Finite Group Databasebeta

← C2×#10593985 #11910270

Subgroups — C2×#10593985 #11910270

Order 1152.

2417 conjugacy classes of subgroups; only the 580 normal subgroups are shown.

normal subgroups only

This group has 2417 conjugacy classes of subgroups — too many to draw. Only its 580 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×#64079C211yesmaximal, characteristic, complemented
2C2×C3×#875C212yesmaximal, complemented
3C2×#63891C214yesmaximal, complemented
4C2×#63887C214yesmaximal, complemented
5C2×#63885C214yesmaximal, complemented
6#10593985C2116yesmaximal, direct product factor
7C2×#5684—32nomaximal
8C22×C3×D12C2212yes—
9C22×C3×Dic6C2212yes—
10C22×#625C2214yes—
11C22×D3×Dic3C2214yes—
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2212yes—
14C2×#3750C2214yes—
15#64079C2218yescomplemented
16C2×C3×(C2×D3)⋊C4C2214yes—
17C2×C3×(C2×D3)⋊C4C2214yes—
18C3×#875C22116yescomplemented
19C2×Dic3⋊Dic3C2214yes—
20C2×(C2×D3)⋊Dic3C2214yes—
21#63891C22132yescomplemented
22#63887C22132yescomplemented
23#63885C22132yescomplemented
24C2×C3×#124—32no—
25C2×#946—34no—
26C2×#939—34no—
27#5684—332no—
28C2×#886—34no—
29C2×#884—34no—
30C2×#883—34no—
31C2×#878—34no—
32C2×#875D312yescomplemented
33C2×#870—32no—
34C2×#870—61no—
35C23×C3×D3C2314yes—
36C22×C32×C4C2311yescharacteristic
37C22×C32×C4C2312yes—
38C22×C3⋊Dic3C2314yes—
39C22×C3×Dic3C2314yes—
40C2×C3×D12—44no—
41C2×C3×D12C2318yes—
42C2×C3×Dic6—44no—
43C2×C3×Dic6C2318yes—
44C2×#625—48no—
45C2×#625C23116yes—
46C2×D3×Dic3—48no—
47C2×D3×Dic3C23116yes—
48C32×C42C2314yes—
49C4⋊(C3⋊Dic3)C2318yes—
50#3750C23116yes—
51C3×(C2×D3)⋊C4C23116yes—
52C3×(C2×D3)⋊C4C23116yes—
53Dic3⋊Dic3C23116yes—
54(C2×D3)⋊Dic3C23116yes—
55C2×#562—91noSylow
56C22×C3×Q8—32no—
57C22×C3×D4—32no—
58C22×#67—34no—
59C22×#67—34no—
60C23×Dic3—34no—
61C22×D12C2×D312yes—
62C22×C4×D3—34no—
63C22×Dic6C2×D312yes—
64C3×#124—316no—
65C2×C3×C22⋊C4—34no—
66C2×C3×C22⋊C4—34no—
67C2×C3×C42—21no—
68C2×C3×C42C2×D312yes—
69C2×#217—34no—
70#946—332no—
71#939—332no—
72C2×(C2×D3)⋊C4—34no—
73C2×(C2×D3)⋊C4C2×D314yes—
74C2×(C2×D3)⋊C4C2×D314yes—
75C2×C4⋊Dic3—32no—
76C2×C4⋊Dic3—32no—
77C2×C4⋊Dic3—34no—
78C2×C4⋊Dic3—62no—
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4—34no—
81C2×Dic3⋊C4—34no—
82C2×Dic3⋊C4—64no—
83#886—332no—
84#884—332no—
85#883—332no—
86#878—332no—
87#875C2×D3116yescomplemented
88#870—316no—
89#870—68no—
90C23×C32C2411yescharacteristic
91C22×C3×D3—28no—
92C22×C3×D3—28no—
93C22×C3×D3—28no—
94C22×C3×D3C2418yes—
95C2×C32×C4—22no—
96C2×C32×C4—24no—
97C2×C32×C4C2412yes—
98C2×C32×C4C2414yes—
99C2×C3⋊Dic3—28no—
100C2×C3⋊Dic3C2418yes—
101C2×C3×Dic3—28no—
102C2×C3×Dic3C2418yes—
103C3×D12—48no—
104C3×Dic6—48no—
105#625—416no—
106D3×Dic3—416no—
107#562—916no—
108C2×#125—91no—
109C2×#124—32no—
110C2×#123—94no—
111C2×C22⋊Q8—94no—
112C2×#121—94no—
113C24×C3—34no—
114C23×D3C22×D314yes—
115C2×C3×Q8—38no—
116C2×C3×Q8—124no—
117C2×C3×D4—38no—
118C2×C3×D4—124no—
119C22×C3×C4—21no—
120C22×C3×C4—22no—
121C22×C3×C4—34no—
122C22×C3×C4C22×D312yes—
123C22×C3×C4C22×D312yes—
124C22×C3×C4C22×D312yes—
125C2×#67—316no—
126C2×#67—316no—
127C2×#67—128no—
128C2×#67—128no—
129C22×Dic3—34no—
130C22×Dic3—34no—
131C22×Dic3—316no—
132C22×Dic3—64no—
133C22×Dic3—128no—
134C22×Dic3C22×D314yes—
135C2×D12—44no—
136C2×D12C22×D318yes—
137C2×C4×D3—316no—
138C2×C4×D3—128no—
139C2×Dic6—44no—
140C2×Dic6C22×D318yes—
141C3×C22⋊C4—316no—
142C3×C22⋊C4—316no—
143C3×C42—24no—
144C3×C42C22×D318yes—
145#217—316no—
146(C2×D3)⋊C4—316no—
147(C2×D3)⋊C4C22×D3116yes—
148(C2×D3)⋊C4C22×D3116yes—
149C4⋊Dic3—38no—
150C4⋊Dic3—38no—
151C4⋊Dic3—316no—
152C4⋊Dic3—68no—
153Dic3⋊C4—316no—
154Dic3⋊C4—316no—
155Dic3⋊C4—316no—
156Dic3⋊C4—616no—
157C22×C32H(5,𝔽2)14yes—
158C22×C322−1+412yes—
159C22×C32C2511yescharacteristic
160C2×C3×D3—28no—
161C2×C3×D3—28no—
162C2×C3×D3—28no—
163C2×C3×D3—416no—
164C32×C4—22no—
165C32×C4—24no—
166C3⋊Dic3—28no—
167C3×Dic3—28no—
168C22×Q8—32no—
169C22×D4—32no—
170C22×D4—94no—
171C23×C4—94no—
172#125—98no—
173#124—316no—
174#123—932no—
175C22⋊Q8—932no—
176#121—932no—
177C2×C4⋊C4—94no—
178C2×C4⋊C4—94no—
179C2×C4⋊C4—92no—
180C2×C22⋊C4—34no—
181C2×C22⋊C4—34no—
182C2×C22⋊C4—94no—
183C2×C42D3211yescharacteristic
184C23×C3—21no—
185C23×C3—38no—
186C23×C3—68no—
187C23×C3—68no—
188C23×C3—68no—
189C23×C3C23×D312yes—
190C22×D3—28no—
191C22×D3—28no—
192C22×D3—28no—
193C22×D3C23×D318yes—
194C3×Q8—128no—
195C3×D4—128no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—22no—
201C2×C3×C4—24no—
202C2×C3×C4—38no—
203C2×C3×C4—44no—
204C2×C3×C4—68no—
205C2×C3×C4C23×D314yes—
206C2×C3×C4C23×D314yes—
207C2×C3×C4C23×D314yes—
208#67—1216no—
209#67—1216no—
210C2×Dic3—28no—
211C2×Dic3—38no—
212C2×Dic3—38no—
213C2×Dic3—68no—
214C2×Dic3—68no—
215C2×Dic3—68no—
216C2×Dic3—128no—
217C2×Dic3—1216no—
218C2×Dic3C23×D318yes—
219D12—48no—
220C4×D3—1216no—
221Dic6—48no—
222C2×C32#56214yescomplemented
223C2×C32C2×H(5,𝔽2)12yes—
224C2×C32C2×2−1+411yescharacteristic
225C3×D3—48no—
226C24—34no—
227C2×Q8—38no—
228C2×Q8—124no—
229C2×D4—38no—
230C2×D4—916no—
231C2×D4—124no—
232C2×D4—368no—
233C22×C4—34no—
234C22×C4—916no—
235C22×C4—94no—
236C22×C4—368no—
237C22×C4C2×D3211yescharacteristic
238C22×C4C2×D3212yes—
239C4⋊C4—916no—
240C4⋊C4—916no—
241C4⋊C4—98no—
242C22⋊C4—316no—
243C22⋊C4—316no—
244C22⋊C4—916no—
245C42C2×D3214yes—
246C22×C3—22no—
247C22×C3—24no—
248C22×C3—21no—
249C22×C3—68no—
250C22×C3—68no—
251C22×C3—68no—
252C22×C3—1216no—
253C22×C3#100414yes—
254C22×C3#100914yes—
255C22×C3#101014yes—
256C22×C3C24×D312yes—
257C2×D3—28no—
258C2×D3—28no—
259C2×D3—28no—
260C2×D3—416no—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—24no—
264C3×C4—24no—
265C3×C4—44no—
266C3×C4—68no—
267Dic3—28no—
268Dic3—68no—
269Dic3—68no—
270Dic3—128no—
271C32C2×#56211yescharacteristic, complemented, Sylow
272C23—38no—
273C23—68no—
274C23—68no—
275C23—68no—
276C23C22×D3211yescharacteristic
277Q8—128no—
278D4—128no—
279D4—3616no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—38no—
283C2×C4—68no—
284C2×C4—98no—
285C2×C4—188no—
286C2×C4—3616no—
287C2×C4C22×D3212yes—
288C2×C4C22×D3214yes—
289C2×C3—21no—
290C2×C3—22no—
291C2×C3—24no—
292C2×C3—128no—
293C2×C3#568418yescomplemented
294C2×C3C2×#100412yes—
295C2×C3C2×#100912yes—
296C2×C3C2×#101012yes—
297D3—48no—
298C22—68no—
299C22—68no—
300C22—68no—
301C22—1216no—
302C22#6429812yes—
303C22#6430714yes—
304C22C23×D3211yescharacteristic
305C4—22no—
306C4—24no—
307C4—68no—
308C4—188no—
309C3—21no—
310C3C2×#568412yescomplemented
311C2—128no—
312C2#1059398514yesdirect product factor
313C2C2×#6429811yescharacteristic
314C2C2×#6430712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
2. C2×C3×#875C2semidirect
3. C2×#63891C2semidirect
4. C2×#63887C2semidirect
5. C2×#63885C2semidirect
6. #10593985C2direct (N × H)
15. #64079C22semidirect
18. C3×#875C22semidirect
21. #63891C22semidirect
22. #63887C22semidirect
23. #63885C22semidirect
32. C2×#875D3semidirect
87. #875C2×D3semidirect
222. C2×C32#562semidirect
271. C32C2×#562semidirect
293. C2×C3#5684semidirect
310. C3C2×#5684semidirect
312. C2#10593985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×#8752
C2×#638912
C2×#638872
C2×#638852
#105939852
C2×#56843