Finite Group Databasebeta

← #25018515

Subgroups — #25018515

Order 11008.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582792C212yesmaximal, complemented
2C2×#14582759C211yesmaximal, characteristic, complemented
3C2×#14582755C211yesmaximal, characteristic
4C2×#14582755C211yesmaximal, characteristic
5C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
6#19132844C212yesmaximal, complemented
7#19132840C212yesmaximal, complemented
8#19132832C212yesmaximal, complemented
9#19132818C211yesmaximal, characteristic, complemented
10#19132818C211yesmaximal, characteristic, complemented
11C23×C22⋊C4×C43C211yesmaximal, characteristic
12C22×C4⋊Dic43C2212yescomplemented
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C22⋊Dic43C2212yes—
16C22×C22⋊Dic43C2212yes—
17C22×C22⋊Dic43C2212yes—
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2212yescomplemented
22#14582792—28no—
23#14582759—24no—
24#14582755—24no—
25#14582755—24no—
26C4×C22⋊Dic43—24no—
27C2×C43⋊#95C2212yescomplemented
28C2×C43⋊#95C2212yescomplemented
29C2×C43⋊#95C2212yescomplemented
30C2×C43⋊#95C2212yescomplemented
31C2×C43⋊#95C2212yescomplemented
32C2×C43⋊#95C2212yescomplemented
33C26×C43C2211yescharacteristic
34C24×C4×C43C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43—28no—
37C22×C22⋊C4×C43C418yescomplemented
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C22⋊C4×C43C2211yescharacteristic
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C23×Dic43C2312yes—
46C2×C4⋊Dic43—24no—
47C2×C4⋊Dic43—24no—
48C2×C4⋊Dic43—42no—
49C2×C22⋊Dic43—22no—
50C2×C22⋊Dic43—22no—
51C2×C22⋊Dic43—22no—
52C2×C22⋊Dic43—22no—
53C2×C22⋊Dic43—24no—
54C2×C22⋊Dic43—24no—
55C2×C22⋊Dic43—22no—
56C2×C22⋊Dic43—22no—
57C2×C22⋊Dic43—22no—
58C2×C22⋊Dic43—24no—
59C2×C22⋊Dic43—24no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—22no—
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×C22⋊Dic43—42no—
70C2×C22⋊Dic43—42no—
71C2×C22⋊Dic43D414yes—
72C2×C22⋊Dic43D414yes—
73C2×C4×Dic43—24no—
74C2×C4×Dic43—24no—
75C2×C4×Dic43—42no—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—42no—
81C43⋊#95—42no—
82C25×C43—24no—
83C25×C43—24no—
84C25×C43—22no—
85C25×C43—22no—
86C25×C43—22no—
87C25×C43—22no—
88C25×C43—22no—
89C25×C43—22no—
90C25×C43—42no—
91C25×C43—42no—
92C25×C43C2×C414yes—
93C25×C43C2311yescharacteristic
94C25×C43C2311yescharacteristic
95C25×C43C2311yescharacteristic
96C23×C4×C43—22no—
97C23×C4×C43—22no—
98C23×C4×C43—22no—
99C23×C4×C43—22no—
100C23×C4×C43—24no—
101C23×C4×C43—24no—
102C23×C4×C43—42no—
103C23×C4×C43—42no—
104C23×C4×C43C2×C414yes—
105C23×C4×C43C2×C414yes—
106C23×C4×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C23×C4×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C2×C22⋊C4×C43—24no—
111C2×C22⋊C4×C43—24no—
112C2×C22⋊C4×C43—24no—
113C2×C22⋊C4×C43—232no—
114C2×C22⋊C4×C43C2×C414yes—
115C2×C22⋊C4×C43C2×C414yes—
116C2×C22⋊C4×C43C2×C414yes—
117C2×C22⋊C4×C43C2×C414yes—
118C2×C22⋊C4×C43D418yes—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43—22no—
122C24×C43—22no—
123C24×C43—216no—
124C24×C43—216no—
125C24×C43—28no—
126C24×C43—28no—
127C24×C43—28no—
128C24×C43—22no—
129C24×C43—21no—
130C24×C43—21no—
131C24×C43—21no—
132C24×C43—21no—
133C24×C43—21no—
134C24×C43—21no—
135C24×C43—22no—
136C24×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—22no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—28no—
147C24×C43—28no—
148C24×C43—44no—
149C24×C43—44no—
150C24×C43—48no—
151C24×C43—48no—
152C24×C43—48no—
153C24×C43—48no—
154C24×C43—48no—
155C24×C43—48no—
156C24×C43—48no—
157C24×C43—48no—
158C24×C43—48no—
159C24×C43—48no—
160C24×C43—44no—
161C24×C43—44no—
162C24×C43—44no—
163C24×C43—44no—
164C24×C43C22×C412yes—
165C24×C43C22×C412yes—
166C24×C43C22×C412yes—
167C24×C43C2×D414yes—
168C24×C43C2×D412yes—
169C24×C43C2×D412yes—
170C24×C43#4114yes—
171C24×C43#4112yes—
172C24×C43#4112yes—
173C24×C43#4112yes—
174C24×C43#4112yes—
175C24×C43C2411yescharacteristic
176C22×C4×C43—28no—
177C22×C4×C43—28no—
178C22×C4×C43—28no—
179C22×C4×C43—28no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—44no—
195C22×C4×C43—44no—
196C22×C4×C43—48no—
197C22×C4×C43—48no—
198C22×C4×C43—48no—
199C22×C4×C43—48no—
200C22×C4×C43C22×C412yes—
201C22×C4×C43C22×C412yes—
202C22×C4×C43C22×C412yes—
203C22×C4×C43C22×C412yes—
204C22×C4×C43C2×D414yes—
205C22×C4×C43C2×D414yes—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—22no—
231C22×Dic43—22no—
232C22×Dic43C2×D414yes—
233C22×Dic43C2×D414yes—
234C22⋊C4×C43—28no—
235C22⋊C4×C43—28no—
236C22⋊C4×C43—28no—
237C22⋊C4×C43C22⋊C4116yescomplemented
238C22⋊Dic43—28no—
239C22⋊Dic43—28no—
240C22⋊Dic43—48no—
241C22⋊Dic43—48no—
242C22⋊Dic43—48no—
243C22⋊Dic43—48no—
244C22⋊Dic43—44no—
245C22⋊Dic43—44no—
246C4⋊Dic43—48no—
247C4×Dic43—48no—
248C23×C43—22no—
249C23×C43—22no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—24no—
253C23×C43—24no—
254C23×C43—24no—
255C23×C43—24no—
256C23×C43—24no—
257C23×C43—24no—
258C23×C43—24no—
259C23×C43—24no—
260C23×C43—24no—
261C23×C43—24no—
262C23×C43—24no—
263C23×C43—24no—
264C23×C43—232no—
265C23×C43—22no—
266C23×C43—22no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—24no—
278C23×C43—24no—
279C23×C43—24no—
280C23×C43—24no—
281C23×C43—24no—
282C23×C43—24no—
283C23×C43—24no—
284C23×C43—24no—
285C23×C43—24no—
286C23×C43—24no—
287C23×C43—24no—
288C23×C43—24no—
289C23×C43—416no—
290C23×C43—416no—
291C23×C43—416no—
292C23×C43—416no—
293C23×C43—416no—
294C23×C43—432no—
295C23×C43—432no—
296C23×C43—432no—
297C23×C43—432no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43—416no—
319C23×C43C2×C22⋊C414yes—
320C23×C43#11714yes—
321C23×C43#11714yes—
322C23×C43C4×D414yes—
323C23×C43C4×D414yes—
324C23×C43#12114yes—
325C23×C43#12314yes—
326C23×C43#12414yes—
327C23×C43#12614yes—
328C23×C43C23×C411yescharacteristic
329C23×C43C22×D411yescharacteristic
330C23×C43C22×D411yescharacteristic
331C23×C43C22×D412yes—
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43C2×#4111yescharacteristic
336C23×C43C2×#4112yes—
337C23×C43H(5,𝔽2)12yes—
338C23×C43H(5,𝔽2)12yes—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—24no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—24no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—416no—
354C2×C4×C43—416no—
355C2×C4×C43—42no—
356C2×C4×C43—42no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43C2×C22⋊C414yes—
360C2×C4×C43C2×C22⋊C414yes—
361C2×Dic43—24no—
362C2×Dic43—24no—
363C2×Dic43—24no—
364C2×Dic43—24no—
365C2×Dic43—24no—
366C2×Dic43—24no—
367C2×Dic43—42no—
368C2×Dic43—42no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—42no—
377C2×Dic43—42no—
378C2×Dic43—42no—
379C2×Dic43—42no—
380C2×Dic43—42no—
381C2×Dic43—42no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384C2×Dic43—42no—
385C2×Dic43—42no—
386C2×Dic43—42no—
387C2×Dic43—42no—
388C2×Dic43—42no—
389#13873—431nomaximal, Sylow
390C22×C43—24no—
391C22×C43—24no—
392C22×C43—24no—
393C22×C43—24no—
394C22×C43—24no—
395C22×C43—28no—
396C22×C43—28no—
397C22×C43—28no—
398C22×C43—28no—
399C22×C43—24no—
400C22×C43—24no—
401C22×C43—24no—
402C22×C43—24no—
403C22×C43—24no—
404C22×C43—24no—
405C22×C43—24no—
406C22×C43—464no—
407C22×C43—42no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—44no—
414C22×C43—44no—
415C22×C43—44no—
416C22×C43—44no—
417C22×C43—44no—
418C22×C43—44no—
419C22×C43—44no—
420C22×C43—44no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43#38818yescomplemented
424C22×C43C22×C22⋊C411yescharacteristic
425C22×C43C2×#11711yescharacteristic
426C22×C43C2×#11711yescharacteristic
427C22×C43C2×C4×D411yescharacteristic
428C22×C43C2×C4×D411yescharacteristic
429C22×C43#51811yescharacteristic
430C22×C43#51811yescharacteristic
431C22×C43C2×#12111yescharacteristic
432C22×C43C2×#12311yescharacteristic
433C22×C43#52512yes—
434C22×C43#52512yes—
435C22×C43C2×#12411yescharacteristic
436C22×C43C2×#12611yescharacteristic
437C22×C43#53812yes—
438C22×C43#53812yes—
439C22×C43D4212yes—
440C22×C43D4212yes—
441C22×C43#54612yes—
442C22×C43#54612yes—
443C22×C43#54612yes—
444C22×C43#54612yes—
445C22×C43#55112yes—
446C22×C43#55112yes—
447C4×C43—24no—
448C4×C43—24no—
449C4×C43—42no—
450C4×C43—42no—
451Dic43—44no—
452Dic43—44no—
453Dic43—82no—
454Dic43—82no—
455C23×C22⋊C4D4311yescharacteristic
456C2×#388—432no—
457C2×#380—431no—
458C2×#379—431no—
459C2×#379—431no—
460C2×C4×C22⋊C4—431no—
461#1440—432no—
462#1439—432no—
463#1437—432no—
464C22⋊#95—431no—
465C22⋊#95—431no—
466C2×C43—28no—
467C2×C43—44no—
468C2×C43—44no—
469C2×C43#228011yescharacteristic
470C2×C43C2×#38811yescharacteristic
471C2×C43#231211yescharacteristic
472C2×C43D4×C22⋊C411yescharacteristic
473C2×C43D4×C22⋊C411yescharacteristic
474C2×C43#234211yescharacteristic
475C2×C43#234211yescharacteristic
476C2×C43#241812yes—
477C2×C43#242412yes—
478C2×C43#247212yes—
479C2×C43#248012yes—
480C26C2×D4311yescharacteristic
481C24×C4C2×D4311yescharacteristic
482C24×C4C2×D4311yescharacteristic
483C22×C4⋊C4—432no—
484C22×C22⋊C4—28no—
485C22×C22⋊C4—431no—
486C22×C22⋊C4—431no—
487C22×C22⋊C4—431no—
488C22×C22⋊C4—431no—
489C22×C22⋊C4—432no—
490C22×C22⋊C4—432no—
491C22×C22⋊C4—432no—
492C22×C22⋊C4—432no—
493C22×C22⋊C4Dic4318yescomplemented
494C22×C22⋊C4C2×D4311yescharacteristic
495C22×C22⋊C4C2×D4311yescharacteristic
496C22×C22⋊C4C2×D4311yescharacteristic
497C22×C22⋊C4C2×D4311yescharacteristic
498C22×C42—432no—
499#388—868no—
500#380—864no—
501#379—864no—
502#379—864no—
503C4×C22⋊C4—864no—
504C2×#95—432no—
505C2×#95—432no—
506C2×#95—432no—
507C2×#95—432no—
508C2×#95—432no—
509C2×#95—432no—
510C43#1387311yescharacteristic, complemented, Sylow
511C25—24no—
512C25—22no—
513C25—22no—
514C25—24no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×Dic4314yes—
522C25C22×D4311yescharacteristic
523C25C22×D4311yescharacteristic
524C25C22×D4311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4—432no—
534C23×C4—432no—
535C23×C4—432no—
536C23×C4—432no—
537C23×C4C2×Dic4314yes—
538C23×C4C2×Dic4314yes—
539C23×C4C22×D4311yescharacteristic
540C23×C4C22×D4311yescharacteristic
541C23×C4C22×D4311yescharacteristic
542C23×C4C22×D4311yescharacteristic
543C2×C4⋊C4—864no—
544C2×C4⋊C4—864no—
545C2×C4⋊C4—1722no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—232no—
550C2×C22⋊C4—434no—
551C2×C22⋊C4—434no—
552C2×C22⋊C4—862no—
553C2×C22⋊C4—862no—
554C2×C22⋊C4—862no—
555C2×C22⋊C4—862no—
556C2×C22⋊C4—864no—
557C2×C22⋊C4—864no—
558C2×C22⋊C4—864no—
559C2×C22⋊C4—864no—
560C2×C22⋊C4—864no—
561C2×C22⋊C4—864no—
562C2×C22⋊C4—862no—
563C2×C22⋊C4—862no—
564C2×C22⋊C4—862no—
565C2×C22⋊C4—862no—
566C2×C22⋊C4—862no—
567C2×C22⋊C4—862no—
568C2×C22⋊C4—864no—
569C2×C22⋊C4—864no—
570C2×C22⋊C4—1722no—
571C2×C22⋊C4—1722no—
572C2×C22⋊C4—1722no—
573C2×C22⋊C4—1722no—
574C2×C22⋊C4C2×Dic4314yes—
575C2×C22⋊C4C2×Dic4314yes—
576C2×C22⋊C4C2×Dic4314yes—
577C2×C22⋊C4C2×Dic4314yes—
578C2×C22⋊C4C22⋊D4318yes—
579C2×C42—864no—
580C2×C42—864no—
581C2×C42—1722no—
582#95—864no—
583#95—864no—
584#95—864no—
585#95—864no—
586#95—1722no—
587#95—1722no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24#1062189814yes—
634C24#1062189812yes—
635C24#1062189812yes—
636C24D4×D4312yes—
637C24D4×D4312yes—
638C24#1062190012yes—
639C24#1062190012yes—
640C24C22×Dic4312yes—
641C24C22×Dic4312yes—
642C24C22×Dic4312yes—
643C24C2×C22⋊D4314yes—
644C24C23×D4311yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—28no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—434no—
670C22×C4—434no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—862no—
679C22×C4—862no—
680C22×C4—862no—
681C22×C4—862no—
682C22×C4—862no—
683C22×C4—862no—
684C22×C4—862no—
685C22×C4—862no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—862no—
693C22×C4—862no—
694C22×C4—862no—
695C22×C4—862no—
696C22×C4—862no—
697C22×C4C22×Dic4312yes—
698C22×C4C22×Dic4312yes—
699C22×C4C22×Dic4312yes—
700C22×C4C22×Dic4312yes—
701C22×C4C2×C22⋊D4314yes—
702C22×C4C2×C22⋊D4314yes—
703C4⋊C4—1728no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—868no—
708C22⋊C4—868no—
709C22⋊C4—1728no—
710C22⋊C4—1728no—
711C22⋊C4—1728no—
712C22⋊C4—1728no—
713C22⋊C4—1724no—
714C22⋊C4—1724no—
715C22⋊C4C22⋊Dic43116yescomplemented
716C42—1728no—
717C23—24no—
718C23—24no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—432no—
765C23—432no—
766C23—416no—
767C23—416no—
768C23—42no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23C2×C22⋊Dic4314yes—
789C23#1306328414yes—
790C23#1306328414yes—
791C23D4×Dic4314yes—
792C23D4×Dic4314yes—
793C23#1306329814yes—
794C23#1306330714yes—
795C23#1306331114yes—
796C23#1306331814yes—
797C23C23×Dic4311yescharacteristic
798C23C2×D4×D4311yescharacteristic
799C23C2×D4×D4311yescharacteristic
800C23C22×C22⋊D4312yes—
801C23C2×#1062190011yescharacteristic
802C23C2×#1062190011yescharacteristic
803C23C2×#1062189812yes—
804C23C2×#1062189811yescharacteristic
805C23C2×#1062189811yescharacteristic
806C23#1306337012yes—
807C23#1306337012yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—864no—
829C2×C4—864no—
830C2×C4—864no—
831C2×C4—864no—
832C2×C4—864no—
833C2×C4—864no—
834C2×C4—1722no—
835C2×C4—1722no—
836C2×C4—1722no—
837C2×C4—1722no—
838C2×C4—1722no—
839C2×C4—1722no—
840C2×C4—1722no—
841C2×C4—1722no—
842C2×C4—1722no—
843C2×C4—1722no—
844C2×C4—1722no—
845C2×C4—1722no—
846C2×C4—1722no—
847C2×C4—1722no—
848C2×C4—1722no—
849C2×C4—1722no—
850C2×C4—1722no—
851C2×C4—1722no—
852C2×C4—1722no—
853C2×C4—1722no—
854C2×C4—1722no—
855C2×C4—1722no—
856C2×C4C2×C22⋊Dic4314yes—
857C2×C4C2×C22⋊Dic4314yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—28no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—42no—
876C22—42no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—44no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22#1458279218yescomplemented
892C22C22×C22⋊Dic4311yescharacteristic
893C22C2×#1306328411yescharacteristic
894C22C2×#1306328411yescharacteristic
895C22C2×D4×Dic4311yescharacteristic
896C22C2×D4×Dic4311yescharacteristic
897C22#1458337411yescharacteristic
898C22#1458337411yescharacteristic
899C22C2×#1306329811yescharacteristic
900C22C2×#1306330711yescharacteristic
901C22#1458341012yes—
902C22#1458341012yes—
903C22C2×#1306331111yescharacteristic
904C22C2×#1306331811yescharacteristic
905C22#1458348712yes—
906C22#1458348712yes—
907C22D4×C22⋊D4312yes—
908C22D4×C22⋊D4312yes—
909C22#1458353912yes—
910C22#1458353912yes—
911C22#1458354312yes—
912C22#1458354312yes—
913C22#1458357512yes—
914C22#1458357512yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—3442no—
920C4—3442no—
921C4—1724no—
922C4—1724no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#1913697811yescharacteristic
927C2C2×#1458279211yescharacteristic
928C2#1913719311yescharacteristic
929C2D4×C22⋊Dic4311yescharacteristic
930C2D4×C22⋊Dic4311yescharacteristic
931C2#1913744411yescharacteristic
932C2#1913744411yescharacteristic
933C2#1913805712yes—
934C2#1913813112yes—
935C2#1913871512yes—
936C2#1913883512yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC23×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC26×C43C22
hypercenterC23×C22⋊C4D43
hypocenterC43#13873
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14582792C2semidirect
2. C2×#14582759C2semidirect
5. C2×C4×C22⋊Dic43C2semidirect
6. #19132844C2semidirect
7. #19132840C2semidirect
8. #19132832C2semidirect
9. #19132818C2semidirect
10. #19132818C2semidirect
12. C22×C4⋊Dic43C22semidirect
21. C22×C4×Dic43C22semidirect
27. C2×C43⋊#95C22semidirect
28. C2×C43⋊#95C22semidirect
29. C2×C43⋊#95C22semidirect
30. C2×C43⋊#95C22semidirect
31. C2×C43⋊#95C22semidirect
32. C2×C43⋊#95C22semidirect
37. C22×C22⋊C4×C43C4semidirect
237. C22⋊C4×C43C22⋊C4semidirect
423. C22×C43#388semidirect
493. C22×C22⋊C4Dic43semidirect
510. C43#13873semidirect
715. C22⋊C4C22⋊Dic43semidirect
891. C22#14582792semidirect

Maximal subgroups

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

subgroupindex
C2×#145827922
C2×#145827592
C2×#145827552
C2×C4×C22⋊Dic432
#191328442
#191328402
#191328322
#191328182
C23×C22⋊C4×C432
#1387343