Finite Group Databasebeta

← #25112015

Subgroups — #25112015

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×#14583537C211yesmaximal, characteristic
2C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
3C2×#102×D43C211yesmaximal, characteristic, complemented
4#19137525C211yesmaximal, characteristic, complemented
5#19135524C211yesmaximal, characteristic, complemented
6#19135403C211yesmaximal, characteristic, complemented
7#19135023C211yesmaximal, characteristic, complemented
8#19135015C211yesmaximal, characteristic, complemented
9#19134917C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C2×C43×#416C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
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×C4⋊C4×D43C2211yescharacteristic
29C22×(C2×D43)⋊C4—21no—
30C8×C22⋊D43—24no—
31C2×Dic43⋊C8C2211yescharacteristic, complemented
32C2×#13063249C2211yescharacteristic, complemented
33C2×#13063249C2211yescharacteristic, complemented
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40#102×D43—24no—
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic, complemented
44#14582793—21no—
45#14582783—21no—
46#14582775—21no—
47#14582764C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic, complemented
49#14582756C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic, complemented
51C4×(C2×D43)⋊C4—21no—
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56C22×#41×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic, complemented
58C2×#117×C43C2211yescharacteristic, complemented
59C43×#416—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×C414yes—
75C23×Dic43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—22no—
81C2×C8×D43—22no—
82C2×C8×D43—41no—
83#13063314—22no—
84#13063314C2×C414yescomplemented
85#13063308—28no—
86#13063301—22no—
87#13063301C2×C414yes—
88#13063299—22no—
89#13063299C2×C414yescomplemented
90#13063297—28no—
91#13063293—28no—
92D4×Dic43—22no—
93D4×Dic43C2×C414yescomplemented
94C4×C22⋊D43C2×C414yes—
95C4×C22⋊D43D414yes—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4D411yescharacteristic
102C4⋊C4×D43—22no—
103C4⋊C4×D43—41no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43D411yescharacteristic
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—28no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4D411yescharacteristic
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×C414yescomplemented
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—21no—
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43—22no—
145C22×C8×C43—22no—
146C22×C8×C43—41no—
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149#117×C43—22no—
150#117×C43—41no—
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C42×C43—21no—
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×C43C22×C412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—22no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43C22⋊C414yes—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—81no—
217C22×Dic43—81no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221D4×D43—28no—
222D4×D43—44no—
223D4×D43—44no—
224D4×D43—44no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172C22×C412yes—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—42no—
236C2×C4×D43—42no—
237C2×C4×D43—81no—
238C2×C4×D43C22×C412yes—
239C2×C4×D43C2×D412yes—
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×C43C2×D412yes—
251C22⋊C4×C43—42no—
252C42×C43—42no—
253C22⋊Dic43—24no—
254C22⋊Dic43—81no—
255C22⋊Dic43C22⋊C414yes—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—42no—
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⋊C4—42no—
270Dic43⋊C4C22⋊C414yes—
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—22no—
282C23×C43—21no—
283C23×C43—22no—
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—22no—
301C22×D43—48no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—48no—
309C22×D43—84no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43C2×C22⋊C412yes—
315C22×D43#13512yes—
316C22×D43#13512yes—
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×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C22⋊D43—28no—
350C22⋊D43—48no—
351C22⋊D43—84no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
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×Dic43C2×C22⋊C412yes—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43C2×C22⋊C412yes—
371D172—22no—
372D172—22no—
373D172—41no—
374D172—41no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—84no—
380C8×C43—22no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384#22414—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×C43C2×#13511yescharacteristic
403C22×C43C2×#13511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—816no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C2×D43#41614yescomplemented
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×C8×D4—431no—
437C2×#416D4311yescharacteristic, complemented
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#1786—431no—
449C4×#102—431no—
450C2×C43—44no—
451C2×C43—42no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43C2×#41611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#328011yescharacteristic
456C2×C43#328211yescharacteristic
457C2×C43#329611yescharacteristic
458C2×C43#329711yescharacteristic
459D43—24no—
460D43—82no—
461C22×#41C2×D4311yescharacteristic
462C23×D4—431no—
463C23×C8—431no—
464C23×C8C2×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×#117C2×D4311yescharacteristic, complemented
476C22×C4⋊C4—431no—
477C22×C22⋊C4—861no—
478C8×D4—864no—
479C2×C4⋊C8—431no—
480#416—24no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic, complemented
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—864no—
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—861no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C4×D4314yescomplemented
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—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—22no—
559#117—41no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—862no—
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—21no—
582C2×C42—431no—
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—862no—
636C2×D4—862no—
637C2×D4—868no—
638C2×D4—864no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—3441no—
645C2×D4—3441no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1724no—
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—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—432no—
668C22×C4—432no—
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—3441no—
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—434no—
704C4⋊C4—432no—
705C4⋊C4—864no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—1722no—
712C4⋊C4C2×C22⋊D4312yes—
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—42no—
724C42—432no—
725C42—432no—
726C42—3441no—
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—432no—
742C23—432no—
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—868no—
772D4—862no—
773D4—862no—
774D4—3444no—
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—432no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
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—41no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—434no—
845C22—862no—
846C22—862no—
847C22—862no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—34416no—
852C22—3441no—
853C22—3441no—
854C22—3441no—
855C22—3441no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22D4×C22⋊D4311yescharacteristic
861C22#1458353911yescharacteristic
862C22#135×D4311yescharacteristic
863C22#135×D4311yescharacteristic
864C22#1458370111yescharacteristic
865C22#1458370611yescharacteristic
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—864no—
883C2—3442no—
884C2C22⋊C4×C22⋊D4311yescharacteristic
885C2#416×D4311yescharacteristic
886C2#1914311711yescharacteristic
887C2#1914627411yescharacteristic
888C2#1914629611yescharacteristic
889C2#1914643111yescharacteristic
890C2#1914644611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
cosocleC22×C4×C43C24
hypercenterC2×#416D43
hypocenterC43#22414
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D43C2semidirect
3. C2×#102×D43C2semidirect
4. #19137525C2semidirect
5. #19135524C2semidirect
6. #19135403C2semidirect
7. #19135023C2semidirect
8. #19135015C2semidirect
9. #19134917C2semidirect
10. #19134899C2semidirect
11. #19134603C2semidirect
12. #19134535C2semidirect
13. #19134524C2semidirect
14. #102×Dic43C2semidirect
15. C2×C43×#416C2semidirect
19. #14583537C4semidirect
31. C2×Dic43⋊C8C22semidirect
32. C2×#13063249C22semidirect
33. 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. C23×C8×C43C22semidirect
58. C2×#117×C43C22semidirect
60. C2×#103×C43C22semidirect
61. C2×#103×C43C22semidirect
84. #13063314C2×C4semidirect
89. #13063299C2×C4semidirect
93. D4×Dic43C2×C4semidirect
138. C2×#41×C43C2×C4semidirect
158. #102×C43D4semidirect
420. C2×D43#416semidirect
437. C2×#416D43semidirect
464. C23×C8C2×D43semidirect
475. C2×#117C2×D43semidirect
483. C2×#103C2×D43semidirect
484. C2×#103C2×D43semidirect
509. C43#22414semidirect
516. C2×#41C4×D43semidirect
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×C8×C22⋊D432
C2×#102×D432
#191375252
#191355242
#191354032
#191350232
#191350152
#191349172
#191348992
#191346032
#191345352
#191345242
#102×Dic432
C2×C43×#4162
#2241443