Finite Group Databasebeta

← #25025913

Subgroups — #25025913

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×#14582815C211yesmaximal, characteristic
2C2×#14582799C211yesmaximal, characteristic
3C2×#14582797C211yesmaximal, characteristic, complemented
4C2×#14582775C211yesmaximal, characteristic
5C2×#14582773C211yesmaximal, characteristic, complemented
6C2×#14582770C211yesmaximal, characteristic, complemented
7#19132858C211yesmaximal, characteristic, complemented
8#19132843C211yesmaximal, characteristic, complemented
9#19132840C211yesmaximal, characteristic, complemented
10#19132838C211yesmaximal, characteristic, complemented
11#19132838C211yesmaximal, characteristic, complemented
12#19132833C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, characteristic, complemented
14#19132821C211yesmaximal, characteristic, complemented
15C2×C43×#388C211yesmaximal, characteristic, complemented
16C23×C22⋊D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×Dic43⋊C4C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×C4×Dic43C2211yescharacteristic
32#14582815C418yescomplemented
33#14582799—24no—
34#14582797—24no—
35#14582775—24no—
36#14582773—24no—
37#14582770—24no—
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
48C2×C43⋊#95C2211yescharacteristic
49C2×C43⋊#95C2211yescharacteristic
50C22×C4⋊C4×C43C2211yescharacteristic
51C22×C22⋊C4×C43C2211yescharacteristic
52C22×C22⋊C4×C43C2211yescharacteristic
53C22×C22⋊C4×C43C2211yescharacteristic
54C22×C42×C43C2211yescharacteristic
55C43×#388—24no—
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C24×D43C2311yescharacteristic
59C22×C22⋊D43—22no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43—22no—
63C22×C22⋊D43—41no—
64C22×C22⋊D43—41no—
65C22×C22⋊D43C2×C414yes—
66C23×Dic43C2311yescharacteristic
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—41no—
85C2×C4⋊Dic43C2×C414yescomplemented
86C2×Dic43⋊C4—22no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4—22no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—41no—
92C2×Dic43⋊C4—41no—
93C2×Dic43⋊C4—41no—
94C2×Dic43⋊C4—41no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—41no—
98C2×C22⋊Dic43—41no—
99C2×C22⋊Dic43—41no—
100C2×C22⋊Dic43—41no—
101C2×C22⋊Dic43—41no—
102C2×C22⋊Dic43—41no—
103C2×C22⋊Dic43C2×C414yescomplemented
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)⋊C4C2×C414yes—
117C2×(C2×D43)⋊C4C2×C414yes—
118C2×(C2×D43)⋊C4D414yes—
119C2×C4×Dic43—22no—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—41no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95C2×C414yescomplemented
133C43⋊#95D414yes—
134C25×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43—22no—
143C2×C4⋊C4×C43—41no—
144C2×C22⋊C4×C43—22no—
145C2×C22⋊C4×C43—22no—
146C2×C22⋊C4×C43—22no—
147C2×C22⋊C4×C43—22no—
148C2×C22⋊C4×C43—22no—
149C2×C22⋊C4×C43—22no—
150C2×C22⋊C4×C43—41no—
151C2×C22⋊C4×C43—41no—
152C2×C22⋊C4×C43C2×C414yescomplemented
153C2×C42×C43—22no—
154C2×C42×C43—22no—
155C2×C42×C43—41no—
156#95×C43—22no—
157#95×C43D414yescomplemented
158C24×C43—21no—
159C24×C43—21no—
160C24×C43—21no—
161C24×C43—21no—
162C24×C43—21no—
163C24×C43—21no—
164C24×C43—21no—
165C24×C43—21no—
166C24×C43—21no—
167C24×C43—21no—
168C24×C43—21no—
169C24×C43—21no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43C22×C412yes—
173C24×C43C2411yescharacteristic
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×D43—21no—
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×C43C22×C412yes—
224C22×C4×C43C22×C412yes—
225C22×C4×C43C2×D412yes—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D412yes—
229C22×C4×C43C2×D412yes—
230C22×C4×C43#4112yes—
231C2×C22⋊D43—28no—
232C2×C22⋊D43—28no—
233C2×C22⋊D43—44no—
234C2×C22⋊D43—44no—
235C2×C22⋊D43—44no—
236C2×C22⋊D43—44no—
237C2×C22⋊D43—44no—
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×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—21no—
279C22×Dic43—21no—
280C22×Dic43C22×C412yes—
281C22×Dic43C22×C412yes—
282C22×Dic43C22×C412yes—
283C22×Dic43C2×D412yes—
284C22×Dic43C2×D412yes—
285C22×Dic43C2×D412yes—
286C22×Dic43#4112yes—
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—44no—
295C22⋊C4×C43—28no—
296C22⋊C4×C43—44no—
297C22⋊C4×C43—44no—
298C42×C43—44no—
299C22⋊Dic43—44no—
300C22⋊Dic43—44no—
301C22⋊Dic43—44no—
302(C2×D43)⋊C4—28no—
303(C2×D43)⋊C4—28no—
304(C2×D43)⋊C4—44no—
305(C2×D43)⋊C4—44no—
306(C2×D43)⋊C4—44no—
307C4⋊Dic43—28no—
308C4⋊Dic43—44no—
309Dic43⋊C4—44no—
310Dic43⋊C4—44no—
311Dic43⋊C4—44no—
312C4×Dic43—44no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—22no—
320C23×C43—41no—
321C23×C43—41no—
322C23×C43—41no—
323C23×C43—41no—
324C23×C43—41no—
325C23×C43—41no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43C23×C411yescharacteristic
349C23×C43C22×D411yescharacteristic
350C23×C43C22×D411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C23×C43C2×#4111yescharacteristic
353C23×C43C2×#4111yescharacteristic
354C23×C43C2×#4111yescharacteristic
355C23×C43H(5,𝔽2)11yescharacteristic
356C23×C43H(5,𝔽2)11yescharacteristic
357C23×C43H(5,𝔽2)11yescharacteristic
358C23×C43H(5,𝔽2)11yescharacteristic
359C23×C43H(5,𝔽2)11yescharacteristic
360C23×C432−1+411yescharacteristic
361C23×C432−1+411yescharacteristic
362C23×C432−1+411yescharacteristic
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—22no—
375C22×D43—22no—
376C22×D43—22no—
377C22×D43—22no—
378C22×D43—22no—
379C22×D43—22no—
380C22×D43—22no—
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—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×C43C4×D414yes—
440C22⋊D43—416no—
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—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—
489C2×Dic43C4×D414yes—
490C4×D43—416no—
491#14518—431nomaximal, Sylow
492C22×C43—42no—
493C22×C43—42no—
494C22×C43—42no—
495C22×C43—42no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43—81no—
500C22×C43—81no—
501C22×C43—81no—
502C22×C43—81no—
503C22×C43—81no—
504C22×C43—81no—
505C22×C43—81no—
506C22×C43—81no—
507C22×C43C2×C4×D411yescharacteristic
508C22×C43C2×C4×D411yescharacteristic
509C22×C43C2×C4×D411yescharacteristic
510C22×C43#51811yescharacteristic
511C22×C43#52011yescharacteristic
512C22×C43#52011yescharacteristic
513C22×C43#52011yescharacteristic
514C22×C43#53411yescharacteristic
515C22×C43#53511yescharacteristic
516C22×C43#53511yescharacteristic
517C22×C43#53611yescharacteristic
518C22×C43#53611yescharacteristic
519C22×C43#53711yescharacteristic
520C22×C43#53911yescharacteristic
521C22×C43#53911yescharacteristic
522C22×C43#54011yescharacteristic
523C22×C43#54211yescharacteristic
524C22×C43#54211yescharacteristic
525C22×C43#54211yescharacteristic
526C22×C43D4211yescharacteristic
527C22×C43D4211yescharacteristic
528C22×C43D4211yescharacteristic
529C22×C43#54611yescharacteristic
530C22×C43#54611yescharacteristic
531C22×C43#54711yescharacteristic
532C22×C43#54711yescharacteristic
533C22×C43#54811yescharacteristic
534C22×C43#54811yescharacteristic
535C22×C43#55111yescharacteristic
536C22×C43#55311yescharacteristic
537C22×C43#55311yescharacteristic
538C22×C43#56011yescharacteristic
539C22×C43#56211yescharacteristic
540C22×C43#56211yescharacteristic
541C22×C43#56311yescharacteristic
542C2×D43—24no—
543C2×D43—24no—
544C2×D43—24no—
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—
557C4×C43—24no—
558C4×C43—42no—
559C4×C43—42no—
560C4×C43—42no—
561C4×C43—42no—
562C4×C43—42no—
563Dic43—24no—
564Dic43—42no—
565Dic43—42no—
566Dic43—42no—
567Dic43—42no—
568Dic43—81no—
569Dic43—81no—
570C2×#394—431no—
571C2×#390—431no—
572C2×#389—431no—
573C2×#388D4311yescharacteristic, complemented
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#1436—431no—
584#1434—431no—
585C2×C43—82no—
586C2×C43#232211yescharacteristic
587C2×C43#232411yescharacteristic
588C2×C43#232611yescharacteristic
589C2×C43#235811yescharacteristic
590C2×C43#236111yescharacteristic
591C2×C43#236111yescharacteristic
592C2×C43#237611yescharacteristic
593C2×C43#266911yescharacteristic
594C2×C43#267211yescharacteristic
595C2×C43#267411yescharacteristic
596C2×C43#268111yescharacteristic
597C2×C43#270111yescharacteristic
598C2×C43#271111yescharacteristic
599C2×C43#272311yescharacteristic
600C2×C43#275711yescharacteristic
601D43—44no—
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⋊C4C2×D4311yescharacteristic
619C22×C22⋊C4C2×D4311yescharacteristic
620C22×C22⋊C4C2×D4311yescharacteristic
621C22×C42—431no—
622C22×C42C2×D4311yescharacteristic
623#394—438no—
624#390—864no—
625#389—864no—
626#388—24no—
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×#95—431no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95C2×D4311yescharacteristic
643C2×#95C2×D4311yescharacteristic
644C43#1451811yescharacteristic, complemented, Sylow
645C25—431no—
646C25C22×D4311yescharacteristic
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—431no—
661C23×C4—862no—
662C23×C4—862no—
663C23×C4—862no—
664C23×C4—1721no—
665C23×C4—1721no—
666C23×C4—1721no—
667C23×C4—1721no—
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—41no—
677C2×C4⋊C4—434no—
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—862no—
686C2×C4⋊C4—862no—
687C2×C4⋊C4—1721no—
688C2×C4⋊C4—1721no—
689C2×C4⋊C4—1721no—
690C2×C4⋊C4—1721no—
691C2×C4⋊C4—1721no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—434no—
701C2×C22⋊C4—434no—
702C2×C22⋊C4—434no—
703C2×C22⋊C4—434no—
704C2×C22⋊C4—862no—
705C2×C22⋊C4—862no—
706C2×C22⋊C4—862no—
707C2×C22⋊C4—862no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C22⋊C4—862no—
711C2×C22⋊C4—862no—
712C2×C22⋊C4—862no—
713C2×C22⋊C4—862no—
714C2×C22⋊C4—1721no—
715C2×C22⋊C4—1721no—
716C2×C22⋊C4—1721no—
717C2×C22⋊C4—1721no—
718C2×C22⋊C4—1721no—
719C2×C22⋊C4—1721no—
720C2×C22⋊C4—1721no—
721C2×C22⋊C4—1721no—
722C2×C22⋊C4—1721no—
723C2×C22⋊C4—1721no—
724C2×C22⋊C4C4×D4314yescomplemented
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—41no—
728C2×C42—862no—
729C2×C42—862no—
730C2×C42—1721no—
731#95—22no—
732#95—434no—
733#95—434no—
734#95—862no—
735#95—862no—
736#95—862no—
737#95—862no—
738#95—862no—
739#95—862no—
740#95—1721no—
741#95—1721no—
742#95—1721no—
743#95—1721no—
744#95C22⋊D4314yescomplemented
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—432no—
760C24—432no—
761C24—432no—
762C24—861no—
763C24—861no—
764C24—861no—
765C24—861no—
766C24—861no—
767C24—861no—
768C24—861no—
769C24—861no—
770C24—861no—
771C24—861no—
772C24—861no—
773C24—861no—
774C24C2×C4×D4312yes—
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—432no—
818C22×C4—432no—
819C22×C4—432no—
820C22×C4—432no—
821C22×C4—432no—
822C22×C4—432no—
823C22×C4—432no—
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—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—1724no—
867C22×C4—1724no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1724no—
871C22×C4—1724no—
872C22×C4—1724no—
873C22×C4C2×C4×D4312yes—
874C22×C4C2×C4×D4312yes—
875C22×C4#1062189812yes—
876C22×C4D4×D4312yes—
877C22×C4D4×D4312yes—
878C22×C4C2×C22⋊D4312yes—
879C22×C4C2×C22⋊D4312yes—
880C22×C4C2×C22⋊D4312yes—
881C4⋊C4—44no—
882C4⋊C4—868no—
883C4⋊C4—1724no—
884C4⋊C4—1724no—
885C4⋊C4—1724no—
886C4⋊C4—1724no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—868no—
891C22⋊C4—868no—
892C22⋊C4—1724no—
893C22⋊C4—1724no—
894C22⋊C4—1724no—
895C22⋊C4—1724no—
896C22⋊C4—1724no—
897C22⋊C4—1724no—
898C42—44no—
899C42—1724no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—434no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—862no—
940C23—862no—
941C23—862no—
942C23—862no—
943C23—862no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—862no—
953C23—862no—
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×C22⋊D4311yescharacteristic
974C23#41×D4311yescharacteristic
975C23#41×D4311yescharacteristic
976C23C2×#1062189811yescharacteristic
977C23#1306337011yescharacteristic
978C23#1306337011yescharacteristic
979C23#1306337111yescharacteristic
980C23#1306337111yescharacteristic
981C23#1306337111yescharacteristic
982C23#1306337211yescharacteristic
983C23#1306337211yescharacteristic
984C23#1306337211yescharacteristic
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—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—434no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—862no—
1039C2×C4—862no—
1040C2×C4—862no—
1041C2×C4—862no—
1042C2×C4—862no—
1043C2×C4—862no—
1044C2×C4—862no—
1045C2×C4—862no—
1046C2×C4—17216no—
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×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×C4C4×C22⋊D4314yes—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—864no—
1094C22—864no—
1095C22—864no—
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
1109C22C4×D4×D4311yescharacteristic
1110C22C2×C4×C22⋊D4311yescharacteristic
1111C22#1458337311yescharacteristic
1112C22#1458337811yescharacteristic
1113C22#1458337811yescharacteristic
1114C22#1458337911yescharacteristic
1115C22#1458345711yescharacteristic
1116C22#1458346311yescharacteristic
1117C22#1458346511yescharacteristic
1118C22#1458346911yescharacteristic
1119C22#1458347111yescharacteristic
1120C22#1458347711yescharacteristic
1121C22#1458349011yescharacteristic
1122C22#1458349211yescharacteristic
1123C22#1458350411yescharacteristic
1124C22#1458351311yescharacteristic
1125C22#1458351511yescharacteristic
1126C22#1458352011yescharacteristic
1127C22D4×C22⋊D4311yescharacteristic
1128C22D4×C22⋊D4311yescharacteristic
1129C22#1458353311yescharacteristic
1130C22#1458354111yescharacteristic
1131C22#1458354211yescharacteristic
1132C22#1458354811yescharacteristic
1133C22#1458355411yescharacteristic
1134C22#1458355611yescharacteristic
1135C22#1458355811yescharacteristic
1136C22#1458357411yescharacteristic
1137C22#1458359811yescharacteristic
1138C22#1458359911yescharacteristic
1139C22#1458363711yescharacteristic
1140C22#1458364311yescharacteristic
1141C22#1458364611yescharacteristic
1142C22#1458365111yescharacteristic
1143C4—24no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—864no—
1150C4—3441no—
1151C4—3441no—
1152C4—1722no—
1153C4—1722no—
1154C4—1722no—
1155C4—1722no—
1156C2—82no—
1157C2—1724no—
1158C2#1913726511yescharacteristic
1159C2#1913728811yescharacteristic
1160C2#1913730411yescharacteristic
1161C2#1913757311yescharacteristic
1162C2#1913760711yescharacteristic
1163C2#1913761211yescharacteristic
1164C2#1913774111yescharacteristic
1165C2#1914080711yescharacteristic
1166C2#1914084111yescharacteristic
1167C2#1914087311yescharacteristic
1168C2#1914094711yescharacteristic
1169C2#1914120511yescharacteristic
1170C2#1914135611yescharacteristic
1171C2#1914151011yescharacteristic
1172C2#1914192911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#388D43
hypocenterC43#14518
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#14582797C2semidirect
5. C2×#14582773C2semidirect
6. C2×#14582770C2semidirect
7. #19132858C2semidirect
8. #19132843C2semidirect
9. #19132840C2semidirect
10. #19132838C2semidirect
11. #19132838C2semidirect
12. #19132833C2semidirect
13. #19132829C2semidirect
14. #19132821C2semidirect
15. C2×C43×#388C2semidirect
32. #14582815C4semidirect
85. C2×C4⋊Dic43C2×C4semidirect
103. C2×C22⋊Dic43C2×C4semidirect
132. C43⋊#95C2×C4semidirect
152. C2×C22⋊C4×C43C2×C4semidirect
157. #95×C43D4semidirect
573. C2×#388D43semidirect
644. C43#14518semidirect
724. C2×C22⋊C4C4×D43semidirect
744. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145828152
C2×#145827992
C2×#145827972
C2×#145827752
C2×#145827732
C2×#145827702
#191328582
#191328432
#191328402
#191328382
#191328332
#191328292
#191328212
C2×C43×#3882
#1451843