Finite Group Databasebeta

← #25018554

Subgroups — #25018554

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×#14582770C212yesmaximal, complemented
4C2×#14582757C211yesmaximal, characteristic, complemented
5C2×#14582754C211yesmaximal, characteristic
6#19132839C212yesmaximal, complemented
7#19132837C212yesmaximal, complemented
8#19132818C211yesmaximal, characteristic, complemented
9#19132817C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C2×C43×#380C211yesmaximal, characteristic, complemented
12C25×D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C23×C4×D43C2212yes—
15C22×Dic43⋊C4C2212yescomplemented
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×(C2×D43)⋊C4—28no—
19C22×(C2×D43)⋊C4C418yescomplemented
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2212yes—
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C2×C22⋊C4×D43—24no—
28C2×C22⋊C4×D43—24no—
29C2×C22⋊C4×D43—24no—
30#14582770—28no—
31#14582757—24no—
32#14582754—24no—
33C2×C43⋊#95C2212yescomplemented
34C2×C43⋊#95C2212yescomplemented
35C2×C43⋊#95C2212yescomplemented
36C2×C43⋊#95C2212yescomplemented
37C2×C43⋊#95C2212yescomplemented
38C24×C4×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2212yescomplemented
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C22⋊C4×C43C2211yescharacteristic
42C43×#380—24no—
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×Dic43⋊C4—24no—
74C2×Dic43⋊C4—24no—
75C2×Dic43⋊C4—42no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43D414yes—
82C2×(C2×D43)⋊C4—24no—
83C2×(C2×D43)⋊C4—24no—
84C2×(C2×D43)⋊C4—24no—
85C2×(C2×D43)⋊C4—24no—
86C2×(C2×D43)⋊C4—24no—
87C2×(C2×D43)⋊C4—24no—
88C2×(C2×D43)⋊C4—232no—
89C2×(C2×D43)⋊C4—24no—
90C2×(C2×D43)⋊C4—24no—
91C2×(C2×D43)⋊C4—24no—
92C2×(C2×D43)⋊C4—24no—
93C2×(C2×D43)⋊C4—42no—
94C2×(C2×D43)⋊C4—42no—
95C2×(C2×D43)⋊C4C2×C414yes—
96C2×(C2×D43)⋊C4C2×C414yes—
97C2×(C2×D43)⋊C4C2×C414yescomplemented
98C2×(C2×D43)⋊C4C2×C414yescomplemented
99C2×(C2×D43)⋊C4D418yes—
100C22⋊C4×D43—232no—
101C43⋊#95—24no—
102C43⋊#95—24no—
103C43⋊#95—24no—
104C43⋊#95—42no—
105C43⋊#95—42no—
106C25×C43C2311yescharacteristic
107C23×C4×C43—22no—
108C23×C4×C43—22no—
109C23×C4×C43—24no—
110C23×C4×C43—42no—
111C23×C4×C43C2×C414yescomplemented
112C23×C4×C43C2312yes—
113C23×C4×C43C2311yescharacteristic
114C23×C4×C43C2312yes—
115C23×C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43—24no—
117C2×C4⋊C4×C43—24no—
118C2×C4⋊C4×C43—42no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—22no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—22no—
124C2×C22⋊C4×C43D414yes—
125#95×C43—24no—
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—21no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
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—21no—
223C22×Dic43—22no—
224C22×Dic43—21no—
225C22×Dic43—22no—
226C22×Dic43—22no—
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—
248C4⋊C4×C43—48no—
249C22⋊C4×C43—28no—
250C22⋊C4×C43—44no—
251C22⋊Dic43—28no—
252C22⋊Dic43—44no—
253(C2×D43)⋊C4—216no—
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4—28no—
257(C2×D43)⋊C4—48no—
258(C2×D43)⋊C4—48no—
259(C2×D43)⋊C4C22⋊C4116yescomplemented
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×#380D4311yescharacteristic, complemented
474C2×#379—431no—
475#1439—432no—
476#1439—432no—
477C22⋊#95—432no—
478C22⋊#95—431no—
479C22⋊#95—431no—
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⋊C4C2×D4312yescomplemented
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—24no—
518#380—864no—
519#379—864no—
520C2×#95—432no—
521C2×#95—432no—
522C2×#95—432no—
523C2×#95—432no—
524C2×#95—432no—
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—24no—
567C2×C4⋊C4—24no—
568C2×C4⋊C4—42no—
569C2×C4⋊C4—864no—
570C2×C4⋊C4—864no—
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⋊C4C22⋊D4314yes—
603#95—24no—
604#95—864no—
605#95—864no—
606#95—864no—
607#95—1722no—
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—
659C24#1062189812yes—
660C24D4×D4312yes—
661C24D4×D4312yes—
662C24Q8×D4312yes—
663C24#1062190212yes—
664C24C2×C22⋊D4312yes—
665C24C23×D4311yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
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—861no—
702C22×C4—862no—
703C22×C4—862no—
704C22×C4—862no—
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×C4D4×D4314yes—
730C22×C4C2×C22⋊D4314yes—
731C4⋊C4—48no—
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—
818C23C4×C22⋊D4314yes—
819C23#1306328714yes—
820C23#1306329314yes—
821C23#1306330114yes—
822C23#1306330314yes—
823C23#1306331014yes—
824C23C22×C4×D4311yescharacteristic
825C23C2×D4×D4312yes—
826C23C2×D4×D4311yescharacteristic
827C23C2×D4×D4311yescharacteristic
828C23C22×C22⋊D4311yescharacteristic
829C23C2×Q8×D4311yescharacteristic
830C23#41×D4312yes—
831C23C2×#1062189811yescharacteristic
832C23C2×#1062190211yescharacteristic
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#1458277018yescomplemented
920C22C2×C22⋊C4×D4311yescharacteristic
921C22C2×C4⋊C4×D4311yescharacteristic
922C22#117×D4311yescharacteristic
923C22C2×C4×C22⋊D4311yescharacteristic
924C22C2×#1306328711yescharacteristic
925C22#1458337211yescharacteristic
926C22#1458337311yescharacteristic
927C22C2×#1306329311yescharacteristic
928C22#121×D4312yes—
929C22C22⋊Q8×D4312yes—
930C22C2×#1306330111yescharacteristic
931C22C2×#1306330311yescharacteristic
932C22C2×#1306331011yescharacteristic
933C22#1458345712yes—
934C22#1458352412yes—
935C22D4×C22⋊D4312yes—
936C22#1458353312yes—
937C22#1458353712yes—
938C22#1458353812yes—
939C22#1458353912yes—
940C22#1458354012yes—
941C22#1458357312yes—
942C22#1458357612yes—
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×#1458277011yescharacteristic
956C2#1913720811yescharacteristic
957C2C22⋊C4×C22⋊D4311yescharacteristic
958C2#1913741511yescharacteristic
959C2#1913744111yescharacteristic
960C2#1913744511yescharacteristic
961C2#1913796612yes—
962C2#1913798812yes—
963C2#1913825812yes—
964C2#1913826312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#380C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenterC2×#380D43
hypocenterC43#13877
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#14582770C2semidirect
4. C2×#14582757C2semidirect
6. #19132839C2semidirect
7. #19132837C2semidirect
8. #19132818C2semidirect
9. #19132817C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C2×C43×#380C2semidirect
15. C22×Dic43⋊C4C22semidirect
19. C22×(C2×D43)⋊C4C4semidirect
33. C2×C43⋊#95C22semidirect
34. C2×C43⋊#95C22semidirect
35. C2×C43⋊#95C22semidirect
36. C2×C43⋊#95C22semidirect
37. C2×C43⋊#95C22semidirect
39. C22×C4⋊C4×C43C22semidirect
43. C2×#95×C43C22semidirect
61. C23×Dic43C2×C4semidirect
97. C2×(C2×D43)⋊C4C2×C4semidirect
98. C2×(C2×D43)⋊C4C2×C4semidirect
111. C23×C4×C43C2×C4semidirect
174. C23×D43C4⋊C4semidirect
259. (C2×D43)⋊C4C22⋊C4semidirect
376. C2×C4×C43C2×C22⋊C4semidirect
401. C2×Dic43C2×C22⋊C4semidirect
414. C22×C43#385semidirect
460. C2×D43#380semidirect
473. C2×#380D43semidirect
499. C22×C4⋊C4C2×D43semidirect
525. C2×#95C2×D43semidirect
526. C43#13877semidirect
561. C23×C4C4×D43semidirect
885. C2×C4C22⋊C4×D43semidirect
919. C22#14582770semidirect

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×#145827702
C2×#145827572
C2×#145827542
#191328392
#191328372
#191328182
#191328172
(C2×D43)⋊#952
C2×C43×#3802
#1387743