Finite Group Databasebeta

← C2×#10591628 #11874218

Subgroups — C2×#10591628 #11874218

Order 1152.

1249 conjugacy classes of subgroups; only the 260 normal subgroups are shown.

normal subgroups only

This group has 1249 conjugacy classes of subgroups — too many to draw. Only its 260 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×#64153C211yesmaximal, characteristic
2C22×C3×#216C212yesmaximal
3C2×#63873C211yesmaximal, characteristic
4C22×#3719C212yesmaximal
5#10591628C218yesmaximal, direct product factor
6C2×#63553C211yesmaximal, characteristic
7C2×#5183—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11#64153—22no—
12#64153C2214yes—
13C2×#3750—22no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×#216—28no—
16C2×C3×#216C2218yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3724—22no—
19#63873—22no—
20#63873C2214yes—
21C2×#3719—28no—
22C2×#3719C2218yes—
23#63553C2214yes—
24C22×C3×Q16—32no—
25C2×#944—32no—
26C2×#944—32no—
27C2×#944—61no—
28C22×#216—32no—
29C22×#216D312yes—
30C22×Dic12—32no—
31#5183—316no—
32C2×C8×Dic3—32no—
33C2×C32×Q8—21no—
34C2×C32×Q8—24no—
35C2×C32×Q8C2312yes—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D412yes—
40C2×#634—24no—
41C2×#634—21no—
42C2×#634C2312yes—
43C22×C3×Dic3—22no—
44C2×C3×Dic6—24no—
45C2×C3×Dic6—24no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6C2314yes—
48#3750—28no—
49C4×C3⋊Dic3D412yes—
50C4×C3⋊Dic3C2312yes—
51C3×#216—216no—
52C2×C3×C3⋊C8D418yes—
53C2×C3×C3⋊C8C2314yes—
54#3724—28no—
55#3719—216no—
56C2×#494—91noSylow
57C22×C3×Q8—21no—
58C22×C3×Q8—32no—
59C22×C3×Q8C2×D312yes—
60C22×Dic6—32no—
61C22×Dic6—61no—
62C22×Dic6C2×D312yes—
63C2×C3×Q16—38no—
64C2×C3×Q16—68no—
65C22×C3×C8—32no—
66#944—38no—
67#944—38no—
68#944—64no—
69#944—64no—
70#944—64no—
71#944—64no—
72C2×#216—28no—
73C2×#216—38no—
74C2×#216—68no—
75C2×#216C2×D318yes—
76C2×Dic3⋊C4—64no—
77C2×Dic3⋊C4—64no—
78C2×Dic3⋊C4—64no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C22×C3⋊C8C2×D312yes—
82C2×Dic12—38no—
83C2×Dic12—68no—
84C8×Dic3—38no—
85C23×C32C2×D411yescharacteristic
86C32×Q8—24no—
87C32×Q8—42no—
88C2×C32×C4—22no—
89C2×C32×C4—42no—
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4C2×D414yes—
92C2×C32×C4C2411yescharacteristic
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—42no—
95C2×C3⋊Dic3Q1618yescomplemented
96C2×C3⋊Dic3C2×D414yes—
97#634—24no—
98#634—42no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—44no—
101C3×Dic6—24no—
102C3×Dic6—24no—
103C3×Dic6—44no—
104C3×C3⋊C8C2×D418yes—
105C22×Q16—32no—
106C22×Q16—92no—
107C2×C4⋊Q8—91no—
108C2×C4⋊Q8—91no—
109#494—98no—
110C2×C4×C8—91no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—24no—
114C2×C3×Q8—24no—
115C2×C3×Q8—22no—
116C2×C3×Q8—34no—
117C2×C3×Q8—44no—
118C2×C3×Q8—62no—
119C2×C3×Q8—64no—
120C2×C3×Q8—64no—
121C2×C3×Q8C22×D314yes—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—21no—
125C22×C3×C4—62no—
126C22×C3×C4C22×D312yes—
127C22×Dic3—22no—
128C22×Dic3—34no—
129C22×Dic3—62no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C2×Dic6—24no—
133C2×Dic6—24no—
134C2×Dic6—22no—
135C2×Dic6—34no—
136C2×Dic6—62no—
137C2×Dic6—64no—
138C2×Dic6—64no—
139C2×Dic6—62no—
140C2×Dic6—62no—
141C2×Dic6—124no—
142C2×Dic6C22×D314yes—
143C3×Q16—616no—
144C2×C3×C8—38no—
145C2×C3×C8—34no—
146#216—216no—
147#216—616no—
148Dic3⋊C4—616no—
149Dic3⋊C4—616no—
150Dic3⋊C4—616no—
151C4×Dic3—34no—
152C4×Dic3—34no—
153C4×Dic3—62no—
154C4×Dic3—62no—
155C2×C3⋊C8#6718yes—
156C2×C3⋊C8C22×D314yes—
157Dic12—616no—
158C22×C32#12712yes—
159C22×C32C2×Q1614yes—
160C22×C32C22×D411yescharacteristic
161C32×C4—42no—
162C32×C4#12712yes—
163C32×C4C22×D412yes—
164C3⋊Dic3—42no—
165C3⋊Dic3C2×Q1618yescomplemented
166C3×Dic3—44no—
167C22×Q8—32no—
168C22×Q8—91no—
169C22×Q8D3211yescharacteristic
170C2×Q16—38no—
171C2×Q16—68no—
172C2×Q16—98no—
173C2×Q16—188no—
174C22×C8—32no—
175C4⋊Q8—94no—
176C4⋊Q8—94no—
177C4⋊Q8—182no—
178C4⋊Q8—182no—
179C2×C4⋊C4—182no—
180C2×C4⋊C4—182no—
181C2×C42—91no—
182C4×C8—94no—
183C23×C3—21no—
184C23×C3D3×D412yes—
185C3×Q8—24no—
186C3×Q8—24no—
187C3×Q8—44no—
188C3×Q8—44no—
189C3×Q8—44no—
190C3×Q8—64no—
191C3×Q8—64no—
192C3×Q8—124no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—21no—
196C2×C3×C4—24no—
197C2×C3×C4—21no—
198C2×C3×C4—44no—
199C2×C3×C4—44no—
200C2×C3×C4—64no—
201C2×C3×C4—124no—
202C2×C3×C4D3×D414yes—
203C2×C3×C4D3×D412yes—
204C2×C3×C4C2×#6714yes—
205C2×C3×C4C23×D312yes—
206C2×Dic3—24no—
207C2×Dic3—316no—
208C2×Dic3—38no—
209C2×Dic3—44no—
210C2×Dic3—68no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—124no—
215C2×Dic3—124no—
216Dic6—24no—
217Dic6—24no—
218Dic6—44no—
219Dic6—64no—
220Dic6—64no—
221Dic6—124no—
222Dic6—124no—
223Dic6—124no—
224C3×C8—38no—
225C3⋊C8C2×#6718yes—
226C2×C32#49414yescomplemented
227C2×C32C2×#12711yescharacteristic
228C2×C32C22×Q1612yes—
229C2×Q8—21no—
230C2×Q8—24no—
231C2×Q8—34no—
232C2×Q8—62no—
233C2×Q8—64no—
234C2×Q8—64no—
235C2×Q8—92no—
236C2×Q8—181no—
237C2×Q8—184no—
238C2×Q8C2×D3212yes—
239C22×C4—21no—
240C22×C4—62no—
241C22×C4—92no—
242C22×C4—181no—
243C22×C4C2×D3211yescharacteristic
244Q16—616no—
245Q16—1816no—
246C2×C8—34no—
247C2×C8—38no—
248C4⋊C4—188no—
249C4⋊C4—188no—
250C42—92no—
251C42—92no—
252C22×C3—21no—
253C22×C3—24no—
254C22×C3—22no—
255C22×C3D3×Q1618yes—
256C22×C3#94014yes—
257C22×C3C2×D3×D412yes—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—44no—
261C3×C4—44no—
262C3×C4—124no—
263C3×C4#94014yes—
264C3×C4C2×D3×D412yes—
265C3×C4C22×#6712yes—
266Dic3—316no—
267Dic3—44no—
268Dic3—68no—
269Dic3—124no—
270Dic3—124no—
271C32C2×#49411yescharacteristic, complemented, Sylow
272C23#381111yescharacteristic
273Q8—24no—
274Q8—42no—
275Q8—64no—
276Q8—64no—
277Q8—124no—
278Q8—184no—
279Q8—362no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—64no—
283C2×C4—94no—
284C2×C4—98no—
285C2×C4—124no—
286C2×C4—182no—
287C2×C4—362no—
288C2×C4D3×#6714yes—
289C2×C4#381111yescharacteristic
290C2×C4C22×D3211yescharacteristic
291C8—38no—
292C2×C3—22no—
293C2×C3—24no—
294C2×C3—21no—
295C2×C3#518318yescomplemented
296C2×C3C2×D3×Q1614yes—
297C2×C3C2×#94012yes—
298C22#6394414yes—
299C22#6397912yes—
300C22C2×#381111yescharacteristic
301C4—42no—
302C4—98no—
303C4—124no—
304C4—362no—
305C4#6397912yes—
306C4C2×D3×#6712yes—
307C3—21no—
308C3C2×#518312yescomplemented
309C2#1059162814yesdirect product factor
310C2C2×#6394412yes—
311C2C2×#6397911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32C2×#494
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
5. #10591628C2direct (N × H)
95. C2×C3⋊Dic3Q16semidirect
165. C3⋊Dic3C2×Q16semidirect
226. C2×C32#494semidirect
271. C32C2×#494semidirect
295. C2×C3#5183semidirect
308. C3C2×#5183semidirect
309. C2#10591628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C22×C3×#2162
C2×#638732
C22×#37192
#105916282
C2×#635532
C2×#51833