Finite Group Databasebeta

← C2×#10593631 #11922922

Subgroups — C2×#10593631 #11922922

Order 1152.

880 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 55 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×C3×#127⋊C3C211yesmaximal, characteristic, complemented
2#10593631C214yesmaximal, direct product factor
3C2×C3⋊#857C212yesmaximal, complemented
4C2×#857⋊C2—33nomaximal
5C2×#5077—31nomaximal
6C22×C3⋊S4—41nomaximal
7C3×#127⋊C3C2212yescomplemented
8C2×C3×C42⋊C3C2211yescharacteristic, complemented
9C3⋊#857C2214yescomplemented
10C2×#1004—31no—
11C2×C3×#127D311yescharacteristic, complemented
12C2×#932—32no—
13C2×#127⋊C3D313yescomplemented
14#857⋊C2—312no—
15C2×#857—36no—
16C2×#833—31no—
17#5077—34no—
18#5077—34no—
19C2×#805—32no—
20C22×C3×A4—41no—
21C2×C3⋊S4—42no—
22C2×C3⋊S4—44no—
23C3×C42⋊C3C2311yescharacteristic, complemented
24C2×#453—91noSylow
25C22×S4—123no—
26C22×C3×D4—31no—
27C22×C3×D4—31no—
28C22×#67—61no—
29C22×#67—61no—
30#1004—34no—
31#1004—64no—
32#1004—62no—
33C2×#237—62no—
34C2×D3×D4—62no—
35C2×#235—32no—
36C3×#127—32no—
37C3×#127C2×D312yescomplemented
38C2×C3×C42C2×D311yescharacteristic, complemented
39C2×#214—62no—
40#932—38no—
41#932—64no—
42C2×#213—62no—
43C2×#208—32no—
44#127⋊C3C2×D316yescomplemented
45C2×C42⋊C3C2×D313yescomplemented
46#857—312no—
47#833—34no—
48#805—34no—
49#805—34no—
50C22×C3⋊D3—161no—
51C2×C3×A4—41no—
52C2×C3×A4—42no—
53C3⋊S4—44no—
54C2×H(5,𝔽2)—91no—
55C2×AGL(1,ℤ/8)—92no—
56C2×#127C3⋊D311yescharacteristic, complemented
57#453—94no—
58#453—94no—
59C2×#104—92no—
60C2×#100—91no—
61C24×C3—31no—
62C24×C3S411yescharacteristic
63C23×D3—61no—
64C23×D3—61no—
65C22×A4—43no—
66C2×S4—126no—
67C2×S4—1212no—
68C2×C3×D4—32no—
69C2×C3×D4—32no—
70C2×C3×D4—32no—
71C2×C3×D4—62no—
72C2×C3×D4—62no—
73C2×C3×D4—62no—
74C2×C3×D4—62no—
75C2×C3×D4—61no—
76C22×C3×C4—31no—
77C2×#67—64no—
78C2×#67—62no—
79C2×#67—62no—
80C2×#67—64no—
81C2×#67—64no—
82C2×#67—62no—
83C2×#67—64no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86#237—68no—
87#237—68no—
88D3×D4—68no—
89D3×D4—68no—
90#235—34no—
91#235—34no—
92#235—62no—
93#235—62no—
94C2×D12—32no—
95C2×C4×D3—62no—
96C2×Dic6—32no—
97C3×C42—31no—
98C3×C42C22×D311yescharacteristic, complemented
99#214—68no—
100#213—68no—
101#208—34no—
102#208—62no—
103C2×C3⋊C8—62no—
104C42⋊C3C22×D313yescomplemented
105C22×C32—161no—
106C2×C3⋊D3—162no—
107C2×C3⋊D3—164no—
108C3×A4—41no—
109H(5,𝔽2)—94no—
110H(5,𝔽2)—182no—
111H(5,𝔽2)—184no—
112C2×#41—92no—
113C2×#41—182no—
114C22×D4—31no—
115C22×D4—31no—
116C22×D4—182no—
117C22×D4—181no—
118C22×D4—181no—
119AGL(1,ℤ/8)—98no—
120AGL(1,ℤ/8)—184no—
121C2×SD16—182no—
122C2×D8—182no—
123C2×M16—92no—
124#127—32no—
125#127C2×C3⋊D312yescomplemented
126C2×C42C2×C3⋊D311yescharacteristic, complemented
127#104—94no—
128#104—94no—
129#100—94no—
130C23×C3—32no—
131C23×C3—61no—
132C23×C3—61no—
133C23×C3—61no—
134C23×C3—61no—
135C23×C3—121no—
136C23×C3—121no—
137C23×C3C2×S411yescharacteristic
138C23×C3C2×S412yes—
139C22×D3—62no—
140C22×D3—64no—
141C22×D3—64no—
142C22×D3—241no—
143C22×D3—241no—
144C22×D3—241no—
145C22×D3—241no—
146C22×D3—483no—
147C2×A4—43no—
148C2×A4—46no—
149S4—1212no—
150C3×D4—64no—
151C3×D4—64no—
152C3×D4—64no—
153C3×D4—122no—
154C2×C3×C4—32no—
155C2×C3×C4—32no—
156C2×C3×C4—31no—
157C2×C3×C4—31no—
158#67—64no—
159#67—68no—
160#67—68no—
161#67—64no—
162C2×Dic3—62no—
163C2×Dic3—64no—
164C2×Dic3—64no—
165D12—34no—
166D12—62no—
167C4×D3—64no—
168C4×D3—64no—
169Dic6—34no—
170Dic6—62no—
171C3⋊C8—64no—
172C2×C32—162no—
173C2×C32—161no—
174C3⋊D3—164no—
175C24—31no—
176C24—181no—
177C24—181no—
178C24C3⋊S411yescharacteristic
179#41—94no—
180#41—94no—
181#41—182no—
182#41—182no—
183#41—188no—
184#41—188no—
185C2×Q8—92no—
186C2×D4—32no—
187C2×D4—32no—
188C2×D4—32no—
189C2×D4—62no—
190C2×D4—62no—
191C2×D4—62no—
192C2×D4—62no—
193C2×D4—61no—
194C2×D4—92no—
195C2×D4—188no—
196C2×D4—188no—
197C2×D4—184no—
198C2×D4—182no—
199C2×D4—182no—
200C2×D4—184no—
201C2×D4—184no—
202C2×D4—182no—
203C2×D4—184no—
204C22×C4—31no—
205C22×C4—182no—
206C22×C4—181no—
207C22×C4—181no—
208SD16—188no—
209D8—188no—
210M16—94no—
211M16—182no—
212C2×C8—182no—
213C42—31no—
214C42C22×C3⋊D311yescharacteristic, complemented
215C22×C3—31no—
216C22×C3—31no—
217C22×C3—41no—
218C22×C3—62no—
219C22×C3—62no—
220C22×C3—121no—
221C22×C3—122no—
222C22×C3—121no—
223C22×C3—121no—
224C22×C3—163no—
225C22×C3—241no—
226C22×C3C22×S411yescharacteristic
227C2×D3—64no—
228C2×D3—122no—
229C2×D3—122no—
230C2×D3—244no—
231C2×D3—244no—
232C2×D3—486no—
233C2×D3—4812no—
234A4—43no—
235C3×C4—32no—
236C3×C4—32no—
237Dic3—64no—
238C32—161noSylow
239C23—32no—
240C23—61no—
241C23—61no—
242C23—61no—
243C23—61no—
244C23—121no—
245C23—121no—
246C23—182no—
247C23—184no—
248C23—184no—
249C23—721no—
250C23—721no—
251C23—721no—
252C23—721no—
253C23C2×C3⋊S411yescharacteristic
254C23C2×C3⋊S412yes—
255Q8—94no—
256Q8—182no—
257D4—64no—
258D4—64no—
259D4—64no—
260D4—94no—
261D4—122no—
262D4—182no—
263D4—184no—
264D4—188no—
265D4—188no—
266D4—184no—
267C2×C4—32no—
268C2×C4—32no—
269C2×C4—31no—
270C2×C4—31no—
271C2×C4—184no—
272C2×C4—184no—
273C2×C4—182no—
274C2×C4—184no—
275C2×C4—184no—
276C8—184no—
277C2×C3—31no—
278C2×C3—31no—
279C2×C3—42no—
280C2×C3—122no—
281C2×C3—166no—
282C2×C3—163no—
283C2×C3#857⋊C211yescharacteristic, complemented
284D3—124no—
285D3—4812no—
286C22—31no—
287C22—31no—
288C22—41no—
289C22—62no—
290C22—62no—
291C22—121no—
292C22—122no—
293C22—121no—
294C22—121no—
295C22—184no—
296C22—241no—
297C22—362no—
298C22—362no—
299C22—724no—
300C22—724no—
301C22C22×C3⋊S411yescharacteristic
302C4—32no—
303C4—32no—
304C4—184no—
305C3—163no—
306C3C2×#857⋊C211yescharacteristic, complemented
307C2—31no—
308C2—31no—
309C2—42no—
310C2—122no—
311C2—364no—
312C2#1059363111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#10593631
commutator, cosocle, hypocenterC3×C42⋊C3C23
FrattiniC22C22×C3⋊S4
FittingC2×C3×#127D3
socleC23×C3C2×S4
LCSG ▷ C3×C42⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#127⋊C3C2semidirect
2. #10593631C2direct (N × H)
3. C2×C3⋊#857C2semidirect
7. C3×#127⋊C3C22semidirect
8. C2×C3×C42⋊C3C22semidirect
9. C3⋊#857C22semidirect
11. C2×C3×#127D3semidirect
13. C2×#127⋊C3D3semidirect
23. C3×C42⋊C3C23semidirect
37. C3×#127C2×D3semidirect
38. C2×C3×C42C2×D3semidirect
44. #127⋊C3C2×D3semidirect
45. C2×C42⋊C3C2×D3semidirect
56. C2×#127C3⋊D3semidirect
98. C3×C42C22×D3semidirect
104. C42⋊C3C22×D3semidirect
125. #127C2×C3⋊D3semidirect
126. C2×C42C2×C3⋊D3semidirect
214. C42C22×C3⋊D3semidirect
283. C2×C3#857⋊C2semidirect
306. C3C2×#857⋊C2semidirect
312. C2#10593631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
#105936312
C2×C3⋊#8572
C2×#857⋊C23
C2×#50773
C22×C3⋊S44