Finite Group Databasebeta

← C2×#10593443 #11874411

Subgroups — C2×#10593443 #11874411

Order 1152.

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

normal subgroups only

This group has 874 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, complemented
2C22×#3775C212yesmaximal
3C2×#63919C211yesmaximal, characteristic, complemented
4C2×#63915C211yesmaximal, characteristic
5C2×#63777C211yesmaximal, characteristic, complemented
6#10593443C218yesmaximal, direct product factor
7C22×#627C2212yes—
8C22×#627C2211yescharacteristic
9C22×#625C2211yescharacteristic
10C22×#622C2212yes—
11C2×#3776—28no—
12C2×#3776C2218yescomplemented
13C2×#3775—28no—
14C2×#3775C2218yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3—21no—
18C2×#3724—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63919—22no—
21#63919C2214yescomplemented
22#63915—22no—
23#63915C2214yes—
24#63777C2214yescomplemented
25C2×#888—61no—
26C2×#885—61no—
27C23×C3×D3—21no—
28C22×C32×C4D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C22×C3×Dic3—22no—
32C22×C3×Dic3—21no—
33C2×#627—24no—
34C2×#627—24no—
35C2×#627—24no—
36C2×#627—21no—
37C2×#627—22no—
38C2×#627C2312yes—
39C2×#627C2314yes—
40C2×#625—24no—
41C2×#625—21no—
42C2×#625C2312yes—
43C2×#622D418yes—
44C2×#622C2314yes—
45#3776—216no—
46#3775—216no—
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3C2312yes—
49C3×(C2×D3)⋊C4—24no—
50C3×C4⋊Dic3—24no—
51#3724—24no—
52(C2×D3)⋊Dic3—24no—
53C2×#497—91nomaximal, Sylow
54C22×#67—61no—
55C22×Dic6—61no—
56C22×Dic6—62no—
57C2×C3×C4⋊C4—61no—
58C2×C3×C22⋊C4—61no—
59C2×#217—61no—
60C2×(C2×D3)⋊C4—21no—
61C2×(C2×D3)⋊C4—61no—
62C2×C4⋊Dic3—21no—
63C2×Dic3⋊C4—62no—
64C2×C4×Dic3—61no—
65C2×C4×Dic3—61no—
66#888—64no—
67#888—64no—
68#885—64no—
69#885—64no—
70C23×C32C2×D411yescharacteristic
71C22×C3×D3—22no—
72C22×C3×D3—42no—
73C22×C3×D3—42no—
74C22×C3×D3—42no—
75C2×C32×C4—22no—
76C2×C32×C4C2×D412yes—
77C2×C3⋊Dic3—22no—
78C2×C3⋊Dic3C2×D412yes—
79C2×C3⋊Dic3C2×D411yescharacteristic
80C2×C3⋊Dic3C2×D414yes—
81C2×C3⋊Dic3C2411yescharacteristic
82C2×C3×Dic3—22no—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—44no—
85C2×C3×Dic3—42no—
86#627—24no—
87#627—24no—
88#627—24no—
89#627—44no—
90#627—42no—
91#625—24no—
92#625—42no—
93#622C2×D418yes—
94C22×Q16—92no—
95C22×SD16—92no—
96C2×C4⋊Q8—91no—
97C2×#124—91no—
98#497—98no—
99C2×#97—91no—
100C24×C3—61no—
101C23×D3—21no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—62no—
105C22×C3×C4—61no—
106C2×#67—62no—
107C2×#67—62no—
108C2×#67—124no—
109C22×Dic3—22no—
110C22×Dic3—21no—
111C22×Dic3—61no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C2×Dic6—62no—
116C2×Dic6—64no—
117C2×Dic6—62no—
118C2×Dic6—64no—
119C2×Dic6—124no—
120C2×Dic6—124no—
121C2×Dic6—124no—
122C3×C4⋊C4—64no—
123C3×C22⋊C4—64no—
124#217—64no—
125(C2×D3)⋊C4—24no—
126(C2×D3)⋊C4—64no—
127C4⋊Dic3—24no—
128Dic3⋊C4—68no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C22×C32#12712yes—
134C22×C32#13712yes—
135C22×C32#13712yes—
136C22×C32C22×D411yescharacteristic
137C2×C3×D3—42no—
138C2×C3×D3—42no—
139C2×C3×D3—42no—
140C2×C3×D3—84no—
141C32×C4—22no—
142C3⋊Dic3—22no—
143C3⋊Dic3#12712yes—
144C3⋊Dic3C22×D412yes—
145C3×Dic3—44no—
146C3×Dic3—42no—
147C22×Q8—91no—
148C22×Q8—92no—
149C22×D4—91no—
150C2×Q16—98no—
151C2×Q16—188no—
152C2×SD16—98no—
153C2×SD16—188no—
154C22×C8—92no—
155C4⋊Q8—94no—
156C4⋊Q8—182no—
157#124—94no—
158#124—182no—
159C2×C4⋊C4—61no—
160C2×C4⋊C4—181no—
161C2×C22⋊C4—61no—
162C2×C22⋊C4—181no—
163C2×C42—91no—
164#97—94no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—62no—
168C23×C3—122no—
169C23×C3—122no—
170C23×C3—122no—
171C22×D3—22no—
172C22×D3—42no—
173C22×D3—42no—
174C22×D3—42no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—42no—
179C2×C3×C4—64no—
180C2×C3×C4—62no—
181C2×C3×C4—124no—
182C2×C3×C4—122no—
183#67—124no—
184#67—124no—
185C2×Dic3—24no—
186C2×Dic3—22no—
187C2×Dic3—44no—
188C2×Dic3—42no—
189C2×Dic3—62no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—62no—
197C2×Dic3—64no—
198C2×Dic3—122no—
199Dic6—124no—
200Dic6—124no—
201Dic6—124no—
202Dic6—128no—
203Dic6—124no—
204C2×C32#49714yescomplemented
205C2×C32C2×#12711yescharacteristic
206C2×C32C2×#13711yescharacteristic
207C2×C32C2×#13711yescharacteristic
208C3×D3—82no—
209C24—61no—
210C2×Q8—92no—
211C2×Q8—94no—
212C2×Q8—181no—
213C2×Q8—182no—
214C2×Q8—184no—
215C2×Q8—184no—
216C2×Q8—184no—
217C2×D4—92no—
218C2×D4—184no—
219C2×D4—181no—
220C22×C4—61no—
221C22×C4—62no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4GO+(4,𝔽2)11yescharacteristic
225Q16—1816no—
226SD16—1816no—
227C2×C8—94no—
228C2×C8—98no—
229C4⋊C4—64no—
230C4⋊C4—184no—
231C22⋊C4—64no—
232C22⋊C4—184no—
233C42—92no—
234C42—92no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—22no—
238C22×C3—22no—
239C22×C3—22no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3—122no—
244C22×C3—122no—
245C22×C3—122no—
246C22×C3—244no—
247C2×D3—42no—
248C2×D3—42no—
249C2×D3—42no—
250C2×D3—84no—
251C3×C4—24no—
252C3×C4—42no—
253C3×C4—124no—
254C3×C4—122no—
255Dic3—44no—
256Dic3—42no—
257Dic3—62no—
258Dic3—62no—
259Dic3—62no—
260Dic3—62no—
261Dic3—64no—
262Dic3—122no—
263C32C2×#49711yescharacteristic, complemented, Sylow
264C23—62no—
265C23—122no—
266C23—122no—
267C23—122no—
268C23C2×GO+(4,𝔽2)11yescharacteristic
269Q8—184no—
270Q8—184no—
271Q8—184no—
272Q8—362no—
273Q8—364no—
274D4—184no—
275D4—362no—
276C2×C4—22no—
277C2×C4—62no—
278C2×C4—64no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—94no—
282C2×C4—92no—
283C2×C4—122no—
284C2×C4—124no—
285C2×C4—182no—
286C2×C4C2×GO+(4,𝔽2)12yes—
287C8—98no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—24no—
293C2×C3—24no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—242no—
297D3—82no—
298C22—122no—
299C22—122no—
300C22—122no—
301C22—244no—
302C22#6422612yes—
303C22#6423112yes—
304C22#6423912yes—
305C22C22×GO+(4,𝔽2)11yescharacteristic
306C4—22no—
307C4—92no—
308C4—92no—
309C4—122no—
310C4—124no—
311C4—182no—
312C3—21no—
313C3—21no—
314C2—242no—
315C2#1059344314yesdirect product factor
316C2C2×#6422611yescharacteristic
317C2C2×#6423111yescharacteristic
318C2C2×#6423911yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#497
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
1. C22×#3776C2semidirect
3. C2×#63919C2semidirect
5. C2×#63777C2semidirect
6. #10593443C2direct (N × H)
12. C2×#3776C22semidirect
21. #63919C22semidirect
24. #63777C22semidirect
204. C2×C32#497semidirect
263. C32C2×#497semidirect
315. C2#10593443direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37762
C22×#37752
C2×#639192
C2×#639152
C2×#637772
#105934432
C2×#4979