Finite Group Databasebeta

← #25025917

Subgroups — #25025917

Order 11008.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582816C211yesmaximal, characteristic
2C2×#14582801C211yesmaximal, characteristic
3C2×#14582798C211yesmaximal, characteristic, complemented
4C2×#14582788C211yesmaximal, characteristic, complemented
5C2×#14582777C211yesmaximal, characteristic
6C2×#14582773C211yesmaximal, characteristic, complemented
7C2×#14582773C211yesmaximal, characteristic, complemented
8#19132859C211yesmaximal, characteristic, complemented
9#19132843C211yesmaximal, characteristic, complemented
10#19132841C211yesmaximal, characteristic, complemented
11#19132841C211yesmaximal, characteristic, complemented
12#19132839C211yesmaximal, characteristic, complemented
13#19132831C211yesmaximal, characteristic, complemented
14#19132822C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582816C418yescomplemented
36#14582801—24no—
37#14582798—24no—
38#14582788—24no—
39#14582777—24no—
40#14582773—24no—
41#14582773—24no—
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×C4⋊C4×C43C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C24×D43C2311yescharacteristic
60C22×D172—22no—
61C22×D172—22no—
62C22×D172—22no—
63C22×D172—22no—
64C22×D172—41no—
65C22×D172—41no—
66C22×D172C2×C414yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69C23×Dic43C2311yescharacteristic
70C23×Dic43C2311yescharacteristic
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2311yescharacteristic
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—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—22no—
83C2×C4⋊Dic43—22no—
84C2×C4⋊Dic43—22no—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—41no—
87C2×C4⋊Dic43—41no—
88C2×C4⋊Dic43—41no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—41no—
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—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)⋊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)⋊C4C2×C414yes—
124C2×(C2×D43)⋊C4C2×C414yes—
125C2×(C2×D43)⋊C4C2×C414yescomplemented
126C2×(C2×D43)⋊C4C2×C414yescomplemented
127C2×(C2×D43)⋊C4D414yes—
128C2×C4×Dic43—22no—
129C2×C4×Dic43—22no—
130C2×C4×Dic43—41no—
131C43⋊#95—22no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C43⋊#95—22no—
135C43⋊#95—41no—
136C43⋊#95—41no—
137C43⋊#95—41no—
138C43⋊#95C2×C414yescomplemented
139C43⋊#95D414yes—
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—22no—
149C2×C4⋊C4×C43C2×C414yescomplemented
150C2×C42×C43—22no—
151C2×C42×C43—22no—
152C2×C42×C43—41no—
153#95×C43—22no—
154#95×C43—22no—
155#95×C43—22no—
156#95×C43—41no—
157#95×C43D414yescomplemented
158C24×C43C2411yescharacteristic
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×D43—21no—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43C22×C412yes—
186C23×D43C22×C412yes—
187C23×D43C2×D412yes—
188C23×D43#4112yes—
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×C43C22×C412yes—
229C22×C4×C43C22×C412yes—
230C22×C4×C43C22×C412yes—
231C22×C4×C43C2×D412yes—
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2×D412yes—
235C22×C4×C43C2×D412yes—
236C22×C4×C43#4112yes—
237C22×C4×C43#4112yes—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—21no—
264C22×Dic43—21no—
265C22×Dic43—21no—
266C22×Dic43—21no—
267C22×Dic43—21no—
268C22×Dic43—21no—
269C22×Dic43—21no—
270C22×Dic43—21no—
271C22×Dic43—21no—
272C22×Dic43—21no—
273C22×Dic43—21no—
274C22×Dic43—21no—
275C22×Dic43C22×C412yes—
276C22×Dic43C22×C412yes—
277C22×Dic43C2×D412yes—
278C22×Dic43C2×D412yes—
279C22×Dic43C2×D412yes—
280C2×D172—28no—
281C2×D172—28no—
282C2×D172—44no—
283C2×D172—44no—
284C2×D172—44no—
285C2×D172—44no—
286C2×D172—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—
294C4⋊C4×C43—28no—
295C42×C43—44no—
296(C2×D43)⋊C4—28no—
297(C2×D43)⋊C4—28no—
298(C2×D43)⋊C4—28no—
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—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307C4⋊Dic43—44no—
308C4⋊Dic43—44no—
309C4⋊Dic43—44no—
310Dic43⋊C4—44no—
311Dic43⋊C4—44no—
312C4×Dic43—44no—
313C23×C43C23×C411yescharacteristic
314C23×C43C22×D411yescharacteristic
315C23×C43C22×D411yescharacteristic
316C23×C43C22×D411yescharacteristic
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×C432−1+411yescharacteristic
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—41no—
354C22×D43—41no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
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×D43—41no—
391C22×D43—41no—
392C22×D43—41no—
393C22×D43—41no—
394C22×D43—41no—
395C22×D43—41no—
396C22×D43—41no—
397C22×D43C4×D414yes—
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—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—22no—
421C2×C4×C43—22no—
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×C43C4×D414yes—
446C2×C4×C43C4×D414yes—
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—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—
491#14518—431nomaximal, Sylow
492C22×C43C2×C4×D411yescharacteristic
493C22×C43C2×C4×D411yescharacteristic
494C22×C43C2×C4×D411yescharacteristic
495C22×C43#51811yescharacteristic
496C22×C43#52011yescharacteristic
497C22×C43#52011yescharacteristic
498C22×C43#52011yescharacteristic
499C22×C43#53411yescharacteristic
500C22×C43#53511yescharacteristic
501C22×C43#53511yescharacteristic
502C22×C43#53611yescharacteristic
503C22×C43#53611yescharacteristic
504C22×C43#53711yescharacteristic
505C22×C43#53911yescharacteristic
506C22×C43#53911yescharacteristic
507C22×C43#54011yescharacteristic
508C22×C43#54211yescharacteristic
509C22×C43#54211yescharacteristic
510C22×C43#54211yescharacteristic
511C22×C43D4211yescharacteristic
512C22×C43D4211yescharacteristic
513C22×C43D4211yescharacteristic
514C22×C43#54611yescharacteristic
515C22×C43#54611yescharacteristic
516C22×C43#54711yescharacteristic
517C22×C43#54711yescharacteristic
518C22×C43#54811yescharacteristic
519C22×C43#54811yescharacteristic
520C22×C43#55111yescharacteristic
521C22×C43#55311yescharacteristic
522C22×C43#55311yescharacteristic
523C22×C43#56011yescharacteristic
524C22×C43#56211yescharacteristic
525C22×C43#56211yescharacteristic
526C22×C43#56311yescharacteristic
527C2×D43—24no—
528C2×D43—24no—
529C2×D43—24no—
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—81no—
550C2×D43—81no—
551C2×D43—81no—
552C2×D43—81no—
553C2×D43—81no—
554C2×D43—81no—
555C2×D43—81no—
556C2×D43—81no—
557C4×C43—24no—
558C4×C43—24no—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563C4×C43—81no—
564Dic43—42no—
565Dic43—42no—
566Dic43—42no—
567Dic43—42no—
568Dic43—42no—
569Dic43—81no—
570C2×#394—431no—
571C2×#390—431no—
572C2×#389—431no—
573C2×#388—431no—
574C2×#386—431no—
575C2×#385—431no—
576C2×#385—431no—
577#1444—431no—
578#1440—431no—
579#1439—431no—
580#1439—431no—
581#1439—431no—
582#1437—431no—
583#1436D4311yescharacteristic, complemented
584#1434—431no—
585C2×C43#232211yescharacteristic
586C2×C43#232411yescharacteristic
587C2×C43#232611yescharacteristic
588C2×C43#235811yescharacteristic
589C2×C43#236111yescharacteristic
590C2×C43#236111yescharacteristic
591C2×C43#237611yescharacteristic
592C2×C43#266911yescharacteristic
593C2×C43#267211yescharacteristic
594C2×C43#267411yescharacteristic
595C2×C43#268111yescharacteristic
596C2×C43#270111yescharacteristic
597C2×C43#271111yescharacteristic
598C2×C43#272311yescharacteristic
599C2×C43#275711yescharacteristic
600D43—44no—
601D43—82no—
602C23×D4—431no—
603C24×C4—431no—
604C22×C4⋊C4—431no—
605C22×C4⋊C4—431no—
606C22×C4⋊C4—431no—
607C22×C4⋊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—
619C22×C22⋊C4—431no—
620C22×C22⋊C4—431no—
621C22×C42—431no—
622C22×C42C2×D4311yescharacteristic
623#394—438no—
624#390—864no—
625#389—864no—
626#388—864no—
627#386—864no—
628#385—864no—
629#385—864no—
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
644C43#1451811yescharacteristic, complemented, Sylow
645C25—431no—
646C25—431no—
647C22×D4—434no—
648C22×D4—862no—
649C22×D4—862no—
650C22×D4—862no—
651C22×D4—862no—
652C22×D4—1721no—
653C22×D4—1721no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—431no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—862no—
661C23×C4—862no—
662C23×C4—862no—
663C23×C4—1721no—
664C23×C4—1721no—
665C23×C4—1721no—
666C23×C4—1721no—
667C23×C4C22×D4311yescharacteristic
668C23×C4C22×D4311yescharacteristic
669C23×C4C22×D4311yescharacteristic
670C23×C4C22×D4311yescharacteristic
671C23×C4C22×D4311yescharacteristic
672C23×C4C22×D4311yescharacteristic
673C23×C4C22×D4311yescharacteristic
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—862no—
677C2×C4⋊C4—862no—
678C2×C4⋊C4—862no—
679C2×C4⋊C4—862no—
680C2×C4⋊C4—862no—
681C2×C4⋊C4—862no—
682C2×C4⋊C4—862no—
683C2×C4⋊C4—862no—
684C2×C4⋊C4—862no—
685C2×C4⋊C4—1721no—
686C2×C4⋊C4—1721no—
687C2×C4⋊C4—1721no—
688C2×C4⋊C4—1721no—
689C2×C4⋊C4—1721no—
690C2×C4⋊C4—1721no—
691C2×C4⋊C4C4×D4314yescomplemented
692C2×C22⋊C4—434no—
693C2×C22⋊C4—434no—
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—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
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—
721C2×C22⋊C4—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4—1721no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—1721no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—41no—
735#95—434no—
736#95—434no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—862no—
741#95—1721no—
742#95—1721no—
743#95—1721no—
744#95D17214yescomplemented
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—
771C24—861no—
772C24—861no—
773C24—861no—
774C24—861no—
775C24C23×D4311yescharacteristic
776C2×D4—868no—
777C2×D4—868no—
778C2×D4—1724no—
779C2×D4—1724no—
780C2×D4—1724no—
781C2×D4—1724no—
782C2×D4—1724no—
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—432no—
823C22×C4—432no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—432no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—861no—
831C22×C4—861no—
832C22×C4—861no—
833C22×C4—861no—
834C22×C4—861no—
835C22×C4—861no—
836C22×C4—861no—
837C22×C4—861no—
838C22×C4—861no—
839C22×C4—861no—
840C22×C4—861no—
841C22×C4—861no—
842C22×C4—861no—
843C22×C4—861no—
844C22×C4—861no—
845C22×C4—861no—
846C22×C4—861no—
847C22×C4—861no—
848C22×C4—861no—
849C22×C4—861no—
850C22×C4—861no—
851C22×C4—861no—
852C22×C4—861no—
853C22×C4—861no—
854C22×C4—861no—
855C22×C4—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—1724no—
865C22×C4—1724no—
866C22×C4—1724no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4C2×C4×D4312yes—
872C22×C4C2×C4×D4312yes—
873C22×C4C2×C4×D4312yes—
874C22×C4C2×D17212yes—
875C22×C4C2×D17212yes—
876C22×C4C2×D17212yes—
877C22×C4#1062189812yes—
878C22×C4D4×D4312yes—
879C22×C4D4×D4312yes—
880C22×C4#1062190012yes—
881C4⋊C4—28no—
882C4⋊C4—1724no—
883C4⋊C4—1724no—
884C4⋊C4—1724no—
885C4⋊C4—1724no—
886C4⋊C4—1724no—
887C22⋊C4—868no—
888C22⋊C4—868no—
889C22⋊C4—868no—
890C22⋊C4—1724no—
891C22⋊C4—1724no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C42—44no—
899C42—1724no—
900C23—434no—
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—1721no—
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—
959C23—1721no—
960C23—1721no—
961C23—1721no—
962C23—1721no—
963C23—1721no—
964C23—1721no—
965C23—1721no—
966C23—1721no—
967C23—1721no—
968C23—1721no—
969C23—1721no—
970C23C22×C4×D4311yescharacteristic
971C23C2×D4×D4311yescharacteristic
972C23C2×D4×D4311yescharacteristic
973C23C22×D17211yescharacteristic
974C23#41×D4311yescharacteristic
975C23C2×#1062190011yescharacteristic
976C23C2×#1062189811yescharacteristic
977C23#1306337011yescharacteristic
978C23#1306337111yescharacteristic
979C23#1306337111yescharacteristic
980C23#1306337111yescharacteristic
981C23#1306337111yescharacteristic
982C23#1306337211yescharacteristic
983C23#1306337311yescharacteristic
984C23#1306337311yescharacteristic
985D4—17216no—
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—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—22no—
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—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—17216no—
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×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(C22⋊D43)⋊C414yes—
1077C2×C4C4×D17214yes—
1078C22—864no—
1079C22—864no—
1080C22—864no—
1081C22—3441no—
1082C22—3441no—
1083C22—3441no—
1084C22—3441no—
1085C22—3441no—
1086C22—3441no—
1087C22—3441no—
1088C22—3441no—
1089C22—1722no—
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—
1108C22C4×D4×D4311yescharacteristic
1109C22C2×(C22⋊D43)⋊C411yescharacteristic
1110C22C2×C4×D17211yescharacteristic
1111C22#1458337111yescharacteristic
1112C22#1458337911yescharacteristic
1113C22#1458338111yescharacteristic
1114C22#1458338111yescharacteristic
1115C22#1458346011yescharacteristic
1116C22#1458346711yescharacteristic
1117C22#1458346811yescharacteristic
1118C22#1458347211yescharacteristic
1119C22#1458347411yescharacteristic
1120C22#1458348011yescharacteristic
1121C22#1458349011yescharacteristic
1122C22#1458349711yescharacteristic
1123C22#1458350011yescharacteristic
1124C22#1458352111yescharacteristic
1125C22#1458352211yescharacteristic
1126C22#1458352211yescharacteristic
1127C22#1458353311yescharacteristic
1128C22D4×D17211yescharacteristic
1129C22D4×D17211yescharacteristic
1130C22#1458353611yescharacteristic
1131C22#1458353811yescharacteristic
1132C22#1458355011yescharacteristic
1133C22#1458355311yescharacteristic
1134C22#1458355811yescharacteristic
1135C22#1458356111yescharacteristic
1136C22#1458357211yescharacteristic
1137C22#1458359311yescharacteristic
1138C22#1458359511yescharacteristic
1139C22#1458364011yescharacteristic
1140C22#1458364511yescharacteristic
1141C22#1458364611yescharacteristic
1142C22#1458365311yescharacteristic
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—3441no—
1151C4—1722no—
1152C4—1722no—
1153C4—1722no—
1154C4—1722no—
1155C4—1722no—
1156C2—3442no—
1157C2—1724no—
1158C2#1913726811yescharacteristic
1159C2#1913728911yescharacteristic
1160C2#1913730911yescharacteristic
1161C2#1913757511yescharacteristic
1162C2#1913760911yescharacteristic
1163C2#1913761311yescharacteristic
1164C2#1913774211yescharacteristic
1165C2#1914081011yescharacteristic
1166C2#1914084911yescharacteristic
1167C2#1914087711yescharacteristic
1168C2#1914094211yescharacteristic
1169C2#1914121211yescharacteristic
1170C2#1914134911yescharacteristic
1171C2#1914151211yescharacteristic
1172C2#1914193611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14518
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
3. C2×#14582798C2semidirect
4. C2×#14582788C2semidirect
6. C2×#14582773C2semidirect
7. C2×#14582773C2semidirect
8. #19132859C2semidirect
9. #19132843C2semidirect
10. #19132841C2semidirect
11. #19132841C2semidirect
12. #19132839C2semidirect
13. #19132831C2semidirect
14. #19132822C2semidirect
15. C43×#1436C2semidirect
35. #14582816C4semidirect
125. C2×(C2×D43)⋊C4C2×C4semidirect
126. C2×(C2×D43)⋊C4C2×C4semidirect
138. C43⋊#95C2×C4semidirect
149. C2×C4⋊C4×C43C2×C4semidirect
157. #95×C43D4semidirect
583. #1436D43semidirect
644. C43#14518semidirect
691. C2×C4⋊C4C4×D43semidirect
744. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828162
C2×#145828012
C2×#145827982
C2×#145827882
C2×#145827772
C2×#145827732
#191328592
#191328432
#191328412
#191328392
#191328312
#191328222
C43×#14362
#1451843