Finite Group Databasebeta

← C2×#10591403 #11873444

Subgroups — C2×#10591403 #11873444

Order 1152.

989 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 989 conjugacy classes of subgroups — too many to draw. Only its 212 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×#64145C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal
4#10591403C218yesmaximal, direct product factor
5C2×#63567C212yesmaximal, complemented
6C2×#63553C211yesmaximal, characteristic, complemented
7C2×#4768—32nomaximal
8C22×C32×D4C2211yescharacteristic
9C22×#634C2211yescharacteristic
10C2×#3757—22no—
11#64145—22no—
12#64145C2214yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic3⋊Dic3—22no—
17#63872—22no—
18#63872C2214yescomplemented
19C3×#832C2218yes—
20#63567C2218yescomplemented
21#63553C2214yescomplemented
22C2×#936—32no—
23C2×#936—61no—
24C2×#890—32no—
25C2×C3×#102—32no—
26C2×#832D312yes—
27C2×#816—32no—
28C2×C8×Dic3—32no—
29C2×#810—32no—
30#4768—316no—
31C24×C32—21no—
32C2×C32×D4—21no—
33C2×C32×D4—24no—
34C2×C32×D4C2312yes—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D412yes—
38C2×#634—24no—
39C2×#634—21no—
40C2×#634C2312yes—
41C22×C3×Dic3—22no—
42#3757—28no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3C2312yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3C2314yes—
47C2×C3×C3⋊C8—24no—
48C2×C3×C3⋊C8C2314yes—
49Dic3⋊Dic3—28no—
50C2×#488—91noSylow
51C22×C3×D4—21no—
52C22×C3×D4C2×D312yes—
53C22×Dic6—32no—
54C22×Dic6—61no—
55C22×C3×C8—32no—
56C2×C3×C4⋊C4—32no—
57C2×#217—62no—
58C2×#217—62no—
59C2×#217—64no—
60#936—38no—
61#936—64no—
62#936—64no—
63#936—64no—
64C2×C4⋊Dic3—62no—
65C2×C4⋊Dic3C2×D312yes—
66C2×Dic3⋊C4—62no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—61no—
69C22×C3⋊C8C2×D312yes—
70#890—38no—
71#890—64no—
72C3×#102—38no—
73#832C2×D318yes—
74#816—38no—
75C8×Dic3—38no—
76#810—38no—
77C23×C32—22no—
78C23×C32—42no—
79C23×C32—44no—
80C23×C32C2×D411yescharacteristic
81C32×D4—24no—
82C32×D4—42no—
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4#4114yes—
85C2×C32×C4C2411yescharacteristic
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3C2×D414yes—
90#634—24no—
91#634—42no—
92C2×C3×Dic3—24no—
93C2×C3×Dic3—44no—
94C3×C3⋊C8—24no—
95C2×#125—91no—
96C2×#124—91no—
97#488—98no—
98C2×#103—92no—
99C2×#102—32no—
100C2×C4×C8—91no—
101C24×C3—22no—
102C24×C3—22no—
103C2×C3×D4—22no—
104C2×C3×D4—24no—
105C2×C3×D4—22no—
106C2×C3×D4—24no—
107C2×C3×D4—22no—
108C2×C3×D4—44no—
109C2×C3×D4C22×D314yes—
110C22×C3×C4—21no—
111C22×C3×C4—62no—
112C22×C3×C4C22×D312yes—
113C22×Dic3—22no—
114C22×Dic3—32no—
115C22×Dic3—32no—
116C22×Dic3—62no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C2×Dic6—34no—
120C2×Dic6—62no—
121C2×Dic6—64no—
122C2×Dic6—64no—
123C2×Dic6—62no—
124C2×Dic6—62no—
125C2×Dic6—124no—
126C2×C3×C8—34no—
127C2×C3×C8—64no—
128C3×C4⋊C4—34no—
129C3×C4⋊C4—62no—
130#217—68no—
131#217—68no—
132#217—616no—
133C4⋊Dic3—22no—
134C4⋊Dic3—68no—
135C4⋊Dic3C22×D314yes—
136Dic3⋊C4—68no—
137C4×Dic3—34no—
138C4×Dic3—34no—
139C4×Dic3—62no—
140C4×Dic3—62no—
141C2×C3⋊C8—24no—
142C2×C3⋊C8C22×D314yes—
143C22×C32—42no—
144C22×C32—44no—
145C22×C32—84no—
146C22×C32#12412yes—
147C22×C32#13514yes—
148C22×C32C22×D411yescharacteristic
149C32×C4#12412yes—
150C32×C4C2×#4112yes—
151C3⋊Dic3—24no—
152C3⋊Dic3—42no—
153C3×Dic3—44no—
154C22×Q8—91no—
155C22×D4D3211yescharacteristic
156C22×C8—32no—
157#125—94no—
158#125—182no—
159#124—94no—
160#124—182no—
161C2×C4⋊C4—32no—
162C2×C4⋊C4—182no—
163C2×C22⋊C4—182no—
164C2×C42—91no—
165#103—98no—
166#102—38no—
167C4×C8—94no—
168C23×C3—24no—
169C23×C3—24no—
170C23×C3—21no—
171C23×C3—44no—
172C23×C3—48no—
173C23×C3—44no—
174C23×C3—44no—
175C23×C3—44no—
176C23×C3D3×D412yes—
177C3×D4—24no—
178C3×D4—24no—
179C3×D4—44no—
180C3×D4—44no—
181C3×D4—44no—
182C2×C3×C4—21no—
183C2×C3×C4—24no—
184C2×C3×C4—21no—
185C2×C3×C4—64no—
186C2×C3×C4—124no—
187C2×C3×C4#23514yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4#23714yes—
190C2×C3×C4C23×D312yes—
191C2×Dic3—24no—
192C2×Dic3—34no—
193C2×Dic3—34no—
194C2×Dic3—44no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—64no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202C2×Dic3—124no—
203Dic6—64no—
204Dic6—64no—
205Dic6—124no—
206Dic6—124no—
207Dic6—124no—
208C3×C8—64no—
209C3⋊C8—24no—
210C2×C32—82no—
211C2×C32#48814yescomplemented
212C2×C32C2×#12411yescharacteristic
213C2×C32C2×#13512yes—
214C24—21no—
215C2×Q8—92no—
216C2×Q8—181no—
217C2×Q8—184no—
218C2×D4—24no—
219C2×D4—21no—
220C2×D4C2×D3212yes—
221C22×C4—62no—
222C22×C4—92no—
223C22×C4—181no—
224C22×C4C2×D3211yescharacteristic
225C2×C8—34no—
226C2×C8—64no—
227C4⋊C4—34no—
228C4⋊C4—62no—
229C4⋊C4—188no—
230C22⋊C4—188no—
231C42—92no—
232C42—92no—
233C22×C3—21no—
234C22×C3—24no—
235C22×C3—22no—
236C22×C3—44no—
237C22×C3—48no—
238C22×C3—44no—
239C22×C3—44no—
240C22×C3—44no—
241C22×C3—88no—
242C22×C3—88no—
243C22×C3#88514yes—
244C22×C3#91214yes—
245C22×C3#91614yes—
246C22×C3C2×D3×D412yes—
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—124no—
250C3×C4#88514yes—
251C3×C4C2×#23512yes—
252C3×C4C2×#23712yes—
253Dic3—44no—
254Dic3—64no—
255Dic3—64no—
256Dic3—124no—
257Dic3—124no—
258Dic3—124no—
259C32C2×#48811yescharacteristic, complemented, Sylow
260C23—22no—
261C23—44no—
262C23—42no—
263C23#381111yescharacteristic
264Q8—184no—
265Q8—362no—
266D4—24no—
267D4—42no—
268C2×C4—64no—
269C2×C4—94no—
270C2×C4—124no—
271C2×C4—184no—
272C2×C4—182no—
273C2×C4—362no—
274C2×C4#380414yes—
275C2×C4#381111yescharacteristic
276C2×C4C22×D3211yescharacteristic
277C8—64no—
278C2×C3—22no—
279C2×C3—21no—
280C2×C3—24no—
281C2×C3—84no—
282C2×C3—84no—
283C2×C3#476818yescomplemented
284C2×C3C2×#88512yes—
285C2×C3C2×#91212yes—
286C2×C3C2×#91612yes—
287C22—44no—
288C22—42no—
289C22—84no—
290C22#6393614yes—
291C22#6395312yes—
292C22C2×#381111yescharacteristic
293C4—124no—
294C4—184no—
295C4—362no—
296C4#6395312yes—
297C4C2×#380412yes—
298C3—21no—
299C3C2×#476812yescomplemented
300C2—82no—
301C2#1059140314yesdirect product factor
302C2C2×#6393612yes—
303C2C2×#6395311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63872C2semidirect
4. #10591403C2direct (N × H)
5. C2×#63567C2semidirect
6. C2×#63553C2semidirect
18. #63872C22semidirect
20. #63567C22semidirect
21. #63553C22semidirect
211. C2×C32#488semidirect
259. C32C2×#488semidirect
283. C2×C3#4768semidirect
299. C3C2×#4768semidirect
301. C2#10591403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C2×#638722
C2×C3×#8322
#105914032
C2×#635672
C2×#635532
C2×#47683