Finite Group Databasebeta

← #11792809

Subgroups — #11792809

Order 1152.

1449 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 1449 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595964C211yesmaximal, characteristic, complemented
2C2×#63977C212yesmaximal, complemented
3C3×#4955C211yesmaximal, characteristic, complemented
4C2×#63581C212yesmaximal, complemented
5C3×#4526C211yesmaximal, characteristic, complemented
6#69500—31nomaximal
7#68965—31nomaximal
8C24×C3×D3C2211yescharacteristic
9C22×#638C2212yes—
10C22×#626—22no—
11C2×C32×C22⋊C4C2211yescharacteristic
12#64139—22no—
13#64095—22no—
14#64091—22no—
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2212yes—
17C2×C3×(C2×D3)⋊C4—22no—
18#63977—24no—
19#63977—24no—
20C2×(C2×D3)⋊Dic3—22no—
21#63581—24no—
22C2×#953—32no—
23#5493—31no—
24#5493—31no—
25#5493—61no—
26C2×#882—32no—
27C3×#379—31no—
28#4955D311yescharacteristic, complemented
29C2×#806—32no—
30C2×#806—32no—
31C3×#342—31no—
32#4526D311yescharacteristic, complemented
33C24×C32C2311yescharacteristic
34C23×C3⋊D3D412yescomplemented
35C23×C3×D3—21no—
36C23×C3×D3—22no—
37C23×C3×D3—22no—
38C23×C3×D3—21no—
39C23×C3×D3—44no—
40C23×C3×D3D412yescomplemented
41C22×C32×C4D412yescomplemented
42C2×#638—22no—
43C2×#638—22no—
44C2×#638—22no—
45C2×#638—22no—
46C2×#638—22no—
47C2×#638—22no—
48C22×C3⋊Dic3D412yescomplemented
49C2×C4⋊(C3⋊D3)—22no—
50C22×C3×Dic3—22no—
51C22×C3×Dic3—21no—
52C2×#626—28no—
53C2×#626—48no—
54C32×C22⋊C4—22no—
55#3752—24no—
56C4⋊(C3⋊Dic3)—22no—
57C3×#217—22no—
58C3×#217—22no—
59C3×#217D414yescomplemented
60C3×(C2×D3)⋊C4—44no—
61(C2×D3)⋊Dic3—28no—
62#2021—91noSylow
63C25×C3—31no—
64C24×D3C2×D311yescharacteristic
65C22×#67—32no—
66C22×#67—32no—
67C22×#67—62no—
68C22×#67—62no—
69C22×D12—62no—
70C2×C3×C22⋊C4—21no—
71C2×C3×C22⋊C4—32no—
72C2×C3×C22⋊C4—31no—
73C2×C3×C22⋊C4—62no—
74C2×C3×C22⋊C4C2×D311yescharacteristic
75C2×C3×C22⋊C4C2×D311yescharacteristic
76#953—64no—
77#953—64no—
78C2×#217—62no—
79C2×#217C2×D311yescharacteristic
80C2×#217C2×D312yes—
81#930—64no—
82#930—62no—
83#930—62no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—62no—
86#886—62no—
87#886—62no—
88#886—64no—
89#882—62no—
90#882—62no—
91#882—64no—
92#882—64no—
93#882—64no—
94#806—64no—
95#806—64no—
96C23×C32—42no—
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D412yes—
99C23×C32C2×D411yescharacteristic
100C23×C32C2×D412yes—
101C23×C32#4111yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—22no—
104C22×C3⋊D3—22no—
105C22×C3⋊D3—44no—
106C22×C3×D3—24no—
107C22×C3×D3—28no—
108C22×C3×D3—24no—
109C22×C3×D3—22no—
110C22×C3×D3—44no—
111C22×C3×D3—48no—
112C22×C3×D3—44no—
113C22×C3×D3—42no—
114C22×C3×D3—44no—
115C22×C3×D3—41no—
116C22×C3×D3—42no—
117C22×C3×D3—41no—
118C2×C32×C4—22no—
119C2×C32×C4—42no—
120#638—42no—
121#638—42no—
122#638—42no—
123#638—42no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C4⋊(C3⋊D3)—82no—
128C2×C3×Dic3—24no—
129C2×C3×Dic3—44no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—41no—
132#626—416no—
133#534—91no—
134C2×#120—92no—
135C2×#99—92no—
136#379—31no—
137#342—31no—
138C24×C3—21no—
139C24×C3—32no—
140C24×C3—61no—
141C24×C3—62no—
142C24×C3—62no—
143C24×C3—61no—
144C24×C3—124no—
145C24×C3C22×D311yescharacteristic
146C24×C3C22×D311yescharacteristic
147C23×D3—22no—
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—22no—
151C23×D3—32no—
152C23×D3—32no—
153C23×D3—44no—
154C23×D3—62no—
155C23×D3D1212yescomplemented
156C22×C3×C4—22no—
157C22×C3×C4—62no—
158C22×C3×C4—61no—
159C22×C3×C4D1212yescomplemented
160C22×C3×C4#6712yescomplemented
161C2×#67—68no—
162C2×#67—64no—
163C2×#67—64no—
164C2×#67—62no—
165C2×#67—62no—
166C2×#67—62no—
167C2×#67—62no—
168C2×#67—62no—
169C2×#67—62no—
170C2×#67—62no—
171C2×#67—62no—
172C2×#67—62no—
173C2×#67—62no—
174C2×#67—62no—
175C2×#67—62no—
176C2×#67—122no—
177C2×#67—122no—
178C2×#67—122no—
179C2×#67—122no—
180C2×#67—128no—
181C22×Dic3—22no—
182C22×Dic3—21no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—62no—
186C2×D12—68no—
187C2×D12—64no—
188C2×D12—62no—
189C2×D12—62no—
190C2×D12—128no—
191C3×C22⋊C4—24no—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—22no—
194C3×C22⋊C4—34no—
195C3×C22⋊C4—62no—
196C3×C22⋊C4—62no—
197C3×C22⋊C4—124no—
198#217—22no—
199#217—22no—
200#217—68no—
201#217D1214yescomplemented
202(C2×D3)⋊C4—44no—
203(C2×D3)⋊C4—68no—
204(C2×D3)⋊C4—64no—
205(C2×D3)⋊C4—64no—
206(C2×D3)⋊C4—68no—
207C4⋊Dic3—64no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C22×C32—22no—
211C22×C32—24no—
212C22×C32—41no—
213C22×C32—42no—
214C22×C32—41no—
215C22×C32#12012yes—
216C22×C32#12011yescharacteristic
217C22×C32#12112yes—
218C22×C32#12111yescharacteristic
219C22×C32#12711yescharacteristic
220C2×C3⋊D3—42no—
221C2×C3⋊D3—44no—
222C2×C3⋊D3—44no—
223C2×C3⋊D3—82no—
224C2×C3×D3—28no—
225C2×C3×D3—24no—
226C2×C3×D3—44no—
227C2×C3×D3—44no—
228C2×C3×D3—42no—
229C2×C3×D3—48no—
230C2×C3×D3—42no—
231C2×C3×D3—44no—
232C32×C4—42no—
233C3⋊Dic3—42no—
234C3×Dic3—44no—
235C3×Dic3—81no—
236C25—31no—
237C22×D4—92no—
238C22×D4—182no—
239#123—182no—
240#121—182no—
241#120—182no—
242#120—184no—
243#120—184no—
244C2×C22⋊C4—32no—
245C2×C22⋊C4—31no—
246C2×C22⋊C4—62no—
247C2×C22⋊C4—182no—
248C2×C22⋊C4D3211yescharacteristic
249#99—184no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—22no—
253C23×C3—21no—
254C23×C3—22no—
255C23×C3—42no—
256C23×C3—42no—
257C23×C3—64no—
258C23×C3—68no—
259C23×C3—64no—
260C23×C3—62no—
261C23×C3—82no—
262C23×C3—124no—
263C23×C3—122no—
264C23×C3—124no—
265C23×C3—128no—
266C23×C3—124no—
267C23×C3—121no—
268C23×C3—121no—
269C23×C3—122no—
270C23×C3C2×D1212yes—
271C23×C3C2×D1211yescharacteristic
272C23×C3C2×D1211yescharacteristic
273C23×C3#23511yescharacteristic
274C23×C3D3×D411yescharacteristic
275C23×C3D3×D412yes—
276C23×C3D3×D412yes—
277C23×C3D3×D412yes—
278C23×C3#23911yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C22×D3—24no—
281C22×D3—28no—
282C22×D3—24no—
283C22×D3—22no—
284C22×D3—44no—
285C22×D3—48no—
286C22×D3—44no—
287C22×D3—42no—
288C22×D3—44no—
289C22×D3—42no—
290C22×D3—41no—
291C22×D3—41no—
292C22×D3—64no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—124no—
302C22×D3—124no—
303C22×D3—244no—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—64no—
310C2×C3×C4—82no—
311C2×C3×C4—124no—
312C2×C3×C4—122no—
313C2×C3×C4—121no—
314#67—1216no—
315#67—124no—
316#67—124no—
317#67—124no—
318#67—124no—
319#67—122no—
320#67—122no—
321#67—122no—
322#67—122no—
323#67—122no—
324#67—122no—
325#67—122no—
326#67—122no—
327C2×Dic3—24no—
328C2×Dic3—44no—
329C2×Dic3—42no—
330C2×Dic3—41no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340D12—1216no—
341D12—244no—
342D12—242no—
343D12—242no—
344C2×C32—22no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32—22no—
348C2×C32#39211yescharacteristic
349C2×C32B(4,𝔽2)12yes—
350C3⋊D3—82no—
351C3×D3—44no—
352C24—32no—
353C24—61no—
354C24—62no—
355C24—61no—
356C24—62no—
357C24—92no—
358C24—124no—
359C24C2×D3211yescharacteristic
360C2×D4—182no—
361C2×D4—188no—
362C2×D4—182no—
363C2×D4—182no—
364C2×D4—182no—
365C2×D4—182no—
366C2×D4—182no—
367C2×D4—182no—
368C2×D4—368no—
369C22×C4—62no—
370C22×C4—61no—
371C22×C4—92no—
372C22×C4#62612yescomplemented
373C4⋊C4—182no—
374C22⋊C4—22no—
375C22⋊C4—34no—
376C22⋊C4—62no—
377C22⋊C4—62no—
378C22⋊C4—124no—
379C22⋊C4—184no—
380C22⋊C4—188no—
381C22×C3—24no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—24no—
385C22×C3—21no—
386C22×C3—22no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—42no—
391C22×C3—44no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—68no—
399C22×C3—64no—
400C22×C3—81no—
401C22×C3—81no—
402C22×C3—82no—
403C22×C3—124no—
404C22×C3—124no—
405C22×C3—128no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—124no—
409C22×C3#87411yescharacteristic
410C22×C3#88212yes—
411C22×C3#88212yes—
412C22×C3#88211yescharacteristic
413C22×C3#88412yes—
414C22×C3#89511yescharacteristic
415C22×C3#89512yes—
416C22×C3#93011yescharacteristic
417C22×C3#93711yescharacteristic
418C22×C3#94011yescharacteristic
419C2×D3—28no—
420C2×D3—24no—
421C2×D3—44no—
422C2×D3—44no—
423C2×D3—42no—
424C2×D3—48no—
425C2×D3—42no—
426C2×D3—44no—
427C2×D3—124no—
428C2×D3—128no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—124no—
434C2×D3—124no—
435C2×D3—244no—
436C2×D3—244no—
437C2×D3—242no—
438C2×D3—242no—
439C3×C4—44no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4—124no—
443C3×C4—241no—
444Dic3—44no—
445Dic3—81no—
446Dic3—124no—
447Dic3—122no—
448Dic3—122no—
449C32#202111yescharacteristic, complemented, Sylow
450C23—42no—
451C23—64no—
452C23—68no—
453C23—62no—
454C23—64no—
455C23—122no—
456C23—124no—
457C23—124no—
458C23—124no—
459C23—128no—
460C23—122no—
461C23—121no—
462C23—121no—
463C23—182no—
464C23—182no—
465C23—182no—
466C23—364no—
467C23#379911yescharacteristic
468C23D3×D1211yescharacteristic
469C23D3×D1212yes—
470C23C2×#62611yescharacteristic
471C23#381112yes—
472D4—3616no—
473D4—362no—
474D4—362no—
475D4—362no—
476D4—362no—
477D4—722no—
478C2×C4—22no—
479C2×C4—42no—
480C2×C4—64no—
481C2×C4—124no—
482C2×C4—122no—
483C2×C4—121no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C3—22no—
488C2×C3—21no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—42no—
498C2×C3—42no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3—124no—
502C2×C3#467111yescharacteristic
503C2×C3#474112yes—
504C2×C3#496011yescharacteristic
505C2×C3#503212yes—
506D3—44no—
507D3—244no—
508D3—242no—
509D3—242no—
510C22—22no—
511C22—24no—
512C22—41no—
513C22—41no—
514C22—42no—
515C22—68no—
516C22—64no—
517C22—124no—
518C22—124no—
519C22—122no—
520C22—128no—
521C22—124no—
522C22—122no—
523C22—364no—
524C22—364no—
525C22—362no—
526C22—722no—
527C22#6390911yescharacteristic
528C22#6391012yes—
529C22#6391111yescharacteristic
530C22#6392312yes—
531C22#6398111yescharacteristic
532C4—42no—
533C4—124no—
534C4—241no—
535C4—362no—
536C3—21no—
537C3#6896511yescharacteristic, complemented
538C3#6950011yescharacteristic, complemented
539C2—22no—
540C2—21no—
541C2—21no—
542C2—22no—
543C2—124no—
544C2—722no—
545C2#1059139511yescharacteristic
546C2#1059153212yes—
subgroupG/H
centerC22#63981
commutator, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32#2021
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595964C2semidirect
2. C2×#63977C2semidirect
3. C3×#4955C2semidirect
4. C2×#63581C2semidirect
5. C3×#4526C2semidirect
28. #4955D3semidirect
32. #4526D3semidirect
34. C23×C3⋊D3D4semidirect
40. C23×C3×D3D4semidirect
41. C22×C32×C4D4semidirect
48. C22×C3⋊Dic3D4semidirect
59. C3×#217D4semidirect
155. C23×D3D12semidirect
159. C22×C3×C4D12semidirect
160. C22×C3×C4#67semidirect
201. #217D12semidirect
372. C22×C4#626semidirect
449. C32#2021semidirect
537. C3#68965semidirect
538. C3#69500semidirect

Maximal subgroups

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

subgroupindex
#105959642
C2×#639772
C3×#49552
C2×#635812
C3×#45262
#695003
#689653