Finite Group Databasebeta

← #11786593

Subgroups — #11786593

Order 1152.

777 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 777 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic
2#10592638C211yesmaximal, characteristic
3#10591131C212yesmaximal, complemented
4C2×#63559C211yesmaximal, characteristic
5C3×#4523C212yesmaximal, complemented
6#68758—32nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C2×C32×C42C2211yescharacteristic
9C2×#3752—22no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C3×#926C2212yes—
12C2×C3×#208C2212yes—
13#63974—22no—
14#63894—22no—
15#63894—22no—
16#63575—22no—
17#63573—22no—
18#63559C414yescomplemented
19#5521—32no—
20C2×#823—32no—
21#5121—32no—
22#4995—32no—
23#4939—32no—
24#4939—61no—
25C3×#339—32no—
26#4523D312yescomplemented
27C23×C3⋊D3D412yes—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4⋊(C3⋊D3)—22no—
33C2×C4⋊(C3⋊D3)C2×C412yes—
34C2×C4⋊(C3⋊D3)Q812yes—
35C2×#624—22no—
36C2×#624—22no—
37C32×C42—22no—
38#3752—44no—
39C4⋊(C3⋊Dic3)—22no—
40C3×#217—22no—
41C3×C4⋊Dic3D412yes—
42C3×C4⋊Dic3D412yes—
43C3×C4×Dic3—22no—
44C3×#208—22no—
45C3×#208C2×C414yescomplemented
46C2×C3×C3⋊C8—22no—
47#3722—24no—
48#1856—91noSylow
49C22×D12—32no—
50C22×D12—61no—
51C2×C3×M16—32no—
52C3×#117—32no—
53C2×C3×C42—21no—
54C2×C3×C42C2×D312yes—
55C2×(C2×D3)⋊C4—64no—
56C2×(C2×D3)⋊C4—64no—
57#926C2×D312yes—
58C2×C4⋊Dic3—32no—
59C2×C4⋊Dic3—61no—
60C2×#208C2×D312yes—
61#893—62no—
62#893—62no—
63D3×C22⋊C4—64no—
64C4×D12—62no—
65C4×D12—62no—
66#823—38no—
67#818—62no—
68#817—62no—
69#808—62no—
70#807—62no—
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3C4⋊C414yes—
77C2×C32×C4—22no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D412yes—
82C2×C32×C4C2×Q811yescharacteristic
83C2×C32×C4#4112yes—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—41no—
86C4⋊(C3⋊D3)—24no—
87C4⋊(C3⋊D3)—24no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90#624—82no—
91#624—82no—
92C3×C3⋊C8—24no—
93#518—91no—
94#428—92no—
95C2×#100—91no—
96#390—91no—
97#339—32no—
98C23×D3—34no—
99C23×D3—62no—
100C22×C3×C4—22no—
101C22×C3×C4—22no—
102C22×C3×C4—21no—
103C22×C3×C4C22×D312yes—
104C22×Dic3—62no—
105C22×Dic3—62no—
106C2×D12—34no—
107C2×D12—34no—
108C2×D12—62no—
109C2×D12—62no—
110C2×D12—62no—
111C2×D12—62no—
112C2×D12—62no—
113C2×D12—62no—
114C2×D12—122no—
115C2×D12—122no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C3×M16—34no—
119C3×M16—62no—
120C2×C3×C8—62no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—32no—
123C3×C22⋊C4—62no—
124C3×C42—22no—
125C3×C42—22no—
126C3×C42—42no—
127C3×C42—62no—
128#217—22no—
129(C2×D3)⋊C4—64no—
130(C2×D3)⋊C4—64no—
131(C2×D3)⋊C4—128no—
132(C2×D3)⋊C4—128no—
133C4⋊Dic3—62no—
134C4⋊Dic3—62no—
135C4⋊Dic3—122no—
136C4⋊Dic3D1212yes—
137C4⋊Dic3D1212yes—
138C4×Dic3—22no—
139#208—22no—
140#208C4×D314yescomplemented
141C2×C3⋊C8—22no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32C2×C4⋊C411yescharacteristic
145C22×C32#12011yescharacteristic
146C22×C32#12311yescharacteristic
147C2×C3⋊D3—24no—
148C2×C3⋊D3—44no—
149C2×C3⋊D3—42no—
150C2×C3⋊D3—42no—
151C2×C3⋊D3—82no—
152C32×C4—42no—
153C32×C4C4×D412yes—
154C32×C4C22⋊Q812yes—
155C3⋊Dic3—81no—
156C3×Dic3—42no—
157C3×Dic3—42no—
158C22×D4—91no—
159C2×M16—32no—
160C4×D4—182no—
161C4×D4—182no—
162#117—32no—
163C2×C4⋊C4—91no—
164C2×C22⋊C4—182no—
165C2×C22⋊C4—182no—
166C2×C42D3211yescharacteristic
167#107—182no—
168#106—182no—
169#100—94no—
170C23×C3—21no—
171C23×C3D3×D412yes—
172C22×D3—38no—
173C22×D3—64no—
174C22×D3—64no—
175C22×D3—64no—
176C22×D3—122no—
177C22×D3—122no—
178C22×D3—124no—
179C22×D3—124no—
180C22×D3—124no—
181C22×D3—124no—
182C2×C3×C4—24no—
183C2×C3×C4—24no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—62no—
193C2×C3×C4—62no—
194C2×C3×C4C2×C4×D312yes—
195C2×C3×C4C2×D1212yes—
196C2×C3×C4#23512yes—
197C2×C3×C4D3×D412yes—
198C2×C3×C4#23712yes—
199C2×C3×C4D3×Q812yes—
200C2×Dic3—22no—
201C2×Dic3—22no—
202C2×Dic3—122no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3—122no—
206D12—64no—
207D12—64no—
208D12—64no—
209D12—64no—
210D12—124no—
211D12—124no—
212C4×D3—244no—
213C4×D3—244no—
214C3×C8—64no—
215C3⋊C8—24no—
216C2×C32—21no—
217C2×C32—21no—
218C2×C32#38511yescharacteristic
219C2×C32#45311yescharacteristic
220C2×C32#45511yescharacteristic
221C3⋊D3—44no—
222C24—92no—
223C2×D4—92no—
224C2×D4—92no—
225C2×D4—182no—
226C2×D4—182no—
227C22×C4—21no—
228C22×C4—182no—
229C22×C4—182no—
230C22×C4—181no—
231C22×C4C2×D3211yescharacteristic
232M16—34no—
233M16—62no—
234C2×C8—62no—
235C4⋊C4—32no—
236C4⋊C4—32no—
237C4⋊C4—182no—
238C22⋊C4—62no—
239C22⋊C4—184no—
240C22⋊C4—364no—
241C42—22no—
242C42—62no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3#88212yes—
251C22×C3#88312yes—
252C22×C3D3×C4⋊C412yes—
253C2×D3—68no—
254C2×D3—124no—
255C2×D3—124no—
256C2×D3—124no—
257C2×D3—128no—
258C2×D3—128no—
259C2×D3—242no—
260C2×D3—242no—
261C2×D3—244no—
262C2×D3—244no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—44no—
266C3×C4—44no—
267C3×C4—122no—
268C3×C4—122no—
269C3×C4C4×D1212yes—
270C3×C4#67⋊C412yes—
271C3×C4#89612yes—
272C3×C4#89712yes—
273Dic3—42no—
274Dic3—42no—
275Dic3—242no—
276Dic3—242no—
277C32#185611yescharacteristic, complemented, Sylow
278C23—94no—
279C23—182no—
280C23—182no—
281C23—362no—
282C23—362no—
283C23#381111yescharacteristic
284D4—184no—
285D4—184no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—62no—
290C2×C4—62no—
291C2×C4—362no—
292C2×C4—361no—
293C2×C4—722no—
294C2×C4—722no—
295C2×C4#379711yescharacteristic
296C2×C4C4×D3211yescharacteristic
297C2×C4D3×D1212yes—
298C2×C4#380412yes—
299C8—64no—
300C2×C3—22no—
301C2×C3—22no—
302C2×C3—22no—
303C2×C3—22no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3#466812yes—
308C2×C3#482212yes—
309C2×C3#482512yes—
310D3—128no—
311D3—244no—
312C22—21no—
313C22—21no—
314C22—184no—
315C22—364no—
316C22—362no—
317C22—362no—
318C22—722no—
319C22#6388311yescharacteristic
320C22#6392311yescharacteristic
321C22#6397511yescharacteristic
322C4—42no—
323C4—122no—
324C4—122no—
325C4—721no—
326C4#6388012yes—
327C4#6389512yes—
328C3—21no—
329C3#6875812yescomplemented
330C2—21no—
331C2—21no—
332C2—364no—
333C2#1059039711yescharacteristic
334C2#1059039811yescharacteristic
335C2#1059137511yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10591131C2semidirect
5. C3×#4523C2semidirect
18. #63559C4semidirect
26. #4523D3semidirect
45. C3×#208C2×C4semidirect
140. #208C4×D3semidirect
277. C32#1856semidirect
329. C3#68758semidirect

Maximal subgroups

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

subgroupindex
#105949962
#105926382
#105911312
C2×#635592
C3×#45232
#687583