Finite Group Databasebeta

← #25113262

Subgroups — #25113262

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583609C211yesmaximal, characteristic
2C2×#14583030C211yesmaximal, characteristic, complemented
3#19135567C211yesmaximal, characteristic, complemented
4#19135563C211yesmaximal, characteristic, complemented
5#19135559C211yesmaximal, characteristic, complemented
6#19135552C211yesmaximal, characteristic, complemented
7#19135552C211yesmaximal, characteristic, complemented
8#19135547C211yesmaximal, characteristic, complemented
9#19134602C211yesmaximal, characteristic
10#19134602C211yesmaximal, characteristic
11#19134592C211yesmaximal, characteristic
12#19134423C211yesmaximal, characteristic
13#19134423C211yesmaximal, characteristic
14C4×#13063245C211yesmaximal, characteristic
15C43×#2355C211yesmaximal, characteristic, complemented
16#14583609—24no—
17#14583609C418yescomplemented
18C2×#13063325C2211yescharacteristic
19C2×#13063317C2211yescharacteristic
20C2×#13063317C2211yescharacteristic
21C2×#13063303—21no—
22C2×#13063303—21no—
23C2×#13063301—21no—
24C2×C4×D172C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×C4×D172C2211yescharacteristic
27C2×C4⋊C4×D43—21no—
28#14583030—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#391—21no—
53C43×#387—21no—
54C43×#387—21no—
55C43×#384C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C4×C4⋊C4×C43—21no—
59C4×C4⋊C4×C43C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86—21no—
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063325—22no—
72#13063325C2×C414yes—
73#13063317—22no—
74#13063317—22no—
75#13063317C2×C414yes—
76#13063317C2×C414yes—
77#13063303—28no—
78#13063303—28no—
79#13063301—28no—
80C4×D172—22no—
81C4×D172—22no—
82C4×D172—22no—
83C4×D172C2×C414yes—
84C4×D172C2×C414yes—
85C4×D172C2×C414yes—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C4⋊C4×D43—28no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C4⋊(C43⋊C8)—22no—
99C4⋊(C43⋊C8)—22no—
100C4⋊(C43⋊C8)—22no—
101#13063245—22no—
102#13063245—22no—
103#13063245—22no—
104#13063245Q814yescomplemented
105#13063236—22no—
106#13063236—22no—
107C4×C43⋊C8—22no—
108C22×Q8×C43D411yescharacteristic
109C4×Q8×C43C2×C414yes—
110C4×Q8×C43D414yes—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C42×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43—21no—
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C23×D43—21no—
134C2×Q8×C43—41no—
135C2×Q8×C43—41no—
136C2×Q8×C43C22⋊C414yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C22×C412yes—
155C2×D172C2×Q812yes—
156C2×D172#4112yes—
157C2×C4×D43—24no—
158C2×C4×D43—24no—
159C2×C4×D43—24no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×Dic86—24no—
167C2×Dic86—81no—
168C2×Dic86—81no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43C22⋊C414yes—
179C4⋊C4×C43C22⋊C414yes—
180C4⋊C4×C43C22⋊C414yes—
181C4⋊C4×C43C2×Q812yes—
182C42×C43—42no—
183C42×C43—81no—
184C42×C43—81no—
185C42×C43C22×C412yes—
186C42×C43C22×C412yes—
187C42×C43C22×C412yes—
188C42×C43C2×D412yes—
189C42×C43C2×D412yes—
190C42×C43C2×D412yes—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—24no—
194C4⋊Dic43—24no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43C22×C412yes—
199C4⋊Dic43C22×C412yes—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—24no—
202Dic43⋊C4—24no—
203Dic43⋊C4—24no—
204Dic43⋊C4—24no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8C2×Q812yes—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225Q8×C43—44no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43C2×C22⋊C412yes—
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C2×C22⋊C412yes—
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C23×C411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C2×C4×C43C22×Q811yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×C4×C432−1+411yescharacteristic
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271D172—22no—
272D172—22no—
273D172—22no—
274D172C4×Q814yes—
275C4×D43—48no—
276C4×D43—84no—
277C4×D43—84no—
278Dic86—84no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283#22526—431nomaximal, Sylow
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43#54811yescharacteristic
286C22×C43D4×Q811yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57511yescharacteristic
289C22×C43#57611yescharacteristic
290C22×C43#57711yescharacteristic
291C2×D43—24no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43C2×C4×Q811yescharacteristic
309C4×C43#51911yescharacteristic
310C4×C43#54811yescharacteristic
311C4×C43D4×Q811yescharacteristic
312Dic43—42no—
313Dic43—42no—
314Dic43—42no—
315C2×#554—431no—
316C2×#446—431no—
317#2355D4311yescharacteristic, complemented
318#1993—431no—
319#1992—431no—
320#1991—431no—
321#1989—431no—
322#1989—431no—
323#1988—431no—
324#1804—431no—
325#1804—431no—
326#1802—431no—
327#1762—431no—
328#1762—431no—
329C4×#102—431no—
330C2×C43Q8×C22⋊C411yescharacteristic
331C2×C43#289611yescharacteristic
332C2×C43#289711yescharacteristic
333C2×C43#337011yescharacteristic
334C2×C43#337611yescharacteristic
335C2×C43#338811yescharacteristic
336C2×C43#338911yescharacteristic
337D43—44no—
338#554—438no—
339#554—864no—
340C2×C4⋊Q8—431no—
341C2×#125—431no—
342C2×#125—431no—
343C2×C22⋊Q8—861no—
344C2×C22⋊Q8—861no—
345C2×C22⋊Q8—861no—
346C2×C4×Q8C2×D4311yescharacteristic
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350C22×C4⋊C4—861no—
351#446—864no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#97—431no—
360C2×#97—431no—
361C2×C4×C8—431no—
362#391—21no—
363#387—21no—
364#387—21no—
365#384C2×D4311yescharacteristic
366#382C2×D4311yescharacteristic
367#382C2×D4311yescharacteristic
368C4×C4⋊C4—21no—
369C4×C4⋊C4C2×D4311yescharacteristic
370C4×C4⋊C4C2×D4311yescharacteristic
371C4×C4⋊C4C2×D4311yescharacteristic
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384C43#2252611yescharacteristic, complemented, Sylow
385C22×Q8—861no—
386C22×Q8C22⋊D4311yescharacteristic
387C22×D4—431no—
388C23×C4—861no—
389C23×C4—861no—
390C23×C4—861no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—431no—
395C4⋊Q8—434no—
396C4⋊Q8—862no—
397#125—434no—
398#125—434no—
399#125—862no—
400#125—862no—
401C22⋊Q8—868no—
402C22⋊Q8—868no—
403C22⋊Q8—868no—
404C4×Q8C4×D4314yes—
405C4×Q8D17214yes—
406C4×D4—434no—
407C4×D4—434no—
408C4×D4—434no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—868no—
423C2×C4⋊C4C22⋊D4311yescharacteristic
424C2×C4⋊C4C22⋊D4311yescharacteristic
425C2×C4⋊C4C22⋊D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C22×D4311yescharacteristic
437C2×C42C22×D4311yescharacteristic
438C2×C42C22×D4311yescharacteristic
439C4⋊C8—862no—
440C4⋊C8—862no—
441C4⋊C8—862no—
442#102—434no—
443#102—862no—
444#102—862no—
445#102—862no—
446#97—862no—
447#97—862no—
448C4×C8—862no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456C24—861no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8—864no—
460C2×Q8—3441no—
461C2×Q8—3441no—
462C2×Q8(C2×D43)⋊C414yes—
463C2×D4—432no—
464C2×D4—432no—
465C2×D4—432no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—864no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—3441no—
480C22×C4—3441no—
481C22×C4—3441no—
482C22×C4—3441no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C2×C22⋊D4311yescharacteristic
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492C2×C8—432no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—42no—
512C4⋊C4—81no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—432no—
516C4⋊C4—864no—
517C4⋊C4—864no—
518C4⋊C4—864no—
519C4⋊C4—864no—
520C4⋊C4—864no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4(C2×D43)⋊C414yes—
525C4⋊C4(C2×D43)⋊C414yes—
526C4⋊C4(C2×D43)⋊C414yes—
527C4⋊C4Q8×D4312yes—
528C22⋊C4—864no—
529C22⋊C4—864no—
530C22⋊C4—864no—
531C42—42no—
532C42—81no—
533C42—81no—
534C42C2×C4×D4312yes—
535C42C2×C4×D4312yes—
536C42C2×C4×D4312yes—
537C42C2×D17212yes—
538C42C2×D17212yes—
539C42C2×D17212yes—
540C23—862no—
541C23—862no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23C22×C22⋊D4311yescharacteristic
548Q8—44no—
549Q8—3444no—
550D4—434no—
551D4—862no—
552D4—862no—
553D4—862no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—3444no—
582C2×C4—3444no—
583C2×C4—1728no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4C2×(C2×D43)⋊C412yes—
591C2×C4C2×(C2×D43)⋊C412yes—
592C2×C4C2×(C2×D43)⋊C412yes—
593C2×C4C2×(C2×D43)⋊C412yes—
594C2×C4C2×(C2×D43)⋊C412yes—
595C2×C4C2×(C2×D43)⋊C412yes—
596C2×C4C22×C4×D4311yescharacteristic
597C2×C4C22×D17211yescharacteristic
598C2×C4C2×Q8×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#1306337211yescharacteristic
601C2×C4#1306337311yescharacteristic
602C8—862no—
603C8—1721no—
604C8—1721no—
605C8—1721no—
606C22—864no—
607C22—1722no—
608C22—1722no—
609C22—1722no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22C22×(C2×D43)⋊C411yescharacteristic
614C22#1458355611yescharacteristic
615C22Q8×C22⋊D4311yescharacteristic
616C22#1458369711yescharacteristic
617C22#1458369711yescharacteristic
618C22#1458370211yescharacteristic
619C22#1458370711yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—1722no—
631C4—1722no—
632C4—1722no—
633C4C4×Q8×D4311yescharacteristic
634C4#1458337511yescharacteristic
635C4#1458356111yescharacteristic
636C4Q8×D17211yescharacteristic
637C2—1724no—
638C2Q8×(C2×D43)⋊C411yescharacteristic
639C2#1914311211yescharacteristic
640C2#1914311811yescharacteristic
641C2#1914734211yescharacteristic
642C2#1914741611yescharacteristic
643C2#1914753411yescharacteristic
644C2#1914754911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2355C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2355D43
hypocenterC43#22526
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×#14583030C2semidirect
3. #19135567C2semidirect
4. #19135563C2semidirect
5. #19135559C2semidirect
6. #19135552C2semidirect
7. #19135552C2semidirect
8. #19135547C2semidirect
15. C43×#2355C2semidirect
17. #14583609C4semidirect
104. #13063245Q8semidirect
317. #2355D43semidirect
384. C43#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#145836092
C2×#145830302
#191355672
#191355632
#191355592
#191355522
#191355472
#191346022
#191345922
#191344232
C4×#130632452
C43×#23552
#2252643