Finite Group Databasebeta

← C2×#19143422 #25960689

Subgroups — C2×#19143422 #25960689

Order 11008.

2946 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063352C211yesmaximal, characteristic
2C2×#14583381C211yesmaximal, characteristic, complemented
3C2×#14583371C211yesmaximal, characteristic, complemented
4#19143422C2116yesmaximal, direct product factor
5C2×#14583010C211yesmaximal, characteristic, complemented
6C2×#14583009C211yesmaximal, characteristic, complemented
7C2×#14583000C211yesmaximal, characteristic, complemented
8C2×#14582997C211yesmaximal, characteristic, complemented
9C2×#14582984C211yesmaximal, characteristic, complemented
10C2×C4×D344C211yesmaximal, characteristic, complemented
11C2×#14582979C211yesmaximal, characteristic, complemented
12C2×#14582938C211yesmaximal, characteristic, complemented
13C2×#14582894C211yesmaximal, characteristic, complemented
14C2×#102×D43C211yesmaximal, characteristic, complemented
15C2×#14582853C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C2×#13063352C4116yescomplemented
20C2×#13063352C2218yes—
21C22×#10621884C2211yescharacteristic
22C22×D344C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583381—24no—
27#14583381C2218yescomplemented
28#14583371—24no—
29#14583371C2218yescomplemented
30C2×Q8×Dic43C2211yescharacteristic, complemented
31C2×C4×D172—21no—
32C2×C4×D172C2211yescharacteristic
33C2×C4×D172C2211yescharacteristic, complemented
34C2×D4×Dic43C2211yescharacteristic
35C2×#13063287—21no—
36C2×#13063287C2211yescharacteristic
37C2×#13063287C2211yescharacteristic, complemented
38C2×C4×C22⋊D43—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C2×#13063282C2211yescharacteristic
43C2×C4⋊C4×D43—21no—
44C2×C4⋊C4×D43C2211yescharacteristic
45C22×(C2×D43)⋊C4—21no—
46C2×C22⋊C4×D43—21no—
47#14583010C2218yescomplemented
48#14583009C2218yescomplemented
49#14583000C2218yescomplemented
50#14582997C2218yescomplemented
51#14582984C2218yescomplemented
52C4×D344C2218yescomplemented
53#14582979C2218yescomplemented
54#14582938C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58#14582894C2218yescomplemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063246C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65#102×D43C2218yescomplemented
66#14582853C2218yescomplemented
67C2×#13063236C2211yescharacteristic, complemented
68C2×#13063235C2211yescharacteristic, complemented
69C2×C8×Dic43C2211yescharacteristic, complemented
70C22×SD16×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic, complemented
72C2×C4×D4×C43C2211yescharacteristic
73C4×SD16×C43C2218yescomplemented
74C2×#106×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic
77C2×C4×C8×C43C2211yescharacteristic, complemented
78C24×D43—21no—
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902C2×C418yescomplemented
82C2×#10621902C2314yes—
83C22×D172—21no—
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C22⋊D43—21no—
87C2×D4×D43—22no—
88C2×D4×D43—24no—
89C2×D4×D43C2×C418yescomplemented
90C2×D4×D43C2314yes—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43C2311yescharacteristic
99#13063352C2×C4164yescomplemented
100C2×#10621884C2×C418yescomplemented
101C2×#10621884C2314yes—
102C2×D344C2×C418yescomplemented
103C2×D344C2314yes—
104C2×#10621882C2×C418yescomplemented
105C2×#10621882C2314yes—
106C2×#10621872C2×C418yescomplemented
107C2×#10621872C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C2×C8×D43—24no—
111C2×C8×D43C2314yes—
112Q8×Dic43—22no—
113Q8×Dic43C2314yescomplemented
114C4×D172—22no—
115C4×D172—22no—
116C4×D172—28no—
117C4×D172C2314yes—
118C4×D172C2314yescomplemented
119D4×Dic43—22no—
120D4×Dic43C2314yes—
121#13063287—28no—
122#13063287—22no—
123#13063287—22no—
124#13063287C2314yes—
125#13063287C2314yescomplemented
126C4×C22⋊D43—28no—
127(C22⋊D43)⋊C4—28no—
128#13063283—22no—
129#13063283C2314yes—
130#13063282—28no—
131#13063282D414yes—
132#13063282C2314yes—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C2×Dic43⋊C4D411yescharacteristic
139C4⋊C4×D43—22no—
140C4⋊C4×D43—28no—
141C4⋊C4×D43C2314yes—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—28no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151C22⋊C4×D43—28no—
152C2×C4×Dic43—21no—
153C2×C4×Dic43—21no—
154C2×C4×Dic43C2311yescharacteristic
155#13063259C2314yescomplemented
156#13063258C2314yescomplemented
157#13063256C2314yescomplemented
158#13063249C2314yescomplemented
159#13063247C2314yes—
160#13063247C2314yescomplemented
161#13063246C2314yes—
162#13063245C2314yes—
163#13063245C2314yescomplemented
164#13063236C2314yescomplemented
165#13063235C2314yescomplemented
166C8×Dic43C2314yescomplemented
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C2×SD16×C43C2×C418yescomplemented
171C2×SD16×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yescomplemented
176C4×D4×C43—22no—
177C4×D4×C43C2314yes—
178C2×C4⋊C4×C43—21no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183C2×C42×C43C2311yescharacteristic
184#106×C43C2314yescomplemented
185#103×C43C2314yescomplemented
186#102×C43C2314yes—
187C4×C8×C43C2314yescomplemented
188C24×C43—21no—
189C23×D43—21no—
190C23×D43—21no—
191C23×D43—28no—
192C23×D43—24no—
193C23×D43—82no—
194C23×D43—82no—
195C23×D43C2×D411yescharacteristic
196C2×Q8×C43—21no—
197C2×Q8×C43—22no—
198C2×Q8×C43C22×C414yes—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43C22×C414yes—
203C2×D4×C43C2412yes—
204C22×C4×C43—24no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—82no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—28no—
213C2×C22⋊D43—24no—
214C22×Dic43—24no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—82no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221#10621902—216no—
222#10621902—28no—
223#10621902C22×C4116yescomplemented
224D4×D43—216no—
225D4×D43—28no—
226D4×D43C22×C4116yescomplemented
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—28no—
232C2×D172—24no—
233C2×D172C22×C414yes—
234C2×D172C22×C414yes—
235C2×D172C2412yes—
236C2×D172C2412yes—
237C2×C4×D43—28no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—24no—
241C2×C4×D43—24no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—82no—
245C2×C4×D43—82no—
246C2×C4×D43—82no—
247C2×C4×D43—82no—
248C2×C4×D43—82no—
249C2×C4×D43C22×C414yes—
250C2×C4×D43C2×D412yes—
251C2×C4×D43#4114yes—
252C2×C4×D43C2412yes—
253SD16×C43C22×C4116yescomplemented
254C2×C8×C43—22no—
255C2×C8×C43C22×C414yes—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43—24no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C22⋊C4×C43—24no—
264C42×C43—24no—
265C42×C43C2×D412yes—
266C42×C43C2412yes—
267C22⋊Dic43—24no—
268#10621884C22×C4116yescomplemented
269#10621882C22×C4116yescomplemented
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4C2×D414yes—
276(C2×D43)⋊C4C2×D414yes—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—24no—
280C4⋊Dic43C2412yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4C2×D414yes—
284Dic43⋊C4C2×D414yes—
285C4×Dic43—24no—
286C4×Dic43—24no—
287C4×Dic43C2×D412yes—
288C4×Dic43C2412yes—
289C2×C43⋊C8—22no—
290C2×C43⋊C8C22×C414yes—
291C2×C43⋊C8C2412yes—
292C2×C43⋊C8C2412yes—
293D344C22×C4116yescomplemented
294#10621872C22×C4116yescomplemented
295C8×D43—28no—
296C23×C43—24no—
297C23×C43—22no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—24no—
304C22×D43—24no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—216no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—816no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43C4×D414yes—
316C22×D43C22×D412yes—
317Q8×C43—24no—
318Q8×C43—22no—
319Q8×C43C23×C414yes—
320D4×C43—24no—
321D4×C43—22no—
322D4×C43C23×C414yes—
323C2×C4×C43—24no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—84no—
332C2×C4×C43C23×C412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4112yes—
337C2×C4×C43C2511yescharacteristic
338C22⋊D43—216no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—84no—
346C2×Dic43C4×D414yes—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349C2×Dic43C22×D412yes—
350D172—216no—
351D172—24no—
352D172—24no—
353D172—22no—
354D172—22no—
355D172C23×C414yes—
356D172C23×C414yes—
357C4×D43—216no—
358C4×D43—84no—
359C4×D43—84no—
360C4×D43—84no—
361C4×D43—84no—
362C4×D43—84no—
363C4×D43C4×D418yes—
364C4×D43C23×C414yes—
365C4×D43C2×#4114yes—
366C8×C43—22no—
367C8×C43C23×C414yes—
368C43⋊C8—22no—
369C43⋊C8C23×C414yes—
370C2×#2946—431nomaximal, Sylow
371C22×C43—24no—
372C22×C43—48no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43C2×C4×D412yes—
376C22×C43#57612yes—
377C22×C43#57712yes—
378C22×C43C23×D411yescharacteristic
379C2×D43—28no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—24no—
383C2×D43—24no—
384C2×D43—48no—
385C2×D43—48no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—816no—
391C2×D43C2×C4×D414yes—
392C4×C43—24no—
393C4×C43—22no—
394C4×C43—22no—
395C4×C43—42no—
396C4×C43—42no—
397C4×C43C2×C4×D412yes—
398C4×C43C24×C411yescharacteristic
399C4×C43C22×#4111yescharacteristic
400Dic43—22no—
401Dic43—22no—
402Dic43—42no—
403Dic43—42no—
404Dic43C2×C4×D414yes—
405C22×AGL(1,ℤ/8)—431no—
406C2×#520—431no—
407C2×#518—431no—
408#2946—4316no—
409C2×#442—431no—
410C2×#442—431no—
411C2×#440—431no—
412C2×#440—431no—
413C2×C4×SD16—431no—
414C2×C4×SD16D4311yescharacteristic, complemented
415C2×C4×D8—431no—
416C2×C4×D8—431no—
417C2×#428—431no—
418C2×#416—431no—
419C22×#102—431no—
420C2×#405—431no—
421C2×C43—44no—
422C2×C43#294614yescomplemented
423C2×C43C22×C4×D411yescharacteristic
424C2×C43C2×#57611yescharacteristic
425C2×C43C2×#57711yescharacteristic
426D43—24no—
427D43—44no—
428D43—44no—
429C22×#41—431no—
430C23×D4—431no—
431C2×AGL(1,ℤ/8)—438no—
432C2×AGL(1,ℤ/8)—4316no—
433C22×SD16—431no—
434C22×SD16C2×D4311yescharacteristic
435C22×D8—431no—
436C22×D8—431no—
437C22×M16—431no—
438C23×C8—431no—
439#520—438no—
440#520—864no—
441#518—438no—
442#518—864no—
443C2×C4×Q8—431no—
444C2×C4×Q8C2×D4311yescharacteristic, complemented
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4—431no—
449C2×C4×D4—431no—
450C2×C4×D4—861no—
451C2×C4×D4—861no—
452C2×C4×D4—861no—
453C2×C4×D4—861no—
454C2×C4×D4C2×D4311yescharacteristic
455C2×#117—431no—
456C2×#117—431no—
457C2×#117—861no—
458C22×C4⋊C4—431no—
459C22×C4⋊C4—861no—
460C22×C22⋊C4—861no—
461C22×C22⋊C4—861no—
462#442—438no—
463#442—438no—
464#440—438no—
465#440—438no—
466C4×SD16—438no—
467C4×SD16C2×D4318yescomplemented
468C4×D8—438no—
469C4×D8—438no—
470#428—438no—
471C2×#107—431no—
472C2×#107—431no—
473C2×#106—431no—
474C2×#106C2×D4311yescharacteristic, complemented
475#416—438no—
476C2×#103—431no—
477C2×#103C2×D4311yescharacteristic, complemented
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—438no—
484C2×#102C2×D4311yescharacteristic
485#405—438no—
486C2×#97—431no—
487C2×#97—431no—
488C2×C4×C8—431no—
489C2×C4×C8C2×D4311yescharacteristic, complemented
490C43C2×#294611yescharacteristic, complemented, Sylow
491C25—861no—
492C2×#41—438no—
493C2×#41—434no—
494C2×#41—862no—
495C2×#41—864no—
496C22×Q8C22×D4311yescharacteristic
497C22×D4—438no—
498C22×D4—434no—
499C22×D4—431no—
500C22×D4—431no—
501C22×D4—861no—
502C22×D4—862no—
503C22×D4—864no—
504C22×D4—861no—
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—431no—
508C23×C4—861no—
509C23×C4—861no—
510C23×C4—861no—
511C23×C4—861no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515AGL(1,ℤ/8)—4364no—
516C2×SD16—438no—
517C2×SD16—434no—
518C2×SD16C4×D4318yescomplemented
519C2×SD16C22×D4314yes—
520C2×D8—438no—
521C2×D8—434no—
522C2×D8—438no—
523C2×D8—434no—
524C2×M16—438no—
525C2×M16—434no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8—434no—
529C22×C8—864no—
530C22×C8C22×D4311yescharacteristic
531C22×C8C22×D4311yescharacteristic
532C4×Q8—22no—
533C4×Q8—434no—
534C4×Q8—862no—
535C4×Q8C22×D4314yescomplemented
536C4×D4—22no—
537C4×D4—434no—
538C4×D4—434no—
539C4×D4—434no—
540C4×D4—434no—
541C4×D4—434no—
542C4×D4—868no—
543C4×D4—862no—
544C4×D4—862no—
545C4×D4—862no—
546C4×D4—868no—
547C4×D4—868no—
548C4×D4—868no—
549C4×D4—862no—
550C4×D4—862no—
551C4×D4C22×D4314yes—
552#117—434no—
553#117—434no—
554#117—434no—
555#117—868no—
556#117—862no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—434no—
563C2×C4⋊C4—868no—
564C2×C4⋊C4—862no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
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×C42—21no—
581C2×C42—431no—
582C2×C42—861no—
583C2×C42—861no—
584C2×C42C22×D4311yescharacteristic
585#107—434no—
586#107—434no—
587#106—434no—
588#106C22×D4314yescomplemented
589#103—434no—
590#103C22×D4314yescomplemented
591#102—434no—
592#102—434no—
593#102—434no—
594#102—434no—
595#102—434no—
596#102C22×D4314yes—
597#97—434no—
598#97—434no—
599C4×C8—434no—
600C4×C8C22×D4314yescomplemented
601C24—21no—
602C24—431no—
603C24—864no—
604C24—868no—
605C24—861no—
606C24—861no—
607C24—3442no—
608C24—3442no—
609#41—4316no—
610#41—8616no—
611#41—868no—
612C2×Q8—21no—
613C2×Q8—22no—
614C2×Q8C2×C4×D4314yes—
615C2×Q8C23×D4312yes—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—4316no—
619C2×D4—434no—
620C2×D4—434no—
621C2×D4—432no—
622C2×D4—432no—
623C2×D4—864no—
624C2×D4—868no—
625C2×D4—8616no—
626C2×D4—868no—
627C2×D4—864no—
628C2×D4—868no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—862no—
632C2×D4—862no—
633C2×D4C2×C4×D4314yes—
634C2×D4C23×D4312yes—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—82no—
640C22×C4—431no—
641C22×C4—434no—
642C22×C4—432no—
643C22×C4—434no—
644C22×C4—432no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—864no—
648C22×C4—868no—
649C22×C4—864no—
650C22×C4—864no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4—864no—
656C22×C4—864no—
657C22×C4—3442no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4—3442no—
661C22×C4—3442no—
662C22×C4—3442no—
663C22×C4D4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4C23×D4311yescharacteristic
666SD16—4316no—
667SD16C2×C4×D43116yescomplemented
668D8—4316no—
669D8—4316no—
670M16—4316no—
671C2×C8—22no—
672C2×C8—434no—
673C2×C8—432no—
674C2×C8—432no—
675C2×C8—868no—
676C2×C8—862no—
677C2×C8C2×C4×D4314yes—
678C2×C8C23×D4312yes—
679C2×C8C23×D4312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—434no—
684C4⋊C4—434no—
685C4⋊C4—432no—
686C4⋊C4—432no—
687C4⋊C4—864no—
688C4⋊C4—864no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4C23×D4312yes—
692C4⋊C4C23×D4312yes—
693C22⋊C4—24no—
694C22⋊C4—434no—
695C22⋊C4—434no—
696C22⋊C4—864no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C42—24no—
703C42—432no—
704C42—432no—
705C42—864no—
706C42—864no—
707C42D4×D4312yes—
708C42C23×D4312yes—
709C23—24no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—434no—
714C23—432no—
715C23—8616no—
716C23—862no—
717C23—862no—
718C23—864no—
719C23—864no—
720C23—862no—
721C23—862no—
722C23—3444no—
723C23—3444no—
724C23—34416no—
725C23—1722no—
726C23—1722no—
727C23—1722no—
728C23—1722no—
729C23C2×D4×D4311yescharacteristic
730Q8—24no—
731Q8—22no—
732Q8C22×C4×D4314yes—
733D4—24no—
734D4—22no—
735D4—434no—
736D4—434no—
737D4—8616no—
738D4—8616no—
739D4—864no—
740D4—864no—
741D4—862no—
742D4—862no—
743D4C22×C4×D4314yes—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—84no—
753C2×C4—434no—
754C2×C4—432no—
755C2×C4—438no—
756C2×C4—434no—
757C2×C4—434no—
758C2×C4—432no—
759C2×C4—432no—
760C2×C4—8616no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—3444no—
766C2×C4—3444no—
767C2×C4—3444no—
768C2×C4—3444no—
769C2×C4—3444no—
770C2×C4—3444no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4C22×C4×D4312yes—
774C2×C4C2×D4×D4312yes—
775C2×C4C2×D4×D4312yes—
776C2×C4C2×D4×D4311yescharacteristic
777C2×C4#41×D4312yes—
778C2×C4C24×D4311yescharacteristic
779C8—22no—
780C8—434no—
781C8—862no—
782C8C22×C4×D4314yes—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—48no—
787C22—434no—
788C22—862no—
789C22—862no—
790C22—868no—
791C22—864no—
792C22—864no—
793C22—34416no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22—1728no—
799C22—1728no—
800C22C4×D4×D4312yes—
801C22#1458370112yes—
802C22#1458370512yes—
803C22C22×D4×D4311yescharacteristic
804C4—22no—
805C4—22no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—434no—
810C4—862no—
811C4—862no—
812C4—1722no—
813C4—1722no—
814C4C4×D4×D4312yes—
815C4C23×C4×D4311yescharacteristic
816C4C2×#41×D4311yescharacteristic
817C2—44no—
818C2—864no—
819C2—1724no—
820C2—1724no—
821C2#1914342214yesdirect product factor
822C2C2×C4×D4×D4311yescharacteristic
823C2C2×#1458370111yescharacteristic
824C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×#13063352C2
cosocleC2×C4×C43C25
hypercenterC2×C4×SD16D43
hypocenterC43C2×#2946
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#14583381C2semidirect
3. C2×#14583371C2semidirect
4. #19143422C2direct (N × H)
5. C2×#14583010C2semidirect
6. C2×#14583009C2semidirect
7. C2×#14583000C2semidirect
8. C2×#14582997C2semidirect
9. C2×#14582984C2semidirect
10. C2×C4×D344C2semidirect
11. C2×#14582979C2semidirect
12. C2×#14582938C2semidirect
13. C2×#14582894C2semidirect
14. C2×#102×D43C2semidirect
15. C2×#14582853C2semidirect
16. C2×C4×SD16×C43C2semidirect
19. C2×#13063352C4semidirect
27. #14583381C22semidirect
29. #14583371C22semidirect
30. C2×Q8×Dic43C22semidirect
33. C2×C4×D172C22semidirect
37. C2×#13063287C22semidirect
47. #14583010C22semidirect
48. #14583009C22semidirect
49. #14583000C22semidirect
50. #14582997C22semidirect
51. #14582984C22semidirect
52. C4×D344C22semidirect
53. #14582979C22semidirect
54. #14582938C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063256C22semidirect
58. #14582894C22semidirect
59. C2×#13063249C22semidirect
61. C2×#13063247C22semidirect
64. C2×#13063245C22semidirect
65. #102×D43C22semidirect
66. #14582853C22semidirect
67. C2×#13063236C22semidirect
68. C2×#13063235C22semidirect
69. C2×C8×Dic43C22semidirect
71. C2×C4×Q8×C43C22semidirect
73. C4×SD16×C43C22semidirect
74. C2×#106×C43C22semidirect
75. C2×#103×C43C22semidirect
77. C2×C4×C8×C43C22semidirect
81. C2×#10621902C2×C4semidirect
89. C2×D4×D43C2×C4semidirect
99. #13063352C2×C4semidirect
100. C2×#10621884C2×C4semidirect
102. C2×D344C2×C4semidirect
104. C2×#10621882C2×C4semidirect
106. C2×#10621872C2×C4semidirect
113. Q8×Dic43C23semidirect
118. C4×D172C23semidirect
125. #13063287C23semidirect
155. #13063259C23semidirect
156. #13063258C23semidirect
157. #13063256C23semidirect
158. #13063249C23semidirect
160. #13063247C23semidirect
163. #13063245C23semidirect
164. #13063236C23semidirect
165. #13063235C23semidirect
166. C8×Dic43C23semidirect
170. C2×SD16×C43C2×C4semidirect
175. C4×Q8×C43C23semidirect
184. #106×C43C23semidirect
185. #103×C43C23semidirect
187. C4×C8×C43C23semidirect
223. #10621902C22×C4semidirect
226. D4×D43C22×C4semidirect
253. SD16×C43C22×C4semidirect
268. #10621884C22×C4semidirect
269. #10621882C22×C4semidirect
293. D344C22×C4semidirect
294. #10621872C22×C4semidirect
414. C2×C4×SD16D43semidirect
422. C2×C43#2946semidirect
444. C2×C4×Q8C2×D43semidirect
467. C4×SD16C2×D43semidirect
474. C2×#106C2×D43semidirect
477. C2×#103C2×D43semidirect
489. C2×C4×C8C2×D43semidirect
490. C43C2×#2946semidirect
518. C2×SD16C4×D43semidirect
535. C4×Q8C22×D43semidirect
588. #106C22×D43semidirect
590. #103C22×D43semidirect
600. C4×C8C22×D43semidirect
667. SD16C2×C4×D43semidirect
821. C2#19143422direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633522
C2×#145833812
C2×#145833712
#191434222
C2×#145830102
C2×#145830092
C2×#145830002
C2×#145829972
C2×#145829842
C2×C4×D3442
C2×#145829792
C2×#145829382
C2×#145828942
C2×#102×D432
C2×#145828532
C2×C4×SD16×C432
C2×#294643