Finite Group Databasebeta

← C2×#10593437 #11865503

Subgroups — C2×#10593437 #11865503

Order 1152.

902 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 143 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×#3775C212yesmaximal
2C2×#63919C211yesmaximal, characteristic, complemented
3C2×C4×#625C211yesmaximal, characteristic
4C2×C4⋊#622C211yesmaximal, characteristic, complemented
5C2×#63740C212yesmaximal, complemented
6#10593437C218yesmaximal, direct product factor
7C22×C3×C4×D3—21no—
8C22×#627C2212yes—
9C22×#625C2211yescharacteristic
10C22×#622C2212yes—
11C2×#3775—28no—
12C2×#3775C2218yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3—21no—
15C2×#3724—21no—
16C2×#3724C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—21no—
18#63919—22no—
19#63919C2214yescomplemented
20C4×#625—22no—
21C4×#625C2214yes—
22C4⋊#622C2214yescomplemented
23#63740C2218yescomplemented
24C2×C4×#67—61no—
25C2×#888—61no—
26C23×C3×D3—21no—
27C22×C32×C4D411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30C22×C3×Dic3—22no—
31C22×C3×Dic3—21no—
32C2×C3×C4×D3—24no—
33C2×C3×C4×D3—44no—
34C2×#627—24no—
35C2×#627—24no—
36C2×#627—22no—
37C2×#627C2314yes—
38C2×#625—21no—
39C2×#625—22no—
40C2×#625D414yes—
41C2×#625C2312yes—
42C2×#622—24no—
43C2×#622C2314yes—
44#3775—216no—
45C4×C3⋊Dic3D412yes—
46C4×C3⋊Dic3C2312yes—
47C3×C4⋊Dic3—24no—
48#3724—21no—
49#3724—24no—
50#3724C2312yes—
51(C2×D3)⋊Dic3—24no—
52C2×#461—91nomaximal, Sylow
53C23×C3×C4—61no—
54C22×#67—61no—
55C22×C4×D3—21no—
56C22×Dic6—62no—
57C2×C3×C4⋊C4—61no—
58C2×#217—61no—
59C4×#67—64no—
60C4×#67—64no—
61C2×(C2×D3)⋊C4—61no—
62C2×C4⋊Dic3—21no—
63C2×Dic3⋊C4—61no—
64C2×Dic3⋊C4—62no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67#888—64no—
68#888—64no—
69C23×C32C2×D411yescharacteristic
70C22×C3×D3—24no—
71C22×C3×D3—22no—
72C22×C3×D3—42no—
73C22×C3×D3—42no—
74C2×C32×C4SD1614yescomplemented
75C2×C32×C4C2×D412yes—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3C2×D412yes—
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2×D412yes—
80C2×C3⋊Dic3#4112yes—
81C2×C3⋊Dic3C2411yescharacteristic
82C2×C3×Dic3—22no—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—44no—
85C2×C3×Dic3—42no—
86C3×C4×D3—48no—
87#627—24no—
88#627—24no—
89#627—44no—
90#625—24no—
91#625—22no—
92#625C2×D414yes—
93#622—24no—
94C22×SD16—92no—
95C2×C4⋊Q8—91no—
96C2×C4×D4—91no—
97#461—98no—
98C2×C4⋊C8—91no—
99C2×#103—92no—
100C24×C3—61no—
101C23×D3—21no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—64no—
105C22×C3×C4—61no—
106C22×C3×C4—62no—
107C22×C3×C4—124no—
108C2×#67—62no—
109C2×#67—64no—
110C2×#67—62no—
111C2×#67—64no—
112C22×Dic3—22no—
113C22×Dic3—21no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—61no—
118C2×C4×D3—24no—
119C2×C4×D3—44no—
120C2×Dic6—64no—
121C2×Dic6—64no—
122C2×Dic6—124no—
123C2×Dic6—124no—
124C3×C4⋊C4—64no—
125#217—64no—
126(C2×D3)⋊C4—64no—
127C4⋊Dic3—24no—
128Dic3⋊C4—62no—
129Dic3⋊C4—68no—
130Dic3⋊C4—62no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C22×C32#12112yes—
136C22×C32C2×SD1612yes—
137C22×C32#13712yes—
138C22×C32C22×D411yescharacteristic
139C2×C3×D3—24no—
140C2×C3×D3—42no—
141C2×C3×D3—42no—
142C2×C3×D3—48no—
143C32×C4C2×SD1614yescomplemented
144C3⋊Dic3—22no—
145C3⋊Dic3#12112yes—
146C3⋊Dic3C22×D411yescharacteristic
147C3⋊Dic3C2×#4111yescharacteristic
148C3×Dic3—44no—
149C3×Dic3—42no—
150C22×Q8—92no—
151C22×D4—91no—
152C23×C4—61no—
153C2×SD16—98no—
154C2×SD16—188no—
155C22×C8—92no—
156C4⋊Q8—94no—
157C4⋊Q8—182no—
158C4×D4—94no—
159C4×D4—182no—
160C2×C4⋊C4—61no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—181no—
163C2×C22⋊C4—181no—
164C2×C42—91no—
165C4⋊C8—94no—
166#103—98no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—62no—
170C23×C3—64no—
171C23×C3—122no—
172C23×C3—122no—
173C22×D3—22no—
174C22×D3—24no—
175C22×D3—42no—
176C22×D3—42no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—24no—
180C2×C3×C4—24no—
181C2×C3×C4—62no—
182C2×C3×C4—64no—
183C2×C3×C4—128no—
184C2×C3×C4—124no—
185C2×C3×C4—122no—
186#67—64no—
187#67—68no—
188#67—64no—
189C2×Dic3—24no—
190C2×Dic3—22no—
191C2×Dic3—44no—
192C2×Dic3—42no—
193C2×Dic3—62no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—62no—
203C2×Dic3—64no—
204C2×Dic3—122no—
205C4×D3—48no—
206Dic6—124no—
207Dic6—124no—
208Dic6—128no—
209C2×C32#46114yescomplemented
210C2×C32C2×#12111yescharacteristic
211C2×C32C22×SD1611yescharacteristic
212C2×C32C2×#13711yescharacteristic
213C3×D3—44no—
214C24—61no—
215C2×Q8—94no—
216C2×Q8—182no—
217C2×Q8—184no—
218C2×Q8—184no—
219C2×D4—92no—
220C2×D4—94no—
221C2×D4—181no—
222C2×D4—182no—
223C22×C4—61no—
224C22×C4—62no—
225C22×C4—64no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—124no—
229C22×C4GO+(4,𝔽2)11yescharacteristic
230SD16—1816no—
231C2×C8—94no—
232C2×C8—184no—
233C4⋊C4—64no—
234C4⋊C4—92no—
235C4⋊C4—181no—
236C4⋊C4—184no—
237C22⋊C4—184no—
238C42—92no—
239C42—92no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—22no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—64no—
249C22×C3—122no—
250C22×C3—122no—
251C22×C3—128no—
252C2×D3—24no—
253C2×D3—42no—
254C2×D3—42no—
255C2×D3—48no—
256C3×C4—24no—
257C3×C4—24no—
258C3×C4—124no—
259C3×C4—122no—
260Dic3—44no—
261Dic3—42no—
262Dic3—62no—
263Dic3—61no—
264Dic3—61no—
265Dic3—62no—
266Dic3—61no—
267Dic3—61no—
268Dic3—64no—
269Dic3—122no—
270C32C2×#46111yescharacteristic, complemented, Sylow
271C23—62no—
272C23—64no—
273C23—122no—
274C23—122no—
275C23C2×GO+(4,𝔽2)11yescharacteristic
276Q8—184no—
277Q8—184no—
278Q8—364no—
279D4—94no—
280D4—182no—
281D4—184no—
282C2×C4—62no—
283C2×C4—64no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—92no—
289C2×C4—124no—
290C2×C4—122no—
291C2×C4—128no—
292C2×C4—182no—
293C2×C4#377514yescomplemented
294C2×C4C2×GO+(4,𝔽2)12yes—
295C8—184no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—24no—
301C2×C3—24no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—124no—
305D3—44no—
306C22—64no—
307C22—122no—
308C22—128no—
309C22—122no—
310C22#6422612yes—
311C22#6423012yes—
312C22C2×#377512yes—
313C22C22×GO+(4,𝔽2)11yescharacteristic
314C4—91no—
315C4—91no—
316C4—92no—
317C4—124no—
318C4—122no—
319C4—182no—
320C4C2×#377514yescomplemented
321C3—21no—
322C3—21no—
323C2—124no—
324C2#1059343714yesdirect product factor
325C2C2×#6422611yescharacteristic
326C2C2×#6423011yescharacteristic
327C2C22×#377511yescharacteristic
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×#461
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
2. C2×#63919C2semidirect
4. C2×C4⋊#622C2semidirect
5. C2×#63740C2semidirect
6. #10593437C2direct (N × H)
19. #63919C22semidirect
22. C4⋊#622C22semidirect
23. #63740C22semidirect
74. C2×C32×C4SD16semidirect
143. C32×C4C2×SD16semidirect
209. C2×C32#461semidirect
270. C32C2×#461semidirect
293. C2×C4#3775semidirect
320. C4C2×#3775semidirect
324. C2#10593437direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37752
C2×#639192
C2×C4×#6252
C2×C4⋊#6222
C2×#637402
#105934372
C2×#4619