Finite Group Databasebeta

← #11783942

Subgroups — #11783942

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2#10591274C211yesmaximal, characteristic, complemented
3C2×#63564C212yesmaximal
4C2×#63553C211yesmaximal, characteristic, complemented
5C3×#4529C212yesmaximal, complemented
6#68780—32nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C22×C4×C3⋊D3—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64102—22no—
13#64102C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17#63579—21no—
18#63564C418yescomplemented
19#63553—22no—
20C2×#893—32no—
21C2×#893—61no—
22C2×#821—32no—
23C2×C8×Dic3—32no—
24Dic3×C4⋊C4—32no—
25C2×#809—32no—
26C3×#340—32no—
27#4529D312yescomplemented
28C23×C3⋊D3—21no—
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C4⋊(C3⋊D3)—21no—
34C2×C4⋊(C3⋊D3)—22no—
35C2×C4⋊(C3⋊D3)C2×C414yes—
36C2×C4⋊(C3⋊D3)C2×C412yes—
37C2×C4×C3⋊D3—24no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3—42no—
40C22×C3×Dic3—22no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4C2×C412yes—
43#3752—24no—
44C4×C3⋊Dic3C2×C412yes—
45C4×C3⋊Dic3D412yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3C2×C414yescomplemented
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8C2×C414yescomplemented
51Dic32—42no—
52C4×#102—91noSylow
53C22×D12—32no—
54C22×D12—61no—
55C22×C4×D3—62no—
56C22×C4×D3—62no—
57C22×C3×C8—32no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C4⋊C4C2×D312yes—
61C2×(C2×D3)⋊C4—62no—
62C2×(C2×D3)⋊C4—62no—
63C2×C4⋊Dic3C2×D312yes—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—62no—
67C22×C3⋊C8C2×D312yes—
68#893—38no—
69#893—64no—
70#893—64no—
71#893—64no—
72C3⋊#95—62no—
73#821—38no—
74C8×Dic3—64no—
75#809—38no—
76C23×C32C2×D411yescharacteristic
77C22×C3⋊D3—22no—
78C22×C3⋊D3—24no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3—42no—
82C2×C32×C4—22no—
83C2×C32×C4—41no—
84C2×C32×C4—41no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C22×C412yes—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4#4112yes—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C22⋊C412yes—
91C2×C3⋊Dic3C22⋊C412yes—
92C2×C3⋊Dic3D812yes—
93C2×C3⋊Dic3SD1612yes—
94C4⋊(C3⋊D3)—22no—
95C4⋊(C3⋊D3)—24no—
96C4⋊(C3⋊D3)C4214yescomplemented
97C4×C3⋊D3—48no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C3×C3⋊C8—24no—
102C2×C4×D4—91no—
103C2×#102—92no—
104C2×C4×C8—91no—
105C4×C4⋊C4—91no—
106#340—32no—
107C23×D3—62no—
108C23×D3—62no—
109C22×C3×C4—22no—
110C22×C3×C4—22no—
111C22×C3×C4—21no—
112C22×C3×C4—62no—
113C22×C3×C4C22×D312yes—
114C22×Dic3—22no—
115C22×Dic3—32no—
116C22×Dic3—32no—
117C22×Dic3—61no—
118C22×Dic3—61no—
119C2×D12—34no—
120C2×D12—34no—
121C2×D12—34no—
122C2×D12—62no—
123C2×D12—64no—
124C2×D12—62no—
125C2×D12—64no—
126C2×D12—62no—
127C2×D12—62no—
128C2×D12—62no—
129C2×C4×D3—68no—
130C2×C4×D3—68no—
131C2×C4×D3—124no—
132C2×C4×D3—124no—
133C2×C4×D3—124no—
134C2×C4×D3—124no—
135C2×C3×C8—34no—
136C2×C3×C8—62no—
137C2×C3×C8—62no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—22no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—34no—
142C3×C4⋊C4—62no—
143C3×C4⋊C4C4×D314yes—
144(C2×D3)⋊C4—68no—
145(C2×D3)⋊C4—68no—
146C4⋊Dic3—22no—
147C4⋊Dic3C4×D314yescomplemented
148C4×Dic3—34no—
149C4×Dic3—34no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—124no—
153C2×C3⋊C8—22no—
154C2×C3⋊C8—22no—
155C2×C3⋊C8C4×D314yescomplemented
156C22×C32C2×C22⋊C411yescharacteristic
157C22×C32C4×D412yes—
158C22×C32C2×D811yescharacteristic
159C22×C32C2×SD1611yescharacteristic
160C22×C32#13512yes—
161C2×C3⋊D3—24no—
162C2×C3⋊D3—42no—
163C2×C3⋊D3—42no—
164C2×C3⋊D3—44no—
165C2×C3⋊D3—44no—
166C32×C4—42no—
167C32×C4C2×C4211yescharacteristic
168C32×C4#11711yescharacteristic
169C32×C4C4×D412yes—
170C3⋊Dic3—22no—
171C3⋊Dic3#10214yescomplemented
172C3×Dic3—44no—
173C22×D4—91no—
174C23×C4—181no—
175C22×C8—32no—
176C4×D4—94no—
177C4×D4—182no—
178C2×C4⋊C4—32no—
179C2×C4⋊C4D3211yescharacteristic
180C2×C22⋊C4—181no—
181C2×C42—91no—
182C2×C42—181no—
183#102—98no—
184C4×C8—182no—
185#95—181no—
186C23×C3—21no—
187C23×C3D3×D412yes—
188C22×D3—64no—
189C22×D3—68no—
190C22×D3—64no—
191C22×D3—64no—
192C22×D3—64no—
193C22×D3—122no—
194C22×D3—122no—
195C22×D3—124no—
196C22×D3—122no—
197C22×D3—122no—
198C22×D3—122no—
199C22×D3—122no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—42no—
210C2×C3×C4—64no—
211C2×C3×C4—122no—
212C2×C3×C4—122no—
213C2×C3×C4C2×C4×D312yes—
214C2×C3×C4C2×C4×D312yes—
215C2×C3×C4C2×C4×D312yes—
216C2×C3×C4D3×D412yes—
217C2×C3×C4#23712yes—
218C2×C3×C4#23912yes—
219C2×Dic3—24no—
220C2×Dic3—34no—
221C2×Dic3—34no—
222C2×Dic3—34no—
223C2×Dic3—34no—
224C2×Dic3—42no—
225C2×Dic3—42no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—122no—
233D12—38no—
234D12—64no—
235D12—64no—
236D12—68no—
237D12—64no—
238D12—64no—
239D12—64no—
240C4×D3—1216no—
241C4×D3—1216no—
242C3×C8—64no—
243C3⋊C8—24no—
244C2×C32C4×C22⋊C411yescharacteristic
245C2×C32C2×#10211yescharacteristic
246C2×C32#41611yescharacteristic
247C2×C32C4×D812yes—
248C2×C32C4×SD1612yes—
249C3⋊D3—44no—
250C24—181no—
251C2×D4—94no—
252C2×D4—92no—
253C2×D4—182no—
254C2×D4—181no—
255C22×C4—21no—
256C22×C4—62no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—184no—
260C22×C4—362no—
261C22×C4—362no—
262C22×C4C2×D3211yescharacteristic
263C2×C8—34no—
264C2×C8—62no—
265C2×C8—62no—
266C4⋊C4—21no—
267C4⋊C4—34no—
268C4⋊C4—62no—
269C4⋊C4#62412yes—
270C22⋊C4—184no—
271C42—92no—
272C42—92no—
273C42—362no—
274C22×C3—22no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3D3×C22⋊C412yes—
280C22×C3#67⋊C412yes—
281C22×C3#89312yes—
282C22×C3D3×D812yes—
283C22×C3D3×SD1612yes—
284C22×C3#91612yes—
285C22×C3#91912yes—
286C2×D3—68no—
287C2×D3—68no—
288C2×D3—124no—
289C2×D3—128no—
290C2×D3—124no—
291C2×D3—128no—
292C2×D3—124no—
293C2×D3—124no—
294C2×D3—124no—
295C2×D3—124no—
296C2×D3—124no—
297C2×D3—124no—
298C3×C4—21no—
299C3×C4—22no—
300C3×C4—21no—
301C3×C4—44no—
302C3×C4—44no—
303C3×C4—124no—
304C3×C4C42×D312yes—
305C3×C4#67⋊C412yes—
306C3×C4#89212yes—
307C3×C4#89312yes—
308Dic3—38no—
309Dic3—44no—
310Dic3—64no—
311Dic3—64no—
312Dic3—122no—
313C32C4×#10211yescharacteristic, complemented, Sylow
314C23—184no—
315C23—182no—
316C23—361no—
317C23—361no—
318C23—362no—
319C23#381111yescharacteristic
320D4—94no—
321D4—182no—
322D4—184no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—64no—
327C2×C4—92no—
328C2×C4—92no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—122no—
332C2×C4—122no—
333C2×C4—182no—
334C2×C4—368no—
335C2×C4#379612yes—
336C2×C4C4×D3212yes—
337C2×C4C2×#62411yescharacteristic
338C2×C4#381111yescharacteristic
339C8—64no—
340C2×C3—22no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—22no—
345C2×C3#466612yes—
346C2×C3#475612yes—
347C2×C3D3×#10212yes—
348C2×C3#478812yes—
349C2×C3#480412yes—
350C2×C3#485212yes—
351C2×C3#487212yes—
352D3—128no—
353D3—128no—
354C22—184no—
355C22—364no—
356C22—362no—
357C22—362no—
358C22—364no—
359C22#6388112yes—
360C22#6392611yescharacteristic
361C22#6393011yescharacteristic
362C22#6395012yes—
363C22#6397411yescharacteristic
364C4—42no—
365C4—94no—
366C4—124no—
367C4—182no—
368C4#6384911yescharacteristic
369C4#6388112yes—
370C4C4×#62411yescharacteristic
371C3—21no—
372C3#6878012yescomplemented
373C2—364no—
374C2#1059045912yes—
375C2#1059048312yes—
376C2#1059126011yescharacteristic
377C2#1059141611yescharacteristic
378C2#1059156011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#102
LCSG ▷ 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
2. #10591274C2semidirect
4. C2×#63553C2semidirect
5. C3×#4529C2semidirect
13. #64102C4semidirect
18. #63564C4semidirect
27. #4529D3semidirect
47. C3×C4⋊Dic3C2×C4semidirect
50. C2×C3×C3⋊C8C2×C4semidirect
96. C4⋊(C3⋊D3)C42semidirect
147. C4⋊Dic3C4×D3semidirect
155. C2×C3⋊C8C4×D3semidirect
171. C3⋊Dic3#102semidirect
313. C32C4×#102semidirect
372. C3#68780semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105912742
C2×#635642
C2×#635532
C3×#45292
#687803