Finite Group Databasebeta

← #25024604

Subgroups — #25024604

Order 11008.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582800C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582773C211yesmaximal, characteristic, complemented
5C2×#14582758C211yesmaximal, characteristic, complemented
6#19132858C211yesmaximal, characteristic, complemented
7#19132841C211yesmaximal, characteristic, complemented
8#19132839C211yesmaximal, characteristic, complemented
9#19132839C211yesmaximal, characteristic, complemented
10#19132839C211yesmaximal, characteristic, complemented
11#19132829C211yesmaximal, characteristic, complemented
12#19132826C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊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
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34#14582800—24no—
35#14582777—24no—
36#14582777C418yescomplemented
37#14582773—24no—
38#14582758—24no—
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
49C22×C4⋊C4×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C24×D43C2311yescharacteristic
57C24×D43C2311yescharacteristic
58C22×D172—41no—
59C22×D172—41no—
60C22×D172—41no—
61C22×D172—41no—
62C22×D172C2×C414yes—
63C22×D172D414yes—
64C22×D172Q814yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2311yescharacteristic
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—22no—
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×D43—41no—
83C22×C4×D43—41no—
84C22×C4×D43C2×C414yescomplemented
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—41no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—41no—
90C2×Dic43⋊C4—41no—
91C2×Dic43⋊C4—41no—
92C2×Dic43⋊C4—41no—
93C2×Dic43⋊C4—41no—
94C2×Dic43⋊C4—41no—
95C2×Dic43⋊C4—41no—
96C2×Dic43⋊C4D414yescomplemented
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—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—22no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4—41no—
120C2×(C2×D43)⋊C4—41no—
121C2×(C2×D43)⋊C4—41no—
122C2×(C2×D43)⋊C4—41no—
123C2×(C2×D43)⋊C4—41no—
124C2×(C2×D43)⋊C4C2×C414yes—
125C2×(C2×D43)⋊C4C2×C414yes—
126C2×(C2×D43)⋊C4C2×C414yescomplemented
127C2×C4×Dic43—22no—
128C2×C4×Dic43—41no—
129C2×C4×Dic43—41no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C43⋊#95—41no—
138C43⋊#95—41no—
139C43⋊#95C2×C414yescomplemented
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43—22no—
148C2×C4⋊C4×C43—41no—
149C2×C4⋊C4×C43—41no—
150#95×C43—22no—
151#95×C43—22no—
152#95×C43—22no—
153#95×C43—41no—
154#95×C43—41no—
155#95×C43C2×C414yescomplemented
156C24×C43C2411yescharacteristic
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×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43—21no—
180C23×D43—21no—
181C23×D43C22×C412yes—
182C23×D43C22×C412yes—
183C23×D43C2×D412yes—
184C23×D43C2×D412yes—
185C23×D43C2×Q812yes—
186C23×D43C2×Q812yes—
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×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C22×C412yes—
232C22×C4×C43C22×C412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×Q812yes—
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×Dic43C22×C412yes—
272C22×Dic43C22×C412yes—
273C22×Dic43C2×D412yes—
274C22×Dic43C2×D412yes—
275C22×Dic43#4112yes—
276C22×Dic43#4112yes—
277C22×Dic43#4112yes—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×D172—44no—
282C2×D172—44no—
283C2×D172—44no—
284C2×D172C4⋊C4116yescomplemented
285C2×C4×D43—28no—
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—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C4⋊C4×C43—44no—
300(C2×D43)⋊C4—28no—
301(C2×D43)⋊C4—44no—
302(C2×D43)⋊C4—44no—
303(C2×D43)⋊C4—44no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307(C2×D43)⋊C4—44no—
308(C2×D43)⋊C4—44no—
309(C2×D43)⋊C4—44no—
310C4⋊Dic43—44no—
311Dic43⋊C4—44no—
312Dic43⋊C4—44no—
313Dic43⋊C4—44no—
314C4×Dic43—44no—
315C23×C43C23×C411yescharacteristic
316C23×C43C22×D411yescharacteristic
317C23×C43C22×D411yescharacteristic
318C23×C43C22×Q811yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C43H(5,𝔽2)11yescharacteristic
324C23×C43H(5,𝔽2)11yescharacteristic
325C23×C43H(5,𝔽2)11yescharacteristic
326C23×C43H(5,𝔽2)11yescharacteristic
327C23×C43H(5,𝔽2)11yescharacteristic
328C23×C43H(5,𝔽2)11yescharacteristic
329C23×C432−1+411yescharacteristic
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—22no—
359C22×D43—22no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
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—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43—41no—
398C22×D43C2×C4⋊C414yes—
399C22×D43C2×C4⋊C414yes—
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—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×C43—41no—
441C2×C4×C43—41no—
442C2×C4×C43—41no—
443C2×C4×C43—41no—
444C2×C4×C43—41no—
445C2×C4×C43—41no—
446C2×C4×C43—41no—
447C2×C4×C43—41no—
448C2×C4×C43C2×C4⋊C414yes—
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—22no—
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×Dic43C4×D414yes—
491D172—416no—
492C4×D43—416no—
493C4×D43—416no—
494#14407—431nomaximal, Sylow
495C22×C43C22×C4⋊C411yescharacteristic
496C22×C43C2×C4×D411yescharacteristic
497C22×C43C4×#4111yescharacteristic
498C22×C43#51811yescharacteristic
499C22×C43#51811yescharacteristic
500C22×C43#51811yescharacteristic
501C22×C43#52011yescharacteristic
502C22×C43#53411yescharacteristic
503C22×C43#53411yescharacteristic
504C22×C43#53411yescharacteristic
505C22×C43#53511yescharacteristic
506C22×C43#53811yescharacteristic
507C22×C43#53811yescharacteristic
508C22×C43#53811yescharacteristic
509C22×C43#53911yescharacteristic
510C22×C43#54011yescharacteristic
511C22×C43#54211yescharacteristic
512C22×C43#54311yescharacteristic
513C22×C43#54311yescharacteristic
514C22×C43D4211yescharacteristic
515C22×C43#54611yescharacteristic
516C22×C43#54611yescharacteristic
517C22×C43#54611yescharacteristic
518C22×C43#54711yescharacteristic
519C22×C43D4×Q811yescharacteristic
520C22×C43#55011yescharacteristic
521C22×C43#55311yescharacteristic
522C22×C43#55411yescharacteristic
523C22×C43#55411yescharacteristic
524C22×C43#55411yescharacteristic
525C22×C43#55511yescharacteristic
526C22×C43#56011yescharacteristic
527C22×C43#56011yescharacteristic
528C22×C43#56211yescharacteristic
529C22×C43#56211yescharacteristic
530C2×D43—24no—
531C2×D43—24no—
532C2×D43—24no—
533C2×D43—24no—
534C2×D43—24no—
535C2×D43—24no—
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—
552C2×D43—42no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—42no—
556C2×D43—42no—
557C2×D43—42no—
558C2×D43—42no—
559C2×D43—42no—
560C4×C43—24no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—81no—
565C4×C43—81no—
566C4×C43—81no—
567Dic43—24no—
568Dic43—42no—
569Dic43—42no—
570Dic43—42no—
571Dic43—42no—
572Dic43—81no—
573C2×#390—431no—
574C2×#386—431no—
575C2×#386—431no—
576C2×#385—431no—
577C2×#380—431no—
578#1444—431no—
579#1442D4311yescharacteristic, complemented
580#1439—431no—
581#1439—431no—
582#1439—431no—
583#1439—431no—
584#1436—431no—
585#1436—431no—
586C22⋊#95—431no—
587C22⋊#95—431no—
588C2×C43#231511yescharacteristic
589C2×C43#232111yescharacteristic
590C2×C43#233511yescharacteristic
591C2×C43D4×C4⋊C411yescharacteristic
592C2×C43#234911yescharacteristic
593C2×C43#236311yescharacteristic
594C2×C43#237711yescharacteristic
595C2×C43#266811yescharacteristic
596C2×C43#267311yescharacteristic
597C2×C43#268611yescharacteristic
598C2×C43#269211yescharacteristic
599C2×C43#270811yescharacteristic
600C2×C43#273211yescharacteristic
601C2×C43#278011yescharacteristic
602C2×C43#278411yescharacteristic
603D43—44no—
604D43—44no—
605C23×D4—431no—
606C24×C4—431no—
607C24×C4—431no—
608C22×C4⋊C4—431no—
609C22×C4⋊C4—431no—
610C22×C4⋊C4—431no—
611C22×C4⋊C4—431no—
612C22×C4⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
621C22×C22⋊C4—431no—
622C22×C22⋊C4—431no—
623C22×C42—431no—
624#390—864no—
625#386—438no—
626#386—864no—
627#385—864no—
628#380—864no—
629C2×#95—431no—
630C2×#95—431no—
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×#95C2×D4311yescharacteristic
640C2×#95C2×D4311yescharacteristic
641C2×#95C2×D4311yescharacteristic
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C2×#95C2×D4311yescharacteristic
645C43#1440711yescharacteristic, complemented, Sylow
646C25—431no—
647C25—431no—
648C22×D4—434no—
649C22×D4—434no—
650C22×D4—434no—
651C22×D4—1721no—
652C22×D4—1721no—
653C22×D4—1721no—
654C22×D4—1721no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—434no—
661C23×C4—431no—
662C23×C4—862no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—862no—
666C23×C4—862no—
667C23×C4—1721no—
668C23×C4—1721no—
669C23×C4—1721no—
670C23×C4—1721no—
671C23×C4—1721no—
672C23×C4—1721no—
673C23×C4—1721no—
674C23×C4—1721no—
675C23×C4C22×D4311yescharacteristic
676C23×C4C22×D4311yescharacteristic
677C23×C4C22×D4311yescharacteristic
678C23×C4C22×D4311yescharacteristic
679C23×C4C22×D4311yescharacteristic
680C23×C4C22×D4311yescharacteristic
681C23×C4C22×D4311yescharacteristic
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4—41no—
685C2×C4⋊C4—434no—
686C2×C4⋊C4—862no—
687C2×C4⋊C4—862no—
688C2×C4⋊C4—862no—
689C2×C4⋊C4—1721no—
690C2×C4⋊C4—1721no—
691C2×C4⋊C4—1721no—
692C2×C4⋊C4—1721no—
693C2×C4⋊C4—1721no—
694C2×C4⋊C4—1721no—
695C2×C4⋊C4—1721no—
696C2×C4⋊C4—1721no—
697C2×C22⋊C4—434no—
698C2×C22⋊C4—434no—
699C2×C22⋊C4—434no—
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—862no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4—1721no—
721C2×C22⋊C4—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4—1721no—
725C2×C22⋊C4—1721no—
726C2×C22⋊C4—1721no—
727C2×C42—862no—
728C2×C42—1721no—
729C2×C42—1721no—
730#95—22no—
731#95—22no—
732#95—22no—
733#95—41no—
734#95—41no—
735#95—434no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—1721no—
742#95—1721no—
743#95—1721no—
744#95—1721no—
745#95C4×D4314yescomplemented
746C24—432no—
747C24—432no—
748C24—432no—
749C24—432no—
750C24—432no—
751C24—432no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
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—
774C24—861no—
775C24—861no—
776C24C23×D4311yescharacteristic
777C2×D4—4316no—
778C2×D4—1724no—
779C2×D4—1724no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
783C2×D4—1724no—
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—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—432no—
828C22×C4—432no—
829C22×C4—432no—
830C22×C4—432no—
831C22×C4—432no—
832C22×C4—432no—
833C22×C4—432no—
834C22×C4—868no—
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—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—861no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4—1724no—
874C22×C4—1724no—
875C22×C4—1724no—
876C22×C4—1724no—
877C22×C4—1724no—
878C22×C4—1724no—
879C22×C4—1724no—
880C22×C4—1724no—
881C22×C4—1724no—
882C22×C4—1724no—
883C22×C4C2×C4×D4312yes—
884C22×C4C2×C4×D4312yes—
885C22×C4C2×C4×D4312yes—
886C22×C4D4×D4312yes—
887C22×C4D4×D4312yes—
888C22×C4Q8×D4312yes—
889C4⋊C4—44no—
890C4⋊C4—1724no—
891C4⋊C4—1724no—
892C4⋊C4—1724no—
893C4⋊C4—1724no—
894C22⋊C4—868no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C22⋊C4—1724no—
899C22⋊C4—1724no—
900C22⋊C4—1724no—
901C22⋊C4—1724no—
902C22⋊C4—1724no—
903C22⋊C4—1724no—
904C42—1724no—
905C23—434no—
906C23—434no—
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—862no—
928C23—862no—
929C23—862no—
930C23—862no—
931C23—862no—
932C23—862no—
933C23—862no—
934C23—862no—
935C23—862no—
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—
971C23—1721no—
972C23—1721no—
973C23—1721no—
974C23—1721no—
975C23C22×C4×D4311yescharacteristic
976C23C2×D4×D4311yescharacteristic
977C23C2×D4×D4311yescharacteristic
978C23C2×Q8×D4311yescharacteristic
979C23#41×D4311yescharacteristic
980C23#41×D4311yescharacteristic
981C23#41×D4311yescharacteristic
982C23#1306337011yescharacteristic
983C23#1306337011yescharacteristic
984C23#1306337111yescharacteristic
985C23#1306337111yescharacteristic
986C23#1306337111yescharacteristic
987C23#1306337111yescharacteristic
988C23#1306337111yescharacteristic
989C23#1306337311yescharacteristic
990D4—17216no—
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—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—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—434no—
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—862no—
1055C2×C4—862no—
1056C2×C4—862no—
1057C2×C4—862no—
1058C2×C4—17216no—
1059C2×C4—17216no—
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×C4—1721no—
1079C2×C4—1721no—
1080C2×C4—1721no—
1081C2×C4—1721no—
1082C2×C4—1721no—
1083C2×C4C4⋊C4×D4314yes—
1084C22—864no—
1085C22—864no—
1086C22—864no—
1087C22—864no—
1088C22—864no—
1089C22—864no—
1090C22—1722no—
1091C22—1722no—
1092C22—1722no—
1093C22—1722no—
1094C22—1722no—
1095C22—1722no—
1096C22—1722no—
1097C22—1722no—
1098C22—1722no—
1099C22—1722no—
1100C22—1722no—
1101C22—1722no—
1102C22—1722no—
1103C22—1722no—
1104C22—1722no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22—1722no—
1113C22—1722no—
1114C22C2×C4⋊C4×D4311yescharacteristic
1115C22C4×D4×D4311yescharacteristic
1116C22#1458336711yescharacteristic
1117C22#1458337111yescharacteristic
1118C22#1458337111yescharacteristic
1119C22#1458337311yescharacteristic
1120C22#1458338111yescharacteristic
1121C22#1458345911yescharacteristic
1122C22#1458346011yescharacteristic
1123C22#1458346011yescharacteristic
1124C22#1458346511yescharacteristic
1125C22#1458348311yescharacteristic
1126C22#1458348811yescharacteristic
1127C22#1458348811yescharacteristic
1128C22#1458349711yescharacteristic
1129C22#1458350111yescharacteristic
1130C22#1458351911yescharacteristic
1131C22#1458352411yescharacteristic
1132C22#1458352411yescharacteristic
1133C22#1458353311yescharacteristic
1134C22#1458354111yescharacteristic
1135C22#1458354211yescharacteristic
1136C22#1458354211yescharacteristic
1137C22#1458355111yescharacteristic
1138C22#1458356411yescharacteristic
1139C22#1458356711yescharacteristic
1140C22#1458360011yescharacteristic
1141C22#1458360511yescharacteristic
1142C22#1458360511yescharacteristic
1143C22#1458360511yescharacteristic
1144C22#1458361111yescharacteristic
1145C22#1458363911yescharacteristic
1146C22#1458364011yescharacteristic
1147C22#1458364511yescharacteristic
1148C22#1458364711yescharacteristic
1149C4—24no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—864no—
1157C4—3441no—
1158C4—1722no—
1159C4—1722no—
1160C4—1722no—
1161C4—1722no—
1162C2—1724no—
1163C2—1724no—
1164C2#1913720611yescharacteristic
1165C2#1913725711yescharacteristic
1166C2#1913739111yescharacteristic
1167C2#1913749611yescharacteristic
1168C2#1913750311yescharacteristic
1169C2#1913762811yescharacteristic
1170C2#1913775011yescharacteristic
1171C2#1914080511yescharacteristic
1172C2#1914086811yescharacteristic
1173C2#1914100611yescharacteristic
1174C2#1914109311yescharacteristic
1175C2#1914131811yescharacteristic
1176C2#1914161611yescharacteristic
1177C2#1914224211yescharacteristic
1178C2#1914229511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1442D43
hypocenterC43#14407
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. C2×#14582773C2semidirect
5. C2×#14582758C2semidirect
6. #19132858C2semidirect
7. #19132841C2semidirect
8. #19132839C2semidirect
9. #19132839C2semidirect
10. #19132839C2semidirect
11. #19132829C2semidirect
12. #19132826C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1442C2semidirect
36. #14582777C4semidirect
84. C22×C4×D43C2×C4semidirect
96. C2×Dic43⋊C4D4semidirect
126. C2×(C2×D43)⋊C4C2×C4semidirect
139. C43⋊#95C2×C4semidirect
155. #95×C43C2×C4semidirect
284. C2×D172C4⋊C4semidirect
579. #1442D43semidirect
645. C43#14407semidirect
745. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828002
C2×#145827772
C2×#145827732
C2×#145827582
#191328582
#191328412
#191328392
#191328292
#191328262
(C2×D43)⋊#952
C43×#14422
#1440743