Finite Group Databasebeta

← C2×#19148261 #26004904

Subgroups — C2×#19148261 #26004904

Order 11008.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063371C211yesmaximal, characteristic, complemented
2C23×#10621902C211yesmaximal, characteristic, complemented
3#19148261C2132yesmaximal, direct product factor
4C2×#14583571C211yesmaximal, characteristic, complemented
5C2×#14583568C211yesmaximal, characteristic, complemented
6C2×#14583560C211yesmaximal, characteristic, complemented
7C2×#14583542C213yesmaximal, complemented
8C2×#14583540C213yesmaximal, complemented
9C2×D4×D172C213yesmaximal, complemented
10C2×#14583533C213yesmaximal, complemented
11C2×#14583479C213yesmaximal, complemented
12C2×#14583467C213yesmaximal, complemented
13C2×#14583408C213yesmaximal, complemented
14C2×#121×D43C213yesmaximal, complemented
15C2×#14583381C211yesmaximal, characteristic, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C2×#13063371—216no—
18C2×#13063371C22116yescomplemented
19C22×#10621902—216no—
20C22×#10621902C2211yescharacteristic
21C22×#10621902C2213yescomplemented
22C22×#10621902C2211yescharacteristic, complemented
23C22×#10621902C2211yescharacteristic, complemented
24C22×#10621902C2213yescomplemented
25C22×#10621902C22116yescomplemented
26C22×#10621898C2213yescomplemented
27C23×D172C2213yescomplemented
28C23×D172C2213yescomplemented
29C22×D4×D43C2213yescomplemented
30C22×D4×D43C2213yescomplemented
31C22×D4×D43C2216yescomplemented
32C23×C4×D43C2213yescomplemented
33#14583571C22116yescomplemented
34#14583568C22116yescomplemented
35#14583560C22116yescomplemented
36#14583542C22148yescomplemented
37#14583540C22148yescomplemented
38D4×D172C22148yescomplemented
39#14583533C22148yescomplemented
40#14583479C22148yescomplemented
41#14583467C22148yescomplemented
42C2×#13063322C2213yescomplemented
43C2×#13063321C2213yescomplemented
44C2×#13063314C2213yescomplemented
45#14583408C22148yescomplemented
46C2×#13063310C2213yescomplemented
47C2×#13063307C2213yescomplemented
48C2×#13063303C2213yescomplemented
49C2×#13063302C2211yescharacteristic, complemented
50C2×#13063301C2213yescomplemented
51C2×#13063300C2213yescomplemented
52C2×#13063300C2216yescomplemented
53C2×#13063300C2213yescomplemented
54C2×#13063299C2213yescomplemented
55C2×#13063299C2213yescomplemented
56C2×#13063298C2216yescomplemented
57C2×#13063298C2216yescomplemented
58C2×#13063298C2213yescomplemented
59C2×#13063297C2213yescomplemented
60C2×#13063296C2213yescomplemented
61#121×D43C22148yescomplemented
62C2×#13063295C2216yescomplemented
63C2×#13063295C2213yescomplemented
64C2×#13063295C2216yescomplemented
65C2×#13063293C2213yescomplemented
66#14583381C22116yescomplemented
67C2×Q8×Dic43C2211yescharacteristic, complemented
68C2×C4×D172C2213yescomplemented
69C2×C4×D172C2213yescomplemented
70C2×#13063287C2213yescomplemented
71C2×C4×C22⋊D43C2213yescomplemented
72C2×C4×C22⋊D43C2213yescomplemented
73C2×#13063282C2213yescomplemented
74C2×C4⋊C4×D43C2213yescomplemented
75C2×C22⋊C4×D43C2216yescomplemented
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×D43C2316yes—
86#13063371—2128no—
87C2×#10621902—28no—
88C2×#10621902—28no—
89C2×#10621902—2128no—
90C2×#10621902—224no—
91C2×#10621902—224no—
92C2×#10621902D4116yescomplemented
93C2×#10621902C2318yes—
94C2×#10621902C2318yescomplemented
95C2×#10621902C2318yescomplemented
96C2×#10621902C23124yescomplemented
97C2×#10621902C23124yescomplemented
98C2×#10621898—224no—
99C2×#10621898C23124yescomplemented
100C22×Dic86C2311yescharacteristic
101C22×D172—224no—
102C22×D172—224no—
103C22×D172C2316yes—
104C22×D172C2313yes—
105C22×D172C2313yes—
106C22×D172C2313yes—
107C22×D172C2313yes—
108C22×D172C2316yes—
109C22×D172C2313yes—
110C22×D172C23124yescomplemented
111C22×D172C23124yescomplemented
112C22×C22⋊D43C2313yes—
113C22×C22⋊D43C2313yes—
114C22×C22⋊D43C2313yes—
115C22×C22⋊D43C2313yes—
116C22×C22⋊D43C2316yes—
117C2×D4×D43—224no—
118C2×D4×D43—224no—
119C2×D4×D43—424no—
120C2×D4×D43C23124yescomplemented
121C2×D4×D43C23124yescomplemented
122C2×D4×D43C23148yescomplemented
123C23×Dic43C2311yescharacteristic
124C22×C4×D43—224no—
125C22×C4×D43C2313yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129C22×C4×D43C2316yes—
130C22×C4×D43C2313yes—
131C22×C4×D43C23124yescomplemented
132#13063322C23124yescomplemented
133#13063321C23124yescomplemented
134#13063314C23124yescomplemented
135#13063310C23124yescomplemented
136#13063307C23124yescomplemented
137#13063303C23124yescomplemented
138#13063302C2318yescomplemented
139#13063301C23124yescomplemented
140#13063300C23124yescomplemented
141#13063300C23124yescomplemented
142#13063300C23148yescomplemented
143#13063299C23124yescomplemented
144#13063299C23124yescomplemented
145#13063298C23148yescomplemented
146#13063298C23124yescomplemented
147#13063298C23148yescomplemented
148#13063297C23124yescomplemented
149#13063296C23124yescomplemented
150#13063295C23124yescomplemented
151#13063295C23148yescomplemented
152#13063295C23148yescomplemented
153#13063293C23124yescomplemented
154Q8×Dic43C2318yescomplemented
155C4×D172C23124yescomplemented
156C4×D172C23124yescomplemented
157#13063287C23124yescomplemented
158C4×C22⋊D43C23124yescomplemented
159C4×C22⋊D43C23124yescomplemented
160#13063282C23124yescomplemented
161C2×C4⋊Dic43C2313yes—
162C2×C4⋊Dic43C2311yescharacteristic
163C2×Dic43⋊C4C2313yes—
164C2×Dic43⋊C4C2311yescharacteristic
165C2×Dic43⋊C4C2311yescharacteristic
166C2×Dic43⋊C4C2313yes—
167C4⋊C4×D43C23124yescomplemented
168C2×C22⋊Dic43C2313yes—
169C2×C22⋊Dic43C2311yescharacteristic
170C2×(C2×D43)⋊C4C2313yes—
171C2×(C2×D43)⋊C4C2316yes—
172C2×(C2×D43)⋊C4C2313yes—
173C2×(C2×D43)⋊C4C2313yes—
174C2×(C2×D43)⋊C4C2313yes—
175C2×(C2×D43)⋊C4C2313yes—
176C2×(C2×D43)⋊C4C2313yes—
177C22⋊C4×D43C23148yescomplemented
178C2×C4×Dic43C2313yes—
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—212no—
203C23×D43—212no—
204C23×D43—224no—
205C23×D43—46no—
206C23×D43—412no—
207C23×D43—412no—
208C23×D43C2413yes—
209C23×D43C2413yes—
210C23×D43C24112yes—
211C23×D43C2413yes—
212C23×D43C24124yes—
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—212no—
233C2×C22⋊D43—212no—
234C2×C22⋊D43—212no—
235C2×C22⋊D43—412no—
236C2×C22⋊D43—46no—
237C2×C22⋊D43C24112yes—
238C2×C22⋊D43C24112yes—
239C2×C22⋊D43C24112yes—
240C2×C22⋊D43C24112yes—
241C2×C22⋊D43C24124yes—
242C22×Dic43—24no—
243C22×Dic43C2411yescharacteristic
244C22×Dic43C2413yes—
245C22×Dic43C2411yescharacteristic
246C22×Dic43C2411yescharacteristic
247C22×Dic43C2414yes—
248C22×Dic43C2411yescharacteristic
249#10621902—232no—
250#10621902—232no—
251#10621902—296no—
252#10621902—296no—
253#10621902C2×D4164yescomplemented
254D4×D43—296no—
255D4×D43—296no—
256D4×D43—496no—
257#10621898—296no—
258C2×D172—212no—
259C2×D172—212no—
260C2×D172—296no—
261C2×D172—296no—
262C2×D172—212no—
263C2×D172—224no—
264C2×D172—412no—
265C2×D172—46no—
266C2×D172C2×D4124yescomplemented
267C2×D172C24124yes—
268C2×D172C24112yes—
269C2×D172C24112yes—
270C2×D172C24112yes—
271C2×D172C24112yes—
272C2×D172C24124yes—
273C2×D172C24112yes—
274C2×C4×D43—212no—
275C2×C4×D43—212no—
276C2×C4×D43—212no—
277C2×C4×D43—296no—
278C2×C4×D43—212no—
279C2×C4×D43—412no—
280C2×C4×D43C2×D4124yescomplemented
281C2×C4×D43C24112yes—
282C2×C4×D43C24112yes—
283C2×C4×D43C24112yes—
284C2×C4×D43C24112yes—
285C2×C4×D43C24124yes—
286C2×C4×D43C24112yes—
287C2×Dic86—24no—
288C2×Dic86C2414yes—
289C4⋊C4×C43C24112yes—
290C4⋊C4×C43C24112yes—
291C22⋊C4×C43C2414yes—
292C22⋊C4×C43C24112yes—
293C22⋊C4×C43C24124yes—
294C42×C43C24112yes—
295C22⋊Dic43C24112yes—
296C22⋊Dic43C2414yes—
297(C2×D43)⋊C4C24112yes—
298(C2×D43)⋊C4C24124yes—
299(C2×D43)⋊C4C24112yes—
300(C2×D43)⋊C4C24112yes—
301(C2×D43)⋊C4C24112yes—
302(C2×D43)⋊C4C24112yes—
303(C2×D43)⋊C4C24112yes—
304C4⋊Dic43C24112yes—
305C4⋊Dic43C2414yes—
306Dic43⋊C4C24112yes—
307Dic43⋊C4C2414yes—
308Dic43⋊C4C2414yes—
309Dic43⋊C4C24112yes—
310C4×Dic43C24112yes—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—26no—
314C23×C43—26no—
315C23×C43—26no—
316C23×C43H(5,𝔽2)14yescomplemented
317C23×C43C2516yes—
318C23×C43C2512yes—
319C23×C43C2511yescharacteristic
320C22×D43—26no—
321C22×D43—26no—
322C22×D43—26no—
323C22×D43—26no—
324C22×D43—26no—
325C22×D43—26no—
326C22×D43—224no—
327C22×D43—26no—
328C22×D43—26no—
329C22×D43—224no—
330C22×D43—248no—
331C22×D43—412no—
332C22×D43—424no—
333C22×D43—424no—
334C22×D43—448no—
335C22×D43—848no—
336C22×D43C22×D4112yes—
337C22×D43C2516yes—
338C22×D43C2516yes—
339C22×D43C2516yes—
340Q8×C43—224no—
341Q8×C43C22×D4116yescomplemented
342D4×C43—224no—
343D4×C43—224no—
344C2×C4×C43—22no—
345C2×C4×C43—26no—
346C2×C4×C43—26no—
347C2×C4×C43—22no—
348C2×C4×C43—224no—
349C2×C4×C43—224no—
350C2×C4×C43C22×D4112yes—
351C2×C4×C43C2512yes—
352C2×C4×C43C2516yes—
353C2×C4×C43C2516yes—
354C2×C4×C43C2512yes—
355C2×C4×C43C2516yes—
356C22⋊D43—224no—
357C22⋊D43—224no—
358C22⋊D43—224no—
359C22⋊D43—424no—
360C22⋊D43—412no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—26no—
364C2×Dic43—22no—
365C2×Dic43—28no—
366C2×Dic43C22×D414yes—
367C2×Dic43C2512yes—
368C2×Dic43C2516yes—
369C2×Dic43C2512yes—
370C2×Dic43C2512yes—
371C2×Dic43C2512yes—
372D172—224no—
373D172—248no—
374D172—224no—
375D172—224no—
376D172—412no—
377D172—424no—
378D172C22×D4148yescomplemented
379C4×D43—224no—
380C4×D43—224no—
381C4×D43—224no—
382C4×D43—224no—
383C4×D43—424no—
384C4×D43C22×D4148yescomplemented
385Dic86—28no—
386C2×#3488—431nomaximal, Sylow
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—28no—
390C22×C43—26no—
391C22×C43—26no—
392C22×C43—26no—
393C22×C43—412no—
394C22×C43C23×D412yes—
395C22×C43C2×H(5,𝔽2)12yes—
396C22×C43C2×H(5,𝔽2)14yescomplemented
397C22×C43#58512yes—
398C22×C43C2611yescharacteristic
399C2×D43—26no—
400C2×D43—26no—
401C2×D43—224no—
402C2×D43—26no—
403C2×D43—26no—
404C2×D43—26no—
405C2×D43—26no—
406C2×D43—26no—
407C2×D43—26no—
408C2×D43—448no—
409C2×D43—412no—
410C2×D43—412no—
411C2×D43—848no—
412C2×D43C23×D4112yes—
413C4×C43—22no—
414C4×C43—26no—
415C4×C43—26no—
416C4×C43—22no—
417C4×C43C23×D4112yes—
418Dic43—22no—
419Dic43—22no—
420Dic43—26no—
421Dic43—22no—
422Dic43C23×D414yes—
423C22×H(5,𝔽2)—431no—
424C23×#41—431no—
425#3488—4332no—
426C2×#550—431no—
427C2×#550—431no—
428C2×#548—431no—
429C2×#548D4311yescharacteristic, complemented
430C2×#546—433no—
431C2×#546—433no—
432C2×D42—433no—
433C2×D42—433no—
434C2×#537—433no—
435C2×#535—433no—
436C2×#525—433no—
437C22×#121—433no—
438C2×#520—431no—
439C2×C43—24no—
440C2×C43—46no—
441C2×C43#348814yescomplemented
442C2×C43C24×D411yescharacteristic
443C2×C43C22×H(5,𝔽2)11yescharacteristic
444C2×C43C2×#58511yescharacteristic
445D43—212no—
446D43—46no—
447D43—46no—
448C2×H(5,𝔽2)—4316no—
449C2×H(5,𝔽2)—8616no—
450C22×#41—431no—
451C22×#41—433no—
452C22×#41—433no—
453C22×#41—431no—
454C22×#41—431no—
455C22×#41—4316no—
456C22×#41—433no—
457C22×#41—8616no—
458C22×#41C2×D4311yescharacteristic, complemented
459C23×Q8C2×D4311yescharacteristic, complemented
460C23×D4—433no—
461C23×D4—433no—
462C23×D4—436no—
463C23×D4—433no—
464C23×D4—433no—
465C24×C4—433no—
466#550—4316no—
467#550—4316no—
468#548—4316no—
469#548C2×D43116yescomplemented
470#546—4348no—
471#546—4348no—
472D42—4348no—
473D42—4348no—
474#537—4348no—
475#535—4348no—
476C2×#127—433no—
477C2×#127—433no—
478C2×#124—433no—
479C2×#124C2×D4313yescomplemented
480#525—4348no—
481C2×#123—433no—
482C2×#123—433no—
483C2×C22⋊Q8—433no—
484C2×C22⋊Q8—433no—
485C2×C22⋊Q8—431no—
486C2×C22⋊Q8C2×D4313yescomplemented
487C2×#121—433no—
488C2×#121—433no—
489C2×#121—433no—
490C2×#121—433no—
491C2×#121—4348no—
492C2×#121—433no—
493C2×#121—436no—
494C2×#121—433no—
495C2×#121—436no—
496C2×#121—433no—
497C2×#121—436no—
498C2×#121C2×D4313yescomplemented
499C2×#120—433no—
500C2×#120—433no—
501C2×#120—436no—
502C2×#120—436no—
503#520—4316no—
504C2×C4×Q8—431no—
505C2×C4×Q8C2×D4311yescharacteristic, complemented
506C2×C4×D4—433no—
507C2×C4×D4—433no—
508C2×C4×D4—433no—
509C2×C4×D4—433no—
510C2×C4×D4—433no—
511C2×C4×D4C2×D4313yescomplemented
512C2×#117—433no—
513C22×C4⋊C4—433no—
514C22×C22⋊C4—436no—
515C43C2×#348811yescharacteristic, complemented, Sylow
516C25—433no—
517C25—436no—
518H(5,𝔽2)—86128no—
519C2×#41—28no—
520C2×#41—4316no—
521C2×#41—438no—
522C2×#41—4324no—
523C2×#41—4324no—
524C2×#41—438no—
525C2×#41—438no—
526C2×#41—4324no—
527C2×#41—8624no—
528C2×#41—8624no—
529C2×#41—8624no—
530C2×#41—86128no—
531C2×#41—868no—
532C2×#41—868no—
533C2×#41C22×D4318yescomplemented
534C22×Q8—28no—
535C22×Q8—431no—
536C22×Q8C22×D4313yes—
537C22×Q8C22×D4311yescharacteristic
538C22×Q8C22×D4318yescomplemented
539C22×D4—433no—
540C22×D4—433no—
541C22×D4—433no—
542C22×D4—433no—
543C22×D4—436no—
544C22×D4—4324no—
545C22×D4—4324no—
546C22×D4—4348no—
547C22×D4—433no—
548C22×D4—436no—
549C22×D4—433no—
550C22×D4—433no—
551C22×D4—433no—
552C22×D4—4324no—
553C22×D4—4324no—
554C22×D4—433no—
555C22×D4—436no—
556C22×D4—8624no—
557C22×D4—8624no—
558C22×D4—8624no—
559C22×D4—8624no—
560C22×D4—17224no—
561C22×D4C22×D4313yes—
562C22×D4C22×D4313yes—
563C23×C4—433no—
564C23×C4—431no—
565C23×C4—433no—
566C23×C4—433no—
567C23×C4—433no—
568C23×C4—433no—
569C23×C4—4324no—
570C23×C4—436no—
571C23×C4—8624no—
572C23×C4C22×D4313yes—
573C23×C4C22×D4313yes—
574#127—4324no—
575#127—4324no—
576#124—4324no—
577#124C22×D43124yescomplemented
578#123—4324no—
579#123—4324no—
580C22⋊Q8—4324no—
581C22⋊Q8—4324no—
582C22⋊Q8—438no—
583C22⋊Q8C22×D43124yescomplemented
584#121—4324no—
585#121—4324no—
586#121—4324no—
587#121—4324no—
588#121—4324no—
589#121—4348no—
590#121—4324no—
591#121—4348no—
592#121—4324no—
593#121—4348no—
594#121C22×D43124yescomplemented
595#120—4324no—
596#120—4324no—
597#120—4348no—
598#120—4348no—
599C4×Q8—438no—
600C4×Q8C22×D4318yescomplemented
601C4×D4—4324no—
602C4×D4—4324no—
603C4×D4—4324no—
604C4×D4—4324no—
605C4×D4—4324no—
606C4×D4C22×D43124yescomplemented
607#117—4324no—
608C2×C4⋊C4—433no—
609C2×C4⋊C4—433no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—431no—
613C2×C4⋊C4—433no—
614C2×C4⋊C4—4324no—
615C2×C4⋊C4C22×D4313yes—
616C2×C4⋊C4C22×D4313yes—
617C2×C22⋊C4—433no—
618C2×C22⋊C4—431no—
619C2×C22⋊C4—433no—
620C2×C22⋊C4—436no—
621C2×C22⋊C4—433no—
622C2×C22⋊C4—433no—
623C2×C22⋊C4—433no—
624C2×C22⋊C4—433no—
625C2×C22⋊C4—433no—
626C2×C22⋊C4—4348no—
627C2×C22⋊C4C22×D4316yes—
628C2×C22⋊C4C22×D4311yescharacteristic
629C2×C22⋊C4C22×D4313yes—
630C2×C42—433no—
631C2×C42C22×D4313yes—
632C24—433no—
633C24—433no—
634C24—433no—
635C24—4312no—
636C24—4324no—
637C24—8624no—
638C24—8612no—
639C24—8612no—
640C24—17212no—
641C24—17212no—
642C24—1726no—
643C24C23×D4313yes—
644C24C23×D4311yescharacteristic
645#41—232no—
646#41—4364no—
647#41—8696no—
648#41—8696no—
649#41—8696no—
650#41—8632no—
651#41—8632no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—434no—
655C2×Q8—864no—
656C2×Q8D4×D4318yescomplemented
657C2×Q8C23×D43112yes—
658C2×Q8C23×D4314yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—4312no—
662C2×D4—4312no—
663C2×D4—4312no—
664C2×D4—4312no—
665C2×D4—4324no—
666C2×D4—4324no—
667C2×D4—4312no—
668C2×D4—4324no—
669C2×D4—4312no—
670C2×D4—4312no—
671C2×D4—4312no—
672C2×D4—4312no—
673C2×D4—4324no—
674C2×D4—8696no—
675C2×D4—8696no—
676C2×D4—8612no—
677C2×D4—8624no—
678C2×D4—8696no—
679C2×D4—8612no—
680C2×D4—8696no—
681C2×D4—8612no—
682C2×D4—8612no—
683C2×D4—8612no—
684C2×D4—8612no—
685C2×D4—17212no—
686C2×D4—1726no—
687C2×D4—17212no—
688C2×D4—1726no—
689C2×D4—17296no—
690C2×D4C23×D43112yes—
691C2×D4C23×D43112yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—431no—
695C22×C4—4324no—
696C22×C4—4312no—
697C22×C4—434no—
698C22×C4—431no—
699C22×C4—433no—
700C22×C4—431no—
701C22×C4—431no—
702C22×C4—4312no—
703C22×C4—4312no—
704C22×C4—4312no—
705C22×C4—4312no—
706C22×C4—4324no—
707C22×C4—8612no—
708C22×C4—8696no—
709C22×C4—8612no—
710C22×C4—864no—
711C22×C4—8612no—
712C22×C4—8612no—
713C22×C4—17212no—
714C22×C4C23×D43112yes—
715C22×C4C23×D43112yes—
716C22×C4C23×D4311yescharacteristic
717C22×C4C23×D4313yes—
718C22×C4C23×D4313yes—
719C22×C4C23×D4311yescharacteristic
720C22×C4C23×D4313yes—
721C4⋊C4—4312no—
722C4⋊C4—4312no—
723C4⋊C4—434no—
724C4⋊C4—434no—
725C4⋊C4—434no—
726C4⋊C4—4312no—
727C4⋊C4C23×D43112yes—
728C4⋊C4C23×D43112yes—
729C22⋊C4—4312no—
730C22⋊C4—434no—
731C22⋊C4—4312no—
732C22⋊C4—4324no—
733C22⋊C4—4312no—
734C22⋊C4—4312no—
735C22⋊C4—4312no—
736C22⋊C4—4312no—
737C22⋊C4—4312no—
738C22⋊C4C23×D43124yes—
739C22⋊C4C23×D4314yes—
740C22⋊C4C23×D43112yes—
741C42—4312no—
742C42C23×D43112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—4312no—
749C23—436no—
750C23—436no—
751C23—436no—
752C23—8648no—
753C23—8624no—
754C23—866no—
755C23—866no—
756C23—866no—
757C23—866no—
758C23—866no—
759C23—866no—
760C23—8624no—
761C23—866no—
762C23—866no—
763C23—34448no—
764C23—17224no—
765C23—17224no—
766C23—17212no—
767C23—17248no—
768C23#1306337114yescomplemented
769C23C24×D4316yes—
770C23C24×D4312yes—
771C23C24×D4311yescharacteristic
772Q8—224no—
773Q8—868no—
774Q8C2×D4×D43116yescomplemented
775D4—224no—
776D4—224no—
777D4—4348no—
778D4—8624no—
779D4—8648no—
780D4—8624no—
781D4—8624no—
782D4—8624no—
783D4—8624no—
784D4—8624no—
785D4—17224no—
786D4—17212no—
787D4—17224no—
788D4—17212no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—434no—
796C2×C4—432no—
797C2×C4—4348no—
798C2×C4—432no—
799C2×C4—436no—
800C2×C4—432no—
801C2×C4—432no—
802C2×C4—8624no—
803C2×C4—8624no—
804C2×C4—868no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—866no—
808C2×C4—862no—
809C2×C4—8624no—
810C2×C4—8624no—
811C2×C4—17224no—
812C2×C4C2×D4×D43112yes—
813C2×C4C24×D4312yes—
814C2×C4C24×D4316yes—
815C2×C4C24×D4316yes—
816C2×C4C24×D4312yes—
817C2×C4C24×D4316yes—
818C22—22no—
819C22—22no—
820C22—28no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—4312no—
826C22—866no—
827C22—866no—
828C22—8624no—
829C22—866no—
830C22—866no—
831C22—866no—
832C22—866no—
833C22—866no—
834C22—866no—
835C22—34448no—
836C22—17248no—
837C22—17212no—
838C22—17212no—
839C22C22×D4×D4312yes—
840C22C2×#1306337112yes—
841C22C2×#1306337114yescomplemented
842C22#1458373612yes—
843C22C25×D4311yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—434no—
849C4—862no—
850C4—862no—
851C4—866no—
852C4—862no—
853C4C22×D4×D43112yes—
854C2—24no—
855C2—46no—
856C2—8612no—
857C2—1726no—
858C2—1726no—
859C2#1914826114yesdirect product factor
860C2C23×D4×D4311yescharacteristic
861C2C22×#1306337111yescharacteristic
862C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×#3488
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#13063371C2semidirect
2. C23×#10621902C2semidirect
3. #19148261C2direct (N × H)
4. C2×#14583571C2semidirect
5. C2×#14583568C2semidirect
6. C2×#14583560C2semidirect
7. C2×#14583542C2semidirect
8. C2×#14583540C2semidirect
9. C2×D4×D172C2semidirect
10. C2×#14583533C2semidirect
11. C2×#14583479C2semidirect
12. C2×#14583467C2semidirect
13. C2×#14583408C2semidirect
14. C2×#121×D43C2semidirect
15. C2×#14583381C2semidirect
16. C2×C43×#548C2semidirect
18. C2×#13063371C22semidirect
21. C22×#10621902C22semidirect
22. C22×#10621902C22semidirect
23. C22×#10621902C22semidirect
24. C22×#10621902C22semidirect
25. C22×#10621902C22semidirect
26. C22×#10621898C22semidirect
27. C23×D172C22semidirect
28. C23×D172C22semidirect
29. C22×D4×D43C22semidirect
30. C22×D4×D43C22semidirect
31. C22×D4×D43C22semidirect
32. C23×C4×D43C22semidirect
33. #14583571C22semidirect
34. #14583568C22semidirect
35. #14583560C22semidirect
36. #14583542C22semidirect
37. #14583540C22semidirect
38. D4×D172C22semidirect
39. #14583533C22semidirect
40. #14583479C22semidirect
41. #14583467C22semidirect
42. C2×#13063322C22semidirect
43. C2×#13063321C22semidirect
44. C2×#13063314C22semidirect
45. #14583408C22semidirect
46. C2×#13063310C22semidirect
47. C2×#13063307C22semidirect
48. C2×#13063303C22semidirect
49. C2×#13063302C22semidirect
50. C2×#13063301C22semidirect
51. C2×#13063300C22semidirect
52. C2×#13063300C22semidirect
53. C2×#13063300C22semidirect
54. C2×#13063299C22semidirect
55. C2×#13063299C22semidirect
56. C2×#13063298C22semidirect
57. C2×#13063298C22semidirect
58. C2×#13063298C22semidirect
59. C2×#13063297C22semidirect
60. C2×#13063296C22semidirect
61. #121×D43C22semidirect
62. C2×#13063295C22semidirect
63. C2×#13063295C22semidirect
64. C2×#13063295C22semidirect
65. C2×#13063293C22semidirect
66. #14583381C22semidirect
67. C2×Q8×Dic43C22semidirect
68. C2×C4×D172C22semidirect
69. C2×C4×D172C22semidirect
70. C2×#13063287C22semidirect
71. C2×C4×C22⋊D43C22semidirect
72. C2×C4×C22⋊D43C22semidirect
73. C2×#13063282C22semidirect
74. C2×C4⋊C4×D43C22semidirect
75. C2×C22⋊C4×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
92. C2×#10621902D4semidirect
94. C2×#10621902C23semidirect
95. C2×#10621902C23semidirect
96. C2×#10621902C23semidirect
97. C2×#10621902C23semidirect
99. C2×#10621898C23semidirect
110. C22×D172C23semidirect
111. C22×D172C23semidirect
120. C2×D4×D43C23semidirect
121. C2×D4×D43C23semidirect
122. C2×D4×D43C23semidirect
131. C22×C4×D43C23semidirect
132. #13063322C23semidirect
133. #13063321C23semidirect
134. #13063314C23semidirect
135. #13063310C23semidirect
136. #13063307C23semidirect
137. #13063303C23semidirect
138. #13063302C23semidirect
139. #13063301C23semidirect
140. #13063300C23semidirect
141. #13063300C23semidirect
142. #13063300C23semidirect
143. #13063299C23semidirect
144. #13063299C23semidirect
145. #13063298C23semidirect
146. #13063298C23semidirect
147. #13063298C23semidirect
148. #13063297C23semidirect
149. #13063296C23semidirect
150. #13063295C23semidirect
151. #13063295C23semidirect
152. #13063295C23semidirect
153. #13063293C23semidirect
154. Q8×Dic43C23semidirect
155. C4×D172C23semidirect
156. C4×D172C23semidirect
157. #13063287C23semidirect
158. C4×C22⋊D43C23semidirect
159. C4×C22⋊D43C23semidirect
160. #13063282C23semidirect
167. C4⋊C4×D43C23semidirect
177. C22⋊C4×D43C23semidirect
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
216. C2×Q8×C43C2×D4semidirect
253. #10621902C2×D4semidirect
266. C2×D172C2×D4semidirect
280. C2×C4×D43C2×D4semidirect
316. C23×C43H(5,𝔽2)semidirect
341. Q8×C43C22×D4semidirect
378. D172C22×D4semidirect
384. C4×D43C22×D4semidirect
396. C22×C43C2×H(5,𝔽2)semidirect
429. C2×#548D43semidirect
441. C2×C43#3488semidirect
458. C22×#41C2×D43semidirect
459. C23×Q8C2×D43semidirect
469. #548C2×D43semidirect
479. C2×#124C2×D43semidirect
486. C2×C22⋊Q8C2×D43semidirect
498. C2×#121C2×D43semidirect
505. C2×C4×Q8C2×D43semidirect
511. C2×C4×D4C2×D43semidirect
515. C43C2×#3488semidirect
533. C2×#41C22×D43semidirect
538. C22×Q8C22×D43semidirect
577. #124C22×D43semidirect
583. C22⋊Q8C22×D43semidirect
594. #121C22×D43semidirect
600. C4×Q8C22×D43semidirect
606. C4×D4C22×D43semidirect
656. C2×Q8D4×D43semidirect
768. C23#13063371semidirect
774. Q8C2×D4×D43semidirect
841. C22C2×#13063371semidirect
859. C2#19148261direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633712
C23×#106219022
#191482612
C2×#145835712
C2×#145835682
C2×#145835602
C2×#145835422
C2×#145835402
C2×D4×D1722
C2×#145835332
C2×#145834792
C2×#145834672
C2×#145834082
C2×#121×D432
C2×#145833812
C2×C43×#5482
C2×#348843