Finite Group Databasebeta

← #11790761

Subgroups — #11790761

Order 1152.

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

normal subgroups only

This group has 897 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
1C2×#63914C211yesmaximal, characteristic
2C2×#63642C211yesmaximal, characteristic, complemented
3C2×C3×#821C212yesmaximal, complemented
4#10591230C211yesmaximal, characteristic, complemented
5C2×#63562C212yesmaximal, complemented
6#70160—32nomaximal
7C22×C3×D12C2212yes—
8C22×#625—22no—
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13#63914—22no—
14#63914C414yescomplemented
15#63642—22no—
16C3×#821—24no—
17#63579—22no—
18#63562—24no—
19C2×#940—32no—
20C2×C3×#102—32no—
21C2×#832—32no—
22C2×#821D312yescomplemented
23C2×#815—32no—
24C2×#815—61no—
25#4977—32no—
26C2×#809—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×#625—28no—
38C2×#625—48no—
39C2×C32×C8—21no—
40C2×C32×C8—21no—
41C2×C32×C8D412yescomplemented
42C4×C3⋊Dic3C2×C412yes—
43C4×C3⋊Dic3D412yes—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D412yescomplemented
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3—22no—
49#1961—91noSylow
50C22×C3×D4—32no—
51C22×#67—64no—
52C22×D12C2×D312yes—
53C22×C3×C8—21no—
54C22×C3×C8C2×D312yes—
55C2×C3×C4⋊C4—32no—
56#940—38no—
57#940—64no—
58C2×C4⋊Dic3C2×D312yes—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61C22×C3⋊C8—32no—
62C22×C3⋊C8—61no—
63C3×#102—64no—
64#832—64no—
65C3⋊#95—64no—
66#821—24no—
67#815—64no—
68#815—64no—
69#809—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—24no—
83C2×C3⋊Dic3C22⋊C414yes—
84C2×C3×Dic3—42no—
85C2×C3×Dic3—44no—
86C3×D12—24no—
87C3×D12—24no—
88C3×D12—42no—
89C3×D12—42no—
90#625—416no—
91C32×C8—22no—
92C3⋊(C3⋊C8)—22no—
93C2×#127—91no—
94C2×#102—32no—
95C2×#102—92no—
96C2×#97—91no—
97#382—91no—
98C24×C3—62no—
99C23×D3—22no—
100C2×C3×D4—34no—
101C2×C3×D4—62no—
102C2×C3×D4—62no—
103C2×C3×D4—62no—
104C2×C3×D4—62no—
105C2×C3×D4—62no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C2×#67—616no—
110C2×#67—128no—
111C2×#67—128no—
112C22×Dic3—22no—
113C22×Dic3—34no—
114C22×Dic3—62no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—22no—
119C2×D12—22no—
120C2×D12C4×D314yes—
121C2×C3×C8—22no—
122C2×C3×C8—22no—
123C2×C3×C8—22no—
124C2×C3×C8—22no—
125C2×C3×C8—22no—
126C2×C3×C8#6714yescomplemented
127C3×C4⋊C4—62no—
128C3×C4⋊C4—62no—
129C4⋊Dic3—22no—
130C4⋊Dic3—22no—
131C4×Dic3—34no—
132C4×Dic3—34no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C2×C3⋊C8—34no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32#12411yescharacteristic
143C22×C32#12711yescharacteristic
144C22×C32AGL(1,ℤ/8)14yes—
145C2×C3×D3—44no—
146C2×C3×D3—48no—
147C2×C3×D3—84no—
148C2×C3×D3—82no—
149C2×C3×D3—82no—
150C32×C4C4×D411yescharacteristic
151C32×C4C4×D411yescharacteristic
152C32×C4#12111yescharacteristic
153C32×C4#12111yescharacteristic
154C3⋊Dic3—24no—
155C3×Dic3—82no—
156C22×D4—32no—
157C22×D4—182no—
158C22×C8—91no—
159C22×C8D3211yescharacteristic
160#127—94no—
161#127—182no—
162C2×C4⋊C4—32no—
163C2×C42—91no—
164#102—64no—
165#102—184no—
166#97—182no—
167#95—182no—
168C23×C3—21no—
169C23×C3—64no—
170C23×C3—122no—
171C23×C3—124no—
172C23×C3—124no—
173C23×C3—122no—
174C23×C3D3×D412yes—
175C22×D3—24no—
176C22×D3—42no—
177C22×D3—44no—
178C22×D3—44no—
179C22×D3—42no—
180C3×D4—64no—
181C3×D4—64no—
182C3×D4—122no—
183C3×D4—122no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—124no—
191C2×C3×C4—122no—
192C2×C3×C4C2×C4×D312yes—
193C2×C3×C4#23512yes—
194C2×C3×C4D3×D412yes—
195C2×C3×C4D3×D412yes—
196C2×C3×C4#23712yes—
197C2×C3×C4C2×#6712yes—
198#67—1232no—
199C2×Dic3—38no—
200C2×Dic3—44no—
201C2×Dic3—42no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—124no—
206D12—24no—
207D12—24no—
208D12—42no—
209D12—42no—
210C3×C8—24no—
211C3×C8—24no—
212C3⋊C8—64no—
213C3⋊C8—64no—
214C2×C32#39011yescharacteristic
215C2×C32#41812yes—
216C2×C32#49012yes—
217C2×C32#49612yes—
218C3×D3—84no—
219C24—62no—
220C2×D4—34no—
221C2×D4—62no—
222C2×D4—62no—
223C2×D4—62no—
224C2×D4—62no—
225C2×D4—62no—
226C2×D4—188no—
227C2×D4—368no—
228C22×C4—62no—
229C22×C4—92no—
230C22×C4C2×D3211yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—92no—
234C2×C8—181no—
235C2×C8—181no—
236C2×C8#62512yescomplemented
237C4⋊C4—62no—
238C4⋊C4—62no—
239C42—92no—
240C42—92no—
241C22×C3—24no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—124no—
246C22×C3—128no—
247C22×C3—242no—
248C22×C3—242no—
249C22×C3—244no—
250C22×C3D3×C22⋊C412yes—
251C22×C3#88512yes—
252C22×C3#91114yes—
253C22×C3#91414yes—
254C22×C3#94012yes—
255C2×D3—44no—
256C2×D3—48no—
257C2×D3—82no—
258C2×D3—82no—
259C2×D3—84no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—242no—
265C3×C4#67⋊C412yes—
266C3×C4#88412yes—
267C3×C4C4×#6712yes—
268C3×C4#93912yes—
269Dic3—68no—
270Dic3—82no—
271Dic3—124no—
272C32#196111yescharacteristic, complemented, Sylow
273C23—64no—
274C23—124no—
275C23—124no—
276C23—122no—
277C23—122no—
278C23#380211yescharacteristic
279D4—64no—
280D4—64no—
281D4—122no—
282D4—122no—
283D4—3616no—
284C2×C4—94no—
285C2×C4—124no—
286C2×C4—122no—
287C2×C4—184no—
288C2×C4#379811yescharacteristic
289C2×C4C4×D3211yescharacteristic
290C2×C4#380211yescharacteristic
291C2×C4#380511yescharacteristic
292C2×C4C2×#62511yescharacteristic
293C2×C4#381111yescharacteristic
294C8—22no—
295C8—182no—
296C2×C3—21no—
297C2×C3—22no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—244no—
301C2×C3#476414yes—
302C2×C3#477014yes—
303C2×C3#495712yes—
304C2×C3#515412yes—
305C2×C3#517612yes—
306D3—84no—
307C22—124no—
308C22—128no—
309C22—242no—
310C22—242no—
311C22—244no—
312C22#6379814yes—
313C22#6391411yescharacteristic
314C22#6391511yescharacteristic
315C22#6392111yescharacteristic
316C4—184no—
317C4—242no—
318C4C4×#62511yescharacteristic
319C4#6390211yescharacteristic
320C4#6391211yescharacteristic
321C4#6398011yescharacteristic
322C3—21no—
323C3#7016012yescomplemented
324C2—244no—
325C2#1059088712yes—
326C2#1059088812yes—
327C2#1059094112yes—
328C2#1059138511yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63914C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1961
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. #10591230C2semidirect
5. C2×#63562C2semidirect
14. #63914C4semidirect
22. C2×#821D3semidirect
41. C2×C32×C8D4semidirect
46. C2×C3⋊(C3⋊C8)D4semidirect
126. C2×C3×C8#67semidirect
236. C2×C8#625semidirect
272. 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
C2×#636422
C2×C3×#8212
#105912302
C2×#635622
#701603