Finite Group Databasebeta

← #25019009

Subgroups — #25019009

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic86C211yesmaximal, characteristic
2C2×#14582803C212yesmaximal
3C2×#14582768C211yesmaximal, characteristic
4C2×C4⋊C4×Dic43C211yesmaximal, characteristic
5#19132847C212yesmaximal
6#19132846C212yesmaximal
7#19132825C211yesmaximal, characteristic
8#19132824C211yesmaximal, characteristic
9#19132824C211yesmaximal, characteristic
10Dic43⋊#95C212yesmaximal
11C43×C4⋊#95C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C2×C4×Dic86—24no—
14C2×C4×Dic86—24no—
15C2×C4×Dic86C418yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×Dic43⋊C4C2212yes—
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2212yes—
23C22×C4×Dic43C2212yes—
24C22×C4×Dic43C2211yescharacteristic
25C22×C4×Dic43C2211yescharacteristic
26#14582803—28no—
27#14582768—24no—
28C4⋊C4×Dic43—24no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C22×C4⋊C4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C42×C43C2211yescharacteristic
39C2×#95×C43C2212yes—
40C2×#95×C43C2212yes—
41C22×Dic86—22no—
42C22×Dic86—22no—
43C22×Dic86—22no—
44C22×Dic86—22no—
45C22×Dic86C2×C414yes—
46C22×Dic86D414yes—
47C22×Dic86Q814yes—
48C23×Dic43C2312yes—
49C23×Dic43C2311yescharacteristic
50C23×Dic43C2312yes—
51C23×Dic43C2311yescharacteristic
52C23×Dic43C2311yescharacteristic
53C23×Dic43C2311yescharacteristic
54C4×Dic86—232no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—22no—
61C2×C4⋊Dic43—22no—
62C2×C4⋊Dic43C2×C414yes—
63C2×C4⋊Dic43Q814yescomplemented
64C2×Dic43⋊C4—22no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4—24no—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4—24no—
71C2×Dic43⋊C4—24no—
72C2×Dic43⋊C4—42no—
73C2×Dic43⋊C4—42no—
74C2×Dic43⋊C4C2×C414yes—
75C2×Dic43⋊C4C2×C414yes—
76C2×C4×Dic43—22no—
77C2×C4×Dic43—22no—
78C2×C4×Dic43—24no—
79C2×C4×Dic43—24no—
80C2×C4×Dic43—24no—
81C2×C4×Dic43C2×C414yes—
82C2×C4×Dic43C2×C414yes—
83C2×C4×Dic43D414yes—
84C2×C4×Dic43D414yes—
85C43⋊#95—24no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95—42no—
90C43⋊#95—42no—
91C43⋊#95—42no—
92C23×C4×C43C2312yes—
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43Q814yescomplemented
103C2×C42×C43—22no—
104C2×C42×C43—22no—
105C2×C42×C43C2×C414yes—
106#95×C43—24no—
107#95×C43—42no—
108C24×C43C2411yescharacteristic
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43C22×C412yes—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C22×C412yes—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×Q814yes—
139C22×C4×C43C2×Q812yes—
140C22×C4×C43C2×Q812yes—
141C22×C4×C43C2×Q812yes—
142C22×C4×C43#4112yes—
143C22×C4×C43#4112yes—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—22no—
171C22×Dic43C22×C412yes—
172C22×Dic43C22×C412yes—
173C22×Dic43C22×C412yes—
174C22×Dic43C22×C412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43C2×D412yes—
177C22×Dic43C2×D412yes—
178C22×Dic43C2×D412yes—
179C22×Dic43C2×D412yes—
180C22×Dic43C2×D412yes—
181C22×Dic43C2×Q814yes—
182C22×Dic43C2×Q812yes—
183C22×Dic43C2×Q812yes—
184C22×Dic43#4112yes—
185C22×Dic43#4112yes—
186C2×Dic86—28no—
187C2×Dic86—28no—
188C2×Dic86—28no—
189C2×Dic86—28no—
190C2×Dic86—28no—
191C2×Dic86—28no—
192C2×Dic86C4⋊C4116yescomplemented
193C4⋊C4×C43—28no—
194C4⋊C4×C43—44no—
195C42×C43—28no—
196C4⋊Dic43—28no—
197C4⋊Dic43—28no—
198C4⋊Dic43—44no—
199Dic43⋊C4—28no—
200Dic43⋊C4—28no—
201Dic43⋊C4—48no—
202Dic43⋊C4—48no—
203C4×Dic43—28no—
204C4×Dic43—48no—
205C4×Dic43C22⋊C4116yes—
206C23×C43C23×C411yescharacteristic
207C23×C43C22×D411yescharacteristic
208C23×C43C22×D411yescharacteristic
209C23×C43C22×D411yescharacteristic
210C23×C43C22×Q811yescharacteristic
211C23×C43C22×Q811yescharacteristic
212C23×C43C22×Q811yescharacteristic
213C23×C43C2×#4111yescharacteristic
214C23×C43C2×#4111yescharacteristic
215C23×C43C2×#4111yescharacteristic
216C23×C43C2×#4111yescharacteristic
217C23×C43H(5,𝔽2)11yescharacteristic
218C23×C43H(5,𝔽2)11yescharacteristic
219C23×C432−1+411yescharacteristic
220C23×C432−1+411yescharacteristic
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43C2×C22⋊C414yes—
249C2×C4×C43C2×C4⋊C414yes—
250C2×C4×C43C4×Q814yes—
251C2×C4×C43C4×Q814yes—
252C2×C4×C43C22⋊Q814yes—
253C2×C4×C43C22⋊Q814yes—
254C2×C4×C43#12414yes—
255C2×C4×C43C4⋊Q814yes—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—42no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43—42no—
289C2×Dic43C2×C22⋊C414yes—
290C2×Dic43C2×C22⋊C414yes—
291C2×Dic43C2×C4⋊C414yes—
292C2×Dic43C2×C4⋊C414yes—
293C2×Dic43#11714yes—
294C2×Dic43#12114yes—
295C2×Dic43#12114yes—
296C2×Dic43C22⋊Q814yes—
297C2×Dic43C22⋊Q814yes—
298Dic86—232no—
299#13926—431nomaximal, Sylow
300C22×C43C22×C22⋊C411yescharacteristic
301C22×C43C22×C4⋊C411yescharacteristic
302C22×C43C2×#11711yescharacteristic
303C22×C43C2×C4×Q811yescharacteristic
304C22×C43C2×C4×Q811yescharacteristic
305C22×C43#52011yescharacteristic
306C22×C43#52011yescharacteristic
307C22×C43C2×#12111yescharacteristic
308C22×C43C2×#12111yescharacteristic
309C22×C43C2×C22⋊Q811yescharacteristic
310C22×C43C2×C22⋊Q811yescharacteristic
311C22×C43C2×C22⋊Q811yescharacteristic
312C22×C43C2×C22⋊Q811yescharacteristic
313C22×C43C2×#12411yescharacteristic
314C22×C43C2×C4⋊Q811yescharacteristic
315C22×C43#53511yescharacteristic
316C22×C43#53611yescharacteristic
317C22×C43#53711yescharacteristic
318C22×C43#53711yescharacteristic
319C22×C43D4×Q811yescharacteristic
320C22×C43D4×Q811yescharacteristic
321C22×C43#55011yescharacteristic
322C22×C43#55011yescharacteristic
323C22×C43#55411yescharacteristic
324C22×C43#55411yescharacteristic
325C22×C43#55611yescharacteristic
326C22×C43#55611yescharacteristic
327C22×C43#55711yescharacteristic
328C22×C43#55711yescharacteristic
329C22×C43#55711yescharacteristic
330C22×C43#55711yescharacteristic
331C22×C43Q8211yescharacteristic
332C22×C43Q8211yescharacteristic
333C22×C43#55911yescharacteristic
334C22×C43#55911yescharacteristic
335C4×C43—24no—
336C4×C43—42no—
337C4×C43—44no—
338C4×C43—82no—
339C4×C43#39118yescomplemented
340Dic43—24no—
341Dic43—24no—
342Dic43—42no—
343Dic43—44no—
344Dic43—82no—
345Dic43#38018yes—
346C22×C4×Q8—431no—
347C2×#391—432no—
348C2×#384—431no—
349C2×C4×C4⋊C4—431no—
350#1441—432no—
351#1441—432no—
352C4⋊#95—431no—
353C4⋊#95—432no—
354C4⋊#95—431no—
355C4⋊#95—431no—
356C4⋊#95D4311yescharacteristic
357C2×C43C2×#38011yescharacteristic
358C2×C43C2×#39111yescharacteristic
359C2×C43#231111yescharacteristic
360C2×C43Q8×C4⋊C411yescharacteristic
361C2×C43Q8×C4⋊C411yescharacteristic
362C2×C43#235511yescharacteristic
363C2×C43#235511yescharacteristic
364C2×C43#253811yescharacteristic
365C2×C43#253811yescharacteristic
366C2×C43#254611yescharacteristic
367C2×C43#254811yescharacteristic
368C2×C43#256711yescharacteristic
369C2×C43#256811yescharacteristic
370C2×C43#258211yescharacteristic
371C2×C43#258211yescharacteristic
372C23×Q8—431no—
373C2×C4×Q8—438no—
374C2×C4×Q8—864no—
375C2×C4×Q8—864no—
376C22×C4⋊C4—431no—
377C22×C4⋊C4—431no—
378C22×C4⋊C4—431no—
379C22×C4⋊C4—431no—
380C22×C4⋊C4—432no—
381C22×C4⋊C4—431no—
382C22×C4⋊C4—432no—
383C22×C4⋊C4C2×D4311yescharacteristic
384C22×C4⋊C4C2×D4311yescharacteristic
385C22×C42—431no—
386C22×C42—431no—
387C22×C42—432no—
388C22×C42C2×D4311yescharacteristic
389#391—868no—
390#384—864no—
391C4×C4⋊C4—864no—
392C2×#95—432no—
393C2×#95—432no—
394C2×#95—432no—
395C2×#95—432no—
396C2×#95—432no—
397C2×#95—432no—
398C2×#95—432no—
399C2×#95C2×D4312yes—
400C2×#95C2×D4312yes—
401C43#1392611yescharacteristic, complemented, Sylow
402C22×Q8—434no—
403C22×Q8—434no—
404C22×Q8—434no—
405C22×Q8—862no—
406C22×Q8—862no—
407C22×Q8—862no—
408C22×Q8—862no—
409C23×C4—431no—
410C23×C4—431no—
411C23×C4—431no—
412C23×C4—431no—
413C23×C4—432no—
414C23×C4—432no—
415C23×C4C22×D4312yes—
416C23×C4C22×D4312yes—
417C23×C4C22×D4311yescharacteristic
418C23×C4C22×D4311yescharacteristic
419C23×C4C22×D4311yescharacteristic
420C4×Q8—8632no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—434no—
427C2×C4⋊C4—434no—
428C2×C4⋊C4—434no—
429C2×C4⋊C4—434no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—862no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4—862no—
437C2×C4⋊C4—862no—
438C2×C4⋊C4—864no—
439C2×C4⋊C4—864no—
440C2×C4⋊C4—864no—
441C2×C4⋊C4—864no—
442C2×C4⋊C4—862no—
443C2×C4⋊C4—862no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—1722no—
446C2×C4⋊C4—1722no—
447C2×C4⋊C4Dic8614yescomplemented
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—434no—
451C2×C42—434no—
452C2×C42—434no—
453C2×C42—434no—
454C2×C42—862no—
455C2×C42—862no—
456C2×C42—864no—
457C2×C42—864no—
458C2×C42—864no—
459C2×C42C4×D4314yes—
460#95—24no—
461#95—42no—
462#95—864no—
463#95—864no—
464#95—864no—
465#95—864no—
466#95—1722no—
467#95—1722no—
468#95—1722no—
469C24C23×D4311yescharacteristic
470C2×Q8—4316no—
471C2×Q8—868no—
472C2×Q8—868no—
473C2×Q8—868no—
474C2×Q8—868no—
475C2×Q8—868no—
476C2×Q8—868no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—432no—
501C22×C4—432no—
502C22×C4—432no—
503C22×C4—432no—
504C22×C4—432no—
505C22×C4—432no—
506C22×C4—432no—
507C22×C4—432no—
508C22×C4—432no—
509C22×C4—432no—
510C22×C4—432no—
511C22×C4—432no—
512C22×C4—432no—
513C22×C4—432no—
514C22×C4—434no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—861no—
530C22×C4—862no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—862no—
534C22×C4—861no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4C2×Dic8614yes—
543C22×C4C2×Dic8612yes—
544C22×C4C2×C4×D4312yes—
545C22×C4C2×C4×D4312yes—
546C22×C4C2×C4×D4312yes—
547C22×C4#1062189812yes—
548C22×C4D4×D4312yes—
549C22×C4D4×D4312yes—
550C22×C4D4×D4312yes—
551C22×C4#1062190012yes—
552C22×C4Q8×D4312yes—
553C22×C4Q8×D4312yes—
554C4⋊C4—28no—
555C4⋊C4—44no—
556C4⋊C4—868no—
557C4⋊C4—868no—
558C4⋊C4—868no—
559C4⋊C4—868no—
560C4⋊C4—1728no—
561C4⋊C4—1728no—
562C4⋊C4—1724no—
563C42—28no—
564C42—4316no—
565C42—868no—
566C42—1728no—
567C23C22×C4×D4311yescharacteristic
568C23C2×D4×D4311yescharacteristic
569C23C2×D4×D4311yescharacteristic
570C23C2×D4×D4311yescharacteristic
571C23C2×Q8×D4311yescharacteristic
572C23C2×Q8×D4311yescharacteristic
573C23C22×Dic8611yescharacteristic
574C23#41×D4311yescharacteristic
575C23#41×D4311yescharacteristic
576C23C2×#1062190011yescharacteristic
577C23C2×#1062189811yescharacteristic
578C23#1306337011yescharacteristic
579C23#1306337111yescharacteristic
580C23#1306337211yescharacteristic
581C23#1306337311yescharacteristic
582Q8—8632no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—434no—
611C2×C4—434no—
612C2×C4—434no—
613C2×C4—434no—
614C2×C4—434no—
615C2×C4—434no—
616C2×C4—434no—
617C2×C4—434no—
618C2×C4—434no—
619C2×C4—862no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—862no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—864no—
632C2×C4—862no—
633C2×C4—864no—
634C2×C4—862no—
635C2×C4—862no—
636C2×C4—864no—
637C2×C4—1722no—
638C2×C4—1722no—
639C2×C4—1722no—
640C2×C4—1722no—
641C2×C4—1722no—
642C2×C4—1722no—
643C2×C4—1722no—
644C2×C4—1722no—
645C2×C4—1722no—
646C2×C4—1722no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1722no—
652C2×C4C22⋊C4×D4314yes—
653C2×C4C4⋊C4×D4314yes—
654C2×C4#1306329014yes—
655C2×C4C4×Dic8614yes—
656C2×C4#1306330214yes—
657C2×C4#1306330314yes—
658C2×C4#1306331114yes—
659C2×C4#1306332414yes—
660C22C2×C22⋊C4×D4311yescharacteristic
661C22C2×C4⋊C4×D4311yescharacteristic
662C22#117×D4311yescharacteristic
663C22C2×#1306329011yescharacteristic
664C22C2×C4×Dic8611yescharacteristic
665C22#1458337911yescharacteristic
666C22#1458338011yescharacteristic
667C22#121×D4311yescharacteristic
668C22#121×D4311yescharacteristic
669C22C22⋊Q8×D4311yescharacteristic
670C22C22⋊Q8×D4311yescharacteristic
671C22C2×#1306330211yescharacteristic
672C22C2×#1306330311yescharacteristic
673C22C2×#1306331111yescharacteristic
674C22C2×#1306332411yescharacteristic
675C22#1458346511yescharacteristic
676C22#1458347211yescharacteristic
677C22#1458347811yescharacteristic
678C22#1458347911yescharacteristic
679C22#1458356411yescharacteristic
680C22D4×Dic8611yescharacteristic
681C22#1458356911yescharacteristic
682C22#1458357011yescharacteristic
683C22#1458360511yescharacteristic
684C22#1458360811yescharacteristic
685C22#1458361811yescharacteristic
686C22#1458362111yescharacteristic
687C22#1458362411yescharacteristic
688C22#1458362511yescharacteristic
689C22#1458362611yescharacteristic
690C22#1458362711yescharacteristic
691C22#1458362911yescharacteristic
692C22Q8×Dic8611yescharacteristic
693C22#1458363111yescharacteristic
694C22#1458363211yescharacteristic
695C4—24no—
696C4—42no—
697C4—44no—
698C4—82no—
699C4—438no—
700C4—864no—
701C4—864no—
702C4—3442no—
703C4—1722no—
704C4—1724no—
705C4#1458280318yescomplemented
706C2#380×D4311yescharacteristic
707C2C2×#1458280311yescharacteristic
708C2#1913718411yescharacteristic
709C2#1913750711yescharacteristic
710C2C4⋊C4×Dic8611yescharacteristic
711C2#1913754711yescharacteristic
712C2#1913755311yescharacteristic
713C2#1913951511yescharacteristic
714C2#1913951611yescharacteristic
715C2#1913958211yescharacteristic
716C2#1913959611yescharacteristic
717C2#1913980211yescharacteristic
718C2#1913980911yescharacteristic
719C2#1913996611yescharacteristic
720C2#1913996711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C4⋊#95C2
socle, prime radical, cosocleC24×C43C24
hypercenterC4⋊#95D43
hypocenterC43#13926
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic86C4semidirect
63. C2×C4⋊Dic43Q8semidirect
102. C2×C4⋊C4×C43Q8semidirect
192. C2×Dic86C4⋊C4semidirect
339. C4×C43#391semidirect
401. C43#13926semidirect
447. C2×C4⋊C4Dic86semidirect
705. C4#14582803semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic862
C2×#145828032
C2×#145827682
C2×C4⋊C4×Dic432
#191328472
#191328462
#191328252
#191328242
Dic43⋊#952
C43×C4⋊#952
#1392643