Finite Group Databasebeta

← C2×#10593448 #11865659

Subgroups — C2×#10593448 #11865659

Order 1152.

774 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 135 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×#3776C212yesmaximal
2C2×#63919C211yesmaximal, characteristic
3C2×#63838C211yesmaximal, characteristic
4C2×#63779C211yesmaximal, characteristic
5C2×#63740C212yesmaximal
6#10593448C218yesmaximal, direct product factor
7C22×#627C2212yes—
8C22×#627C2211yescharacteristic
9C22×#622C2212yes—
10C2×#3776—28no—
11C2×#3776C2218yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3—21no—
14C2×C3×Dic3⋊C4—21no—
15C2×#3724—21no—
16C2×#3724C2211yescharacteristic
17C2×Dic32—21no—
18#63919—22no—
19#63919C2214yes—
20#63838—22no—
21#63838C2214yes—
22#63779C2214yes—
23#63740C2218yes—
24C2×#888—61no—
25C2×#887—61no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—22no—
32C2×#627—21no—
33C2×#627—22no—
34C2×#627—24no—
35C2×#627—24no—
36C2×#627—22no—
37C2×#627D414yes—
38C2×#627C2314yes—
39C2×#627C2312yes—
40C2×#622—24no—
41C2×#622C2314yes—
42#3776—216no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3C2312yes—
45C3×C4⋊Dic3—24no—
46C3×Dic3⋊C4—24no—
47#3724—21no—
48#3724—24no—
49#3724C2312yes—
50Dic32—24no—
51C2×#462—91nomaximal, Sylow
52C22×Dic6—61no—
53C22×Dic6—62no—
54C2×C3×C4⋊C4—61no—
55C2×C3×C4⋊C4—61no—
56C2×C4⋊Dic3—21no—
57C2×Dic3⋊C4—21no—
58C2×Dic3⋊C4—61no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—61no—
63C2×C4×Dic3—61no—
64#888—64no—
65#888—64no—
66#887—64no—
67#887—64no—
68C23×C32C2×D411yescharacteristic
69C2×C32×C4—22no—
70C2×C32×C4C2×D412yes—
71C2×C3⋊Dic3Q1614yescomplemented
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3#4112yes—
76C2×C3⋊Dic3C2411yescharacteristic
77C2×C3×Dic3—24no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—44no—
82C2×C3×Dic3—42no—
83#627—24no—
84#627—22no—
85#627—24no—
86#627—24no—
87#627—44no—
88#627C2×D414yes—
89#622—24no—
90C22×Q16—92no—
91C2×C4⋊Q8—91no—
92C2×C4×Q8—91no—
93#462—98no—
94C2×C4⋊C8—91no—
95C2×#103—92no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—61no—
99C22×C3×C4—61no—
100C22×C3×C4—62no—
101C22×Dic3—21no—
102C22×Dic3—21no—
103C22×Dic3—22no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C2×Dic6—62no—
109C2×Dic6—64no—
110C2×Dic6—64no—
111C2×Dic6—62no—
112C2×Dic6—64no—
113C2×Dic6—64no—
114C2×Dic6—124no—
115C2×Dic6—124no—
116C3×C4⋊C4—64no—
117C3×C4⋊C4—64no—
118C4⋊Dic3—24no—
119Dic3⋊C4—24no—
120Dic3⋊C4—62no—
121Dic3⋊C4—62no—
122Dic3⋊C4—68no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C4×Dic3—64no—
128C4×Dic3—64no—
129C22×C32#12112yes—
130C22×C32C2×Q1612yes—
131C22×C32#13712yes—
132C22×C32C22×D411yescharacteristic
133C32×C4—22no—
134C3⋊Dic3#12112yes—
135C3⋊Dic3C2×Q1614yescomplemented
136C3⋊Dic3C22×D411yescharacteristic
137C3⋊Dic3C2×#4111yescharacteristic
138C3×Dic3—24no—
139C3×Dic3—44no—
140C3×Dic3—42no—
141C22×Q8—91no—
142C22×Q8—92no—
143C2×Q16—98no—
144C2×Q16—188no—
145C22×C8—92no—
146C4⋊Q8—94no—
147C4⋊Q8—182no—
148C4×Q8—94no—
149C4×Q8—182no—
150C2×C4⋊C4—61no—
151C2×C4⋊C4—61no—
152C2×C4⋊C4—91no—
153C2×C4⋊C4—181no—
154C2×C42—91no—
155C2×C42—181no—
156C4⋊C8—94no—
157#103—98no—
158C23×C3—21no—
159C23×C3—21no—
160C2×C3×C4—24no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—42no—
164C2×C3×C4—62no—
165C2×C3×C4—64no—
166C2×C3×C4—62no—
167C2×C3×C4—64no—
168C2×C3×C4—124no—
169C2×C3×C4—122no—
170C2×Dic3—22no—
171C2×Dic3—24no—
172C2×Dic3—22no—
173C2×Dic3—24no—
174C2×Dic3—44no—
175C2×Dic3—42no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188Dic6—64no—
189Dic6—68no—
190Dic6—64no—
191Dic6—124no—
192Dic6—124no—
193Dic6—128no—
194C2×C32#46214yescomplemented
195C2×C32C2×#12111yescharacteristic
196C2×C32C22×Q1611yescharacteristic
197C2×C32C2×#13711yescharacteristic
198C2×Q8—92no—
199C2×Q8—94no—
200C2×Q8—94no—
201C2×Q8—181no—
202C2×Q8—182no—
203C2×Q8—182no—
204C2×Q8—184no—
205C2×Q8—184no—
206C22×C4—61no—
207C22×C4—61no—
208C22×C4—62no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4GO+(4,𝔽2)11yescharacteristic
212Q16—1816no—
213C2×C8—94no—
214C2×C8—184no—
215C4⋊C4—64no—
216C4⋊C4—64no—
217C4⋊C4—92no—
218C4⋊C4—181no—
219C4⋊C4—184no—
220C42—92no—
221C42—92no—
222C42—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—
231C3×C4—24no—
232C3×C4—42no—
233C3×C4—64no—
234C3×C4—124no—
235C3×C4—122no—
236Dic3—24no—
237Dic3—44no—
238Dic3—42no—
239Dic3—62no—
240Dic3—61no—
241Dic3—61no—
242Dic3—62no—
243Dic3—61no—
244Dic3—61no—
245Dic3—64no—
246Dic3—64no—
247C32C2×#46211yescharacteristic, complemented, Sylow
248C23C2×GO+(4,𝔽2)11yescharacteristic
249Q8—94no—
250Q8—182no—
251Q8—184no—
252Q8—184no—
253Q8—184no—
254Q8—364no—
255C2×C4—22no—
256C2×C4—62no—
257C2×C4—64no—
258C2×C4—62no—
259C2×C4—64no—
260C2×C4—92no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—94no—
264C2×C4—92no—
265C2×C4—92no—
266C2×C4—124no—
267C2×C4—122no—
268C2×C4C2×GO+(4,𝔽2)12yes—
269C8—184no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—24no—
275C2×C3—24no—
276C2×C3—21no—
277C2×C3—21no—
278C22#6422812yes—
279C22#6423012yes—
280C22#6423912yes—
281C22C22×GO+(4,𝔽2)11yescharacteristic
282C4—22no—
283C4—64no—
284C4—94no—
285C4—91no—
286C4—91no—
287C4—92no—
288C4—124no—
289C4—122no—
290C3—21no—
291C3—21no—
292C2#1059344814yesdirect product factor
293C2C2×#6422811yescharacteristic
294C2C2×#6423011yescharacteristic
295C2C2×#6423911yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#462
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
6. #10593448C2direct (N × H)
71. C2×C3⋊Dic3Q16semidirect
135. C3⋊Dic3C2×Q16semidirect
194. C2×C32#462semidirect
247. C32C2×#462semidirect
292. C2#10593448direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37762
C2×#639192
C2×#638382
C2×#637792
C2×#637402
#105934482
C2×#4629