Finite Group Databasebeta

← #25018541

Subgroups — #25018541

Order 11008.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582793C211yesmaximal, characteristic
2C2×#14582787C211yesmaximal, characteristic
3C2×#14582768C211yesmaximal, characteristic, complemented
4C2×#14582757C211yesmaximal, characteristic
5C2×#14582757C211yesmaximal, characteristic
6C2×#14582750C211yesmaximal, characteristic, complemented
7C2×C22⋊C4×Dic43C211yesmaximal, characteristic
8#19132853C211yesmaximal, characteristic, complemented
9#19132850C211yesmaximal, characteristic, complemented
10#19132840C211yesmaximal, characteristic
11#19132829C211yesmaximal, characteristic, complemented
12#19132827C211yesmaximal, characteristic, complemented
13Dic43⋊#95C211yesmaximal, characteristic, complemented
14Dic43⋊#95C211yesmaximal, characteristic, complemented
15C43×#1439C211yesmaximal, characteristic
16C24×Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2211yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×Dic43⋊C4C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C22×C4×Dic43C2211yescharacteristic
31#14582793—24no—
32#14582787—24no—
33#14582768—24no—
34#14582757—24no—
35#14582757—24no—
36#14582750—24no—
37C22⋊C4×Dic43C418yescomplemented
38C2×C43⋊#95C2211yescharacteristic
39C2×C43⋊#95C2211yescharacteristic
40C2×C43⋊#95C2211yescharacteristic
41C2×C43⋊#95C2211yescharacteristic
42C2×C43⋊#95C2211yescharacteristic
43C2×C43⋊#95C2211yescharacteristic
44C2×C43⋊#95C2211yescharacteristic
45C2×C43⋊#95C2211yescharacteristic
46C2×C43⋊#95C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C2×C43⋊#95C2211yescharacteristic
51C22×C4⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C22⋊C4×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—22no—
61C23×Dic43—22no—
62C23×Dic43—22no—
63C23×Dic43—22no—
64C23×Dic43C2×C414yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—22no—
75C2×C4⋊Dic43—41no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4—22no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—22no—
83C2×Dic43⋊C4—22no—
84C2×Dic43⋊C4—22no—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—41no—
91C2×Dic43⋊C4—41no—
92C2×Dic43⋊C4D414yes—
93C2×Dic43⋊C4D414yes—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43—41no—
100C2×C22⋊Dic43C2×C414yes—
101C2×C22⋊Dic43D414yes—
102C2×C22⋊Dic43Q814yes—
103C2×C4×Dic43—22no—
104C2×C4×Dic43—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—22no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—41no—
112C2×C4×Dic43—41no—
113C2×C4×Dic43C2×C414yes—
114C2×C4×Dic43C2×C414yes—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—41no—
126C43⋊#95C2×C414yes—
127C43⋊#95C2×C414yes—
128C25×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—41no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43—22no—
142C2×C22⋊C4×C43—22no—
143C2×C22⋊C4×C43—22no—
144C2×C22⋊C4×C43—41no—
145C2×C22⋊C4×C43—41no—
146C2×C22⋊C4×C43C2×C414yes—
147#95×C43—22no—
148#95×C43—22no—
149#95×C43—41no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43C22×C412yes—
163C24×C43C2×D412yes—
164C24×C43C2×Q812yes—
165C24×C43C2411yescharacteristic
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
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—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43C22×C412yes—
203C22×C4×C43C22×C412yes—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2×D412yes—
206C22×C4×C43#4112yes—
207C22×C4×C43#4112yes—
208C22×Dic43—28no—
209C22×Dic43—28no—
210C22×Dic43—28no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
232C22×Dic43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—44no—
252C22×Dic43—44no—
253C22×Dic43—44no—
254C22×Dic43—44no—
255C22×Dic43C22×C412yes—
256C22×Dic43C22×C412yes—
257C22×Dic43C22×C412yes—
258C22×Dic43C22×C412yes—
259C22×Dic43C2×D412yes—
260C22×Dic43C2×D412yes—
261C22×Dic43C2×D412yes—
262C22×Dic43C2×D412yes—
263C22×Dic43C2×D412yes—
264C22×Dic43C2×D412yes—
265C22×Dic43C2×Q812yes—
266C22×Dic43C2×Q812yes—
267C22×Dic43#4112yes—
268C22×Dic43#4112yes—
269C22×Dic43#4112yes—
270C22×Dic43#4112yes—
271C4⋊C4×C43—44no—
272C22⋊C4×C43—28no—
273C22⋊C4×C43—44no—
274C22⋊C4×C43—44no—
275C22⋊Dic43—44no—
276C22⋊Dic43—44no—
277C22⋊Dic43C4⋊C4116yescomplemented
278C4⋊Dic43—44no—
279Dic43⋊C4—28no—
280Dic43⋊C4—28no—
281Dic43⋊C4—44no—
282Dic43⋊C4—44no—
283Dic43⋊C4—44no—
284Dic43⋊C4—44no—
285C4×Dic43—28no—
286C4×Dic43—28no—
287C4×Dic43—44no—
288C4×Dic43—44no—
289C23×C43—22no—
290C23×C43—22no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43—22no—
300C23×C43—22no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43—41no—
311C23×C43—41no—
312C23×C43—41no—
313C23×C43—41no—
314C23×C43—41no—
315C23×C43—41no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43—41no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43C2×C4⋊C414yes—
324C23×C43C23×C411yescharacteristic
325C23×C43C22×D411yescharacteristic
326C23×C43C22×D411yescharacteristic
327C23×C43C22×D411yescharacteristic
328C23×C43C22×Q811yescharacteristic
329C23×C43C2×#4111yescharacteristic
330C23×C43C2×#4111yescharacteristic
331C23×C43C2×#4111yescharacteristic
332C23×C43C2×#4111yescharacteristic
333C23×C43C2×#4111yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43H(5,𝔽2)11yescharacteristic
336C23×C43H(5,𝔽2)11yescharacteristic
337C23×C432−1+411yescharacteristic
338C23×C432−1+411yescharacteristic
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
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—22no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43#11714yes—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—416no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43C2×C4⋊C414yes—
430C2×Dic43C2×C4⋊C414yes—
431C2×Dic43#11714yes—
432C2×Dic43C4×D414yes—
433C2×Dic43C4×D414yes—
434C2×Dic43#12114yes—
435C2×Dic43#12314yes—
436C2×Dic43#12414yes—
437C2×Dic43#12614yes—
438#13876—431nomaximal, Sylow
439C22×C43—24no—
440C22×C43—24no—
441C22×C43—24no—
442C22×C43—42no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43—42no—
447C22×C43—42no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43C22×C4⋊C411yescharacteristic
455C22×C43C2×#11711yescharacteristic
456C22×C43C2×#11711yescharacteristic
457C22×C43C2×C4×D411yescharacteristic
458C22×C43C2×C4×D411yescharacteristic
459C22×C43#52011yescharacteristic
460C22×C43#52011yescharacteristic
461C22×C43C2×#12111yescharacteristic
462C22×C43C2×#12311yescharacteristic
463C22×C43C2×#12411yescharacteristic
464C22×C43C2×#12611yescharacteristic
465C22×C43#53211yescharacteristic
466C22×C43#53211yescharacteristic
467C22×C43#53311yescharacteristic
468C22×C43#53311yescharacteristic
469C22×C43#54011yescharacteristic
470C22×C43#54111yescharacteristic
471C22×C43#54211yescharacteristic
472C22×C43#54211yescharacteristic
473C22×C43D4211yescharacteristic
474C22×C43D4211yescharacteristic
475C22×C43#54611yescharacteristic
476C22×C43#54711yescharacteristic
477C22×C43#54711yescharacteristic
478C22×C43#54711yescharacteristic
479C22×C43#54811yescharacteristic
480C22×C43D4×Q811yescharacteristic
481C22×C43D4×Q811yescharacteristic
482C22×C43#55011yescharacteristic
483C22×C43#55211yescharacteristic
484C22×C43#55311yescharacteristic
485C22×C43#55411yescharacteristic
486C22×C43#55411yescharacteristic
487C22×C43#55511yescharacteristic
488C22×C43#55611yescharacteristic
489C4×C43—24no—
490C4×C43—42no—
491C4×C43—42no—
492C4×C43—42no—
493C4×C43—81no—
494C4×C43—81no—
495Dic43—24no—
496Dic43—24no—
497Dic43—42no—
498Dic43—42no—
499Dic43—42no—
500Dic43—81no—
501Dic43—81no—
502Dic43#38818yescomplemented
503C2×#388—431no—
504C2×#388—431no—
505C2×#384—431no—
506C2×#380—431no—
507C2×#380—431no—
508C2×C4×C4⋊C4—431no—
509C2×C4×C22⋊C4—431no—
510#1442—431no—
511#1442—431no—
512#1439—431no—
513#1439D4311yescharacteristic
514#1436—431no—
515#1436—431no—
516C4⋊#95—431no—
517C4⋊#95—431no—
518C2×C43—44no—
519C2×C43#228511yescharacteristic
520C2×C43C2×#38811yescharacteristic
521C2×C43#231411yescharacteristic
522C2×C43D4×C4⋊C411yescharacteristic
523C2×C43D4×C4⋊C411yescharacteristic
524C2×C43#235211yescharacteristic
525C2×C43#235411yescharacteristic
526C2×C43#242211yescharacteristic
527C2×C43#242311yescharacteristic
528C2×C43#242811yescharacteristic
529C2×C43#242911yescharacteristic
530C2×C43#249111yescharacteristic
531C2×C43#249211yescharacteristic
532C2×C43#249611yescharacteristic
533C2×C43#249711yescharacteristic
534C24×C4—431no—
535C22×C4⋊C4—431no—
536C22×C4⋊C4—431no—
537C22×C4⋊C4—431no—
538C22×C4⋊C4—431no—
539C22×C4⋊C4—431no—
540C22×C4⋊C4—431no—
541C22×C4⋊C4—431no—
542C22×C4⋊C4C2×D4311yescharacteristic
543C22×C22⋊C4—431no—
544C22×C22⋊C4—431no—
545C22×C22⋊C4—431no—
546C22×C22⋊C4C2×D4311yescharacteristic
547C22×C22⋊C4C2×D4311yescharacteristic
548C22×C22⋊C4C2×D4311yescharacteristic
549C22×C42—431no—
550C22×C42—431no—
551C22×C42—431no—
552C22×C42—431no—
553#388—864no—
554#388—864no—
555#384—864no—
556#380—864no—
557#380—864no—
558C4×C4⋊C4—864no—
559C4×C22⋊C4—438no—
560C2×#95—431no—
561C2×#95—431no—
562C2×#95—431no—
563C2×#95—431no—
564C2×#95—431no—
565C2×#95—431no—
566C2×#95—431no—
567C2×#95—431no—
568C2×#95—431no—
569C2×#95—431no—
570C2×#95—431no—
571C2×#95—431no—
572C2×#95—431no—
573C2×#95C2×D4311yescharacteristic
574C2×#95C2×D4311yescharacteristic
575C2×#95C2×D4311yescharacteristic
576C43#1387611yescharacteristic, complemented, Sylow
577C25C22×D4311yescharacteristic
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—431no—
581C23×C4—434no—
582C23×C4—431no—
583C23×C4—431no—
584C23×C4—431no—
585C23×C4—431no—
586C23×C4—431no—
587C23×C4—862no—
588C23×C4—862no—
589C23×C4—862no—
590C23×C4—862no—
591C23×C4—862no—
592C23×C4—862no—
593C23×C4C22×D4311yescharacteristic
594C23×C4C22×D4311yescharacteristic
595C23×C4C22×D4311yescharacteristic
596C23×C4C22×D4311yescharacteristic
597C23×C4C22×D4311yescharacteristic
598C23×C4C22×D4311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—434no—
603C2×C4⋊C4—434no—
604C2×C4⋊C4—862no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4—862no—
608C2×C4⋊C4—862no—
609C2×C4⋊C4—862no—
610C2×C4⋊C4—862no—
611C2×C4⋊C4—862no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—862no—
614C2×C4⋊C4—862no—
615C2×C4⋊C4—862no—
616C2×C4⋊C4—862no—
617C2×C4⋊C4—862no—
618C2×C4⋊C4—862no—
619C2×C4⋊C4—862no—
620C2×C4⋊C4—1721no—
621C2×C4⋊C4—1721no—
622C2×C4⋊C4—1721no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4—434no—
632C2×C22⋊C4—434no—
633C2×C22⋊C4—434no—
634C2×C22⋊C4—862no—
635C2×C22⋊C4—862no—
636C2×C22⋊C4—862no—
637C2×C22⋊C4—862no—
638C2×C22⋊C4—1721no—
639C2×C22⋊C4—1721no—
640C2×C22⋊C4C4×D4314yes—
641C2×C42—434no—
642C2×C42—434no—
643C2×C42—862no—
644C2×C42—862no—
645C2×C42—862no—
646C2×C42—862no—
647C2×C42—862no—
648C2×C42—862no—
649C2×C42—862no—
650C2×C42—862no—
651C2×C42—1721no—
652C2×C42—1721no—
653#95—22no—
654#95—22no—
655#95—41no—
656#95—434no—
657#95—434no—
658#95—862no—
659#95—862no—
660#95—862no—
661#95—862no—
662#95—862no—
663#95—862no—
664#95—862no—
665#95—862no—
666#95—862no—
667#95—862no—
668#95—1721no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D4312yes—
682C24D4×D4312yes—
683C24Q8×D4312yes—
684C24C23×D4311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—432no—
722C22×C4—432no—
723C22×C4—432no—
724C22×C4—432no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4—432no—
728C22×C4—432no—
729C22×C4—432no—
730C22×C4—432no—
731C22×C4—432no—
732C22×C4—432no—
733C22×C4—432no—
734C22×C4—432no—
735C22×C4—432no—
736C22×C4—432no—
737C22×C4—868no—
738C22×C4—868no—
739C22×C4—868no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—1724no—
781C22×C4—1724no—
782C22×C4—1724no—
783C22×C4—1724no—
784C22×C4C2×C4×D4312yes—
785C22×C4C2×C4×D4312yes—
786C22×C4D4×D4312yes—
787C22×C4D4×D4312yes—
788C22×C4#1062190012yes—
789C22×C4#1062190012yes—
790C4⋊C4—44no—
791C4⋊C4—868no—
792C4⋊C4—868no—
793C4⋊C4—1724no—
794C4⋊C4—1724no—
795C4⋊C4—1724no—
796C4⋊C4—1724no—
797C4⋊C4—1724no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—4316no—
802C22⋊C4—1724no—
803C22⋊C4—1724no—
804C42—868no—
805C42—868no—
806C42—1724no—
807C42—1724no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C4⋊C4×D4314yes—
843C23C22×C4×D4311yescharacteristic
844C23C2×D4×D4311yescharacteristic
845C23C2×D4×D4311yescharacteristic
846C23C2×D4×D4311yescharacteristic
847C23C2×Q8×D4311yescharacteristic
848C23#41×D4311yescharacteristic
849C23#41×D4311yescharacteristic
850C23#41×D4311yescharacteristic
851C23#41×D4311yescharacteristic
852C23C2×#1062190011yescharacteristic
853C23C2×#1062190011yescharacteristic
854C23#1306337011yescharacteristic
855C23#1306337011yescharacteristic
856C23#1306337211yescharacteristic
857C23#1306337211yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—434no—
900C2×C4—434no—
901C2×C4—434no—
902C2×C4—434no—
903C2×C4—434no—
904C2×C4—434no—
905C2×C4—434no—
906C2×C4—434no—
907C2×C4—434no—
908C2×C4—862no—
909C2×C4—862no—
910C2×C4—862no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—862no—
914C2×C4—862no—
915C2×C4—862no—
916C2×C4—862no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—17216no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1721no—
941C2×C4—1721no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1721no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4—1721no—
953C2×C4—1721no—
954C2×C4—1721no—
955C2×C4—1721no—
956C2×C4#1306328114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C4⋊C4×D4311yescharacteristic
973C22#117×D4311yescharacteristic
974C22C2×#1306328111yescharacteristic
975C22C4×D4×D4311yescharacteristic
976C22C4×D4×D4311yescharacteristic
977C22#1458337811yescharacteristic
978C22#1458337811yescharacteristic
979C22#121×D4311yescharacteristic
980C22#123×D4311yescharacteristic
981C22#124×D4311yescharacteristic
982C22#126×D4311yescharacteristic
983C22#1458344411yescharacteristic
984C22#1458344411yescharacteristic
985C22#1458345111yescharacteristic
986C22#1458345111yescharacteristic
987C22#1458349911yescharacteristic
988C22#1458350611yescharacteristic
989C22#1458351311yescharacteristic
990C22#1458351711yescharacteristic
991C22#1458353111yescharacteristic
992C22#1458353111yescharacteristic
993C22#1458353611yescharacteristic
994C22#1458354711yescharacteristic
995C22#1458354711yescharacteristic
996C22#1458354911yescharacteristic
997C22#1458355511yescharacteristic
998C22#1458356211yescharacteristic
999C22#1458356211yescharacteristic
1000C22#1458356911yescharacteristic
1001C22#1458358611yescharacteristic
1002C22#1458359211yescharacteristic
1003C22#1458360311yescharacteristic
1004C22#1458360311yescharacteristic
1005C22#1458361311yescharacteristic
1006C22#1458361811yescharacteristic
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—438no—
1014C4—864no—
1015C4—864no—
1016C4—3441no—
1017C4—3441no—
1018C4—1722no—
1019C4—1722no—
1020C4—1722no—
1021C2—44no—
1022C2#1913699711yescharacteristic
1023C2#388×D4311yescharacteristic
1024C2#1913719911yescharacteristic
1025C2#1913749311yescharacteristic
1026C2#1913749311yescharacteristic
1027C2#1913752211yescharacteristic
1028C2#1913754311yescharacteristic
1029C2#1913810211yescharacteristic
1030C2#1913811311yescharacteristic
1031C2#1913817611yescharacteristic
1032C2#1913818711yescharacteristic
1033C2#1913895111yescharacteristic
1034C2#1913896211yescharacteristic
1035C2#1913901011yescharacteristic
1036C2#1913902111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#13876
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
3. C2×#14582768C2semidirect
6. C2×#14582750C2semidirect
8. #19132853C2semidirect
9. #19132850C2semidirect
11. #19132829C2semidirect
12. #19132827C2semidirect
13. Dic43⋊#95C2semidirect
14. Dic43⋊#95C2semidirect
37. C22⋊C4×Dic43C4semidirect
277. C22⋊Dic43C4⋊C4semidirect
502. Dic43#388semidirect
576. C43#13876semidirect

Maximal subgroups

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

subgroupindex
C2×#145827932
C2×#145827872
C2×#145827682
C2×#145827572
C2×#145827502
C2×C22⋊C4×Dic432
#191328532
#191328502
#191328402
#191328292
#191328272
Dic43⋊#952
C43×#14392
#1387643