Finite Group Databasebeta

← C2×#19148084 #26003558

Subgroups — C2×#19148084 #26003558

Order 11008.

12314 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
1C23×#10621902C211yesmaximal, characteristic, complemented
2C22×#41×D43C211yesmaximal, characteristic, complemented
3#19148084C2132yesmaximal, direct product factor
4C2×#14583568C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
6C2×#14583561C211yesmaximal, characteristic, complemented
7C2×#14583551C213yesmaximal, complemented
8C2×#14583545C213yesmaximal, complemented
9C2×#14583542C213yesmaximal, complemented
10C2×#14583533C213yesmaximal, complemented
11C2×#14583448C213yesmaximal, complemented
12C2×#14583412C213yesmaximal, complemented
13C2×#14583409C213yesmaximal, complemented
14C2×C4×#10621902C211yesmaximal, characteristic, complemented
15C2×C4×D4×D43C213yesmaximal, complemented
16C2×C43×#548C211yesmaximal, characteristic, complemented
17C22×#10621902—216no—
18C22×#10621902C2211yescharacteristic
19C22×#10621902C2213yescomplemented
20C22×#10621902C2211yescharacteristic, complemented
21C22×#10621902C2213yescomplemented
22C22×#10621902C22116yescomplemented
23C22×#10621898C2213yescomplemented
24C22×#10621900C2213yescomplemented
25C2×#41×D43—216no—
26C2×#41×D43C22116yescomplemented
27C22×Q8×D43C2211yescharacteristic, complemented
28C23×D172C2213yescomplemented
29C22×D4×D43C2213yes—
30C22×D4×D43C2213yescomplemented
31C23×C4×D43C2213yescomplemented
32C23×C4×D43C2213yescomplemented
33#14583568C22116yescomplemented
34Q8×C22⋊D43C22116yescomplemented
35#14583561C22116yescomplemented
36#14583551C22148yescomplemented
37#14583545C22148yescomplemented
38#14583542C22148yescomplemented
39#14583533C22148yescomplemented
40#14583448C22148yescomplemented
41C2×#13063323C2213yescomplemented
42C2×#13063321C2213yescomplemented
43C2×#13063313C2213yescomplemented
44#14583412C22148yescomplemented
45#14583409C22148yescomplemented
46C2×#13063310C2216yescomplemented
47C2×#13063307C2216yescomplemented
48C2×#13063305C2213yescomplemented
49C2×#13063304C2213yescomplemented
50C2×#13063301C2213yescomplemented
51C2×#13063300C2213yescomplemented
52C2×#13063299C2213yescomplemented
53C2×#13063298C2216yescomplemented
54C2×#13063298C2216yescomplemented
55C2×#13063296C2213yescomplemented
56C2×#13063295C2216yescomplemented
57C2×#13063293C2216yescomplemented
58C4×#10621902C22116yescomplemented
59C2×Q8×Dic43C2211yescharacteristic, complemented
60C2×C4×D172C2213yescomplemented
61C2×C4×D172C2213yescomplemented
62C2×D4×Dic43C2213yescomplemented
63C2×#13063287C2213yescomplemented
64C2×#13063287C2213yescomplemented
65C2×C4×C22⋊D43C2213yes—
66C2×C4×C22⋊D43C2213yescomplemented
67C2×(C22⋊D43)⋊C4C2211yescharacteristic
68C2×(C22⋊D43)⋊C4C2216yescomplemented
69C2×(C22⋊D43)⋊C4C2213yescomplemented
70C4×D4×D43C22148yescomplemented
71C2×#13063283C2213yescomplemented
72C2×C4⋊C4×D43C2213yescomplemented
73C2×C22⋊C4×D43C2213yescomplemented
74C2×C22⋊C4×D43C2213yescomplemented
75C2×C42×D43C2213yescomplemented
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×D43C2313yes—
86C2×#10621902—28no—
87C2×#10621902—2128no—
88C2×#10621902—224no—
89C2×#10621902—224no—
90C2×#10621902D4116yescomplemented
91C2×#10621902C2318yes—
92C2×#10621902C2318yescomplemented
93C2×#10621902C23124yescomplemented
94C2×#10621902C23124yescomplemented
95C2×#10621898—224no—
96C2×#10621898C23124yescomplemented
97C2×#10621900—224no—
98C2×#10621900C23124yescomplemented
99#41×D43—2128no—
100C22×Dic86C2313yes—
101C2×Q8×D43—28no—
102C2×Q8×D43C2318yescomplemented
103C22×D172—224no—
104C22×D172C2313yes—
105C22×D172C2316yes—
106C22×D172C2313yes—
107C22×D172C2313yes—
108C22×D172C23124yescomplemented
109C22×C22⋊D43C2313yes—
110C22×C22⋊D43C2316yes—
111C22×C22⋊D43C2316yes—
112C22×C22⋊D43C2311yescharacteristic
113C2×D4×D43—224no—
114C2×D4×D43—224no—
115C2×D4×D43C23124yes—
116C2×D4×D43C23124yescomplemented
117C23×Dic43C2311yescharacteristic
118C23×Dic43C2313yes—
119C22×C4×D43—224no—
120C22×C4×D43—224no—
121C22×C4×D43C2313yes—
122C22×C4×D43C2313yes—
123C22×C4×D43C2313yes—
124C22×C4×D43C2311yescharacteristic
125C22×C4×D43C2313yes—
126C22×C4×D43C2313yes—
127C22×C4×D43C2313yes—
128C22×C4×D43C2313yes—
129C22×C4×D43C2313yes—
130C22×C4×D43C23124yescomplemented
131C22×C4×D43C23124yescomplemented
132#13063323C23124yescomplemented
133#13063321C23124yescomplemented
134#13063313C23124yescomplemented
135#13063310C23148yescomplemented
136#13063307C23148yescomplemented
137#13063305C23124yescomplemented
138#13063304C23124yescomplemented
139#13063301C23124yescomplemented
140#13063300C23124yescomplemented
141#13063299C23124yescomplemented
142#13063298C23148yescomplemented
143#13063298C23148yescomplemented
144#13063296C23124yescomplemented
145#13063295C23148yescomplemented
146#13063293C23148yescomplemented
147Q8×Dic43C2318yescomplemented
148C4×D172C23124yescomplemented
149C4×D172C23124yescomplemented
150D4×Dic43C23124yescomplemented
151#13063287C23124yescomplemented
152#13063287C23124yescomplemented
153C4×C22⋊D43C23124yes—
154C4×C22⋊D43C23124yescomplemented
155(C22⋊D43)⋊C4C2318yes—
156(C22⋊D43)⋊C4C23124yescomplemented
157(C22⋊D43)⋊C4C23148yescomplemented
158#13063283C23124yescomplemented
159C2×C4⋊Dic43C2313yes—
160C2×C4⋊Dic43C2313yes—
161C2×Dic43⋊C4C2311yescharacteristic
162C2×Dic43⋊C4C2313yes—
163C2×Dic43⋊C4C2316yes—
164C4⋊C4×D43C23124yescomplemented
165C2×C22⋊Dic43C2313yes—
166C2×C22⋊Dic43C2313yes—
167C2×(C2×D43)⋊C4C2311yescharacteristic
168C2×(C2×D43)⋊C4C2313yes—
169C2×(C2×D43)⋊C4C2313yes—
170C2×(C2×D43)⋊C4C2313yes—
171C2×(C2×D43)⋊C4C2316yes—
172C2×(C2×D43)⋊C4C2316yes—
173C22⋊C4×D43C23124yescomplemented
174C22⋊C4×D43C23124yescomplemented
175C2×C4×Dic43C2311yescharacteristic
176C2×C4×Dic43C2313yes—
177C2×C4×Dic43C2313yes—
178C42×D43C23124yescomplemented
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—212no—
205C23×D43—212no—
206C23×D43—46no—
207C23×D43—46no—
208C23×D43C2413yes—
209C23×D43C24112yes—
210C23×D43C24112yes—
211C23×D43C2413yes—
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—212no—
233C2×C22⋊D43—224no—
234C2×C22⋊D43—412no—
235C2×C22⋊D43#4118yescomplemented
236C2×C22⋊D43C24112yes—
237C2×C22⋊D43C24124yes—
238C2×C22⋊D43C24124yes—
239C2×C22⋊D43C2414yes—
240C22×Dic43—24no—
241C22×Dic43—212no—
242C22×Dic43C2413yes—
243C22×Dic43C2413yes—
244C22×Dic43C2411yescharacteristic
245C22×Dic43C2414yes—
246C22×Dic43C24112yes—
247C22×Dic43C2411yescharacteristic
248C22×Dic43C2411yescharacteristic
249#10621902—232no—
250#10621902—296no—
251#10621902—296no—
252#10621902C2×D4164yescomplemented
253Q8×D43—232no—
254#10621900—296no—
255D4×D43—296no—
256D4×D43—296no—
257#10621898—296no—
258C2×D172—212no—
259C2×D172—296no—
260C2×D172—224no—
261C2×D172—212no—
262C2×D172C2×D4124yescomplemented
263C2×D172C24112yes—
264C2×D172C24124yes—
265C2×D172C24112yes—
266C2×D172C24112yes—
267C2×C4×D43—212no—
268C2×C4×D43—212no—
269C2×C4×D43—24no—
270C2×C4×D43—212no—
271C2×C4×D43—212no—
272C2×C4×D43—296no—
273C2×C4×D43—296no—
274C2×C4×D43—212no—
275C2×C4×D43—212no—
276C2×C4×D43—46no—
277C2×C4×D43C2×D4124yescomplemented
278C2×C4×D43C24112yes—
279C2×C4×D43C24112yes—
280C2×C4×D43C24112yes—
281C2×C4×D43C2414yes—
282C2×C4×D43C24112yes—
283C2×C4×D43C24112yes—
284C2×C4×D43C24112yes—
285C2×C4×D43C24112yes—
286C2×C4×D43C24112yes—
287C2×Dic86—212no—
288C2×Dic86C24112yes—
289C4⋊C4×C43C24112yes—
290C4⋊C4×C43C24112yes—
291C22⋊C4×C43C2414yes—
292C22⋊C4×C43C24112yes—
293C22⋊C4×C43C24124yes—
294C42×C43C24112yes—
295C22⋊Dic43C24112yes—
296C22⋊Dic43C24112yes—
297(C2×D43)⋊C4C2414yes—
298(C2×D43)⋊C4C24112yes—
299(C2×D43)⋊C4C24112yes—
300(C2×D43)⋊C4C24112yes—
301(C2×D43)⋊C4C24124yes—
302(C2×D43)⋊C4C24124yes—
303C4⋊Dic43C24112yes—
304C4⋊Dic43C24112yes—
305Dic43⋊C4C2414yes—
306Dic43⋊C4C24112yes—
307Dic43⋊C4C24124yes—
308C4×Dic43C2414yes—
309C4×Dic43C24112yes—
310C4×Dic43C24112yes—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—26no—
314C23×C43—26no—
315C23×C43—26no—
316C23×C43C2×#4114yescomplemented
317C23×C43C2516yes—
318C23×C43C2512yes—
319C23×C43C2511yescharacteristic
320C22×D43—22no—
321C22×D43—26no—
322C22×D43—26no—
323C22×D43—22no—
324C22×D43—26no—
325C22×D43—26no—
326C22×D43—224no—
327C22×D43—26no—
328C22×D43—224no—
329C22×D43—224no—
330C22×D43—224no—
331C22×D43—412no—
332C22×D43—412no—
333C22×D43—448no—
334C22×D43—448no—
335C22×D43C22×D4112yes—
336C22×D43C2×#4114yescomplemented
337C22×D43C2516yes—
338C22×D43C2516yes—
339C22×D43C2512yes—
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×C43C2516yes—
352C2×C4×C43C2512yes—
353C2×C4×C43C2516yes—
354C2×C4×C43C2512yes—
355C2×C4×C43C2516yes—
356C22⋊D43—248no—
357C22⋊D43—224no—
358C22⋊D43—424no—
359C22⋊D43C2×#41116yescomplemented
360C2×Dic43—26no—
361C2×Dic43—22no—
362C2×Dic43—26no—
363C2×Dic43—28no—
364C2×Dic43—224no—
365C2×Dic43C22×D414yes—
366C2×Dic43C2×#4114yescomplemented
367C2×Dic43C2516yes—
368C2×Dic43C2516yes—
369C2×Dic43C2512yes—
370C2×Dic43C2512yes—
371C2×Dic43C2512yes—
372D172—248no—
373D172—224no—
374D172—224no—
375D172C22×D4148yescomplemented
376C4×D43—224no—
377C4×D43—224no—
378C4×D43—224no—
379C4×D43—224no—
380C4×D43—28no—
381C4×D43—224no—
382C4×D43—224no—
383C4×D43—412no—
384C4×D43C22×D4148yescomplemented
385Dic86—224no—
386C2×D4×#41—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×C43C22×#4112yes—
396C22×C43C22×#4114yescomplemented
397C22×C43#58512yes—
398C22×C43C2611yescharacteristic
399C2×D43—22no—
400C2×D43—26no—
401C2×D43—22no—
402C2×D43—26no—
403C2×D43—28no—
404C2×D43—224no—
405C2×D43—26no—
406C2×D43—26no—
407C2×D43—26no—
408C2×D43—448no—
409C2×D43—448no—
410C2×D43—412no—
411C2×D43C23×D4112yes—
412C2×D43C22×#4114yescomplemented
413C4×C43—22no—
414C4×C43—26no—
415C4×C43—26no—
416C4×C43—22no—
417C4×C43C23×D4112yes—
418Dic43—26no—
419Dic43—22no—
420Dic43—26no—
421Dic43C23×D414yes—
422Dic43C22×#4114yescomplemented
423C23×#41—431no—
424C23×#41—431no—
425D4×#41—4332no—
426C2×#550—431no—
427C2×D4×Q8—431no—
428C2×#548—431no—
429C2×#548D4311yescharacteristic, complemented
430C2×#547—433no—
431C2×#546—433no—
432C2×#546—433no—
433C2×D42—433no—
434C2×#532—433no—
435C2×#525—433no—
436C2×#525—433no—
437C2×C4×#41—431no—
438C22×C4×D4—433no—
439C2×C43—24no—
440C2×C43—46no—
441C2×C43D4×#4114yescomplemented
442C2×C43C24×D411yescharacteristic
443C2×C43C23×#4111yescharacteristic
444C2×C43C2×#58511yescharacteristic
445D43—24no—
446D43—212no—
447D43—46no—
448C22×#41—4316no—
449C22×#41—431no—
450C22×#41—433no—
451C22×#41—433no—
452C22×#41—431no—
453C22×#41—4316no—
454C22×#41—433no—
455C22×#41—433no—
456C22×#41—8616no—
457C22×#41—8616no—
458C22×#41C2×D4311yescharacteristic, complemented
459C23×Q8—431no—
460C23×Q8C2×D4311yescharacteristic, complemented
461C23×D4—433no—
462C23×D4—433no—
463C23×D4—433no—
464C24×C4—433no—
465C24×C4—433no—
466#550—4316no—
467D4×Q8—4316no—
468#548—4316no—
469#548C2×D43116yescomplemented
470#547—4348no—
471#546—4348no—
472#546—4348no—
473D42—4348no—
474#532—4348no—
475C2×C4⋊Q8—433no—
476C2×#127—433no—
477C2×#124—433no—
478C2×#124C2×D4313yescomplemented
479#525—4348no—
480#525—4348no—
481C2×#123—436no—
482C2×#123—436no—
483C2×C22⋊Q8—433no—
484C2×C22⋊Q8—433no—
485C2×C22⋊Q8—433no—
486C2×C22⋊Q8C2×D4313yescomplemented
487C2×#121—433no—
488C2×#121—433no—
489C2×#121—433no—
490C2×#121—436no—
491C2×#121—436no—
492C2×#121C2×D4313yescomplemented
493C2×#120—436no—
494C2×#120—436no—
495C4×#41—4316no—
496C2×C4×Q8—431no—
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—431no—
505C2×C4×D4—433no—
506C2×C4×D4—436no—
507C2×C4×D4—433no—
508C2×C4×D4—433no—
509C2×C4×D4C2×D4313yescomplemented
510C2×#117—433no—
511C22×C4⋊C4—433no—
512C22×C22⋊C4—433no—
513C22×C22⋊C4—433no—
514C22×C42—433no—
515C43C2×D4×#4111yescharacteristic, complemented, Sylow
516C25—433no—
517C25—433no—
518C2×#41—28no—
519C2×#41—4316no—
520C2×#41—438no—
521C2×#41—4324no—
522C2×#41—4324no—
523C2×#41—438no—
524C2×#41—4324no—
525C2×#41—4324no—
526C2×#41—8624no—
527C2×#41—8624no—
528C2×#41—8624no—
529C2×#41—8624no—
530C2×#41—86128no—
531C2×#41—86128no—
532C2×#41—868no—
533C2×#41C22×D4318yescomplemented
534C22×Q8—28no—
535C22×Q8—438no—
536C22×Q8—433no—
537C22×Q8—868no—
538C22×Q8C22×D4313yes—
539C22×Q8C22×D4311yescharacteristic
540C22×Q8C22×D4318yescomplemented
541C22×D4—431no—
542C22×D4—433no—
543C22×D4—436no—
544C22×D4—436no—
545C22×D4—4324no—
546C22×D4—4324no—
547C22×D4—433no—
548C22×D4—433no—
549C22×D4—436no—
550C22×D4—433no—
551C22×D4—4324no—
552C22×D4—8624no—
553C22×D4—8624no—
554C22×D4—8624no—
555C22×D4C22×D4313yes—
556C22×D4C22×D4313yes—
557C23×C4—433no—
558C23×C4—431no—
559C23×C4—433no—
560C23×C4—433no—
561C23×C4—433no—
562C23×C4—433no—
563C23×C4—431no—
564C23×C4—433no—
565C23×C4—433no—
566C23×C4—433no—
567C23×C4—4324no—
568C23×C4—4324no—
569C23×C4—433no—
570C23×C4—8624no—
571C23×C4—8624no—
572C23×C4C22×D4313yes—
573C23×C4C22×D4313yes—
574C4⋊Q8—4324no—
575#127—4324no—
576#124—4324no—
577#124C22×D43124yescomplemented
578#123—4348no—
579#123—4348no—
580C22⋊Q8—4324no—
581C22⋊Q8—4324no—
582C22⋊Q8—4324no—
583C22⋊Q8C22×D43124yescomplemented
584#121—4324no—
585#121—4324no—
586#121—4324no—
587#121—4348no—
588#121—4348no—
589#121C22×D43124yescomplemented
590#120—4348no—
591#120—4348no—
592C4×Q8—438no—
593C4×Q8C22×D4318yescomplemented
594C4×D4—4324no—
595C4×D4—4324no—
596C4×D4—4324no—
597C4×D4—4324no—
598C4×D4—4324no—
599C4×D4—438no—
600C4×D4—4324no—
601C4×D4—4348no—
602C4×D4—4324no—
603C4×D4—4324no—
604C4×D4C22×D43124yescomplemented
605#117—4324no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—433no—
608C2×C4⋊C4—433no—
609C2×C4⋊C4—433no—
610C2×C4⋊C4—436no—
611C2×C4⋊C4—4324no—
612C2×C4⋊C4C22×D4313yes—
613C2×C4⋊C4C22×D4313yes—
614C2×C22⋊C4—433no—
615C2×C22⋊C4—433no—
616C2×C22⋊C4—431no—
617C2×C22⋊C4—433no—
618C2×C22⋊C4—433no—
619C2×C22⋊C4—433no—
620C2×C22⋊C4—436no—
621C2×C22⋊C4—436no—
622C2×C22⋊C4—4324no—
623C2×C22⋊C4—4324no—
624C2×C22⋊C4C22×D4311yescharacteristic
625C2×C22⋊C4C22×D4313yes—
626C2×C22⋊C4C22×D4316yes—
627C2×C42—433no—
628C2×C42—431no—
629C2×C42—433no—
630C2×C42—4324no—
631C2×C42C22×D4313yes—
632C24—431no—
633C24—433no—
634C24—433no—
635C24—4312no—
636C24—4312no—
637C24—8612no—
638C24—8612no—
639C24—8612no—
640C24—8612no—
641C24—1726no—
642C24—1726no—
643C24C23×D4313yes—
644C24C23×D4311yescharacteristic
645#41—232no—
646#41—4364no—
647#41—8696no—
648#41—8696no—
649#41—8696no—
650#41—8696no—
651#41—8632no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—4312no—
655C2×Q8—8632no—
656C2×Q8—8612no—
657C2×Q8D4×D4318yescomplemented
658C2×Q8C23×D43112yes—
659C2×Q8C23×D4314yes—
660C2×D4—212no—
661C2×D4—212no—
662C2×D4—438no—
663C2×D4—434no—
664C2×D4—4312no—
665C2×D4—4324no—
666C2×D4—4324no—
667C2×D4—4324no—
668C2×D4—4312no—
669C2×D4—4312no—
670C2×D4—4324no—
671C2×D4—4312no—
672C2×D4—8696no—
673C2×D4—8624no—
674C2×D4—8612no—
675C2×D4—8612no—
676C2×D4—8696no—
677C2×D4—8696no—
678C2×D4—8624no—
679C2×D4—8612no—
680C2×D4—17212no—
681C2×D4C23×D43112yes—
682C2×D4C23×D43112yes—
683C22×C4—212no—
684C22×C4—212no—
685C22×C4—431no—
686C22×C4—431no—
687C22×C4—4324no—
688C22×C4—4312no—
689C22×C4—434no—
690C22×C4—4312no—
691C22×C4—433no—
692C22×C4—431no—
693C22×C4—433no—
694C22×C4—4312no—
695C22×C4—4312no—
696C22×C4—4312no—
697C22×C4—434no—
698C22×C4—4312no—
699C22×C4—4312no—
700C22×C4—4312no—
701C22×C4—4312no—
702C22×C4—864no—
703C22×C4—8612no—
704C22×C4—8696no—
705C22×C4—8696no—
706C22×C4—8612no—
707C22×C4—8612no—
708C22×C4—8612no—
709C22×C4—864no—
710C22×C4—8612no—
711C22×C4—8612no—
712C22×C4—8612no—
713C22×C4—1726no—
714C22×C4C23×D43112yes—
715C22×C4C23×D43112yes—
716C22×C4C23×D4311yescharacteristic
717C22×C4C23×D4313yes—
718C22×C4C23×D4311yescharacteristic
719C22×C4C23×D4313yes—
720C22×C4C23×D4313yes—
721C4⋊C4—434no—
722C4⋊C4—4312no—
723C4⋊C4—4312no—
724C4⋊C4—4312no—
725C4⋊C4—4324no—
726C4⋊C4C23×D43112yes—
727C4⋊C4C23×D43112yes—
728C22⋊C4—4312no—
729C22⋊C4—4312no—
730C22⋊C4—434no—
731C22⋊C4—4312no—
732C22⋊C4—4312no—
733C22⋊C4—4312no—
734C22⋊C4—4324no—
735C22⋊C4—4324no—
736C22⋊C4C23×D4314yes—
737C22⋊C4C23×D43112yes—
738C22⋊C4C23×D43124yes—
739C42—434no—
740C42—4312no—
741C42—4312no—
742C42C23×D43112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—4312no—
749C23—434no—
750C23—432no—
751C23—436no—
752C23—436no—
753C23—8624no—
754C23—8624no—
755C23—8624no—
756C23—862no—
757C23—866no—
758C23—866no—
759C23—862no—
760C23—866no—
761C23—866no—
762C23—8624no—
763C23—866no—
764C23—17212no—
765C23—17212no—
766C23—17248no—
767C23—17248no—
768C23#41×D4314yescomplemented
769C23C24×D4316yes—
770C23C24×D4312yes—
771C23C24×D4311yescharacteristic
772Q8—224no—
773Q8—8624no—
774Q8C2×D4×D43116yescomplemented
775D4—224no—
776D4—224no—
777D4—4316no—
778D4—4348no—
779D4—8648no—
780D4—8624no—
781D4—8624no—
782D4—8648no—
783D4—8624no—
784D4—17224no—
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—22no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—434no—
792C2×C4—434no—
793C2×C4—432no—
794C2×C4—432no—
795C2×C4—4348no—
796C2×C4—436no—
797C2×C4—432no—
798C2×C4—436no—
799C2×C4—868no—
800C2×C4—8624no—
801C2×C4—8624no—
802C2×C4—8624no—
803C2×C4—8624no—
804C2×C4—868no—
805C2×C4—8624no—
806C2×C4—862no—
807C2×C4—866no—
808C2×C4—866no—
809C2×C4—8624no—
810C2×C4—8624no—
811C2×C4—17212no—
812C2×C4C2×D4×D43112yes—
813C2×C4C24×D4312yes—
814C2×C4C24×D4316yes—
815C2×C4C24×D4312yes—
816C2×C4C24×D4316yes—
817C2×C4C24×D4316yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—4312no—
826C22—434no—
827C22—868no—
828C22—8624no—
829C22—862no—
830C22—866no—
831C22—866no—
832C22—862no—
833C22—866no—
834C22—866no—
835C22—866no—
836C22—17248no—
837C22—17248no—
838C22—17212no—
839C22C22×D4×D4312yes—
840C22C2×#41×D4312yes—
841C22C2×#41×D4314yescomplemented
842C22#1458373612yes—
843C22C25×D4311yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—434no—
849C4—434no—
850C4—862no—
851C4—866no—
852C4—866no—
853C4C22×D4×D43112yes—
854C2—24no—
855C2—46no—
856C2—864no—
857C2—8612no—
858C2—1726no—
859C2#1914808414yesdirect product factor
860C2C23×D4×D4311yescharacteristic
861C2C22×#41×D4311yescharacteristic
862C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#548C2
socleC23×C43C25
hypercenterC2×#548D43
hypocenterC43C2×D4×#41
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C23×#10621902C2semidirect
2. C22×#41×D43C2semidirect
3. #19148084C2direct (N × H)
4. C2×#14583568C2semidirect
5. C2×Q8×C22⋊D43C2semidirect
6. C2×#14583561C2semidirect
7. C2×#14583551C2semidirect
8. C2×#14583545C2semidirect
9. C2×#14583542C2semidirect
10. C2×#14583533C2semidirect
11. C2×#14583448C2semidirect
12. C2×#14583412C2semidirect
13. C2×#14583409C2semidirect
14. C2×C4×#10621902C2semidirect
15. C2×C4×D4×D43C2semidirect
16. C2×C43×#548C2semidirect
19. C22×#10621902C22semidirect
20. C22×#10621902C22semidirect
21. C22×#10621902C22semidirect
22. C22×#10621902C22semidirect
23. C22×#10621898C22semidirect
24. C22×#10621900C22semidirect
26. C2×#41×D43C22semidirect
27. C22×Q8×D43C22semidirect
28. C23×D172C22semidirect
30. C22×D4×D43C22semidirect
31. C23×C4×D43C22semidirect
32. C23×C4×D43C22semidirect
33. #14583568C22semidirect
34. Q8×C22⋊D43C22semidirect
35. #14583561C22semidirect
36. #14583551C22semidirect
37. #14583545C22semidirect
38. #14583542C22semidirect
39. #14583533C22semidirect
40. #14583448C22semidirect
41. C2×#13063323C22semidirect
42. C2×#13063321C22semidirect
43. C2×#13063313C22semidirect
44. #14583412C22semidirect
45. #14583409C22semidirect
46. C2×#13063310C22semidirect
47. C2×#13063307C22semidirect
48. C2×#13063305C22semidirect
49. C2×#13063304C22semidirect
50. C2×#13063301C22semidirect
51. C2×#13063300C22semidirect
52. C2×#13063299C22semidirect
53. C2×#13063298C22semidirect
54. C2×#13063298C22semidirect
55. C2×#13063296C22semidirect
56. C2×#13063295C22semidirect
57. C2×#13063293C22semidirect
58. C4×#10621902C22semidirect
59. C2×Q8×Dic43C22semidirect
60. C2×C4×D172C22semidirect
61. C2×C4×D172C22semidirect
62. C2×D4×Dic43C22semidirect
63. C2×#13063287C22semidirect
64. C2×#13063287C22semidirect
66. C2×C4×C22⋊D43C22semidirect
68. C2×(C22⋊D43)⋊C4C22semidirect
69. C2×(C22⋊D43)⋊C4C22semidirect
70. C4×D4×D43C22semidirect
71. C2×#13063283C22semidirect
72. C2×C4⋊C4×D43C22semidirect
73. C2×C22⋊C4×D43C22semidirect
74. C2×C22⋊C4×D43C22semidirect
75. C2×C42×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
90. C2×#10621902D4semidirect
92. C2×#10621902C23semidirect
93. C2×#10621902C23semidirect
94. C2×#10621902C23semidirect
96. C2×#10621898C23semidirect
98. C2×#10621900C23semidirect
102. C2×Q8×D43C23semidirect
108. C22×D172C23semidirect
116. C2×D4×D43C23semidirect
130. C22×C4×D43C23semidirect
131. C22×C4×D43C23semidirect
132. #13063323C23semidirect
133. #13063321C23semidirect
134. #13063313C23semidirect
135. #13063310C23semidirect
136. #13063307C23semidirect
137. #13063305C23semidirect
138. #13063304C23semidirect
139. #13063301C23semidirect
140. #13063300C23semidirect
141. #13063299C23semidirect
142. #13063298C23semidirect
143. #13063298C23semidirect
144. #13063296C23semidirect
145. #13063295C23semidirect
146. #13063293C23semidirect
147. Q8×Dic43C23semidirect
148. C4×D172C23semidirect
149. C4×D172C23semidirect
150. D4×Dic43C23semidirect
151. #13063287C23semidirect
152. #13063287C23semidirect
154. C4×C22⋊D43C23semidirect
156. (C22⋊D43)⋊C4C23semidirect
157. (C22⋊D43)⋊C4C23semidirect
158. #13063283C23semidirect
164. C4⋊C4×D43C23semidirect
173. C22⋊C4×D43C23semidirect
174. C22⋊C4×D43C23semidirect
178. C42×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
235. C2×C22⋊D43#41semidirect
252. #10621902C2×D4semidirect
262. C2×D172C2×D4semidirect
277. C2×C4×D43C2×D4semidirect
316. C23×C43C2×#41semidirect
336. C22×D43C2×#41semidirect
341. Q8×C43C22×D4semidirect
359. C22⋊D43C2×#41semidirect
366. C2×Dic43C2×#41semidirect
375. D172C22×D4semidirect
384. C4×D43C22×D4semidirect
396. C22×C43C22×#41semidirect
412. C2×D43C22×#41semidirect
422. Dic43C22×#41semidirect
429. C2×#548D43semidirect
441. C2×C43D4×#41semidirect
458. C22×#41C2×D43semidirect
460. C23×Q8C2×D43semidirect
469. #548C2×D43semidirect
478. C2×#124C2×D43semidirect
486. C2×C22⋊Q8C2×D43semidirect
492. C2×#121C2×D43semidirect
497. C2×C4×Q8C2×D43semidirect
509. C2×C4×D4C2×D43semidirect
515. C43C2×D4×#41semidirect
533. C2×#41C22×D43semidirect
540. C22×Q8C22×D43semidirect
577. #124C22×D43semidirect
583. C22⋊Q8C22×D43semidirect
589. #121C22×D43semidirect
593. C4×Q8C22×D43semidirect
604. C4×D4C22×D43semidirect
657. C2×Q8D4×D43semidirect
768. C23#41×D43semidirect
774. Q8C2×D4×D43semidirect
841. C22C2×#41×D43semidirect
859. C2#19148084direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#106219022
C22×#41×D432
#191480842
C2×#145835682
C2×Q8×C22⋊D432
C2×#145835612
C2×#145835512
C2×#145835452
C2×#145835422
C2×#145835332
C2×#145834482
C2×#145834122
C2×#145834092
C2×C4×#106219022
C2×C4×D4×D432
C2×C43×#5482
C2×D4×#4143