Finite Group Databasebeta

← #25101476

Subgroups — #25101476

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582953C211yesmaximal, characteristic
2#19136997C211yesmaximal, characteristic
3#117×Dic43C211yesmaximal, characteristic
4#19135357C211yesmaximal, characteristic, complemented
5#19135355C211yesmaximal, characteristic, complemented
6#19135352C211yesmaximal, characteristic, complemented
7#19135350C211yesmaximal, characteristic, complemented
8#19134796C211yesmaximal, characteristic
9#19134794C211yesmaximal, characteristic
10#19134792C211yesmaximal, characteristic
11#19134495C211yesmaximal, characteristic, complemented
12#19134494C211yesmaximal, characteristic, complemented
13#19134491C211yesmaximal, characteristic, complemented
14#19134491C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C2×#13063281—21no—
18C22×C4×Dic43C2211yescharacteristic
19#14582953C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31#14582768C2211yescharacteristic
32#14582768C2211yescharacteristic
33#14582763—21no—
34#14582759C2211yescharacteristic
35#14582757—21no—
36C4⋊C4×Dic43C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42#14582750—21no—
43C22⋊C4×Dic43—21no—
44C22⋊C4×Dic43—21no—
45#14582745—21no—
46C42×Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C23×Dic43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063284—22no—
65#13063284—22no—
66#13063281—44no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2×C414yes—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43Q814yes—
88C2×C4×Dic43C2311yescharacteristic
89C2×C4×Dic43C2311yescharacteristic
90#13063259—22no—
91#13063258—22no—
92#13063258—22no—
93#13063257—22no—
94#13063256—22no—
95#13063256—22no—
96Dic43⋊C8C2×C414yes—
97Dic43⋊C8C2×C414yes—
98C22⋊(C43⋊C8)C2×C414yes—
99#13063235C2×C414yes—
100#13063235C2×C414yes—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111#117×C43—22no—
112#117×C43—22no—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120#107×C43—22no—
121#106×C43—22no—
122C22⋊C8×C43C2×C414yes—
123#95×C43—21no—
124C24×C43C2×D411yescharacteristic
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×Q812yes—
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—41no—
144C22×Dic43—41no—
145C22×Dic43C4⋊C414yes—
146C22×Dic43C4⋊C414yes—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43C22×C412yes—
156C2×C8×C43C22×C412yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43#4112yes—
164C4⋊C4×C43#4112yes—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—42no—
167C42×C43—24no—
168C22⋊Dic43—24no—
169C22⋊Dic43—42no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43#4112yes—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182C4×Dic43—24no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43—42no—
187C4×Dic43—42no—
188C4×Dic43—42no—
189C4×Dic43C4⋊C414yes—
190C4×Dic43C4⋊C414yes—
191C4×Dic43C22×C412yes—
192C4×Dic43C22×C412yes—
193C4×Dic43C2×Q812yes—
194C4×Dic43C2×Q812yes—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C22×C412yes—
200C2×C43⋊C8C22×C412yes—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43C2×C4⋊C412yes—
208C23×C43C22×D411yescharacteristic
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C2×C4⋊C412yes—
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×Q811yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—28no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—44no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43C2×C4⋊C412yes—
255C2×Dic43C2×C4⋊C412yes—
256C2×Dic43C2×C4⋊C412yes—
257C2×Dic43C2×C4⋊C412yes—
258C2×Dic43AGL(1,ℤ/8)12yes—
259C2×Dic43#13712yes—
260C8×C43—22no—
261C8×C43—22no—
262C43⋊C8—22no—
263C43⋊C8—22no—
264#21364—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43C22×C4⋊C411yescharacteristic
273C22×C43#52511yescharacteristic
274C22×C43#52511yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—81no—
283C4×C43—81no—
284C4×C43C4×#4111yescharacteristic
285C4×C43C4×#4111yescharacteristic
286C4×C43#53311yescharacteristic
287C4×C43#53311yescharacteristic
288Dic43—22no—
289Dic43—22no—
290Dic43—22no—
291Dic43—42no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43#42814yes—
296C2×#432—431no—
297#2285—431no—
298C4×#117—431no—
299#1948—431no—
300#1948—431no—
301#1947—431no—
302#1947—431no—
303#1854—431no—
304#1854—431no—
305#1854—431no—
306#1854D4311yescharacteristic
307#1776—431no—
308#1776—431no—
309#1776—431no—
310#1776—431no—
311C2×C43—42no—
312C2×C43#229611yescharacteristic
313C2×C43C2×#42811yescharacteristic
314C2×C43#291111yescharacteristic
315C2×C43#311511yescharacteristic
316C2×C43#311511yescharacteristic
317C2×C43#311611yescharacteristic
318C2×C43#311611yescharacteristic
319C2×#117—431no—
320C2×#117—861no—
321C2×#117C2×D4311yescharacteristic
322C22×C42—431no—
323#432—438no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#107—431no—
327C2×#107C2×D4311yescharacteristic
328C2×#106—431no—
329C2×#106—431no—
330C2×#106—431no—
331C2×#106C2×D4311yescharacteristic
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334C2×C22⋊C8—431no—
335C2×C22⋊C8C2×D4311yescharacteristic
336C2×#97—431no—
337C2×#97—431no—
338#384—431no—
339#384—431no—
340#382—861no—
341#380—431no—
342#380—861no—
343#380C2×D4311yescharacteristic
344C4×C4⋊C4—431no—
345C4×C4⋊C4—431no—
346C4×C4⋊C4—431no—
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4—861no—
351C4×C22⋊C4—861no—
352C4×C22⋊C4—861no—
353#376—861no—
354C43—861no—
355#340—431no—
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#340C2×D4311yescharacteristic
363C43#2136411yescharacteristic, complemented, Sylow
364C23×C4—431no—
365C23×C4—431no—
366C23×C4C22×D4311yescharacteristic
367C22×C8—431no—
368C22×C8—431no—
369C22×C8C22×D4311yescharacteristic
370C22×C8C22×D4311yescharacteristic
371#117—22no—
372#117—22no—
373#117—862no—
374#117—862no—
375#117—1724no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—21no—
393C2×C42—434no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—434no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—861no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42—861no—
403C2×C42—861no—
404C2×C42—861no—
405C2×C42—861no—
406#107—22no—
407#107—862no—
408#107—862no—
409#107—862no—
410#106—22no—
411#106—862no—
412#106—862no—
413#106—862no—
414C4⋊C8—434no—
415C4⋊C8—434no—
416C22⋊C8—434no—
417C22⋊C8C4×D4314yes—
418#97—434no—
419#97—434no—
420#95—21no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428C24D4×D4311yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—434no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—434no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4C2×C4×D4312yes—
452C22×C4D4×D4311yescharacteristic
453C22×C4Q8×D4312yes—
454C22×C4C23×D4311yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—432no—
460C2×C8—432no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8C2×C4×D4312yes—
466C2×C8C2×C4×D4312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4#1062190012yes—
486C4⋊C4#1062190012yes—
487C22⋊C4—24no—
488C22⋊C4—42no—
489C22⋊C4—864no—
490C22⋊C4—1722no—
491C42—24no—
492C42—434no—
493C42—434no—
494C42—432no—
495C42—432no—
496C42—432no—
497C42—432no—
498C42—864no—
499C42—1722no—
500C42—1722no—
501C42—1722no—
502C42—1722no—
503C42—1722no—
504C42—1722no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4⋊C4×D4312yes—
512C23C2×D4×D4311yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—868no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—1724no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C4⋊C4×D4312yes—
558C2×C4C22×C4×D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4#41×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4C2×#1062190011yescharacteristic
563C2×C4C2×#1062190011yescharacteristic
564C8—22no—
565C8—22no—
566C8—862no—
567C8—862no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×C4⋊C4×D4311yescharacteristic
576C22#1458340511yescharacteristic
577C22#1458340711yescharacteristic
578C22AGL(1,ℤ/8)×D4311yescharacteristic
579C22#137×D4311yescharacteristic
580C22#1458369611yescharacteristic
581C22#1458369611yescharacteristic
582C4—22no—
583C4—42no—
584C4—42no—
585C4—81no—
586C4—81no—
587C4—434no—
588C4—862no—
589C4—862no—
590C4—862no—
591C4—3441no—
592C4—3441no—
593C4—1722no—
594C4—1722no—
595C4C4×#1062190011yescharacteristic
596C4C4×#1062190011yescharacteristic
597C4#1458345111yescharacteristic
598C4#1458345111yescharacteristic
599C2—42no—
600C2#1913707411yescharacteristic
601C2#428×D4311yescharacteristic
602C2#1914318311yescharacteristic
603C2#1914473911yescharacteristic
604C2#1914474111yescharacteristic
605C2#1914475011yescharacteristic
606C2#1914475211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#21364
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #19135357C2semidirect
5. #19135355C2semidirect
6. #19135352C2semidirect
7. #19135350C2semidirect
11. #19134495C2semidirect
12. #19134494C2semidirect
13. #19134491C2semidirect
14. #19134491C2semidirect
19. #14582953C4semidirect
363. C43#21364semidirect

Maximal subgroups

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

subgroupindex
C2×#145829532
#191369972
#117×Dic432
#191353572
#191353552
#191353522
#191353502
#191347962
#191347942
#191347922
#191344952
#191344942
#191344912
C43×#18542
#2136443