Finite Group Databasebeta

← #25106406

Subgroups — #25106406

Order 11008.

1158 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×#14583433C211yesmaximal, characteristic
2#19137002C211yesmaximal, characteristic, complemented
3#19135580C212yesmaximal, complemented
4#19135431C212yesmaximal
5#19135051C214yesmaximal, complemented
6#19134580C214yesmaximal, complemented
7C43×#2283C211yesmaximal, characteristic, complemented
8#14583433—21no—
9#14583433—21no—
10#14583433—21no—
11#14583433—21no—
12#14583433—21no—
13#14583433—21no—
14#14583433—21no—
15#14583433—21no—
16C2×#13063319C412yescomplemented
17C2×#13063317C411yescharacteristic, complemented
18C2×#13063313C411yescharacteristic, complemented
19C2×#13063308C2212yes—
20C2×#13063304C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22C2×C4×Dic86C411yescharacteristic, complemented
23C2×C4×D172C411yescharacteristic, complemented
24C2×C4×C22⋊D43C2212yes—
25C2×#13063284C2212yes—
26C2×#13063282C412yescomplemented
27C2×#13063239C2218yes—
28#14582769—21no—
29#14582765—21no—
30#14582759C2212yes—
31#14582759C2212yes—
32C4×C4⋊Dic43—21no—
33C4×C4⋊Dic43—21no—
34#14582665C2218yes—
35C22×C42×C43C2211yescharacteristic
36C43×#383—21no—
37C43×#382—21no—
38C43×#381C2212yes—
39C43×#380C2212yes—
40C4×C4⋊C4×C43—21no—
41C4×C22⋊C4×C43C2212yes—
42C43×#376—21no—
43C22×Dic86C2×C411yescharacteristic
44C22×D172C2×C411yescharacteristic
45C22×C22⋊D43C2312yes—
46C22×C4×D43C2×C412yes—
47#13063319—22no—
48#13063319—22no—
49#13063319—22no—
50#13063319—22no—
51#13063317—21no—
52#13063317—21no—
53#13063317—21no—
54#13063317—21no—
55#13063313—21no—
56#13063313—21no—
57#13063313—21no—
58#13063313—21no—
59#13063308—22no—
60#13063308—22no—
61#13063308—22no—
62#13063308—22no—
63#13063304—21no—
64#13063304—21no—
65#13063304—21no—
66#13063304—21no—
67#13063299—21no—
68#13063299—21no—
69#13063299—21no—
70#13063299—21no—
71C4×Dic86—21no—
72C4×Dic86—21no—
73C4×Dic86—21no—
74C4×Dic86—21no—
75C4×D172—21no—
76C4×D172—21no—
77C4×D172—21no—
78C4×D172—21no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—22no—
83#13063284—44no—
84#13063282—22no—
85#13063282—22no—
86#13063282—22no—
87#13063282—22no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—22no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×C4⋊Dic43C2×C411yescharacteristic
93C2×Dic43⋊C4C2×C412yes—
94C2×Dic43⋊C4C2×C412yes—
95C2×Dic43⋊C4C2×C412yes—
96C2×Dic43⋊C4C2×C412yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2312yes—
99C2×(C2×D43)⋊C4C2×C412yes—
100C2×(C2×D43)⋊C4C2×C412yes—
101C2×(C2×D43)⋊C4C2×C412yes—
102C2×(C2×D43)⋊C4C2×C412yes—
103C2×C4×Dic43—22no—
104C2×C4×Dic43C2×C412yes—
105#13063239—48no—
106C43⋊#95—22no—
107C43⋊#95—22no—
108C23×C4×C43C2311yescharacteristic
109C23×C4×C43C2311yescharacteristic
110C23×C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43—22no—
112C2×C22⋊C4×C43C2314yes—
113C2×C42×C43—22no—
114C2×C42×C43C2×C411yescharacteristic
115C2×C42×C43C2×C411yescharacteristic
116C2×C42×C43C2×C411yescharacteristic
117C2×C42×C43C2×C411yescharacteristic
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43D411yescharacteristic
121C2×C42×C43D411yescharacteristic
122C2×C42×C43D411yescharacteristic
123C2×C42×C43D411yescharacteristic
124C2×C42×C43D411yescharacteristic
125C2×C42×C43D411yescharacteristic
126#95×C43—22no—
127#95×C43—22no—
128#95×C43—22no—
129#95×C43—22no—
130C24×C43C2411yescharacteristic
131C23×D43C22×C412yes—
132C22×C4×C43—24no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43C22×C411yescharacteristic
138C22×C4×C43C22×C411yescharacteristic
139C22×C4×C43C22×C411yescharacteristic
140C22×C4×C43C22×C411yescharacteristic
141C22×C4×C43C22×C411yescharacteristic
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
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×C43C2×D411yescharacteristic
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—24no—
158C2×C22⋊D43—24no—
159C22×Dic43—24no—
160C22×Dic43C22×C412yes—
161C22×Dic43C22×C412yes—
162C22×Dic43C22×C412yes—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—42no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—44no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—42no—
172C4⋊C4×C43—44no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C42×C43—44no—
176C42×C43C22⋊C411yescharacteristic
177C42×C43C22⋊C411yescharacteristic
178C42×C43C22⋊C411yescharacteristic
179C42×C43C22⋊C411yescharacteristic
180C42×C43C22⋊C411yescharacteristic
181C42×C43C22⋊C411yescharacteristic
182C42×C43C22⋊C411yescharacteristic
183C42×C43C22⋊C411yescharacteristic
184C42×C43C22⋊C411yescharacteristic
185C42×C43C22⋊C411yescharacteristic
186C42×C43C22⋊C411yescharacteristic
187C42×C43C22⋊C411yescharacteristic
188C42×C43C22⋊C411yescharacteristic
189C42×C43C22⋊C411yescharacteristic
190C42×C43C22⋊C411yescharacteristic
191C42×C43C22⋊C411yescharacteristic
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—28no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—44no—
208C4⋊Dic43—44no—
209C4⋊Dic43—44no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—44no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43C23×C411yescharacteristic
224C23×C43C22×D411yescharacteristic
225C23×C43C22×D411yescharacteristic
226C23×C43H(5,𝔽2)12yes—
227C23×C432−1+412yes—
228C22×D43—22no—
229C22×D43—24no—
230C22×D43—42no—
231C22×D43—42no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—44no—
253C2×C4×C43—44no—
254C2×C4×C43—44no—
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C2×C22⋊C411yescharacteristic
261C2×C4×C43C2×C22⋊C411yescharacteristic
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C22⋊C411yescharacteristic
267C22⋊D43—42no—
268C22⋊D43—42no—
269C22⋊D43—44no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—24no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43—44no—
277C2×Dic43—44no—
278C2×Dic43—44no—
279D172—42no—
280D172—42no—
281C4×D43—44no—
282C4×D43—44no—
283Dic86—42no—
284Dic86—42no—
285#21875—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43C22×C22⋊C411yescharacteristic
295C22×C43#52012yes—
296C22×C43#53511yescharacteristic
297C22×C43#53611yescharacteristic
298C22×C43#53712yes—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—42no—
302C2×D43—84no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—21no—
312C4×C43—21no—
313C4×C43—84no—
314C4×C43#41012yes—
315C4×C43#41012yes—
316Dic43—42no—
317Dic43—42no—
318Dic43—42no—
319Dic43—84no—
320C2×#529—431no—
321#2285—431no—
322#2283D4311yescharacteristic, complemented
323#1996—432no—
324#1964—432no—
325#1899—434no—
326#1799—434no—
327C2×C43—21no—
328C2×C43—22no—
329C2×C43—22no—
330C2×C43—21no—
331C2×C43#231111yescharacteristic
332C2×C43C2×#41011yescharacteristic
333C2×C43C2×#41011yescharacteristic
334D43—82no—
335#529—861no—
336#529—861no—
337#529—861no—
338#529—861no—
339#529—861no—
340#529—861no—
341#529—861no—
342#529—861no—
343C2×#126—432no—
344C2×#125—431no—
345C2×#124—431no—
346C2×#123—432no—
347C2×C22⋊Q8—431no—
348C2×#121—431no—
349C2×C4×Q8—431no—
350C2×C4×D4—432no—
351C2×C4×D4—431no—
352C2×#117—432no—
353C2×#117—432no—
354C22×C42C2×D4311yescharacteristic
355C2×#99—438no—
356#384—861no—
357#383—21no—
358#382—21no—
359#382—861no—
360#381C2×D4312yes—
361#380—432no—
362#380—432no—
363#380C2×D4312yes—
364C4×C4⋊C4—21no—
365C4×C4⋊C4—861no—
366C4×C4⋊C4—861no—
367C4×C22⋊C4C2×D4312yes—
368#376—21no—
369#342—438no—
370C43#2187511yescharacteristic, complemented, Sylow
371C22×Q8—431no—
372C22×D4—432no—
373C22×D4—431no—
374C23×C4—432no—
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C23×C4C22×D4311yescharacteristic
378#126—862no—
379#126—862no—
380#126—862no—
381#126—862no—
382#125—861no—
383#125—861no—
384#125—861no—
385#125—861no—
386#124—861no—
387#124—861no—
388#124—861no—
389#124—861no—
390#123—862no—
391#123—862no—
392#123—862no—
393#123—862no—
394C22⋊Q8—861no—
395C22⋊Q8—861no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398#121—861no—
399#121—861no—
400#121—861no—
401#121—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8—861no—
406C4×D4—862no—
407C4×D4—862no—
408C4×D4—862no—
409C4×D4—862no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414#117—862no—
415#117—862no—
416#117—862no—
417#117—862no—
418#117—1724no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—862no—
429C2×C22⋊C4—432no—
430C2×C22⋊C4—432no—
431C2×C22⋊C4—432no—
432C2×C22⋊C4—432no—
433C2×C22⋊C4—432no—
434C2×C22⋊C4—434no—
435C2×C22⋊C4C22×D4314yes—
436C2×C42—22no—
437C2×C42—432no—
438C2×C42—862no—
439C2×C42C4×D4311yescharacteristic
440C2×C42C4×D4311yescharacteristic
441C2×C42C4×D4311yescharacteristic
442C2×C42C4×D4311yescharacteristic
443C2×C42D17211yescharacteristic
444C2×C42D17211yescharacteristic
445C2×C42D17211yescharacteristic
446C2×C42D17211yescharacteristic
447C2×C42C22⋊D4311yescharacteristic
448C2×C42C22⋊D4311yescharacteristic
449C2×C42C22⋊D4311yescharacteristic
450C2×C42C22⋊D4311yescharacteristic
451#99—1728no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—862no—
457#95—862no—
458C24—432no—
459C24C23×D4311yescharacteristic
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—1722no—
463C2×D4—862no—
464C2×D4—862no—
465C2×D4—864no—
466C2×D4—864no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—1722no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—432no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—862no—
479C22×C4—862no—
480C22×C4—864no—
481C22×C4—1724no—
482C22×C4C2×C4×D4311yescharacteristic
483C22×C4C2×C4×D4311yescharacteristic
484C22×C4C2×C4×D4311yescharacteristic
485C22×C4C2×C4×D4311yescharacteristic
486C22×C4C2×C4×D4311yescharacteristic
487C22×C4C2×C4×D4311yescharacteristic
488C22×C4C2×D17211yescharacteristic
489C22×C4C2×D17211yescharacteristic
490C22×C4C2×D17211yescharacteristic
491C22×C4C2×D17211yescharacteristic
492C22×C4C2×D17211yescharacteristic
493C22×C4C2×D17211yescharacteristic
494C22×C4C2×C22⋊D4311yescharacteristic
495C22×C4C2×C22⋊D4311yescharacteristic
496C22×C4C2×C22⋊D4311yescharacteristic
497C22×C4C2×C22⋊D4311yescharacteristic
498C22×C4C2×C22⋊D4311yescharacteristic
499C22×C4C2×C22⋊D4311yescharacteristic
500C4⋊C4—44no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—862no—
508C4⋊C4—862no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—1724no—
514C4⋊C4—1724no—
515C4⋊C4—1724no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—868no—
529C42—44no—
530C42—862no—
531C42—862no—
532C42—1724no—
533C42(C2×D43)⋊C411yescharacteristic
534C42(C2×D43)⋊C411yescharacteristic
535C42(C2×D43)⋊C411yescharacteristic
536C42(C2×D43)⋊C411yescharacteristic
537C42(C2×D43)⋊C411yescharacteristic
538C42(C2×D43)⋊C411yescharacteristic
539C42(C2×D43)⋊C411yescharacteristic
540C42(C2×D43)⋊C411yescharacteristic
541C42(C2×D43)⋊C411yescharacteristic
542C42(C2×D43)⋊C411yescharacteristic
543C42(C2×D43)⋊C411yescharacteristic
544C42(C2×D43)⋊C411yescharacteristic
545C42(C2×D43)⋊C411yescharacteristic
546C42(C2×D43)⋊C411yescharacteristic
547C42(C2×D43)⋊C411yescharacteristic
548C42(C2×D43)⋊C411yescharacteristic
549C23—41no—
550C23—41no—
551C23—864no—
552C23—862no—
553C23—1722no—
554C23—1722no—
555C23C22×C4×D4311yescharacteristic
556C23C22×C22⋊D4311yescharacteristic
557C23C22×D17211yescharacteristic
558C23#1306337112yes—
559C23#1306337212yes—
560Q8—1722no—
561Q8—1722no—
562D4—1722no—
563D4—1722no—
564D4—1722no—
565D4—1724no—
566D4—1722no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—864no—
594C2×C4—1724no—
595C2×C4—1724no—
596C2×C4—1724no—
597C2×C4—1724no—
598C2×C4—1724no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4C2×(C2×D43)⋊C411yescharacteristic
602C2×C4C2×(C2×D43)⋊C411yescharacteristic
603C2×C4C2×(C2×D43)⋊C411yescharacteristic
604C2×C4C2×(C2×D43)⋊C411yescharacteristic
605C2×C4C2×(C2×D43)⋊C411yescharacteristic
606C2×C4C2×(C2×D43)⋊C411yescharacteristic
607C2×C4C2×(C2×D43)⋊C411yescharacteristic
608C2×C4C2×(C2×D43)⋊C411yescharacteristic
609C2×C4C2×(C2×D43)⋊C411yescharacteristic
610C2×C4C2×(C2×D43)⋊C411yescharacteristic
611C2×C4C2×(C2×D43)⋊C411yescharacteristic
612C2×C4C2×(C2×D43)⋊C411yescharacteristic
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—42no—
620C22—42no—
621C22—3444no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C22×(C2×D43)⋊C411yescharacteristic
626C22#1458337912yes—
627C22#1458346811yescharacteristic
628C22#1458347511yescharacteristic
629C22#1458347712yes—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—84no—
641C4—3444no—
642C4—1722no—
643C4—1722no—
644C4—1722no—
645C4#1458287212yes—
646C4#1458287212yes—
647C2—22no—
648C2—21no—
649C2—22no—
650C2—21no—
651C2—3442no—
652C2#1913718311yescharacteristic
653C2C2×#1458287211yescharacteristic
654C2C2×#1458287211yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2283C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063299C22
cosocleC24×C43C24
hypercenter#2283D43
hypocenterC43#21875
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. #19137002C2semidirect
3. #19135580C2semidirect
5. #19135051C2semidirect
6. #19134580C2semidirect
7. C43×#2283C2semidirect
16. C2×#13063319C4semidirect
17. C2×#13063317C4semidirect
18. C2×#13063313C4semidirect
22. C2×C4×Dic86C4semidirect
23. C2×C4×D172C4semidirect
26. C2×#13063282C4semidirect
322. #2283D43semidirect
370. C43#21875semidirect

Maximal subgroups

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

subgroupindex
C2×#145834332
#191370022
#191355802
#191354312
#191350512
#191345802
C43×#22832
#2187543