Finite Group Databasebeta

← #25023949

Subgroups — #25023949

Order 11008.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063302C211yesmaximal, characteristic
2C2×#14582805C211yesmaximal, characteristic, complemented
3C2×#14582796C211yesmaximal, characteristic, complemented
4C2×#14582783C211yesmaximal, characteristic, complemented
5C2×#14582757C211yesmaximal, characteristic
6#19132865C211yesmaximal, characteristic, complemented
7#19132847C211yesmaximal, characteristic, complemented
8#19132847C211yesmaximal, characteristic, complemented
9#19132846C211yesmaximal, characteristic, complemented
10#19132840C211yesmaximal, characteristic
11#19132838C211yesmaximal, characteristic
12#19132832C211yesmaximal, characteristic
13#19132826C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic
15C43×#1437C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C2×#13063302—24no—
19C2×#13063302—24no—
20C2×#13063302C418yescomplemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14582805—24no—
33#14582796—24no—
34#14582783—24no—
35#14582757—24no—
36C2×C43⋊#95C2211yescharacteristic
37C2×C43⋊#95C2211yescharacteristic
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×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C22×Dic86—22no—
59C22×Dic86—22no—
60C22×Dic86—22no—
61C22×Dic86—22no—
62C22×Dic86—41no—
63C22×Dic86—41no—
64C22×Dic86C2×C414yes—
65C23×Dic43—22no—
66C23×Dic43—22no—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—41no—
70C23×Dic43—41no—
71C23×Dic43C2×C414yes—
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80#13063302—232no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—41no—
86C2×C4⋊Dic43C2×C414yes—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—41no—
95C2×Dic43⋊C4—41no—
96C2×Dic43⋊C4—41no—
97C2×Dic43⋊C4—41no—
98C2×Dic43⋊C4C2×C414yes—
99C2×Dic43⋊C4C2×C414yes—
100C2×Dic43⋊C4D414yes—
101C2×Dic43⋊C4D414yes—
102C2×C22⋊Dic43—22no—
103C2×C22⋊Dic43—22no—
104C2×C22⋊Dic43—22no—
105C2×C22⋊Dic43—22no—
106C2×C22⋊Dic43—22no—
107C2×C22⋊Dic43—41no—
108C2×C22⋊Dic43—41no—
109C2×C22⋊Dic43—41no—
110C2×C22⋊Dic43C2×C414yes—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—41no—
113C2×C4×Dic43—41no—
114C43⋊#95—22no—
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—41no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C43⋊#95—41no—
128C43⋊#95D414yes—
129C25×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—41no—
141C2×C22⋊C4×C43—41no—
142C2×C22⋊C4×C43—41no—
143C2×C22⋊C4×C43C2×C414yes—
144C2×C22⋊C4×C43Q814yescomplemented
145C2×C42×C43—22no—
146C2×C42×C43—22no—
147C2×C42×C43—41no—
148#95×C43—22no—
149#95×C43—41no—
150#95×C43—41no—
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×C43—21no—
163C24×C43C22×C412yes—
164C24×C43C2×Q812yes—
165C24×C43#4112yes—
166C24×C43C2411yescharacteristic
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×C43C2×D412yes—
207C22×C4×C43C2×Q812yes—
208C22×C4×C43C2×Q812yes—
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—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—44no—
257C22×Dic43—44no—
258C22×Dic43—44no—
259C22×Dic43—44no—
260C22×Dic43—44no—
261C22×Dic43C22×C412yes—
262C22×Dic43C22×C412yes—
263C22×Dic43C22×C412yes—
264C22×Dic43C22×C412yes—
265C22×Dic43C2×D412yes—
266C22×Dic43C2×D412yes—
267C22×Dic43C2×D412yes—
268C22×Dic43C2×D412yes—
269C22×Dic43C2×D412yes—
270C22×Dic43C2×D412yes—
271C22×Dic43#4112yes—
272C2×Dic86—28no—
273C2×Dic86—28no—
274C2×Dic86—44no—
275C2×Dic86—44no—
276C2×Dic86—44no—
277C2×Dic86—44no—
278C2×Dic86—44no—
279C22⋊C4×C43—28no—
280C22⋊C4×C43—44no—
281C22⋊C4×C43—44no—
282C42×C43—44no—
283C22⋊Dic43—28no—
284C22⋊Dic43—44no—
285C22⋊Dic43—44no—
286C4⋊Dic43—28no—
287C4⋊Dic43—44no—
288Dic43⋊C4—28no—
289Dic43⋊C4—44no—
290Dic43⋊C4—44no—
291Dic43⋊C4—44no—
292Dic43⋊C4C22⋊C4116yescomplemented
293C4×Dic43—44no—
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—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
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×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43C4×Q814yes—
329C23×C43C23×C411yescharacteristic
330C23×C43C22×D411yescharacteristic
331C23×C43C22×D411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C23×C43C22×Q811yescharacteristic
334C23×C43C2×#4111yescharacteristic
335C23×C43C2×#4111yescharacteristic
336C23×C43H(5,𝔽2)11yescharacteristic
337C23×C43H(5,𝔽2)11yescharacteristic
338C23×C43H(5,𝔽2)11yescharacteristic
339C23×C43H(5,𝔽2)11yescharacteristic
340C23×C432−1+411yescharacteristic
341C23×C432−1+411yescharacteristic
342C23×C432−1+411yescharacteristic
343C23×C432−1+411yescharacteristic
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—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
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—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43C2×C22⋊C414yes—
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—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—416no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
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×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43C2×C22⋊C414yes—
441C2×Dic43C2×C22⋊C414yes—
442C2×Dic43C4×D414yes—
443Dic86—416no—
444#14362—431nomaximal, Sylow
445C22×C43—24no—
446C22×C43—24no—
447C22×C43—24no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43—42no—
455C22×C43—42no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—42no—
459C22×C43—42no—
460C22×C43C22×C22⋊C411yescharacteristic
461C22×C43C2×C4×D411yescharacteristic
462C22×C43C2×C4×Q811yescharacteristic
463C22×C43#51811yescharacteristic
464C22×C43#51911yescharacteristic
465C22×C43#52011yescharacteristic
466C22×C43#52011yescharacteristic
467C22×C43#53511yescharacteristic
468C22×C43#53611yescharacteristic
469C22×C43#53611yescharacteristic
470C22×C43#53711yescharacteristic
471C22×C43#53711yescharacteristic
472C22×C43#53711yescharacteristic
473C22×C43#53811yescharacteristic
474C22×C43#53911yescharacteristic
475C22×C43#54111yescharacteristic
476C22×C43#54211yescharacteristic
477C22×C43#54311yescharacteristic
478C22×C43#54411yescharacteristic
479C22×C43D4211yescharacteristic
480C22×C43D4211yescharacteristic
481C22×C43#54611yescharacteristic
482C22×C43#54611yescharacteristic
483C22×C43#54611yescharacteristic
484C22×C43#54811yescharacteristic
485C22×C43#54811yescharacteristic
486C22×C43D4×Q811yescharacteristic
487C22×C43D4×Q811yescharacteristic
488C22×C43D4×Q811yescharacteristic
489C22×C43#55211yescharacteristic
490C22×C43#55411yescharacteristic
491C22×C43#56211yescharacteristic
492C22×C43#56211yescharacteristic
493C22×C43#56311yescharacteristic
494C22×C43#56311yescharacteristic
495C4×C43—24no—
496C4×C43—42no—
497C4×C43—42no—
498C4×C43—42no—
499C4×C43—42no—
500C4×C43—81no—
501Dic43—24no—
502Dic43—24no—
503Dic43—24no—
504Dic43—42no—
505Dic43—42no—
506Dic43—81no—
507Dic43—81no—
508Dic43—81no—
509C22×C22⋊Q8—431no—
510C2×#391—431no—
511C2×#389—431no—
512C2×#387—431no—
513C2×#380—431no—
514#1446—431no—
515#1441—431no—
516#1441—431no—
517#1441—431no—
518#1439—431no—
519#1439—431no—
520#1437—431no—
521#1437D4311yescharacteristic
522#1436—431no—
523C22⋊#95—431no—
524C2×C43—44no—
525C2×C43#231111yescharacteristic
526C2×C43#232311yescharacteristic
527C2×C43#232911yescharacteristic
528C2×C43D4×C22⋊C411yescharacteristic
529C2×C43Q8×C22⋊C411yescharacteristic
530C2×C43#236011yescharacteristic
531C2×C43#237811yescharacteristic
532C2×C43#267611yescharacteristic
533C2×C43#267711yescharacteristic
534C2×C43#268111yescharacteristic
535C2×C43#268311yescharacteristic
536C2×C43#269011yescharacteristic
537C2×C43#269211yescharacteristic
538C2×C43#270211yescharacteristic
539C2×C43#270411yescharacteristic
540C23×Q8—431no—
541C24×C4—431no—
542C2×C22⋊Q8—438no—
543C2×C22⋊Q8—864no—
544C2×C22⋊Q8—864no—
545C22×C4⋊C4—431no—
546C22×C4⋊C4—431no—
547C22×C4⋊C4—431no—
548C22×C4⋊C4—431no—
549C22×C4⋊C4—431no—
550C22×C4⋊C4—431no—
551C22×C4⋊C4—431no—
552C22×C22⋊C4—431no—
553C22×C22⋊C4—431no—
554C22×C22⋊C4—431no—
555C22×C22⋊C4C2×D4311yescharacteristic
556C22×C22⋊C4C2×D4311yescharacteristic
557C22×C22⋊C4C2×D4311yescharacteristic
558C22×C42—431no—
559C22×C42C2×D4311yescharacteristic
560#391—864no—
561#389—864no—
562#387—864no—
563#380—864no—
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×#95—431no—
574C2×#95—431no—
575C2×#95—431no—
576C2×#95—431no—
577C2×#95—431no—
578C2×#95—431no—
579C2×#95C2×D4311yescharacteristic
580C2×#95C2×D4311yescharacteristic
581C2×#95C2×D4311yescharacteristic
582C43#1436211yescharacteristic, complemented, Sylow
583C25C22×D4311yescharacteristic
584C22×Q8—434no—
585C22×Q8—862no—
586C22×Q8—862no—
587C22×Q8—862no—
588C22×Q8—862no—
589C22×Q8—1721no—
590C22×Q8—1721no—
591C23×C4—431no—
592C23×C4—431no—
593C23×C4—431no—
594C23×C4—431no—
595C23×C4—431no—
596C23×C4—434no—
597C23×C4—431no—
598C23×C4—431no—
599C23×C4—431no—
600C23×C4—862no—
601C23×C4—862no—
602C23×C4—862no—
603C23×C4—862no—
604C23×C4—1721no—
605C23×C4—1721no—
606C23×C4C22×D4311yescharacteristic
607C23×C4C22×D4311yescharacteristic
608C23×C4C22×D4311yescharacteristic
609C23×C4C22×D4311yescharacteristic
610C23×C4C22×D4311yescharacteristic
611C23×C4C22×D4311yescharacteristic
612C22⋊Q8—8632no—
613C2×C4⋊C4—434no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—434no—
616C2×C4⋊C4—434no—
617C2×C4⋊C4—434no—
618C2×C4⋊C4—862no—
619C2×C4⋊C4—862no—
620C2×C4⋊C4—862no—
621C2×C4⋊C4—862no—
622C2×C4⋊C4—862no—
623C2×C4⋊C4—862no—
624C2×C4⋊C4—862no—
625C2×C4⋊C4—862no—
626C2×C4⋊C4—862no—
627C2×C4⋊C4—862no—
628C2×C4⋊C4—862no—
629C2×C4⋊C4—1721no—
630C2×C4⋊C4—1721no—
631C2×C4⋊C4—1721no—
632C2×C4⋊C4—1721no—
633C2×C4⋊C4—1721no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—434no—
642C2×C22⋊C4—862no—
643C2×C22⋊C4—862no—
644C2×C22⋊C4—862no—
645C2×C22⋊C4—862no—
646C2×C22⋊C4—862no—
647C2×C22⋊C4—1721no—
648C2×C22⋊C4—1721no—
649C2×C22⋊C4—1721no—
650C2×C22⋊C4Dic8614yescomplemented
651C2×C22⋊C4C4×D4314yes—
652C2×C42—22no—
653C2×C42—22no—
654C2×C42—41no—
655C2×C42—862no—
656C2×C42—1721no—
657C2×C42—1721no—
658#95—22no—
659#95—41no—
660#95—41no—
661#95—434no—
662#95—862no—
663#95—862no—
664#95—862no—
665#95—862no—
666#95—862no—
667#95—862no—
668#95—862no—
669#95—862no—
670#95—862no—
671#95—862no—
672#95—1721no—
673#95—1721no—
674#95—1721no—
675#95—1721no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24C2×Dic8612yes—
689C24C2×C4×D4312yes—
690C24#1062189812yes—
691C24C23×D4311yescharacteristic
692C2×Q8—868no—
693C2×Q8—868no—
694C2×Q8—1724no—
695C2×Q8—1724no—
696C2×Q8—1724no—
697C2×Q8—1724no—
698C2×Q8—1724no—
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—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—432no—
735C22×C4—432no—
736C22×C4—432no—
737C22×C4—432no—
738C22×C4—432no—
739C22×C4—432no—
740C22×C4—432no—
741C22×C4—432no—
742C22×C4—432no—
743C22×C4—432no—
744C22×C4—432no—
745C22×C4—868no—
746C22×C4—868no—
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—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—861no—
786C22×C4—861no—
787C22×C4—861no—
788C22×C4—861no—
789C22×C4—861no—
790C22×C4—861no—
791C22×C4—861no—
792C22×C4—1724no—
793C22×C4—1724no—
794C22×C4—1724no—
795C22×C4—1724no—
796C22×C4—1724no—
797C22×C4C2×Dic8612yes—
798C22×C4C2×Dic8612yes—
799C22×C4C2×C4×D4312yes—
800C22×C4C2×C4×D4312yes—
801C22×C4D4×D4312yes—
802C22×C4D4×D4312yes—
803C22×C4D4×D4312yes—
804C4⋊C4—4316no—
805C4⋊C4—868no—
806C4⋊C4—868no—
807C4⋊C4—1724no—
808C4⋊C4—1724no—
809C4⋊C4—1724no—
810C4⋊C4—1724no—
811C22⋊C4—28no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—868no—
815C22⋊C4—1724no—
816C22⋊C4—1724no—
817C42—44no—
818C42—1724no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23C4×Dic8614yes—
854C23C22×C4×D4311yescharacteristic
855C23C2×D4×D4311yescharacteristic
856C23C2×D4×D4311yescharacteristic
857C23C2×D4×D4311yescharacteristic
858C23C22×Dic8611yescharacteristic
859C23#41×D4311yescharacteristic
860C23C2×#1062189811yescharacteristic
861C23#1306337011yescharacteristic
862C23#1306337011yescharacteristic
863C23#1306337011yescharacteristic
864C23#1306337111yescharacteristic
865C23#1306337211yescharacteristic
866C23#1306337211yescharacteristic
867C23#1306337211yescharacteristic
868C23#1306337211yescharacteristic
869Q8—17216no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
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—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—434no—
912C2×C4—434no—
913C2×C4—434no—
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—862no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—862no—
937C2×C4—862no—
938C2×C4—17216no—
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—1721no—
957C2×C4—1721no—
958C2×C4—1721no—
959C2×C4—1721no—
960C2×C4—1721no—
961C2×C4—1721no—
962C2×C4—1721no—
963C2×C4—1721no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4—1721no—
967C2×C4—1721no—
968C2×C4C22⋊C4×D4314yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×C22⋊C4×D4311yescharacteristic
985C22C4×D4×D4311yescharacteristic
986C22C2×C4×Dic8611yescharacteristic
987C22#1458337111yescharacteristic
988C22#1458337611yescharacteristic
989C22#1458337811yescharacteristic
990C22#1458337811yescharacteristic
991C22#1458346211yescharacteristic
992C22#1458346911yescharacteristic
993C22#1458347111yescharacteristic
994C22#1458347811yescharacteristic
995C22#1458347811yescharacteristic
996C22#1458347811yescharacteristic
997C22#1458348211yescharacteristic
998C22#1458349111yescharacteristic
999C22#1458350611yescharacteristic
1000C22#1458351311yescharacteristic
1001C22#1458352511yescharacteristic
1002C22#1458352711yescharacteristic
1003C22#1458353111yescharacteristic
1004C22#1458353311yescharacteristic
1005C22#1458353811yescharacteristic
1006C22#1458353911yescharacteristic
1007C22#1458354111yescharacteristic
1008C22#1458355811yescharacteristic
1009C22#1458355811yescharacteristic
1010C22D4×Dic8611yescharacteristic
1011C22D4×Dic8611yescharacteristic
1012C22D4×Dic8611yescharacteristic
1013C22#1458358211yescharacteristic
1014C22#1458360811yescharacteristic
1015C22#1458364311yescharacteristic
1016C22#1458364411yescharacteristic
1017C22#1458365111yescharacteristic
1018C22#1458365211yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—864no—
1026C4—864no—
1027C4—864no—
1028C4—3441no—
1029C4—3441no—
1030C4—3441no—
1031C4—1722no—
1032C4—1722no—
1033C2—44no—
1034C2#1913718511yescharacteristic
1035C2#1913727411yescharacteristic
1036C2#1913732311yescharacteristic
1037C2#1913741311yescharacteristic
1038C2C22⋊C4×Dic8611yescharacteristic
1039C2#1913760111yescharacteristic
1040C2#1913776211yescharacteristic
1041C2#1914089311yescharacteristic
1042C2#1914090711yescharacteristic
1043C2#1914095111yescharacteristic
1044C2#1914096811yescharacteristic
1045C2#1914105811yescharacteristic
1046C2#1914108811yescharacteristic
1047C2#1914122411yescharacteristic
1048C2#1914125411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1437D43
hypocenterC43#14362
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#14582805C2semidirect
3. C2×#14582796C2semidirect
4. C2×#14582783C2semidirect
6. #19132865C2semidirect
7. #19132847C2semidirect
8. #19132847C2semidirect
9. #19132846C2semidirect
13. #19132826C2semidirect
20. C2×#13063302C4semidirect
144. C2×C22⋊C4×C43Q8semidirect
292. Dic43⋊C4C22⋊C4semidirect
582. C43#14362semidirect
650. C2×C22⋊C4Dic86semidirect

Maximal subgroups

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

subgroupindex
C22×#130633022
C2×#145828052
C2×#145827962
C2×#145827832
C2×#145827572
#191328652
#191328472
#191328462
#191328402
#191328382
#191328322
#191328262
#191328172
C43×#14372
#1436243