Finite Group Databasebeta

← #25024117

Subgroups — #25024117

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582801C211yesmaximal, characteristic
2C2×#14582791C211yesmaximal, characteristic, complemented
3C2×#14582777C211yesmaximal, characteristic
4C2×#14582761C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic, complemented
6#19132860C211yesmaximal, characteristic, complemented
7#19132843C211yesmaximal, characteristic, complemented
8#19132841C211yesmaximal, characteristic, complemented
9#19132841C211yesmaximal, characteristic, complemented
10#19132837C211yesmaximal, characteristic, complemented
11#19132835C211yesmaximal, characteristic
12#19132831C211yesmaximal, characteristic, complemented
13#19132829C211yesmaximal, 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×(C2×D43)⋊C4C2211yescharacteristic
22C22×(C2×D43)⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33#14582801—24no—
34#14582791—24no—
35#14582777C418yescomplemented
36#14582761—24no—
37#14582756—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
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C42×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—41no—
63C22×D172—41no—
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—41no—
76C22×C4×D43—41no—
77C22×C4×D43C2×C414yes—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—22no—
82C2×C4⋊Dic43—41no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43—41no—
86C2×C4⋊Dic43—41no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4—22no—
89C2×(C2×D43)⋊C4—22no—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—22no—
92C2×(C2×D43)⋊C4—22no—
93C2×(C2×D43)⋊C4—22no—
94C2×(C2×D43)⋊C4—22no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—41no—
99C2×(C2×D43)⋊C4—41no—
100C2×(C2×D43)⋊C4—41no—
101C2×(C2×D43)⋊C4—41no—
102C2×(C2×D43)⋊C4—41no—
103C2×(C2×D43)⋊C4—41no—
104C2×(C2×D43)⋊C4—41no—
105C2×(C2×D43)⋊C4—41no—
106C2×(C2×D43)⋊C4—41no—
107C2×(C2×D43)⋊C4—41no—
108C2×(C2×D43)⋊C4—41no—
109C2×(C2×D43)⋊C4—41no—
110C2×(C2×D43)⋊C4—41no—
111C2×(C2×D43)⋊C4—41no—
112C2×(C2×D43)⋊C4—41no—
113C2×(C2×D43)⋊C4—41no—
114C2×(C2×D43)⋊C4—41no—
115C2×(C2×D43)⋊C4—41no—
116C2×(C2×D43)⋊C4C2×C414yes—
117C2×(C2×D43)⋊C4C2×C414yes—
118C2×(C2×D43)⋊C4C2×C414yes—
119C2×(C2×D43)⋊C4D414yes—
120C2×C4×Dic43—22no—
121C2×C4×Dic43—41no—
122C2×C4×Dic43—41no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C43⋊#95—22no—
130C43⋊#95—41no—
131C43⋊#95—41no—
132C43⋊#95—41no—
133C43⋊#95C2×C414yes—
134C23×C4×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×C42×C43—22no—
145C2×C42×C43—22no—
146C2×C42×C43—41no—
147#95×C43—22no—
148#95×C43—41no—
149#95×C43—41no—
150#95×C43C2×C414yes—
151#95×C43D414yescomplemented
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×D43—21no—
176C23×D43—21no—
177C23×D43—21no—
178C23×D43—21no—
179C23×D43C22×C412yes—
180C23×D43C22×C412yes—
181C23×D43C2×D412yes—
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×C43C22×C412yes—
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×C43#4112yes—
230C22×C4×C43#4112yes—
231C22×C4×C43#4112yes—
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×Dic43—21no—
271C22×Dic43C22×C412yes—
272C22×Dic43C22×C412yes—
273C22×Dic43C2×D412yes—
274C2×D172—28no—
275C2×D172—28no—
276C2×D172—44no—
277C2×D172—44no—
278C2×D172—44no—
279C2×D172—44no—
280C2×D172—44no—
281C2×C4×D43—28no—
282C2×C4×D43—28no—
283C2×C4×D43—44no—
284C2×C4×D43—44no—
285C2×C4×D43—44no—
286C2×C4×D43—44no—
287C2×C4×D43—44no—
288C4⋊C4×C43—44no—
289C42×C43—44no—
290(C2×D43)⋊C4—28no—
291(C2×D43)⋊C4—44no—
292(C2×D43)⋊C4—44no—
293(C2×D43)⋊C4—44no—
294(C2×D43)⋊C4—44no—
295(C2×D43)⋊C4—44no—
296(C2×D43)⋊C4—44no—
297(C2×D43)⋊C4—44no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4—44no—
301C4⋊Dic43—44no—
302C4⋊Dic43—44no—
303C4⋊Dic43—44no—
304C4×Dic43—44no—
305C23×C43C23×C411yescharacteristic
306C23×C43C22×D411yescharacteristic
307C23×C43C22×D411yescharacteristic
308C23×C43C2×#4111yescharacteristic
309C23×C43C2×#4111yescharacteristic
310C23×C43C2×#4111yescharacteristic
311C23×C43C2×#4111yescharacteristic
312C23×C43H(5,𝔽2)11yescharacteristic
313C23×C43H(5,𝔽2)11yescharacteristic
314C23×C43H(5,𝔽2)11yescharacteristic
315C23×C43H(5,𝔽2)11yescharacteristic
316C23×C43H(5,𝔽2)11yescharacteristic
317C23×C43H(5,𝔽2)11yescharacteristic
318C23×C432−1+411yescharacteristic
319C23×C432−1+411yescharacteristic
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—41no—
348C22×D43—41no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—41no—
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×D43C4×D414yes—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—22no—
394C2×C4×C43—22no—
395C2×C4×C43—22no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—22no—
412C2×C4×C43—22no—
413C2×C4×C43—22no—
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#11714yes—
438C2×C4×C43C4×D414yes—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—22no—
444C2×Dic43—22no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43—41no—
451C2×Dic43—41no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—41no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—41no—
459C2×Dic43—41no—
460C2×Dic43—41no—
461C2×Dic43—41no—
462C2×Dic43—41no—
463C2×Dic43—41no—
464C2×Dic43—41no—
465C2×Dic43—41no—
466C2×Dic43—41no—
467C2×Dic43—41no—
468C2×Dic43—41no—
469C2×Dic43—41no—
470C2×Dic43—41no—
471C2×Dic43—41no—
472C2×Dic43—41no—
473C2×Dic43—41no—
474C2×Dic43—41no—
475C2×Dic43—41no—
476C2×Dic43—41no—
477C2×Dic43—41no—
478C2×Dic43—41no—
479C2×Dic43—41no—
480C2×Dic43—41no—
481D172—416no—
482C4×D43—416no—
483#14374—431nomaximal, Sylow
484C22×C43C2×#11711yescharacteristic
485C22×C43C2×C4×D411yescharacteristic
486C22×C43C2×C4×D411yescharacteristic
487C22×C43#51811yescharacteristic
488C22×C43#51811yescharacteristic
489C22×C43#52011yescharacteristic
490C22×C43#52011yescharacteristic
491C22×C43#53411yescharacteristic
492C22×C43#53511yescharacteristic
493C22×C43#53611yescharacteristic
494C22×C43#53711yescharacteristic
495C22×C43#53911yescharacteristic
496C22×C43#53911yescharacteristic
497C22×C43#54011yescharacteristic
498C22×C43#54011yescharacteristic
499C22×C43#54011yescharacteristic
500C22×C43#54211yescharacteristic
501C22×C43#54211yescharacteristic
502C22×C43#54211yescharacteristic
503C22×C43D4211yescharacteristic
504C22×C43#54611yescharacteristic
505C22×C43#54611yescharacteristic
506C22×C43#54611yescharacteristic
507C22×C43#54611yescharacteristic
508C22×C43#54711yescharacteristic
509C22×C43#55011yescharacteristic
510C22×C43#55111yescharacteristic
511C22×C43#55111yescharacteristic
512C22×C43#55111yescharacteristic
513C22×C43#55511yescharacteristic
514C22×C43#55611yescharacteristic
515C22×C43#56011yescharacteristic
516C22×C43#56011yescharacteristic
517C22×C43#56211yescharacteristic
518C22×C43#56211yescharacteristic
519C2×D43—24no—
520C2×D43—24no—
521C2×D43—24no—
522C2×D43—42no—
523C2×D43—42no—
524C2×D43—42no—
525C2×D43—42no—
526C2×D43—42no—
527C2×D43—42no—
528C2×D43—42no—
529C2×D43—42no—
530C2×D43—42no—
531C2×D43—42no—
532C2×D43—42no—
533C2×D43—42no—
534C2×D43—42no—
535C2×D43—42no—
536C2×D43—42no—
537C2×D43—42no—
538C2×D43—42no—
539C2×D43—42no—
540C2×D43—42no—
541C2×D43—81no—
542C2×D43—81no—
543C2×D43—81no—
544C2×D43—81no—
545C2×D43—81no—
546C2×D43—81no—
547C2×D43—81no—
548C2×D43—81no—
549C4×C43—24no—
550C4×C43—24no—
551C4×C43—42no—
552C4×C43—42no—
553C4×C43—42no—
554C4×C43—42no—
555C4×C43—81no—
556Dic43—42no—
557Dic43—42no—
558Dic43—42no—
559Dic43—81no—
560Dic43—81no—
561Dic43—81no—
562C2×#390—431no—
563C2×#388—431no—
564C2×#386—431no—
565C2×#381—431no—
566C2×#380—431no—
567#1444—431no—
568#1440—431no—
569#1439—431no—
570#1439—431no—
571#1439—431no—
572#1438—431no—
573#1437—431no—
574#1436—431no—
575#1436D4311yescharacteristic, complemented
576#1434—431no—
577C2×C43#231911yescharacteristic
578C2×C43#232211yescharacteristic
579C2×C43#232411yescharacteristic
580C2×C43#234211yescharacteristic
581C2×C43#235411yescharacteristic
582C2×C43#235811yescharacteristic
583C2×C43#237711yescharacteristic
584C2×C43#267211yescharacteristic
585C2×C43#267311yescharacteristic
586C2×C43#269911yescharacteristic
587C2×C43#270011yescharacteristic
588C2×C43#270511yescharacteristic
589C2×C43#270611yescharacteristic
590C2×C43#273711yescharacteristic
591C2×C43#274011yescharacteristic
592D43—44no—
593D43—82no—
594C23×D4—431no—
595C24×C4—431no—
596C22×C4⋊C4—431no—
597C22×C4⋊C4—431no—
598C22×C4⋊C4—431no—
599C22×C4⋊C4C2×D4311yescharacteristic
600C22×C22⋊C4—431no—
601C22×C22⋊C4—431no—
602C22×C22⋊C4—431no—
603C22×C22⋊C4—431no—
604C22×C22⋊C4—431no—
605C22×C22⋊C4—431no—
606C22×C22⋊C4—431no—
607C22×C22⋊C4—431no—
608C22×C22⋊C4—431no—
609C22×C22⋊C4—431no—
610C22×C22⋊C4—431no—
611C22×C42—431no—
612C22×C42C2×D4311yescharacteristic
613#390—864no—
614#388—864no—
615#386—438no—
616#381—864no—
617#380—864no—
618C2×#95—431no—
619C2×#95—431no—
620C2×#95—431no—
621C2×#95—431no—
622C2×#95—431no—
623C2×#95—431no—
624C2×#95—431no—
625C2×#95—431no—
626C2×#95—431no—
627C2×#95—431no—
628C2×#95—431no—
629C2×#95C2×D4311yescharacteristic
630C2×#95C2×D4311yescharacteristic
631C2×#95C2×D4311yescharacteristic
632C2×#95C2×D4311yescharacteristic
633C2×#95C2×D4311yescharacteristic
634C43#1437411yescharacteristic, complemented, Sylow
635C25—431no—
636C25—431no—
637C22×D4—434no—
638C22×D4—862no—
639C22×D4—862no—
640C22×D4—862no—
641C22×D4—862no—
642C22×D4—1721no—
643C22×D4—1721no—
644C23×C4—431no—
645C23×C4—431no—
646C23×C4—431no—
647C23×C4—434no—
648C23×C4—431no—
649C23×C4—431no—
650C23×C4—431no—
651C23×C4—862no—
652C23×C4—862no—
653C23×C4—862no—
654C23×C4—862no—
655C23×C4—1721no—
656C23×C4—1721no—
657C23×C4C22×D4311yescharacteristic
658C23×C4C22×D4311yescharacteristic
659C23×C4C22×D4311yescharacteristic
660C23×C4C22×D4311yescharacteristic
661C23×C4C22×D4311yescharacteristic
662C23×C4C22×D4311yescharacteristic
663C23×C4C22×D4311yescharacteristic
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—862no—
668C2×C4⋊C4—862no—
669C2×C4⋊C4—862no—
670C2×C4⋊C4—862no—
671C2×C4⋊C4—1721no—
672C2×C4⋊C4—1721no—
673C2×C4⋊C4—1721no—
674C2×C4⋊C4—1721no—
675C2×C4⋊C4—1721no—
676C2×C22⋊C4—434no—
677C2×C22⋊C4—434no—
678C2×C22⋊C4—434no—
679C2×C22⋊C4—434no—
680C2×C22⋊C4—862no—
681C2×C22⋊C4—862no—
682C2×C22⋊C4—862no—
683C2×C22⋊C4—862no—
684C2×C22⋊C4—862no—
685C2×C22⋊C4—862no—
686C2×C22⋊C4—862no—
687C2×C22⋊C4—862no—
688C2×C22⋊C4—862no—
689C2×C22⋊C4—862no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—1721no—
692C2×C22⋊C4—1721no—
693C2×C22⋊C4—1721no—
694C2×C22⋊C4—1721no—
695C2×C22⋊C4—1721no—
696C2×C22⋊C4—1721no—
697C2×C22⋊C4—1721no—
698C2×C22⋊C4—1721no—
699C2×C22⋊C4—1721no—
700C2×C22⋊C4—1721no—
701C2×C22⋊C4—1721no—
702C2×C22⋊C4—1721no—
703C2×C22⋊C4—1721no—
704C2×C22⋊C4—1721no—
705C2×C22⋊C4—1721no—
706C2×C22⋊C4—1721no—
707C2×C22⋊C4—1721no—
708C2×C22⋊C4—1721no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—862no—
713C2×C42—1721no—
714C2×C42—1721no—
715#95—22no—
716#95—41no—
717#95—41no—
718#95—434no—
719#95—862no—
720#95—862no—
721#95—862no—
722#95—862no—
723#95—862no—
724#95—862no—
725#95—862no—
726#95—1721no—
727#95—1721no—
728#95—1721no—
729#95C4×D4314yes—
730#95D17214yescomplemented
731C24—432no—
732C24—432no—
733C24—432no—
734C24—432no—
735C24—861no—
736C24—861no—
737C24—861no—
738C24—861no—
739C24—861no—
740C24—861no—
741C24—861no—
742C24—861no—
743C24—861no—
744C24—861no—
745C24—861no—
746C24—861no—
747C24—861no—
748C24—861no—
749C24—861no—
750C24—861no—
751C24—861no—
752C24—861no—
753C24—861no—
754C24—861no—
755C24—861no—
756C24—861no—
757C24—861no—
758C24—861no—
759C24—861no—
760C24—861no—
761C24C23×D4311yescharacteristic
762C2×D4—868no—
763C2×D4—868no—
764C2×D4—1724no—
765C2×D4—1724no—
766C2×D4—1724no—
767C2×D4—1724no—
768C2×D4—1724no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—432no—
809C22×C4—432no—
810C22×C4—432no—
811C22×C4—868no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—861no—
816C22×C4—861no—
817C22×C4—861no—
818C22×C4—861no—
819C22×C4—861no—
820C22×C4—861no—
821C22×C4—861no—
822C22×C4—861no—
823C22×C4—861no—
824C22×C4—861no—
825C22×C4—861no—
826C22×C4—861no—
827C22×C4—861no—
828C22×C4—861no—
829C22×C4—861no—
830C22×C4—868no—
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—1724no—
853C22×C4—1724no—
854C22×C4—1724no—
855C22×C4—1724no—
856C22×C4—1724no—
857C22×C4C2×C4×D4312yes—
858C22×C4C2×C4×D4312yes—
859C22×C4C2×C4×D4312yes—
860C22×C4C2×D17212yes—
861C22×C4C2×D17212yes—
862C22×C4C2×D17212yes—
863C22×C4#1062189812yes—
864C22×C4D4×D4312yes—
865C22×C4#1062190012yes—
866C22×C4#1062190212yes—
867C4⋊C4—44no—
868C4⋊C4—1724no—
869C4⋊C4—1724no—
870C4⋊C4—1724no—
871C22⋊C4—868no—
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—
882C42—44no—
883C42—1724no—
884C23—434no—
885C23—862no—
886C23—862no—
887C23—862no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—862no—
892C23—862no—
893C23—862no—
894C23—862no—
895C23—862no—
896C23—862no—
897C23—862no—
898C23—862no—
899C23—862no—
900C23—862no—
901C23—862no—
902C23—862no—
903C23—862no—
904C23—862no—
905C23—862no—
906C23—862no—
907C23—862no—
908C23—862no—
909C23—862no—
910C23—1721no—
911C23—1721no—
912C23—1721no—
913C23—1721no—
914C23—1721no—
915C23—1721no—
916C23—1721no—
917C23—1721no—
918C23—1721no—
919C23—1721no—
920C23—1721no—
921C23—1721no—
922C23—1721no—
923C23—1721no—
924C23—1721no—
925C23—1721no—
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—
954C23C22×C4×D4311yescharacteristic
955C23C2×D4×D4311yescharacteristic
956C23C22×D17211yescharacteristic
957C23#41×D4311yescharacteristic
958C23C2×#1062190011yescharacteristic
959C23C2×#1062189811yescharacteristic
960C23C2×#1062190211yescharacteristic
961C23#1306337011yescharacteristic
962C23#1306337011yescharacteristic
963C23#1306337111yescharacteristic
964C23#1306337111yescharacteristic
965C23#1306337111yescharacteristic
966C23#1306337111yescharacteristic
967C23#1306337211yescharacteristic
968C23#1306337311yescharacteristic
969D4—17216no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—862no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—17216no—
1027C2×C4—1721no—
1028C2×C4—1721no—
1029C2×C4—1721no—
1030C2×C4—1721no—
1031C2×C4—1721no—
1032C2×C4—1721no—
1033C2×C4—1721no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1721no—
1040C2×C4—1721no—
1041C2×C4—1721no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4—1721no—
1048C2×C4—1721no—
1049C2×C4—1721no—
1050C2×C4—1721no—
1051C2×C4—1721no—
1052C2×C4—1721no—
1053C2×C4—1721no—
1054C2×C4—1721no—
1055C2×C4—1721no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4#1306328314yes—
1061C2×C4C4×D17214yes—
1062C22—864no—
1063C22—864no—
1064C22—864no—
1065C22—3441no—
1066C22—3441no—
1067C22—3441no—
1068C22—3441no—
1069C22—3441no—
1070C22—3441no—
1071C22—3441no—
1072C22—3441no—
1073C22—1722no—
1074C22—1722no—
1075C22—1722no—
1076C22—1722no—
1077C22—1722no—
1078C22—1722no—
1079C22—1722no—
1080C22—1722no—
1081C22—1722no—
1082C22—1722no—
1083C22—1722no—
1084C22—1722no—
1085C22—1722no—
1086C22—1722no—
1087C22—1722no—
1088C22—1722no—
1089C22—1722no—
1090C22—1722no—
1091C22—1722no—
1092C22C2×#1306328311yescharacteristic
1093C22C4×D4×D4311yescharacteristic
1094C22C2×C4×D17211yescharacteristic
1095C22#1458337111yescharacteristic
1096C22#1458337111yescharacteristic
1097C22#1458337911yescharacteristic
1098C22#1458338111yescharacteristic
1099C22#1458346011yescharacteristic
1100C22#1458346811yescharacteristic
1101C22#1458347211yescharacteristic
1102C22#1458348011yescharacteristic
1103C22#1458349011yescharacteristic
1104C22#1458349711yescharacteristic
1105C22#1458350011yescharacteristic
1106C22#1458350211yescharacteristic
1107C22#1458350511yescharacteristic
1108C22#1458352111yescharacteristic
1109C22#1458352211yescharacteristic
1110C22#1458352311yescharacteristic
1111C22D4×D17211yescharacteristic
1112C22#1458353611yescharacteristic
1113C22#1458353911yescharacteristic
1114C22#1458354011yescharacteristic
1115C22#1458354411yescharacteristic
1116C22#1458355311yescharacteristic
1117C22#1458357111yescharacteristic
1118C22#1458357211yescharacteristic
1119C22#1458357311yescharacteristic
1120C22#1458357611yescharacteristic
1121C22#1458361411yescharacteristic
1122C22#1458362211yescharacteristic
1123C22#1458363711yescharacteristic
1124C22#1458364011yescharacteristic
1125C22#1458364311yescharacteristic
1126C22#1458364611yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—81no—
1134C4—3441no—
1135C4—3441no—
1136C4—3441no—
1137C4—1722no—
1138C4—1722no—
1139C4—1722no—
1140C2—3442no—
1141C2—1724no—
1142C2#1913723411yescharacteristic
1143C2#1913726811yescharacteristic
1144C2#1913728911yescharacteristic
1145C2#1913744211yescharacteristic
1146C2#1913754211yescharacteristic
1147C2#1913757711yescharacteristic
1148C2#1913774811yescharacteristic
1149C2#1914084911yescharacteristic
1150C2#1914086411yescharacteristic
1151C2#1914118411yescharacteristic
1152C2#1914119611yescharacteristic
1153C2#1914126611yescharacteristic
1154C2#1914128111yescharacteristic
1155C2#1914164511yescharacteristic
1156C2#1914169011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1436C2
socle, cosocleC24×C43C24
prime radicalC23×D172C22
hypercenter#1436D43
hypocenterC43#14374
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#14582791C2semidirect
4. C2×#14582761C2semidirect
5. C2×#14582756C2semidirect
6. #19132860C2semidirect
7. #19132843C2semidirect
8. #19132841C2semidirect
9. #19132841C2semidirect
10. #19132837C2semidirect
12. #19132831C2semidirect
13. #19132829C2semidirect
14. #19132822C2semidirect
15. C43×#1436C2semidirect
35. #14582777C4semidirect
151. #95×C43D4semidirect
575. #1436D43semidirect
634. C43#14374semidirect
730. #95D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828012
C2×#145827912
C2×#145827772
C2×#145827612
C2×#145827562
#191328602
#191328432
#191328412
#191328372
#191328352
#191328312
#191328292
#191328222
C43×#14362
#1437443