Finite Group Databasebeta

← #25020305

Subgroups — #25020305

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582773C211yesmaximal, characteristic
2C2×#14582773C211yesmaximal, characteristic
3C2×#14582770C211yesmaximal, characteristic
4C2×#14582746C211yesmaximal, characteristic
5C2×#95×D43C211yesmaximal, characteristic
6#19132850C211yesmaximal, characteristic, complemented
7#19132847C211yesmaximal, characteristic, complemented
8#19132846C211yesmaximal, characteristic, complemented
9#19132829C211yesmaximal, characteristic, complemented
10#19132829C211yesmaximal, characteristic, complemented
11#19132824C211yesmaximal, characteristic, complemented
12Dic43⋊#95C211yesmaximal, characteristic, complemented
13(C2×D43)⋊#95C211yesmaximal, characteristic
14(C2×D43)⋊#95C211yesmaximal, characteristic
15C43×#1442C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30#14582773—24no—
31#14582773C418yescomplemented
32#14582770—24no—
33#14582746—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
57C23×Dic43C2311yescharacteristic
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C23×Dic43C2311yescharacteristic
62C23×Dic43C2311yescharacteristic
63C23×Dic43C2311yescharacteristic
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—22no—
69C22×C4×D43—22no—
70C22×C4×D43—22no—
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×D43—41no—
78C22×C4×D43—41no—
79C22×C4×D43—41no—
80C22×C4×D43—41no—
81C22×C4×D43—41no—
82C22×C4×D43—41no—
83C22×C4×D43C2×C414yes—
84C22×C4×D43D414yes—
85C2×C4⋊Dic43—22no—
86C2×C4⋊Dic43—22no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—41no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43C2×C414yescomplemented
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—22no—
94C2×Dic43⋊C4—41no—
95C2×Dic43⋊C4—41no—
96C2×Dic43⋊C4—41no—
97C2×Dic43⋊C4—41no—
98C2×Dic43⋊C4—41no—
99C2×Dic43⋊C4C2×C414yescomplemented
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)⋊C4C2×C414yes—
108C2×(C2×D43)⋊C4C2×C414yes—
109C2×(C2×D43)⋊C4D414yes—
110C2×(C2×D43)⋊C4Q814yes—
111C2×(C2×D43)⋊C4Q814yes—
112C2×C4×Dic43—22no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43—41no—
117C2×C4×Dic43—41no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—41no—
127C43⋊#95—41no—
128C43⋊#95—41no—
129C43⋊#95—41no—
130C43⋊#95—41no—
131C43⋊#95C2×C414yescomplemented
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43—41no—
142#95×C43—22no—
143#95×C43—22no—
144#95×C43—22no—
145#95×C43—22no—
146#95×C43—41no—
147#95×C43C2×C414yescomplemented
148C24×C43C2411yescharacteristic
149C23×D43—21no—
150C23×D43—21no—
151C23×D43—21no—
152C23×D43—21no—
153C23×D43—21no—
154C23×D43—21no—
155C23×D43—21no—
156C23×D43—21no—
157C23×D43C22×C412yes—
158C23×D43C2×D412yes—
159C23×D43C2×D412yes—
160C23×D43C2×Q812yes—
161C23×D43C2×Q812yes—
162C23×D43#4112yes—
163C23×D43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
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×C43C22×C412yes—
206C22×C4×C43C22×C412yes—
207C22×C4×C43C22×C412yes—
208C22×C4×C43C2×D412yes—
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2×Q812yes—
211C22×C4×C43C2×Q812yes—
212C22×C4×C43#4112yes—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—21no—
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×Dic43C22×C412yes—
253C22×Dic43C22×C412yes—
254C22×Dic43C22×C412yes—
255C22×Dic43C2×D412yes—
256C22×Dic43C2×D412yes—
257C22×Dic43C2×Q812yes—
258C22×Dic43C2×Q812yes—
259C22×Dic43#4112yes—
260C22×Dic43#4112yes—
261C22×Dic43#4112yes—
262C2×C4×D43—28no—
263C2×C4×D43—28no—
264C2×C4×D43—28no—
265C2×C4×D43—28no—
266C2×C4×D43—44no—
267C2×C4×D43—44no—
268C2×C4×D43—44no—
269C2×C4×D43—44no—
270C2×C4×D43—44no—
271C2×C4×D43—44no—
272C2×C4×D43—44no—
273C2×C4×D43—44no—
274C2×C4×D43—44no—
275C2×C4×D43—44no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×C4×D43—44no—
279C2×C4×D43—44no—
280C2×C4×D43—44no—
281C2×C4×D43—44no—
282C2×C4×D43—44no—
283C4⋊C4×C43—44no—
284(C2×D43)⋊C4—28no—
285(C2×D43)⋊C4—28no—
286(C2×D43)⋊C4—44no—
287(C2×D43)⋊C4C4⋊C4116yescomplemented
288C4⋊Dic43—44no—
289C4⋊Dic43—44no—
290Dic43⋊C4—44no—
291Dic43⋊C4—44no—
292Dic43⋊C4—44no—
293C4×Dic43—44no—
294C4×Dic43—44no—
295C23×C43C23×C411yescharacteristic
296C23×C43C22×D411yescharacteristic
297C23×C43C22×D411yescharacteristic
298C23×C43C22×Q811yescharacteristic
299C23×C43C22×Q811yescharacteristic
300C23×C43C2×#4111yescharacteristic
301C23×C43C2×#4111yescharacteristic
302C23×C43C2×#4111yescharacteristic
303C23×C43C2×#4111yescharacteristic
304C23×C43C2×#4111yescharacteristic
305C23×C43C2×#4111yescharacteristic
306C23×C43H(5,𝔽2)11yescharacteristic
307C23×C43H(5,𝔽2)11yescharacteristic
308C23×C43H(5,𝔽2)11yescharacteristic
309C23×C43H(5,𝔽2)11yescharacteristic
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
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×D43C2×C4⋊C414yes—
339C22×D43C4×D414yes—
340C22×D43C4×Q814yes—
341C22×D43#12114yes—
342C22×D43C22⋊Q814yes—
343C22×D43#12514yes—
344C22×D43C4⋊Q814yes—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—41no—
389C2×C4×C43—41no—
390C2×C4×C43—41no—
391C2×C4×C43—41no—
392C2×C4×C43—41no—
393C2×C4×C43C2×C4⋊C414yes—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—41no—
419C2×Dic43—41no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—41no—
423C2×Dic43—41no—
424C2×Dic43—41no—
425C2×Dic43—41no—
426C2×Dic43—41no—
427C2×Dic43—41no—
428C2×Dic43—41no—
429C2×Dic43—41no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—41no—
436C2×Dic43—41no—
437C2×Dic43—41no—
438C2×Dic43—41no—
439C2×Dic43—41no—
440C2×Dic43—41no—
441C2×Dic43C2×C4⋊C414yes—
442C2×Dic43#12314yes—
443C4×D43—416no—
444C4×D43—416no—
445C4×D43—416no—
446#14044—431nomaximal, Sylow
447C22×C43C22×C4⋊C411yescharacteristic
448C22×C43C2×C4×D411yescharacteristic
449C22×C43C2×C4×Q811yescharacteristic
450C22×C43C4×#4111yescharacteristic
451C22×C43C4×#4111yescharacteristic
452C22×C43#51811yescharacteristic
453C22×C43#51811yescharacteristic
454C22×C43C2×#12111yescharacteristic
455C22×C43C2×C22⋊Q811yescharacteristic
456C22×C43C2×#12311yescharacteristic
457C22×C43#52511yescharacteristic
458C22×C43C2×#12511yescharacteristic
459C22×C43#52911yescharacteristic
460C22×C43#52911yescharacteristic
461C22×C43C2×C4⋊Q811yescharacteristic
462C22×C43#53411yescharacteristic
463C22×C43#53511yescharacteristic
464C22×C43#53811yescharacteristic
465C22×C43#53811yescharacteristic
466C22×C43#54611yescharacteristic
467C22×C43#54611yescharacteristic
468C22×C43#54611yescharacteristic
469C22×C43#54611yescharacteristic
470C22×C43#55111yescharacteristic
471C22×C43#55111yescharacteristic
472C22×C43#55111yescharacteristic
473C22×C43#55111yescharacteristic
474C22×C43#55411yescharacteristic
475C22×C43#55411yescharacteristic
476C22×C43#55411yescharacteristic
477C22×C43#55411yescharacteristic
478C22×C43#55411yescharacteristic
479C22×C43#55411yescharacteristic
480C22×C43#55411yescharacteristic
481C22×C43#55411yescharacteristic
482C2×D43—24no—
483C2×D43—24no—
484C2×D43—24no—
485C2×D43—24no—
486C2×D43—24no—
487C2×D43—24no—
488C2×D43—24no—
489C2×D43—24no—
490C2×D43—24no—
491C2×D43—24no—
492C2×D43—24no—
493C2×D43—24no—
494C2×D43—24no—
495C2×D43—24no—
496C2×D43#38918yes—
497C4×C43—24no—
498C4×C43—42no—
499C4×C43—42no—
500C4×C43—42no—
501C4×C43—42no—
502C4×C43—42no—
503C4×C43—81no—
504Dic43—24no—
505Dic43—24no—
506Dic43—42no—
507Dic43—42no—
508Dic43—42no—
509Dic43—42no—
510Dic43—81no—
511C2×#385—431no—
512C2×#385—431no—
513C2×#385—431no—
514C2×C4×C22⋊C4—431no—
515C22×#95—431no—
516#1442—431no—
517#1442D4311yescharacteristic, complemented
518#1441—431no—
519#1441—431no—
520#1436—431no—
521#1436—431no—
522C4⋊#95—431no—
523C4⋊#95—431no—
524C22⋊#95—431no—
525C22⋊#95—431no—
526C2×C43C2×#38911yescharacteristic
527C2×C43C4×#12311yescharacteristic
528C2×C43#232111yescharacteristic
529C2×C43#234911yescharacteristic
530C2×C43#234911yescharacteristic
531C2×C43#236811yescharacteristic
532C2×C43#236811yescharacteristic
533C2×C43#241111yescharacteristic
534C2×C43#241211yescharacteristic
535C2×C43#245011yescharacteristic
536C2×C43#245011yescharacteristic
537C2×C43#250211yescharacteristic
538C2×C43#250511yescharacteristic
539C2×C43#250511yescharacteristic
540C2×C43#258311yescharacteristic
541D43—28no—
542C24×C4—431no—
543C24×C4—431no—
544C24×C4—431no—
545C22×C4⋊C4—431no—
546C22×C4⋊C4—431no—
547C22×C4⋊C4—431no—
548C22×C4⋊C4—431no—
549C22×C4⋊C4—431no—
550C22×C4⋊C4C2×D4311yescharacteristic
551C22×C22⋊C4—431no—
552C22×C22⋊C4—431no—
553C22×C22⋊C4—431no—
554C22×C22⋊C4—431no—
555C22×C42—431no—
556C22×C42—431no—
557#385—438no—
558#385—864no—
559#385—864no—
560C4×C22⋊C4—864no—
561C2×#95—431no—
562C2×#95—431no—
563C2×#95—431no—
564C2×#95—431no—
565C2×#95—431no—
566C2×#95—431no—
567C2×#95—431no—
568C2×#95—431no—
569C2×#95—431no—
570C2×#95—431no—
571C2×#95—431no—
572C2×#95—431no—
573C2×#95—431no—
574C2×#95—431no—
575C2×#95—864no—
576C2×#95C2×D4311yescharacteristic
577C2×#95C2×D4311yescharacteristic
578C2×#95C2×D4311yescharacteristic
579C2×#95C2×D4311yescharacteristic
580C2×#95C2×D4311yescharacteristic
581C2×#95C2×D4311yescharacteristic
582C43#1404411yescharacteristic, complemented, Sylow
583C25—431no—
584C23×C4—431no—
585C23×C4—431no—
586C23×C4—431no—
587C23×C4—431no—
588C23×C4—431no—
589C23×C4—431no—
590C23×C4—434no—
591C23×C4—434no—
592C23×C4—431no—
593C23×C4—862no—
594C23×C4—862no—
595C23×C4—862no—
596C23×C4—862no—
597C23×C4—862no—
598C23×C4—862no—
599C23×C4—862no—
600C23×C4—862no—
601C23×C4—862no—
602C23×C4—862no—
603C23×C4—862no—
604C23×C4—1721no—
605C23×C4—1721no—
606C23×C4—1721no—
607C23×C4—1721no—
608C23×C4—1721no—
609C23×C4—1721no—
610C23×C4—1721no—
611C23×C4—1721no—
612C23×C4C22×D4311yescharacteristic
613C23×C4C22×D4311yescharacteristic
614C23×C4C22×D4311yescharacteristic
615C23×C4C22×D4311yescharacteristic
616C23×C4C22×D4311yescharacteristic
617C23×C4C22×D4311yescharacteristic
618C23×C4C22×D4311yescharacteristic
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—862no—
625C2×C4⋊C4—862no—
626C2×C4⋊C4—862no—
627C2×C4⋊C4—862no—
628C2×C4⋊C4—862no—
629C2×C4⋊C4—862no—
630C2×C4⋊C4—1721no—
631C2×C4⋊C4—1721no—
632C2×C4⋊C4—1721no—
633C2×C4⋊C4—1721no—
634C2×C4⋊C4—1721no—
635C2×C4⋊C4—1721no—
636C2×C4⋊C4—1721no—
637C2×C22⋊C4—434no—
638C2×C22⋊C4—434no—
639C2×C22⋊C4—434no—
640C2×C22⋊C4—434no—
641C2×C22⋊C4—434no—
642C2×C22⋊C4—862no—
643C2×C22⋊C4—862no—
644C2×C22⋊C4—862no—
645C2×C22⋊C4—862no—
646C2×C22⋊C4—862no—
647C2×C22⋊C4—862no—
648C2×C22⋊C4—862no—
649C2×C42—862no—
650C2×C42—862no—
651C2×C42—862no—
652C2×C42—862no—
653C2×C42—1721no—
654C2×C42—1721no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—41no—
660#95—434no—
661#95—862no—
662#95—862no—
663#95—862no—
664#95—862no—
665#95—862no—
666#95—862no—
667#95—862no—
668#95—862no—
669#95—1721no—
670#95—1721no—
671#95—1721no—
672#95—1721no—
673#95—1721no—
674#95C4×D4314yescomplemented
675C24—432no—
676C24—432no—
677C24—432no—
678C24—432no—
679C24—432no—
680C24—432no—
681C24—432no—
682C24—861no—
683C24—861no—
684C24—861no—
685C24—861no—
686C24—861no—
687C24—861no—
688C24—861no—
689C24—861no—
690C24C23×D4311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—432no—
733C22×C4—432no—
734C22×C4—432no—
735C22×C4—432no—
736C22×C4—432no—
737C22×C4—432no—
738C22×C4—432no—
739C22×C4—432no—
740C22×C4—432no—
741C22×C4—432no—
742C22×C4—868no—
743C22×C4—868no—
744C22×C4—868no—
745C22×C4—868no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—861no—
760C22×C4—861no—
761C22×C4—861no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—861no—
785C22×C4—1724no—
786C22×C4—1724no—
787C22×C4—1724no—
788C22×C4—1724no—
789C22×C4—1724no—
790C22×C4—1724no—
791C22×C4—1724no—
792C22×C4—1724no—
793C22×C4—1724no—
794C22×C4—1724no—
795C22×C4—1724no—
796C22×C4—1724no—
797C22×C4—1724no—
798C22×C4—1724no—
799C22×C4—1724no—
800C22×C4—1724no—
801C22×C4—1724no—
802C22×C4C2×C4×D4312yes—
803C22×C4C2×C4×D4312yes—
804C22×C4C2×C4×D4312yes—
805C22×C4D4×D4312yes—
806C22×C4D4×D4312yes—
807C22×C4#1062190012yes—
808C22×C4Q8×D4312yes—
809C22×C4Q8×D4312yes—
810C4⋊C4—44no—
811C4⋊C4—1724no—
812C4⋊C4—1724no—
813C4⋊C4—1724no—
814C4⋊C4—1724no—
815C4⋊C4—1724no—
816C22⋊C4—4316no—
817C22⋊C4—868no—
818C22⋊C4—868no—
819C22⋊C4—1724no—
820C42—1724no—
821C42—1724no—
822C23—434no—
823C23—434no—
824C23—434no—
825C23—434no—
826C23—434no—
827C23—434no—
828C23—434no—
829C23—862no—
830C23—862no—
831C23—862no—
832C23—862no—
833C23—862no—
834C23—862no—
835C23—862no—
836C23—862no—
837C23—862no—
838C23—862no—
839C23—862no—
840C23—862no—
841C23—862no—
842C23—862no—
843C23—862no—
844C23—862no—
845C23—862no—
846C23—862no—
847C23—862no—
848C23—862no—
849C23—862no—
850C23—862no—
851C23—862no—
852C23—862no—
853C23—862no—
854C23—862no—
855C23—862no—
856C23—862no—
857C23C22×C4×D4311yescharacteristic
858C23C2×D4×D4311yescharacteristic
859C23C2×D4×D4311yescharacteristic
860C23C2×Q8×D4311yescharacteristic
861C23C2×Q8×D4311yescharacteristic
862C23#41×D4311yescharacteristic
863C23#41×D4311yescharacteristic
864C23#41×D4311yescharacteristic
865C23#41×D4311yescharacteristic
866C23#41×D4311yescharacteristic
867C23C2×#1062190011yescharacteristic
868C23#1306337011yescharacteristic
869C23#1306337111yescharacteristic
870C23#1306337111yescharacteristic
871C23#1306337111yescharacteristic
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—434no—
921C2×C4—434no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—862no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—862no—
937C2×C4—862no—
938C2×C4—862no—
939C2×C4—862no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—17216no—
947C2×C4—17216no—
948C2×C4—17216no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4—1721no—
953C2×C4—1721no—
954C2×C4—1721no—
955C2×C4—1721no—
956C2×C4—1721no—
957C2×C4—1721no—
958C2×C4—1721no—
959C2×C4—1721no—
960C2×C4—1721no—
961C2×C4—1721no—
962C2×C4—1721no—
963C2×C4—1721no—
964C2×C4—1721no—
965C2×C4—1721no—
966C2×C4—1721no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4C4⋊C4×D4314yes—
973C22—438no—
974C22—864no—
975C22—864no—
976C22—864no—
977C22—864no—
978C22—864no—
979C22—864no—
980C22—864no—
981C22—864no—
982C22—864no—
983C22—864no—
984C22—864no—
985C22—864no—
986C22—864no—
987C22—864no—
988C22C2×C4⋊C4×D4311yescharacteristic
989C22C4×D4×D4311yescharacteristic
990C22C4×Q8×D4311yescharacteristic
991C22C4×#1062190011yescharacteristic
992C22#1458336711yescharacteristic
993C22#1458337111yescharacteristic
994C22#1458337311yescharacteristic
995C22#121×D4311yescharacteristic
996C22C22⋊Q8×D4311yescharacteristic
997C22#123×D4311yescharacteristic
998C22#1458340911yescharacteristic
999C22#125×D4311yescharacteristic
1000C22#1458342811yescharacteristic
1001C22#1458343211yescharacteristic
1002C22C4⋊Q8×D4311yescharacteristic
1003C22#1458346011yescharacteristic
1004C22#1458346511yescharacteristic
1005C22#1458348311yescharacteristic
1006C22#1458348811yescharacteristic
1007C22#1458353611yescharacteristic
1008C22#1458354111yescharacteristic
1009C22#1458354211yescharacteristic
1010C22#1458354211yescharacteristic
1011C22#1458357211yescharacteristic
1012C22#1458357411yescharacteristic
1013C22#1458357411yescharacteristic
1014C22#1458357711yescharacteristic
1015C22#1458360311yescharacteristic
1016C22#1458360311yescharacteristic
1017C22#1458360511yescharacteristic
1018C22#1458360511yescharacteristic
1019C22#1458360511yescharacteristic
1020C22#1458360511yescharacteristic
1021C22#1458360711yescharacteristic
1022C22#1458360711yescharacteristic
1023C4—24no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—81no—
1030C4—864no—
1031C4—864no—
1032C4—3441no—
1033C4—1722no—
1034C4—1722no—
1035C4—1722no—
1036C4—1722no—
1037C2—868no—
1038C2#389×D4311yescharacteristic
1039C2#1913712211yescharacteristic
1040C2#1913725711yescharacteristic
1041C2#1913750111yescharacteristic
1042C2#1913750311yescharacteristic
1043C2#1913767211yescharacteristic
1044C2#1913767711yescharacteristic
1045C2#1913797311yescharacteristic
1046C2#1913798411yescharacteristic
1047C2#1913841211yescharacteristic
1048C2#1913842211yescharacteristic
1049C2#1913906811yescharacteristic
1050C2#1913908911yescharacteristic
1051C2#1913909911yescharacteristic
1052C2#1913996911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1442D43
hypocenterC43#14044
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
6. #19132850C2semidirect
7. #19132847C2semidirect
8. #19132846C2semidirect
9. #19132829C2semidirect
10. #19132829C2semidirect
11. #19132824C2semidirect
12. Dic43⋊#95C2semidirect
15. C43×#1442C2semidirect
31. #14582773C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
99. C2×Dic43⋊C4C2×C4semidirect
131. C43⋊#95C2×C4semidirect
147. #95×C43C2×C4semidirect
287. (C2×D43)⋊C4C4⋊C4semidirect
517. #1442D43semidirect
582. C43#14044semidirect
674. #95C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145827732
C2×#145827702
C2×#145827462
C2×#95×D432
#191328502
#191328472
#191328462
#191328292
#191328242
Dic43⋊#952
(C2×D43)⋊#952
C43×#14422
#1404443