Finite Group Databasebeta

← #25018548

Subgroups — #25018548

Order 11008.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C212yesmaximal
2C2×#14582769C211yesmaximal, characteristic, complemented
3C2×#14582759C211yesmaximal, characteristic
4C2×#14582759C211yesmaximal, characteristic
5C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
6#19132852C212yesmaximal, complemented
7#19132840C212yesmaximal
8#19132829C212yesmaximal, complemented
9#19132825C211yesmaximal, characteristic, complemented
10#19132825C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×C4⋊Dic43C2212yes—
15C22×C4⋊Dic43C2212yes—
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2212yes—
20C22×C4×Dic43C2212yes—
21#14582792—28no—
22#14582769—24no—
23#14582759—24no—
24#14582759—24no—
25C4×C4⋊Dic43—24no—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C24×C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C4×C22⋊C4×C43C418yescomplemented
39C2×#95×C43C2211yescharacteristic
40C2×#95×C43C2211yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—24no—
58C2×C4⋊Dic43—24no—
59C2×C4⋊Dic43—42no—
60C2×C4⋊Dic43—42no—
61C2×C4⋊Dic43D414yes—
62C2×C4⋊Dic43D414yes—
63C2×C22⋊Dic43—24no—
64C2×C22⋊Dic43—24no—
65C2×C22⋊Dic43—24no—
66C2×C22⋊Dic43—24no—
67C2×C22⋊Dic43—42no—
68C2×C22⋊Dic43—42no—
69C2×C4×Dic43—24no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43—42no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C43⋊#95—24no—
75C43⋊#95—24no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—42no—
79C25×C43C2311yescharacteristic
80C23×C4×C43—22no—
81C23×C4×C43—22no—
82C23×C4×C43—22no—
83C23×C4×C43—22no—
84C23×C4×C43—22no—
85C23×C4×C43—22no—
86C23×C4×C43C2×C414yes—
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43C2×C414yes—
96C2×C22⋊C4×C43C2×C414yes—
97C2×C22⋊C4×C43D414yes—
98C2×C22⋊C4×C43Q814yes—
99C2×C42×C43—22no—
100C2×C42×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43—22no—
103C2×C42×C43C2×C414yes—
104C2×C42×C43C2×C414yes—
105#95×C43C2×C414yes—
106#95×C43C2×C414yes—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—21no—
111C24×C43—21no—
112C24×C43—21no—
113C24×C43—21no—
114C24×C43—21no—
115C24×C43—21no—
116C24×C43—21no—
117C24×C43—21no—
118C24×C43—21no—
119C24×C43C22×C412yes—
120C24×C43C2×D412yes—
121C24×C43C2×Q812yes—
122C24×C43C2411yescharacteristic
123C22×C4×C43—28no—
124C22×C4×C43—28no—
125C22×C4×C43—28no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—44no—
151C22×C4×C43—44no—
152C22×C4×C43—44no—
153C22×C4×C43—44no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C22×C412yes—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×Q812yes—
165C22×C4×C43C2×Q812yes—
166C22×C4×C43#4112yes—
167C22×C4×C43#4112yes—
168C22×C4×C43#4112yes—
169C22×C4×C43#4112yes—
170C22×C4×C43#4112yes—
171C22×C4×C43#4112yes—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43C2×D414yes—
199C22×Dic43C2×D414yes—
200C22⋊C4×C43—28no—
201C22⋊C4×C43C4⋊C4116yescomplemented
202C42×C43—28no—
203C42×C43—28no—
204C22⋊Dic43—48no—
205C22⋊Dic43—48no—
206C4⋊Dic43—28no—
207C4⋊Dic43—28no—
208C4⋊Dic43—48no—
209C4⋊Dic43—48no—
210C4⋊Dic43—44no—
211C4⋊Dic43—44no—
212C4×Dic43—48no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43—22no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—22no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43C2×C4⋊C414yes—
248C23×C43C23×C411yescharacteristic
249C23×C43C22×D411yescharacteristic
250C23×C43C22×D411yescharacteristic
251C23×C43C22×D411yescharacteristic
252C23×C43C22×Q811yescharacteristic
253C23×C43C2×#4111yescharacteristic
254C23×C43C2×#4111yescharacteristic
255C23×C43C2×#4111yescharacteristic
256C23×C43C2×#4111yescharacteristic
257C23×C43C2×#4111yescharacteristic
258C23×C43C2×#4111yescharacteristic
259C23×C43H(5,𝔽2)11yescharacteristic
260C23×C43H(5,𝔽2)11yescharacteristic
261C23×C432−1+411yescharacteristic
262C23×C432−1+411yescharacteristic
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—416no—
296C2×C4×C43C2×C4⋊C414yes—
297C2×C4×C43C2×C4⋊C414yes—
298C2×C4×C43#11714yes—
299C2×C4×C43#11714yes—
300C2×C4×C43C4×D414yes—
301C2×C4×C43C4×D414yes—
302C2×C4×C43#12114yes—
303C2×C4×C43#12314yes—
304C2×C4×C43#12414yes—
305C2×C4×C43#12614yes—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—24no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334#13876—431nomaximal, Sylow
335C22×C43—24no—
336C22×C43—24no—
337C22×C43—24no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43C22×C4⋊C411yescharacteristic
351C22×C43C2×#11711yescharacteristic
352C22×C43C2×#11711yescharacteristic
353C22×C43C2×C4×D411yescharacteristic
354C22×C43C2×C4×D411yescharacteristic
355C22×C43#52011yescharacteristic
356C22×C43#52011yescharacteristic
357C22×C43C2×#12111yescharacteristic
358C22×C43C2×#12311yescharacteristic
359C22×C43C2×#12411yescharacteristic
360C22×C43C2×#12611yescharacteristic
361C22×C43#53211yescharacteristic
362C22×C43#53211yescharacteristic
363C22×C43#53311yescharacteristic
364C22×C43#53311yescharacteristic
365C22×C43#54011yescharacteristic
366C22×C43#54111yescharacteristic
367C22×C43#54211yescharacteristic
368C22×C43#54211yescharacteristic
369C22×C43D4211yescharacteristic
370C22×C43D4211yescharacteristic
371C22×C43#54611yescharacteristic
372C22×C43#54711yescharacteristic
373C22×C43#54711yescharacteristic
374C22×C43#54711yescharacteristic
375C22×C43#54811yescharacteristic
376C22×C43D4×Q811yescharacteristic
377C22×C43D4×Q811yescharacteristic
378C22×C43#55011yescharacteristic
379C22×C43#55211yescharacteristic
380C22×C43#55311yescharacteristic
381C22×C43#55411yescharacteristic
382C22×C43#55411yescharacteristic
383C22×C43#55511yescharacteristic
384C22×C43#55611yescharacteristic
385C4×C43—24no—
386C4×C43—24no—
387C4×C43—24no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43#38818yescomplemented
391Dic43—44no—
392Dic43—44no—
393Dic43—82no—
394Dic43—82no—
395C2×#388—432no—
396C2×#384—431no—
397C2×#380—431no—
398C2×#380—431no—
399C2×C4×C4⋊C4—431no—
400C2×C4×C22⋊C4D4311yescharacteristic
401#1442—432no—
402#1439—432no—
403#1436—432no—
404C4⋊#95—431no—
405C4⋊#95—431no—
406C2×C43—44no—
407C2×C43#228511yescharacteristic
408C2×C43C2×#38811yescharacteristic
409C2×C43#231411yescharacteristic
410C2×C43D4×C4⋊C411yescharacteristic
411C2×C43D4×C4⋊C411yescharacteristic
412C2×C43#235211yescharacteristic
413C2×C43#235411yescharacteristic
414C2×C43#242211yescharacteristic
415C2×C43#242311yescharacteristic
416C2×C43#242811yescharacteristic
417C2×C43#242911yescharacteristic
418C2×C43#249111yescharacteristic
419C2×C43#249211yescharacteristic
420C2×C43#249611yescharacteristic
421C2×C43#249711yescharacteristic
422C24×C4C2×D4311yescharacteristic
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4—432no—
428C22×C4⋊C4—432no—
429C22×C22⋊C4—432no—
430C22×C22⋊C4—432no—
431C22×C22⋊C4C2×D4311yescharacteristic
432C22×C22⋊C4C2×D4311yescharacteristic
433C22×C42—432no—
434C22×C42C2×D4311yescharacteristic
435C22×C42C2×D4311yescharacteristic
436#388—868no—
437#384—864no—
438#380—864no—
439#380—864no—
440C4×C4⋊C4—864no—
441C4×C22⋊C4Dic4318yescomplemented
442C2×#95—432no—
443C2×#95—432no—
444C2×#95—432no—
445C2×#95—432no—
446C2×#95—432no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95C2×D4311yescharacteristic
450C2×#95C2×D4311yescharacteristic
451C43#1387611yescharacteristic, complemented, Sylow
452C25C22×D4311yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—432no—
460C23×C4—432no—
461C23×C4—432no—
462C23×C4—432no—
463C23×C4C2×Dic4314yes—
464C23×C4C22×D4311yescharacteristic
465C23×C4C22×D4311yescharacteristic
466C23×C4C22×D4311yescharacteristic
467C23×C4C22×D4311yescharacteristic
468C23×C4C22×D4311yescharacteristic
469C23×C4C22×D4311yescharacteristic
470C2×C4⋊C4—434no—
471C2×C4⋊C4—434no—
472C2×C4⋊C4—862no—
473C2×C4⋊C4—862no—
474C2×C4⋊C4—862no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—864no—
477C2×C4⋊C4—864no—
478C2×C4⋊C4—864no—
479C2×C4⋊C4—864no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—1722no—
487C2×C4⋊C4—1722no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—864no—
492C2×C22⋊C4—864no—
493C2×C22⋊C4—864no—
494C2×C22⋊C4—1722no—
495C2×C22⋊C4—1722no—
496C2×C22⋊C4Dic8614yes—
497C2×C22⋊C4D17214yes—
498C2×C22⋊C4C2×Dic4314yes—
499C2×C22⋊C4C2×Dic4314yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—864no—
505C2×C42—864no—
506C2×C42—1722no—
507C2×C42C2×Dic4314yes—
508C2×C42C2×Dic4314yes—
509#95—864no—
510#95—864no—
511#95—864no—
512#95—864no—
513#95—864no—
514#95—864no—
515#95—1722no—
516#95C2×Dic4314yes—
517#95C2×Dic4314yes—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C2×Dic8612yes—
531C24C2×D17212yes—
532C24C22×Dic4312yes—
533C24C23×D4311yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—434no—
566C22×C4—434no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4C2×Dic8612yes—
594C22×C4C2×Dic8612yes—
595C22×C4C2×D17212yes—
596C22×C4C2×D17212yes—
597C22×C4#1062189812yes—
598C22×C4#1062189812yes—
599C22×C4#1062189812yes—
600C22×C4#1062189812yes—
601C22×C4D4×D4312yes—
602C22×C4D4×D4312yes—
603C22×C4#1062190012yes—
604C22×C4#1062190012yes—
605C22×C4C22×Dic4312yes—
606C22×C4C22×Dic4312yes—
607C22×C4C22×Dic4312yes—
608C22×C4C22×Dic4312yes—
609C22×C4C22×Dic4312yes—
610C22×C4C22×Dic4312yes—
611C4⋊C4—868no—
612C4⋊C4—868no—
613C4⋊C4—1728no—
614C4⋊C4—1728no—
615C4⋊C4—1724no—
616C4⋊C4—1724no—
617C22⋊C4—28no—
618C22⋊C4—1728no—
619C22⋊C4—1728no—
620C22⋊C4C4⋊Dic43116yescomplemented
621C42—28no—
622C42—28no—
623C42—1728no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊Dic4314yes—
659C23C23×Dic4311yescharacteristic
660C23C2×D4×D4311yescharacteristic
661C23C2×D4×D4311yescharacteristic
662C23C22×D17211yescharacteristic
663C23C22×Dic8611yescharacteristic
664C23C2×#1062190011yescharacteristic
665C23C2×#1062190011yescharacteristic
666C23C2×#1062189811yescharacteristic
667C23C2×#1062189811yescharacteristic
668C23C2×#1062189811yescharacteristic
669C23C2×#1062189811yescharacteristic
670C23#1306337111yescharacteristic
671C23#1306337111yescharacteristic
672C23#1306337211yescharacteristic
673C23#1306337211yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—416no—
707C2×C4—864no—
708C2×C4—864no—
709C2×C4—864no—
710C2×C4—864no—
711C2×C4—864no—
712C2×C4—864no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1722no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4—1722no—
722C2×C4—1722no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4C2×C4⋊Dic4314yes—
736C2×C4C2×C4⋊Dic4314yes—
737C2×C4#1306328414yes—
738C2×C4#1306328414yes—
739C2×C4D4×Dic4314yes—
740C2×C4D4×Dic4314yes—
741C2×C4#1306329814yes—
742C2×C4#1306330714yes—
743C2×C4#1306331114yes—
744C2×C4#1306331814yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊Dic4311yescharacteristic
761C22C2×#1306328411yescharacteristic
762C22C2×#1306328411yescharacteristic
763C22C2×D4×Dic4311yescharacteristic
764C22C2×D4×Dic4311yescharacteristic
765C22#1458338211yescharacteristic
766C22#1458338211yescharacteristic
767C22C2×#1306329811yescharacteristic
768C22C2×#1306330711yescharacteristic
769C22C2×#1306331111yescharacteristic
770C22C2×#1306331811yescharacteristic
771C22#1458344911yescharacteristic
772C22#1458344911yescharacteristic
773C22#1458345611yescharacteristic
774C22#1458345611yescharacteristic
775C22#1458350411yescharacteristic
776C22#1458351111yescharacteristic
777C22#1458352011yescharacteristic
778C22#1458352011yescharacteristic
779C22D4×D17211yescharacteristic
780C22D4×D17211yescharacteristic
781C22#1458354511yescharacteristic
782C22#1458355311yescharacteristic
783C22#1458355311yescharacteristic
784C22#1458355411yescharacteristic
785C22#1458355811yescharacteristic
786C22D4×Dic8611yescharacteristic
787C22D4×Dic8611yescharacteristic
788C22#1458357011yescharacteristic
789C22#1458358911yescharacteristic
790C22#1458359511yescharacteristic
791C22#1458360611yescharacteristic
792C22#1458360611yescharacteristic
793C22#1458361411yescharacteristic
794C22#1458361911yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—3442no—
801C4—3442no—
802C4—1724no—
803C4—1724no—
804C4#1458279218yescomplemented
805C2—44no—
806C2#1913700211yescharacteristic
807C2C2×#1458279211yescharacteristic
808C2#1913720411yescharacteristic
809C2D4×C4⋊Dic4311yescharacteristic
810C2D4×C4⋊Dic4311yescharacteristic
811C2#1913752411yescharacteristic
812C2#1913754411yescharacteristic
813C2#1913810911yescharacteristic
814C2#1913812011yescharacteristic
815C2#1913818311yescharacteristic
816C2#1913819411yescharacteristic
817C2#1913895811yescharacteristic
818C2#1913896911yescharacteristic
819C2#1913901711yescharacteristic
820C2#1913902811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13876
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14582769C2semidirect
5. C2×C4×C4⋊Dic43C2semidirect
6. #19132852C2semidirect
8. #19132829C2semidirect
9. #19132825C2semidirect
10. #19132825C2semidirect
38. C4×C22⋊C4×C43C4semidirect
201. C22⋊C4×C43C4⋊C4semidirect
390. C4×C43#388semidirect
441. C4×C22⋊C4Dic43semidirect
451. C43#13876semidirect
620. C22⋊C4C4⋊Dic43semidirect
804. C4#14582792semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
C2×#145827692
C2×#145827592
C2×C4×C4⋊Dic432
#191328522
#191328402
#191328292
#191328252
C2×C4×C22⋊C4×C432
#1387643