Finite Group Databasebeta

← #25118896

Subgroups — #25118896

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583121C211yesmaximal, characteristic
2C2×C4×#10621885C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic
4#19137664C211yesmaximal, characteristic
5#19135404C211yesmaximal, characteristic
6#19135361C211yesmaximal, characteristic, complemented
7#19135277C211yesmaximal, characteristic
8#19135270C211yesmaximal, characteristic, complemented
9#19134950C211yesmaximal, characteristic
10#19134936C211yesmaximal, characteristic, complemented
11#19134862C211yesmaximal, characteristic, complemented
12#19134841C211yesmaximal, characteristic
13C4⋊C4×C43⋊C8C211yesmaximal, characteristic, complemented
14C4×#13063249C211yesmaximal, characteristic, complemented
15C43×#2351C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583121C418yescomplemented
22C4×#10621885—24no—
23C4×#10621884—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582789—21no—
41#14582788—21no—
42#14582770—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582746—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C43×#389—21no—
55C43×#389—21no—
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#382—21no—
59C43×#382C2211yescharacteristic
60C4×C4⋊C4×C43—21no—
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C4×D43—21no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885C2×C414yescomplemented
68C2×#10621884—22no—
69C2×#10621884—22no—
70C2×#10621884C2×C414yes—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063313—22no—
76#13063313C2×C414yes—
77C4×Dic86—22no—
78C4×Dic86—41no—
79C4×D172—22no—
80C4×D172—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91#13063258—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)C2×C414yescomplemented
94#13063249—22no—
95#13063249D414yes—
96#13063248—22no—
97#13063248—41no—
98#13063248C2×C414yescomplemented
99#13063245—22no—
100#13063245—41no—
101#13063245C2×C414yes—
102C4×C43⋊C8—22no—
103C4×C43⋊C8—22no—
104C4×C43⋊C8—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C4×Q8×C43—22no—
110C4×Q8×C43—22no—
111C4×Q8×C43—22no—
112C4×Q8×C43—41no—
113C4×Q8×C43—41no—
114C4×Q8×C43C2×C414yescomplemented
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C2×C42×C43C2311yescharacteristic
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C23×D43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22×C412yes—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—81no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86C22×C412yes—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43C22×C412yes—
186C42×C43—24no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—42no—
192C42×C43—42no—
193C42×C43C22×C412yes—
194C42×C43#4112yes—
195#10621885—28no—
196#10621884—28no—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—42no—
201(C2×D43)⋊C4—81no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43C2×D412yes—
206Dic43⋊C4—42no—
207C4×Dic43—42no—
208C4×Dic43—81no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C22×C412yes—
219C2×C43⋊C8C22×C412yes—
220C2×C43⋊C8C2×D412yes—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229Q8×C43—22no—
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43C4×D414yes—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C4×D412yes—
260C2×C4×C43C4×D412yes—
261C2×C4×C43#13512yes—
262C2×C4×C43#13512yes—
263C2×C4×C43C23×C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278D172—22no—
279D172—22no—
280D172—41no—
281D172—41no—
282C4×D43—84no—
283Dic86—22no—
284Dic86—22no—
285Dic86—41no—
286Dic86—41no—
287C43⋊C8—22no—
288C43⋊C8—22no—
289C43⋊C8—22no—
290C43⋊C8—41no—
291#23000—431nomaximal, Sylow
292C22×C43C2×C4×D411yescharacteristic
293C22×C43D4211yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43C2×#13511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—24no—
307C4×C43—22no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—42no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43C2×C4×D411yescharacteristic
317C4×C43#52011yescharacteristic
318C4×C43#54711yescharacteristic
319C4×C43#55311yescharacteristic
320Dic43—42no—
321Dic43—42no—
322Dic43—81no—
323C2×#464—431no—
324C2×C4×Q16—431no—
325C2×C4×SD16—431no—
326#2367—431no—
327#2351D4311yescharacteristic, complemented
328#1958—431no—
329#1949—431no—
330#1934—431no—
331#1933—431no—
332#1880—431no—
333#1878—431no—
334#1865—431no—
335#1862—431no—
336C8×C4⋊C4—431no—
337C4×#103—431no—
338C2×C43#236111yescharacteristic
339C2×C43C4×#13511yescharacteristic
340C2×C43#294711yescharacteristic
341C2×C43#328211yescharacteristic
342C2×C43#328511yescharacteristic
343C2×C43#336411yescharacteristic
344C2×C43#336511yescharacteristic
345D43—82no—
346C22×Q16—431no—
347C22×SD16—431no—
348C2×#124—431no—
349C2×C4×Q8—431no—
350C2×C4×Q8C2×D4311yescharacteristic
351C2×C4×Q8C2×D4311yescharacteristic
352C2×C4×Q8C2×D4311yescharacteristic
353C2×C4×D4—431no—
354#464—438no—
355C4×Q16—864no—
356C4×SD16—864no—
357C2×#107—431no—
358C2×#106—431no—
359C2×C4⋊C8—431no—
360C2×#103—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102—431no—
368C2×C4×C8—431no—
369C2×C4×C8—431no—
370C2×C4×C8—431no—
371#391—431no—
372#390—431no—
373#389—21no—
374#389—21no—
375#389C2×D4311yescharacteristic
376#389C2×D4311yescharacteristic
377#388—861no—
378#388—861no—
379#385—861no—
380#382—21no—
381#382C2×D4311yescharacteristic
382C4×C4⋊C4—21no—
383C4×C4⋊C4—431no—
384C4×C4⋊C4C2×D4311yescharacteristic
385C4×C22⋊C4—861no—
386#340—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#336—431no—
391#336—431no—
392C43#2300011yescharacteristic, complemented, Sylow
393C22×Q8—431no—
394C22×Q8C22×D4311yescharacteristic
395C22×D4—431no—
396C23×C4—861no—
397C2×Q16—434no—
398C2×Q16—862no—
399C2×Q16—862no—
400C2×SD16—434no—
401C2×SD16—862no—
402C2×SD16—862no—
403C22×C8—431no—
404C22×C8—431no—
405C22×C8—431no—
406C22×C8—431no—
407#124—434no—
408#124—862no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—41no—
413C4×Q8—41no—
414C4×Q8—862no—
415C4×Q8—1721no—
416C4×Q8C4×D4314yescomplemented
417C4×D4—862no—
418C4×D4—1721no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22⋊D4311yescharacteristic
428C2×C4⋊C4C22⋊D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C4⋊C4C22×D4311yescharacteristic
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—861no—
441C2×C42—861no—
442C2×C42C22×D4311yescharacteristic
443C2×C42C22×D4311yescharacteristic
444C2×C42C22×D4311yescharacteristic
445#107—862no—
446#106—862no—
447C4⋊C8—434no—
448#103—434no—
449#103—434no—
450#103—862no—
451#103—862no—
452#103—1721no—
453#102—434no—
454#102—862no—
455#102—1721no—
456C4×C8—862no—
457C4×C8—862no—
458C4×C8—862no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95C22⋊D4311yescharacteristic
467#95C22⋊D4311yescharacteristic
468C24—861no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—432no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8C2×C4×D4312yes—
479C2×Q8D4×D4312yes—
480C2×Q8#1062190212yes—
481C2×D4—432no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—861no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—3441no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C2×C22⋊D4311yescharacteristic
500C22×C4C2×C22⋊D4311yescharacteristic
501C22×C4C2×C22⋊D4311yescharacteristic
502C22×C4C2×C22⋊D4311yescharacteristic
503C22×C4C23×D4311yescharacteristic
504Q16—868no—
505SD16—868no—
506C2×C8—432no—
507C2×C8—432no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C4⋊C4—24no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—432no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—1722no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—864no—
537C22⋊C4—864no—
538C22⋊C4—3441no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C42—24no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—42no—
547C42—42no—
548C42—3441no—
549C42—1722no—
550C42C2×C4×D4312yes—
551C42#1062189812yes—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23—1721no—
557C23—1721no—
558C23—1721no—
559C23C22×C22⋊D4311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—22no—
563Q8—862no—
564Q8—862no—
565Q8—1721no—
566Q8—1721no—
567Q8#1306328714yes—
568D4—862no—
569D4—862no—
570D4—1721no—
571D4—1721no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—3444no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4C4×C22⋊D4312yes—
609C2×C4C4×C22⋊D4312yes—
610C2×C4#1306334512yes—
611C2×C4#1306334512yes—
612C2×C4C22×C4×D4311yescharacteristic
613C2×C4C2×D4×D4311yescharacteristic
614C2×C4C2×#1062189811yescharacteristic
615C2×C4C2×#1062190211yescharacteristic
616C2×C4#1306337011yescharacteristic
617C2×C4#1306337311yescharacteristic
618C8—862no—
619C8—862no—
620C8—862no—
621C8—1721no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22C2×C4×C22⋊D4311yescharacteristic
630C22D4×C22⋊D4311yescharacteristic
631C22#1458356011yescharacteristic
632C22C2×#1306334511yescharacteristic
633C22C2×#1306334511yescharacteristic
634C22#1458370711yescharacteristic
635C22#1458371411yescharacteristic
636C4—22no—
637C4—22no—
638C4—24no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—3441no—
647C4—1722no—
648C4—1722no—
649C4C2×#1306328711yescharacteristic
650C4#1458338011yescharacteristic
651C4#1458355011yescharacteristic
652C4#1458359711yescharacteristic
653C2—3442no—
654C2#1913761111yescharacteristic
655C2C4×#1306334511yescharacteristic
656C2#1914343811yescharacteristic
657C2#1914630311yescharacteristic
658C2#1914633211yescharacteristic
659C2#1914728011yescharacteristic
660C2#1914729111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2351C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2351D43
hypocenterC43#23000
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621885C2semidirect
6. #19135361C2semidirect
8. #19135270C2semidirect
10. #19134936C2semidirect
11. #19134862C2semidirect
13. C4⋊C4×C43⋊C8C2semidirect
14. C4×#13063249C2semidirect
15. C43×#2351C2semidirect
21. #14583121C4semidirect
67. C2×#10621885C2×C4semidirect
93. C4⋊(C43⋊C8)C2×C4semidirect
98. #13063248C2×C4semidirect
114. C4×Q8×C43C2×C4semidirect
327. #2351D43semidirect
392. C43#23000semidirect
416. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831212
C2×C4×#106218852
C2×C4×#106218842
#191376642
#191354042
#191353612
#191352772
#191352702
#191349502
#191349362
#191348622
#191348412
C4⋊C4×C43⋊C82
C4×#130632492
C43×#23512
#2300043