Finite Group Databasebeta

← #11786374

Subgroups — #11786374

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3710C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3C4×#3722C211yesmaximal, characteristic
4C2×Dic3⋊(C3⋊C8)C212yesmaximal, complemented
5C3×#4550C212yesmaximal, complemented
6#68666—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C32×C8C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4×Dic3C2212yes—
11C22×C3×C3⋊C8C2212yes—
12C2×#3722C411yescharacteristic
13C2×#3722C411yescharacteristic
14C2×#3710—22no—
15C2×#3710—24no—
16#63647—22no—
17#63579C412yes—
18Dic3⋊(C3⋊C8)—24no—
19C22×D3×C8—32no—
20C2×(C2×D3)⋊C8—32no—
21C2×(C2×D3)⋊C8—61no—
22C2×Dic3⋊C8—32no—
23C4×(C2×D3)⋊C4—32no—
24C2×C4⋊(C3⋊C8)—32no—
25C3×#336—32no—
26#4550D312yescomplemented
27C23×C3⋊D3C2×C411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C2×C4×C3⋊D3—22no—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3D412yes—
33C2×C4×C3⋊D3Q812yes—
34C22×C3×Dic3C2×C412yes—
35C22×C3×Dic3C2×C412yes—
36C2×C32×C8—21no—
37C2×C32×C8—22no—
38C2×C3⋊(C3⋊C8)—21no—
39C2×C3⋊(C3⋊C8)—22no—
40C3×C4×Dic3—22no—
41C3×C4×Dic3—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8D414yes—
45#3722—22no—
46#3722C814yescomplemented
47#3710—28no—
48#1850—91noSylow
49C22×C4×D3—32no—
50C22×C4×D3—61no—
51C22×C3×C8—21no—
52C22×C3×C8—32no—
53C22×C3×C8C2×D312yes—
54C2×C3×C42—32no—
55C2×(C2×D3)⋊C4—32no—
56C2×(C2×D3)⋊C4—32no—
57C2×C4×Dic3C2×D312yes—
58C22×C3⋊C8—32no—
59C22×C3⋊C8—61no—
60C22×C3⋊C8C2×D312yes—
61C2×D3×C8—64no—
62C2×D3×C8—64no—
63C2×D3×C8—64no—
64C3⋊#95—32no—
65C3⋊#95—32no—
66(C2×D3)⋊C8—64no—
67(C2×D3)⋊C8—64no—
68Dic3⋊C8—64no—
69C4⋊(C3⋊C8)—64no—
70C23×C32C22×C411yescharacteristic
71C22×C3⋊D3—22no—
72C22×C3⋊D3—22no—
73C22×C3⋊D3C4⋊C412yes—
74C22×C3⋊D3C2×C812yes—
75C22×C3⋊D3M1612yes—
76C2×C32×C4C2×D412yes—
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×Q811yescharacteristic
79C2×C32×C4#4112yes—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3C4⋊C412yes—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—24no—
84C4×C3⋊D3—22no—
85C2×C3×Dic3—22no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3C2×C814yescomplemented
91C32×C8—41no—
92C3⋊(C3⋊C8)—41no—
93C3×C3⋊C8—24no—
94C23×C8—91no—
95C2×C4⋊C8—92no—
96C2×C22⋊C8—91no—
97C4×C22⋊C4—91no—
98#336—32no—
99C23×D3—32no—
100C23×D3—61no—
101C22×C3×C4—21no—
102C22×C3×C4—32no—
103C22×C3×C4—32no—
104C22×C3×C4C22×D312yes—
105C22×Dic3—32no—
106C22×Dic3—61no—
107C22×Dic3C4×D312yes—
108C22×Dic3C4×D312yes—
109C2×C4×D3—34no—
110C2×C4×D3—34no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—122no—
118C2×C4×D3—122no—
119C2×C3×C8—22no—
120C2×C3×C8—22no—
121C2×C3×C8—22no—
122C2×C3×C8—22no—
123C2×C3×C8—34no—
124C2×C3×C8—42no—
125C2×C3×C8—62no—
126C2×C3×C8—62no—
127C3×C42—62no—
128C3×C42—62no—
129(C2×D3)⋊C4—38no—
130(C2×D3)⋊C4—64no—
131C4×Dic3—22no—
132C4×Dic3—22no—
133C2×C3⋊C8—22no—
134C2×C3⋊C8—22no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—122no—
140C2×C3⋊C8D1214yes—
141D3×C8—616no—
142C22×C32C2×C4⋊C411yescharacteristic
143C22×C32C4×D412yes—
144C22×C32C22×C811yescharacteristic
145C22×C32C2×M1611yescharacteristic
146C22×C32#13112yes—
147C2×C3⋊D3—22no—
148C2×C3⋊D3—22no—
149C2×C3⋊D3—24no—
150C2×C3⋊D3—24no—
151C2×C3⋊D3C4⋊C814yescomplemented
152C32×C4#12011yescharacteristic
153C32×C4C22⋊Q812yes—
154C32×C4#12311yescharacteristic
155C3⋊Dic3—22no—
156C3×Dic3—24no—
157C3×Dic3—42no—
158C23×C4—91no—
159C22×C8—32no—
160C22×C8—91no—
161C22×C8—184no—
162C22×C8—182no—
163C22×C8D3211yescharacteristic
164C2×C22⋊C4—91no—
165C2×C22⋊C4—91no—
166C2×C42—32no—
167C4⋊C8—184no—
168C22⋊C8—182no—
169#95—92no—
170C23×C3—21no—
171C23×C3C2×C4×D312yes—
172C22×D3—34no—
173C22×D3—34no—
174C22×D3—34no—
175C22×D3—62no—
176C22×D3—62no—
177C22×D3—62no—
178C22×D3—62no—
179C22×D3—62no—
180C22×D3—62no—
181C22×D3—62no—
182C22×D3—122no—
183C22×D3—122no—
184C2×C3×C4—21no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—21no—
188C2×C3×C4—34no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×C3×C4—62no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4C2×D1212yes—
195C2×C3×C4#23512yes—
196C2×C3×C4D3×D412yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4#23712yes—
199C2×C3×C4D3×Q812yes—
200C2×Dic3—22no—
201C2×Dic3—22no—
202C2×Dic3—22no—
203C2×Dic3—22no—
204C2×Dic3—22no—
205C2×Dic3—34no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—122no—
210C2×Dic3D3×C814yescomplemented
211C4×D3—64no—
212C4×D3—64no—
213C4×D3—64no—
214C4×D3—64no—
215C4×D3—124no—
216C4×D3—122no—
217C4×D3—122no—
218C3×C8—42no—
219C3×C8—42no—
220C3×C8—64no—
221C3⋊C8—24no—
222C3⋊C8—122no—
223C3⋊C8—122no—
224C2×C32#38511yescharacteristic
225C2×C32C2×C4⋊C811yescharacteristic
226C2×C32#42411yescharacteristic
227C2×C32C8×D412yes—
228C2×C32#43512yes—
229C3⋊D3—24no—
230C24—91no—
231C22×C4—32no—
232C22×C4—32no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4—182no—
237C22×C4—182no—
238C22×C4C2×D3211yescharacteristic
239C2×C8—22no—
240C2×C8—21no—
241C2×C8—34no—
242C2×C8—62no—
243C2×C8—62no—
244C2×C8—188no—
245C2×C8—182no—
246C2×C8—181no—
247C22⋊C4—94no—
248C22⋊C4—182no—
249C42—62no—
250C42—62no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3C4×D1212yes—
257C22×C3#67⋊C412yes—
258C22×C3D3×C4⋊C412yes—
259C22×C3C2×D3×C812yes—
260C22×C3#90112yes—
261C22×C3D3×M1612yes—
262C22×C3#90712yes—
263C2×D3—38no—
264C2×D3—64no—
265C2×D3—64no—
266C2×D3—64no—
267C2×D3—64no—
268C2×D3—64no—
269C2×D3—64no—
270C2×D3—64no—
271C2×D3—122no—
272C2×D3—124no—
273C2×D3—124no—
274C2×D3—122no—
275C3×C4—22no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—64no—
279C3×C4—122no—
280C3×C4#88212yes—
281C3×C4#88312yes—
282C3×C4#89612yes—
283C3×C4#89712yes—
284Dic3—24no—
285Dic3—42no—
286Dic3—64no—
287Dic3—122no—
288C32#185011yescharacteristic, complemented, Sylow
289C23—92no—
290C23—92no—
291C23—92no—
292C23—182no—
293C23—182no—
294C23C4×D3211yescharacteristic
295C2×C4—34no—
296C2×C4—62no—
297C2×C4—62no—
298C2×C4—62no—
299C2×C4—62no—
300C2×C4—62no—
301C2×C4—92no—
302C2×C4—182no—
303C2×C4—184no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4#379711yescharacteristic
307C2×C4D3×D1212yes—
308C2×C4#380412yes—
309C2×C4#381111yescharacteristic
310C8—41no—
311C8—64no—
312C8—361no—
313C2×C3—22no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3#466812yes—
319C2×C3C8×D1212yes—
320C2×C3#470612yes—
321C2×C3#67⋊C812yes—
322C2×C3#472812yes—
323C2×C3D3×C4⋊C812yes—
324C2×C3#483912yes—
325D3—68no—
326D3—124no—
327C22—94no—
328C22—184no—
329C22—184no—
330C22—182no—
331C22—182no—
332C22D32×C811yescharacteristic
333C22#6379111yescharacteristic
334C22#6380412yes—
335C22#6388012yes—
336C22#6388311yescharacteristic
337C4—64no—
338C4—122no—
339C4—182no—
340C4#6389512yes—
341C4#6392311yescharacteristic
342C4#6397511yescharacteristic
343C3—21no—
344C3#6866612yescomplemented
345C2—184no—
346C2#1059065811yescharacteristic
347C2#1059070211yescharacteristic
348C2#1059072112yes—
349C2#1059073912yes—
350C2#1059137511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1850
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×Dic3⋊(C3⋊C8)C2semidirect
5. C3×#4550C2semidirect
26. #4550D3semidirect
46. #3722C8semidirect
90. C2×C3×Dic3C2×C8semidirect
151. C2×C3⋊D3C4⋊C8semidirect
210. C2×Dic3D3×C8semidirect
288. C32#1850semidirect
344. C3#68666semidirect

Maximal subgroups

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

subgroupindex
C22×#37102
C2×#636472
C4×#37222
C2×Dic3⋊(C3⋊C8)2
C3×#45502
#686663