Finite Group Databasebeta

← #11792810

Subgroups — #11792810

Order 1152.

1347 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 1347 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
1C3×#5493C211yesmaximal, characteristic, complemented
2C2×#63976C212yesmaximal, complemented
3C3×#4955C211yesmaximal, characteristic, complemented
4C2×#63580C212yesmaximal, complemented
5#10589392C211yesmaximal, characteristic, complemented
6#71851—31nomaximal
7#69500—31nomaximal
8C24×C3×D3C2211yescharacteristic
9C22×C3×#67C2212yes—
10C22×#625—22no—
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2212yes—
13C2×C3×#217C2211yescharacteristic
14C3×#930—22no—
15C2×C3×(C2×D3)⋊C4—22no—
16C3×#886—22no—
17C3×#882—22no—
18#63976—24no—
19#63976—24no—
20C2×(C2×D3)⋊Dic3—22no—
21#63580—24no—
22C3×#534—31no—
23C2×#953—32no—
24C2×#937—32no—
25#5493D311yescharacteristic, complemented
26C3×#379—31no—
27C2×#834—32no—
28#4955D311yescharacteristic, complemented
29C2×#806—32no—
30#4526—31no—
31#4526—31no—
32#4526—61no—
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—22no—
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—21no—
50C22×C3×Dic3D412yescomplemented
51C2×C3×D12—22no—
52C2×#625—28no—
53C2×#625—48no—
54C32×C22⋊C4—22no—
55#3757—22no—
56#3757D414yescomplemented
57C3×#217—22no—
58C3×(C2×D3)⋊C4—24no—
59C3×(C2×D3)⋊C4—44no—
60C3×C4⋊Dic3—22no—
61(C2×D3)⋊Dic3—28no—
62#2021—91noSylow
63C25×C3—31no—
64C24×D3C2×D311yescharacteristic
65C22×C3×D4—32no—
66C22×#67—62no—
67C22×#67—62no—
68C22×#67C2×D312yes—
69C3×#123—62no—
70C3×#121—62no—
71C3×#120—62no—
72C2×C3×C22⋊C4—21no—
73C2×C3×C22⋊C4—31no—
74C2×C3×C22⋊C4—62no—
75C2×C3×C22⋊C4C2×D311yescharacteristic
76C2×C3×C22⋊C4C2×D311yescharacteristic
77#953—64no—
78#953—64no—
79C2×#217—32no—
80C2×#217—32no—
81C2×#217—62no—
82C2×#217—62no—
83C2×#217C2×D311yescharacteristic
84#937—64no—
85#937—64no—
86#930—22no—
87C2×(C2×D3)⋊C4—22no—
88C2×(C2×D3)⋊C4—62no—
89#886—22no—
90#882—22no—
91#834—64no—
92#806—64no—
93C23×C32—42no—
94C23×C32C2×D411yescharacteristic
95C23×C32C2×D412yes—
96C23×C32C2×D412yes—
97C23×C32C2×D411yescharacteristic
98C23×C32#4111yescharacteristic
99C22×C3×D3—24no—
100C22×C3×D3—28no—
101C22×C3×D3—24no—
102C22×C3×D3—22no—
103C22×C3×D3—22no—
104C22×C3×D3—22no—
105C22×C3×D3—22no—
106C22×C3×D3—44no—
107C22×C3×D3—48no—
108C22×C3×D3—44no—
109C22×C3×D3—42no—
110C22×C3×D3—44no—
111C22×C3×D3—41no—
112C22×C3×D3—42no—
113C22×C3×D3—41no—
114C22×C3×D3—44no—
115C2×C32×C4—22no—
116C2×C32×C4—42no—
117C2×C3⋊Dic3—24no—
118C2×C3⋊Dic3—44no—
119C3×#67—42no—
120C3×#67—42no—
121C3×#67—42no—
122C3×#67—42no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—41no—
128C3×D12—82no—
129#625—416no—
130#534—31no—
131C2×#120—92no—
132C2×#99—92no—
133#379—31no—
134#342—91no—
135C24×C3—21no—
136C24×C3—32no—
137C24×C3—32no—
138C24×C3—62no—
139C24×C3—61no—
140C24×C3—62no—
141C24×C3—61no—
142C24×C3—124no—
143C24×C3C22×D311yescharacteristic
144C24×C3C22×D311yescharacteristic
145C23×D3—22no—
146C23×D3—21no—
147C23×D3—21no—
148C23×D3—22no—
149C23×D3—44no—
150C23×D3D1212yescomplemented
151C23×D3#6712yescomplemented
152C2×C3×D4—62no—
153C2×C3×D4—62no—
154C2×C3×D4—62no—
155C2×C3×D4—62no—
156C2×C3×D4—62no—
157C2×C3×D4—62no—
158C2×C3×D4—62no—
159C22×C3×C4—22no—
160C22×C3×C4—32no—
161C22×C3×C4—61no—
162C22×C3×C4#6712yescomplemented
163C22×C3×C4#6712yescomplemented
164C2×#67—22no—
165C2×#67—22no—
166C2×#67—22no—
167C2×#67—22no—
168C2×#67—22no—
169C2×#67—22no—
170C2×#67—68no—
171C2×#67—68no—
172C2×#67—128no—
173C2×#67—128no—
174C22×Dic3—21no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—122no—
178C22×Dic3#6712yescomplemented
179C2×D12—22no—
180C3×C4⋊C4—62no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—42no—
184C3×C22⋊C4—64no—
185C3×C22⋊C4—62no—
186C3×C22⋊C4—124no—
187#217—22no—
188#217—34no—
189#217—34no—
190#217—64no—
191#217—68no—
192#217—62no—
193#217—62no—
194#217—122no—
195(C2×D3)⋊C4—24no—
196(C2×D3)⋊C4—44no—
197(C2×D3)⋊C4—68no—
198C4⋊Dic3—22no—
199C22×C32—22no—
200C22×C32—24no—
201C22×C32—41no—
202C22×C32—42no—
203C22×C32—41no—
204C22×C32#12012yes—
205C22×C32#12011yescharacteristic
206C22×C32#12112yes—
207C22×C32#12111yescharacteristic
208C22×C32#12711yescharacteristic
209C2×C3×D3—28no—
210C2×C3×D3—24no—
211C2×C3×D3—44no—
212C2×C3×D3—44no—
213C2×C3×D3—42no—
214C2×C3×D3—48no—
215C2×C3×D3—42no—
216C2×C3×D3—44no—
217C2×C3×D3—44no—
218C2×C3×D3—42no—
219C2×C3×D3—44no—
220C2×C3×D3—82no—
221C32×C4—42no—
222C3⋊Dic3—44no—
223C3×Dic3—42no—
224C3×Dic3—81no—
225C25—31no—
226C22×D4—32no—
227C22×D4—182no—
228#123—62no—
229#121—62no—
230#120—62no—
231#120—184no—
232#120—184no—
233C2×C22⋊C4—31no—
234C2×C22⋊C4—62no—
235C2×C22⋊C4—92no—
236C2×C22⋊C4—182no—
237C2×C22⋊C4D3211yescharacteristic
238#99—184no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—22no—
242C23×C3—21no—
243C23×C3—22no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3—64no—
247C23×C3—68no—
248C23×C3—64no—
249C23×C3—62no—
250C23×C3—62no—
251C23×C3—62no—
252C23×C3—62no—
253C23×C3—82no—
254C23×C3—124no—
255C23×C3—122no—
256C23×C3—124no—
257C23×C3—124no—
258C23×C3—128no—
259C23×C3—124no—
260C23×C3—122no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3C2×D1211yescharacteristic
264C23×C3#23511yescharacteristic
265C23×C3D3×D411yescharacteristic
266C23×C3D3×D412yes—
267C23×C3D3×D412yes—
268C23×C3D3×D412yes—
269C23×C3#23711yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C23×C3C2×#6711yescharacteristic
272C23×C3C2×#6712yes—
273C22×D3—24no—
274C22×D3—28no—
275C22×D3—24no—
276C22×D3—22no—
277C22×D3—22no—
278C22×D3—22no—
279C22×D3—22no—
280C22×D3—44no—
281C22×D3—48no—
282C22×D3—44no—
283C22×D3—42no—
284C22×D3—44no—
285C22×D3—42no—
286C22×D3—41no—
287C22×D3—41no—
288C22×D3—44no—
289C3×D4—122no—
290C3×D4—122no—
291C3×D4—122no—
292C3×D4—122no—
293C3×D4—242no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—82no—
303C2×C3×C4—122no—
304C2×C3×C4—121no—
305#67—42no—
306#67—42no—
307#67—42no—
308#67—42no—
309#67—1216no—
310#67—1216no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—42no—
315C2×Dic3—41no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—124no—
319C2×Dic3—124no—
320C2×Dic3—124no—
321C2×Dic3—244no—
322D12—82no—
323C2×C32—21no—
324C2×C32—22no—
325C2×C32—21no—
326C2×C32—22no—
327C2×C32#39211yescharacteristic
328C2×C32B(4,𝔽2)12yes—
329C3×D3—44no—
330C3×D3—82no—
331C24—32no—
332C24—32no—
333C24—61no—
334C24—62no—
335C24—61no—
336C24—62no—
337C24—124no—
338C24C2×D3211yescharacteristic
339C2×D4—62no—
340C2×D4—62no—
341C2×D4—62no—
342C2×D4—62no—
343C2×D4—62no—
344C2×D4—62no—
345C2×D4—62no—
346C2×D4—188no—
347C2×D4—368no—
348C22×C4—32no—
349C22×C4—61no—
350C22×C4—182no—
351C22×C4#62512yescomplemented
352C4⋊C4—62no—
353C22⋊C4—22no—
354C22⋊C4—64no—
355C22⋊C4—62no—
356C22⋊C4—94no—
357C22⋊C4—124no—
358C22⋊C4—188no—
359C22⋊C4—182no—
360C22×C3—24no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—24no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—44no—
370C22×C3—42no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—42no—
374C22×C3—41no—
375C22×C3—42no—
376C22×C3—41no—
377C22×C3—68no—
378C22×C3—64no—
379C22×C3—81no—
380C22×C3—81no—
381C22×C3—82no—
382C22×C3—124no—
383C22×C3—124no—
384C22×C3—128no—
385C22×C3—122no—
386C22×C3—124no—
387C22×C3—122no—
388C22×C3—124no—
389C22×C3—122no—
390C22×C3—124no—
391C22×C3—242no—
392C22×C3#88212yes—
393C22×C3#88412yes—
394C22×C3#93011yescharacteristic
395C22×C3#93712yes—
396C22×C3#93711yescharacteristic
397C22×C3#93811yescharacteristic
398C22×C3#93912yes—
399C22×C3#94011yescharacteristic
400C22×C3#94011yescharacteristic
401C22×C3#95311yescharacteristic
402C2×D3—28no—
403C2×D3—24no—
404C2×D3—44no—
405C2×D3—44no—
406C2×D3—42no—
407C2×D3—48no—
408C2×D3—42no—
409C2×D3—44no—
410C2×D3—44no—
411C2×D3—42no—
412C2×D3—44no—
413C2×D3—82no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—82no—
417C3×C4—122no—
418C3×C4—241no—
419Dic3—42no—
420Dic3—81no—
421Dic3—124no—
422Dic3—124no—
423Dic3—244no—
424C32#202111yescharacteristic, complemented, Sylow
425C23—42no—
426C23—64no—
427C23—68no—
428C23—62no—
429C23—64no—
430C23—62no—
431C23—62no—
432C23—62no—
433C23—122no—
434C23—124no—
435C23—124no—
436C23—124no—
437C23—124no—
438C23—128no—
439C23—122no—
440C23—121no—
441C23—121no—
442C23#379511yescharacteristic
443C23D3×D1211yescharacteristic
444C23#380212yes—
445C23C2×#62511yescharacteristic
446C23D3×#6712yes—
447D4—122no—
448D4—122no—
449D4—122no—
450D4—122no—
451D4—242no—
452D4—3616no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—122no—
459C2×C4—121no—
460C2×C4—184no—
461C2×C4—364no—
462C2×C3—21no—
463C2×C3—22no—
464C2×C3—21no—
465C2×C3—22no—
466C2×C3—22no—
467C2×C3—21no—
468C2×C3—22no—
469C2×C3—21no—
470C2×C3—22no—
471C2×C3—21no—
472C2×C3—42no—
473C2×C3—41no—
474C2×C3—41no—
475C2×C3—42no—
476C2×C3—124no—
477C2×C3—242no—
478C2×C3#496011yescharacteristic
479C2×C3#503212yes—
480C2×C3#522311yescharacteristic
481C2×C3#524412yes—
482D3—44no—
483D3—82no—
484C22—22no—
485C22—24no—
486C22—41no—
487C22—41no—
488C22—42no—
489C22—68no—
490C22—64no—
491C22—124no—
492C22—124no—
493C22—122no—
494C22—128no—
495C22—124no—
496C22—124no—
497C22—122no—
498C22—124no—
499C22—122no—
500C22—242no—
501C22#6388512yes—
502C22#6390811yescharacteristic
503C22#6391411yescharacteristic
504C22#6392212yes—
505C22#6397611yescharacteristic
506C4—42no—
507C4—122no—
508C4—241no—
509C4—364no—
510C3—21no—
511C3#6950011yescharacteristic, complemented
512C3#7185111yescharacteristic, complemented
513C2—21no—
514C2—22no—
515C2—21no—
516C2—22no—
517C2—124no—
518C2—242no—
519C2#1059138911yescharacteristic
520C2#1059153012yes—
subgroupG/H
centerC22#63976
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×#63976C2semidirect
3. C3×#4955C2semidirect
4. C2×#63580C2semidirect
5. #10589392C2semidirect
25. #5493D3semidirect
28. #4955D3semidirect
39. C23×C3×D3D4semidirect
40. C23×C3×D3D4semidirect
41. C22×C32×C4D4semidirect
50. C22×C3×Dic3D4semidirect
56. #3757D4semidirect
150. C23×D3D12semidirect
151. C23×D3#67semidirect
162. C22×C3×C4#67semidirect
163. C22×C3×C4#67semidirect
178. C22×Dic3#67semidirect
351. C22×C4#625semidirect
424. C32#2021semidirect
511. C3#69500semidirect
512. 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×#639762
C3×#49552
C2×#635802
#105893922
#718513
#695003