Finite Group Databasebeta

← #25025773

Subgroups — #25025773

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063309C211yesmaximal, characteristic
2C2×#14582792C211yesmaximal, characteristic, complemented
3#19132864C211yesmaximal, characteristic, complemented
4#19132862C211yesmaximal, characteristic, complemented
5#19132841C211yesmaximal, characteristic, complemented
6#19132837C211yesmaximal, characteristic, complemented
7#19132834C211yesmaximal, characteristic
8#19132834C211yesmaximal, characteristic
9#19132833C211yesmaximal, characteristic, complemented
10#19132831C211yesmaximal, characteristic, complemented
11#19132825C211yesmaximal, characteristic, complemented
12#19132824C211yesmaximal, characteristic, complemented
13#19132817C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C2×#13063309—24no—
19C2×#13063309—24no—
20C2×#13063309C418yescomplemented
21C22×C4⋊Dic43C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582792—24no—
34C2×C43⋊#95C2211yescharacteristic
35C2×C43⋊#95C2211yescharacteristic
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
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C22⋊C4×C43C2211yescharacteristic
50C22×C22⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C43×#388—24no—
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C22×C22⋊D43—22no—
58C22×C22⋊D43—22no—
59C22×C22⋊D43—41no—
60C22×C22⋊D43—41no—
61C22×C22⋊D43—41no—
62C22×C22⋊D43—41no—
63C22×C22⋊D43C2×C414yes—
64C23×Dic43—22no—
65C23×Dic43—22no—
66C23×Dic43—41no—
67C23×Dic43—41no—
68C23×Dic43—41no—
69C23×Dic43—41no—
70C23×Dic43C2×C414yes—
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78#13063309—232no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—22no—
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×C4⋊Dic43C2×C414yes—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43—22no—
90C2×C22⋊Dic43—22no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—41no—
93C2×C22⋊Dic43—41no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—41no—
103C2×(C2×D43)⋊C4—41no—
104C2×(C2×D43)⋊C4—41no—
105C2×(C2×D43)⋊C4—41no—
106C2×(C2×D43)⋊C4—41no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4C2×C414yes—
111C2×(C2×D43)⋊C4C2×C414yes—
112C2×C4×Dic43—22no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—41no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—41no—
118C43⋊#95—41no—
119C43⋊#95—41no—
120C43⋊#95—41no—
121C43⋊#95—41no—
122C43⋊#95—41no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C43⋊#95—41no—
128C43⋊#95—41no—
129C25×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43—22no—
138C2×C4⋊C4×C43—41no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43—22no—
142C2×C22⋊C4×C43—22no—
143C2×C22⋊C4×C43—41no—
144C2×C22⋊C4×C43—41no—
145C2×C22⋊C4×C43C2×C414yes—
146C2×C22⋊C4×C43D414yes—
147C2×C22⋊C4×C43D414yes—
148C2×C42×C43—22no—
149C2×C42×C43—22no—
150C2×C42×C43—41no—
151#95×C43—22no—
152#95×C43—22no—
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×C43—21no—
164C24×C43—21no—
165C24×C43C22×C412yes—
166C24×C43C2×D412yes—
167C24×C43C2×D412yes—
168C24×C43C2411yescharacteristic
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43—21no—
182C23×D43—21no—
183C23×D43C22×C412yes—
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×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43C22×C412yes—
219C22×C4×C43C22×C412yes—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×D412yes—
224C22×C4×C43#4112yes—
225C22×C4×C43#4112yes—
226C2×C22⋊D43—28no—
227C2×C22⋊D43—44no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—44no—
232C2×C22⋊D43—44no—
233C22×Dic43—28no—
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—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—44no—
279C22×Dic43—44no—
280C22×Dic43—44no—
281C22×Dic43—44no—
282C22×Dic43—44no—
283C22×Dic43—44no—
284C22×Dic43C22×C412yes—
285C22×Dic43C22×C412yes—
286C22×Dic43C22×C412yes—
287C22×Dic43#4112yes—
288C22×Dic43#4112yes—
289C4⋊C4×C43—44no—
290C22⋊C4×C43—44no—
291C22⋊C4×C43—44no—
292C22⋊C4×C43C22⋊C4116yescomplemented
293C42×C43—44no—
294C22⋊Dic43—44no—
295C22⋊Dic43—44no—
296(C2×D43)⋊C4—28no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301(C2×D43)⋊C4—44no—
302C4⋊Dic43—28no—
303C4⋊Dic43—28no—
304C4⋊Dic43—44no—
305C4×Dic43—44no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—22no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—22no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43C2×C22⋊C414yes—
341C23×C43C23×C411yescharacteristic
342C23×C43C22×D411yescharacteristic
343C23×C43C22×D411yescharacteristic
344C23×C43C2×#4111yescharacteristic
345C23×C43C2×#4111yescharacteristic
346C23×C43C2×#4111yescharacteristic
347C23×C43C2×#4111yescharacteristic
348C23×C43H(5,𝔽2)11yescharacteristic
349C23×C43H(5,𝔽2)11yescharacteristic
350C23×C43H(5,𝔽2)11yescharacteristic
351C23×C43H(5,𝔽2)11yescharacteristic
352C23×C43H(5,𝔽2)11yescharacteristic
353C23×C43H(5,𝔽2)11yescharacteristic
354C23×C432−1+411yescharacteristic
355C23×C432−1+411yescharacteristic
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—41no—
364C22×D43—41no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—41no—
370C22×D43—41no—
371C22×D43—41no—
372C22×D43—41no—
373C22×D43—41no—
374C22×D43—41no—
375C22×D43—41no—
376C22×D43—41no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43—41no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—41no—
388C22×D43—41no—
389C22×D43—41no—
390C22×D43—41no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—41no—
421C2×C4×C43—41no—
422C2×C4×C43—41no—
423C2×C4×C43—41no—
424C2×C4×C43—41no—
425C2×C4×C43—41no—
426C2×C4×C43—41no—
427C2×C4×C43—41no—
428C2×C4×C43—41no—
429C2×C4×C43—41no—
430C2×C4×C43—41no—
431C2×C4×C43C2×C22⋊C414yes—
432C2×C4×C43C2×C22⋊C414yes—
433C22⋊D43—416no—
434C2×Dic43—22no—
435C2×Dic43—22no—
436C2×Dic43—22no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—416no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481C2×Dic43—41no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484#14506—431nomaximal, Sylow
485C22×C43—24no—
486C22×C43—24no—
487C22×C43—24no—
488C22×C43—42no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43—42no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—42no—
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—42no—
500C22×C43C22×C22⋊C411yescharacteristic
501C22×C43C4×#4111yescharacteristic
502C22×C43C4×#4111yescharacteristic
503C22×C43#51811yescharacteristic
504C22×C43#51811yescharacteristic
505C22×C43#52011yescharacteristic
506C22×C43#52011yescharacteristic
507C22×C43#53511yescharacteristic
508C22×C43#53511yescharacteristic
509C22×C43#53511yescharacteristic
510C22×C43#53511yescharacteristic
511C22×C43#53811yescharacteristic
512C22×C43#53811yescharacteristic
513C22×C43#53911yescharacteristic
514C22×C43#53911yescharacteristic
515C22×C43#54011yescharacteristic
516C22×C43#54011yescharacteristic
517C22×C43#54211yescharacteristic
518C22×C43#54211yescharacteristic
519C22×C43#54611yescharacteristic
520C22×C43#54611yescharacteristic
521C22×C43#54611yescharacteristic
522C22×C43#54611yescharacteristic
523C22×C43#54711yescharacteristic
524C22×C43#54711yescharacteristic
525C22×C43#54711yescharacteristic
526C22×C43#54711yescharacteristic
527C22×C43#55111yescharacteristic
528C22×C43#55311yescharacteristic
529C22×C43#55311yescharacteristic
530C22×C43#55911yescharacteristic
531C22×C43#56011yescharacteristic
532C22×C43#56211yescharacteristic
533C22×C43#56211yescharacteristic
534C22×C43#56311yescharacteristic
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—81no—
543C2×D43—81no—
544C2×D43—81no—
545C2×D43—81no—
546C2×D43—81no—
547C2×D43—81no—
548C2×D43—81no—
549C2×D43—81no—
550C4×C43—24no—
551C4×C43—24no—
552C4×C43—42no—
553C4×C43—42no—
554C4×C43—81no—
555C4×C43—81no—
556Dic43—42no—
557Dic43—42no—
558Dic43—42no—
559Dic43—42no—
560Dic43—42no—
561Dic43—81no—
562Dic43—81no—
563C22×#123—431no—
564C2×#388—431no—
565C2×#388D4311yescharacteristic, complemented
566#1445—431no—
567#1445—431no—
568#1439—431no—
569#1439—431no—
570#1438—431no—
571#1438—431no—
572#1437—431no—
573#1437—431no—
574C4⋊#95—431no—
575C4⋊#95—431no—
576C22⋊#95—431no—
577C22⋊#95—431no—
578C2×C43—44no—
579C2×C43#230911yescharacteristic
580C2×C43#233511yescharacteristic
581C2×C43#233511yescharacteristic
582C2×C43#233911yescharacteristic
583C2×C43#233911yescharacteristic
584C2×C43#237411yescharacteristic
585C2×C43#237611yescharacteristic
586C2×C43#270311yescharacteristic
587C2×C43#270311yescharacteristic
588C2×C43#270611yescharacteristic
589C2×C43#270611yescharacteristic
590C2×C43#271011yescharacteristic
591C2×C43#271011yescharacteristic
592C2×C43#271811yescharacteristic
593C2×C43#271811yescharacteristic
594D43—82no—
595C23×D4—431no—
596C24×C4—431no—
597C2×#123—438no—
598C2×#123—864no—
599C2×#123—864no—
600C22×C4⋊C4—431no—
601C22×C4⋊C4—431no—
602C22×C4⋊C4—431no—
603C22×C4⋊C4C2×D4311yescharacteristic
604C22×C22⋊C4—431no—
605C22×C22⋊C4—431no—
606C22×C22⋊C4—431no—
607C22×C22⋊C4—431no—
608C22×C22⋊C4—431no—
609C22×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C22⋊C4—431no—
612C22×C22⋊C4C2×D4311yescharacteristic
613C22×C22⋊C4C2×D4311yescharacteristic
614C22×C22⋊C4C2×D4311yescharacteristic
615C22×C42—431no—
616C22×C42C2×D4311yescharacteristic
617#388—24no—
618#388—864no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95—431no—
630C2×#95—431no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95C2×D4311yescharacteristic
634C2×#95C2×D4311yescharacteristic
635C43#1450611yescharacteristic, complemented, Sylow
636C25—431no—
637C25C22×D4311yescharacteristic
638C22×D4—434no—
639C22×D4—862no—
640C22×D4—862no—
641C22×D4—1721no—
642C22×D4—1721no—
643C22×D4—1721no—
644C22×D4—1721no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—431no—
649C23×C4—431no—
650C23×C4—434no—
651C23×C4—431no—
652C23×C4—431no—
653C23×C4—862no—
654C23×C4—862no—
655C23×C4—1721no—
656C23×C4—1721no—
657C23×C4—1721no—
658C23×C4—1721no—
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C23×C4C22×D4311yescharacteristic
662C23×C4C22×D4311yescharacteristic
663C23×C4C22×D4311yescharacteristic
664C23×C4C22×D4311yescharacteristic
665#123—8632no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—434no—
670C2×C4⋊C4—434no—
671C2×C4⋊C4—862no—
672C2×C4⋊C4—862no—
673C2×C4⋊C4—862no—
674C2×C4⋊C4—862no—
675C2×C4⋊C4—862no—
676C2×C4⋊C4—862no—
677C2×C4⋊C4—1721no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—434no—
685C2×C22⋊C4—434no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—862no—
688C2×C22⋊C4—862no—
689C2×C22⋊C4—862no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4—862no—
695C2×C22⋊C4—862no—
696C2×C22⋊C4—862no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—1721no—
699C2×C22⋊C4—1721no—
700C2×C22⋊C4—1721no—
701C2×C22⋊C4—1721no—
702C2×C22⋊C4—1721no—
703C2×C22⋊C4—1721no—
704C2×C22⋊C4—1721no—
705C2×C22⋊C4—1721no—
706C2×C22⋊C4—1721no—
707C2×C22⋊C4—1721no—
708C2×C22⋊C4C4×D4314yes—
709C2×C22⋊C4D17214yes—
710C2×C22⋊C4C22⋊D4314yes—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—41no—
714C2×C42—862no—
715C2×C42—862no—
716C2×C42—1721no—
717#95—22no—
718#95—22no—
719#95—862no—
720#95—862no—
721#95—1721no—
722#95—1721no—
723#95—1721no—
724#95—1721no—
725#95—1721no—
726#95—1721no—
727#95—1721no—
728#95—1721no—
729#95—1721no—
730#95—1721no—
731#95—1721no—
732#95—1721no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—432no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24C2×C4×D4312yes—
761C24C2×D17212yes—
762C24C2×C22⋊D4312yes—
763C24C23×D4311yescharacteristic
764C2×D4—868no—
765C2×D4—1724no—
766C2×D4—1724no—
767C2×D4—1724no—
768C2×D4—1724no—
769C2×D4—1724no—
770C2×D4—1724no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—432no—
806C22×C4—432no—
807C22×C4—432no—
808C22×C4—432no—
809C22×C4—432no—
810C22×C4—868no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4—1724no—
858C22×C4—1724no—
859C22×C4—1724no—
860C22×C4—1724no—
861C22×C4C2×C4×D4312yes—
862C22×C4C2×C4×D4312yes—
863C22×C4C2×D17212yes—
864C22×C4C2×D17212yes—
865C22×C4#1062190012yes—
866C22×C4#1062190012yes—
867C22×C4C2×C22⋊D4312yes—
868C22×C4C2×C22⋊D4312yes—
869C4⋊C4—44no—
870C4⋊C4—868no—
871C4⋊C4—868no—
872C4⋊C4—1724no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—868no—
876C22⋊C4—868no—
877C22⋊C4—1724no—
878C22⋊C4—1724no—
879C22⋊C4—1724no—
880C22⋊C4—1724no—
881C22⋊C4—1724no—
882C22⋊C4—1724no—
883C22⋊C4(C2×D43)⋊C4116yescomplemented
884C42—44no—
885C42—1724no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—862no—
921C23—862no—
922C23—862no—
923C23—862no—
924C23—862no—
925C23—862no—
926C23—862no—
927C23—1721no—
928C23—1721no—
929C23—1721no—
930C23—1721no—
931C23—1721no—
932C23—1721no—
933C23—1721no—
934C23—1721no—
935C23—1721no—
936C23—1721no—
937C23—1721no—
938C23—1721no—
939C23—1721no—
940C23—1721no—
941C23—1721no—
942C23—1721no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23C2×(C2×D43)⋊C414yes—
956C23C22×C4×D4311yescharacteristic
957C23C22×C22⋊D4311yescharacteristic
958C23C22×D17211yescharacteristic
959C23#41×D4311yescharacteristic
960C23#41×D4311yescharacteristic
961C23C2×#1062190011yescharacteristic
962C23C2×#1062190011yescharacteristic
963C23#1306337011yescharacteristic
964C23#1306337011yescharacteristic
965C23#1306337111yescharacteristic
966C23#1306337111yescharacteristic
967C23#1306337111yescharacteristic
968C23#1306337111yescharacteristic
969C23#1306337211yescharacteristic
970C23#1306337211yescharacteristic
971D4—17216no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—862no—
1013C2×C4—862no—
1014C2×C4—862no—
1015C2×C4—862no—
1016C2×C4—862no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—1721no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—17216no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4C2×(C2×D43)⋊C414yes—
1063C2×C4C2×(C2×D43)⋊C414yes—
1064C22—24no—
1065C22—24no—
1066C22—24no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—3441no—
1080C22—3441no—
1081C22—3441no—
1082C22—3441no—
1083C22—3441no—
1084C22—3441no—
1085C22—3441no—
1086C22—3441no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22C22×(C2×D43)⋊C411yescharacteristic
1095C22C4×#1062190011yescharacteristic
1096C22C4×#1062190011yescharacteristic
1097C22#1458337311yescharacteristic
1098C22#1458337311yescharacteristic
1099C22#1458337811yescharacteristic
1100C22#1458337811yescharacteristic
1101C22#1458346311yescharacteristic
1102C22#1458346311yescharacteristic
1103C22#1458346811yescharacteristic
1104C22#1458346811yescharacteristic
1105C22#1458348311yescharacteristic
1106C22#1458348611yescharacteristic
1107C22#1458349011yescharacteristic
1108C22#1458349311yescharacteristic
1109C22#1458350111yescharacteristic
1110C22#1458350211yescharacteristic
1111C22#1458351511yescharacteristic
1112C22#1458351811yescharacteristic
1113C22#1458354311yescharacteristic
1114C22#1458354311yescharacteristic
1115C22#1458354411yescharacteristic
1116C22#1458354411yescharacteristic
1117C22#1458354811yescharacteristic
1118C22#1458354811yescharacteristic
1119C22#1458355311yescharacteristic
1120C22#1458355311yescharacteristic
1121C22#1458357211yescharacteristic
1122C22#1458360011yescharacteristic
1123C22#1458360111yescharacteristic
1124C22#1458363111yescharacteristic
1125C22#1458363711yescharacteristic
1126C22#1458364311yescharacteristic
1127C22#1458364611yescharacteristic
1128C22#1458365111yescharacteristic
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—81no—
1135C4—3441no—
1136C4—3441no—
1137C4—1722no—
1138C4—1722no—
1139C4—1722no—
1140C4—1722no—
1141C4—1722no—
1142C2—44no—
1143C2—3442no—
1144C2#1913717511yescharacteristic
1145C2#1913737811yescharacteristic
1146C2#1913739011yescharacteristic
1147C2#1913742011yescharacteristic
1148C2#1913742011yescharacteristic
1149C2#1913772511yescharacteristic
1150C2#1913774111yescharacteristic
1151C2#1914123411yescharacteristic
1152C2#1914123611yescharacteristic
1153C2#1914127911yescharacteristic
1154C2#1914128111yescharacteristic
1155C2#1914133111yescharacteristic
1156C2#1914133511yescharacteristic
1157C2#1914143911yescharacteristic
1158C2#1914144311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14506
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582792C2semidirect
3. #19132864C2semidirect
4. #19132862C2semidirect
5. #19132841C2semidirect
6. #19132837C2semidirect
9. #19132833C2semidirect
10. #19132831C2semidirect
11. #19132825C2semidirect
12. #19132824C2semidirect
13. #19132817C2semidirect
14. #19132817C2semidirect
15. C2×C43×#388C2semidirect
20. C2×#13063309C4semidirect
292. C22⋊C4×C43C22⋊C4semidirect
565. C2×#388D43semidirect
635. C43#14506semidirect
883. C22⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633092
C2×#145827922
#191328642
#191328622
#191328412
#191328372
#191328342
#191328332
#191328312
#191328252
#191328242
#191328172
C2×C43×#3882
#1450643