Finite Group Databasebeta

← C2×#548×D43 #26003527

Subgroups — C2×#548×D43 #26003527

Order 11008.

12142 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D43C211yesmaximal, characteristic, complemented
2C23×Q8×D43C211yesmaximal, characteristic, complemented
3C2×#14583561C211yesmaximal, characteristic, complemented
4C2×#14583560C211yesmaximal, characteristic, complemented
5C2×#14583559C213yesmaximal, complemented
6C2×#14583558C213yesmaximal, complemented
7C2×#14583557C213yesmaximal, complemented
8C2×#14583556C211yesmaximal, characteristic, complemented
9C2×#14583555C213yesmaximal, complemented
10#548×D43C2132yesmaximal, direct product factor
11C2×#124×D43C213yesmaximal, complemented
12C2×C22⋊Q8×D43C213yesmaximal, complemented
13C2×#121×D43C213yesmaximal, complemented
14C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
15C2×C4×D4×D43C213yesmaximal, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic, complemented
18C22×#10621898C2213yescomplemented
19C22×#10621900C2213yescomplemented
20C2×#41×D43—216no—
21C2×#41×D43C22116yescomplemented
22C23×Dic86C2213yescomplemented
23C22×Q8×D43—216no—
24C22×Q8×D43C2213yes—
25C22×Q8×D43C2211yescharacteristic
26C22×Q8×D43C2211yescharacteristic, complemented
27C22×Q8×D43C2213yescomplemented
28C22×Q8×D43C22116yescomplemented
29C22×D4×D43C2213yes—
30C22×D4×D43C2213yes—
31C23×C4×D43C2213yes—
32C23×C4×D43C2213yes—
33#14583561C22116yescomplemented
34#14583560C22116yescomplemented
35#14583559C22148yescomplemented
36#14583558C22148yescomplemented
37#14583557C22148yescomplemented
38#14583556C22116yescomplemented
39#14583555C22148yescomplemented
40C2×#13063314C2213yescomplemented
41C2×#13063313C2213yescomplemented
42C2×#13063312C2213yescomplemented
43C2×#13063311C2216yescomplemented
44C2×#13063311C2216yescomplemented
45#124×D43C22148yescomplemented
46C2×#13063305C2213yescomplemented
47C2×#13063304C2213yescomplemented
48C2×#13063303C2216yescomplemented
49C2×#13063302C2216yescomplemented
50C2×#13063301C2213yescomplemented
51C22⋊Q8×D43C22148yescomplemented
52C2×#13063300C2213yescomplemented
53C2×#13063299C2213yescomplemented
54C2×#13063298C2216yescomplemented
55C2×#13063297C2216yescomplemented
56C2×#13063296C2213yescomplemented
57#121×D43C22148yescomplemented
58C2×Q8×Dic43C2211yescharacteristic, complemented
59C2×C4×Dic86C2213yescomplemented
60C2×#13063290C2213yescomplemented
61C4×Q8×D43C22116yescomplemented
62C2×C4×D172C2213yescomplemented
63C2×D4×Dic43C2213yescomplemented
64C2×#13063287C2213yescomplemented
65C2×C4×C22⋊D43C2213yescomplemented
66C2×C4×C22⋊D43C2213yescomplemented
67C2×(C22⋊D43)⋊C4C2213yescomplemented
68C2×(C22⋊D43)⋊C4C2213yescomplemented
69C4×D4×D43C22148yescomplemented
70C2×C4⋊C4×D43C2213yes—
71C2×C4⋊C4×D43C2213yes—
72C2×C22⋊C4×D43C2216yes—
73C2×C22⋊C4×D43C2213yes—
74C2×C22⋊C4×D43C2211yescharacteristic
75C2×C42×D43C2213yes—
76C22×#41×C43C2211yescharacteristic, complemented
77C23×Q8×C43C2211yescharacteristic, complemented
78C43×#548C22116yescomplemented
79C2×#124×C43C2213yescomplemented
80C2×C22⋊Q8×C43C2213yescomplemented
81C2×#121×C43C2213yescomplemented
82C2×C4×Q8×C43C2211yescharacteristic, complemented
83C2×C4×D4×C43C2213yescomplemented
84C24×D43C2313yes—
85C24×D43C2311yescharacteristic
86C2×#10621902—28no—
87C2×#10621902C2318yescomplemented
88C2×#10621898—224no—
89C2×#10621898C23124yescomplemented
90C2×#10621900—224no—
91C2×#10621900C23124yescomplemented
92#41×D43—2128no—
93C22×Dic86—224no—
94C22×Dic86C2316yes—
95C22×Dic86C2313yes—
96C22×Dic86C2313yes—
97C22×Dic86C23124yescomplemented
98C2×Q8×D43—28no—
99C2×Q8×D43—2128no—
100C2×Q8×D43—224no—
101C2×Q8×D43—224no—
102C2×Q8×D43D4116yescomplemented
103C2×Q8×D43C23124yes—
104C2×Q8×D43C2318yes—
105C2×Q8×D43C2318yescomplemented
106C2×Q8×D43C23124yescomplemented
107C22×D172C2313yes—
108C22×D172C2313yes—
109C22×C22⋊D43C2313yes—
110C22×C22⋊D43C2313yes—
111C22×C22⋊D43C2316yes—
112C2×D4×D43—224no—
113C2×D4×D43—224no—
114C2×D4×D43C23124yes—
115C2×D4×D43C23124yes—
116C23×Dic43C2313yes—
117C23×Dic43C2313yes—
118C22×C4×D43—224no—
119C22×C4×D43—224no—
120C22×C4×D43C2311yescharacteristic
121C22×C4×D43C2313yes—
122C22×C4×D43C2313yes—
123C22×C4×D43C2311yescharacteristic
124C22×C4×D43C23124yes—
125C22×C4×D43C23124yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129C22×C4×D43C2313yes—
130C22×C4×D43C2313yes—
131#13063314C23124yescomplemented
132#13063313C23124yescomplemented
133#13063312C23124yescomplemented
134#13063311C23148yescomplemented
135#13063311C23148yescomplemented
136#13063305C23124yescomplemented
137#13063304C23124yescomplemented
138#13063303C23148yescomplemented
139#13063302C23148yescomplemented
140#13063301C23124yescomplemented
141#13063300C23124yescomplemented
142#13063299C23124yescomplemented
143#13063298C23148yescomplemented
144#13063297C23148yescomplemented
145#13063296C23124yescomplemented
146Q8×Dic43C2318yescomplemented
147C4×Dic86C23124yescomplemented
148#13063290C23124yescomplemented
149C4×D172C23124yescomplemented
150D4×Dic43C23124yescomplemented
151#13063287C23124yescomplemented
152C4×C22⋊D43C23124yescomplemented
153C4×C22⋊D43C23124yescomplemented
154(C22⋊D43)⋊C4C23124yescomplemented
155(C22⋊D43)⋊C4C23124yescomplemented
156C2×C4⋊Dic43C2313yes—
157C2×C4⋊Dic43C2313yes—
158C2×Dic43⋊C4C2313yes—
159C2×Dic43⋊C4C2313yes—
160C2×Dic43⋊C4C2316yes—
161C4⋊C4×D43C23124yes—
162C4⋊C4×D43C23124yes—
163C2×C22⋊Dic43C2311yescharacteristic
164C2×C22⋊Dic43C2313yes—
165C2×C22⋊Dic43C2316yes—
166C2×(C2×D43)⋊C4C2311yescharacteristic
167C2×(C2×D43)⋊C4C2313yes—
168C2×(C2×D43)⋊C4C2311yescharacteristic
169C2×(C2×D43)⋊C4C2313yes—
170C2×(C2×D43)⋊C4C2316yes—
171C2×(C2×D43)⋊C4C2316yes—
172C22⋊C4×D43C2318yes—
173C22⋊C4×D43C23124yes—
174C22⋊C4×D43C23148yes—
175C2×C4×Dic43C2313yes—
176C2×C4×Dic43C2313yes—
177C2×C4×Dic43C2313yes—
178C42×D43C23124yes—
179C2×#41×C43—28no—
180C2×#41×C43C2318yescomplemented
181C22×Q8×C43—28no—
182C22×Q8×C43C2313yes—
183C22×Q8×C43C2311yescharacteristic
184C22×Q8×C43C2318yescomplemented
185C22×D4×C43C2313yes—
186C22×D4×C43C2313yes—
187C23×C4×C43C2313yes—
188C23×C4×C43C2313yes—
189#124×C43C23124yescomplemented
190C22⋊Q8×C43C23124yescomplemented
191#121×C43C23124yescomplemented
192C4×Q8×C43C2318yescomplemented
193C4×D4×C43C23124yescomplemented
194C2×C4⋊C4×C43C2313yes—
195C2×C4⋊C4×C43C2313yes—
196C2×C22⋊C4×C43C2311yescharacteristic
197C2×C22⋊C4×C43C2313yes—
198C2×C22⋊C4×C43C2316yes—
199C2×C42×C43C2313yes—
200C24×C43C2413yes—
201C24×C43C2411yescharacteristic
202C23×D43—24no—
203C23×D43—24no—
204C23×D43—212no—
205C23×D43—212no—
206C23×D43—212no—
207C23×D43#4118yescomplemented
208C23×D43C24112yes—
209C23×D43C2413yes—
210C23×D43C2414yes—
211C23×D43C2411yescharacteristic
212C23×D43C2411yescharacteristic
213#41×C43—232no—
214C2×Q8×C43—232no—
215C2×Q8×C43—212no—
216C2×Q8×C43C2×D418yescomplemented
217C2×Q8×C43C24112yes—
218C2×Q8×C43C2414yes—
219C2×D4×C43—212no—
220C2×D4×C43—212no—
221C2×D4×C43C24112yes—
222C2×D4×C43C24112yes—
223C22×C4×C43—212no—
224C22×C4×C43—212no—
225C22×C4×C43C2411yescharacteristic
226C22×C4×C43C2413yes—
227C22×C4×C43C2413yes—
228C22×C4×C43C2411yescharacteristic
229C22×C4×C43C24112yes—
230C22×C4×C43C24112yes—
231C22×C4×C43C2413yes—
232C2×C22⋊D43—224no—
233C2×C22⋊D43—212no—
234C2×C22⋊D43—212no—
235C2×C22⋊D43C24112yes—
236C2×C22⋊D43C24112yes—
237C2×C22⋊D43C24124yes—
238C22×Dic43—212no—
239C22×Dic43—212no—
240C22×Dic43C2411yescharacteristic
241C22×Dic43C2413yes—
242C22×Dic43C2413yes—
243C22×Dic43C2411yescharacteristic
244C22×Dic43C24112yes—
245C22×Dic43C24112yes—
246C22×Dic43C2413yes—
247#10621902—232no—
248Q8×D43—232no—
249Q8×D43—296no—
250Q8×D43—296no—
251Q8×D43C2×D4164yescomplemented
252#10621900—296no—
253D4×D43—296no—
254D4×D43—296no—
255#10621898—296no—
256C2×D172—212no—
257C2×D172—212no—
258C2×D172C24112yes—
259C2×D172C24112yes—
260C2×C4×D43—212no—
261C2×C4×D43—212no—
262C2×C4×D43—212no—
263C2×C4×D43—212no—
264C2×C4×D43—296no—
265C2×C4×D43—296no—
266C2×C4×D43—24no—
267C2×C4×D43—212no—
268C2×C4×D43—212no—
269C2×C4×D43—24no—
270C2×C4×D43C2×D4124yes—
271C2×C4×D43C2414yes—
272C2×C4×D43C24112yes—
273C2×C4×D43C24112yes—
274C2×C4×D43C2414yes—
275C2×C4×D43C24112yes—
276C2×C4×D43C24112yes—
277C2×C4×D43C24112yes—
278C2×C4×D43C24112yes—
279C2×C4×D43C24112yes—
280C2×Dic86—212no—
281C2×Dic86—224no—
282C2×Dic86—296no—
283C2×Dic86C2×D4124yescomplemented
284C2×Dic86C24124yes—
285C2×Dic86C24112yes—
286C2×Dic86C24112yes—
287C4⋊C4×C43C24112yes—
288C4⋊C4×C43C24112yes—
289C22⋊C4×C43C2414yes—
290C22⋊C4×C43C24112yes—
291C22⋊C4×C43C24124yes—
292C42×C43C24112yes—
293C22⋊Dic43C2414yes—
294C22⋊Dic43C24112yes—
295C22⋊Dic43C24124yes—
296(C2×D43)⋊C4C2414yes—
297(C2×D43)⋊C4C24112yes—
298(C2×D43)⋊C4C2414yes—
299(C2×D43)⋊C4C24112yes—
300(C2×D43)⋊C4C24124yes—
301(C2×D43)⋊C4C24124yes—
302C4⋊Dic43C24112yes—
303C4⋊Dic43C24112yes—
304Dic43⋊C4C24112yes—
305Dic43⋊C4C24112yes—
306Dic43⋊C4C24124yes—
307C4×Dic43C24112yes—
308C4×Dic43C24112yes—
309C4×Dic43C24112yes—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—26no—
313C23×C43—26no—
314C23×C43—26no—
315C23×C43C2×#4114yescomplemented
316C23×C43C2516yes—
317C23×C43C2512yes—
318C23×C43C2511yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—232no—
322C22×D43—28no—
323C22×D43—28no—
324C22×D43—26no—
325C22×D43—26no—
326C22×D43—26no—
327C22×D43—224no—
328C22×D43—224no—
329C22×D43—224no—
330C22×D43—448no—
331C22×D43C22×D414yes—
332C22×D43C2×#4114yes—
333C22×D43C2×#41116yescomplemented
334C22×D43C2×#4114yescomplemented
335C22×D432−1+414yes—
336C22×D43C2516yes—
337C22×D43C2512yes—
338C22×D43C2512yes—
339Q8×C43—224no—
340Q8×C43C22×D4116yescomplemented
341D4×C43—224no—
342D4×C43—224no—
343C2×C4×C43—26no—
344C2×C4×C43—22no—
345C2×C4×C43—26no—
346C2×C4×C43—22no—
347C2×C4×C43—224no—
348C2×C4×C43—224no—
349C2×C4×C43C22×D4112yes—
350C2×C4×C43C2512yes—
351C2×C4×C43C2516yes—
352C2×C4×C43C2512yes—
353C2×C4×C43C2516yes—
354C2×C4×C43C2516yes—
355C22⋊D43—224no—
356C22⋊D43—224no—
357C22⋊D43—248no—
358C2×Dic43—26no—
359C2×Dic43—22no—
360C2×Dic43—26no—
361C2×Dic43—22no—
362C2×Dic43—224no—
363C2×Dic43—224no—
364C2×Dic43C22×D4112yes—
365C2×Dic43C2512yes—
366C2×Dic43C2516yes—
367C2×Dic43C2512yes—
368C2×Dic43C2516yes—
369C2×Dic43C2516yes—
370D172—224no—
371D172—224no—
372C4×D43—28no—
373C4×D43—224no—
374C4×D43—224no—
375C4×D43—28no—
376C4×D43—224no—
377C4×D43—224no—
378C4×D43—224no—
379C4×D43—224no—
380C4×D43C22×D4148yes—
381Dic86—224no—
382Dic86—248no—
383Dic86C22×D4148yescomplemented
384C22×#548—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—28no—
388C22×C43—26no—
389C22×C43—26no—
390C22×C43—26no—
391C22×C43—412no—
392C22×C43C23×D412yes—
393C22×C43C22×#4112yes—
394C22×C43C22×#4114yescomplemented
395C22×C43C2×2−1+412yes—
396C22×C43C2611yescharacteristic
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—28no—
400C2×D43—232no—
401C2×D43—26no—
402C2×D43—26no—
403C2×D43—26no—
404C2×D43—412no—
405C2×D43—448no—
406C2×D43#548116yesdirect product factor
407C2×D43C23×D414yes—
408C2×D43C22×#4114yes—
409C2×D43C22×#4114yescomplemented
410C2×D43C2×2−1+414yes—
411C4×C43—26no—
412C4×C43—22no—
413C4×C43—26no—
414C4×C43—22no—
415C4×C43C23×D4112yes—
416Dic43—26no—
417Dic43—22no—
418Dic43—26no—
419Dic43—22no—
420Dic43C23×D4112yes—
421C23×#41—431no—
422C24×Q8—431no—
423C2×#548—431no—
424C2×#548—431no—
425C2×#548—4332no—
426C2×#548—433no—
427C2×#548—433no—
428C2×#548—433no—
429C2×#548—431no—
430C2×#548—433no—
431C2×#548D4311yescharacteristic, direct product factor
432C22×#124—433no—
433C22×C22⋊Q8—433no—
434C22×#121—433no—
435C22×C4×Q8—431no—
436C22×C4×D4—433no—
437C2×C43—24no—
438C2×C43—46no—
439C2×C43C2×#54814yescomplemented
440C2×C43C24×D411yescharacteristic
441C2×C43C23×#4111yescharacteristic
442C2×C43C22×2−1+411yescharacteristic
443D43—24no—
444D43—46no—
445D43C2×#54818yesdirect product factor
446C22×#41—4316no—
447C22×#41—431no—
448C22×#41—433no—
449C22×#41—433no—
450C22×#41—8616no—
451C22×#41C2×D4311yescharacteristic, complemented
452C23×Q8—431no—
453C23×Q8—433no—
454C23×Q8—433no—
455C23×Q8—431no—
456C23×Q8—4316no—
457C23×Q8—433no—
458C23×Q8—8616no—
459C23×Q8C2×D4311yescharacteristic, complemented
460C23×D4—433no—
461C23×D4—433no—
462C24×C4—433no—
463C24×C4—433no—
464#548—4316no—
465#548—4316no—
466#548—4348no—
467#548—4348no—
468#548—4348no—
469#548—4316no—
470#548—4348no—
471#548C2×D43116yesdirect product factor
472C2×#124—433no—
473C2×#124—433no—
474C2×#124—4348no—
475C2×#124—436no—
476C2×#124—436no—
477C2×#124—433no—
478C2×#124C2×D4313yescomplemented
479C2×C22⋊Q8—433no—
480C2×C22⋊Q8—433no—
481C2×C22⋊Q8—4348no—
482C2×C22⋊Q8—436no—
483C2×C22⋊Q8—433no—
484C2×C22⋊Q8—436no—
485C2×C22⋊Q8C2×D4313yescomplemented
486C2×#121—433no—
487C2×#121—436no—
488C2×#121—433no—
489C2×#121—4348no—
490C2×#121—433no—
491C2×#121—436no—
492C2×#121C2×D4313yescomplemented
493C2×C4×Q8—431no—
494C2×C4×Q8—4316no—
495C2×C4×Q8—433no—
496C2×C4×Q8—433no—
497C2×C4×Q8C2×D4311yescharacteristic, complemented
498C2×C4×D4—433no—
499C2×C4×D4—433no—
500C2×C4×D4—433no—
501C2×C4×D4—4348no—
502C2×C4×D4—433no—
503C2×C4×D4—433no—
504C2×C4×D4—433no—
505C2×C4×D4—433no—
506C2×C4×D4C2×D4313yescomplemented
507C22×C4⋊C4—433no—
508C22×C4⋊C4—433no—
509C22×C22⋊C4—431no—
510C22×C22⋊C4—433no—
511C22×C22⋊C4—436no—
512C22×C42—433no—
513C43C22×#54811yescharacteristic, complemented, Sylow
514C25—431no—
515C25—433no—
516C2×#41—28no—
517C2×#41—438no—
518C2×#41—4324no—
519C2×#41—4324no—
520C2×#41—8624no—
521C2×#41—8624no—
522C2×#41—86128no—
523C2×#41—868no—
524C2×#41C22×D4318yescomplemented
525C22×Q8—28no—
526C22×Q8—4316no—
527C22×Q8—438no—
528C22×Q8—4324no—
529C22×Q8—4324no—
530C22×Q8—438no—
531C22×Q8—433no—
532C22×Q8—436no—
533C22×Q8—433no—
534C22×Q8—4324no—
535C22×Q8—8624no—
536C22×Q8—8624no—
537C22×Q8—86128no—
538C22×Q8—8624no—
539C22×Q8—868no—
540C22×Q8C22×D4313yes—
541C22×Q8C22×D4311yescharacteristic
542C22×Q8C22×D4318yescomplemented
543C22×D4—433no—
544C22×D4—433no—
545C22×D4—436no—
546C22×D4—4324no—
547C22×D4—4324no—
548C22×D4—433no—
549C22×D4—433no—
550C22×D4—8624no—
551C22×D4—8624no—
552C22×D4C22×D4313yes—
553C22×D4C22×D4313yes—
554C23×C4—433no—
555C23×C4—433no—
556C23×C4—433no—
557C23×C4—431no—
558C23×C4—433no—
559C23×C4—433no—
560C23×C4—431no—
561C23×C4—433no—
562C23×C4—4324no—
563C23×C4—433no—
564C23×C4—433no—
565C23×C4—4324no—
566C23×C4—433no—
567C23×C4—8624no—
568C23×C4—8624no—
569C23×C4C22×D4313yes—
570C23×C4C22×D4313yes—
571#124—4324no—
572#124—4324no—
573#124—4348no—
574#124—4348no—
575#124—4324no—
576#124C22×D43124yescomplemented
577C22⋊Q8—4324no—
578C22⋊Q8—4324no—
579C22⋊Q8—4348no—
580C22⋊Q8—4324no—
581C22⋊Q8—4348no—
582C22⋊Q8C22×D43124yescomplemented
583#121—4324no—
584#121—4348no—
585#121—4324no—
586#121—4324no—
587#121—4348no—
588#121C22×D43124yescomplemented
589C4×Q8—438no—
590C4×Q8—4324no—
591C4×Q8—4324no—
592C4×Q8C22×D4318yescomplemented
593C4×D4—4324no—
594C4×D4—4324no—
595C4×D4—4324no—
596C4×D4—4324no—
597C4×D4—4324no—
598C4×D4—4324no—
599C4×D4—4324no—
600C4×D4C22×D43124yescomplemented
601C2×C4⋊C4—433no—
602C2×C4⋊C4—433no—
603C2×C4⋊C4—433no—
604C2×C4⋊C4—436no—
605C2×C4⋊C4—433no—
606C2×C4⋊C4—4324no—
607C2×C4⋊C4—4324no—
608C2×C4⋊C4C22×D4313yes—
609C2×C4⋊C4C22×D4313yes—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—433no—
612C2×C22⋊C4—436no—
613C2×C22⋊C4—431no—
614C2×C22⋊C4—431no—
615C2×C22⋊C4—433no—
616C2×C22⋊C4—433no—
617C2×C22⋊C4—436no—
618C2×C22⋊C4—436no—
619C2×C22⋊C4—438no—
620C2×C22⋊C4—4324no—
621C2×C22⋊C4—4348no—
622C2×C22⋊C4C22×D4311yescharacteristic
623C2×C22⋊C4C22×D4313yes—
624C2×C22⋊C4C22×D4316yes—
625C2×C42—433no—
626C2×C42—433no—
627C2×C42—433no—
628C2×C42—4324no—
629C2×C42C22×D4313yes—
630C24—431no—
631C24—438no—
632C24—434no—
633C24—431no—
634C24—4312no—
635C24—433no—
636C24—864no—
637C24—864no—
638C24—8612no—
639C24—8612no—
640C24—8612no—
641C24C23×D4313yes—
642C24C23×D4311yescharacteristic
643#41—232no—
644#41—8696no—
645#41—8696no—
646#41—8632no—
647C2×Q8—232no—
648C2×Q8—212no—
649C2×Q8—4364no—
650C2×Q8—4324no—
651C2×Q8—4312no—
652C2×Q8—4324no—
653C2×Q8—4312no—
654C2×Q8—8624no—
655C2×Q8—8696no—
656C2×Q8—8696no—
657C2×Q8—8696no—
658C2×Q8—8632no—
659C2×Q8—8612no—
660C2×Q8D4×D4318yescomplemented
661C2×Q8C23×D43112yes—
662C2×Q8C23×D4314yes—
663C2×D4—212no—
664C2×D4—212no—
665C2×D4—4312no—
666C2×D4—4312no—
667C2×D4—4324no—
668C2×D4—4312no—
669C2×D4—4312no—
670C2×D4—8612no—
671C2×D4—8696no—
672C2×D4—8624no—
673C2×D4—8696no—
674C2×D4—8612no—
675C2×D4—8612no—
676C2×D4—8612no—
677C2×D4C23×D43112yes—
678C2×D4C23×D43112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—433no—
682C22×C4—4324no—
683C22×C4—4312no—
684C22×C4—4312no—
685C22×C4—4312no—
686C22×C4—431no—
687C22×C4—433no—
688C22×C4—433no—
689C22×C4—431no—
690C22×C4—434no—
691C22×C4—4312no—
692C22×C4—4312no—
693C22×C4—434no—
694C22×C4—4312no—
695C22×C4—4312no—
696C22×C4—4312no—
697C22×C4—4312no—
698C22×C4—8612no—
699C22×C4—8696no—
700C22×C4—8612no—
701C22×C4—8696no—
702C22×C4—864no—
703C22×C4—8612no—
704C22×C4—8612no—
705C22×C4—864no—
706C22×C4—8612no—
707C22×C4—8612no—
708C22×C4—8612no—
709C22×C4—8612no—
710C22×C4C23×D43112yes—
711C22×C4C23×D43112yes—
712C22×C4C23×D4311yescharacteristic
713C22×C4C23×D4313yes—
714C22×C4C23×D4313yes—
715C22×C4C23×D4311yescharacteristic
716C22×C4C23×D4313yes—
717C4⋊C4—4312no—
718C4⋊C4—4312no—
719C4⋊C4—4312no—
720C4⋊C4—4324no—
721C4⋊C4—4312no—
722C4⋊C4C23×D43112yes—
723C4⋊C4C23×D43112yes—
724C22⋊C4—434no—
725C22⋊C4—4312no—
726C22⋊C4—4324no—
727C22⋊C4—434no—
728C22⋊C4—434no—
729C22⋊C4—4312no—
730C22⋊C4—4312no—
731C22⋊C4—4324no—
732C22⋊C4—4324no—
733C22⋊C4C23×D4314yes—
734C22⋊C4C23×D43112yes—
735C22⋊C4C23×D43124yes—
736C42—4312no—
737C42—4312no—
738C42—4312no—
739C42C23×D43112yes—
740C23—22no—
741C23—22no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—434no—
746C23—434no—
747C23—434no—
748C23—432no—
749C23—434no—
750C23—4316no—
751C23—432no—
752C23—436no—
753C23—868no—
754C23—8632no—
755C23—868no—
756C23—8624no—
757C23—8624no—
758C23—8624no—
759C23—862no—
760C23—862no—
761C23—866no—
762C23—866no—
763C23—866no—
764C23—17248no—
765C23#41×D4314yescomplemented
766C23C24×D4316yes—
767C23C24×D4312yes—
768C23C24×D4311yescharacteristic
769Q8—224no—
770Q8—4348no—
771Q8—8648no—
772Q8—8624no—
773Q8C2×D4×D43116yescomplemented
774D4—224no—
775D4—224no—
776D4—8624no—
777D4—8648no—
778D4—8624no—
779D4—8624no—
780D4—8624no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—4312no—
788C2×C4—436no—
789C2×C4—4348no—
790C2×C4—432no—
791C2×C4—436no—
792C2×C4—436no—
793C2×C4—432no—
794C2×C4—8624no—
795C2×C4—8624no—
796C2×C4—868no—
797C2×C4—8624no—
798C2×C4—8624no—
799C2×C4—868no—
800C2×C4—8624no—
801C2×C4—8624no—
802C2×C4—862no—
803C2×C4—866no—
804C2×C4—866no—
805C2×C4—862no—
806C2×C4—8624no—
807C2×C4—8624no—
808C2×C4C2×D4×D43112yes—
809C2×C4C24×D4312yes—
810C2×C4C24×D4316yes—
811C2×C4C24×D4316yes—
812C2×C4C24×D4312yes—
813C2×C4C24×D4316yes—
814C22—28no—
815C22—22no—
816C22—22no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—4316no—
822C22—434no—
823C22—434no—
824C22—434no—
825C22—434no—
826C22—8632no—
827C22—868no—
828C22—862no—
829C22—862no—
830C22—866no—
831C22—866no—
832C22—866no—
833C22—17248no—
834C22—17212no—
835C22C22×D4×D4312yes—
836C22C2×#41×D4312yes—
837C22C2×#41×D4314yescomplemented
838C222−1+4×D4312yes—
839C22C25×D4311yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—4312no—
845C4—862no—
846C4—866no—
847C4—866no—
848C4—862no—
849C4C22×D4×D43112yes—
850C2—24no—
851C2—46no—
852C2—438no—
853C2—864no—
854C2—1726no—
855C2#548×D4314yesdirect product factor
856C2C23×D4×D4311yescharacteristic
857C2C22×#41×D4311yescharacteristic
858C2C2×2−1+4×D4311yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C22×#548
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#41×D43C2semidirect
2. C23×Q8×D43C2semidirect
3. C2×#14583561C2semidirect
4. C2×#14583560C2semidirect
5. C2×#14583559C2semidirect
6. C2×#14583558C2semidirect
7. C2×#14583557C2semidirect
8. C2×#14583556C2semidirect
9. C2×#14583555C2semidirect
10. #548×D43C2direct (N × H)
11. C2×#124×D43C2semidirect
12. C2×C22⋊Q8×D43C2semidirect
13. C2×#121×D43C2semidirect
14. C2×C4×Q8×D43C2semidirect
15. C2×C4×D4×D43C2semidirect
16. C2×C43×#548C2semidirect
17. C22×#10621902C22semidirect
18. C22×#10621898C22semidirect
19. C22×#10621900C22semidirect
21. C2×#41×D43C22semidirect
22. C23×Dic86C22semidirect
26. C22×Q8×D43C22semidirect
27. C22×Q8×D43C22semidirect
28. C22×Q8×D43C22semidirect
33. #14583561C22semidirect
34. #14583560C22semidirect
35. #14583559C22semidirect
36. #14583558C22semidirect
37. #14583557C22semidirect
38. #14583556C22semidirect
39. #14583555C22semidirect
40. C2×#13063314C22semidirect
41. C2×#13063313C22semidirect
42. C2×#13063312C22semidirect
43. C2×#13063311C22semidirect
44. C2×#13063311C22semidirect
45. #124×D43C22semidirect
46. C2×#13063305C22semidirect
47. C2×#13063304C22semidirect
48. C2×#13063303C22semidirect
49. C2×#13063302C22semidirect
50. C2×#13063301C22semidirect
51. C22⋊Q8×D43C22semidirect
52. C2×#13063300C22semidirect
53. C2×#13063299C22semidirect
54. C2×#13063298C22semidirect
55. C2×#13063297C22semidirect
56. C2×#13063296C22semidirect
57. #121×D43C22semidirect
58. C2×Q8×Dic43C22semidirect
59. C2×C4×Dic86C22semidirect
60. C2×#13063290C22semidirect
61. C4×Q8×D43C22semidirect
62. C2×C4×D172C22semidirect
63. C2×D4×Dic43C22semidirect
64. C2×#13063287C22semidirect
65. C2×C4×C22⋊D43C22semidirect
66. C2×C4×C22⋊D43C22semidirect
67. C2×(C22⋊D43)⋊C4C22semidirect
68. C2×(C22⋊D43)⋊C4C22semidirect
69. C4×D4×D43C22semidirect
76. C22×#41×C43C22semidirect
77. C23×Q8×C43C22semidirect
78. C43×#548C22semidirect
79. C2×#124×C43C22semidirect
80. C2×C22⋊Q8×C43C22semidirect
81. C2×#121×C43C22semidirect
82. C2×C4×Q8×C43C22semidirect
83. C2×C4×D4×C43C22semidirect
87. C2×#10621902C23semidirect
89. C2×#10621898C23semidirect
91. C2×#10621900C23semidirect
97. C22×Dic86C23semidirect
102. C2×Q8×D43D4semidirect
105. C2×Q8×D43C23semidirect
106. C2×Q8×D43C23semidirect
131. #13063314C23semidirect
132. #13063313C23semidirect
133. #13063312C23semidirect
134. #13063311C23semidirect
135. #13063311C23semidirect
136. #13063305C23semidirect
137. #13063304C23semidirect
138. #13063303C23semidirect
139. #13063302C23semidirect
140. #13063301C23semidirect
141. #13063300C23semidirect
142. #13063299C23semidirect
143. #13063298C23semidirect
144. #13063297C23semidirect
145. #13063296C23semidirect
146. Q8×Dic43C23semidirect
147. C4×Dic86C23semidirect
148. #13063290C23semidirect
149. C4×D172C23semidirect
150. D4×Dic43C23semidirect
151. #13063287C23semidirect
152. C4×C22⋊D43C23semidirect
153. C4×C22⋊D43C23semidirect
154. (C22⋊D43)⋊C4C23semidirect
155. (C22⋊D43)⋊C4C23semidirect
180. C2×#41×C43C23semidirect
184. C22×Q8×C43C23semidirect
189. #124×C43C23semidirect
190. C22⋊Q8×C43C23semidirect
191. #121×C43C23semidirect
192. C4×Q8×C43C23semidirect
193. C4×D4×C43C23semidirect
207. C23×D43#41semidirect
216. C2×Q8×C43C2×D4semidirect
251. Q8×D43C2×D4semidirect
283. C2×Dic86C2×D4semidirect
315. C23×C43C2×#41semidirect
333. C22×D43C2×#41semidirect
334. C22×D43C2×#41semidirect
340. Q8×C43C22×D4semidirect
383. Dic86C22×D4semidirect
394. C22×C43C22×#41semidirect
406. C2×D43#548direct (N × H)
409. C2×D43C22×#41semidirect
431. C2×#548D43direct (N × H)
439. C2×C43C2×#548semidirect
445. D43C2×#548direct (N × H)
451. C22×#41C2×D43semidirect
459. C23×Q8C2×D43semidirect
471. #548C2×D43direct (N × H)
478. C2×#124C2×D43semidirect
485. C2×C22⋊Q8C2×D43semidirect
492. C2×#121C2×D43semidirect
497. C2×C4×Q8C2×D43semidirect
506. C2×C4×D4C2×D43semidirect
513. C43C22×#548semidirect
524. C2×#41C22×D43semidirect
542. C22×Q8C22×D43semidirect
576. #124C22×D43semidirect
582. C22⋊Q8C22×D43semidirect
588. #121C22×D43semidirect
592. C4×Q8C22×D43semidirect
600. C4×D4C22×D43semidirect
660. C2×Q8D4×D43semidirect
765. C23#41×D43semidirect
773. Q8C2×D4×D43semidirect
837. C22C2×#41×D43semidirect
855. C2#548×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D432
C23×Q8×D432
C2×#145835612
C2×#145835602
C2×#145835592
C2×#145835582
C2×#145835572
C2×#145835562
C2×#145835552
#548×D432
C2×#124×D432
C2×C22⋊Q8×D432
C2×#121×D432
C2×C4×Q8×D432
C2×C4×D4×D432
C2×C43×#5482
C22×#54843