Finite Group Databasebeta

← #25096101

Subgroups — #25096101

Order 11008.

1602 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583371C211yesmaximal, characteristic
2C2×#14582924C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic
4C2×#102×D43C211yesmaximal, characteristic
5#19137216C211yesmaximal, characteristic, complemented
6#19134606C211yesmaximal, characteristic, complemented
7#19134605C211yesmaximal, characteristic, complemented
8#19134604C211yesmaximal, characteristic, complemented
9#19134603C211yesmaximal, characteristic, complemented
10#19134594C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12#19134592C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134310C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583371—24no—
20#14583371C418yescomplemented
21C2×C4×D172C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063282C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C22×(C2×D43)⋊C4—21no—
31C2×C22⋊C4×D43—21no—
32#14582924—24no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
34C2×Dic43⋊C8C2211yescharacteristic, complemented
35C2×Dic43⋊C8C2211yescharacteristic, complemented
36#14582902—24no—
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43#102×D43—24no—
44#14582794—21no—
45#14582794—21no—
46#14582770—21no—
47#14582770—21no—
48#14582768C2211yescharacteristic, complemented
49#14582765C2211yescharacteristic, complemented
50#14582764C2211yescharacteristic, complemented
51#14582662C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#384C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43C2×C414yes—
71C2×D4×D43D414yes—
72C2×D4×D43Q814yes—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—22no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85C2×C8×D43—22no—
86C4×D172—22no—
87C4×D172C2×C414yescomplemented
88D4×Dic43—22no—
89D4×Dic43C2×C414yescomplemented
90#13063287—22no—
91#13063287C2×C414yescomplemented
92C4×C22⋊D43—28no—
93(C22⋊D43)⋊C4—28no—
94#13063283—22no—
95#13063283—22no—
96#13063283—22no—
97#13063283C2×C414yes—
98#13063282C2×C414yes—
99#13063282D414yes—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4D411yescharacteristic
107C2×Dic43⋊C4D411yescharacteristic
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—28no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×(C2×D43)⋊C4D411yescharacteristic
118C22⋊C4×D43—28no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43C2311yescharacteristic
122C4⋊(C43⋊C8)—22no—
123Dic43⋊C8—22no—
124Dic43⋊C8—22no—
125#13063247—22no—
126#13063247—22no—
127#13063246—22no—
128#13063246—22no—
129#13063245—22no—
130#13063245—22no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C4×D4×C43—22no—
140C4×D4×C43C2×C414yescomplemented
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C4⋊C8×C43—22no—
149#102×C43—22no—
150#102×C43—22no—
151C24×C43—21no—
152C23×D43—21no—
153C23×D43—24no—
154C23×D43—24no—
155C23×D43—24no—
156C23×D43—81no—
157C23×D43—81no—
158C23×D43—81no—
159C23×D43—81no—
160C23×D43C2×D411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43C22×C412yes—
165C2×D4×C43C2×D412yes—
166C2×D4×C43C2×Q812yes—
167C22×C4×C43—24no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C22×Dic43—24no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—81no—
184C22×Dic43—81no—
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188D4×D43—28no—
189D4×D43—28no—
190D4×D43—28no—
191D4×D43C4⋊C4116yescomplemented
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172C22×C412yes—
196C2×D172C2×D412yes—
197C2×D172C2×Q812yes—
198C2×C4×D43—24no—
199C2×C4×D43—24no—
200C2×C4×D43—42no—
201C2×C4×D43—81no—
202C2×C4×D43—81no—
203C2×C4×D43—81no—
204C2×C4×D43—81no—
205C2×C4×D43—81no—
206C2×C4×D43—81no—
207C2×C4×D43C22×C412yes—
208C2×C4×D43C2×D412yes—
209C2×C4×D43C2×D412yes—
210C2×C4×D43C2×Q812yes—
211C2×C4×D43#4112yes—
212C2×C4×D43#4112yes—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—81no—
225C4⋊C4×C43—81no—
226C4⋊C4×C43C22×C412yes—
227C22⋊C4×C43—24no—
228C42×C43C22×C412yes—
229C42×C43C2×D412yes—
230C22⋊Dic43—24no—
231(C2×D43)⋊C4—24no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4C22⋊C414yes—
236(C2×D43)⋊C4C22⋊C414yes—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43C22×C412yes—
243Dic43⋊C4—42no—
244Dic43⋊C4—81no—
245Dic43⋊C4—81no—
246Dic43⋊C4C22⋊C414yes—
247Dic43⋊C4C22⋊C414yes—
248C4×Dic43—24no—
249C4×Dic43—42no—
250C4×Dic43C22×C412yes—
251C4×Dic43C2×D412yes—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258#10621872—44no—
259C8×D43—44no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43C22×D411yescharacteristic
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—216no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43—84no—
281C22×D43—84no—
282C22×D43—84no—
283C22×D43—84no—
284C22×D43—84no—
285C22×D43—84no—
286C22×D43C2×C22⋊C412yes—
287C22×D43#12112yes—
288C22×D43C22⋊Q812yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43C2×C4⋊C414yes—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—84no—
307C2×C4×C43C2×C22⋊C412yes—
308C2×C4×C43C2×C22⋊C412yes—
309C2×C4×C43C23×C411yescharacteristic
310C2×C4×C43C22×D411yescharacteristic
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C22×Q811yescharacteristic
313C2×C4×C43C2×#4111yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C22⋊D43—216no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—22no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—84no—
330C2×Dic43C2×C22⋊C412yes—
331C2×Dic43C2×C22⋊C412yes—
332C2×Dic43C2×C22⋊C412yes—
333C2×Dic43#12112yes—
334C2×Dic43C22⋊Q812yes—
335D172—22no—
336D172—22no—
337D172—22no—
338D172C2×C4⋊C414yes—
339C4×D43—84no—
340C4×D43—84no—
341C4×D43—84no—
342C4×D43C2×C4⋊C414yes—
343C4×D43#11714yes—
344C4×D43#12114yes—
345C4×D43C22⋊Q814yes—
346C8×C43—41no—
347C8×C43—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350#20650—431nomaximal, Sylow
351C22×C43—24no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43C22×C22⋊C411yescharacteristic
359C22×C43C2×#12111yescharacteristic
360C22×C43C2×C22⋊Q811yescharacteristic
361C22×C43#57611yescharacteristic
362C22×C43#57611yescharacteristic
363C22×C43#57711yescharacteristic
364C22×C43#57711yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—24no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—816no—
379C2×D43#38014yes—
380C4×C43—22no—
381C4×C43—22no—
382C4×C43—42no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43C22×C4⋊C411yescharacteristic
386C4×C43C2×#11711yescharacteristic
387C4×C43C2×#12111yescharacteristic
388C4×C43C2×C22⋊Q811yescharacteristic
389Dic43—22no—
390Dic43—22no—
391Dic43—42no—
392Dic43—81no—
393Dic43—81no—
394Dic43#38014yes—
395C2×#518—431no—
396C2×#424—431no—
397C2×#418—431no—
398C22×#102—431no—
399#2317—431no—
400#1804—431no—
401#1804—431no—
402#1804—431no—
403#1804—431no—
404#1802—431no—
405#1802—431no—
406#1802—431no—
407#1802D4311yescharacteristic, complemented
408#1736—431no—
409#1735—431no—
410C2×C43—44no—
411C2×C43C2×#38011yescharacteristic
412C2×C43#289711yescharacteristic
413C2×C43#289711yescharacteristic
414C2×C43#304111yescharacteristic
415C2×C43#304211yescharacteristic
416C2×C43#308111yescharacteristic
417C2×C43#308111yescharacteristic
418D43—24no—
419D43—44no—
420C23×D4—431no—
421C22×M16—431no—
422C23×C8—431no—
423#518—438no—
424#518—864no—
425C2×C4×D4—431no—
426C2×C4×D4—431no—
427C2×C4×D4—431no—
428C2×C4×D4—861no—
429C2×C4×D4—861no—
430C2×C4×D4C2×D4311yescharacteristic
431C2×#117—431no—
432C2×#117—431no—
433C2×#117—431no—
434C22×C4⋊C4—431no—
435C22×C22⋊C4—861no—
436C22×C22⋊C4—861no—
437#424—864no—
438C2×C4⋊C8—431no—
439C2×C4⋊C8—431no—
440C2×C4⋊C8—431no—
441C2×C4⋊C8C2×D4311yescharacteristic, complemented
442#418—864no—
443C2×#102—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×#102—431no—
448C2×#102—431no—
449C2×#102—864no—
450C2×#102C2×D4311yescharacteristic
451C2×#102C2×D4311yescharacteristic
452#389—861no—
453#389—861no—
454#385—861no—
455#385—861no—
456#384—431no—
457#384C2×D4311yescharacteristic, complemented
458#382—431no—
459#382—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#340—431no—
465#340—431no—
466#340C2×D4311yescharacteristic, complemented
467#340C2×D4311yescharacteristic, complemented
468C43#2065011yescharacteristic, complemented, Sylow
469C25—861no—
470C22×D4—434no—
471C22×D4—434no—
472C22×D4—434no—
473C22×D4—431no—
474C22×D4—862no—
475C22×D4—862no—
476C22×D4—862no—
477C22×D4—861no—
478C22×D4C22×D4311yescharacteristic
479C23×C4—21no—
480C23×C4—431no—
481C23×C4—861no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C2×M16—862no—
486C2×M16—862no—
487C2×M16—862no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8—862no—
491C22×C8—862no—
492C22×C8—862no—
493C22×C8C22×D4311yescharacteristic
494C22×C8C22×D4311yescharacteristic
495C4×D4—22no—
496C4×D4—434no—
497C4×D4—434no—
498C4×D4—434no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—868no—
502C4×D4—868no—
503C4×D4—862no—
504C4×D4C4×D4314yescomplemented
505#117—434no—
506#117—434no—
507#117—434no—
508#117—862no—
509#117—862no—
510#117—862no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4—862no—
520C2×C4⋊C4—861no—
521C2×C4⋊C4—861no—
522C2×C4⋊C4—861no—
523C2×C4⋊C4C22×D4311yescharacteristic
524C2×C4⋊C4C22×D4311yescharacteristic
525C2×C4⋊C4C22×D4311yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—868no—
530C2×C22⋊C4—868no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C42—431no—
537C2×C42—861no—
538C2×C42—861no—
539C2×C42C22×D4311yescharacteristic
540C4⋊C8—22no—
541C4⋊C8—862no—
542C4⋊C8—862no—
543C4⋊C8—862no—
544#102—22no—
545#102—22no—
546#102—862no—
547#102—862no—
548#102—862no—
549#102—862no—
550#102—862no—
551#102—862no—
552#95—861no—
553#95—861no—
554#95—861no—
555#95—861no—
556C24—21no—
557C24—431no—
558C24—864no—
559C24—864no—
560C24—864no—
561C24—861no—
562C24—3441no—
563C24—3441no—
564C24—3441no—
565C24—3441no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—4316no—
570C2×D4—432no—
571C2×D4—432no—
572C2×D4—432no—
573C2×D4—868no—
574C2×D4—868no—
575C2×D4—868no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4C2×C4×D4312yes—
583C2×D4D4×D4312yes—
584C2×D4Q8×D4312yes—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—431no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—861no—
603C22×C4—864no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—3441no—
607C22×C4—3441no—
608C22×C4—3441no—
609C22×C4—3441no—
610C22×C4—3441no—
611C22×C4—3441no—
612C22×C4—3441no—
613C22×C4—3441no—
614C22×C4—1722no—
615C22×C4D4×D4311yescharacteristic
616C22×C4D4×D4311yescharacteristic
617C22×C4C23×D4311yescharacteristic
618M16—1724no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—1724no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—81no—
638C4⋊C4—81no—
639C4⋊C4—434no—
640C4⋊C4—434no—
641C4⋊C4—432no—
642C4⋊C4—861no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—3441no—
648C4⋊C4—3441no—
649C4⋊C4—1722no—
650C4⋊C4C2×C4×D4312yes—
651C22⋊C4—24no—
652C22⋊C4—434no—
653C22⋊C4—434no—
654C22⋊C4—864no—
655C22⋊C4—864no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—1722no—
659C42—432no—
660C42—432no—
661C42—864no—
662C42—1722no—
663C42C2×C4×D4312yes—
664C42D4×D4312yes—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—432no—
673C23—432no—
674C23—432no—
675C23—8616no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23—862no—
681C23—862no—
682C23—862no—
683C23—3444no—
684C23—3444no—
685C23—3444no—
686C23—3444no—
687C23—3444no—
688C23—3444no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23C2×D4×D4311yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—434no—
698D4—8616no—
699D4—862no—
700D4—862no—
701D4—862no—
702D4C4⋊C4×D4314yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—432no—
718C2×C4—432no—
719C2×C4—432no—
720C2×C4—434no—
721C2×C4—434no—
722C2×C4—434no—
723C2×C4—434no—
724C2×C4—432no—
725C2×C4—432no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—862no—
731C2×C4—3444no—
732C2×C4—3444no—
733C2×C4—3444no—
734C2×C4—3444no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4C22⋊C4×D4312yes—
744C2×C4C22⋊C4×D4312yes—
745C2×C4C22×C4×D4311yescharacteristic
746C2×C4C2×D4×D4311yescharacteristic
747C2×C4C2×D4×D4311yescharacteristic
748C2×C4C2×Q8×D4311yescharacteristic
749C2×C4#41×D4311yescharacteristic
750C2×C4#41×D4311yescharacteristic
751C8—41no—
752C8—41no—
753C8—1721no—
754C8—1721no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—434no—
763C22—862no—
764C22—862no—
765C22—862no—
766C22—862no—
767C22—862no—
768C22—862no—
769C22—864no—
770C22—34416no—
771C22—1722no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22C2×C22⋊C4×D4311yescharacteristic
778C22#121×D4311yescharacteristic
779C22C22⋊Q8×D4311yescharacteristic
780C22#1458370011yescharacteristic
781C22#1458370311yescharacteristic
782C22#1458370511yescharacteristic
783C22#1458370811yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—81no—
788C4—81no—
789C4—434no—
790C4—862no—
791C4—862no—
792C4—3441no—
793C4—3441no—
794C4—1722no—
795C4C2×C4⋊C4×D4311yescharacteristic
796C4#117×D4311yescharacteristic
797C4#121×D4311yescharacteristic
798C4C22⋊Q8×D4311yescharacteristic
799C2—44no—
800C2—864no—
801C2—1724no—
802C2#380×D4311yescharacteristic
803C2#1914311611yescharacteristic
804C2#1914311911yescharacteristic
805C2#1914409311yescharacteristic
806C2#1914410211yescharacteristic
807C2#1914441911yescharacteristic
808C2#1914442111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1802D43
hypocenterC43#20650
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#14582924C2semidirect
5. #19137216C2semidirect
6. #19134606C2semidirect
7. #19134605C2semidirect
8. #19134604C2semidirect
9. #19134603C2semidirect
10. #19134594C2semidirect
11. #19134593C2semidirect
12. #19134592C2semidirect
13. #19134313C2semidirect
14. #19134310C2semidirect
15. C43×#1802C2semidirect
20. #14583371C4semidirect
33. C2×C4⋊(C43⋊C8)C22semidirect
34. C2×Dic43⋊C8C22semidirect
35. C2×Dic43⋊C8C22semidirect
48. #14582768C22semidirect
49. #14582765C22semidirect
50. #14582764C22semidirect
51. #14582662C22semidirect
52. #14582662C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×C4⋊C8×C43C22semidirect
61. C43×#384C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
87. C4×D172C2×C4semidirect
89. D4×Dic43C2×C4semidirect
91. #13063287C2×C4semidirect
140. C4×D4×C43C2×C4semidirect
191. D4×D43C4⋊C4semidirect
407. #1802D43semidirect
441. C2×C4⋊C8C2×D43semidirect
457. #384C2×D43semidirect
466. #340C2×D43semidirect
467. #340C2×D43semidirect
468. C43#20650semidirect
504. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833712
C2×#145829242
C2×#145829022
C2×#102×D432
#191372162
#191346062
#191346052
#191346042
#191346032
#191345942
#191345932
#191345922
#191343132
#191343102
C43×#18022
#2065043