Finite Group Databasebeta

← #11791105

Subgroups — #11791105

Order 1152.

825 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 825 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C22×#3713C211yesmaximal, characteristic
2C2×#63642C211yesmaximal, characteristic, complemented
3C2×C3×#821C212yesmaximal, complemented
4#10591323C212yesmaximal, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6#70191—32nomaximal
7C22×C3×D12C2212yes—
8C22×C32×C8C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×C4⋊Dic3C2212yes—
12C2×(C2×D3)⋊Dic3—24no—
13C2×#3713—22no—
14C2×#3713—22no—
15C2×#3713C414yescomplemented
16#63642—22no—
17C3×#821—24no—
18#63574—22no—
19C22×#213—32no—
20C2×C3×#102—32no—
21#5221—32no—
22C2×#821D312yescomplemented
23C2×#815—32no—
24C2×#815—61no—
25#4988—32no—
26C2×#808—32no—
27C23×C3×D3—22no—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3D412yes—
30C22×C3×Dic3—22no—
31C2×C3×D12—22no—
32C2×C3×D12—22no—
33C2×C3×D12—22no—
34C2×C3×D12—22no—
35C2×C3×D12—22no—
36C2×C3×D12C2×C414yes—
37C2×C32×C8—21no—
38C2×C32×C8—21no—
39C2×C32×C8D412yes—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3—21no—
42C2×C3⋊(C3⋊C8)C2×C412yes—
43C2×C3⋊(C3⋊C8)D412yes—
44C2×C3⋊(C3⋊C8)D412yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47(C2×D3)⋊Dic3—48no—
48#3713—28no—
49#1972—91noSylow
50C22×C3×D4—32no—
51C22×D12C2×D312yes—
52C22×C3×C8—21no—
53C22×C3×C8C2×D312yes—
54C2×C3×C4⋊C4—32no—
55C2×#217—64no—
56C2×#213—38no—
57C2×#213—64no—
58C2×#213—64no—
59C2×(C2×D3)⋊C4—64no—
60C2×C4⋊Dic3C2×D312yes—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C22×C3⋊C8—32no—
64C22×C3⋊C8—61no—
65C3×#102—64no—
66#821—24no—
67#815—64no—
68#815—64no—
69#808—64no—
70C23×C32C2×D411yescharacteristic
71C22×C3×D3—24no—
72C22×C3×D3—42no—
73C22×C3×D3—42no—
74C22×C3×D3—44no—
75C22×C3×D3—44no—
76C2×C32×C4C22×C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4#4111yescharacteristic
81C2×C32×C4#4111yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—24no—
84C2×C3×Dic3—42no—
85C2×C3×Dic3—44no—
86C3×D12—24no—
87C3×D12—24no—
88C3×D12—42no—
89C3×D12—42no—
90C32×C8—22no—
91C3⋊(C3⋊C8)C22⋊C414yescomplemented
92C22×D8—91no—
93C2×#106—91no—
94C2×#102—32no—
95C2×#97—91no—
96#390—92no—
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—21no—
106C22×C3×C4—62no—
107C22×C3×C4C22×D312yes—
108C22×Dic3—22no—
109C22×Dic3—34no—
110C22×Dic3—62no—
111C2×D12—22no—
112C2×D12—22no—
113C2×D12—22no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12C4×D314yes—
117C2×C3×C8—22no—
118C2×C3×C8—22no—
119C2×C3×C8—22no—
120C2×C3×C8—22no—
121C2×C3×C8—22no—
122C2×C3×C8#6714yes—
123C3×C4⋊C4—62no—
124C3×C4⋊C4—62no—
125#217—128no—
126#213—616no—
127(C2×D3)⋊C4—128no—
128C4⋊Dic3—22no—
129C4⋊Dic3—22no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C2×C3⋊C8—34no—
135C2×C3⋊C8—34no—
136C2×C3⋊C8—34no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—62no—
140C22×C32C4×D411yescharacteristic
141C22×C32#12111yescharacteristic
142C22×C32#12711yescharacteristic
143C22×C32AGL(1,ℤ/8)14yes—
144C2×C3×D3—44no—
145C2×C3×D3—48no—
146C2×C3×D3—84no—
147C2×C3×D3—82no—
148C2×C3×D3—82no—
149C32×C4C2×C22⋊C411yescharacteristic
150C32×C4C4×D411yescharacteristic
151C32×C4#12111yescharacteristic
152C32×C4#12411yescharacteristic
153C3⋊Dic3—42no—
154C3×Dic3—82no—
155C22×D4—32no—
156C2×D8—94no—
157C2×D8—182no—
158C2×D8—182no—
159C22×C8—91no—
160C22×C8D3211yescharacteristic
161C2×C4⋊C4—32no—
162C2×C22⋊C4—184no—
163C2×C42—91no—
164#106—182no—
165#102—64no—
166#97—182no—
167C23×C3—21no—
168C23×C3—64no—
169C23×C3—122no—
170C23×C3—124no—
171C23×C3—124no—
172C23×C3—122no—
173C23×C3D3×D412yes—
174C22×D3—24no—
175C22×D3—42no—
176C22×D3—44no—
177C22×D3—44no—
178C22×D3—42no—
179C3×D4—64no—
180C3×D4—64no—
181C3×D4—122no—
182C3×D4—122no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—124no—
190C2×C3×C4—122no—
191C2×C3×C4C2×C4×D312yes—
192C2×C3×C4#23512yes—
193C2×C3×C4D3×D412yes—
194C2×C3×C4D3×D412yes—
195C2×C3×C4#23712yes—
196C2×C3×C4C2×#6712yes—
197C2×Dic3—44no—
198C2×Dic3—42no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—124no—
204D12—24no—
205D12—24no—
206D12—42no—
207D12—42no—
208C3×C8—24no—
209C3×C8—24no—
210C3⋊C8—38no—
211C3⋊C8—64no—
212C2×C32#39011yescharacteristic
213C2×C32#44212yes—
214C2×C32#46912yes—
215C2×C32#49612yes—
216C3×D3—84no—
217C24—62no—
218C2×D4—34no—
219C2×D4—62no—
220C2×D4—62no—
221C2×D4—62no—
222C2×D4—62no—
223C2×D4—62no—
224C22×C4—62no—
225C22×C4—92no—
226C22×C4C2×D3211yescharacteristic
227D8—188no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—92no—
231C2×C8—92no—
232C2×C8—92no—
233C2×C8#62512yes—
234C4⋊C4—62no—
235C4⋊C4—62no—
236C22⋊C4—368no—
237C42—181no—
238C42—181no—
239C22×C3—24no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—124no—
244C22×C3—128no—
245C22×C3—242no—
246C22×C3—242no—
247C22×C3—244no—
248C22×C3#67⋊C412yes—
249C22×C3#88412yes—
250C22×C3#91114yes—
251C22×C3#91414yes—
252C22×C3#94012yes—
253C2×D3—44no—
254C2×D3—48no—
255C2×D3—82no—
256C2×D3—82no—
257C2×D3—84no—
258C3×C4—21no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—242no—
263C3×C4D3×C22⋊C412yes—
264C3×C4#88512yes—
265C3×C4C4×#6712yes—
266C3×C4#93912yes—
267Dic3—82no—
268Dic3—124no—
269Dic3—124no—
270C32#197211yescharacteristic, complemented, Sylow
271C23—64no—
272C23—124no—
273C23—124no—
274C23—122no—
275C23—122no—
276C23#380211yescharacteristic
277D4—64no—
278D4—64no—
279D4—122no—
280D4—122no—
281C2×C4—124no—
282C2×C4—122no—
283C2×C4—184no—
284C2×C4—182no—
285C2×C4#379811yescharacteristic
286C2×C4C4×D3211yescharacteristic
287C2×C4#380211yescharacteristic
288C2×C4#380511yescharacteristic
289C2×C4C2×#62511yescharacteristic
290C2×C4#381111yescharacteristic
291C8—22no—
292C8—94no—
293C2×C3—22no—
294C2×C3—22no—
295C2×C3—21no—
296C2×C3—22no—
297C2×C3—244no—
298C2×C3#478214yes—
299C2×C3#478514yes—
300C2×C3#495712yes—
301C2×C3#515412yes—
302C2×C3#517612yes—
303D3—84no—
304C22—128no—
305C22—124no—
306C22—244no—
307C22—242no—
308C22—242no—
309C22#6379814yes—
310C22#6390211yescharacteristic
311C22#6391211yescharacteristic
312C22#6391411yescharacteristic
313C4—242no—
314C4—362no—
315C4C4×#62511yescharacteristic
316C4#6391511yescharacteristic
317C4#6392111yescharacteristic
318C4#6398011yescharacteristic
319C3—21no—
320C3#7019112yescomplemented
321C2—244no—
322C2#1059074112yes—
323C2#1059084012yes—
324C2#1059088712yes—
325C2#1059138511yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1972
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63642C2semidirect
3. C2×C3×#821C2semidirect
4. #10591323C2semidirect
5. C2×#63574C2semidirect
15. C2×#3713C4semidirect
22. C2×#821D3semidirect
91. C3⋊(C3⋊C8)C22⋊C4semidirect
270. C32#1972semidirect
320. C3#70191semidirect

Maximal subgroups

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

subgroupindex
C22×#37132
C2×#636422
C2×C3×#8212
#105913232
C2×#635742
#701913