Finite Group Databasebeta

← #11788179

Subgroups — #11788179

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic
2C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5#10589162C212yesmaximal, complemented
6#71532—31nomaximal
7#69965—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3828C2211yescharacteristic
10C23×C3×Dic3—21no—
11#64162—21no—
12#64139C412yescomplemented
13#64138—21no—
14C4×#638—22no—
15#64135C2211yescharacteristic
16#64133C412yescomplemented
17C2×C3×C4×Dic3—21no—
18C2×C3×C4×Dic3—24no—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×#208C2212yes—
21C3×#830—22no—
22#63570—24no—
23C22×C3×C42—31no—
24#5791—31no—
25#5791—31no—
26#5791—61no—
27C22×C4×Dic3D311yescharacteristic, complemented
28C3×#407—31no—
29#5207D311yescharacteristic, complemented
30C2×#825—32no—
31C2×#805—32no—
32#4555—32no—
33#4523—32no—
34C24×C32D411yescharacteristic
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4C2×C412yes—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—22no—
42C2×#638—21no—
43#3828—22no—
44#3828—22no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
46C2×C4×C3⋊D3—21no—
47C2×#634C2×C411yescharacteristic, complemented
48C22×C3×Dic3—24no—
49C22×C3×Dic3—28no—
50C22×C3×Dic3—22no—
51#3757—22no—
52#3757—21no—
53#3752—22no—
54C4⋊(C3⋊Dic3)C2×C412yescomplemented
55#3750—22no—
56C4×C3⋊Dic3—21no—
57C3×C4×Dic3—24no—
58C3×C4×Dic3—22no—
59C3×C4×Dic3D414yescomplemented
60C3×#208—22no—
61C3×#208—22no—
62C2×C3×C3⋊C8—22no—
63#1896—91noSylow
64C23×C3×C4—21no—
65C23×C3×C4—61no—
66C23×C3×C4C2×D311yescharacteristic
67C23×C3×C4C2×D311yescharacteristic
68C23×Dic3—21no—
69C2×#235—31no—
70C2×#235—31no—
71C2×#235—61no—
72C2×C3×M16—32no—
73C2×C3×C42—32no—
74C2×C3×C42—64no—
75C2×C3×C42—61no—
76#953—62no—
77#953—61no—
78#953—61no—
79#930—32no—
80#930—32no—
81#930—62no—
82#929—62no—
83#929—61no—
84#929—61no—
85C4×#67—64no—
86C4×#67—62no—
87C4×#67—62no—
88#926—31no—
89#926—31no—
90#926—61no—
91#924—32no—
92#924—32no—
93#924—62no—
94C2×C4×Dic3—21no—
95C2×C4×Dic3—24no—
96C2×C4×Dic3C2×D312yes—
97C2×#208C2×D312yes—
98C3×C22⋊C8—62no—
99#830—22no—
100#825—64no—
101#805—64no—
102C23×C32—24no—
103C23×C32—21no—
104C23×C32—21no—
105C23×C32C22⋊C412yes—
106C23×C32C2×D411yescharacteristic
107C22×C3⋊D3—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—24no—
111C2×C32×C4—24no—
112C2×C32×C4C22⋊C412yes—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D412yes—
116C2×C32×C4#4112yes—
117#638—44no—
118#638—41no—
119#638—41no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C4⋊(C3⋊D3)—22no—
123C4×C3⋊D3—42no—
124#634—22no—
125C2×C3×Dic3—216no—
126C2×C3×Dic3—28no—
127C2×C3×Dic3—24no—
128C3×C3⋊C8—42no—
129#525—91no—
130C22×C42—31no—
131C2×#104—92no—
132#407—31no—
133#339—92no—
134C24×C3—21no—
135C24×C3D1211yescharacteristic
136C24×C3#6711yescharacteristic
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—42no—
146C22×C3×C4—42no—
147C22×C3×C4—64no—
148C22×C3×C4—68no—
149C22×C3×C4—62no—
150C22×C3×C4C4×D312yes—
151C22×C3×C4C4×D312yes—
152C22×C3×C4D1211yescharacteristic
153C22×C3×C4D1212yes—
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4#6712yes—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—64no—
159C2×#67—62no—
160C2×#67—62no—
161C2×#67—62no—
162C2×#67—61no—
163C2×#67—61no—
164C22×Dic3—24no—
165C22×Dic3—28no—
166C22×Dic3—22no—
167#235—62no—
168#235—62no—
169#235—62no—
170#235—62no—
171#235—122no—
172#235—122no—
173C2×D12—31no—
174C2×D12—31no—
175C2×D12—61no—
176C2×C4×D3—62no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×Dic6—31no—
180C2×Dic6—31no—
181C2×Dic6—61no—
182C3×M16—62no—
183C3×M16—62no—
184C2×C3×C8—62no—
185C3×C42—34no—
186C3×C42—64no—
187C3×C42—62no—
188#217—64no—
189#217—62no—
190#217—62no—
191#217—62no—
192#217—61no—
193#217—61no—
194(C2×D3)⋊C4—64no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—62no—
197C4⋊Dic3—32no—
198C4⋊Dic3—32no—
199C4⋊Dic3—62no—
200Dic3⋊C4—64no—
201Dic3⋊C4—62no—
202Dic3⋊C4—62no—
203C4×Dic3—24no—
204C4×Dic3—22no—
205C4×Dic3—62no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3#6714yescomplemented
209#208—22no—
210#208—22no—
211C2×C3⋊C8—22no—
212C22×C32—24no—
213C22×C32—24no—
214C22×C32—22no—
215C22×C32—22no—
216C22×C32—22no—
217C22×C32#10414yescomplemented
218C22×C32C2×C22⋊C411yescharacteristic
219C22×C32#12011yescharacteristic
220C22×C32#12311yescharacteristic
221C2×C3⋊D3—41no—
222C2×C3⋊D3—42no—
223C32×C4—22no—
224C32×C4C4×D412yes—
225C32×C4#12112yes—
226C3⋊Dic3—41no—
227C3⋊Dic3—42no—
228C3×Dic3—28no—
229C2×#41—91no—
230C23×C4—61no—
231C23×C4D3211yescharacteristic
232C2×M16—32no—
233#123—181no—
234C22⋊Q8—92no—
235#121—92no—
236#120—181no—
237C4×D4—182no—
238#117—91no—
239C2×C42—32no—
240C2×C42—64no—
241C2×C42—61no—
242#104—184no—
243C22⋊C8—62no—
244C23×C3—24no—
245C23×C3—24no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—41no—
253C23×C3—41no—
254C23×C3—44no—
255C23×C3(C2×D3)⋊C412yes—
256C23×C3(C2×D3)⋊C412yes—
257C23×C3C2×D1211yescharacteristic
258C23×C3C2×#6711yescharacteristic
259C22×D3—62no—
260C22×D3—61no—
261C22×D3—61no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—44no—
276C2×C3×C4—44no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—616no—
280C2×C3×C4—68no—
281C2×C3×C4—64no—
282C2×C3×C4(C2×D3)⋊C412yes—
283C2×C3×C4(C2×D3)⋊C412yes—
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×D1211yescharacteristic
287C2×C3×C4#23512yes—
288C2×C3×C4D3×D412yes—
289C2×C3×C4#23712yes—
290C2×C3×C4C2×#6711yescharacteristic
291C2×C3×C4C2×#6712yes—
292#67—122no—
293#67—122no—
294#67—128no—
295#67—124no—
296#67—124no—
297#67—121no—
298#67—121no—
299#67—121no—
300#67—121no—
301C2×Dic3—216no—
302C2×Dic3—28no—
303C2×Dic3—24no—
304C2×Dic3—64no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310D12—62no—
311D12—62no—
312D12—122no—
313C4×D3—124no—
314C4×D3—122no—
315C4×D3—122no—
316Dic6—62no—
317Dic6—62no—
318Dic6—122no—
319C3×C8—122no—
320C3⋊C8—42no—
321C2×C32—21no—
322C2×C32—24no—
323C2×C32—21no—
324C2×C32#38611yescharacteristic
325C2×C32C2×#10412yes—
326C3⋊D3—81no—
327C24#62611yescharacteristic
328#41—182no—
329#41—182no—
330C2×Q8—91no—
331C2×D4—91no—
332C2×D4—182no—
333C2×D4—181no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—64no—
337C22×C4—68no—
338C22×C4—62no—
339C22×C4—181no—
340C22×C4#62412yes—
341C22×C4#62611yescharacteristic
342C22×C4#62612yes—
343C22×C4C2×D3211yescharacteristic
344M16—62no—
345M16—62no—
346C2×C8—62no—
347C4⋊C4—92no—
348C4⋊C4—182no—
349C22⋊C4—182no—
350C22⋊C4—181no—
351C22⋊C4—182no—
352C42—34no—
353C42—64no—
354C42—62no—
355C42—181no—
356C22×C3—24no—
357C22×C3—24no—
358C22×C3—24no—
359C22×C3—24no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—24no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—44no—
374C22×C3—44no—
375C22×C3#80514yescomplemented
376C22×C3#82514yescomplemented
377C22×C3#88211yescharacteristic
378C22×C3#88611yescharacteristic
379C22×C3C2×(C2×D3)⋊C411yescharacteristic
380C22×C3C2×(C2×D3)⋊C411yescharacteristic
381C22×C3#92911yescharacteristic
382C22×C3#95311yescharacteristic
383C2×D3—122no—
384C2×D3—124no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—121no—
388C2×D3—121no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—42no—
394C3×C4—68no—
395C3×C4#67⋊C412yes—
396C3×C4C4×#6712yes—
397C3×C4#93012yes—
398C3×C4#93912yes—
399Dic3—28no—
400Dic3—122no—
401Dic3—124no—
402Dic3—122no—
403Dic3—122no—
404Dic3—121no—
405Dic3—121no—
406C32#189611yescharacteristic, complemented, Sylow
407C23—24no—
408C23—21no—
409C23—21no—
410C23—181no—
411C23#372212yes—
412C23C2×#62611yescharacteristic
413Q8—182no—
414D4—182no—
415D4—364no—
416D4—361no—
417D4—361no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—616no—
423C2×C4—68no—
424C2×C4—64no—
425C2×C4—182no—
426C2×C4—181no—
427C2×C4—362no—
428C2×C4#372212yes—
429C2×C4#380412yes—
430C2×C4C2×#62411yescharacteristic
431C2×C4C2×#62611yescharacteristic
432C2×C4D3×#6712yes—
433C8—122no—
434C2×C3—21no—
435C2×C3—24no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—24no—
439C2×C3—21no—
440C2×C3—22no—
441C2×C3—21no—
442C2×C3—41no—
443C2×C3—44no—
444C2×C3—41no—
445C2×C3C2×#80512yes—
446C2×C3#495811yescharacteristic
447C2×C3C2×#82512yes—
448C2×C3#521311yescharacteristic
449D3—242no—
450D3—241no—
451D3—241no—
452C22—24no—
453C22—24no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—362no—
458C22—361no—
459C22#6357014yescomplemented
460C22C2×#372211yescharacteristic
461C22#6396611yescharacteristic
462C22#6397711yescharacteristic
463C4—22no—
464C4—68no—
465C4—362no—
466C4—361no—
467C4#6395212yes—
468C4#6397812yes—
469C3—21no—
470C3#6996511yescharacteristic, complemented
471C3#7153211yescharacteristic, complemented
472C2—21no—
473C2—24no—
474C2—21no—
475C2—721no—
476C2C2×#6357012yes—
477C2#1059171111yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×Dic3C2semidirect
3. C3×#5207C2semidirect
4. C2×#63570C2semidirect
5. #10589162C2semidirect
12. #64139C4semidirect
16. #64133C4semidirect
27. C22×C4×Dic3D3semidirect
29. #5207D3semidirect
45. C2×C4⋊(C3⋊D3)C2×C4semidirect
47. C2×#634C2×C4semidirect
54. C4⋊(C3⋊Dic3)C2×C4semidirect
59. C3×C4×Dic3D4semidirect
208. C4×Dic3#67semidirect
217. C22×C32#104semidirect
375. C22×C3#805semidirect
376. C22×C3#825semidirect
406. C32#1896semidirect
459. C22#63570semidirect
470. C3#69965semidirect
471. C3#71532semidirect

Maximal subgroups

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

subgroupindex
#105962622
C22×C3×C4×Dic32
C3×#52072
C2×#635702
#105891622
#715323
#699653