Finite Group Databasebeta

← #25018556

Subgroups — #25018556

Order 11008.

4046 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×(C2×D43)⋊C4C211yesmaximal, characteristic
2C22×C22⋊C4×D43C211yesmaximal, characteristic
3C2×#14582773C212yesmaximal, complemented
4C2×#14582759C211yesmaximal, characteristic, complemented
5C2×#14582757C211yesmaximal, characteristic, complemented
6C2×#14582754C211yesmaximal, characteristic
7#19132841C212yesmaximal, complemented
8#19132839C212yesmaximal, complemented
9#19132817C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C43×C22⋊#95C211yesmaximal, characteristic, complemented
12C25×D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C23×C4×D43C2212yes—
15C22×C4⋊Dic43C2212yescomplemented
16C22×Dic43⋊C4C2212yescomplemented
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4—28no—
20C22×(C2×D43)⋊C4C418yescomplemented
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2212yes—
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C2×C22⋊C4×D43—24no—
29C2×C22⋊C4×D43—24no—
30C2×C22⋊C4×D43—24no—
31#14582773—28no—
32#14582759—24no—
33#14582757—24no—
34#14582754—24no—
35C2×C43⋊#95C2212yescomplemented
36C2×C43⋊#95C2212yescomplemented
37C2×C43⋊#95C2212yescomplemented
38C2×C43⋊#95C2212yescomplemented
39C24×C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C22⋊C4×C43C2211yescharacteristic
42C2×#95×C43C2212yescomplemented
43C2×#95×C43C2212yescomplemented
44C24×D43—22no—
45C24×D43—22no—
46C24×D43—22no—
47C24×D43—22no—
48C24×D43—24no—
49C24×D43—24no—
50C24×D43—42no—
51C24×D43—42no—
52C24×D43C2×C414yes—
53C24×D43D414yes—
54C24×D43Q814yes—
55C24×D43C2311yescharacteristic
56C24×D43C2311yescharacteristic
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—24no—
60C23×Dic43—42no—
61C23×Dic43C2×C414yescomplemented
62C23×Dic43C2312yes—
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2312yes—
65C23×Dic43C2311yescharacteristic
66C22×C4×D43—24no—
67C22×C4×D43—24no—
68C22×C4×D43—24no—
69C22×C4×D43—24no—
70C22×C4×D43—24no—
71C22×C4×D43—42no—
72C22×C4×D43—42no—
73C2×C4⋊Dic43—24no—
74C2×C4⋊Dic43—24no—
75C2×C4⋊Dic43—42no—
76C2×Dic43⋊C4—24no—
77C2×Dic43⋊C4—24no—
78C2×Dic43⋊C4—42no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43D414yes—
85C2×(C2×D43)⋊C4—24no—
86C2×(C2×D43)⋊C4—24no—
87C2×(C2×D43)⋊C4—24no—
88C2×(C2×D43)⋊C4—24no—
89C2×(C2×D43)⋊C4—24no—
90C2×(C2×D43)⋊C4—24no—
91C2×(C2×D43)⋊C4—232no—
92C2×(C2×D43)⋊C4—24no—
93C2×(C2×D43)⋊C4—24no—
94C2×(C2×D43)⋊C4—24no—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—42no—
97C2×(C2×D43)⋊C4—42no—
98C2×(C2×D43)⋊C4C2×C414yes—
99C2×(C2×D43)⋊C4C2×C414yes—
100C2×(C2×D43)⋊C4C2×C414yescomplemented
101C2×(C2×D43)⋊C4C2×C414yescomplemented
102C2×(C2×D43)⋊C4D418yes—
103C22⋊C4×D43—232no—
104C43⋊#95—24no—
105C43⋊#95—24no—
106C43⋊#95—24no—
107C43⋊#95—42no—
108C25×C43C2311yescharacteristic
109C23×C4×C43—22no—
110C23×C4×C43—22no—
111C23×C4×C43—24no—
112C23×C4×C43—42no—
113C23×C4×C43C2×C414yescomplemented
114C23×C4×C43C2312yes—
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2312yes—
117C23×C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—22no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43D414yes—
124#95×C43—24no—
125#95×C43—42no—
126C24×C43—22no—
127C24×C43—22no—
128C24×C43—22no—
129C24×C43—22no—
130C24×C43C22×C412yes—
131C24×C43C2×D412yes—
132C24×C43C2×D412yes—
133C24×C43C2×D412yes—
134C24×C43C2×Q812yes—
135C24×C43#4112yes—
136C24×C43#4112yes—
137C24×C43C2411yescharacteristic
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—22no—
143C23×D43—22no—
144C23×D43—28no—
145C23×D43—28no—
146C23×D43—28no—
147C23×D43—28no—
148C23×D43—28no—
149C23×D43—28no—
150C23×D43—22no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—22no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—28no—
159C23×D43—28no—
160C23×D43—216no—
161C23×D43—216no—
162C23×D43—44no—
163C23×D43—44no—
164C23×D43—48no—
165C23×D43—48no—
166C23×D43—48no—
167C23×D43—48no—
168C23×D43—48no—
169C23×D43—48no—
170C23×D43—48no—
171C23×D43—48no—
172C23×D43—48no—
173C23×D43—48no—
174C23×D43C4⋊C4116yescomplemented
175C23×D43C22×C412yes—
176C23×D43C22×C412yes—
177C23×D43C2×D412yes—
178C23×D43C2×D414yes—
179C23×D43C2×D412yes—
180C23×D43C2×Q812yes—
181C23×D43C2×Q812yes—
182C23×D43#4114yes—
183C22×C4×C43—28no—
184C22×C4×C43—28no—
185C22×C4×C43—21no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—21no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—44no—
206C22×C4×C43—48no—
207C22×C4×C43—48no—
208C22×C4×C43C22×C412yes—
209C22×C4×C43C22×C412yes—
210C22×C4×C43C2×D414yes—
211C22×C4×C43C2×D414yes—
212C22×Dic43—28no—
213C22×Dic43—28no—
214C22×Dic43—21no—
215C22×Dic43—21no—
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—21no—
225C22×Dic43—22no—
226C22×Dic43—21no—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—22no—
231C22×Dic43—22no—
232C22×Dic43—22no—
233C22×Dic43—22no—
234C22×Dic43—44no—
235C22×Dic43—48no—
236C22×Dic43—48no—
237C22×Dic43C22×C412yes—
238C22×Dic43C22×C412yes—
239C22×Dic43C2×D414yes—
240C22×Dic43C2×D414yes—
241C2×C4×D43—216no—
242C2×C4×D43—48no—
243C2×C4×D43—48no—
244C2×C4×D43—48no—
245C2×C4×D43—48no—
246C2×C4×D43—48no—
247C2×C4×D43—48no—
248C22⋊C4×C43—28no—
249C22⋊C4×C43—44no—
250C22⋊Dic43—28no—
251C22⋊Dic43—44no—
252(C2×D43)⋊C4—216no—
253(C2×D43)⋊C4—28no—
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4—48no—
257(C2×D43)⋊C4—48no—
258(C2×D43)⋊C4C22⋊C4116yescomplemented
259C4⋊Dic43—48no—
260Dic43⋊C4—48no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—22no—
265C23×C43—24no—
266C23×C43—24no—
267C23×C43—24no—
268C23×C43—24no—
269C23×C43—24no—
270C23×C43—24no—
271C23×C43—24no—
272C23×C43—24no—
273C23×C43—24no—
274C23×C43—24no—
275C23×C43—24no—
276C23×C43—24no—
277C23×C43C2×C4⋊C414yes—
278C23×C43C4×D414yes—
279C23×C43C4×D414yes—
280C23×C43#12014yes—
281C23×C43C22⋊Q814yes—
282C23×C43C22⋊Q814yes—
283C23×C43#12314yes—
284C23×C43C23×C411yescharacteristic
285C23×C43C22×D412yes—
286C23×C43C22×D411yescharacteristic
287C23×C43C22×D411yescharacteristic
288C23×C43C22×D411yescharacteristic
289C23×C43C22×Q811yescharacteristic
290C23×C43C2×#4112yes—
291C23×C43C2×#4111yescharacteristic
292C23×C43C2×#4111yescharacteristic
293C23×C43H(5,𝔽2)12yes—
294C23×C43H(5,𝔽2)12yes—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—24no—
304C22×D43—24no—
305C22×D43—24no—
306C22×D43—24no—
307C22×D43—24no—
308C22×D43—24no—
309C22×D43—24no—
310C22×D43—24no—
311C22×D43—24no—
312C22×D43—24no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—24no—
321C22×D43—24no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—24no—
326C22×D43—24no—
327C22×D43—232no—
328C22×D43—232no—
329C22×D43—416no—
330C22×D43—416no—
331C22×D43—416no—
332C22×D43—416no—
333C22×D43—416no—
334C22×D43—432no—
335C22×D43—432no—
336C22×D43—432no—
337C22×D43—432no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43C2×C22⋊C414yes—
347C22×D43C2×C4⋊C414yes—
348C22×D43C2×C4⋊C414yes—
349C22×D43#11714yes—
350C22×D43#12118yes—
351C22×D43C22⋊Q818yes—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—24no—
355C2×C4×C43—24no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—24no—
360C2×C4×C43—24no—
361C2×C4×C43—24no—
362C2×C4×C43—416no—
363C2×C4×C43—42no—
364C2×C4×C43—42no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—42no—
370C2×C4×C43—42no—
371C2×C4×C43—42no—
372C2×C4×C43—42no—
373C2×C4×C43—42no—
374C2×C4×C43—42no—
375C2×C4×C43—42no—
376C2×C4×C43C2×C22⋊C414yescomplemented
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—24no—
380C2×Dic43—24no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—24no—
385C2×Dic43—24no—
386C2×Dic43—24no—
387C2×Dic43—416no—
388C2×Dic43—42no—
389C2×Dic43—42no—
390C2×Dic43—42no—
391C2×Dic43—42no—
392C2×Dic43—42no—
393C2×Dic43—42no—
394C2×Dic43—42no—
395C2×Dic43—42no—
396C2×Dic43—42no—
397C2×Dic43—42no—
398C2×Dic43—42no—
399C2×Dic43—42no—
400C2×Dic43—42no—
401C2×Dic43C2×C22⋊C414yescomplemented
402C4×D43—432no—
403#13877—431nomaximal, Sylow
404C22×C43—24no—
405C22×C43—24no—
406C22×C43—24no—
407C22×C43—24no—
408C22×C43—24no—
409C22×C43—28no—
410C22×C43—28no—
411C22×C43—28no—
412C22×C43—28no—
413C22×C43—24no—
414C22×C43#38518yescomplemented
415C22×C43C22×C22⋊C411yescharacteristic
416C22×C43C22×C4⋊C411yescharacteristic
417C22×C43C2×#11711yescharacteristic
418C22×C43C2×C4×D411yescharacteristic
419C22×C43C2×C4×D411yescharacteristic
420C22×C43#51811yescharacteristic
421C22×C43#51811yescharacteristic
422C22×C43C2×#12011yescharacteristic
423C22×C43C2×#12112yes—
424C22×C43C2×C22⋊Q812yes—
425C22×C43C2×C22⋊Q811yescharacteristic
426C22×C43C2×C22⋊Q811yescharacteristic
427C22×C43C2×#12311yescharacteristic
428C22×C43#53412yes—
429C22×C43#54312yes—
430C22×C43D4212yes—
431C22×C43D4212yes—
432C22×C43#54612yes—
433C22×C43#54612yes—
434C22×C43#54612yes—
435C22×C43#54612yes—
436C22×C43#55112yes—
437C22×C43#55112yes—
438C2×D43—24no—
439C2×D43—24no—
440C2×D43—24no—
441C2×D43—24no—
442C2×D43—24no—
443C2×D43—28no—
444C2×D43—28no—
445C2×D43—28no—
446C2×D43—28no—
447C2×D43—24no—
448C2×D43—24no—
449C2×D43—24no—
450C2×D43—24no—
451C2×D43—464no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—42no—
455C2×D43—42no—
456C2×D43—44no—
457C2×D43—44no—
458C2×D43—44no—
459C2×D43—44no—
460C2×D43#38018yescomplemented
461C4×C43—24no—
462C4×C43—42no—
463C4×C43—44no—
464C4×C43—82no—
465Dic43—24no—
466Dic43—42no—
467Dic43—44no—
468Dic43—82no—
469C23×C22⋊C4—431no—
470C23×C22⋊C4—431no—
471C2×#385—432no—
472C2×#380—431no—
473C2×#380—431no—
474C2×#379—431no—
475#1439—432no—
476#1439—432no—
477C22⋊#95—432no—
478C22⋊#95—431no—
479C22⋊#95D4311yescharacteristic, complemented
480C2×C43—28no—
481C2×C43C2×#38011yescharacteristic
482C2×C43C2×#38511yescharacteristic
483C2×C43#231511yescharacteristic
484C2×C43D4×C22⋊C411yescharacteristic
485C2×C43D4×C22⋊C411yescharacteristic
486C2×C43#234211yescharacteristic
487C2×C43#234211yescharacteristic
488C2×C43#241012yes—
489C2×C43#241212yes—
490C2×C43#243712yes—
491C2×C43#243712yes—
492D43—28no—
493D43—44no—
494C26—431no—
495C24×C4—431no—
496C24×C4—432no—
497C24×C4C2×D4311yescharacteristic
498C22×C4⋊C4—432no—
499C22×C4⋊C4—432no—
500C22×C22⋊C4—431no—
501C22×C22⋊C4—431no—
502C22×C22⋊C4—431no—
503C22×C22⋊C4—431no—
504C22×C22⋊C4—431no—
505C22×C22⋊C4—438no—
506C22×C22⋊C4—431no—
507C22×C22⋊C4—432no—
508C22×C22⋊C4—432no—
509C22×C22⋊C4—432no—
510C22×C22⋊C4—864no—
511C22×C22⋊C4—864no—
512C22×C22⋊C4—868no—
513C22×C22⋊C4—864no—
514C22×C22⋊C4C2×D4311yescharacteristic
515C22×C22⋊C4C2×D4311yescharacteristic
516#385—868no—
517#380—864no—
518#380—864no—
519#379—864no—
520C2×#95—432no—
521C2×#95—432no—
522C2×#95—432no—
523C2×#95—432no—
524C2×#95C2×D4312yescomplemented
525C2×#95C2×D4312yescomplemented
526C43#1387711yescharacteristic, complemented, Sylow
527C25—431no—
528C25—431no—
529C25—434no—
530C25—434no—
531C25—434no—
532C25—864no—
533C25—864no—
534C25—862no—
535C25—862no—
536C25—862no—
537C25—862no—
538C25—1722no—
539C25—1722no—
540C25C22×D4311yescharacteristic
541C23×C4—22no—
542C23×C4—22no—
543C23×C4—24no—
544C23×C4—42no—
545C23×C4—431no—
546C23×C4—432no—
547C23×C4—431no—
548C23×C4—434no—
549C23×C4—432no—
550C23×C4—864no—
551C23×C4—864no—
552C23×C4—864no—
553C23×C4—864no—
554C23×C4—864no—
555C23×C4—862no—
556C23×C4—862no—
557C23×C4—864no—
558C23×C4—1722no—
559C23×C4—1722no—
560C23×C4—1722no—
561C23×C4C4×D4314yescomplemented
562C23×C4C22×D4312yes—
563C23×C4C22×D4311yescharacteristic
564C23×C4C22×D4312yes—
565C23×C4C22×D4311yescharacteristic
566C2×C4⋊C4—864no—
567C2×C4⋊C4—864no—
568C2×C4⋊C4—864no—
569C2×C4⋊C4—864no—
570C2×C4⋊C4—1722no—
571C2×C4⋊C4—1722no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—434no—
578C2×C22⋊C4—438no—
579C2×C22⋊C4—434no—
580C2×C22⋊C4—434no—
581C2×C22⋊C4—434no—
582C2×C22⋊C4—434no—
583C2×C22⋊C4—8632no—
584C2×C22⋊C4—8632no—
585C2×C22⋊C4—864no—
586C2×C22⋊C4—864no—
587C2×C22⋊C4—864no—
588C2×C22⋊C4—864no—
589C2×C22⋊C4—862no—
590C2×C22⋊C4—862no—
591C2×C22⋊C4—864no—
592C2×C22⋊C4—864no—
593C2×C22⋊C4—864no—
594C2×C22⋊C4—864no—
595C2×C22⋊C4—864no—
596C2×C22⋊C4—864no—
597C2×C22⋊C4—862no—
598C2×C22⋊C4—862no—
599C2×C22⋊C4—862no—
600C2×C22⋊C4—1722no—
601C2×C22⋊C4—1722no—
602C2×C22⋊C4D17214yes—
603#95—24no—
604#95—42no—
605#95—864no—
606#95—864no—
607#95—864no—
608#95—1722no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—432no—
614C24—434no—
615C24—432no—
616C24—432no—
617C24—434no—
618C24—432no—
619C24—432no—
620C24—432no—
621C24—4316no—
622C24—868no—
623C24—868no—
624C24—8616no—
625C24—8616no—
626C24—861no—
627C24—861no—
628C24—861no—
629C24—861no—
630C24—862no—
631C24—862no—
632C24—868no—
633C24—868no—
634C24—868no—
635C24—868no—
636C24—868no—
637C24—868no—
638C24—862no—
639C24—861no—
640C24—861no—
641C24—862no—
642C24—861no—
643C24—861no—
644C24—862no—
645C24—862no—
646C24—1724no—
647C24—1724no—
648C24—1728no—
649C24—1728no—
650C24—1728no—
651C24—1728no—
652C24—1728no—
653C24—1728no—
654C24—1728no—
655C24—1728no—
656C24—1728no—
657C24—1728no—
658C24C2×C4×D4312yes—
659C24C2×D17212yes—
660C24#1062189812yes—
661C24D4×D4312yes—
662C24D4×D4312yes—
663C24#1062190012yes—
664C24Q8×D4312yes—
665C24C23×D4311yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—28no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—44no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—432no—
692C22×C4—434no—
693C22×C4—432no—
694C22×C4—434no—
695C22×C4—8616no—
696C22×C4—868no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—862no—
700C22×C4—868no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—861no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—861no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—862no—
715C22×C4—862no—
716C22×C4—862no—
717C22×C4—862no—
718C22×C4—1728no—
719C22×C4—1728no—
720C22×C4—1728no—
721C22×C4—1728no—
722C22×C4—1728no—
723C22×C4—1728no—
724C22×C4—1724no—
725C22×C4—1728no—
726C22×C4—1728no—
727C22×C4C2×C4×D4312yes—
728C22×C4C2×C4×D4312yes—
729C22×C4C2×D17214yes—
730C22×C4D4×D4314yes—
731C4⋊C4—1728no—
732C4⋊C4—1728no—
733C22⋊C4—28no—
734C22⋊C4—44no—
735C22⋊C4—4316no—
736C22⋊C4—868no—
737C22⋊C4—868no—
738C22⋊C4—8616no—
739C22⋊C4—868no—
740C22⋊C4—868no—
741C22⋊C4—1728no—
742C22⋊C4—1728no—
743C22⋊C4—1724no—
744C23—24no—
745C23—24no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—434no—
761C23—434no—
762C23—434no—
763C23—438no—
764C23—438no—
765C23—434no—
766C23—8632no—
767C23—864no—
768C23—864no—
769C23—862no—
770C23—862no—
771C23—862no—
772C23—862no—
773C23—862no—
774C23—862no—
775C23—862no—
776C23—862no—
777C23—864no—
778C23—864no—
779C23—864no—
780C23—864no—
781C23—864no—
782C23—864no—
783C23—864no—
784C23—864no—
785C23—862no—
786C23—862no—
787C23—862no—
788C23—862no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—864no—
793C23—864no—
794C23—862no—
795C23—862no—
796C23—862no—
797C23—864no—
798C23—864no—
799C23—8632no—
800C23—17216no—
801C23—17216no—
802C23—17216no—
803C23—17216no—
804C23—17216no—
805C23—17232no—
806C23—17232no—
807C23—17232no—
808C23—17232no—
809C23—1722no—
810C23—1722no—
811C23—1722no—
812C23—1722no—
813C23—1722no—
814C23—1722no—
815C23—1722no—
816C23—1722no—
817C23C4⋊C4×D4314yes—
818C23(C22⋊D43)⋊C414yes—
819C23C4×D17214yes—
820C23#1306329514yes—
821C23#1306330314yes—
822C23#1306330514yes—
823C23#1306330714yes—
824C23C22×C4×D4311yescharacteristic
825C23C2×D4×D4312yes—
826C23C2×D4×D4311yescharacteristic
827C23C2×D4×D4311yescharacteristic
828C23C22×D17211yescharacteristic
829C23C2×Q8×D4311yescharacteristic
830C23#41×D4312yes—
831C23C2×#1062190011yescharacteristic
832C23C2×#1062189811yescharacteristic
833C23#1306337012yes—
834C23#1306337112yes—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—416no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—434no—
860C2×C4—862no—
861C2×C4—862no—
862C2×C4—864no—
863C2×C4—864no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—864no—
868C2×C4—864no—
869C2×C4—864no—
870C2×C4—17232no—
871C2×C4—17216no—
872C2×C4—1722no—
873C2×C4—1722no—
874C2×C4—1722no—
875C2×C4—1722no—
876C2×C4—1722no—
877C2×C4—1722no—
878C2×C4—1722no—
879C2×C4—1722no—
880C2×C4—1722no—
881C2×C4—1722no—
882C2×C4—1722no—
883C2×C4—1722no—
884C2×C4—1722no—
885C2×C4C22⋊C4×D4314yescomplemented
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—28no—
891C22—24no—
892C22—24no—
893C22—28no—
894C22—28no—
895C22—28no—
896C22—438no—
897C22—864no—
898C22—864no—
899C22—864no—
900C22—864no—
901C22—868no—
902C22—864no—
903C22—868no—
904C22—868no—
905C22—868no—
906C22—864no—
907C22—864no—
908C22—864no—
909C22—864no—
910C22—17264no—
911C22—1722no—
912C22—1722no—
913C22—1722no—
914C22—1722no—
915C22—1724no—
916C22—1724no—
917C22—1724no—
918C22—1724no—
919C22#1458277318yescomplemented
920C22C2×C22⋊C4×D4311yescharacteristic
921C22C2×C4⋊C4×D4311yescharacteristic
922C22#117×D4311yescharacteristic
923C22C2×(C22⋊D43)⋊C411yescharacteristic
924C22C2×C4×D17211yescharacteristic
925C22#1458337211yescharacteristic
926C22#1458337311yescharacteristic
927C22C2×#1306329511yescharacteristic
928C22#121×D4312yes—
929C22C22⋊Q8×D4312yes—
930C22C2×#1306330311yescharacteristic
931C22C2×#1306330511yescharacteristic
932C22C2×#1306330711yescharacteristic
933C22#1458345712yes—
934C22#1458352412yes—
935C22#1458353112yes—
936C22D4×D17212yes—
937C22#1458353612yes—
938C22#1458354112yes—
939C22#1458354412yes—
940C22#1458354512yes—
941C22#1458357212yes—
942C22#1458357812yes—
943C4—24no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4—864no—
948C4—3442no—
949C4—1722no—
950C4—1724no—
951C2—28no—
952C2—868no—
953C2—1724no—
954C2#380×D4311yescharacteristic
955C2C2×#1458277311yescharacteristic
956C2#1913720811yescharacteristic
957C2#1913741111yescharacteristic
958C2C22⋊C4×D17211yescharacteristic
959C2#1913743711yescharacteristic
960C2#1913744711yescharacteristic
961C2#1913796812yes—
962C2#1913799012yes—
963C2#1913825912yes—
964C2#1913826012yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×C22⋊#95C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenterC22⋊#95D43
hypocenterC43#13877
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#14582773C2semidirect
4. C2×#14582759C2semidirect
5. C2×#14582757C2semidirect
7. #19132841C2semidirect
8. #19132839C2semidirect
9. #19132817C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C43×C22⋊#95C2semidirect
15. C22×C4⋊Dic43C22semidirect
16. C22×Dic43⋊C4C22semidirect
20. C22×(C2×D43)⋊C4C4semidirect
35. C2×C43⋊#95C22semidirect
36. C2×C43⋊#95C22semidirect
37. C2×C43⋊#95C22semidirect
38. C2×C43⋊#95C22semidirect
42. C2×#95×C43C22semidirect
43. C2×#95×C43C22semidirect
61. C23×Dic43C2×C4semidirect
100. C2×(C2×D43)⋊C4C2×C4semidirect
101. C2×(C2×D43)⋊C4C2×C4semidirect
113. C23×C4×C43C2×C4semidirect
174. C23×D43C4⋊C4semidirect
258. (C2×D43)⋊C4C22⋊C4semidirect
376. C2×C4×C43C2×C22⋊C4semidirect
401. C2×Dic43C2×C22⋊C4semidirect
414. C22×C43#385semidirect
460. C2×D43#380semidirect
479. C22⋊#95D43semidirect
524. C2×#95C2×D43semidirect
525. C2×#95C2×D43semidirect
526. C43#13877semidirect
561. C23×C4C4×D43semidirect
885. C2×C4C22⋊C4×D43semidirect
919. C22#14582773semidirect

Maximal subgroups

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

subgroupindex
C23×(C2×D43)⋊C42
C22×C22⋊C4×D432
C2×#145827732
C2×#145827592
C2×#145827572
C2×#145827542
#191328412
#191328392
#191328172
(C2×D43)⋊#952
C43×C22⋊#952
#1387743