Finite Group Databasebeta

← #11787259

Subgroups — #11787259

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 425 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63567C212yesmaximal, complemented
4C2×#63557C211yesmaximal, characteristic
5C3×#4529C212yesmaximal, complemented
6#68878—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#634C2211yescharacteristic
9C22×#624—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3752—21no—
12C2×C4⋊(C3⋊Dic3)—21no—
13#64106—22no—
14#64106C414yescomplemented
15C2×C3×C4⋊Dic3C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C2×#3724—21no—
18#63900—24no—
19#63567—24no—
20#63557—22no—
21C2×#897—32no—
22C2×#897—61no—
23C2×D3×C4⋊C4—32no—
24C2×(C2×D3)⋊C8—32no—
25C2×#816—32no—
26C2×#810—32no—
27C3×#340—32no—
28#4529D312yescomplemented
29C23×C3⋊D3D411yescharacteristic
30C22×C32×C4—21no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—22no—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3D412yes—
38C2×#634—22no—
39C2×#634—22no—
40C2×#634—21no—
41C2×#634C2×C412yescomplemented
42C22×C3×Dic3—22no—
43C2×#624—24no—
44C2×#624—42no—
45C2×#624—42no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C412yescomplemented
48#3752—24no—
49C4⋊(C3⋊Dic3)—24no—
50C3×C4⋊Dic3—22no—
51C3×C4⋊Dic3D414yes—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—22no—
55#3724—24no—
56#1872—91noSylow
57C22×C4×D3—32no—
58C22×C4×D3—61no—
59C22×C4×D3—62no—
60C22×Dic6—32no—
61C22×Dic6—61no—
62C22×C3×C8—32no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C4⋊C4C2×D312yes—
66C2×(C2×D3)⋊C4—62no—
67C2×(C2×D3)⋊C4—62no—
68C2×C4⋊Dic3—62no—
69C2×C4⋊Dic3—62no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—62no—
72C22×C3⋊C8C2×D312yes—
73#897—38no—
74#897—64no—
75#897—64no—
76#897—64no—
77D3×C4⋊C4—64no—
78D3×C4⋊C4—64no—
79(C2×D3)⋊C8—64no—
80#816—64no—
81#810—64no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—21no—
84C22×C3⋊D3—21no—
85C22×C3⋊D3—21no—
86C22×C3⋊D3—21no—
87C22×C3⋊D3C22⋊C412yes—
88C22×C3⋊D3SD1612yes—
89C22×C3⋊D3Q1612yes—
90C2×C32×C4—22no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4112yes—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3C22⋊C412yes—
103C4×C3⋊D3—24no—
104C4×C3⋊D3—24no—
105#634—24no—
106#634—42no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110#624—48no—
111C3×C3⋊C8—42no—
112C2×C22⋊Q8—91no—
113C22×C4⋊C4—91no—
114C2×#103—92no—
115C2×C22⋊C8—91no—
116#340—32no—
117C23×D3—32no—
118C23×D3—61no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4—62no—
123C22×C3×C4C22×D312yes—
124C22×Dic3—22no—
125C22×Dic3—32no—
126C22×Dic3—61no—
127C22×Dic3—62no—
128C22×Dic3—62no—
129C2×C4×D3—34no—
130C2×C4×D3—34no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—68no—
138C2×C4×D3—122no—
139C2×C4×D3—122no—
140C2×C4×D3—124no—
141C2×C4×D3—124no—
142C2×Dic6—34no—
143C2×Dic6—62no—
144C2×Dic6—62no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—62no—
148C2×Dic6—62no—
149C2×Dic6—62no—
150C2×Dic6—122no—
151C2×Dic6—122no—
152C2×C3×C8—62no—
153C2×C3×C8—62no—
154C2×C3×C8—62no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—34no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4C4×D314yescomplemented
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163C4⋊Dic3—22no—
164C4⋊Dic3—68no—
165C4⋊Dic3—68no—
166C4⋊Dic3D1214yes—
167Dic3⋊C4—68no—
168C2×C3⋊C8—22no—
169C2×C3⋊C8—22no—
170C2×C3⋊C8—22no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32#12011yescharacteristic
173C22×C32#12311yescharacteristic
174C22×C32C2×SD1611yescharacteristic
175C22×C32C2×Q1611yescharacteristic
176C22×C32AGL(1,ℤ/8)11yescharacteristic
177C22×C32#13711yescharacteristic
178C2×C3⋊D3—22no—
179C2×C3⋊D3—22no—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—22no—
182C2×C3⋊D3—22no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3#10314yescomplemented
185C32×C4—42no—
186C32×C4C4×D412yes—
187C32×C4#12112yes—
188C3⋊Dic3—22no—
189C3⋊Dic3—42no—
190C3×Dic3—44no—
191C22×Q8—91no—
192C23×C4—91no—
193C23×C4—181no—
194C22×C8—32no—
195C22⋊Q8—94no—
196C22⋊Q8—182no—
197C2×C4⋊C4—32no—
198C2×C4⋊C4—184no—
199C2×C4⋊C4—181no—
200C2×C4⋊C4—181no—
201C2×C4⋊C4D3211yescharacteristic
202C2×C22⋊C4—181no—
203#103—184no—
204C22⋊C8—182no—
205C23×C3—21no—
206C23×C3D3×D412yes—
207C22×D3—34no—
208C22×D3—34no—
209C22×D3—34no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—62no—
213C22×D3—62no—
214C22×D3—62no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—121no—
218C22×D3—121no—
219C22×D3—121no—
220C22×D3—121no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—42no—
231C2×C3×C4—64no—
232C2×C3×C4—122no—
233C2×C3×C4—122no—
234C2×C3×C4C2×C4×D312yes—
235C2×C3×C4C2×D1212yes—
236C2×C3×C4#23512yes—
237C2×C3×C4D3×D412yes—
238C2×C3×C4D3×D412yes—
239C2×C3×C4#23912yes—
240C2×Dic3—24no—
241C2×Dic3—34no—
242C2×Dic3—42no—
243C2×Dic3—42no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249C2×Dic3—121no—
250C2×Dic3—121no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C4×D3—64no—
256C4×D3—64no—
257C4×D3—64no—
258C4×D3—64no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—1216no—
262Dic6—64no—
263Dic6—64no—
264Dic6—124no—
265Dic6—124no—
266Dic6—122no—
267Dic6—122no—
268C3×C8—122no—
269C3⋊C8—42no—
270C2×C32#38611yescharacteristic
271C2×C32C2×#10311yescharacteristic
272C2×C32#41711yescharacteristic
273C2×C32#45011yescharacteristic
274C2×C32#45111yescharacteristic
275C2×C32#48311yescharacteristic
276C2×C32#48411yescharacteristic
277C3⋊D3—24no—
278C24—91no—
279C2×Q8—92no—
280C2×Q8—181no—
281C2×Q8—182no—
282C2×Q8—182no—
283C22×C4—21no—
284C22×C4—62no—
285C22×C4—91no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—184no—
289C22×C4—182no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4—362no—
293C22×C4—362no—
294C22×C4C2×D3211yescharacteristic
295C2×C8—62no—
296C2×C8—62no—
297C2×C8—62no—
298C4⋊C4—21no—
299C4⋊C4—34no—
300C4⋊C4—62no—
301C4⋊C4—184no—
302C4⋊C4—184no—
303C4⋊C4#62412yescomplemented
304C22⋊C4—184no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3D3×C22⋊C412yes—
313C22×C3#88212yes—
314C22×C3#89412yes—
315C22×C3#91112yes—
316C22×C3D3×SD1612yes—
317C22×C3#91512yes—
318C22×C3D3×Q1612yes—
319C2×D3—38no—
320C2×D3—64no—
321C2×D3—64no—
322C2×D3—64no—
323C2×D3—64no—
324C2×D3—64no—
325C2×D3—64no—
326C2×D3—64no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—122no—
331C2×D3—122no—
332C2×D3—122no—
333C3×C4—22no—
334C3×C4—22no—
335C3×C4—44no—
336C3×C4—44no—
337C3×C4—124no—
338C3×C4C4×D1212yes—
339C3×C4#88412yes—
340C3×C4#89312yes—
341C3×C4#89512yes—
342Dic3—44no—
343Dic3—64no—
344Dic3—122no—
345Dic3—124no—
346Dic3—124no—
347C32#187211yescharacteristic, complemented, Sylow
348C23—92no—
349C23—92no—
350C23—92no—
351C23—181no—
352C23—181no—
353C23—181no—
354C23—181no—
355C23#381111yescharacteristic
356Q8—184no—
357Q8—362no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—64no—
362C2×C4—92no—
363C2×C4—122no—
364C2×C4—122no—
365C2×C4—181no—
366C2×C4—181no—
367C2×C4—184no—
368C2×C4—184no—
369C2×C4—182no—
370C2×C4—368no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4#379912yes—
374C2×C4D3×D1212yes—
375C2×C4C2×#62411yescharacteristic
376C2×C4#381111yescharacteristic
377C8—122no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3#466512yes—
386C2×C3#477112yes—
387C2×C3#477612yes—
388C2×C3D3×#10312yes—
389C2×C3#480912yes—
390C2×C3#486212yes—
391C2×C3#488412yes—
392D3—68no—
393D3—124no—
394C22—94no—
395C22—182no—
396C22—182no—
397C22—182no—
398C22—182no—
399C22—182no—
400C22—182no—
401C22#6389711yescharacteristic
402C22#6392311yescharacteristic
403C22#6392711yescharacteristic
404C22#6393111yescharacteristic
405C22#6394011yescharacteristic
406C22#6394411yescharacteristic
407C22#6397411yescharacteristic
408C4—42no—
409C4—124no—
410C4—182no—
411C4—362no—
412C4#6389412yes—
413C4#6391012yes—
414C3—21no—
415C3#6887812yescomplemented
416C2—184no—
417C2#1059044311yescharacteristic
418C2#1059044411yescharacteristic
419C2#1059059711yescharacteristic
420C2#1059060511yescharacteristic
421C2#1059138011yescharacteristic
422C2#1059141811yescharacteristic
423C2#1059155211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1872
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63567C2semidirect
5. C3×#4529C2semidirect
14. #64106C4semidirect
28. #4529D3semidirect
41. C2×#634C2×C4semidirect
47. C32×C4⋊C4C2×C4semidirect
160. C3×C4⋊C4C4×D3semidirect
184. C2×C3⋊D3#103semidirect
303. C4⋊C4#624semidirect
347. C32#1872semidirect
415. C3#68878semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#639002
C2×#635672
C2×#635572
C3×#45292
#688783