—
240M16×C43—44no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
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—42no—
254C22⋊Dic43C22⋊C414yes—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
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—
280#10621872—44no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—21no—
284C23×C43—22no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—22no—
303C22×D43—48no—
304C22×D43—48no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43C2×C22⋊C412yes—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—48no—
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—22no—
334C2×C4×C43—48no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—84no—
343C2×C4×C43C2×C22⋊C412yes—
344C2×C4×C43C23×C411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C2×#4111yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C22⋊D43—44no—
351C22⋊D43—48no—
352C22⋊D43—84no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—21no—
359C2×Dic43—22no—
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—
372D172—22no—
373D172—22no—
374D172—41no—
375D172—41no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22427—431nomaximal, Sylow
385C22×C43—24no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—41no—
393C22×C43—42no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—41no—
397C22×C43—42no—
398C22×C43—41no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—41no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—816no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43—81no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43—81no—
425C4×C43C2×C4×D411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—22no—
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—81no—
434Dic43—81no—
435C2×#546—431no—
436C2×#436—431no—
437C2×#417D4311yescharacteristic, complemented
438C2×#418—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1895—431no—
443#1894—431no—
444#1874—431no—
445#1873—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—44no—
451C2×C43—42no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43#289611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#327311yescharacteristic
456C2×C43#327511yescharacteristic
457C2×C43#332211yescharacteristic
458C2×C43#332311yescharacteristic
459D43—42no—
460D43—82no—
461C22×#41C2×D4311yescharacteristic
462C23×D4—431no—
463C22×M16—431no—
464C22×M16C2×D4311yescharacteristic, complemented
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, complemented
477C22×C22⋊C4—861no—
478#436—864no—
479C2×C4⋊C8—431no—
480#418—864no—
481#417—24no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#103C2×D4311yescharacteristic, complemented
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
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#2242711yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C4×D4314yes—
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—434no—
521C22×D4—431no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—431no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—862no—
539C2×M16—862no—
540C2×M16—1721no—
541C22×C8—431no—
542C22×C8—431no—
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—22no—
586#103—22no—
587#103—1721no—
588#103—1721no—
589#102—22no—
590#102—862no—
591#102—862no—
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—431no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24D4×D4311yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C2×C4×D4312yes—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—434no—
633C2×D4—432no—
634C2×D4—864no—
635C2×D4—868no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1721no—
648C2×D4—1721no—
649C2×D4—1722no—
650C2×D4—1722no—
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—24no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—81no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—432no—
671C22×C4—432no—
672C22×C4—864no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—3441no—
681C22×C4—3441no—
682C22×C4C2×C4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4312yes—
685C22×C4C23×D4311yescharacteristic
686M16—44no—
687M16—1724no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
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—22no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—432no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—862no—
748C23—3444no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—1728no—
754C23—1728no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23C22⋊C4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—48no—
771D4—862no—
772D4—862no—
773D4—3444no—
774D4—1724no—
775D4—1728no—
776D4—1721no—
777D4—1721no—
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—22no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—432no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—861no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—3444no—
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—24no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—862no—
845C22—862no—
846C22—862no—
847C22—34416no—
848C22—3441no—
849C22—3441no—
850C22—3441no—
851C22—3441no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1721no—
856C22—1721no—
857C22—1721no—
858C22—1721no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22D4×C22⋊D4311yescharacteristic
861C22#1458353911yescharacteristic
862C22#1458369511yescharacteristic
863C22#1458369811yescharacteristic
864C22#1458370311yescharacteristic
865C22#1458370811yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—862no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—3441no—
875C4—1722no—
876C4C2×C4×C22⋊D4311yescharacteristic
877C4#1458337211yescharacteristic
878C4D4×C22⋊D4311yescharacteristic
879C4#1458353911yescharacteristic
880C2—42no—
881C2—44no—
882C2—3442no—
883C2—1722no—
884C2C22⋊C4×C22⋊D4311yescharacteristic
885C2#1914311111yescharacteristic
886C2#1914311911yescharacteristic
887C2#1914620011yescharacteristic
888C2#1914622011yescharacteristic
889C2#1914679711yescharacteristic
890C2#1914681211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22427
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582902C2semidirect
4. #19137520C2semidirect
5. #19135524C2semidirect
6. #19135403C2semidirect
7. #19135033C2semidirect
8. #19135025C2semidirect
9. #19134912C2semidirect
10. #19134904C2semidirect
11. #19134603C2semidirect
12. #19134535C2semidirect
13. #19134524C2semidirect
14. #102×Dic43C2semidirect
15. C2×C43×#417C2semidirect
19. #14583537C4semidirect
31. C2×Dic43⋊C8C22semidirect
33. C2×#13063249C22semidirect
34. C2×#13063249C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
43. C2×C8×Dic43C22semidirect
47. #14582764C22semidirect
48. #14582759C22semidirect
50. C4⋊C4×Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
57. C22×M16×C43C22semidirect
58. C22×C4⋊C4×C43C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#103×C43C22semidirect
74. C2×D4×D43C2×C4semidirect
83. #13063314C2×C4semidirect
86. #13063301C2×C4semidirect
92. D4×Dic43C2×C4semidirect
158. #102×C43D4semidirect
437. C2×#417D43semidirect
464. C22×M16C2×D43semidirect
476. C22×C4⋊C4C2×D43semidirect
484. C2×#103C2×D43semidirect
485. C2×#103C2×D43semidirect
509. C43#22427semidirect
596. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835372
C2×#145829752
C2×#145829022
#191375202
#191355242
#191354032
#191350332
#191350252
#191349122
#191349042
#191346032
#191345352
#191345242
#102×Dic432
C2×C43×#4172
#2242743