Finite Group Databasebeta

← C2×#10593362 #11873557

Subgroups — C2×#10593362 #11873557

Order 1152.

746 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 119 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×#63919C211yesmaximal, characteristic, complemented
2C2×#63915C211yesmaximal, characteristic
3C2×#63777C211yesmaximal, characteristic, complemented
4C2×#63740C212yesmaximal, complemented
5C2×#63739C212yesmaximal
6#10593362C218yesmaximal, direct product factor
7C22×#627—21no—
8C22×#627C2211yescharacteristic
9C22×#625C2211yescharacteristic
10C22×#622C2212yes—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×(C2×D3)⋊C4—21no—
13C2×C3×C4⋊Dic3—21no—
14C2×#3724C2212yes—
15C2×(C2×D3)⋊Dic3—21no—
16#63919—22no—
17#63919C2214yescomplemented
18#63915—22no—
19#63915C2214yes—
20#63777C2214yescomplemented
21#63740C2218yescomplemented
22#63739C2218yes—
23C2×#888—61no—
24C2×#885—61no—
25C23×C3×D3—21no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—22no—
30C22×C3×Dic3—21no—
31C2×#627—24no—
32C2×#627—24no—
33C2×#627—21no—
34C2×#627—44no—
35C2×#627C2312yes—
36C2×#625—24no—
37C2×#625—21no—
38C2×#625C2312yes—
39C2×#622—24no—
40C2×#622C2314yes—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3C2312yes—
43C3×(C2×D3)⋊C4—24no—
44C3×C4⋊Dic3—24no—
45#3724—22no—
46#3724C2314yes—
47(C2×D3)⋊Dic3—24no—
48C2×#489—91nomaximal, Sylow
49C22×#67—61no—
50C22×Dic6—61no—
51C22×Dic6—62no—
52C2×C3×C4⋊C4—61no—
53C2×C3×C22⋊C4—61no—
54C2×#217—61no—
55C2×(C2×D3)⋊C4—21no—
56C2×(C2×D3)⋊C4—61no—
57C2×C4⋊Dic3—21no—
58C2×Dic3⋊C4—62no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61#888—64no—
62#888—64no—
63#885—64no—
64#885—64no—
65C23×C32C2×D411yescharacteristic
66C22×C3×D3—22no—
67C22×C3×D3—42no—
68C22×C3×D3—42no—
69C22×C3×D3—42no—
70C2×C32×C4—22no—
71C2×C32×C4C2×D412yes—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3#4114yes—
76C2×C3⋊Dic3C2411yescharacteristic
77C2×C3×Dic3—22no—
78C2×C3×Dic3—24no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—44no—
81#627—24no—
82#627—48no—
83#627—42no—
84#625—24no—
85#625—42no—
86#622—24no—
87C2×C4⋊Q8—91no—
88C2×#124—91no—
89#489—98no—
90C2×#103—92no—
91C2×#102—92no—
92C2×#97—91no—
93C24×C3—61no—
94C23×D3—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—62no—
98C22×C3×C4—61no—
99C2×#67—62no—
100C2×#67—62no—
101C2×#67—124no—
102C22×Dic3—22no—
103C22×Dic3—21no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—61no—
108C2×Dic6—62no—
109C2×Dic6—62no—
110C2×Dic6—68no—
111C2×Dic6—124no—
112C2×Dic6—128no—
113C3×C4⋊C4—64no—
114C3×C22⋊C4—64no—
115#217—64no—
116(C2×D3)⋊C4—24no—
117(C2×D3)⋊C4—64no—
118C4⋊Dic3—24no—
119Dic3⋊C4—64no—
120Dic3⋊C4—64no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C4×Dic3—62no—
125C22×C32#12412yes—
126C22×C32AGL(1,ℤ/8)12yes—
127C22×C32#13712yes—
128C22×C32C22×D411yescharacteristic
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132C2×C3×D3—84no—
133C32×C4—22no—
134C3⋊Dic3—22no—
135C3⋊Dic3#12412yes—
136C3⋊Dic3C2×#4112yes—
137C3×Dic3—42no—
138C3×Dic3—44no—
139C22×Q8—91no—
140C22×Q8—181no—
141C22×D4—91no—
142C22×C8—92no—
143C4⋊Q8—94no—
144C4⋊Q8—182no—
145#124—94no—
146#124—182no—
147C2×C4⋊C4—61no—
148C2×C4⋊C4—92no—
149C2×C22⋊C4—61no—
150C2×C22⋊C4—181no—
151C2×C42—91no—
152#103—98no—
153#102—98no—
154#97—94no—
155C23×C3—21no—
156C23×C3—21no—
157C23×C3—62no—
158C23×C3—122no—
159C23×C3—122no—
160C23×C3—122no—
161C22×D3—22no—
162C22×D3—42no—
163C22×D3—42no—
164C22×D3—42no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—42no—
169C2×C3×C4—64no—
170C2×C3×C4—62no—
171C2×C3×C4—122no—
172C2×C3×C4—124no—
173#67—124no—
174#67—124no—
175C2×Dic3—24no—
176C2×Dic3—22no—
177C2×Dic3—42no—
178C2×Dic3—44no—
179C2×Dic3—61no—
180C2×Dic3—62no—
181C2×Dic3—61no—
182C2×Dic3—64no—
183C2×Dic3—64no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—62no—
187C2×Dic3—64no—
188C2×Dic3—122no—
189Dic6—124no—
190Dic6—124no—
191Dic6—1216no—
192C2×C32#48914yescomplemented
193C2×C32C2×#12411yescharacteristic
194C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C32C2×#13711yescharacteristic
196C3×D3—82no—
197C24—61no—
198C2×Q8—92no—
199C2×Q8—181no—
200C2×Q8—184no—
201C2×Q8—184no—
202C2×Q8—364no—
203C2×D4—92no—
204C2×D4—184no—
205C2×D4—181no—
206C22×C4—61no—
207C22×C4—62no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4GO+(4,𝔽2)11yescharacteristic
211C2×C8—94no—
212C2×C8—184no—
213C4⋊C4—64no—
214C4⋊C4—94no—
215C4⋊C4—182no—
216C22⋊C4—64no—
217C22⋊C4—184no—
218C42—92no—
219C42—92no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—122no—
229C22×C3—122no—
230C22×C3—122no—
231C22×C3—244no—
232C2×D3—42no—
233C2×D3—42no—
234C2×D3—42no—
235C2×D3—84no—
236C3×C4—24no—
237C3×C4—42no—
238C3×C4—122no—
239C3×C4—124no—
240Dic3—42no—
241Dic3—44no—
242Dic3—62no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—64no—
247Dic3—122no—
248C32C2×#48911yescharacteristic, complemented, Sylow
249C23—62no—
250C23—122no—
251C23—122no—
252C23—122no—
253C23C2×GO+(4,𝔽2)11yescharacteristic
254Q8—184no—
255Q8—362no—
256Q8—368no—
257D4—184no—
258D4—362no—
259C2×C4—22no—
260C2×C4—62no—
261C2×C4—64no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—94no—
265C2×C4—92no—
266C2×C4—122no—
267C2×C4—124no—
268C2×C4—182no—
269C2×C4C2×GO+(4,𝔽2)12yes—
270C8—184no—
271C2×C3—24no—
272C2×C3—24no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—242no—
280D3—82no—
281C22—122no—
282C22—122no—
283C22—122no—
284C22—244no—
285C22#6422112yes—
286C22#6422412yes—
287C22#6423912yes—
288C22C22×GO+(4,𝔽2)11yescharacteristic
289C4—22no—
290C4—92no—
291C4—92no—
292C4—122no—
293C4—124no—
294C4—182no—
295C3—21no—
296C3—21no—
297C2—242no—
298C2#1059336214yesdirect product factor
299C2C2×#6422111yescharacteristic
300C2C2×#6422411yescharacteristic
301C2C2×#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×#489
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. C2×#63919C2semidirect
3. C2×#63777C2semidirect
4. C2×#63740C2semidirect
6. #10593362C2direct (N × H)
17. #63919C22semidirect
20. #63777C22semidirect
21. #63740C22semidirect
192. C2×C32#489semidirect
248. C32C2×#489semidirect
298. C2#10593362direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#639152
C2×#637772
C2×#637402
C2×#637392
#105933622
C2×#4899