Finite Group Databasebeta

← #25021038

Subgroups — #25021038

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063309C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic
3C2×#14582784C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
6#19132847C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132840C211yesmaximal, characteristic, complemented
9#19132834C211yesmaximal, characteristic
10#19132833C211yesmaximal, characteristic, complemented
11#19132831C211yesmaximal, characteristic, complemented
12#19132831C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14#19132817C211yesmaximal, characteristic, complemented
15C43×#1437C211yesmaximal, 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×Dic43⋊C4C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36#14582799—24no—
37#14582784—24no—
38C4×C4⋊Dic43—24no—
39C22⋊C4×Dic43—24no—
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
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—41no—
64C22×C22⋊D43—41no—
65C22×C22⋊D43C2×C414yes—
66C23×Dic43—22no—
67C23×Dic43—22no—
68C23×Dic43—22no—
69C23×Dic43—22no—
70C23×Dic43—41no—
71C23×Dic43—41no—
72C23×Dic43C2×C414yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80#13063309—232no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43C2×C414yes—
87C2×C4⋊Dic43C2×C414yes—
88C2×C4⋊Dic43D414yes—
89C2×C4⋊Dic43D414yes—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—41no—
93C2×C22⋊Dic43—22no—
94C2×C22⋊Dic43—22no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—41no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×(C2×D43)⋊C4—22no—
106C2×(C2×D43)⋊C4—22no—
107C2×(C2×D43)⋊C4—22no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4C2×C414yes—
116C2×(C2×D43)⋊C4C2×C414yes—
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—22no—
122C2×C4×Dic43—22no—
123C2×C4×Dic43—41no—
124C2×C4×Dic43—41no—
125C2×C4×Dic43—41no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—41no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C25×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—22no—
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43—41no—
151C2×C22⋊C4×C43C2×C414yes—
152C2×C22⋊C4×C43D414yes—
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—22no—
156#95×C43—22no—
157#95×C43—22no—
158#95×C43—41no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43C22×C412yes—
172C24×C43C2×D412yes—
173C24×C43#4112yes—
174C24×C43C2411yescharacteristic
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×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43C22×C412yes—
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×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43#4112yes—
230C22×C4×C43#4112yes—
231C22×C4×C43#4112yes—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—28no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—44no—
236C2×C22⋊D43—44no—
237C2×C22⋊D43—44no—
238C2×C22⋊D43—44no—
239C22×Dic43—28no—
240C22×Dic43—28no—
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—21no—
279C22×Dic43—21no—
280C22×Dic43—44no—
281C22×Dic43—44no—
282C22×Dic43—44no—
283C22×Dic43—44no—
284C22×Dic43—44no—
285C22×Dic43C22×C412yes—
286C22×Dic43C22×C412yes—
287C22×Dic43C22×C412yes—
288C22×Dic43C2×D412yes—
289C22×Dic43C2×D412yes—
290C22×Dic43C2×D412yes—
291C22×Dic43C2×D412yes—
292C22×Dic43#4112yes—
293C22×Dic43#4112yes—
294C22×Dic43#4112yes—
295C22⋊C4×C43—28no—
296C22⋊C4×C43—28no—
297C22⋊C4×C43—44no—
298C42×C43—28no—
299C22⋊Dic43—28no—
300C22⋊Dic43—44no—
301(C2×D43)⋊C4—28no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307C4⋊Dic43—28no—
308C4⋊Dic43—28no—
309C4⋊Dic43C22⋊C4116yescomplemented
310Dic43⋊C4—44no—
311C4×Dic43—44no—
312C4×Dic43—44no—
313C4×Dic43—44no—
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—22no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
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×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43C4×D414yes—
349C23×C43C23×C411yescharacteristic
350C23×C43C22×D411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C23×C43C2×#4111yescharacteristic
354C23×C43C2×#4111yescharacteristic
355C23×C43C2×#4111yescharacteristic
356C23×C43C2×#4111yescharacteristic
357C23×C43C2×#4111yescharacteristic
358C23×C43C2×#4111yescharacteristic
359C23×C43C2×#4111yescharacteristic
360C23×C43H(5,𝔽2)11yescharacteristic
361C23×C43H(5,𝔽2)11yescharacteristic
362C23×C43H(5,𝔽2)11yescharacteristic
363C23×C432−1+411yescharacteristic
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
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—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43—41no—
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—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—22no—
418C2×C4×C43—22no—
419C2×C4×C43—22no—
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×C43—41no—
432C2×C4×C43—41no—
433C2×C4×C43—41no—
434C2×C4×C43—41no—
435C2×C4×C43—41no—
436C2×C4×C43—41no—
437C2×C4×C43—41no—
438C2×C4×C43—41no—
439C2×C4×C43C2×C22⋊C414yes—
440C2×C4×C43#12314yescomplemented
441C22⋊D43—416no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—22no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—22no—
463C2×Dic43—22no—
464C2×Dic43—22no—
465C2×Dic43—22no—
466C2×Dic43—416no—
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—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489C2×Dic43—41no—
490C2×Dic43C2×C22⋊C414yes—
491C2×Dic43C2×C22⋊C414yes—
492#14095—431nomaximal, Sylow
493C22×C43—24no—
494C22×C43—24no—
495C22×C43—24no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—42no—
500C22×C43—42no—
501C22×C43—42no—
502C22×C43—42no—
503C22×C43—42no—
504C22×C43—42no—
505C22×C43—42no—
506C22×C43—42no—
507C22×C43—42no—
508C22×C43C22×C22⋊C411yescharacteristic
509C22×C43C2×C4×D411yescharacteristic
510C22×C43C4×#4111yescharacteristic
511C22×C43C4×#4111yescharacteristic
512C22×C43C4×#4111yescharacteristic
513C22×C43#51811yescharacteristic
514C22×C43#52011yescharacteristic
515C22×C43C2×#12311yescharacteristic
516C22×C43#52511yescharacteristic
517C22×C43#52511yescharacteristic
518C22×C43#52511yescharacteristic
519C22×C43#52911yescharacteristic
520C22×C43#52911yescharacteristic
521C22×C43#53211yescharacteristic
522C22×C43#53211yescharacteristic
523C22×C43#53811yescharacteristic
524C22×C43#53911yescharacteristic
525C22×C43#54011yescharacteristic
526C22×C43#54211yescharacteristic
527C22×C43D4211yescharacteristic
528C22×C43D4211yescharacteristic
529C22×C43#54611yescharacteristic
530C22×C43#54611yescharacteristic
531C22×C43#54611yescharacteristic
532C22×C43#54711yescharacteristic
533C22×C43#54811yescharacteristic
534C22×C43#54811yescharacteristic
535C22×C43#55011yescharacteristic
536C22×C43#55011yescharacteristic
537C22×C43#55111yescharacteristic
538C22×C43#55111yescharacteristic
539C22×C43#55211yescharacteristic
540C22×C43#55311yescharacteristic
541C22×C43#55311yescharacteristic
542C22×C43#55911yescharacteristic
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—81no—
551C2×D43—81no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C2×D43—81no—
558C4×C43—24no—
559C4×C43—24no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—81no—
564Dic43—24no—
565Dic43—24no—
566Dic43—42no—
567Dic43—42no—
568Dic43—42no—
569Dic43—42no—
570Dic43—81no—
571C22×#123—431no—
572C2×#390—431no—
573C2×#387—431no—
574C2×C4×C4⋊C4—431no—
575C2×C4×C22⋊C4—431no—
576#1441—431no—
577#1439—431no—
578#1439—431no—
579#1438—431no—
580#1437—431no—
581#1437—431no—
582#1437—431no—
583#1437D4311yescharacteristic, complemented
584#1436—431no—
585C22⋊#95—431no—
586C2×C43—44no—
587C2×C43#229711yescharacteristic
588C2×C43C4×#12311yescharacteristic
589C2×C43#233511yescharacteristic
590C2×C43D4×C22⋊C411yescharacteristic
591C2×C43#234111yescharacteristic
592C2×C43#235911yescharacteristic
593C2×C43#237411yescharacteristic
594C2×C43#244311yescharacteristic
595C2×C43#244511yescharacteristic
596C2×C43#245611yescharacteristic
597C2×C43#245811yescharacteristic
598C2×C43#246111yescharacteristic
599C2×C43#247111yescharacteristic
600C2×C43#255411yescharacteristic
601C2×C43#255811yescharacteristic
602D43—82no—
603C23×D4—431no—
604C24×C4—431no—
605C2×#123—438no—
606C2×#123—864no—
607C2×#123—864no—
608C22×C4⋊C4—431no—
609C22×C4⋊C4—431no—
610C22×C4⋊C4—431no—
611C22×C4⋊C4—431no—
612C22×C22⋊C4—431no—
613C22×C22⋊C4—431no—
614C22×C22⋊C4—431no—
615C22×C22⋊C4—431no—
616C22×C22⋊C4—431no—
617C22×C22⋊C4—431no—
618C22×C22⋊C4—431no—
619C22×C22⋊C4—431no—
620C22×C22⋊C4C2×D4311yescharacteristic
621C22×C22⋊C4C2×D4311yescharacteristic
622C22×C22⋊C4C2×D4311yescharacteristic
623C22×C42—431no—
624C22×C42—431no—
625C22×C42—431no—
626C22×C42C2×D4311yescharacteristic
627#390—864no—
628#387—864no—
629C4×C4⋊C4—864no—
630C4×C22⋊C4—864no—
631C2×#95—431no—
632C2×#95—431no—
633C2×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—431no—
638C2×#95—431no—
639C2×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C2×#95C2×D4311yescharacteristic
645C43#1409511yescharacteristic, complemented, Sylow
646C25—431no—
647C25C22×D4311yescharacteristic
648C22×D4—434no—
649C22×D4—862no—
650C22×D4—862no—
651C22×D4—862no—
652C22×D4—862no—
653C22×D4—1721no—
654C22×D4—1721no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—431no—
661C23×C4—434no—
662C23×C4—431no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—862no—
666C23×C4—862no—
667C23×C4—1721no—
668C23×C4—1721no—
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C23×C4C22×D4311yescharacteristic
675#123—8632no—
676C2×C4⋊C4—434no—
677C2×C4⋊C4—434no—
678C2×C4⋊C4—434no—
679C2×C4⋊C4—434no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—862no—
685C2×C4⋊C4—862no—
686C2×C4⋊C4—862no—
687C2×C4⋊C4—1721no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—434no—
696C2×C22⋊C4—434no—
697C2×C22⋊C4—862no—
698C2×C22⋊C4—862no—
699C2×C22⋊C4—862no—
700C2×C22⋊C4—862no—
701C2×C22⋊C4—862no—
702C2×C22⋊C4—862no—
703C2×C22⋊C4—862no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—862no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4C4×D4314yes—
720C2×C22⋊C4D17214yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—862no—
725C2×C42—862no—
726C2×C42—862no—
727C2×C42—862no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—1721no—
731C2×C42—1721no—
732C2×C42—1721no—
733#95—22no—
734#95—22no—
735#95—41no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—862no—
742#95—862no—
743#95—862no—
744#95—1721no—
745#95—1721no—
746#95—1721no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—432no—
760C24—861no—
761C24—861no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24C2×C4×D4312yes—
775C24C2×D17212yes—
776C24#1062189812yes—
777C24C23×D4311yescharacteristic
778C2×D4—868no—
779C2×D4—868no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
783C2×D4—1724no—
784C2×D4—1724no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—432no—
819C22×C4—432no—
820C22×C4—432no—
821C22×C4—432no—
822C22×C4—432no—
823C22×C4—432no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—432no—
828C22×C4—868no—
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—868no—
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—861no—
856C22×C4—861no—
857C22×C4—861no—
858C22×C4—861no—
859C22×C4—861no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4—1724no—
874C22×C4C2×C4×D4312yes—
875C22×C4C2×C4×D4312yes—
876C22×C4C2×D17212yes—
877C22×C4C2×D17212yes—
878C22×C4D4×D4312yes—
879C22×C4D4×D4312yes—
880C22×C4#1062190012yes—
881C22×C4#1062190012yes—
882C22×C4#1062190012yes—
883C4⋊C4—4316no—
884C4⋊C4—868no—
885C4⋊C4—868no—
886C4⋊C4—1724no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—44no—
890C22⋊C4—868no—
891C22⋊C4—868no—
892C22⋊C4—868no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C42—28no—
899C42—1724no—
900C42—1724no—
901C42—1724no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—1721no—
944C23—1721no—
945C23—1721no—
946C23—1721no—
947C23—1721no—
948C23—1721no—
949C23—1721no—
950C23—1721no—
951C23—1721no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23—1721no—
971C23C4×D17214yes—
972C23C22×C4×D4311yescharacteristic
973C23C2×D4×D4311yescharacteristic
974C23C2×D4×D4311yescharacteristic
975C23C22×D17211yescharacteristic
976C23#41×D4311yescharacteristic
977C23#41×D4311yescharacteristic
978C23#41×D4311yescharacteristic
979C23C2×#1062190011yescharacteristic
980C23C2×#1062190011yescharacteristic
981C23C2×#1062190011yescharacteristic
982C23C2×#1062189811yescharacteristic
983C23#1306337011yescharacteristic
984C23#1306337111yescharacteristic
985C23#1306337111yescharacteristic
986C23#1306337211yescharacteristic
987D4—17216no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—434no—
1029C2×C4—434no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—862no—
1054C2×C4—17216no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4—1721no—
1068C2×C4—1721no—
1069C2×C4—1721no—
1070C2×C4—1721no—
1071C2×C4—1721no—
1072C2×C4—1721no—
1073C2×C4—1721no—
1074C2×C4—1721no—
1075C2×C4—1721no—
1076C2×C4—1721no—
1077C2×C4—1721no—
1078C2×C4C22⋊C4×D4314yes—
1079C2×C4#1306330914yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—3441no—
1096C22—3441no—
1097C22—3441no—
1098C22—3441no—
1099C22—3441no—
1100C22—3441no—
1101C22—3441no—
1102C22—3441no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22C2×C22⋊C4×D4311yescharacteristic
1111C22C2×C4×D17211yescharacteristic
1112C22C4×#1062190011yescharacteristic
1113C22C4×#1062190011yescharacteristic
1114C22C4×#1062190011yescharacteristic
1115C22#1458337311yescharacteristic
1116C22#1458337811yescharacteristic
1117C22C2×#1306330911yescharacteristic
1118C22#1458340511yescharacteristic
1119C22#1458340711yescharacteristic
1120C22#1458341111yescharacteristic
1121C22#1458342911yescharacteristic
1122C22#1458342911yescharacteristic
1123C22#1458344411yescharacteristic
1124C22#1458344411yescharacteristic
1125C22#1458348311yescharacteristic
1126C22#1458349311yescharacteristic
1127C22#1458350211yescharacteristic
1128C22#1458351511yescharacteristic
1129C22D4×D17211yescharacteristic
1130C22D4×D17211yescharacteristic
1131C22#1458354411yescharacteristic
1132C22#1458354511yescharacteristic
1133C22#1458354511yescharacteristic
1134C22#1458355311yescharacteristic
1135C22#1458355511yescharacteristic
1136C22#1458355711yescharacteristic
1137C22#1458356711yescharacteristic
1138C22#1458356911yescharacteristic
1139C22#1458357211yescharacteristic
1140C22#1458357511yescharacteristic
1141C22#1458358211yescharacteristic
1142C22#1458360011yescharacteristic
1143C22#1458360111yescharacteristic
1144C22#1458363111yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—81no—
1151C4—864no—
1152C4—864no—
1153C4—3441no—
1154C4—1722no—
1155C4—1722no—
1156C4—1722no—
1157C4—1722no—
1158C2—44no—
1159C2—3442no—
1160C2#1913708011yescharacteristic
1161C2C4×#1306330911yescharacteristic
1162C2#1913739011yescharacteristic
1163C2C22⋊C4×D17211yescharacteristic
1164C2#1913743411yescharacteristic
1165C2#1913758911yescharacteristic
1166C2#1913772511yescharacteristic
1167C2#1913832811yescharacteristic
1168C2#1913835811yescharacteristic
1169C2#1913848411yescharacteristic
1170C2#1913851411yescharacteristic
1171C2#1913856011yescharacteristic
1172C2#1913870311yescharacteristic
1173C2#1913965211yescharacteristic
1174C2#1913970611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenter#1437D43
hypocenterC43#14095
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#14582784C2semidirect
4. C2×C4×C4⋊Dic43C2semidirect
5. C2×C22⋊C4×Dic43C2semidirect
6. #19132847C2semidirect
7. #19132841C2semidirect
8. #19132840C2semidirect
10. #19132833C2semidirect
11. #19132831C2semidirect
12. #19132831C2semidirect
13. #19132829C2semidirect
14. #19132817C2semidirect
15. C43×#1437C2semidirect
20. C2×#13063309C4semidirect
309. C4⋊Dic43C22⋊C4semidirect
440. C2×C4×C43#123semidirect
583. #1437D43semidirect
645. C43#14095semidirect
1079. C2×C4#13063309semidirect

Maximal subgroups

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

subgroupindex
C22×#130633092
C2×#145827992
C2×#145827842
C2×C4×C4⋊Dic432
C2×C22⋊C4×Dic432
#191328472
#191328412
#191328402
#191328342
#191328332
#191328312
#191328292
#191328172
C43×#14372
#1409543