Finite Group Databasebeta

← #25111871

Subgroups — #25111871

Order 11008.

1928 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D172C211yesmaximal, characteristic
2C2×#14582972C212yesmaximal, complemented
3C2×#14582861C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×D43C211yesmaximal, characteristic, complemented
5#19135393C212yesmaximal, complemented
6#19134891C212yesmaximal, complemented
7#19134886C212yesmaximal, complemented
8#19134575C211yesmaximal, characteristic, complemented
9#19134504C211yesmaximal, characteristic, complemented
10#19134504C211yesmaximal, characteristic, complemented
11C43×#1749C211yesmaximal, characteristic, complemented
12C23×D172C411yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C23×C4×D43C2211yescharacteristic
15C22×#10621872C2212yescomplemented
16C22×C8×D43C2212yescomplemented
17C2×C4×D172—28no—
18C2×C4×D172C411yescharacteristic
19C2×C4×D172C411yescharacteristic
20C2×C4×D172C411yescharacteristic
21C2×C4×D172C411yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C22×C4⋊Dic43C411yescharacteristic
27C22×(C2×D43)⋊C4C411yescharacteristic
28C22×(C2×D43)⋊C4C411yescharacteristic
29#14582972—28no—
30C2×C4⋊(C43⋊C8)C2212yescomplemented
31#14582861—24no—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×(C2×D43)⋊C8C2212yescomplemented
35C2×(C2×D43)⋊C8C2212yescomplemented
36C2×(C2×D43)⋊C8C2212yescomplemented
37C2×(C2×D43)⋊C8C2212yescomplemented
38C2×(C2×D43)⋊C8C2212yescomplemented
39C2×(C2×D43)⋊C8C2212yescomplemented
40C22⋊C8×D43—24no—
41#14582654C2212yescomplemented
42C22×C42×C43C2211yescharacteristic
43C2×C22⋊C8×C43C2211yescharacteristic
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×#97×C43C2212yescomplemented
46C43×#336C2212yescomplemented
47C24×D43C2×C411yescharacteristic
48C24×D43C2×C411yescharacteristic
49C22×D172—24no—
50C22×D172—24no—
51C22×D172—24no—
52C22×D172C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C23×Dic43C2×C411yescharacteristic
57C23×Dic43C2×C411yescharacteristic
58C22×C4×D43—22no—
59C22×C4×D43—22no—
60C22×C4×D43—22no—
61C22×C4×D43—22no—
62C22×C4×D43—24no—
63C22×C4×D43—24no—
64C22×C4×D43—42no—
65C22×C4×D43—42no—
66C22×C4×D43C2×C411yescharacteristic
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2×C411yescharacteristic
69C22×C4×D43C2×C411yescharacteristic
70C22×C4×D43C2311yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621872—24no—
75C2×#10621872—24no—
76C2×#10621872—42no—
77C22×C43⋊C8C2312yes—
78C22×C43⋊C8C2312yes—
79C2×C8×D43—24no—
80C2×C8×D43—24no—
81C2×C8×D43—42no—
82C4×D172—24no—
83C4×D172—24no—
84C4×D172—24no—
85C4×D172—24no—
86C4×D172—24no—
87C4×D172—24no—
88C4×D172—24no—
89C4×D172D418yes—
90C2×C4⋊Dic43—24no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—24no—
97C2×(C2×D43)⋊C4C2×C411yescharacteristic
98C2×(C2×D43)⋊C4C2×C411yescharacteristic
99C2×(C2×D43)⋊C4C2×C411yescharacteristic
100C2×(C2×D43)⋊C4C2×C411yescharacteristic
101C2×(C2×D43)⋊C4C2×C411yescharacteristic
102C2×(C2×D43)⋊C4C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C4⋊(C43⋊C8)—24no—
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)—22no—
108(C2×D43)⋊C8—24no—
109(C2×D43)⋊C8—24no—
110(C2×D43)⋊C8—24no—
111(C2×D43)⋊C8—24no—
112(C2×D43)⋊C8—42no—
113(C2×D43)⋊C8—42no—
114C23×C4×C43C2×C411yescharacteristic
115C23×C4×C43C2×C411yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C22×C8×C43C2312yes—
118C22×C8×C43C2312yes—
119C2×C42×C43—24no—
120C2×C42×C43C2×C411yescharacteristic
121C2×C42×C43C2×C411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C22⋊C8×C43—22no—
125C22⋊C8×C43D414yescomplemented
126#97×C43—24no—
127C24×C43C22×C411yescharacteristic
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—22no—
131C23×D43—22no—
132C23×D43—22no—
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—41no—
138C23×D43—41no—
139C23×D43—41no—
140C23×D43—41no—
141C23×D43M1614yescomplemented
142C23×D43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C23×D43C22×C411yescharacteristic
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—41no—
154C22×C4×C43C22×C411yescharacteristic
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C22×C411yescharacteristic
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2×D412yes—
160C22×C4×C43#4112yes—
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—41no—
167C22×Dic43—41no—
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C2×D172—232no—
173C2×D172—22no—
174C2×D172—22no—
175C2×D172—22no—
176C2×D172—22no—
177C2×D172—22no—
178C2×D172—22no—
179C2×D172—22no—
180C2×D172—22no—
181C2×D172—22no—
182C2×D172—22no—
183C2×D172C22⋊C414yes—
184C2×D172M1614yescomplemented
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—22no—
190C2×C4×D43—22no—
191C2×C4×D43—22no—
192C2×C4×D43—22no—
193C2×C4×D43—22no—
194C2×C4×D43—22no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—22no—
198C2×C4×D43—22no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—22no—
204C2×C4×D43—22no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—41no—
208C2×C4×D43—41no—
209C2×C4×D43—41no—
210C2×C4×D43—41no—
211C2×C4×D43—48no—
212C2×C4×D43—48no—
213C2×C4×D43—48no—
214C2×C4×D43—48no—
215C2×C4×D43C2×D414yes—
216C2×C4×D43C2×D414yes—
217C2×C8×C43—22no—
218C2×C8×C43—22no—
219C2×C8×C43—22no—
220C2×C8×C43—22no—
221C2×C8×C43—22no—
222C2×C8×C43C2×D414yescomplemented
223C42×C43—22no—
224C42×C43—22no—
225C42×C43—22no—
226C42×C43C2×D414yes—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4C22⋊C414yes—
234(C2×D43)⋊C4C22⋊C414yes—
235C4⋊Dic43—22no—
236C4⋊Dic43—22no—
237C4⋊Dic43—22no—
238C4⋊Dic43C22⋊C414yes—
239C2×C43⋊C8—22no—
240C2×C43⋊C8—22no—
241C2×C43⋊C8—22no—
242C2×C43⋊C8—22no—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245#10621872—48no—
246C8×D43—48no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43C4×D412yes—
252C23×C43C2×M1612yes—
253C23×C43#13112yes—
254C23×C43C23×C411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—28no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—44no—
281C22×D43—44no—
282C22×D43—44no—
283C22×D43—44no—
284C22×D43—44no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—44no—
291C22×D43C2×C22⋊C412yes—
292C22×D43C2×C22⋊C412yes—
293C22×D43C2×M1612yes—
294C22×D43C2×M1612yes—
295C22×D43C2×M1612yes—
296C22×D43C2×M1612yes—
297C2×C4×C43—28no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—24no—
307C2×C4×C43—24no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—44no—
312C2×C4×C43C2×C22⋊C412yes—
313C2×C4×C43C2×C22⋊C412yes—
314C2×C4×C43C4×D412yes—
315C2×C4×C43C2×M1612yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×C4×C43H(5,𝔽2)12yes—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—44no—
331C2×Dic43—44no—
332C2×Dic43C2×C22⋊C412yes—
333C2×Dic43C2×C22⋊C412yes—
334D172—28no—
335D172—28no—
336D172—28no—
337D172—28no—
338C4×D43—24no—
339C4×D43—24no—
340C4×D43—24no—
341C4×D43—24no—
342C4×D43—44no—
343C4×D43—44no—
344C4×D43—44no—
345C4×D43—44no—
346C4×D43—42no—
347C4×D43—42no—
348C4×D43—42no—
349C4×D43—42no—
350C8×C43—24no—
351C8×C43—42no—
352C43⋊C8—42no—
353C43⋊C8—42no—
354#22399—431nomaximal, Sylow
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—22no—
359C22×C43—22no—
360C22×C43—22no—
361C22×C43#43514yescomplemented
362C22×C43C22×C22⋊C411yescharacteristic
363C22×C43C2×C4×D411yescharacteristic
364C22×C43#51811yescharacteristic
365C22×C43C22×M1611yescharacteristic
366C22×C43C22×M1611yescharacteristic
367C22×C43C2×#13111yescharacteristic
368C22×C43#56811yescharacteristic
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—22no—
381C2×D43—22no—
382C2×D43—22no—
383C2×D43—22no—
384C2×D43—416no—
385C2×D43—416no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43—41no—
390C2×D43—41no—
391C2×D43—41no—
392C2×D43—41no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43#40714yescomplemented
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—22no—
402C4×C43—22no—
403C4×C43—41no—
404C4×C43D4212yes—
405C4×C43#54612yes—
406Dic43—22no—
407Dic43—22no—
408Dic43—41no—
409Dic43—41no—
410C22×C4×D4—431no—
411C2×#435—432no—
412C2×#407—431no—
413C22×C22⋊C8—431no—
414#1955—432no—
415#1870—432no—
416#1869—432no—
417#1797—431no—
418#1779—431no—
419#1779—431no—
420#1749D4311yescharacteristic, complemented
421C2×C43—24no—
422C2×C43D4×C22⋊C411yescharacteristic
423C2×C43C2×#40711yescharacteristic
424C2×C43#288011yescharacteristic
425C2×C43C2×#43511yescharacteristic
426C2×C43D4×M1611yescharacteristic
427C2×C43#297311yescharacteristic
428C2×C43#297411yescharacteristic
429D43—24no—
430D43—42no—
431D43—42no—
432D43—42no—
433C23×D4—431no—
434C24×C4—431no—
435C24×C4—431no—
436C22×M16—432no—
437C23×C8—432no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—431no—
441C2×C4×D4—431no—
442C2×C4×D4—431no—
443C2×C4×D4—431no—
444C2×C4×D4—431no—
445C2×C4×D4—431no—
446C2×C4×D4—868no—
447C22×C4⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C42C2×D4311yescharacteristic
451#435—868no—
452C2×C4⋊C8—432no—
453#407—864no—
454C2×C22⋊C8—431no—
455C2×C22⋊C8—431no—
456C2×C22⋊C8—432no—
457C2×C22⋊C8—432no—
458C2×C22⋊C8—432no—
459C2×C22⋊C8—432no—
460C2×C22⋊C8—432no—
461C2×C22⋊C8—432no—
462C2×C22⋊C8—864no—
463C2×C22⋊C8C2×D4311yescharacteristic
464C2×C22⋊C8C2×D4311yescharacteristic
465C2×#97C2×D4312yescomplemented
466#336—432no—
467#336C2×D4312yescomplemented
468C43#2239911yescharacteristic, complemented, Sylow
469C25—431no—
470C25—431no—
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—431no—
474C22×D4—431no—
475C22×D4—864no—
476C22×D4—864no—
477C22×D4—864no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—864no—
489C23×C4—864no—
490C23×C4—862no—
491C23×C4—862no—
492C23×C4—862no—
493C23×C4—862no—
494C23×C4—1722no—
495C23×C4—1722no—
496C23×C4C4×D4311yescharacteristic
497C23×C4C4×D4311yescharacteristic
498C23×C4C22×D4311yescharacteristic
499C2×M16—864no—
500C2×M16—864no—
501C2×M16—1722no—
502C22×C8—432no—
503C22×C8—432no—
504C22×C8—864no—
505C22×C8—864no—
506C22×C8—1722no—
507C22×C8C22×D4312yes—
508C22×C8C22×D4312yes—
509C4×D4—438no—
510C4×D4—864no—
511C4×D4—864no—
512C4×D4—864no—
513C4×D4—864no—
514C4×D4—864no—
515C4×D4—864no—
516C4×D4—864no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4—864no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—431no—
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—864no—
531C2×C22⋊C4—864no—
532C2×C42—24no—
533C2×C42C4×D4311yescharacteristic
534C2×C42C4×D4311yescharacteristic
535C2×C42C22×D4311yescharacteristic
536C2×C42C22×D4311yescharacteristic
537C4⋊C8—864no—
538C22⋊C8—22no—
539C22⋊C8—864no—
540C22⋊C8—864no—
541C22⋊C8—862no—
542C22⋊C8—862no—
543C22⋊C8—864no—
544C22⋊C8—864no—
545C22⋊C8—1722no—
546C22⋊C8—1722no—
547C22⋊C8D17214yescomplemented
548#97—24no—
549C24—431no—
550C24—431no—
551C24—431no—
552C24—431no—
553C24—434no—
554C24—862no—
555C24—862no—
556C24—862no—
557C24—862no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—1721no—
564C24—1721no—
565C24—1721no—
566C24—1721no—
567C24C2×C4×D4311yescharacteristic
568C2×D4—434no—
569C2×D4—434no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—8632no—
579C2×D4—862no—
580C2×D4—862no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—41no—
589C22×C4—431no—
590C22×C4—431no—
591C22×C4—434no—
592C22×C4—434no—
593C22×C4—431no—
594C22×C4—431no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—1721no—
622C22×C4—1721no—
623C22×C4—1721no—
624C22×C4—1721no—
625C22×C4—1728no—
626C22×C4—1728no—
627C22×C4—1728no—
628C22×C4—1728no—
629C22×C4—1721no—
630C22×C4—1721no—
631C22×C4C2×C4×D4311yescharacteristic
632C22×C4C2×C4×D4311yescharacteristic
633C22×C4C2×C4×D4311yescharacteristic
634C22×C4C2×C4×D4311yescharacteristic
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4C2×D17212yes—
637C22×C4#1062189812yes—
638C22×C4C23×D4311yescharacteristic
639M16—1728no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—862no—
646C2×C8—862no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8—862no—
650C2×C8—862no—
651C2×C8—1728no—
652C2×C8C2×D17214yescomplemented
653C4⋊C4—434no—
654C4⋊C4—862no—
655C4⋊C4—862no—
656C4⋊C4—862no—
657C22⋊C4—434no—
658C22⋊C4—434no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—862no—
662C22⋊C4—862no—
663C22⋊C4—862no—
664C22⋊C4—862no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42D4×D4314yes—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—432no—
674C23—432no—
675C23—432no—
676C23—432no—
677C23—432no—
678C23—432no—
679C23—868no—
680C23—868no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—861no—
691C23—861no—
692C23—861no—
693C23—861no—
694C23—861no—
695C23—861no—
696C23—861no—
697C23—861no—
698C23—861no—
699C23—861no—
700C23—861no—
701C23—861no—
702C23—861no—
703C23—868no—
704C23—1724no—
705C23—1724no—
706C23—1724no—
707C23—1724no—
708C23—1724no—
709C23—1724no—
710C23—1724no—
711C23—1724no—
712C23—1724no—
713C23—1724no—
714C23—1724no—
715C23C4×D17212yes—
716C23M16×D4312yes—
717C23#1306333312yes—
718C23C22×C4×D4311yescharacteristic
719D4—868no—
720D4—868no—
721D4—868no—
722D4—868no—
723C2×C4—28no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—432no—
739C2×C4—432no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—864no—
745C2×C4—864no—
746C2×C4—864no—
747C2×C4—864no—
748C2×C4—861no—
749C2×C4—861no—
750C2×C4—861no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—1724no—
755C2×C4—1724no—
756C2×C4—1724no—
757C2×C4—1724no—
758C2×C4—1724no—
759C2×C4—1724no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4C22⋊C4×D4312yes—
765C2×C4C22⋊C4×D4312yes—
766C2×C4C4×D17212yes—
767C2×C4M16×D4312yes—
768C2×C4C2×D4×D4312yes—
769C2×C4C22×D17211yescharacteristic
770C2×C4C2×#1062189811yescharacteristic
771C2×C4#1306337112yes—
772C8—24no—
773C8—42no—
774C8—1722no—
775C8—1722no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—434no—
783C22—862no—
784C22—862no—
785C22—862no—
786C22—862no—
787C22—862no—
788C22—862no—
789C22—862no—
790C22—862no—
791C22—862no—
792C22—862no—
793C22—862no—
794C22—862no—
795C22—862no—
796C22—862no—
797C22—862no—
798C22—17216no—
799C22—17216no—
800C22—1721no—
801C22—1721no—
802C22—1721no—
803C22—1721no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22—1721no—
808C22—1721no—
809C22—1721no—
810C22—1721no—
811C22—1721no—
812C22#1458297214yescomplemented
813C22C2×C22⋊C4×D4311yescharacteristic
814C22C2×C4×D17211yescharacteristic
815C22#1458337311yescharacteristic
816C22C2×M16×D4311yescharacteristic
817C22C2×M16×D4311yescharacteristic
818C22C2×#1306333311yescharacteristic
819C22#1458366511yescharacteristic
820C4—22no—
821C4—22no—
822C4—22no—
823C4—22no—
824C4—41no—
825C4—862no—
826C4—862no—
827C4—1721no—
828C4—1721no—
829C4D4×D17212yes—
830C4#1458354512yes—
831C2—24no—
832C2—864no—
833C2—1722no—
834C2—1722no—
835C2—1722no—
836C2C22⋊C4×D17211yescharacteristic
837C2#407×D4311yescharacteristic
838C2#1914304511yescharacteristic
839C2C2×#1458297211yescharacteristic
840C2M16×D17211yescharacteristic
841C2#1914362311yescharacteristic
842C2#1914363211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1749C2
prime radicalC23×D172C4
cosocleC22×C4×C43C24
hypercenter#1749D43
hypocenterC43#22399
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. C2×#14582861C2semidirect
4. C2×C22⋊C8×D43C2semidirect
5. #19135393C2semidirect
6. #19134891C2semidirect
7. #19134886C2semidirect
8. #19134575C2semidirect
9. #19134504C2semidirect
10. #19134504C2semidirect
11. C43×#1749C2semidirect
15. C22×#10621872C22semidirect
16. C22×C8×D43C22semidirect
30. C2×C4⋊(C43⋊C8)C22semidirect
34. C2×(C2×D43)⋊C8C22semidirect
35. C2×(C2×D43)⋊C8C22semidirect
36. C2×(C2×D43)⋊C8C22semidirect
37. C2×(C2×D43)⋊C8C22semidirect
38. C2×(C2×D43)⋊C8C22semidirect
39. C2×(C2×D43)⋊C8C22semidirect
41. #14582654C22semidirect
45. C2×#97×C43C22semidirect
46. C43×#336C22semidirect
125. C22⋊C8×C43D4semidirect
141. C23×D43M16semidirect
184. C2×D172M16semidirect
222. C2×C8×C43C2×D4semidirect
361. C22×C43#435semidirect
398. C2×D43#407semidirect
420. #1749D43semidirect
465. C2×#97C2×D43semidirect
467. #336C2×D43semidirect
468. C43#22399semidirect
547. C22⋊C8D172semidirect
652. C2×C8C2×D172semidirect
812. C22#14582972semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D1722
C2×#145829722
C2×#145828612
C2×C22⋊C8×D432
#191353932
#191348912
#191348862
#191345752
#191345042
C43×#17492
#2239943