Finite Group Databasebeta

← #25098391

Subgroups — #25098391

Order 11008.

1994 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582872C212yesmaximal, complemented
3#19136978C211yesmaximal, characteristic, complemented
4#19135053C214yesmaximal, complemented
5#19135048C214yesmaximal, complemented
6#19134327C212yesmaximal, complemented
7C22×#117×C43C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9#14583410—22no—
10#14583410—22no—
11#14583410—21no—
12#14583410—21no—
13#14583410—21no—
14#14583410—21no—
15C2×#13063308C2212yes—
16C2×#13063304C412yescomplemented
17C2×#13063299C412yescomplemented
18C2×#13063294C2212yes—
19C2×C4×C22⋊D43C414yescomplemented
20C2×#13063284C2212yes—
21C2×#13063284C2211yescharacteristic
22#14582872—28no—
23C2×#13063239C2218yes—
24#14582762C2212yes—
25#14582759—22no—
26#14582755C2212yes—
27C4×C22⋊Dic43—22no—
28#14582665C2218yes—
29C24×C4×C43C2211yescharacteristic
30C2×#117×C43—21no—
31C2×#117×C43—21no—
32C2×#117×C43—28no—
33C2×#117×C43C2212yes—
34C2×#117×C43C2212yes—
35C22×C4⋊C4×C43—21no—
36C22×C22⋊C4×C43C2212yes—
37C22×C42×C43—21no—
38C2×#10621898—24no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—24no—
44C22×Dic86C2×C411yescharacteristic, complemented
45C22×D172C2×C411yescharacteristic, complemented
46C22×C22⋊D43C2×C414yes—
47C22×C22⋊D43C2312yes—
48C22×C4×D43C2×C412yescomplemented
49#13063308—24no—
50#13063308—22no—
51#13063308—22no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304—22no—
56#13063299—22no—
57#13063299—22no—
58#13063299—22no—
59#13063299—22no—
60#13063294—24no—
61#13063294—22no—
62#13063294—22no—
63C4×C22⋊D43—24no—
64C4×C22⋊D43—24no—
65C4×C22⋊D43—24no—
66C4×C22⋊D43—24no—
67#13063284—21no—
68#13063284—21no—
69#13063284—21no—
70#13063284—21no—
71#13063284—24no—
72#13063284—24no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43C2×C412yescomplemented
75C2×Dic43⋊C4C2×C414yescomplemented
76C2×C22⋊Dic43—24no—
77C2×C22⋊Dic43C2×C414yes—
78C2×C22⋊Dic43C2314yes—
79C2×C22⋊Dic43C2312yes—
80C2×(C2×D43)⋊C4C2×C414yescomplemented
81C2×C4×Dic43—22no—
82C2×C4×Dic43C2×C412yescomplemented
83#13063239—216no—
84C43⋊#95—24no—
85C25×C43C2311yescharacteristic
86C23×C4×C43—24no—
87C23×C4×C43—24no—
88C23×C4×C43—22no—
89C23×C4×C43C2×C412yes—
90C23×C4×C43C2×C412yes—
91C23×C4×C43D412yes—
92C23×C4×C43D412yes—
93C23×C4×C43D411yescharacteristic
94C23×C4×C43D411yescharacteristic
95C23×C4×C43D411yescharacteristic
96C23×C4×C43D411yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99#117×C43—28no—
100#117×C43—28no—
101#117×C43—24no—
102#117×C43—28no—
103#117×C43D418yescomplemented
104C2×C4⋊C4×C43—28no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—22no—
107C2×C22⋊C4×C43—22no—
108C2×C22⋊C4×C43—28no—
109C2×C22⋊C4×C43C2314yes—
110C2×C42×C43—28no—
111C2×C42×C43—22no—
112C2×C42×C43—22no—
113C24×C43—22no—
114C24×C43—22no—
115C24×C43—44no—
116C24×C43C22×C412yes—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D412yes—
119C24×C43C2×D411yescharacteristic
120C24×C43C2411yescharacteristic
121C23×D43C22×C412yes—
122C22×C4×C43—28no—
123C22×C4×C43—28no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—28no—
129C22×C4×C43—28no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—28no—
135C22×C4×C43—22no—
136C22×C4×C43—24no—
137C22×C4×C43—22no—
138C22×C4×C43—48no—
139C22×C4×C43C22⋊C412yes—
140C22×C4×C43C22⋊C412yes—
141C22×C4×C43C22⋊C412yes—
142C22×C4×C43C22⋊C412yes—
143C22×C4×C43C22⋊C412yes—
144C22×C4×C43C22⋊C412yes—
145C22×C4×C43C22⋊C412yes—
146C22×C4×C43C22⋊C412yes—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D414yes—
158C22×C4×C43#4114yes—
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—24no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—24no—
165C2×C22⋊D43—48no—
166C22×Dic43—24no—
167C22×Dic43C22×C412yes—
168C22×Dic43C22×C414yes—
169#10621898—42no—
170#10621898—42no—
171#10621898—44no—
172#10621898—44no—
173#10621898—42no—
174#10621898—42no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—24no—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—28no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—24no—
184C4⋊C4×C43—28no—
185C4⋊C4×C43—28no—
186C22⋊C4×C43—28no—
187C22⋊C4×C43—24no—
188C22⋊C4×C43C2×D418yes—
189C42×C43—28no—
190C42×C43—28no—
191C22⋊Dic43—24no—
192C22⋊Dic43—24no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—24no—
196C22⋊Dic43—24no—
197C22⋊Dic43—48no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—24no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—44no—
203Dic43⋊C4—24no—
204Dic43⋊C4—24no—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43—44no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—24no—
211C23×C43—24no—
212C23×C43—21no—
213C23×C43—24no—
214C23×C43—21no—
215C23×C43—24no—
216C23×C43—24no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—48no—
222C23×C43—48no—
223C23×C43C2×C22⋊C412yes—
224C23×C43C2×C22⋊C412yes—
225C23×C43C23×C411yescharacteristic
226C23×C43C22×D411yescharacteristic
227C23×C43C22×D412yes—
228C23×C43C22×D411yescharacteristic
229C23×C43C2×#4112yes—
230C22×D43—22no—
231C22×D43—24no—
232C22×D43—44no—
233C2×C4×C43—24no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—24no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—24no—
240C2×C4×C43—24no—
241C2×C4×C43—24no—
242C2×C4×C43—24no—
243C2×C4×C43—24no—
244C2×C4×C43—24no—
245C2×C4×C43—24no—
246C2×C4×C43—24no—
247C2×C4×C43—28no—
248C2×C4×C43—416no—
249C2×C4×C43—48no—
250C2×C4×C43C2×C22⋊C412yes—
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C4×D414yes—
257C2×C4×C43C4×D414yes—
258C2×C4×C43#12012yes—
259C2×C4×C43#12012yes—
260C2×C4×C43#12114yes—
261C2×C4×C43#12114yes—
262C2×C4×C43#12312yes—
263C2×C4×C43#12312yes—
264C22⋊D43—48no—
265C22⋊D43—42no—
266C22⋊D43—44no—
267C22⋊D43—42no—
268C22⋊D43—48no—
269C2×Dic43—24no—
270C2×Dic43—22no—
271C2×Dic43—24no—
272C2×Dic43—44no—
273C2×Dic43—48no—
274C2×Dic43—44no—
275D172—42no—
276D172—42no—
277C4×D43—44no—
278C4×D43—44no—
279Dic86—42no—
280Dic86—42no—
281#20983—431nomaximal, Sylow
282C22×C43—24no—
283C22×C43—24no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—22no—
289C22×C43—22no—
290C22×C43—22no—
291C22×C43—22no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—48no—
295C22×C43—48no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43#41014yescomplemented
299C22×C43C22×C22⋊C411yescharacteristic
300C22×C43C2×C4×D412yes—
301C22×C43C2×#12011yescharacteristic
302C22×C43C2×#12112yes—
303C22×C43C2×#12311yescharacteristic
304C2×D43—44no—
305C2×D43—42no—
306C2×D43—84no—
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—48no—
310C4×C43#38612yes—
311C4×C43#38612yes—
312C4×C43#38612yes—
313C4×C43#38612yes—
314Dic43—44no—
315Dic43—42no—
316Dic43—84no—
317C2×#525—431no—
318C22×#117D4311yescharacteristic, complemented
319C2×#410—432no—
320#2280—431no—
321#1899—434no—
322#1898—434no—
323#1740—432no—
324C2×C43—22no—
325C2×C43—21no—
326C2×C43—22no—
327C2×C43—21no—
328C2×C43—24no—
329C2×C43—42no—
330C2×C43C2×#38611yescharacteristic
331C2×C43C2×#41012yes—
332D43—82no—
333C22×#41—431no—
334C24×C4C2×D4311yescharacteristic
335#525—862no—
336#525—862no—
337#525—861no—
338#525—861no—
339#525—861no—
340#525—861no—
341C2×#123—432no—
342C2×C22⋊Q8—432no—
343C2×#121—432no—
344C2×#120—432no—
345C2×C4×D4—434no—
346C2×#117—21no—
347C2×#117—21no—
348C2×#117—28no—
349C2×#117—431no—
350C2×#117—432no—
351C2×#117C2×D4312yes—
352C2×#117C2×D4312yes—
353C22×C4⋊C4—21no—
354C22×C22⋊C4C2×D4312yes—
355C22×C42—21no—
356#410—868no—
357C2×#99—438no—
358#381—432no—
359#380—862no—
360#379—432no—
361C4×C22⋊C4—862no—
362#342—438no—
363C43#2098311yescharacteristic, complemented, Sylow
364C25C22×D4311yescharacteristic
365C2×#41—861no—
366C2×#41—861no—
367C2×#41—864no—
368C2×#41—861no—
369C2×#41—861no—
370C2×#41—864no—
371C22×Q8—431no—
372C22×D4—432no—
373C22×D4—434no—
374C22×D4—431no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—22no—
378C23×C4—432no—
379C23×C4C4×D4312yes—
380C23×C4C4×D4312yes—
381C23×C4D17212yes—
382C23×C4D17212yes—
383C23×C4C22⋊D4311yescharacteristic
384C23×C4C22⋊D4311yescharacteristic
385C23×C4C22⋊D4311yescharacteristic
386C23×C4C22⋊D4311yescharacteristic
387C23×C4C22×D4311yescharacteristic
388C23×C4C22×D4311yescharacteristic
389#123—864no—
390#123—862no—
391#123—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—862no—
396#121—862no—
397#121—862no—
398#121—862no—
399#121—862no—
400#120—864no—
401#120—862no—
402#120—862no—
403C4×D4—864no—
404C4×D4—864no—
405C4×D4—864no—
406C4×D4—864no—
407#117—28no—
408#117—28no—
409#117—24no—
410#117—28no—
411#117—861no—
412#117—861no—
413#117—861no—
414#117—861no—
415#117—864no—
416#117—864no—
417#117C22⋊D4318yescomplemented
418C2×C4⋊C4—28no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—434no—
423C2×C4⋊C4—862no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—434no—
427C2×C22⋊C4—432no—
428C2×C22⋊C4—434no—
429C2×C22⋊C4—434no—
430C2×C22⋊C4—864no—
431C2×C22⋊C4C22×D4314yes—
432C2×C42—28no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—432no—
436C2×C42—862no—
437#99—8616no—
438#95—864no—
439C24—22no—
440C24—22no—
441C24—44no—
442C24—432no—
443C24C2×C4×D4312yes—
444C24C2×D17212yes—
445C24C2×C22⋊D4311yescharacteristic
446C24C2×C22⋊D4311yescharacteristic
447C24C23×D4311yescharacteristic
448#41—1722no—
449#41—1722no—
450#41—1724no—
451#41—1724no—
452#41—1722no—
453#41—1722no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—864no—
457C2×D4—864no—
458C2×D4—864no—
459C2×D4—864no—
460C2×D4—862no—
461C2×D4—862no—
462C2×D4—864no—
463C2×D4—861no—
464C2×D4—861no—
465C2×D4—864no—
466C2×D4—1728no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—24no—
483C22×C4—48no—
484C22×C4—432no—
485C22×C4—434no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—868no—
489C22×C4—864no—
490C22×C4(C2×D43)⋊C412yes—
491C22×C4(C2×D43)⋊C412yes—
492C22×C4(C2×D43)⋊C412yes—
493C22×C4(C2×D43)⋊C412yes—
494C22×C4(C2×D43)⋊C412yes—
495C22×C4(C2×D43)⋊C412yes—
496C22×C4(C2×D43)⋊C412yes—
497C22×C4(C2×D43)⋊C412yes—
498C22×C4C2×C4×D4312yes—
499C22×C4C2×C4×D4311yescharacteristic
500C22×C4C2×C4×D4311yescharacteristic
501C22×C4C2×D17212yes—
502C22×C4C2×D17211yescharacteristic
503C22×C4C2×D17211yescharacteristic
504C22×C4#1062189814yes—
505C22×C4C2×C22⋊D4311yescharacteristic
506C22×C4C2×C22⋊D4311yescharacteristic
507C22×C4C2×C22⋊D4311yescharacteristic
508C22×C4C2×C22⋊D4311yescharacteristic
509C22×C4C2×C22⋊D4314yes—
510C4⋊C4—28no—
511C4⋊C4—28no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—864no—
515C4⋊C4—864no—
516C4⋊C4—1724no—
517C22⋊C4—28no—
518C22⋊C4—24no—
519C22⋊C4—864no—
520C22⋊C4—864no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—864no—
527C22⋊C4—1728no—
528C22⋊C4C2×C22⋊D4318yes—
529C42—28no—
530C42—28no—
531C42—862no—
532C42—862no—
533C42—1724no—
534C23—24no—
535C23—21no—
536C23—21no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—21no—
541C23—24no—
542C23—21no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—48no—
548C23—48no—
549C23—864no—
550C23—862no—
551C23—1724no—
552C23C2×(C2×D43)⋊C412yes—
553C23C2×(C2×D43)⋊C412yes—
554C23C22×C4×D4311yescharacteristic
555C23C22×C22⋊D4311yescharacteristic
556C23C22×C22⋊D4312yes—
557C23C22×D17211yescharacteristic
558C23C2×#1062189812yes—
559Q8—1722no—
560Q8—1722no—
561D4—1728no—
562D4—1728no—
563D4—1722no—
564D4—1724no—
565D4—1722no—
566D4—1722no—
567D4—1722no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—28no—
583C2×C4—416no—
584C2×C4—48no—
585C2×C4—864no—
586C2×C4—862no—
587C2×C4—864no—
588C2×C4—1728no—
589C2×C4—1724no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1724no—
593C2×C4C2×(C2×D43)⋊C412yes—
594C2×C4C2×(C2×D43)⋊C412yes—
595C2×C4C2×(C2×D43)⋊C411yescharacteristic
596C2×C4C2×(C2×D43)⋊C411yescharacteristic
597C2×C4C2×(C2×D43)⋊C411yescharacteristic
598C2×C4C2×(C2×D43)⋊C411yescharacteristic
599C2×C4C4×C22⋊D4314yes—
600C2×C4C4×C22⋊D4314yes—
601C2×C4#1306329412yes—
602C2×C4#1306329412yes—
603C2×C4#1306329914yes—
604C2×C4#1306329914yes—
605C2×C4#1306330812yes—
606C2×C4#1306330812yes—
607C22—24no—
608C22—24no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—42no—
618C22—42no—
619C22—48no—
620C22—48no—
621C22—42no—
622C22—42no—
623C22—3444no—
624C22—1724no—
625C22—1722no—
626C22#1458287214yescomplemented
627C22C22×(C2×D43)⋊C411yescharacteristic
628C22C2×C4×C22⋊D4312yes—
629C22C2×#1306329411yescharacteristic
630C22C2×#1306329912yes—
631C22C2×#1306330811yescharacteristic
632C4—22no—
633C4—22no—
634C4—48no—
635C4—3444no—
636C4—1724no—
637C4—1722no—
638C4#1458277812yes—
639C4#1458277812yes—
640C4#1458277812yes—
641C4#1458277812yes—
642C2—21no—
643C2—22no—
644C2—24no—
645C2—21no—
646C2—22no—
647C2—42no—
648C2—3442no—
649C2C2×#1458277811yescharacteristic
650C2C2×#1458287212yes—
subgroupG/H
centerC2×C4C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC22×#117×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583410C2
cosocleC24×C43C24
hypercenterC22×#117D43
hypocenterC43#20983
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#14582872C2semidirect
3. #19136978C2semidirect
4. #19135053C2semidirect
5. #19135048C2semidirect
6. #19134327C2semidirect
7. C22×#117×C43C2semidirect
16. C2×#13063304C4semidirect
17. C2×#13063299C4semidirect
19. C2×C4×C22⋊D43C4semidirect
44. C22×Dic86C2×C4semidirect
45. C22×D172C2×C4semidirect
48. C22×C4×D43C2×C4semidirect
74. C2×C4⋊Dic43C2×C4semidirect
75. C2×Dic43⋊C4C2×C4semidirect
80. C2×(C2×D43)⋊C4C2×C4semidirect
82. C2×C4×Dic43C2×C4semidirect
103. #117×C43D4semidirect
298. C22×C43#410semidirect
318. C22×#117D43semidirect
363. C43#20983semidirect
417. #117C22⋊D43semidirect
626. C22#14582872semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145828722
#191369782
#191350532
#191350482
#191343272
C22×#117×C432
#2098343