Finite Group Databasebeta

← C2×#10593386 #11869406

Subgroups — C2×#10593386 #11869406

Order 1152.

830 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 127 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×#63900C211yesmaximal, characteristic
2C2×#63865C211yesmaximal, characteristic
3C2×#63778C211yesmaximal, characteristic
4C2×#63742C212yesmaximal, complemented
5C2×#63740C212yesmaximal, complemented
6#10593386C218yesmaximal, direct product factor
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#627C2211yescharacteristic
9C22×#624—21no—
10C22×#622C2212yes—
11C2×C3×C4⋊Dic3—21no—
12C2×C3×Dic3⋊C4—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2212yes—
15C2×#3722—21no—
16#63900—22no—
17#63900C2214yes—
18#63865—22no—
19#63865C2214yes—
20#63778C2214yes—
21#63742C2218yescomplemented
22#63740C2218yescomplemented
23C2×#896—61no—
24C2×D3×C4⋊C4—61no—
25C23×C3⋊D3D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3C2311yescharacteristic
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3D412yes—
30C2×C4×C3⋊D3C2312yes—
31C22×C3×Dic3—21no—
32C22×C3×Dic3—21no—
33C22×C3×Dic3—22no—
34C2×#627—24no—
35C2×#627—21no—
36C2×#627C2312yes—
37C2×#624—24no—
38C2×#624—44no—
39C2×#622—24no—
40C2×#622C2314yes—
41C3×C4⋊Dic3—24no—
42C3×Dic3⋊C4—24no—
43#3724—21no—
44#3724—22no—
45#3724C2312yes—
46#3724C2314yes—
47#3722—24no—
48C2×#483—91nomaximal, Sylow
49C22×C4×D3—61no—
50C22×C4×D3—61no—
51C22×C4×D3—62no—
52C22×Dic6—61no—
53C2×C3×C4⋊C4—61no—
54C2×C3×C4⋊C4—61no—
55C2×(C2×D3)⋊C4—61no—
56C2×(C2×D3)⋊C4—61no—
57C2×C4⋊Dic3—21no—
58C2×Dic3⋊C4—21no—
59C2×Dic3⋊C4—62no—
60C2×Dic3⋊C4—61no—
61#896—64no—
62#896—64no—
63D3×C4⋊C4—64no—
64D3×C4⋊C4—64no—
65C23×C32C2×D411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—22no—
68C22×C3⋊D3SD1614yes—
69C22×C3⋊D3C2×D412yes—
70C2×C32×C4—22no—
71C2×C32×C4C2×D412yes—
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3#4114yes—
74C2×C3⋊Dic3C2411yescharacteristic
75C4×C3⋊D3—24no—
76C4×C3⋊D3—24no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—44no—
82C2×C3×Dic3—42no—
83#627—24no—
84#627—42no—
85#624—48no—
86#622—24no—
87C2×C22⋊Q8—91no—
88C22×C4⋊C4—91no—
89#483—98no—
90C2×#106—92no—
91C2×#103—92no—
92C2×C22⋊C8—91no—
93C23×D3—61no—
94C23×D3—61no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—61no—
98C22×C3×C4—62no—
99C22×C3×C4—61no—
100C22×Dic3—21no—
101C22×Dic3—21no—
102C22×Dic3—22no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—68no—
110C2×C4×D3—68no—
111C2×C4×D3—124no—
112C2×C4×D3—128no—
113C2×Dic6—62no—
114C2×Dic6—62no—
115C2×Dic6—124no—
116C3×C4⋊C4—64no—
117C3×C4⋊C4—64no—
118(C2×D3)⋊C4—64no—
119(C2×D3)⋊C4—64no—
120C4⋊Dic3—24no—
121Dic3⋊C4—24no—
122Dic3⋊C4—64no—
123Dic3⋊C4—62no—
124Dic3⋊C4—64no—
125Dic3⋊C4—62no—
126C22×C32#12312yes—
127C22×C32C2×SD1612yes—
128C22×C32#13712yes—
129C22×C32C22×D411yescharacteristic
130C2×C3⋊D3—22no—
131C2×C3⋊D3—22no—
132C2×C3⋊D3—28no—
133C2×C3⋊D3C2×SD1614yes—
134C32×C4—22no—
135C3⋊Dic3#12312yes—
136C3⋊Dic3C2×#4112yes—
137C3×Dic3—42no—
138C3×Dic3—44no—
139C3×Dic3—42no—
140C22×Q8—91no—
141C23×C4—91no—
142C23×C4—181no—
143C22×C8—92no—
144C22⋊Q8—94no—
145C22⋊Q8—182no—
146C2×C4⋊C4—61no—
147C2×C4⋊C4—61no—
148C2×C4⋊C4—94no—
149C2×C4⋊C4—92no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—182no—
152C2×C22⋊C4—181no—
153#106—98no—
154#103—98no—
155C22⋊C8—94no—
156C23×C3—21no—
157C23×C3—21no—
158C22×D3—64no—
159C22×D3—62no—
160C22×D3—64no—
161C22×D3—62no—
162C22×D3—64no—
163C22×D3—64no—
164C22×D3—122no—
165C22×D3—122no—
166C2×C3×C4—24no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—42no—
170C2×C3×C4—62no—
171C2×C3×C4—64no—
172C2×C3×C4—62no—
173C2×C3×C4—122no—
174C2×C3×C4—124no—
175C2×C3×C4—122no—
176C2×Dic3—22no—
177C2×Dic3—22no—
178C2×Dic3—24no—
179C2×Dic3—42no—
180C2×Dic3—44no—
181C2×Dic3—42no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C4×D3—68no—
189C4×D3—68no—
190C4×D3—124no—
191C4×D3—124no—
192C4×D3—1216no—
193Dic6—124no—
194Dic6—124no—
195C2×C32#48314yescomplemented
196C2×C32C2×#12311yescharacteristic
197C2×C32C22×SD1611yescharacteristic
198C2×C32C2×#13711yescharacteristic
199C3⋊D3—24no—
200C24—91no—
201C2×Q8—92no—
202C2×Q8—181no—
203C2×Q8—184no—
204C22×C4—61no—
205C22×C4—61no—
206C22×C4—62no—
207C22×C4—91no—
208C22×C4—92no—
209C22×C4—92no—
210C22×C4—184no—
211C22×C4—184no—
212C22×C4—364no—
213C22×C4GO+(4,𝔽2)11yescharacteristic
214C2×C8—94no—
215C2×C8—184no—
216C4⋊C4—64no—
217C4⋊C4—64no—
218C4⋊C4—94no—
219C4⋊C4—92no—
220C4⋊C4—182no—
221C4⋊C4—181no—
222C22⋊C4—184no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—22no—
230C22×C3—22no—
231C2×D3—64no—
232C2×D3—64no—
233C2×D3—64no—
234C2×D3—616no—
235C2×D3—64no—
236C2×D3—122no—
237C2×D3—128no—
238C2×D3—122no—
239C3×C4—24no—
240C3×C4—42no—
241C3×C4—122no—
242C3×C4—124no—
243C3×C4—122no—
244Dic3—42no—
245Dic3—44no—
246Dic3—42no—
247Dic3—62no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251C32C2×#48311yescharacteristic, complemented, Sylow
252C23—92no—
253C23—94no—
254C23—182no—
255C23—182no—
256C23C2×GO+(4,𝔽2)11yescharacteristic
257Q8—184no—
258Q8—362no—
259C2×C4—22no—
260C2×C4—62no—
261C2×C4—62no—
262C2×C4—64no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—94no—
266C2×C4—122no—
267C2×C4—124no—
268C2×C4—122no—
269C2×C4—184no—
270C2×C4—184no—
271C2×C4—368no—
272C2×C4C2×GO+(4,𝔽2)12yes—
273C8—184no—
274C2×C3—24no—
275C2×C3—24no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282D3—68no—
283D3—124no—
284C22—94no—
285C22—188no—
286C22—182no—
287C22—182no—
288C22#6422612yes—
289C22#6422712yes—
290C22#6423312yes—
291C22C22×GO+(4,𝔽2)11yescharacteristic
292C4—22no—
293C4—92no—
294C4—92no—
295C4—122no—
296C4—124no—
297C4—122no—
298C3—21no—
299C3—21no—
300C2—184no—
301C2#1059338614yesdirect product factor
302C2C2×#6422611yescharacteristic
303C2C2×#6422711yescharacteristic
304C2C2×#6423311yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#483
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63742C2semidirect
5. C2×#63740C2semidirect
6. #10593386C2direct (N × H)
21. #63742C22semidirect
22. #63740C22semidirect
195. C2×C32#483semidirect
251. C32C2×#483semidirect
301. C2#10593386direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638652
C2×#637782
C2×#637422
C2×#637402
#105933862
C2×#4839