Finite Group Databasebeta

← #25025862

Subgroups — #25025862

Order 11008.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582801C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4#19132852C211yesmaximal, characteristic, complemented
5#19132851C211yesmaximal, characteristic, complemented
6#19132839C211yesmaximal, characteristic, complemented
7#19132839C211yesmaximal, characteristic, complemented
8#19132837C211yesmaximal, characteristic, complemented
9#19132837C211yesmaximal, characteristic, complemented
10#19132828C211yesmaximal, characteristic, complemented
11(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
12(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31#14582801—24no—
32#14582777—24no—
33#14582777C418yescomplemented
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
47C22×C4⋊C4×C43C2211yescharacteristic
48C22×C42×C43C2211yescharacteristic
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C24×D43C2311yescharacteristic
55C24×D43C2311yescharacteristic
56C22×D172—41no—
57C22×D172—41no—
58C22×D172—41no—
59C22×D172—41no—
60C22×D172C2×C414yes—
61C22×D172D414yes—
62C22×D172Q814yes—
63C23×Dic43C2311yescharacteristic
64C23×Dic43C2311yescharacteristic
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C22×C4×D43—22no—
70C22×C4×D43—22no—
71C22×C4×D43—22no—
72C22×C4×D43—41no—
73C22×C4×D43—41no—
74C22×C4×D43—41no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43—41no—
78C22×C4×D43—41no—
79C22×C4×D43—41no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43C2×C414yescomplemented
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43—41no—
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—41no—
88C2×Dic43⋊C4—41no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
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)⋊C4—41no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4C2×C414yes—
117C2×(C2×D43)⋊C4C2×C414yes—
118C2×(C2×D43)⋊C4C2×C414yescomplemented
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—41no—
122C43⋊#95—41no—
123C43⋊#95—41no—
124C43⋊#95—41no—
125C43⋊#95—41no—
126C43⋊#95—41no—
127C43⋊#95—41no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95C2×C414yescomplemented
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—41no—
141C2×C4⋊C4×C43—41no—
142C2×C42×C43—22no—
143C2×C42×C43—41no—
144C2×C42×C43—41no—
145#95×C43—22no—
146#95×C43—22no—
147#95×C43—41no—
148#95×C43—41no—
149#95×C43C2×C414yescomplemented
150C24×C43C2411yescharacteristic
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—21no—
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—21no—
167C23×D43—21no—
168C23×D43—21no—
169C23×D43—21no—
170C23×D43—21no—
171C23×D43—21no—
172C23×D43—21no—
173C23×D43—21no—
174C23×D43—21no—
175C23×D43C22×C412yes—
176C23×D43C22×C412yes—
177C23×D43C2×D412yes—
178C23×D43C2×D412yes—
179C23×D43C2×Q812yes—
180C23×D43C2×Q812yes—
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×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×C43C22×C412yes—
223C22×C4×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×Q812yes—
227C22×C4×C43#4112yes—
228C22×C4×C43#4112yes—
229C22×C4×C43#4112yes—
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—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×Dic43C22×C412yes—
270C22×Dic43C22×C412yes—
271C22×Dic43#4112yes—
272C2×D172—44no—
273C2×D172—44no—
274C2×D172—44no—
275C2×D172—44no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172C4⋊C4116yescomplemented
279C2×C4×D43—44no—
280C2×C4×D43—44no—
281C2×C4×D43—44no—
282C2×C4×D43—44no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C2×C4×D43—44no—
289C2×C4×D43—44no—
290C2×C4×D43—44no—
291C2×C4×D43—44no—
292C2×C4×D43—44no—
293C4⋊C4×C43—44no—
294C42×C43—44no—
295(C2×D43)⋊C4—44no—
296(C2×D43)⋊C4—44no—
297(C2×D43)⋊C4—44no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301(C2×D43)⋊C4—44no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305C4⋊Dic43—44no—
306Dic43⋊C4—44no—
307C23×C43C23×C411yescharacteristic
308C23×C43C22×D411yescharacteristic
309C23×C43C22×Q811yescharacteristic
310C23×C43C2×#4111yescharacteristic
311C23×C43C2×#4111yescharacteristic
312C23×C43C2×#4111yescharacteristic
313C23×C43C2×#4111yescharacteristic
314C23×C43H(5,𝔽2)11yescharacteristic
315C23×C43H(5,𝔽2)11yescharacteristic
316C23×C43H(5,𝔽2)11yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C43H(5,𝔽2)11yescharacteristic
319C23×C43H(5,𝔽2)11yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—22no—
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—22no—
358C22×D43—41no—
359C22×D43—41no—
360C22×D43—41no—
361C22×D43—41no—
362C22×D43—41no—
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×D43C2×C4⋊C414yes—
391C22×D43C2×C4⋊C414yes—
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—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
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×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×C43—41no—
440C2×C4×C43C2×C4⋊C414yes—
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—22no—
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—
483D172—416no—
484C4×D43—416no—
485C4×D43—416no—
486#14513—431nomaximal, Sylow
487C22×C43C22×C4⋊C411yescharacteristic
488C22×C43C4×#4111yescharacteristic
489C22×C43C4×#4111yescharacteristic
490C22×C43#51811yescharacteristic
491C22×C43#51811yescharacteristic
492C22×C43#51811yescharacteristic
493C22×C43#51811yescharacteristic
494C22×C43#53411yescharacteristic
495C22×C43#53411yescharacteristic
496C22×C43#53811yescharacteristic
497C22×C43#53811yescharacteristic
498C22×C43#53811yescharacteristic
499C22×C43#53811yescharacteristic
500C22×C43#54011yescharacteristic
501C22×C43#54011yescharacteristic
502C22×C43#54011yescharacteristic
503C22×C43#54011yescharacteristic
504C22×C43#54311yescharacteristic
505C22×C43#54311yescharacteristic
506C22×C43#54611yescharacteristic
507C22×C43#54611yescharacteristic
508C22×C43#54611yescharacteristic
509C22×C43#54611yescharacteristic
510C22×C43#55111yescharacteristic
511C22×C43#55311yescharacteristic
512C22×C43#55311yescharacteristic
513C22×C43#55411yescharacteristic
514C22×C43#55411yescharacteristic
515C22×C43#55411yescharacteristic
516C22×C43#55411yescharacteristic
517C22×C43#55911yescharacteristic
518C22×C43#56011yescharacteristic
519C22×C43#56011yescharacteristic
520C22×C43#56011yescharacteristic
521C22×C43H(3,𝔽4)11yescharacteristic
522C2×D43—24no—
523C2×D43—24no—
524C2×D43—24no—
525C2×D43—24no—
526C2×D43—24no—
527C2×D43—24no—
528C2×D43—42no—
529C2×D43—42no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—42no—
542C2×D43—42no—
543C2×D43—42no—
544C2×D43—42no—
545C2×D43—42no—
546C2×D43—42no—
547C2×D43—42no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C4×C43—24no—
553C4×C43—42no—
554C4×C43—42no—
555C4×C43—42no—
556C4×C43—42no—
557C4×C43—42no—
558C4×C43—81no—
559Dic43—42no—
560Dic43—42no—
561Dic43—42no—
562Dic43—81no—
563Dic43—81no—
564Dic43—81no—
565C2×#390—431no—
566C2×#386—431no—
567C2×#386—431no—
568#1442—431no—
569#1442—431no—
570#1439—431no—
571#1439—431no—
572#1439—431no—
573#1439—431no—
574#1436—431no—
575#1436D4311yescharacteristic, complemented
576C22⋊#95—431no—
577C22⋊#95—431no—
578C22⋊#95—431no—
579C22⋊#95—431no—
580C2×C43#231511yescharacteristic
581C2×C43#233311yescharacteristic
582C2×C43#233311yescharacteristic
583C2×C43#234911yescharacteristic
584C2×C43#234911yescharacteristic
585C2×C43#237411yescharacteristic
586C2×C43#237511yescharacteristic
587C2×C43#268411yescharacteristic
588C2×C43#268811yescharacteristic
589C2×C43#268811yescharacteristic
590C2×C43#270911yescharacteristic
591C2×C43#274811yescharacteristic
592C2×C43#278011yescharacteristic
593C2×C43#278011yescharacteristic
594C2×C43#280411yescharacteristic
595D43—44no—
596D43—44no—
597C23×D4—431no—
598C24×C4—431no—
599C24×C4—431no—
600C22×C4⋊C4—431no—
601C22×C4⋊C4—431no—
602C22×C4⋊C4C2×D4311yescharacteristic
603C22×C22⋊C4—431no—
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⋊C4—431no—
613C22×C42C2×D4311yescharacteristic
614#390—864no—
615#386—438no—
616#386—864no—
617C2×#95—431no—
618C2×#95—431no—
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×#95C2×D4311yescharacteristic
631C2×#95C2×D4311yescharacteristic
632C2×#95C2×D4311yescharacteristic
633C2×#95C2×D4311yescharacteristic
634C2×#95C2×D4311yescharacteristic
635C43#1451311yescharacteristic, complemented, Sylow
636C25—431no—
637C25—431no—
638C22×D4—434no—
639C22×D4—434no—
640C22×D4—434no—
641C22×D4—1721no—
642C22×D4—1721no—
643C22×D4—1721no—
644C22×D4—1721no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—431no—
648C23×C4—434no—
649C23×C4—431no—
650C23×C4—431no—
651C23×C4—431no—
652C23×C4—862no—
653C23×C4—862no—
654C23×C4—862no—
655C23×C4—1721no—
656C23×C4—1721no—
657C23×C4—1721no—
658C23×C4—1721no—
659C23×C4—1721no—
660C23×C4—1721no—
661C23×C4—1721no—
662C23×C4—1721no—
663C23×C4—1721no—
664C23×C4—1721no—
665C23×C4C22×D4311yescharacteristic
666C23×C4C22×D4311yescharacteristic
667C23×C4C22×D4311yescharacteristic
668C23×C4C22×D4311yescharacteristic
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C2×C4⋊C4—22no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4—862no—
676C2×C4⋊C4—862no—
677C2×C4⋊C4—1721no—
678C2×C4⋊C4—1721no—
679C2×C4⋊C4—1721no—
680C2×C4⋊C4—1721no—
681C2×C22⋊C4—434no—
682C2×C22⋊C4—434no—
683C2×C22⋊C4—434no—
684C2×C22⋊C4—862no—
685C2×C22⋊C4—862no—
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—1721no—
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⋊C4—1721no—
709C2×C22⋊C4—1721no—
710C2×C22⋊C4—1721no—
711C2×C42—22no—
712C2×C42—41no—
713C2×C42—41no—
714#95—22no—
715#95—22no—
716#95—41no—
717#95—41no—
718#95—434no—
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#95C4×D4314yescomplemented
732C24—432no—
733C24—432no—
734C24—432no—
735C24—432no—
736C24—432no—
737C24—432no—
738C24—861no—
739C24—861no—
740C24—861no—
741C24—861no—
742C24—861no—
743C24—861no—
744C24—861no—
745C24—861no—
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—
760C24—861no—
761C24—861no—
762C24C23×D4311yescharacteristic
763C2×D4—4316no—
764C2×D4—1724no—
765C2×D4—1724no—
766C2×D4—1724no—
767C2×D4—1724no—
768C2×D4—1724no—
769C2×D4—1724no—
770C22×C4—21no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—432no—
812C22×C4—432no—
813C22×C4—432no—
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—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4—1724no—
858C22×C4—1724no—
859C22×C4—1724no—
860C22×C4—1724no—
861C22×C4—1724no—
862C22×C4—1724no—
863C22×C4—1724no—
864C22×C4—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4C2×C4×D4312yes—
868C22×C4C2×C4×D4312yes—
869C22×C4C2×C4×D4312yes—
870C22×C4#1062189812yes—
871C22×C4#1062189812yes—
872C22×C4D4×D4312yes—
873C22×C4Q8×D4312yes—
874C22×C4#1062190212yes—
875C4⋊C4—44no—
876C4⋊C4—1724no—
877C4⋊C4—1724no—
878C22⋊C4—1724no—
879C22⋊C4—1724no—
880C22⋊C4—1724no—
881C22⋊C4—1724no—
882C22⋊C4—1724no—
883C22⋊C4—1724no—
884C22⋊C4—1724no—
885C22⋊C4—1724no—
886C22⋊C4—1724no—
887C22⋊C4—1724no—
888C42—44no—
889C23—434no—
890C23—434no—
891C23—862no—
892C23—862no—
893C23—862no—
894C23—862no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—862no—
912C23—862no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—862no—
919C23—862no—
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—
955C23—1721no—
956C23—1721no—
957C23—1721no—
958C23—1721no—
959C23C22×C4×D4311yescharacteristic
960C23C2×D4×D4311yescharacteristic
961C23C2×Q8×D4311yescharacteristic
962C23#41×D4311yescharacteristic
963C23C2×#1062189811yescharacteristic
964C23C2×#1062189811yescharacteristic
965C23C2×#1062190211yescharacteristic
966C23#1306337011yescharacteristic
967C23#1306337011yescharacteristic
968C23#1306337011yescharacteristic
969C23#1306337111yescharacteristic
970C23#1306337111yescharacteristic
971C23#1306337111yescharacteristic
972C23#1306337111yescharacteristic
973C23#1306337111yescharacteristic
974D4—17216no—
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—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
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—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—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—17216no—
1033C2×C4—17216no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
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×C4—1721no—
1063C2×C4—1721no—
1064C2×C4—1721no—
1065C2×C4—1721no—
1066C2×C4—1721no—
1067C2×C4C4⋊C4×D4314yes—
1068C22—864no—
1069C22—864no—
1070C22—864no—
1071C22—864no—
1072C22—864no—
1073C22—864no—
1074C22—1722no—
1075C22—1722no—
1076C22—1722no—
1077C22—1722no—
1078C22—1722no—
1079C22—1722no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22C2×C4⋊C4×D4311yescharacteristic
1099C22C4×#1062189811yescharacteristic
1100C22C4×#1062190211yescharacteristic
1101C22#1458337111yescharacteristic
1102C22#1458337111yescharacteristic
1103C22#1458337111yescharacteristic
1104C22#1458337311yescharacteristic
1105C22#1458345911yescharacteristic
1106C22#1458346011yescharacteristic
1107C22#1458348211yescharacteristic
1108C22#1458348711yescharacteristic
1109C22#1458348811yescharacteristic
1110C22#1458348911yescharacteristic
1111C22#1458350011yescharacteristic
1112C22#1458350111yescharacteristic
1113C22#1458350411yescharacteristic
1114C22#1458350511yescharacteristic
1115C22#1458352411yescharacteristic
1116C22#1458352411yescharacteristic
1117C22#1458354011yescharacteristic
1118C22#1458354511yescharacteristic
1119C22#1458354511yescharacteristic
1120C22#1458354611yescharacteristic
1121C22#1458357311yescharacteristic
1122C22#1458359711yescharacteristic
1123C22#1458359811yescharacteristic
1124C22#1458360511yescharacteristic
1125C22#1458360911yescharacteristic
1126C22#1458360911yescharacteristic
1127C22#1458361011yescharacteristic
1128C22#1458363411yescharacteristic
1129C22#1458363711yescharacteristic
1130C22#1458363911yescharacteristic
1131C22#1458364011yescharacteristic
1132C22#1458364111yescharacteristic
1133C4—24no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—81no—
1140C4—3441no—
1141C4—3441no—
1142C4—3441no—
1143C4—1722no—
1144C4—1722no—
1145C4—1722no—
1146C2—1724no—
1147C2—1724no—
1148C2#1913720611yescharacteristic
1149C2#1913735511yescharacteristic
1150C2#1913735911yescharacteristic
1151C2#1913750411yescharacteristic
1152C2#1913750611yescharacteristic
1153C2#1913772411yescharacteristic
1154C2#1913773511yescharacteristic
1155C2#1914097611yescharacteristic
1156C2#1914103211yescharacteristic
1157C2#1914103411yescharacteristic
1158C2#1914132711yescharacteristic
1159C2#1914180311yescharacteristic
1160C2#1914223711yescharacteristic
1161C2#1914224611yescharacteristic
1162C2#1914253911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14513
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #19132852C2semidirect
5. #19132851C2semidirect
6. #19132839C2semidirect
7. #19132839C2semidirect
8. #19132837C2semidirect
9. #19132837C2semidirect
10. #19132828C2semidirect
11. (C2×D43)⋊#95C2semidirect
12. (C2×D43)⋊#95C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1436C2semidirect
33. #14582777C4semidirect
82. C22×C4×D43C2×C4semidirect
118. C2×(C2×D43)⋊C4C2×C4semidirect
131. C43⋊#95C2×C4semidirect
149. #95×C43C2×C4semidirect
278. C2×D172C4⋊C4semidirect
575. #1436D43semidirect
635. C43#14513semidirect
731. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827772
#191328522
#191328512
#191328392
#191328372
#191328282
(C2×D43)⋊#952
C43×#14362
#1451343