Finite Group Databasebeta

← #25104156

Subgroups — #25104156

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583177C211yesmaximal, characteristic
2#19137166C211yesmaximal, characteristic, complemented
3C4×D4×Dic43C211yesmaximal, characteristic
4#19135545C211yesmaximal, characteristic, complemented
5#19135350C211yesmaximal, characteristic, complemented
6#19135167C211yesmaximal, characteristic, complemented
7#19135163C211yesmaximal, characteristic, complemented
8#19134842C211yesmaximal, characteristic
9#19134593C211yesmaximal, characteristic
10#107×Dic43C211yesmaximal, characteristic, complemented
11#19134487C211yesmaximal, characteristic, complemented
12#19134443C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#1862C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063290—21no—
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C22×C4×Dic43—21no—
21#14583177C418yescomplemented
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31#14582803—21no—
32#14582797C2211yescharacteristic
33#14582794—21no—
34#14582768C2211yescharacteristic
35C4⋊C4×Dic43C2211yescharacteristic
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40#14582750—21no—
41C22⋊C4×Dic43—21no—
42C22⋊C4×Dic43—21no—
43C4×C22⋊Dic43—21no—
44C42×Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C23×Dic43—21no—
62C23×Dic43—21no—
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063324—22no—
66#13063324C2×C414yescomplemented
67#13063290—44no—
68D4×Dic43—22no—
69D4×Dic43—22no—
70D4×Dic43C2×C414yes—
71D4×Dic43Q814yescomplemented
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—44no—
88C2×C4×Dic43D411yescharacteristic
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94#13063259C2×C414yescomplemented
95#13063258—22no—
96#13063258C2×C414yescomplemented
97Dic43⋊C8—22no—
98Dic43⋊C8C2×C414yescomplemented
99#13063246—22no—
100#13063246C2×C414yes—
101C8×Dic43—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#102×C43—22no—
123#102×C43C2×C414yes—
124#95×C43—21no—
125C24×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43C22×C412yes—
130C2×D4×C43C2×Q812yes—
131C2×D4×C43#4112yes—
132C22×C4×C43—24no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—24no—
142C22×Dic43—24no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—42no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C2×Dic86—24no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C412yes—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43C22×C412yes—
170C4⋊C4×C43#4112yes—
171C22⋊C4×C43—24no—
172C42×C43—21no—
173C42×C43—21no—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43C22×C412yes—
182C4⋊Dic43C22×C412yes—
183C4⋊Dic43C2×Q812yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—42no—
186Dic43⋊C4—42no—
187Dic43⋊C4—42no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—41no—
191C4×Dic43—42no—
192C4×Dic43—42no—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C4×Dic43D814yes—
197C4×Dic43C22×C412yes—
198C4×Dic43C2×Q812yes—
199C4×Dic43#4112yes—
200C4×Dic43#4112yes—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C412yes—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C22×D411yescharacteristic
215D4×C43—22no—
216D4×C43—22no—
217D4×C43—22no—
218D4×C43C4×Q814yescomplemented
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—22no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—48no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C2×D812yes—
235C2×C4×C43C23×C411yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—48no—
255C2×Dic43—48no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43C4×D412yes—
260C2×Dic43C4×D412yes—
261C2×Dic43C22⋊Q812yes—
262C2×Dic43C22⋊Q812yes—
263C2×Dic43C2×D812yes—
264C2×Dic43C2×D812yes—
265C2×Dic43#13512yes—
266C2×Dic43#13712yes—
267Dic86—48no—
268C8×C43—22no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—41no—
272C4×#474—431nomaximal, Sylow
273C22×C43—24no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43C2×C4×D411yescharacteristic
281C22×C43C2×C22⋊Q811yescharacteristic
282C22×C43#52511yescharacteristic
283C22×C43C22×D811yescharacteristic
284C22×C43C2×#13511yescharacteristic
285C22×C43C2×#13711yescharacteristic
286C22×C43#57511yescharacteristic
287C4×C43—22no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43C2×C4×Q811yescharacteristic
293C4×C43C4×#4111yescharacteristic
294C4×C43#52911yescharacteristic
295C4×C43#53311yescharacteristic
296Dic43—22no—
297Dic43—22no—
298Dic43—42no—
299Dic43—42no—
300Dic43—42no—
301Dic43—81no—
302Dic43C4×D814yes—
303Dic43#47414yescomplemented
304C2×#474—431no—
305C4×C4⋊Q8—431no—
306C42×D4—431no—
307#1988—431no—
308#1947—431no—
309#1918—431no—
310#1918—431no—
311#1862—431no—
312#1862D4311yescharacteristic
313#1802—431no—
314C4×#107—431no—
315C4×#107—431no—
316C4×C4⋊C8—431no—
317C4×#102—431no—
318C4×#102—431no—
319C2×C43—44no—
320C2×C43C4×C22⋊Q811yescharacteristic
321C2×C43C2×C4×D811yescharacteristic
322C2×C43C4×#13711yescharacteristic
323C2×C43C2×#47411yescharacteristic
324C2×C43#307611yescharacteristic
325C2×C43#310011yescharacteristic
326C2×C43#310711yescharacteristic
327C2×C4⋊Q8—431no—
328C2×C4×Q8—861no—
329C2×C4×D4—431no—
330C2×C4×D4—431no—
331C2×C4×D4C2×D4311yescharacteristic
332C22×C42—861no—
333#474—438no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#107—431no—
337C2×#107C2×D4311yescharacteristic
338C2×C4⋊C8—431no—
339C2×C4⋊C8—431no—
340C2×#102—431no—
341C2×#102—431no—
342C2×#102C2×D4311yescharacteristic
343C2×#102C2×D4311yescharacteristic
344C2×C4×C8—431no—
345C2×C4×C8—431no—
346#391—861no—
347#389—431no—
348#389—861no—
349#389C2×D4311yescharacteristic
350#384—431no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—431no—
356C4×C4⋊C4—861no—
357C4×C22⋊C4—861no—
358C4×C22⋊C4—861no—
359C4×C22⋊C4—861no—
360C43—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336C2×D4311yescharacteristic
371C43C4×#47411yescharacteristic, complemented, Sylow
372C22×Q8—861no—
373C22×D4C22×D4311yescharacteristic
374C23×C4—21no—
375C23×C4—861no—
376C23×C4—861no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8C22×D4311yescharacteristic
380C22×C8C22×D4311yescharacteristic
381C4⋊Q8—434no—
382C4⋊Q8—862no—
383C4×Q8—1724no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—434no—
387C4×D4—434no—
388C4×D4—862no—
389C4×D4—862no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C42—431no—
406C2×C42—431no—
407C2×C42—431no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—1724no—
417C2×C42C22×D4311yescharacteristic
418#107—22no—
419#107—434no—
420#107—434no—
421#107—862no—
422C4⋊C8—434no—
423C4⋊C8—862no—
424#102—22no—
425#102—434no—
426#102—862no—
427#102C4×D4314yes—
428C4×C8—862no—
429C4×C8—862no—
430#95—21no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437C24—21no—
438C2×Q8—864no—
439C2×Q8—1722no—
440C2×Q8—1722no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×C4×D4312yes—
445C2×D4#1062190012yes—
446C2×D4Q8×D4312yes—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—864no—
458C22×C4—864no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1722no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4D4×D4311yescharacteristic
468C22×C4D4×D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8C2×C4×D4312yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4C2×C4×D4312yes—
500C4⋊C4#1062190012yes—
501C22⋊C4—24no—
502C22⋊C4—864no—
503C22⋊C4—864no—
504C42—21no—
505C42—21no—
506C42—434no—
507C42—432no—
508C42—432no—
509C42—432no—
510C42—432no—
511C42—862no—
512C42—862no—
513C42—1721no—
514C42—1722no—
515C42—1722no—
516C42—1722no—
517C42—1722no—
518C42—1722no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23C2×D4×D4311yescharacteristic
527Q8—1728no—
528D4—22no—
529D4—22no—
530D4—22no—
531D4#1306329014yescomplemented
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—48no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—1728no—
563C2×C4—1728no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4D8×D4312yes—
574C2×C4C22×C4×D4311yescharacteristic
575C2×C4C2×Q8×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C8—22no—
581C8—41no—
582C8—862no—
583C8—1721no—
584C22—24no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22C4×D4×D4311yescharacteristic
592C22C22⋊Q8×D4311yescharacteristic
593C22#1458340511yescharacteristic
594C22C2×D8×D4311yescharacteristic
595C22#135×D4311yescharacteristic
596C22#137×D4311yescharacteristic
597C22#1458369511yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—81no—
603C4—434no—
604C4—434no—
605C4—862no—
606C4—862no—
607C4—3441no—
608C4—1722no—
609C4—1722no—
610C4—1722no—
611C4C2×#1306329011yescharacteristic
612C4C4×#1062190011yescharacteristic
613C4#1458342611yescharacteristic
614C4#1458345111yescharacteristic
615C2—44no—
616C2#1913712711yescharacteristic
617C2C4×D8×D4311yescharacteristic
618C2#1914341711yescharacteristic
619C2#474×D4311yescharacteristic
620C2#1914438011yescharacteristic
621C2#1914459011yescharacteristic
622C2#1914465911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1862D43
hypocenterC43C4×#474
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #19137166C2semidirect
4. #19135545C2semidirect
5. #19135350C2semidirect
6. #19135167C2semidirect
7. #19135163C2semidirect
10. #107×Dic43C2semidirect
11. #19134487C2semidirect
12. #19134443C2semidirect
21. #14583177C4semidirect
66. #13063324C2×C4semidirect
71. D4×Dic43Q8semidirect
94. #13063259C2×C4semidirect
96. #13063258C2×C4semidirect
98. Dic43⋊C8C2×C4semidirect
218. D4×C43C4×Q8semidirect
303. Dic43#474semidirect
371. C43C4×#474semidirect
531. D4#13063290semidirect

Maximal subgroups

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

subgroupindex
C2×#145831772
#191371662
C4×D4×Dic432
#191355452
#191353502
#191351672
#191351632
#191348422
#191345932
#107×Dic432
#191344872
#191344432
#102×Dic432
C43×#18622
C4×#47443