Finite Group Databasebeta

← #25256020

Subgroups — #25256020

Order 11008.

2434 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063290C211yesmaximal, characteristic
2#19137549C214yesmaximal, complemented
3#19137548C212yesmaximal, complemented
4#19137509C212yesmaximal, complemented
5#19137473C212yesmaximal
6#19137472C211yesmaximal, characteristic
7#19137467C212yesmaximal
8C22⋊C4×Dic86C211yesmaximal, characteristic
9#19137427C211yesmaximal, characteristic
10#19137068C214yesmaximal, complemented
11#19137066C212yesmaximal, complemented
12#19136997C211yesmaximal, characteristic
13#19136997C212yesmaximal
14C4×#13063290C212yesmaximal, complemented
15C4×#13063281C211yesmaximal, characteristic
16C4×#13063281C212yesmaximal
17C43×#2345C211yesmaximal, characteristic
18C23×Dic86C2211yescharacteristic
19C2×C4×Dic86C2212yes—
20C2×#13063290C4116yescomplemented
21C2×#13063290C2212yes—
22C2×#13063290C2211yescharacteristic
23C2×#13063290C2212yes—
24C2×#13063290C2211yescharacteristic
25C2×#13063290C2212yes—
26C2×#13063290C2211yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×#13063281C2211yescharacteristic
29C2×#13063281C2212yes—
30C2×#13063281C2211yescharacteristic
31C22×Dic43⋊C4C2212yes—
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2212yes—
34#14582805C2212yes—
35#14582804C2212yes—
36#14582803C2214yes—
37#14582803C2214yes—
38#14582798C2212yes—
39#14582796C2214yes—
40#14582794C2214yes—
41#14582786C2214yes—
42#14582785C2214yes—
43#14582783C2214yes—
44#14582781C2214yes—
45#14582780C2214yes—
46#14582768C2212yes—
47#14582768C2214yes—
48#14582763C2214yes—
49#14582763C2212yes—
50#14582759C2211yescharacteristic
51#14582759C2212yes—
52#14582757C2212yes—
53#14582757C2212yes—
54#14582757C2212yes—
55C4⋊C4×Dic43C2212yes—
56C4⋊C4×Dic43C2214yes—
57C4⋊C4×Dic43C2212yes—
58C4×Dic43⋊C4C2214yes—
59C4×Dic43⋊C4C2212yes—
60C4×Dic43⋊C4C2214yes—
61#14582750C2212yes—
62#14582750C2214yes—
63#14582750C2214yes—
64#14582750C2212yes—
65#14582750C2214yes—
66C22⋊C4×Dic43C2212yes—
67C22⋊C4×Dic43C2212yes—
68C22⋊C4×Dic43C2211yescharacteristic
69C22⋊C4×Dic43C2211yescharacteristic
70C4×C22⋊Dic43C2211yescharacteristic
71C4×C22⋊Dic43C2212yes—
72#14582744C2214yes—
73#14582744C2212yes—
74C42×Dic43C2212yes—
75C42×Dic43C2214yes—
76C22×C4⋊C4×C43C2211yescharacteristic
77C43×#389C2212yes—
78C43×#387C2214yes—
79C43×#380C2211yescharacteristic
80C43×#380C2212yes—
81C4×C4⋊C4×C43C2212yes—
82C4×C22⋊C4×C43C2211yescharacteristic
83C4×C22⋊C4×C43C2212yes—
84C22×Dic86—28no—
85C22×Dic86C2×C418yes—
86C22×Dic86C2312yes—
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2311yescharacteristic
89C23×Dic43C2312yes—
90C23×Dic43C2311yescharacteristic
91C23×Dic43C2311yescharacteristic
92C4×Dic86—28no—
93#13063290—28no—
94#13063290C2×C418yes—
95#13063290C2×C4116yes—
96#13063290C2×C418yes—
97#13063290C2×C4116yes—
98#13063290C2×C418yes—
99#13063290C2×C418yes—
100#13063281—24no—
101#13063281—28no—
102#13063281Q818yescomplemented
103C2×C4⋊Dic43C2312yes—
104C2×C4⋊Dic43C2314yes—
105C2×Dic43⋊C4C2×C4116yes—
106C2×Dic43⋊C4C2314yes—
107C2×Dic43⋊C4C2314yes—
108C2×Dic43⋊C4C2312yes—
109C2×Dic43⋊C4C2314yes—
110C2×Dic43⋊C4C2314yes—
111C2×Dic43⋊C4C2312yes—
112C2×Dic43⋊C4C2312yes—
113C2×Dic43⋊C4C2312yes—
114C2×Dic43⋊C4C2312yes—
115C2×Dic43⋊C4C2312yes—
116C2×C22⋊Dic43C2311yescharacteristic
117C2×C22⋊Dic43C2312yes—
118C2×C22⋊Dic43C2311yescharacteristic
119C2×C4×Dic43C2×C4116yes—
120C2×C4×Dic43C2×C418yes—
121C2×C4×Dic43C2314yes—
122C2×C4×Dic43C2314yes—
123C2×C4×Dic43C2312yes—
124C2×C4×Dic43C2312yes—
125C2×C4×Dic43C2314yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2312yes—
128C2×C4×Dic43C2312yes—
129C2×C4×Dic43C2312yes—
130C2×C4×Dic43C2311yescharacteristic
131C2×C4×Dic43C2311yescharacteristic
132C2×C4×Dic43C2312yes—
133C2×C4×Dic43C2311yescharacteristic
134C2×C4×Dic43C2312yes—
135C2×C4×Dic43C2312yes—
136C2×C4×Dic43C2311yescharacteristic
137C2×C4×Dic43C2312yes—
138C43⋊#95C2312yes—
139C43⋊#95C2312yes—
140C43⋊#95C2314yes—
141C43⋊#95C2314yes—
142C43⋊#95C2314yes—
143C43⋊#95C2314yes—
144C43⋊#95C2314yes—
145C43⋊#95C2312yes—
146C43⋊#95C2312yes—
147C43⋊#95C2314yes—
148C43⋊#95C2314yes—
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2312yes—
151C2×C4⋊C4×C43C2×C418yes—
152C2×C4⋊C4×C43C2312yes—
153C2×C4⋊C4×C43C2314yes—
154C2×C4⋊C4×C43C2312yes—
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C22⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43C2312yes—
159C2×C22⋊C4×C43C2311yescharacteristic
160C2×C42×C43C2312yes—
161C2×C42×C43C2314yes—
162#95×C43C2314yes—
163#95×C43C2312yes—
164#95×C43C2312yes—
165#95×C43C2314yes—
166C24×C43C2411yescharacteristic
167C22×C4×C43—24no—
168C22×C4×C43—44no—
169C22×C4×C43C22×C414yes—
170C22×C4×C43C22×C418yes—
171C22×C4×C43C2414yes—
172C22×C4×C43C2412yes—
173C22×C4×C43C2411yescharacteristic
174C22×C4×C43C2412yes—
175C22×C4×C43C2412yes—
176C22×C4×C43C2412yes—
177C22×C4×C43C2411yescharacteristic
178C22×Dic43—28no—
179C22×Dic43—42no—
180C22×Dic43C22×C418yes—
181C22×Dic43C22×C414yes—
182C22×Dic43C22×C414yes—
183C22×Dic43C2×Q814yes—
184C22×Dic43#4114yes—
185C22×Dic43C2412yes—
186C22×Dic43C2414yes—
187C22×Dic43C2412yes—
188C22×Dic43C2411yescharacteristic
189C22×Dic43C2411yescharacteristic
190C22×Dic43C2412yes—
191C22×Dic43C2411yescharacteristic
192C22×Dic43C2411yescharacteristic
193C22×Dic43C2412yes—
194C2×Dic86—24no—
195C2×Dic86—28no—
196C2×Dic86—232no—
197C2×Dic86C22×C414yes—
198C2×Dic86C22×C418yes—
199C2×Dic86C22×C414yes—
200C2×Dic86#4118yes—
201C4⋊C4×C43—24no—
202C4⋊C4×C43—44no—
203C4⋊C4×C43C22×C418yes—
204C4⋊C4×C43C22×C414yes—
205C4⋊C4×C43C22×C414yes—
206C22⋊C4×C43—22no—
207C22⋊C4×C43—24no—
208C22⋊C4×C43C2×Q814yes—
209C42×C43—24no—
210C42×C43—44no—
211C22⋊Dic43—22no—
212C22⋊Dic43—24no—
213C22⋊Dic43C2×Q814yes—
214C4⋊Dic43—24no—
215C4⋊Dic43—44no—
216Dic43⋊C4—24no—
217Dic43⋊C4—28no—
218Dic43⋊C4—28no—
219Dic43⋊C4—28no—
220Dic43⋊C4—44no—
221Dic43⋊C4C22×C418yes—
222Dic43⋊C4C22×C418yes—
223Dic43⋊C4C22×C418yes—
224Dic43⋊C4C22×C418yes—
225Dic43⋊C4C2×Q818yescomplemented
226C4×Dic43—24no—
227C4×Dic43—24no—
228C4×Dic43—28no—
229C4×Dic43—28no—
230C4×Dic43—28no—
231C4×Dic43—42no—
232C4×Dic43—44no—
233C4×Dic43—42no—
234C4×Dic43C22×C414yes—
235C4×Dic43C22×C414yes—
236C4×Dic43C22×C414yes—
237C4×Dic43C22×C414yes—
238C4×Dic43C22×C418yes—
239C4×Dic43C22×C418yes—
240C4×Dic43C22×C418yes—
241C4×Dic43C22×C418yes—
242C4×Dic43C2×Q818yescomplemented
243C23×C43—22no—
244C23×C43—22no—
245C23×C43C23×C412yes—
246C23×C43C22×Q812yes—
247C23×C43C2×#4112yes—
248C23×C43C2511yescharacteristic
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—28no—
255C2×C4×C43—24no—
256C2×C4×C43—22no—
257C2×C4×C43—24no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
260C2×C4×C43—24no—
261C2×C4×C43—48no—
262C2×C4×C43C23×C414yes—
263C2×C4×C43C23×C414yes—
264C2×C4×C43C23×C412yes—
265C2×C4×C43C23×C412yes—
266C2×C4×C43C22×Q814yes—
267C2×C4×C43C2×#4114yes—
268C2×Dic43—22no—
269C2×Dic43—24no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—216no—
274C2×Dic43—22no—
275C2×Dic43—24no—
276C2×Dic43—22no—
277C2×Dic43—24no—
278C2×Dic43—24no—
279C2×Dic43—22no—
280C2×Dic43—44no—
281C2×Dic43C4×Q8116yescomplemented
282C2×Dic43C23×C412yes—
283C2×Dic43C23×C412yes—
284C2×Dic43C23×C414yes—
285C2×Dic43C23×C414yes—
286C2×Dic43C23×C412yes—
287C2×Dic43C23×C412yes—
288C2×Dic43C22×Q814yes—
289C2×Dic43C22×Q812yes—
290C2×Dic43C22×Q812yes—
291C2×Dic43C2×#4118yes—
292C2×Dic43C2×#4112yes—
293C2×Dic43C2×#4112yes—
294Dic86—28no—
295Dic86—216no—
296Dic86#117116yescomplemented
297Q8×#117—431nomaximal, Sylow
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—24no—
301C22×C43—24no—
302C22×C43C2×C4×Q814yes—
303C22×C43C24×C411yescharacteristic
304C22×C43C23×Q811yescharacteristic
305C22×C43C22×#4112yes—
306C22×C43C22×#4111yescharacteristic
307C22×C43#58512yes—
308C4×C43—22no—
309C4×C43—24no—
310C4×C43—24no—
311C4×C43—24no—
312C4×C43—44no—
313C4×C43—42no—
314C4×C43C2×#11714yes—
315Dic43—24no—
316Dic43—22no—
317Dic43—22no—
318Dic43—24no—
319Dic43—42no—
320Dic43—44no—
321Dic43C2×#11718yes—
322Dic43C2×C4×Q814yes—
323Dic43C2×C4×Q814yes—
324C22×C4×Q8—431no—
325#2355—434no—
326#2355—432no—
327Q8×C4⋊C4—432no—
328#2345—432no—
329#2345—432no—
330#2345—431no—
331#2345D4311yescharacteristic
332Q8×C22⋊C4—431no—
333Q8×C22⋊C4—431no—
334#2295—432no—
335#2295—434no—
336#2285—431no—
337#2285—432no—
338C42×Q8—432no—
339C4×#117—431no—
340C4×#117—432no—
341C2×C43—24no—
342C2×C43C22×#11711yescharacteristic
343C2×C43C22×C4×Q811yescharacteristic
344C2×C43#342811yescharacteristic
345C2×C43Q8×#4112yes—
346C2×C43#348012yes—
347C23×Q8—431no—
348C2×C4×Q8—431no—
349C2×C4×Q8—432no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×Q8—432no—
354C2×C4×Q8—432no—
355C2×C4×Q8—4316no—
356C2×C4×Q8—432no—
357C2×#117—431no—
358C2×#117—432no—
359C2×#117—431no—
360C22×C4⋊C4—432no—
361C22×C4⋊C4C2×D4311yescharacteristic
362C22×C42—432no—
363C22×C42—431no—
364#391—432no—
365#391—432no—
366#391—434no—
367#391—434no—
368#389—434no—
369#389—432no—
370#389—434no—
371#389C2×D4312yes—
372#387—434no—
373#387—434no—
374#387—434no—
375#387—434no—
376#387—434no—
377#387C2×D4314yes—
378#384—434no—
379#384—432no—
380#382—432no—
381#382—434no—
382#380—431no—
383#380—432no—
384#380—432no—
385#380—432no—
386#380—432no—
387#380C2×D4311yescharacteristic
388#380C2×D4312yes—
389C4×C4⋊C4—432no—
390C4×C4⋊C4—432no—
391C4×C4⋊C4—434no—
392C4×C4⋊C4—434no—
393C4×C4⋊C4—432no—
394C4×C4⋊C4—434no—
395C4×C4⋊C4—434no—
396C4×C4⋊C4—434no—
397C4×C4⋊C4—432no—
398C4×C4⋊C4—434no—
399C4×C4⋊C4—432no—
400C4×C4⋊C4C2×D4312yes—
401C4×C22⋊C4—431no—
402C4×C22⋊C4—432no—
403C4×C22⋊C4—432no—
404C4×C22⋊C4—432no—
405C4×C22⋊C4—431no—
406C4×C22⋊C4—431no—
407C4×C22⋊C4C2×D4311yescharacteristic
408C4×C22⋊C4C2×D4312yes—
409#376—432no—
410#376—434no—
411C43—434no—
412C43—432no—
413C43Q8×#11711yescharacteristic, complemented, Sylow
414C22×Q8—438no—
415C22×Q8—431no—
416C22×Q8—432no—
417C22×Q8—431no—
418C22×Q8—868no—
419C23×C4—431no—
420C23×C4—432no—
421C23×C4—431no—
422C23×C4C22×D4311yescharacteristic
423C23×C4C22×D4312yes—
424C4×Q8—438no—
425C4×Q8—438no—
426C4×Q8—4316no—
427C4×Q8—438no—
428C4×Q8—4316no—
429C4×Q8—438no—
430C4×Q8—868no—
431C4×Q8—868no—
432#117—438no—
433#117—868no—
434#117—864no—
435C2×C4⋊C4—4316no—
436C2×C4⋊C4—432no—
437C2×C4⋊C4—432no—
438C2×C4⋊C4—432no—
439C2×C4⋊C4—432no—
440C2×C4⋊C4—432no—
441C2×C4⋊C4—432no—
442C2×C4⋊C4—434no—
443C2×C4⋊C4—434no—
444C2×C4⋊C4—434no—
445C2×C4⋊C4—432no—
446C2×C4⋊C4—434no—
447C2×C4⋊C4—434no—
448C2×C4⋊C4C4×D4318yes—
449C2×C4⋊C4C22×D4312yes—
450C2×C4⋊C4C22×D4314yes—
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C4⋊C4C22×D4312yes—
453C2×C4⋊C4C22×D4311yescharacteristic
454C2×C22⋊C4—431no—
455C2×C22⋊C4—431no—
456C2×C22⋊C4—432no—
457C2×C22⋊C4C22×D4312yes—
458C2×C22⋊C4C22×D4311yescharacteristic
459C2×C22⋊C4C22×D4311yescharacteristic
460C2×C42—4316no—
461C2×C42—438no—
462C2×C42—432no—
463C2×C42—432no—
464C2×C42—431no—
465C2×C42—432no—
466C2×C42—431no—
467C2×C42—432no—
468C2×C42—431no—
469C2×C42—432no—
470C2×C42—431no—
471C2×C42—434no—
472C2×C42—432no—
473C2×C42—434no—
474C2×C42—434no—
475C2×C42—432no—
476C2×C42—432no—
477C2×C42—434no—
478C2×C42—432no—
479C2×C42C22×D4312yes—
480C2×C42C22×D4314yes—
481#95—432no—
482#95—434no—
483#95—432no—
484#95—434no—
485#95—434no—
486#95—432no—
487#95—434no—
488#95—434no—
489#95—434no—
490#95—434no—
491#95—432no—
492#95C22×D4314yes—
493#95C22×D4312yes—
494#95C22×D4314yes—
495#95C22×D4312yes—
496C24C23×D4311yescharacteristic
497C2×Q8—434no—
498C2×Q8—438no—
499C2×Q8—434no—
500C2×Q8—438no—
501C2×Q8—868no—
502C2×Q8—8632no—
503C2×Q8—864no—
504C22×C4—24no—
505C22×C4—44no—
506C22×C4—434no—
507C22×C4—434no—
508C22×C4—434no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—432no—
512C22×C4—438no—
513C22×C4—432no—
514C22×C4—432no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—434no—
518C22×C4—432no—
519C22×C4—434no—
520C22×C4—868no—
521C22×C4—1722no—
522C22×C4C2×C4×D4314yes—
523C22×C4C2×C4×D4318yes—
524C22×C4C23×D4312yes—
525C22×C4C23×D4314yes—
526C22×C4C23×D4311yescharacteristic
527C22×C4C23×D4312yes—
528C22×C4C23×D4312yes—
529C22×C4C23×D4312yes—
530C22×C4C23×D4311yescharacteristic
531C4⋊C4—24no—
532C4⋊C4—44no—
533C4⋊C4—438no—
534C4⋊C4—438no—
535C4⋊C4—438no—
536C4⋊C4—438no—
537C4⋊C4—438no—
538C4⋊C4—864no—
539C4⋊C4—868no—
540C4⋊C4—868no—
541C4⋊C4—868no—
542C4⋊C4—864no—
543C4⋊C4—1724no—
544C4⋊C4—1724no—
545C4⋊C4C2×C4×D4318yes—
546C4⋊C4C2×C4×D4314yes—
547C4⋊C4C2×C4×D4314yes—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—434no—
551C22⋊C4—862no—
552C22⋊C4—864no—
553C22⋊C4Q8×D4314yes—
554C42—24no—
555C42—44no—
556C42—438no—
557C42—438no—
558C42—434no—
559C42—434no—
560C42—434no—
561C42—434no—
562C42—438no—
563C42—438no—
564C42—438no—
565C42—868no—
566C42—864no—
567C42—868no—
568C42—868no—
569C42—864no—
570C42—1722no—
571C42—1724no—
572C42—1722no—
573C23—22no—
574C23—22no—
575C23C22×C4×D4312yes—
576C23C2×Q8×D4312yes—
577C23#41×D4312yes—
578C23C24×D4311yescharacteristic
579Q8—4316no—
580Q8—8616no—
581Q8—868no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—28no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—48no—
595C2×C4—4316no—
596C2×C4—432no—
597C2×C4—432no—
598C2×C4—434no—
599C2×C4—432no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—438no—
603C2×C4—432no—
604C2×C4—432no—
605C2×C4—432no—
606C2×C4—434no—
607C2×C4—434no—
608C2×C4—8616no—
609C2×C4—862no—
610C2×C4—864no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—864no—
616C2×C4—864no—
617C2×C4—862no—
618C2×C4—864no—
619C2×C4—862no—
620C2×C4—1724no—
621C2×C4C22×C4×D4314yes—
622C2×C4C22×C4×D4314yes—
623C2×C4C22×C4×D4312yes—
624C2×C4C22×C4×D4312yes—
625C2×C4C2×Q8×D4314yes—
626C2×C4#41×D4314yes—
627C22—22no—
628C22—24no—
629C22—24no—
630C22—22no—
631C22C4×Q8×D4314yes—
632C22C23×C4×D4311yescharacteristic
633C22C22×Q8×D4311yescharacteristic
634C22C2×#41×D4312yes—
635C22C2×#41×D4311yescharacteristic
636C22#1458373412yes—
637C4—24no—
638C4—24no—
639C4—24no—
640C4—22no—
641C4—42no—
642C4—44no—
643C4—438no—
644C4—434no—
645C4—434no—
646C4—862no—
647C4—862no—
648C4—864no—
649C4—864no—
650C4—1724no—
651C4—1722no—
652C4#117×D4314yes—
653C2—24no—
654C2C2×#117×D4311yescharacteristic
655C2C2×C4×Q8×D4311yescharacteristic
656C2#1914779311yescharacteristic
657C2#1914817412yes—
658C2#1914818912yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2345C2
socle, cosocleC23×C43C25
prime radicalC24×C43C24
hypercenter#2345D43
hypocenterC43Q8×#117
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2345

Complements

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

NH ≅ G/Ntype
2. #19137549C2semidirect
3. #19137548C2semidirect
4. #19137509C2semidirect
10. #19137068C2semidirect
11. #19137066C2semidirect
14. C4×#13063290C2semidirect
20. C2×#13063290C4semidirect
102. #13063281Q8semidirect
225. Dic43⋊C4C2×Q8semidirect
242. C4×Dic43C2×Q8semidirect
281. C2×Dic43C4×Q8semidirect
296. Dic86#117semidirect
413. C43Q8×#117semidirect

Maximal subgroups

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

subgroupindex
C22×#130632902
#191375492
#191375482
#191375092
#191374732
#191374722
#191374672
C22⋊C4×Dic862
#191374272
#191370682
#191370662
#191369972
C4×#130632902
C4×#130632812
C43×#23452
Q8×#11743