Finite Group Databasebeta

← #25022980

Subgroups — #25022980

Order 11008.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582777C211yesmaximal, characteristic
2C2×#14582777C211yesmaximal, characteristic
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582770C211yesmaximal, characteristic, complemented
5C2×#95×D43C211yesmaximal, characteristic, complemented
6#19132857C211yesmaximal, characteristic, complemented
7#19132855C211yesmaximal, characteristic, complemented
8#19132850C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132843C211yesmaximal, characteristic, complemented
11#19132839C211yesmaximal, characteristic, complemented
12#19132837C211yesmaximal, 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
19C23×C4×D43C2211yescharacteristic
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
30#14582777—24no—
31#14582777—24no—
32#14582777C418yescomplemented
33#14582770—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
48#95×D43—24no—
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—22no—
59C22×D172—22no—
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172C2×C414yes—
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—22no—
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×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43—41no—
87C22×C4×D43—41no—
88C22×C4×D43—41no—
89C22×C4×D43C2×C414yes—
90C22×C4×D43D414yes—
91C22×C4×D43D414yes—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—41no—
94C2×Dic43⋊C4—41no—
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—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—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)⋊C4—41no—
117C2×(C2×D43)⋊C4—41no—
118C2×(C2×D43)⋊C4—41no—
119C2×(C2×D43)⋊C4C2×C414yes—
120C2×(C2×D43)⋊C4C2×C414yescomplemented
121C2×(C2×D43)⋊C4C2×C414yescomplemented
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95—41no—
134C43⋊#95—41no—
135C43⋊#95C2×C414yescomplemented
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43—22no—
144C2×C4⋊C4×C43—41no—
145C2×C4⋊C4×C43—41no—
146#95×C43—22no—
147#95×C43—22no—
148#95×C43—22no—
149#95×C43—41no—
150#95×C43—41no—
151#95×C43C2×C414yescomplemented
152C24×C43C2411yescharacteristic
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×D43#4112yes—
180C23×D43#4112yes—
181C23×D43#4112yes—
182C23×D43#4112yes—
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×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43C22×C412yes—
228C22×C4×C43C22×C412yes—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C2×D412yes—
231C22×C4×C43C2×D412yes—
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×Dic43—21no—
270C22×Dic43C22×C412yes—
271C22×Dic43C22×C412yes—
272C22×Dic43C2×D412yes—
273C22×Dic43C2×D412yes—
274C2×D172—28no—
275C2×D172—28no—
276C2×D172—28no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×C4×D43—28no—
282C2×C4×D43—28no—
283C2×C4×D43—28no—
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—
293C2×C4×D43—44no—
294C2×C4×D43—44no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—44no—
299C2×C4×D43—44no—
300C2×C4×D43—44no—
301C2×C4×D43—44no—
302C4⋊C4×C43—44no—
303(C2×D43)⋊C4—28no—
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—
310(C2×D43)⋊C4—44no—
311(C2×D43)⋊C4—44no—
312Dic43⋊C4—44no—
313C23×C43C23×C411yescharacteristic
314C23×C43C22×D411yescharacteristic
315C23×C43C22×D411yescharacteristic
316C23×C43C2×#4111yescharacteristic
317C23×C43C2×#4111yescharacteristic
318C23×C43C2×#4111yescharacteristic
319C23×C43C2×#4111yescharacteristic
320C23×C43H(5,𝔽2)11yescharacteristic
321C23×C43H(5,𝔽2)11yescharacteristic
322C23×C43H(5,𝔽2)11yescharacteristic
323C23×C43H(5,𝔽2)11yescharacteristic
324C23×C43H(5,𝔽2)11yescharacteristic
325C23×C43H(5,𝔽2)11yescharacteristic
326C23×C432−1+411yescharacteristic
327C23×C432−1+411yescharacteristic
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—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—
391C22×D43#11714yes—
392C22×D43C4×D414yes—
393C22×D43C4×D414yes—
394C22×D43#12114yes—
395C22×D43#12314yes—
396C22×D43#12414yes—
397C22×D43#12614yes—
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×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×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—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—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—41no—
489D172—416no—
490C4×D43—416no—
491C4×D43—416no—
492C4×D43—416no—
493#14259—431nomaximal, Sylow
494C22×C43C2×#11711yescharacteristic
495C22×C43C2×C4×D411yescharacteristic
496C22×C43C2×C4×D411yescharacteristic
497C22×C43#51811yescharacteristic
498C22×C43#51811yescharacteristic
499C22×C43#52011yescharacteristic
500C22×C43#52011yescharacteristic
501C22×C43C2×#12111yescharacteristic
502C22×C43C2×#12311yescharacteristic
503C22×C43C2×#12411yescharacteristic
504C22×C43C2×#12611yescharacteristic
505C22×C43#53411yescharacteristic
506C22×C43#53411yescharacteristic
507C22×C43#53411yescharacteristic
508C22×C43#53411yescharacteristic
509C22×C43#53511yescharacteristic
510C22×C43#53611yescharacteristic
511C22×C43#53711yescharacteristic
512C22×C43#53711yescharacteristic
513C22×C43#53811yescharacteristic
514C22×C43#53811yescharacteristic
515C22×C43#53811yescharacteristic
516C22×C43#53811yescharacteristic
517C22×C43#53811yescharacteristic
518C22×C43#53811yescharacteristic
519C22×C43#53811yescharacteristic
520C22×C43#53811yescharacteristic
521C22×C43#53911yescharacteristic
522C22×C43#53911yescharacteristic
523C22×C43#53911yescharacteristic
524C22×C43#53911yescharacteristic
525C22×C43#53911yescharacteristic
526C22×C43#53911yescharacteristic
527C22×C43#53911yescharacteristic
528C22×C43#53911yescharacteristic
529C2×D43—24no—
530C2×D43—24no—
531C2×D43—24no—
532C2×D43—24no—
533C2×D43—24no—
534C2×D43—24no—
535C2×D43—24no—
536C2×D43—24no—
537C2×D43—24no—
538C2×D43—24no—
539C2×D43—24no—
540C2×D43—24no—
541C2×D43—24no—
542C2×D43—24no—
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—
558C2×D43#38818yes—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—42no—
564C4×C43—81no—
565C4×C43—81no—
566Dic43—42no—
567Dic43—42no—
568Dic43—42no—
569Dic43—42no—
570Dic43—81no—
571Dic43—81no—
572C2×#386—431no—
573C2×#386—431no—
574C2×#386—431no—
575C2×#385—431no—
576C22×#95—431no—
577#1443—431no—
578#1443—431no—
579#1442—431no—
580#1442D4311yescharacteristic, complemented
581#1440—431no—
582#1440—431no—
583#1439—431no—
584#1439—431no—
585C22⋊#95—431no—
586C22⋊#95—431no—
587C2×C43C2×#38811yescharacteristic
588C2×C43#231811yescharacteristic
589C2×C43#231811yescharacteristic
590C2×C43#232111yescharacteristic
591C2×C43#232211yescharacteristic
592C2×C43#232511yescharacteristic
593C2×C43#232511yescharacteristic
594C2×C43#261711yescharacteristic
595C2×C43#261811yescharacteristic
596C2×C43#262211yescharacteristic
597C2×C43#262311yescharacteristic
598C2×C43#263911yescharacteristic
599C2×C43#263911yescharacteristic
600C2×C43#264311yescharacteristic
601C2×C43#264311yescharacteristic
602D43—28no—
603D43—82no—
604C23×D4—431no—
605C24×C4—431no—
606C24×C4—431no—
607C24×C4—431no—
608C22×C4⋊C4—431no—
609C22×C4⋊C4C2×D4311yescharacteristic
610C22×C22⋊C4—431no—
611C22×C22⋊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—
619#386—438no—
620#386—864no—
621#386—864no—
622#385—864no—
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×#95—431no—
634C2×#95—431no—
635C2×#95—431no—
636C2×#95—431no—
637C2×#95—864no—
638C2×#95C2×D4311yescharacteristic
639C2×#95C2×D4311yescharacteristic
640C2×#95C2×D4311yescharacteristic
641C2×#95C2×D4311yescharacteristic
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C43#1425911yescharacteristic, complemented, Sylow
645C25—431no—
646C25—431no—
647C22×D4—434no—
648C22×D4—862no—
649C22×D4—862no—
650C22×D4—862no—
651C22×D4—862no—
652C22×D4—862no—
653C22×D4—862no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—434no—
659C23×C4—434no—
660C23×C4—434no—
661C23×C4—431no—
662C23×C4—431no—
663C23×C4—862no—
664C23×C4—862no—
665C23×C4—862no—
666C23×C4—862no—
667C23×C4—862no—
668C23×C4—862no—
669C23×C4—1721no—
670C23×C4—1721no—
671C23×C4—1721no—
672C23×C4—1721no—
673C23×C4—1721no—
674C23×C4—1721no—
675C23×C4—1721no—
676C23×C4—1721no—
677C23×C4—1721no—
678C23×C4—1721no—
679C23×C4—1721no—
680C23×C4—1721no—
681C23×C4C22×D4311yescharacteristic
682C23×C4C22×D4311yescharacteristic
683C23×C4C22×D4311yescharacteristic
684C23×C4C22×D4311yescharacteristic
685C23×C4C22×D4311yescharacteristic
686C23×C4C22×D4311yescharacteristic
687C23×C4C22×D4311yescharacteristic
688C2×C4⋊C4—22no—
689C2×C4⋊C4—41no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—862no—
692C2×C4⋊C4—1721no—
693C2×C4⋊C4—1721no—
694C2×C22⋊C4—434no—
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—1721no—
710C2×C22⋊C4—1721no—
711C2×C22⋊C4—1721no—
712C2×C22⋊C4—1721no—
713C2×C22⋊C4—1721no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4—1721no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—41no—
725#95—41no—
726#95—434no—
727#95—862no—
728#95—862no—
729#95—862no—
730#95—862no—
731#95—862no—
732#95—862no—
733#95—862no—
734#95—1721no—
735#95—1721no—
736#95—1721no—
737#95—1721no—
738#95—1721no—
739#95—1721no—
740#95C4×D4314yescomplemented
741C24—432no—
742C24—432no—
743C24—432no—
744C24—432no—
745C24—432no—
746C24—432no—
747C24—432no—
748C24—432no—
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—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24C23×D4311yescharacteristic
772C2×D4—868no—
773C2×D4—868no—
774C2×D4—868no—
775C2×D4—1724no—
776C2×D4—1724no—
777C2×D4—1724no—
778C2×D4—1724no—
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—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—432no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—868no—
828C22×C4—868no—
829C22×C4—868no—
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—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—1724no—
869C22×C4—1724no—
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×C4—1724no—
884C22×C4—1724no—
885C22×C4—1724no—
886C22×C4C2×C4×D4312yes—
887C22×C4C2×C4×D4312yes—
888C22×C4C2×C4×D4312yes—
889C22×C4D4×D4312yes—
890C22×C4D4×D4312yes—
891C4⋊C4—44no—
892C4⋊C4—1724no—
893C22⋊C4—868no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C22⋊C4—1724no—
899C22⋊C4—1724no—
900C22⋊C4—1724no—
901C22⋊C4—1724no—
902C23—434no—
903C23—434no—
904C23—434no—
905C23—434no—
906C23—434no—
907C23—434no—
908C23—434no—
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—862no—
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—
972C23C22×C4×D4311yescharacteristic
973C23C2×D4×D4311yescharacteristic
974C23C2×D4×D4311yescharacteristic
975C23#41×D4311yescharacteristic
976C23#41×D4311yescharacteristic
977C23#41×D4311yescharacteristic
978C23#41×D4311yescharacteristic
979C23#1306337011yescharacteristic
980C23#1306337011yescharacteristic
981C23#1306337111yescharacteristic
982C23#1306337111yescharacteristic
983C23#1306337111yescharacteristic
984C23#1306337111yescharacteristic
985C23#1306337311yescharacteristic
986C23#1306337311yescharacteristic
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—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—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—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—17216no—
1050C2×C4—17216no—
1051C2×C4—17216no—
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×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—
1082C22—438no—
1083C22—864no—
1084C22—864no—
1085C22—864no—
1086C22—864no—
1087C22—864no—
1088C22—864no—
1089C22—864no—
1090C22—864no—
1091C22—864no—
1092C22—864no—
1093C22—864no—
1094C22—864no—
1095C22—864no—
1096C22—864no—
1097C22—3441no—
1098C22—3441no—
1099C22—3441no—
1100C22—3441no—
1101C22—3441no—
1102C22—3441no—
1103C22—3441no—
1104C22—3441no—
1105C22—1722no—
1106C22—1722no—
1107C22—1722no—
1108C22—1722no—
1109C22—1722no—
1110C22—1722no—
1111C22—1722no—
1112C22#117×D4311yescharacteristic
1113C22C4×D4×D4311yescharacteristic
1114C22C4×D4×D4311yescharacteristic
1115C22#1458337111yescharacteristic
1116C22#1458337311yescharacteristic
1117C22#1458338011yescharacteristic
1118C22#1458338111yescharacteristic
1119C22#121×D4311yescharacteristic
1120C22#123×D4311yescharacteristic
1121C22#124×D4311yescharacteristic
1122C22#126×D4311yescharacteristic
1123C22#1458345711yescharacteristic
1124C22#1458345911yescharacteristic
1125C22#1458346011yescharacteristic
1126C22#1458346011yescharacteristic
1127C22#1458346511yescharacteristic
1128C22#1458347411yescharacteristic
1129C22#1458347911yescharacteristic
1130C22#1458347911yescharacteristic
1131C22#1458348311yescharacteristic
1132C22#1458348311yescharacteristic
1133C22#1458348311yescharacteristic
1134C22#1458348511yescharacteristic
1135C22#1458348511yescharacteristic
1136C22#1458348811yescharacteristic
1137C22#1458348811yescharacteristic
1138C22#1458348811yescharacteristic
1139C22#1458349511yescharacteristic
1140C22#1458349511yescharacteristic
1141C22#1458349511yescharacteristic
1142C22#1458349711yescharacteristic
1143C22#1458349711yescharacteristic
1144C22#1458349711yescharacteristic
1145C22#1458349711yescharacteristic
1146C22#1458349711yescharacteristic
1147C4—42no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—81no—
1153C4—81no—
1154C4—3441no—
1155C4—3441no—
1156C4—1722no—
1157C4—1722no—
1158C4—1722no—
1159C4—1722no—
1160C2—868no—
1161C2—3442no—
1162C2#388×D4311yescharacteristic
1163C2#1913722711yescharacteristic
1164C2#1913723111yescharacteristic
1165C2#1913725711yescharacteristic
1166C2#1913725911yescharacteristic
1167C2#1913729211yescharacteristic
1168C2#1913729411yescharacteristic
1169C2#1914033411yescharacteristic
1170C2#1914033811yescharacteristic
1171C2#1914036911yescharacteristic
1172C2#1914037611yescharacteristic
1173C2#1914052411yescharacteristic
1174C2#1914052711yescharacteristic
1175C2#1914054911yescharacteristic
1176C2#1914054911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1442D43
hypocenterC43#14259
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. C2×#14582770C2semidirect
5. C2×#95×D43C2semidirect
6. #19132857C2semidirect
7. #19132855C2semidirect
8. #19132850C2semidirect
9. #19132843C2semidirect
10. #19132843C2semidirect
11. #19132839C2semidirect
12. #19132837C2semidirect
13. (C2×D43)⋊#95C2semidirect
14. (C2×D43)⋊#95C2semidirect
15. C43×#1442C2semidirect
32. #14582777C4semidirect
120. C2×(C2×D43)⋊C4C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
135. C43⋊#95C2×C4semidirect
151. #95×C43C2×C4semidirect
580. #1442D43semidirect
644. C43#14259semidirect
740. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827772
C2×#145827702
C2×#95×D432
#191328572
#191328552
#191328502
#191328432
#191328392
#191328372
(C2×D43)⋊#952
C43×#14422
#1425943