Finite Group Databasebeta

← #11787975

Subgroups — #11787975

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic
3C2×#63661C211yesmaximal, characteristic
4#10591696C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6#71704—31nomaximal
7#71655—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C2211yescharacteristic
10C2×#3757C2212yes—
11C2×C3×#217—21no—
12C2×C3×#217—21no—
13C2×C3×#217C2212yes—
14C2×C3×#217C2211yescharacteristic
15C3×#935—22no—
16C3×#935C414yescomplemented
17C3×D4×Dic3—24no—
18C3×#926—21no—
19C2×C3×Dic3⋊C4—21no—
20#63661—22no—
21#63579—24no—
22C2×C3×#123—31no—
23C3×#518—31no—
24#5798D311yescharacteristic
25C2×#935D311yescharacteristic
26C2×#834—31no—
27C2×#834—31no—
28C2×#834—61no—
29#5211—32no—
30#4943—32no—
31#4527—32no—
32#4526—32no—
33C24×C32D411yescharacteristic
34C24×C32C2311yescharacteristic
35C2×C32×D4—22no—
36C2×C32×D4—22no—
37C2×C32×D4C2×C412yes—
38C2×C32×D4D412yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3—22no—
41C22×C3×Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3C2×C412yescomplemented
48C22×C3×Dic3D414yes—
49#3757—22no—
50#3757—22no—
51C3×#217—22no—
52C3×#217—24no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217—21no—
56C3×#217C2×C412yescomplemented
57C3×C4⋊Dic3—22no—
58C3×Dic3⋊C4—24no—
59C3×C4×Dic3—22no—
60#1890—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C2×D311yescharacteristic
64C23×C3×C4—31no—
65C23×Dic3C2×D311yescharacteristic
66C3×#123—34no—
67C3×#123—62no—
68C3×C4×D4—64no—
69C3×#117—61no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C22⋊C4—31no—
72C2×C3×C22⋊C4—32no—
73C2×C3×C22⋊C4—61no—
74C2×C3×C22⋊C4—61no—
75C2×#217—21no—
76C2×#217—21no—
77C2×#217—32no—
78C2×#217—32no—
79C2×#217—62no—
80C2×#217C2×D312yes—
81C2×#217C2×D311yescharacteristic
82#935—22no—
83#935Dic314yescomplemented
84D4×Dic3—24no—
85#926—21no—
86C2×Dic3⋊C4—21no—
87#834—64no—
88#834—62no—
89#834—62no—
90C3⋊#95—64no—
91C3⋊#95—64no—
92C23×C32—21no—
93C23×C32—21no—
94C23×C32—42no—
95C23×C32—42no—
96C23×C32C22⋊C412yes—
97C23×C32C22×C411yescharacteristic
98C23×C32C2×D411yescharacteristic
99C23×C32C2×D412yes—
100C23×C32C2×D411yescharacteristic
101C23×C32#4112yes—
102C32×D4—24no—
103C32×D4—24no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4C22⋊C412yes—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—44no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—44no—
118C2×C3×Dic3—82no—
119C2×#123—31no—
120#518—31no—
121C2×#99—91no—
122#381—92no—
123#342—92no—
124C24×C3—21no—
125C24×C3—21no—
126C24×C3#6711yescharacteristic
127C24×C3#6711yescharacteristic
128C24×C3C22×D311yescharacteristic
129C24×C3C22×D311yescharacteristic
130C2×C3×D4—22no—
131C2×C3×D4—22no—
132C2×C3×D4—22no—
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—42no—
137C2×C3×D4—42no—
138C2×C3×D4C4×D312yes—
139C2×C3×D4D1212yes—
140C2×C3×D4C2×Dic312yes—
141C2×C3×D4#6712yes—
142C22×C3×C4—21no—
143C22×C3×C4—32no—
144C22×C3×C4—34no—
145C22×C3×C4—61no—
146C22×C3×C4—62no—
147C22×C3×C4—62no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—62no—
151C22×C3×C4#6711yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×Dic3—22no—
154C22×Dic3—22no—
155C22×Dic3—21no—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—22no—
159C22×Dic3—62no—
160C22×Dic3—62no—
161C22×Dic3—122no—
162C22×Dic3C2×Dic312yescomplemented
163C22×Dic3#6714yes—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—64no—
166C3×C22⋊C4—32no—
167C3×C22⋊C4—62no—
168C3×C22⋊C4—64no—
169C3×C22⋊C4—61no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—62no—
172C3×C42—62no—
173#217—22no—
174#217—24no—
175#217—22no—
176#217—22no—
177#217—21no—
178#217—64no—
179#217—62no—
180#217—62no—
181#217—62no—
182#217—62no—
183#217—122no—
184#217C2×Dic312yescomplemented
185C4⋊Dic3—22no—
186Dic3⋊C4—24no—
187C4×Dic3—22no—
188C22×C32—24no—
189C22×C32—22no—
190C22×C32—22no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32—42no—
196C22×C32—81no—
197C22×C32C2×C22⋊C411yescharacteristic
198C22×C32C4×D412yes—
199C22×C32#12011yescharacteristic
200C22×C32#12112yes—
201C22×C32#12311yescharacteristic
202C32×C4—22no—
203C3⋊Dic3—82no—
204C3×Dic3—42no—
205C3×Dic3—42no—
206C3×Dic3—44no—
207C22×D4D3211yescharacteristic
208C23×C4—31no—
209#123—34no—
210#123—62no—
211C4×D4—64no—
212#117—61no—
213C2×C4⋊C4—61no—
214C2×C22⋊C4—31no—
215C2×C22⋊C4—32no—
216C2×C22⋊C4—61no—
217C2×C22⋊C4—61no—
218C2×C22⋊C4—92no—
219#99—182no—
220#95—184no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—22no—
226C23×C3—21no—
227C23×C3—22no—
228C23×C3—21no—
229C23×C3—21no—
230C23×C3—22no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—82no—
238C23×C3—82no—
239C23×C3(C2×D3)⋊C412yes—
240C23×C3#21712yes—
241C23×C3C2×C4×D311yescharacteristic
242C23×C3C2×D1211yescharacteristic
243C23×C3#23512yes—
244C23×C3D3×D412yes—
245C23×C3#23712yes—
246C23×C3C22×Dic311yescharacteristic
247C23×C3C2×#6711yescharacteristic
248C23×C3C2×#6711yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C23×C3C2×#6712yes—
251C3×D4—24no—
252C3×D4—24no—
253C3×D4—24no—
254C3×D4—24no—
255C3×D4—44no—
256C3×D4—44no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—22no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—64no—
267C2×C3×C4—64no—
268C2×C3×C4—122no—
269C2×C3×C4—121no—
270C2×C3×C4—122no—
271C2×C3×C4—121no—
272C2×C3×C4—124no—
273C2×C3×C4—242no—
274C2×C3×C4(C2×D3)⋊C412yes—
275C2×C3×C4#21712yes—
276C2×Dic3—24no—
277C2×Dic3—22no—
278C2×Dic3—22no—
279C2×Dic3—24no—
280C2×Dic3—42no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—42no—
284C2×Dic3—44no—
285C2×Dic3—82no—
286C2×Dic3—124no—
287C2×Dic3—124no—
288C2×Dic3—124no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3—244no—
292C2×C32—21no—
293C2×C32—22no—
294C2×C32—21no—
295C2×C32—22no—
296C2×C32—42no—
297C2×C32#38611yescharacteristic
298C2×C32#45812yes—
299C24#62511yescharacteristic
300C24C2×D3211yescharacteristic
301C2×D4—22no—
302C2×D4—22no—
303C2×D4D3×Dic312yes—
304C2×D4#62612yes—
305C22×C4—32no—
306C22×C4—34no—
307C22×C4—62no—
308C22×C4—61no—
309C22×C4—61no—
310C22×C4—61no—
311C22×C4—62no—
312C22×C4—62no—
313C22×C4—182no—
314C22×C4#62511yescharacteristic
315C4⋊C4—62no—
316C4⋊C4—64no—
317C22⋊C4—32no—
318C22⋊C4—62no—
319C22⋊C4—64no—
320C22⋊C4—62no—
321C22⋊C4—61no—
322C22⋊C4—62no—
323C22⋊C4—182no—
324C22⋊C4—182no—
325C42—62no—
326C22×C3—24no—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—24no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—22no—
337C22×C3—44no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—82no—
351C22×C3—81no—
352C22×C3—82no—
353C22×C3—81no—
354C22×C3—82no—
355C22×C3—81no—
356C22×C3—81no—
357C22×C3—82no—
358C22×C3C2×(C2×D3)⋊C411yescharacteristic
359C22×C3C4×#6712yes—
360C22×C3#92911yescharacteristic
361C22×C3#93012yes—
362C22×C3D4×Dic312yes—
363C22×C3#93511yescharacteristic
364C22×C3#93711yescharacteristic
365C22×C3#93912yes—
366C22×C3C2×#21711yescharacteristic
367C22×C3#95311yescharacteristic
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—42no—
371C3×C4—122no—
372C3×C4—122no—
373C3×C4—124no—
374Dic3—42no—
375Dic3—42no—
376Dic3—44no—
377Dic3—242no—
378Dic3—242no—
379Dic3—244no—
380C32#189011yescharacteristic, complemented, Sylow
381C23—21no—
382C23—21no—
383C23—42no—
384C23—42no—
385C23(C2×D3)⋊Dic312yes—
386C23C2×D3×Dic311yescharacteristic
387C23#380412yes—
388C23C2×#62511yescharacteristic
389C23C2×#62611yescharacteristic
390C23D3×#6712yes—
391D4—24no—
392D4—24no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—62no—
396C2×C4—62no—
397C2×C4—64no—
398C2×C4—64no—
399C2×C4—122no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—122no—
403C2×C4—124no—
404C2×C4—242no—
405C2×C4—364no—
406C2×C4—362no—
407C2×C4(C2×D3)⋊Dic312yes—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—21no—
411C2×C3—22no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—42no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—42no—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3—82no—
425C2×C3#505312yes—
426C2×C3#521311yescharacteristic
427C2×C3#522011yescharacteristic
428C2×C3#524312yes—
429C22—24no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—42no—
434C22—41no—
435C22—42no—
436C22—42no—
437C22—81no—
438C22C2×(C2×D3)⋊Dic311yescharacteristic
439C22#6396111yescharacteristic
440C22Dic3×#6712yes—
441C22#6397611yescharacteristic
442C22#6397812yes—
443C4—22no—
444C4—122no—
445C4—124no—
446C4—122no—
447C4—722no—
448C3—21no—
449C3#7165511yescharacteristic, complemented
450C3#7170411yescharacteristic, complemented
451C2—21no—
452C2—22no—
453C2—21no—
454C2—22no—
455C2—42no—
456C2#1059153312yes—
457C2#1059171011yescharacteristic
subgroupG/H
centerC22#63976
commutatorC23×C32C22×C4
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591696C2semidirect
5. #10589186C2semidirect
16. C3×#935C4semidirect
47. C22×C3×Dic3C2×C4semidirect
56. C3×#217C2×C4semidirect
83. #935Dic3semidirect
162. C22×Dic3C2×Dic3semidirect
184. #217C2×Dic3semidirect
380. C32#1890semidirect
449. C3#71655semidirect
450. C3#71704semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C2×C3×#9352
C2×#636612
#105916962
#105891862
#717043
#716553