Finite Group Databasebeta

← #11792808

Subgroups — #11792808

Order 1152.

1529 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 1529 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C3×#5493C211yesmaximal, characteristic, complemented
2C2×#63981C212yesmaximal, complemented
3#10592654C211yesmaximal, characteristic, complemented
4C2×#63580C212yesmaximal, complemented
5C3×#4526C211yesmaximal, characteristic, complemented
6#71851—31nomaximal
7#68965—31nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C22×C3×#67C2212yes—
10C22×#626—22no—
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3752—22no—
14C2×C3×#217C2212yes—
15C3×#930—22no—
16C3×#886—22no—
17C3×#882—22no—
18#63981—24no—
19#63981—24no—
20C2×#3722—22no—
21#63580—24no—
22C3×#534—31no—
23C2×#937—32no—
24#5493D311yescharacteristic, complemented
25C2×#882—32no—
26C2×#834—32no—
27#4955—31no—
28#4955—31no—
29#4955—61no—
30C2×#806—32no—
31C3×#342—31no—
32#4526D311yescharacteristic, complemented
33C24×C32C2311yescharacteristic
34C23×C3⋊D3—21no—
35C23×C3⋊D3—22no—
36C23×C3⋊D3—22no—
37C23×C3⋊D3—21no—
38C23×C3⋊D3—44no—
39C23×C3⋊D3D412yescomplemented
40C23×C3×D3D412yescomplemented
41C22×C32×C4D412yescomplemented
42C22×C3⋊Dic3—21no—
43C2×C3×#67—22no—
44C2×C3×#67—22no—
45C2×C3×#67—22no—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C2×C3×#67—22no—
49C22×C3×Dic3—22no—
50C22×C3×Dic3D412yescomplemented
51C2×C3×D12—22no—
52C2×#626—28no—
53C2×#626—48no—
54C32×C22⋊C4—22no—
55#3757—22no—
56#3752—44no—
57C3×#217—22no—
58C3×#217D414yescomplemented
59C3×(C2×D3)⋊C4—24no—
60C3×C4⋊Dic3—22no—
61#3722—28no—
62#2021—91noSylow
63C24×D3—31no—
64C24×D3—31no—
65C24×D3—61no—
66C22×C3×D4—32no—
67C22×#67—62no—
68C22×#67C2×D312yes—
69C22×D12—62no—
70C3×#123—62no—
71C3×#121—62no—
72C3×#120—62no—
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—32no—
75C2×C3×C22⋊C4C2×D311yescharacteristic
76C2×C3×C22⋊C4C2×D311yescharacteristic
77C2×#217—31no—
78C2×#217—31no—
79C2×#217—61no—
80C2×#217C2×D312yes—
81#937—64no—
82#937—64no—
83#930—22no—
84C2×(C2×D3)⋊C4—62no—
85C2×(C2×D3)⋊C4—62no—
86C2×(C2×D3)⋊C4—64no—
87C2×(C2×D3)⋊C4—62no—
88C2×(C2×D3)⋊C4—62no—
89#886—22no—
90#882—22no—
91#882—64no—
92#882—64no—
93#834—64no—
94#806—64no—
95C23×C32—42no—
96C23×C32C2×D412yes—
97C23×C32C2×D411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32#4111yescharacteristic
101C22×C3⋊D3—24no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3—28no—
104C22×C3⋊D3—24no—
105C22×C3⋊D3—44no—
106C22×C3⋊D3—44no—
107C22×C3⋊D3—48no—
108C22×C3⋊D3—42no—
109C22×C3⋊D3—44no—
110C22×C3⋊D3—41no—
111C22×C3⋊D3—42no—
112C22×C3⋊D3—41no—
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—22no—
116C22×C3×D3—44no—
117C2×C32×C4—22no—
118C2×C32×C4—42no—
119C2×C3⋊Dic3—42no—
120C2×C3⋊Dic3—41no—
121C3×#67—42no—
122C3×#67—42no—
123C3×#67—42no—
124C3×#67—42no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—44no—
130C3×D12—82no—
131#626—416no—
132#534—31no—
133C2×#120—92no—
134C2×#99—92no—
135#379—91no—
136#342—31no—
137C24×C3—21no—
138C24×C3—32no—
139C24×C3C22×D311yescharacteristic
140C24×C3C22×D311yescharacteristic
141C23×D3—32no—
142C23×D3—32no—
143C23×D3—62no—
144C23×D3—62no—
145C23×D3—61no—
146C23×D3—62no—
147C23×D3—61no—
148C23×D3—62no—
149C23×D3—62no—
150C23×D3—62no—
151C23×D3—62no—
152C23×D3—61no—
153C23×D3—61no—
154C23×D3—122no—
155C23×D3—122no—
156C23×D3—124no—
157C23×D3—124no—
158C23×D3—128no—
159C23×D3#6712yescomplemented
160C2×C3×D4—62no—
161C2×C3×D4—62no—
162C2×C3×D4—62no—
163C2×C3×D4—62no—
164C2×C3×D4—62no—
165C2×C3×D4—62no—
166C2×C3×D4—62no—
167C22×C3×C4—22no—
168C22×C3×C4—32no—
169C22×C3×C4—62no—
170C22×C3×C4D1212yescomplemented
171C22×C3×C4#6712yescomplemented
172C2×#67—22no—
173C2×#67—22no—
174C2×#67—22no—
175C2×#67—22no—
176C2×#67—22no—
177C2×#67—22no—
178C2×#67—68no—
179C2×#67—128no—
180C22×Dic3—22no—
181C22×Dic3—62no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3#6712yescomplemented
185C2×D12—22no—
186C2×D12—68no—
187C2×D12—128no—
188C3×C4⋊C4—62no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—22no—
191C3×C22⋊C4—34no—
192C3×C22⋊C4—42no—
193C3×C22⋊C4—64no—
194C3×C22⋊C4—62no—
195#217—22no—
196#217—62no—
197#217—62no—
198#217—122no—
199#217D1214yescomplemented
200(C2×D3)⋊C4—24no—
201(C2×D3)⋊C4—68no—
202(C2×D3)⋊C4—68no—
203(C2×D3)⋊C4—124no—
204(C2×D3)⋊C4—124no—
205(C2×D3)⋊C4—128no—
206C4⋊Dic3—22no—
207C22×C32—22no—
208C22×C32—24no—
209C22×C32—42no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32#12012yes—
213C22×C32#12011yescharacteristic
214C22×C32#12111yescharacteristic
215C22×C32#12112yes—
216C22×C32#12711yescharacteristic
217C2×C3⋊D3—24no—
218C2×C3⋊D3—28no—
219C2×C3⋊D3—44no—
220C2×C3⋊D3—42no—
221C2×C3⋊D3—44no—
222C2×C3⋊D3—48no—
223C2×C3⋊D3—42no—
224C2×C3⋊D3—44no—
225C2×C3×D3—44no—
226C2×C3×D3—42no—
227C2×C3×D3—44no—
228C2×C3×D3—82no—
229C32×C4—42no—
230C3⋊Dic3—81no—
231C3×Dic3—44no—
232C3×Dic3—42no—
233C25—91no—
234C22×D4—32no—
235C22×D4—182no—
236#123—62no—
237#121—62no—
238#120—62no—
239#120—184no—
240#120—184no—
241C2×C22⋊C4—32no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—182no—
244C2×C22⋊C4—182no—
245C2×C22⋊C4D3211yescharacteristic
246#99—184no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—22no—
252C23×C3—42no—
253C23×C3—42no—
254C23×C3—44no—
255C23×C3—62no—
256C23×C3—62no—
257C23×C3—62no—
258C23×C3—124no—
259C23×C3C2×D1212yes—
260C23×C3C2×D1211yescharacteristic
261C23×C3D3×D412yes—
262C23×C3D3×D411yescharacteristic
263C23×C3D3×D411yescharacteristic
264C23×C3D3×D412yes—
265C23×C3#23711yescharacteristic
266C23×C3#23911yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C23×C3C2×#6712yes—
269C22×D3—22no—
270C22×D3—22no—
271C22×D3—22no—
272C22×D3—44no—
273C22×D3—68no—
274C22×D3—64no—
275C22×D3—64no—
276C22×D3—68no—
277C22×D3—68no—
278C22×D3—64no—
279C22×D3—64no—
280C22×D3—62no—
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—124no—
284C22×D3—128no—
285C22×D3—124no—
286C22×D3—124no—
287C22×D3—128no—
288C22×D3—128no—
289C22×D3—128no—
290C22×D3—124no—
291C22×D3—124no—
292C22×D3—128no—
293C22×D3—124no—
294C22×D3—122no—
295C22×D3—124no—
296C22×D3—124no—
297C22×D3—122no—
298C22×D3—124no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—128no—
302C22×D3—1216no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—121no—
308C22×D3—121no—
309C3×D4—122no—
310C3×D4—122no—
311C3×D4—122no—
312C3×D4—122no—
313C3×D4—242no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—44no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—64no—
324C2×C3×C4—124no—
325#67—42no—
326#67—42no—
327#67—42no—
328#67—42no—
329#67—1216no—
330C2×Dic3—24no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—44no—
335C2×Dic3—124no—
336C2×Dic3—122no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341D12—82no—
342D12—1216no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—22no—
346C2×C32—22no—
347C2×C32#39211yescharacteristic
348C2×C32B(4,𝔽2)12yes—
349C3⋊D3—44no—
350C3×D3—82no—
351C24—32no—
352C24—92no—
353C24—181no—
354C24—182no—
355C24—181no—
356C24—182no—
357C24—364no—
358C24C2×D3211yescharacteristic
359C2×D4—62no—
360C2×D4—62no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4—62no—
364C2×D4—62no—
365C2×D4—62no—
366C2×D4—188no—
367C2×D4—368no—
368C22×C4—32no—
369C22×C4—62no—
370C22×C4—181no—
371C22×C4#62612yescomplemented
372C4⋊C4—62no—
373C22⋊C4—22no—
374C22⋊C4—34no—
375C22⋊C4—64no—
376C22⋊C4—62no—
377C22⋊C4—188no—
378C22⋊C4—182no—
379C22⋊C4—364no—
380C22×C3—24no—
381C22×C3—22no—
382C22×C3—24no—
383C22×C3—24no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—44no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—42no—
398C22×C3—44no—
399C22×C3—42no—
400C22×C3—124no—
401C22×C3—122no—
402C22×C3—124no—
403C22×C3—242no—
404C22×C3#87411yescharacteristic
405C22×C3#88212yes—
406C22×C3#88211yescharacteristic
407C22×C3#89512yes—
408C22×C3#89511yescharacteristic
409C22×C3#93712yes—
410C22×C3#93811yescharacteristic
411C22×C3#93912yes—
412C22×C3#94011yescharacteristic
413C22×C3#95311yescharacteristic
414C2×D3—44no—
415C2×D3—42no—
416C2×D3—44no—
417C2×D3—68no—
418C2×D3—68no—
419C2×D3—68no—
420C2×D3—64no—
421C2×D3—64no—
422C2×D3—82no—
423C2×D3—128no—
424C2×D3—128no—
425C2×D3—124no—
426C2×D3—124no—
427C2×D3—124no—
428C2×D3—122no—
429C2×D3—128no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—128no—
434C2×D3—128no—
435C2×D3—124no—
436C2×D3—128no—
437C2×D3—1216no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—124no—
441C2×D3—124no—
442C3×C4—42no—
443C3×C4—42no—
444C3×C4—82no—
445C3×C4—124no—
446C3×C4—122no—
447Dic3—44no—
448Dic3—42no—
449Dic3—242no—
450Dic3—241no—
451Dic3—241no—
452C32#202111yescharacteristic, complemented, Sylow
453C23—42no—
454C23—62no—
455C23—62no—
456C23—62no—
457C23—124no—
458C23—184no—
459C23—188no—
460C23—182no—
461C23—184no—
462C23—362no—
463C23—364no—
464C23—364no—
465C23—364no—
466C23—368no—
467C23—362no—
468C23—361no—
469C23—361no—
470C23#379611yescharacteristic
471C23D3×D1212yes—
472C23#380211yescharacteristic
473C23C2×#62611yescharacteristic
474C23D3×#6712yes—
475D4—122no—
476D4—122no—
477D4—122no—
478D4—122no—
479D4—242no—
480D4—3616no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—62no—
484C2×C4—64no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—124no—
488C2×C4—362no—
489C2×C4—361no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—22no—
501C2×C3—21no—
502C2×C3—42no—
503C2×C3—42no—
504C2×C3—242no—
505C2×C3#467111yescharacteristic
506C2×C3#474112yes—
507C2×C3#522311yescharacteristic
508C2×C3#524412yes—
509D3—82no—
510D3—128no—
511D3—124no—
512D3—124no—
513C22—22no—
514C22—24no—
515C22—41no—
516C22—42no—
517C22—41no—
518C22—124no—
519C22—124no—
520C22—122no—
521C22—188no—
522C22—184no—
523C22—242no—
524C22—364no—
525C22—364no—
526C22—362no—
527C22—368no—
528C22—364no—
529C22—362no—
530C22#6388612yes—
531C22#6391111yescharacteristic
532C22#6391611yescharacteristic
533C22#6392212yes—
534C22#6397711yescharacteristic
535C4—42no—
536C4—124no—
537C4—122no—
538C4—721no—
539C3—21no—
540C3#6896511yescharacteristic, complemented
541C3#7185111yescharacteristic, complemented
542C2—22no—
543C2—21no—
544C2—21no—
545C2—22no—
546C2—242no—
547C2—364no—
548C2#1059139111yescharacteristic
549C2#1059153112yes—
subgroupG/H
centerC22#63977
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. C3×#5493C2semidirect
2. C2×#63981C2semidirect
3. #10592654C2semidirect
4. C2×#63580C2semidirect
5. C3×#4526C2semidirect
24. #5493D3semidirect
32. #4526D3semidirect
39. C23×C3⋊D3D4semidirect
40. C23×C3×D3D4semidirect
41. C22×C32×C4D4semidirect
50. C22×C3×Dic3D4semidirect
58. C3×#217D4semidirect
159. C23×D3#67semidirect
170. C22×C3×C4D12semidirect
171. C22×C3×C4#67semidirect
184. C22×Dic3#67semidirect
199. #217D12semidirect
371. C22×C4#626semidirect
452. C32#2021semidirect
540. C3#68965semidirect
541. C3#71851semidirect

Maximal subgroups

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

subgroupindex
C3×#54932
C2×#639812
#105926542
C2×#635802
C3×#45262
#718513
#689653