Finite Group Databasebeta

← #11790759

Subgroups — #11790759

Order 1152.

901 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 901 conjugacy classes of subgroups — too many to draw. Only its 162 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
1C2×#63914C211yesmaximal, characteristic
2#10592676C211yesmaximal, characteristic, complemented
3C2×C3×#809C212yesmaximal, complemented
4C2×#63563C212yesmaximal, complemented
5C2×#63555C211yesmaximal, characteristic, complemented
6#70160—32nomaximal
7C22×C3×D12C2212yes—
8C22×#625—22no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3×C3⋊C8C2212yes—
13#63914—22no—
14#63914C414yescomplemented
15#63658—22no—
16C3×#809—24no—
17#63563—24no—
18#63555—22no—
19C2×#940—32no—
20C2×C3×#102—32no—
21C2×#832—32no—
22C2×#821—32no—
23C2×#815—32no—
24#4977—32no—
25#4977—61no—
26C2×#809D312yescomplemented
27C23×C3×D3—22no—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D412yes—
32C2×C3×D12—22no—
33C2×C3×D12—22no—
34C2×C3×D12—22no—
35C2×C3×D12—22no—
36C2×C3×D12—22no—
37C2×C3×D12C2×C414yes—
38C2×#625—28no—
39C2×#625—44no—
40C2×#625—44no—
41C32×C4⋊C4—22no—
42C4⋊(C3⋊Dic3)—22no—
43C4×C3⋊Dic3C2×C412yes—
44C4×C3⋊Dic3D412yes—
45C2×C3×C3⋊C8—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8D414yescomplemented
48#1961—91noSylow
49C22×C3×D4—32no—
50C22×#67—64no—
51C22×D12C2×D312yes—
52C22×C3×C8—32no—
53C2×C3×C4⋊C4—21no—
54C2×C3×C4⋊C4C2×D312yes—
55#940—38no—
56#940—64no—
57C2×C4⋊Dic3—32no—
58C2×C4⋊Dic3—61no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61C22×C3⋊C8C2×D312yes—
62C3×#102—64no—
63#832—64no—
64C3⋊#95—64no—
65C3⋊#95—64no—
66#821—64no—
67#815—64no—
68#809—24no—
69C23×C32C2×D411yescharacteristic
70C22×C3×D3—24no—
71C22×C3×D3—42no—
72C22×C3×D3—42no—
73C22×C3×D3—44no—
74C22×C3×D3—44no—
75C2×C32×C4—41no—
76C2×C32×C4—42no—
77C2×C32×C4C22×C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D412yes—
80C2×C32×C4#4112yes—
81C2×C3⋊Dic3—22no—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3C22⋊C414yes—
86C3×D12—24no—
87C3×D12—24no—
88C3×D12—42no—
89C3×D12—42no—
90#625—416no—
91C3×C3⋊C8—24no—
92C2×#127—91no—
93C2×#102—32no—
94C2×#102—92no—
95C2×#97—91no—
96#382—91no—
97C24×C3—62no—
98C23×D3—22no—
99C2×C3×D4—34no—
100C2×C3×D4—62no—
101C2×C3×D4—62no—
102C2×C3×D4—62no—
103C2×C3×D4—62no—
104C2×C3×D4—62no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—21no—
108C22×C3×C4C22×D312yes—
109C2×#67—616no—
110C2×#67—128no—
111C2×#67—128no—
112C22×Dic3—34no—
113C22×Dic3—62no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12—22no—
120C2×D12—22no—
121C2×D12C4×D314yes—
122C2×C3×C8—34no—
123C2×C3×C8—62no—
124C2×C3×C8—62no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—42no—
128C4⋊Dic3—62no—
129C4⋊Dic3—62no—
130C4⋊Dic3—122no—
131C4×Dic3—34no—
132C4×Dic3—34no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—22no—
137C2×C3⋊C8#6714yescomplemented
138C22×C32C2×C22⋊C411yescharacteristic
139C22×C32#12411yescharacteristic
140C22×C32#12711yescharacteristic
141C22×C32AGL(1,ℤ/8)12yes—
142C22×C32AGL(1,ℤ/8)12yes—
143C2×C3×D3—44no—
144C2×C3×D3—48no—
145C2×C3×D3—84no—
146C2×C3×D3—82no—
147C2×C3×D3—82no—
148C32×C4—81no—
149C32×C4C4×D412yes—
150C32×C4#12112yes—
151C3⋊Dic3—24no—
152C3⋊Dic3—81no—
153C22×D4—32no—
154C22×D4—182no—
155C22×C8—32no—
156#127—94no—
157#127—182no—
158C2×C4⋊C4—91no—
159C2×C4⋊C4D3211yescharacteristic
160C2×C42—91no—
161#102—64no—
162#102—184no—
163#97—182no—
164#95—182no—
165C23×C3—21no—
166C23×C3—64no—
167C23×C3—122no—
168C23×C3—124no—
169C23×C3—124no—
170C23×C3—122no—
171C23×C3D3×D412yes—
172C22×D3—24no—
173C22×D3—42no—
174C22×D3—44no—
175C22×D3—44no—
176C22×D3—42no—
177C3×D4—64no—
178C3×D4—64no—
179C3×D4—122no—
180C3×D4—122no—
181C2×C3×C4—22no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—42no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—42no—
189C2×C3×C4C2×C4×D312yes—
190C2×C3×C4#23512yes—
191C2×C3×C4D3×D412yes—
192C2×C3×C4D3×D412yes—
193C2×C3×C4#23712yes—
194C2×C3×C4C2×#6712yes—
195#67—1232no—
196C2×Dic3—38no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×Dic3—122no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3—122no—
206D12—24no—
207D12—24no—
208D12—42no—
209D12—42no—
210C3×C8—64no—
211C3⋊C8—24no—
212C2×C32#39011yescharacteristic
213C2×C32#41812yes—
214C2×C32#49012yes—
215C2×C32#49611yescharacteristic
216C2×C32#49611yescharacteristic
217C3×D3—84no—
218C24—62no—
219C2×D4—34no—
220C2×D4—62no—
221C2×D4—62no—
222C2×D4—62no—
223C2×D4—62no—
224C2×D4—62no—
225C2×D4—188no—
226C2×D4—364no—
227C2×D4—364no—
228C22×C4—21no—
229C22×C4—92no—
230C22×C4—181no—
231C22×C4C2×D3211yescharacteristic
232C2×C8—34no—
233C2×C8—62no—
234C2×C8—62no—
235C4⋊C4—22no—
236C4⋊C4—182no—
237C42—92no—
238C42—92no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3—21no—
244C22×C3—124no—
245C22×C3—128no—
246C22×C3—242no—
247C22×C3—242no—
248C22×C3—244no—
249C22×C3D3×C22⋊C412yes—
250C22×C3#88512yes—
251C22×C3#91114yes—
252C22×C3#91414yes—
253C22×C3#94012yes—
254C2×D3—44no—
255C2×D3—48no—
256C2×D3—82no—
257C2×D3—82no—
258C2×D3—84no—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—82no—
262C3×C4—82no—
263C3×C4#67⋊C412yes—
264C3×C4#88412yes—
265C3×C4C4×#6712yes—
266C3×C4#93912yes—
267Dic3—68no—
268Dic3—124no—
269Dic3—242no—
270Dic3—242no—
271C32#196111yescharacteristic, complemented, Sylow
272C23—64no—
273C23—122no—
274C23—124no—
275C23—124no—
276C23—122no—
277C23#381111yescharacteristic
278D4—64no—
279D4—64no—
280D4—122no—
281D4—122no—
282D4—3616no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—94no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—362no—
289C2×C4—361no—
290C2×C4#379512yes—
291C2×C4C4×D3211yescharacteristic
292C2×C4#380211yescharacteristic
293C2×C4D3×#6712yes—
294C8—64no—
295C2×C3—22no—
296C2×C3—22no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—244no—
301C2×C3#476414yes—
302C2×C3#477014yes—
303C2×C3#495712yes—
304C2×C3#515412yes—
305C2×C3#517612yes—
306D3—84no—
307C22—128no—
308C22—124no—
309C22—244no—
310C22—242no—
311C22—242no—
312C22#6391311yescharacteristic
313C22#6392111yescharacteristic
314C22#6392712yes—
315C22#6394112yes—
316C22#6397911yescharacteristic
317C4—81no—
318C4—184no—
319C4—721no—
320C4#6387912yes—
321C4#6388512yes—
322C3—21no—
323C3#7016012yescomplemented
324C2—244no—
325C2#1059055412yes—
326C2#1059059412yes—
327C2#1059138611yescharacteristic
328C2#1059148511yescharacteristic
329C2#1059162111yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1961
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
2. #10592676C2semidirect
3. C2×C3×#809C2semidirect
4. C2×#63563C2semidirect
5. C2×#63555C2semidirect
14. #63914C4semidirect
26. C2×#809D3semidirect
47. C2×C3×C3⋊C8D4semidirect
137. C2×C3⋊C8#67semidirect
271. C32#1961semidirect
323. C3#70160semidirect

Maximal subgroups

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

subgroupindex
C2×#639142
#105926762
C2×C3×#8092
C2×#635632
C2×#635552
#701603