Finite Group Databasebeta

← #25255196

Subgroups — #25255196

Order 11008.

2390 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2#19137205C211yesmaximal, characteristic, complemented
3#19137204C211yesmaximal, characteristic, complemented
4#19137203C211yesmaximal, characteristic, complemented
5#19137202C212yesmaximal, complemented
6#19137200C212yesmaximal, complemented
7#19137194C214yesmaximal, complemented
8#19137189C214yesmaximal
9#19137089C214yesmaximal, complemented
10#19137087C214yesmaximal, complemented
11#19137001C211yesmaximal, characteristic, complemented
12#19137000C211yesmaximal, characteristic, complemented
13#19136977C212yesmaximal
14C4×#13063283C212yesmaximal, complemented
15C43×#2314C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063283C2212yes—
19C2×#13063283C2212yes—
20C2×#13063283C2212yes—
21C2×#13063282C2211yescharacteristic
22C2×#13063282C2211yescharacteristic
23C2×#13063281C2212yes—
24#117×D43C4116yescomplemented
25C2×C4⋊C4×D43C2212yes—
26C2×C22⋊C4×D43C2212yes—
27C2×C42×D43C2211yescharacteristic
28C2×C42×D43C2211yescharacteristic
29#14582793C2214yes—
30#14582792C2214yes—
31#14582791C2214yes—
32#14582790C2214yes—
33#14582789C2214yes—
34#14582788C2214yes—
35#14582787C2214yes—
36#14582786C2214yescomplemented
37#14582785C2214yescomplemented
38#14582784C2214yescomplemented
39#14582783C2214yescomplemented
40#14582782C2214yescomplemented
41#14582781C2214yescomplemented
42#14582780C2214yescomplemented
43#14582769C2211yescharacteristic, complemented
44#14582768C2212yescomplemented
45#14582765C2211yescharacteristic, complemented
46#14582764C2212yescomplemented
47#14582761C2214yes—
48#14582759C2212yes—
49#14582758C2214yes—
50#14582756C2214yes—
51#14582756C2212yes—
52#14582756C2212yes—
53#14582754C2214yes—
54C4⋊C4×Dic43C2214yescomplemented
55C4⋊C4×Dic43C2212yescomplemented
56C4⋊C4×Dic43C2212yescomplemented
57C4×C4⋊Dic43C2212yescomplemented
58#14582750C2214yescomplemented
59C22⋊C4×Dic43C2214yes—
60C4×(C2×D43)⋊C4C2214yes—
61#14582746C2214yes—
62#14582746C2214yes—
63#14582744C2214yescomplemented
64C42×Dic43C2214yescomplemented
65C2×#117×C43C2211yescharacteristic
66C43×#388C2214yes—
67C43×#387C2214yescomplemented
68C43×#384C2211yescharacteristic, complemented
69C43×#382C2211yescharacteristic, complemented
70C43×#380C2212yes—
71C4×C4⋊C4×C43C2212yescomplemented
72C24×D43C2311yescharacteristic
73C23×Dic43C2311yescharacteristic
74C22×C4×D43—24no—
75C22×C4×D43—24no—
76C22×C4×D43C2×C418yes—
77C22×C4×D43C2311yescharacteristic
78C22×C4×D43C2311yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2312yes—
81C22×C4×D43C2312yes—
82C22×C4×D43C2311yescharacteristic
83#13063284C2×C418yes—
84#13063283—28no—
85#13063283—28no—
86#13063283C2×C4116yes—
87#13063282C2×C418yes—
88#13063282C2×C418yes—
89#13063281C2×C4116yes—
90C2×C4⋊Dic43C2312yes—
91C2×C4⋊Dic43C2312yes—
92C2×C4⋊Dic43C2314yes—
93C2×C4⋊Dic43C2312yes—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2312yes—
97C2×Dic43⋊C4C2312yes—
98C4⋊C4×D43C2×C4116yes—
99C2×C22⋊Dic43C2314yes—
100C2×C22⋊Dic43C2312yes—
101C2×(C2×D43)⋊C4C2314yes—
102C2×(C2×D43)⋊C4C2314yes—
103C2×(C2×D43)⋊C4C2314yes—
104C2×(C2×D43)⋊C4C2314yes—
105C2×(C2×D43)⋊C4C2312yes—
106C2×(C2×D43)⋊C4C2312yes—
107C22⋊C4×D43C2×C4116yes—
108C2×C4×Dic43C2314yes—
109C2×C4×Dic43C2314yes—
110C2×C4×Dic43C2314yes—
111C2×C4×Dic43C2314yes—
112C2×C4×Dic43C2314yes—
113C2×C4×Dic43C2312yes—
114C2×C4×Dic43C2312yes—
115C2×C4×Dic43C2311yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117C42×D43C2×C418yes—
118C42×D43C2×C418yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C23×C4×C43C2311yescharacteristic
129#117×C43C2×C418yes—
130C2×C4⋊C4×C43C2312yes—
131C2×C4⋊C4×C43C2312yes—
132C2×C4⋊C4×C43C2314yes—
133C2×C4⋊C4×C43C2312yes—
134C2×C22⋊C4×C43C2314yes—
135C2×C22⋊C4×C43C2312yes—
136C2×C42×C43C2314yes—
137C2×C42×C43C2311yescharacteristic
138C2×C42×C43C2311yescharacteristic
139#95×C43C2314yes—
140#95×C43C2314yes—
141#95×C43C2314yes—
142C24×C43C2411yescharacteristic
143C23×D43—22no—
144C23×D43—22no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43C22×C414yes—
148C23×D43C2411yescharacteristic
149C23×D43C2411yescharacteristic
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43C22×C414yes—
153C22×C4×C43C2414yes—
154C22×C4×C43C2414yes—
155C22×C4×C43C2411yescharacteristic
156C22×C4×C43C2412yes—
157C22×C4×C43C2412yes—
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43C22×C414yes—
162C22×Dic43C2414yes—
163C22×Dic43C2414yes—
164C22×Dic43C2411yescharacteristic
165C22×Dic43C2412yes—
166C22×Dic43C2412yes—
167C22×Dic43C2411yescharacteristic
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—232no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—42no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43C22×C414yes—
180C2×C4×D43C22×C414yes—
181C2×C4×D43C22×C414yes—
182C2×C4×D43C22×C418yes—
183C2×C4×D43C22×C418yes—
184C2×C4×D43C22×C414yes—
185C2×C4×D43#4114yes—
186C2×C4×D43#4114yes—
187C4⋊C4×C43—24no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—44no—
190C4⋊C4×C43C22×C418yes—
191C22⋊C4×C43—44no—
192C22⋊C4×C43C22×C418yes—
193C42×C43—44no—
194C42×C43C22×C414yes—
195C42×C43C22×C414yes—
196C22⋊Dic43—44no—
197C22⋊Dic43C22×C418yes—
198(C2×D43)⋊C4—28no—
199(C2×D43)⋊C4—28no—
200(C2×D43)⋊C4—44no—
201(C2×D43)⋊C4—44no—
202(C2×D43)⋊C4C22×C418yes—
203(C2×D43)⋊C4C22×C418yes—
204C4⋊Dic43—24no—
205C4⋊Dic43—24no—
206C4⋊Dic43—44no—
207C4⋊Dic43C22×C418yes—
208Dic43⋊C4—44no—
209Dic43⋊C4—44no—
210Dic43⋊C4C22×C418yes—
211Dic43⋊C4C22×C418yes—
212C4×Dic43—28no—
213C4×Dic43—28no—
214C4×Dic43—44no—
215C4×Dic43—44no—
216C4×Dic43—44no—
217C4×Dic43C22×C418yes—
218C4×Dic43C22×C418yes—
219C4×Dic43C22×C414yes—
220C4×Dic43C22×C414yes—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—22no—
224C23×C43—22no—
225C23×C43C23×C412yes—
226C23×C43C2511yescharacteristic
227C22×D43—22no—
228C22×D43—22no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—28no—
234C22×D43—48no—
235C22×D43—44no—
236C22×D43—48no—
237C22×D43—44no—
238C22×D43C23×C412yes—
239C22×D43C23×C412yes—
240C22×D43C2×#4112yes—
241C22×D43C2×#4112yes—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—28no—
249C2×C4×C43—24no—
250C2×C4×C43—24no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—24no—
254C2×C4×C43—24no—
255C2×C4×C43C23×C414yes—
256C2×C4×C43C23×C414yes—
257C2×C4×C43C23×C412yes—
258C2×C4×C43C23×C412yes—
259C2×C4×C43C2×#4112yes—
260C2×C4×C43C2×#4112yes—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—28no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43C23×C414yes—
275C2×Dic43C23×C414yes—
276C2×Dic43C23×C412yes—
277C2×Dic43C23×C412yes—
278C2×Dic43C2×#4112yes—
279C2×Dic43C2×#4112yes—
280C4×D43—28no—
281C4×D43—28no—
282C4×D43—28no—
283C4×D43—48no—
284C4×D43—48no—
285C4×D43#117116yes—
286#34048—431nomaximal, Sylow
287C22×C43—22no—
288C22×C43—24no—
289C22×C43—41no—
290C22×C43—42no—
291C22×C43—41no—
292C22×C43C24×C411yescharacteristic
293C22×C43C22×#4111yescharacteristic
294C22×C43C22×#4111yescharacteristic
295C22×C43#58512yes—
296C22×C43#58512yes—
297C2×D43—24no—
298C2×D43—22no—
299C2×D43—24no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—24no—
303C2×D43—416no—
304C2×D43—41no—
305C2×D43—42no—
306C2×D43—41no—
307C2×D43C2×#11714yes—
308C4×C43—22no—
309C4×C43—24no—
310C4×C43—24no—
311C4×C43—44no—
312C4×C43—44no—
313C4×C43C2×#11714yes—
314Dic43—22no—
315Dic43—24no—
316Dic43—24no—
317Dic43—44no—
318Dic43—44no—
319Dic43C2×#11714yes—
320C22×#117—431no—
321#2314—431no—
322#2314—431no—
323#2314—432no—
324#2314—432no—
325#2314—431no—
326#2314D4311yescharacteristic, complemented
327#2313—434no—
328#2312—434no—
329#2298—434no—
330#2298—434no—
331#2285—431no—
332#2285—431no—
333#2280—432no—
334C4×#117—432no—
335C2×C43—42no—
336C2×C43C22×#11711yescharacteristic
337C2×C43#342812yes—
338C2×C43#345511yescharacteristic
339C2×C43#345512yes—
340C2×C43#345511yescharacteristic
341D43—24no—
342D43—42no—
343C24×C4—431no—
344C2×#117—431no—
345C2×#117—4316no—
346C2×#117—432no—
347C2×#117—432no—
348C2×#117—432no—
349C2×#117—432no—
350C2×#117—431no—
351C2×#117—431no—
352C2×#117C2×D4311yescharacteristic
353C22×C4⋊C4—432no—
354C22×C22⋊C4—432no—
355C22×C42—431no—
356C22×C42—431no—
357#388—434no—
358#388—434no—
359#388—434no—
360#388—434no—
361#388—434no—
362#388—434no—
363#388—434no—
364#388C2×D4314yes—
365#387—434no—
366#387—434no—
367#387—434no—
368#387—434no—
369#387—434no—
370#387—434no—
371#387—434no—
372#387C2×D4314yescomplemented
373#384—432no—
374#384—431no—
375#384C2×D4311yescharacteristic, complemented
376#382—432no—
377#382—431no—
378#382C2×D4311yescharacteristic, complemented
379#381—434no—
380#380—432no—
381#380—434no—
382#380—432no—
383#380—432no—
384#380—434no—
385#380C2×D4312yes—
386#379—434no—
387C4×C4⋊C4—432no—
388C4×C4⋊C4—432no—
389C4×C4⋊C4—434no—
390C4×C4⋊C4—432no—
391C4×C4⋊C4—434no—
392C4×C4⋊C4C2×D4312yescomplemented
393C4×C22⋊C4—434no—
394C4×C22⋊C4—434no—
395C4×C22⋊C4—434no—
396C4×C22⋊C4—434no—
397#376—434no—
398C43—434no—
399C43#3404811yescharacteristic, complemented, Sylow
400C25—431no—
401C23×C4—431no—
402C23×C4—431no—
403C23×C4—438no—
404C23×C4—431no—
405C23×C4—431no—
406C23×C4—431no—
407C23×C4—432no—
408C23×C4—432no—
409C23×C4—864no—
410C23×C4—864no—
411C23×C4C22×D4311yescharacteristic
412#117—438no—
413#117—4316no—
414#117—4316no—
415#117—438no—
416#117—438no—
417#117—868no—
418#117—868no—
419#117C4×D4318yes—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—4316no—
424C2×C4⋊C4—432no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4—434no—
427C2×C4⋊C4—434no—
428C2×C4⋊C4—434no—
429C2×C4⋊C4C22×D4312yes—
430C2×C4⋊C4C22×D4312yes—
431C2×C4⋊C4C22×D4314yes—
432C2×C4⋊C4C22×D4312yes—
433C2×C22⋊C4—432no—
434C2×C22⋊C4—432no—
435C2×C22⋊C4—432no—
436C2×C22⋊C4—4316no—
437C2×C22⋊C4—434no—
438C2×C22⋊C4—434no—
439C2×C22⋊C4—434no—
440C2×C22⋊C4—434no—
441C2×C22⋊C4—434no—
442C2×C22⋊C4C22×D4314yes—
443C2×C22⋊C4C22×D4312yes—
444C2×C42—432no—
445C2×C42—432no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—438no—
449C2×C42—438no—
450C2×C42—434no—
451C2×C42—434no—
452C2×C42—434no—
453C2×C42—434no—
454C2×C42—434no—
455C2×C42C22×D4314yes—
456C2×C42C22×D4311yescharacteristic
457C2×C42C22×D4311yescharacteristic
458#95—434no—
459#95—434no—
460#95—434no—
461#95—434no—
462#95—434no—
463#95—434no—
464#95—434no—
465#95—434no—
466#95—434no—
467#95C22×D4314yes—
468#95C22×D4314yes—
469#95C22×D4314yes—
470C24—431no—
471C24—431no—
472C24—434no—
473C24—862no—
474C24—862no—
475C24—1722no—
476C24—1722no—
477C24C23×D4311yescharacteristic
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—431no—
481C22×C4—434no—
482C22×C4—434no—
483C22×C4—434no—
484C22×C4—434no—
485C22×C4—431no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—434no—
489C22×C4—434no—
490C22×C4—434no—
491C22×C4—438no—
492C22×C4—438no—
493C22×C4—434no—
494C22×C4—434no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—8632no—
498C22×C4—862no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4—1722no—
508C22×C4C2×C4×D4314yes—
509C22×C4C23×D4314yes—
510C22×C4C23×D4314yes—
511C22×C4C23×D4311yescharacteristic
512C22×C4C23×D4312yes—
513C22×C4C23×D4312yes—
514C22×C4C23×D4311yescharacteristic
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—44no—
518C4⋊C4—438no—
519C4⋊C4—438no—
520C4⋊C4—438no—
521C4⋊C4—864no—
522C4⋊C4—864no—
523C4⋊C4—1724no—
524C4⋊C4—1724no—
525C4⋊C4—1724no—
526C4⋊C4C2×C4×D4318yes—
527C22⋊C4—44no—
528C22⋊C4—438no—
529C22⋊C4—438no—
530C22⋊C4—438no—
531C22⋊C4—868no—
532C22⋊C4—868no—
533C22⋊C4—1724no—
534C22⋊C4—1724no—
535C22⋊C4—1724no—
536C22⋊C4C2×C4×D4318yes—
537C42—44no—
538C42—438no—
539C42—438no—
540C42—434no—
541C42—434no—
542C42—868no—
543C42—868no—
544C42—1724no—
545C42—1724no—
546C42—1724no—
547C42C2×C4×D4314yes—
548C42C2×C4×D4314yes—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—22no—
553C23—432no—
554C23—432no—
555C23—432no—
556C23—432no—
557C23—868no—
558C23—862no—
559C23—862no—
560C23—861no—
561C23—861no—
562C23—862no—
563C23—862no—
564C23—1728no—
565C23—1724no—
566C23—1728no—
567C23—1724no—
568C23C22×C4×D4312yes—
569C23C24×D4311yescharacteristic
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—28no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—4316no—
587C2×C4—434no—
588C2×C4—434no—
589C2×C4—432no—
590C2×C4—868no—
591C2×C4—868no—
592C2×C4—868no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—868no—
600C2×C4—864no—
601C2×C4—864no—
602C2×C4—864no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—1728no—
607C2×C4—1728no—
608C2×C4C22×C4×D4314yes—
609C2×C4C22×C4×D4314yes—
610C2×C4C22×C4×D4312yes—
611C2×C4C22×C4×D4312yes—
612C2×C4#41×D4312yes—
613C2×C4#41×D4312yes—
614C22—24no—
615C22—22no—
616C22—41no—
617C22—42no—
618C22—41no—
619C22—434no—
620C22—864no—
621C22—862no—
622C22—864no—
623C22—862no—
624C22—864no—
625C22—862no—
626C22—17216no—
627C22—1721no—
628C22—1722no—
629C22—1721no—
630C22C23×C4×D4311yescharacteristic
631C22C2×#41×D4311yescharacteristic
632C22C2×#41×D4311yescharacteristic
633C22#1458373412yes—
634C22#1458373612yes—
635C4—24no—
636C4—24no—
637C4—22no—
638C4—44no—
639C4—44no—
640C4—434no—
641C4—864no—
642C4—864no—
643C4—862no—
644C4—1724no—
645C4—1724no—
646C4#117×D4314yes—
647C2—42no—
648C2—864no—
649C2—1722no—
650C2C2×#117×D4311yescharacteristic
651C2#1914779512yes—
652C2#1914797911yescharacteristic
653C2#1914798212yes—
654C2#1914798611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2314C2
socle, cosocleC23×C43C25
prime radicalC24×D43C23
hypercenter#2314D43
hypocenterC43#34048
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. #19137205C2semidirect
3. #19137204C2semidirect
4. #19137203C2semidirect
5. #19137202C2semidirect
6. #19137200C2semidirect
7. #19137194C2semidirect
9. #19137089C2semidirect
10. #19137087C2semidirect
11. #19137001C2semidirect
12. #19137000C2semidirect
14. C4×#13063283C2semidirect
15. C43×#2314C2semidirect
24. #117×D43C4semidirect
36. #14582786C22semidirect
37. #14582785C22semidirect
38. #14582784C22semidirect
39. #14582783C22semidirect
40. #14582782C22semidirect
41. #14582781C22semidirect
42. #14582780C22semidirect
43. #14582769C22semidirect
44. #14582768C22semidirect
45. #14582765C22semidirect
46. #14582764C22semidirect
54. C4⋊C4×Dic43C22semidirect
55. C4⋊C4×Dic43C22semidirect
56. C4⋊C4×Dic43C22semidirect
57. C4×C4⋊Dic43C22semidirect
58. #14582750C22semidirect
63. #14582744C22semidirect
64. C42×Dic43C22semidirect
67. C43×#387C22semidirect
68. C43×#384C22semidirect
69. C43×#382C22semidirect
71. C4×C4⋊C4×C43C22semidirect
326. #2314D43semidirect
372. #387C2×D43semidirect
375. #384C2×D43semidirect
378. #382C2×D43semidirect
392. C4×C4⋊C4C2×D43semidirect
399. C43#34048semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
#191372052
#191372042
#191372032
#191372022
#191372002
#191371942
#191371892
#191370892
#191370872
#191370012
#191370002
#191369772
C4×#130632832
C43×#23142
#3404843