Finite Group Databasebeta

← #25033243

Subgroups — #25033243

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582835C212yesmaximal
2C2×#14582798C211yesmaximal, characteristic, complemented
3C2×#14582795C211yesmaximal, characteristic, complemented
4C2×#14582768C211yesmaximal, characteristic, complemented
5C2×#14582759C211yesmaximal, characteristic
6C2×C4×C22⋊Dic43C211yesmaximal, characteristic
7#19132861C212yesmaximal, complemented
8#19132859C212yesmaximal, complemented
9#19132838C212yesmaximal
10#19132824C211yesmaximal, characteristic, complemented
11C2×C43×#380C211yesmaximal, characteristic
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×Dic43⋊C4C2212yes—
16C22×Dic43⋊C4C2212yes—
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14582835—28no—
24#14582798—24no—
25#14582795—24no—
26#14582768—24no—
27#14582759—24no—
28C4×C22⋊Dic43—24no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2212yes—
36C24×C4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2212yes—
40C43×#380—24no—
41C2×#95×C43C2212yes—
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2312yes—
45C23×Dic43C2311yescharacteristic
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2311yescharacteristic
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—24no—
55C2×C4⋊Dic43—42no—
56C2×C4⋊Dic43D414yes—
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—24no—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4—42no—
64C2×Dic43⋊C4—42no—
65C2×Dic43⋊C4—42no—
66C2×C22⋊Dic43—22no—
67C2×C22⋊Dic43—22no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—22no—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43—24no—
72C2×C22⋊Dic43—42no—
73C2×C22⋊Dic43D414yes—
74C2×C22⋊Dic43Q814yes—
75C2×C4×Dic43—22no—
76C2×C4×Dic43—22no—
77C2×C4×Dic43—22no—
78C2×C4×Dic43—22no—
79C2×C4×Dic43—22no—
80C2×C4×Dic43D414yes—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—22no—
85C43⋊#95—22no—
86C43⋊#95—24no—
87C43⋊#95—24no—
88C25×C43C2311yescharacteristic
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43—22no—
93C23×C4×C43—22no—
94C23×C4×C43—22no—
95C23×C4×C43Q814yes—
96C23×C4×C43C2312yes—
97C23×C4×C43C2312yes—
98C23×C4×C43C2311yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43D414yes—
106C2×C22⋊C4×C43—24no—
107C2×C22⋊C4×C43—24no—
108C2×C22⋊C4×C43—42no—
109#95×C43—24no—
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×C43—21no—
120C24×C43—21no—
121C24×C43—21no—
122C24×C43C2×D412yes—
123C24×C43C2×Q812yes—
124C24×C43C2×Q812yes—
125C24×C43C2411yescharacteristic
126C22×C4×C43—28no—
127C22×C4×C43—28no—
128C22×C4×C43—28no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—44no—
149C22×C4×C43—44no—
150C22×C4×C43—44no—
151C22×C4×C43—44no—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D414yes—
155C22×C4×C43C2×D412yes—
156C22×C4×C43C2×Q812yes—
157C22×C4×C43C2×Q812yes—
158C22×C4×C43#4112yes—
159C22×C4×C43#4112yes—
160C22×C4×C43#4112yes—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—22no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—22no—
193C22×Dic43—21no—
194C22×Dic43C2×D414yes—
195C22×Dic43C2×D412yes—
196C22×Dic43C2×D412yes—
197C22×Dic43C2×D412yes—
198C22×Dic43C2×D412yes—
199C22×Dic43C2×Q812yes—
200C22×Dic43C2×Q812yes—
201C22×Dic43#4112yes—
202C22×Dic43#4112yes—
203C4⋊C4×C43—28no—
204C4⋊C4×C43—44no—
205C22⋊C4×C43—48no—
206C22⋊Dic43—28no—
207C22⋊Dic43—28no—
208C22⋊Dic43—48no—
209C4⋊Dic43—28no—
210C4⋊Dic43—48no—
211C4⋊Dic43—44no—
212Dic43⋊C4—48no—
213Dic43⋊C4—48no—
214Dic43⋊C4—48no—
215C4×Dic43—28no—
216C4×Dic43—44no—
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—22no—
232C23×C43—22no—
233C23×C43—22no—
234C23×C43—22no—
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×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C4⋊Q814yes—
252C23×C43C22×D411yescharacteristic
253C23×C43C22×D411yescharacteristic
254C23×C43C22×D411yescharacteristic
255C23×C43C22×D411yescharacteristic
256C23×C43C22×Q811yescharacteristic
257C23×C43C22×Q811yescharacteristic
258C23×C43C2×#4111yescharacteristic
259C23×C43C2×#4111yescharacteristic
260C23×C43C2×#4111yescharacteristic
261C23×C43C2×#4111yescharacteristic
262C23×C43C2×#4111yescharacteristic
263C23×C43H(5,𝔽2)11yescharacteristic
264C23×C43H(5,𝔽2)11yescharacteristic
265C23×C432−1+411yescharacteristic
266C23×C432−1+411yescharacteristic
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—24no—
271C2×C4×C43—24no—
272C2×C4×C43—24no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43—416no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43C22⋊Q814yes—
290C2×C4×C43C22⋊Q814yes—
291C2×C4×C43C22⋊Q814yes—
292C2×C4×C43#12314yes—
293C2×C4×C43#12314yes—
294C2×C4×C43#12314yes—
295C2×C4×C43#12714yes—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—24no—
311C2×Dic43—22no—
312C2×Dic43—24no—
313C2×Dic43—22no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—42no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—42no—
323C2×Dic43—41no—
324C2×Dic43—42no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43#12114yes—
337C2×Dic43C22⋊Q814yes—
338#15135—431nomaximal, Sylow
339C22×C43—24no—
340C22×C43—24no—
341C22×C43—24no—
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×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43C2×#12111yescharacteristic
355C22×C43C2×C22⋊Q811yescharacteristic
356C22×C43C2×C22⋊Q811yescharacteristic
357C22×C43C2×C22⋊Q811yescharacteristic
358C22×C43C2×C22⋊Q811yescharacteristic
359C22×C43C2×#12311yescharacteristic
360C22×C43C2×#12311yescharacteristic
361C22×C43C2×#12311yescharacteristic
362C22×C43C2×#12711yescharacteristic
363C22×C43C2×C4⋊Q811yescharacteristic
364C22×C43#53211yescharacteristic
365C22×C43#53311yescharacteristic
366C22×C43#53311yescharacteristic
367C22×C43#53511yescharacteristic
368C22×C43#53611yescharacteristic
369C22×C43#54211yescharacteristic
370C22×C43#54211yescharacteristic
371C22×C43#54411yescharacteristic
372C22×C43#54411yescharacteristic
373C22×C43D4211yescharacteristic
374C22×C43D4211yescharacteristic
375C22×C43#54711yescharacteristic
376C22×C43#54711yescharacteristic
377C22×C43#54711yescharacteristic
378C22×C43#54711yescharacteristic
379C22×C43D4×Q811yescharacteristic
380C22×C43D4×Q811yescharacteristic
381C22×C43#55011yescharacteristic
382C22×C43#55011yescharacteristic
383C22×C43#55211yescharacteristic
384C22×C43#55211yescharacteristic
385C22×C43#55311yescharacteristic
386C22×C43#55311yescharacteristic
387C22×C43#55411yescharacteristic
388C22×C43#55411yescharacteristic
389C4×C43—42no—
390C4×C43—44no—
391C4×C43—82no—
392C4×C43#39918yescomplemented
393Dic43—24no—
394Dic43—24no—
395Dic43—44no—
396Dic43—42no—
397Dic43—42no—
398Dic43—82no—
399C2×#399—432no—
400C2×#389—431no—
401C2×#389—431no—
402C2×#384—431no—
403C2×#380—431no—
404C2×#380D4311yescharacteristic
405C2×C4×C22⋊C4—431no—
406#1445—432no—
407#1444—432no—
408#1439—432no—
409C4⋊#95—431no—
410C2×C43—44no—
411C2×C43C2×#39911yescharacteristic
412C2×C43#242211yescharacteristic
413C2×C43#242211yescharacteristic
414C2×C43#242311yescharacteristic
415C2×C43#242311yescharacteristic
416C2×C43#244011yescharacteristic
417C2×C43#244011yescharacteristic
418C2×C43#244111yescharacteristic
419C2×C43#244111yescharacteristic
420C2×C43#248611yescharacteristic
421C2×C43#248711yescharacteristic
422C2×C43#254111yescharacteristic
423C2×C43#254211yescharacteristic
424C2×C43#262811yescharacteristic
425C2×C43#285711yescharacteristic
426C24×C4C2×D4311yescharacteristic
427C22×C4⋊C4—431no—
428C22×C4⋊C4—432no—
429C22×C4⋊C4—431no—
430C22×C4⋊C4—432no—
431C22×C4⋊C4—432no—
432C22×C4⋊C4—432no—
433C22×C4⋊C4C2×D4311yescharacteristic
434C22×C4⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4—431no—
436C22×C22⋊C4—431no—
437C22×C22⋊C4—432no—
438C22×C22⋊C4C2×D4312yes—
439C22×C42—431no—
440C22×C42—431no—
441#399—868no—
442#389—864no—
443#389—864no—
444#384—864no—
445#380—24no—
446#380—864no—
447C4×C22⋊C4—864no—
448C2×#95—432no—
449C2×#95—432no—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—431no—
453C2×#95—432no—
454C2×#95—431no—
455C2×#95C2×D4312yes—
456C43#1513511yescharacteristic, complemented, Sylow
457C25C22×D4311yescharacteristic
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—431no—
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—432no—
468C23×C4—431no—
469C23×C4—432no—
470C23×C4Dic8614yes—
471C23×C4C22×D4312yes—
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4312yes—
474C23×C4C22×D4311yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—434no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—864no—
484C2×C4⋊C4—864no—
485C2×C4⋊C4—864no—
486C2×C4⋊C4—864no—
487C2×C4⋊C4—864no—
488C2×C4⋊C4—864no—
489C2×C4⋊C4—864no—
490C2×C4⋊C4—862no—
491C2×C4⋊C4—862no—
492C2×C4⋊C4—864no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—1722no—
495C2×C4⋊C4—1722no—
496C2×C4⋊C4—1722no—
497C2×C4⋊C4—1722no—
498C2×C4⋊C4C22⋊D4314yes—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—434no—
504C2×C22⋊C4—862no—
505C2×C22⋊C4—862no—
506C2×C22⋊C4—862no—
507C2×C22⋊C4—862no—
508C2×C22⋊C4—864no—
509C2×C22⋊C4—864no—
510C2×C22⋊C4—1722no—
511C2×C42—434no—
512C2×C42—862no—
513C2×C42—862no—
514C2×C42—862no—
515C2×C42—862no—
516C2×C42—862no—
517#95—24no—
518#95—864no—
519#95—862no—
520#95—862no—
521#95—864no—
522#95—864no—
523#95—864no—
524#95—864no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×Dic8612yes—
538C24D4×D4312yes—
539C24Q8×D4312yes—
540C24C23×D4311yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—432no—
568C22×C4—432no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—434no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—862no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—862no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—861no—
597C22×C4—862no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4C2×Dic8612yes—
610C22×C4C2×Dic8612yes—
611C22×C4#1062189812yes—
612C22×C4D4×D4312yes—
613C22×C4D4×D4312yes—
614C22×C4#1062190012yes—
615C22×C4#1062190012yes—
616C22×C4C2×C22⋊D4314yes—
617C22×C4C2×C22⋊D4312yes—
618C4⋊C4—28no—
619C4⋊C4—44no—
620C4⋊C4—868no—
621C4⋊C4—1728no—
622C4⋊C4—1728no—
623C4⋊C4—1728no—
624C4⋊C4—1728no—
625C4⋊C4—1724no—
626C22⋊C4—48no—
627C22⋊C4—868no—
628C22⋊C4—868no—
629C22⋊C4—1728no—
630C42—868no—
631C42—1724no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#1306332414yes—
667C23C2×D4×D4311yescharacteristic
668C23C2×D4×D4311yescharacteristic
669C23C2×D4×D4311yescharacteristic
670C23C22×C22⋊D4311yescharacteristic
671C23C2×Q8×D4311yescharacteristic
672C23C22×Dic8611yescharacteristic
673C23#41×D4311yescharacteristic
674C23#41×D4311yescharacteristic
675C23C2×#1062190011yescharacteristic
676C23C2×#1062190011yescharacteristic
677C23C2×#1062189811yescharacteristic
678C23#1306337011yescharacteristic
679C23#1306337111yescharacteristic
680C23#1306337211yescharacteristic
681C23#1306337311yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—434no—
705C2×C4—434no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—864no—
723C2×C4—862no—
724C2×C4—864no—
725C2×C4—862no—
726C2×C4—864no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1722no—
733C2×C4—1722no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1722no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1722no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1722no—
743C2×C4—1721no—
744C2×C4—1722no—
745C2×C4—1721no—
746C2×C4#1306330214yes—
747C2×C4#1306330214yes—
748C2×C4#1306330414yes—
749C2×C4#1306330614yes—
750C2×C4#1306330714yes—
751C2×C4#1306330714yes—
752C2×C4#1306332114yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22#121×D4311yescharacteristic
769C22C22⋊Q8×D4311yescharacteristic
770C22C2×#1306330211yescharacteristic
771C22C2×#1306330211yescharacteristic
772C22C2×#1306330411yescharacteristic
773C22C2×#1306330611yescharacteristic
774C22C2×#1306330711yescharacteristic
775C22C2×#1306330711yescharacteristic
776C22C2×#1306332111yescharacteristic
777C22C2×#1306332411yescharacteristic
778C22#1458344411yescharacteristic
779C22#1458345111yescharacteristic
780C22#1458345211yescharacteristic
781C22#1458346511yescharacteristic
782C22#1458347211yescharacteristic
783C22#1458351611yescharacteristic
784C22#1458352211yescharacteristic
785C22#1458352711yescharacteristic
786C22#1458353011yescharacteristic
787C22D4×C22⋊D4311yescharacteristic
788C22#1458353311yescharacteristic
789C22#1458354811yescharacteristic
790C22#1458354911yescharacteristic
791C22#1458355011yescharacteristic
792C22#1458355111yescharacteristic
793C22#1458356211yescharacteristic
794C22Q8×C22⋊D4311yescharacteristic
795C22#1458356711yescharacteristic
796C22#1458356811yescharacteristic
797C22#1458358311yescharacteristic
798C22#1458358811yescharacteristic
799C22#1458359311yescharacteristic
800C22#1458359611yescharacteristic
801C22#1458360411yescharacteristic
802C22#1458360711yescharacteristic
803C4—42no—
804C4—44no—
805C4—82no—
806C4—864no—
807C4—864no—
808C4—3442no—
809C4—1724no—
810C4—1722no—
811C4—1722no—
812C4#1458283518yescomplemented
813C2—44no—
814C2C2×#1458283511yescharacteristic
815C2#1913810511yescharacteristic
816C2#1913811111yescharacteristic
817C2#1913811611yescharacteristic
818C2#1913812211yescharacteristic
819C2#1913829111yescharacteristic
820C2#1913829811yescharacteristic
821C2#1913830211yescharacteristic
822C2#1913830911yescharacteristic
823C2#1913889911yescharacteristic
824C2#1913890811yescharacteristic
825C2#1913953811yescharacteristic
826C2#1913954511yescharacteristic
827C2#1914042011yescharacteristic
828C2#1914294511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutator, socle, cosocleC24×C43C24
FittingC2×C43×#380C2
prime radicalC25×C43C23
hypercenterC2×#380D43
hypocenterC43#15135
LCSG ▷ C24×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#14582798C2semidirect
3. C2×#14582795C2semidirect
4. C2×#14582768C2semidirect
7. #19132861C2semidirect
8. #19132859C2semidirect
10. #19132824C2semidirect
392. C4×C43#399semidirect
456. C43#15135semidirect
812. C4#14582835semidirect

Maximal subgroups

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

subgroupindex
C2×#145828352
C2×#145827982
C2×#145827952
C2×#145827682
C2×#145827592
C2×C4×C22⋊Dic432
#191328612
#191328592
#191328382
#191328242
C2×C43×#3802
#1513543