Finite Group Databasebeta

← #11790786

Subgroups — #11790786

Order 1152.

783 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 783 conjugacy classes of subgroups — too many to draw. Only its 134 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#10595032C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic, complemented
3C2×C3×#825C212yesmaximal, complemented
4C4×Dic32C211yesmaximal, characteristic, complemented
5C2×#63569C212yesmaximal, complemented
6#70356—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×M16C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×C4×Dic3C2212yes—
12#63980—22no—
13C2×Dic32—22no—
14#63914C411yescharacteristic, complemented
15C4×#625—22no—
16#63873C411yescharacteristic, complemented
17#63863C412yescomplemented
18#63641—22no—
19C3×#825—24no—
20#63569—24no—
21#5832—32no—
22C2×C3×#104—32no—
23C2×#837—32no—
24C2×#825D312yescomplemented
25#5118—32no—
26#5118—61no—
27C42×Dic3—32no—
28C2×#805—32no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3D412yes—
31C2×C3×#67—22no—
32C22×C3×Dic3—22no—
33C3×#235—22no—
34C3×#235—22no—
35C3×#235—22no—
36C3×#235—22no—
37C2×C3×D12C2×C412yes—
38C2×C3×C4×D3—22no—
39C2×C3×Dic6C2×C412yes—
40C2×#625—22no—
41C32×M16—22no—
42C2×C32×C8—21no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D412yes—
46#3748—22no—
47C2×C3⋊(C3⋊C8)—21no—
48C3×C4×Dic3—22no—
49C3×C4×Dic3D414yescomplemented
50#3724—22no—
51(C2×D3)⋊Dic3—24no—
52Dic32—28no—
53#1962—91noSylow
54C2×C3×#41—32no—
55C2×#235C2×D312yes—
56C2×C3×M16—21no—
57C2×C3×M16C2×D312yes—
58C2×C3×C42—32no—
59#947—32no—
60#944—32no—
61#940—32no—
62#939—64no—
63#936—32no—
64C4×#67—64no—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—64no—
68C2×C4×Dic3C2×D312yes—
69C2×#208—32no—
70C2×#208—61no—
71C3×#104—64no—
72#837—64no—
73#825—24no—
74Dic3⋊C8—64no—
75Dic3⋊C8—64no—
76#805—64no—
77C23×C32C2×D411yescharacteristic
78C22×C3×D3—22no—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D412yes—
82C2×C32×C4#4112yes—
83C2×C3⋊Dic3—24no—
84C2×C3⋊Dic3C22⋊C412yes—
85C2×C3⋊Dic3C22⋊C412yes—
86C3×#67—42no—
87C3×#67—42no—
88C2×C3×Dic3—28no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3—22no—
91C3×D12—22no—
92C3×D12—22no—
93C3×C4×D3—42no—
94C3×C4×D3—42no—
95C3×Dic6—22no—
96C3×Dic6—22no—
97#625—44no—
98C32×C8—41no—
99C3⋊(C3⋊C8)—41no—
100#532—91no—
101#423—91no—
102C2×#104—32no—
103C2×#104—92no—
104C43—91no—
105C3×#41—62no—
106C3×#41—62no—
107C3×#41—62no—
108C3×#41—62no—
109C2×C3×Q8—32no—
110C2×C3×D4—32no—
111C2×C3×D4—62no—
112C22×C3×C4—21no—
113C22×C3×C4—62no—
114C22×C3×C4—62no—
115C22×C3×C4C22×D312yes—
116C2×#67—22no—
117C2×#67—64no—
118C22×Dic3—22no—
119C22×Dic3—34no—
120C22×Dic3—62no—
121#235—22no—
122#235—22no—
123#235—22no—
124#235—22no—
125C2×D12C4×D312yes—
126C2×C4×D3—22no—
127C2×Dic6C4×D312yes—
128C3×M16—22no—
129C3×M16—22no—
130C3×M16—42no—
131C2×C3×C8—22no—
132C2×C3×C8—22no—
133C3×C42—34no—
134C3×C42—62no—
135#217—64no—
136(C2×D3)⋊C4—64no—
137Dic3⋊C4—64no—
138C4×Dic3—22no—
139C4×Dic3—32no—
140C4×Dic3—32no—
141C4×Dic3—34no—
142C4×Dic3—62no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—616no—
146C4×Dic3#6714yescomplemented
147#208—62no—
148#208—62no—
149#208—122no—
150C2×C3⋊C8—62no—
151C2×C3⋊C8—62no—
152C22×C32—22no—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32#12112yes—
155C2×C3×D3—42no—
156C2×C3×D3—44no—
157C32×C4C4×D412yes—
158C32×C4#12411yescharacteristic
159C32×C4#12711yescharacteristic
160C3⋊Dic3—22no—
161C3⋊Dic3#10414yescomplemented
162C3×Dic3—28no—
163C3×Dic3—42no—
164C2×#41—32no—
165C2×M16—91no—
166C2×M16D3211yescharacteristic
167C4⋊Q8—91no—
168#127—91no—
169#124—92no—
170#121—182no—
171C4×D4—182no—
172C2×C42—32no—
173C2×C42—91no—
174C2×C42—182no—
175C4⋊C8—182no—
176#104—64no—
177#104—184no—
178C23×C3—21no—
179C23×C3—62no—
180C23×C3D3×D412yes—
181C22×D3—22no—
182C3×Q8—62no—
183C3×Q8—62no—
184C3×D4—62no—
185C3×D4—62no—
186C3×D4—122no—
187C3×D4—122no—
188C2×C3×C4—22no—
189C2×C3×C4—21no—
190C2×C3×C4—22no—
191C2×C3×C4—21no—
192C2×C3×C4—68no—
193C2×C3×C4—64no—
194C2×C3×C4—62no—
195C2×C3×C4—122no—
196C2×C3×C4—122no—
197C2×C3×C4C2×C4×D312yes—
198C2×C3×C4#23512yes—
199C2×C3×C4D3×D412yes—
200C2×C3×C4D3×D412yes—
201C2×C3×C4#23712yes—
202C2×C3×C4C2×#6712yes—
203#67—42no—
204#67—42no—
205#67—128no—
206C2×Dic3—28no—
207C2×Dic3—24no—
208C2×Dic3—22no—
209C2×Dic3—34no—
210C2×Dic3—34no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—68no—
214C2×Dic3—124no—
215D12—22no—
216D12—22no—
217C4×D3—42no—
218C4×D3—42no—
219Dic6—22no—
220Dic6—22no—
221C3×C8—42no—
222C3×C8—42no—
223C3⋊C8—122no—
224C3⋊C8—122no—
225C2×C32—22no—
226C2×C32#39011yescharacteristic
227C2×C32C2×#10412yes—
228C3×D3—82no—
229#41—62no—
230#41—62no—
231#41—62no—
232#41—62no—
233C2×Q8—32no—
234C2×D4—32no—
235C2×D4—62no—
236C2×D4—182no—
237C22×C4—62no—
238C22×C4—62no—
239C22×C4—92no—
240C22×C4C2×D3211yescharacteristic
241M16—22no—
242M16—182no—
243C2×C8—21no—
244C2×C8—181no—
245C4⋊C4—182no—
246C22⋊C4—184no—
247C42—34no—
248C42—62no—
249C42—91no—
250C42—91no—
251C42—92no—
252C42—188no—
253C22×C3—24no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—42no—
257C22×C3—122no—
258C22×C3—124no—
259C22×C3D3×C22⋊C412yes—
260C22×C3#88412yes—
261C22×C3#93912yes—
262C2×D3—42no—
263C2×D3—44no—
264C3×C4—22no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—68no—
268C3×C4—122no—
269C3×C4#67⋊C412yes—
270C3×C4#88512yes—
271C3×C4C4×#6712yes—
272C3×C4#94012yes—
273Dic3—28no—
274Dic3—38no—
275Dic3—42no—
276Dic3—64no—
277Dic3—64no—
278Dic3—122no—
279C32#196211yescharacteristic, complemented, Sylow
280C23—62no—
281C23#380211yescharacteristic
282Q8—62no—
283Q8—62no—
284D4—62no—
285D4—62no—
286D4—122no—
287D4—122no—
288D4—364no—
289C2×C4—68no—
290C2×C4—64no—
291C2×C4—62no—
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—122no—
295C2×C4—122no—
296C2×C4—184no—
297C2×C4#379512yes—
298C2×C4C4×D3211yescharacteristic
299C2×C4D3×#6712yes—
300C2×C4#381111yescharacteristic
301C8—41no—
302C8—361no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—21no—
307C2×C3—42no—
308C2×C3—242no—
309C2×C3D3×#10414yes—
310C2×C3#495712yes—
311D3—82no—
312C22—22no—
313C22—124no—
314C22—122no—
315C22#6388512yes—
316C22#6392111yescharacteristic
317C4—68no—
318C4—94no—
319C4—122no—
320C4—182no—
321C4#6387912yes—
322C4#6391311yescharacteristic
323C4#6397911yescharacteristic
324C3—21no—
325C3#7035612yescomplemented
326C2—22no—
327C2—242no—
328C2#1059100812yes—
329C2#1059138611yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1962
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592817C2semidirect
3. C2×C3×#825C2semidirect
4. C4×Dic32C2semidirect
5. C2×#63569C2semidirect
14. #63914C4semidirect
16. #63873C4semidirect
17. #63863C4semidirect
24. C2×#825D3semidirect
49. C3×C4×Dic3D4semidirect
146. C4×Dic3#67semidirect
161. C3⋊Dic3#104semidirect
279. C32#1962semidirect
325. C3#70356semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105928172
C2×C3×#8252
C4×Dic322
C2×#635692
#703563