Finite Group Databasebeta

← C2×#10593639 #11922996

Subgroups — C2×#10593639 #11922996

Order 1152.

632 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 89 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×#64266C211yesmaximal, characteristic
2C2×C3×#131⋊C3C211yesmaximal, characteristic, complemented
3C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
4#10593639C214yesmaximal, direct product factor
5C2×#5405—33nomaximal
6C2×#5145—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#64266C412yescomplemented
9#64266C2212yes—
10C2×C3⋊GL(2,𝔽3)C411yescharacteristic, complemented
11C2×C3⋊#226C411yescharacteristic, complemented
12C2×#3743—41nomaximal
13C3×#131⋊C3C2212yescomplemented
14C3⋊GU(2,𝔽3)C2212yescomplemented
15C2×#985—33no—
16C2×C3×#131D311yescharacteristic, complemented
17C2×#950—31no—
18C2×#901—31no—
19C2×#131⋊C3D313yescomplemented
20C2×GU(2,𝔽3)—33no—
21#5405—312no—
22C2×#837—31no—
23#5145—34no—
24#5145—34no—
25C2×#825—31no—
26C2×#822—31no—
27C2×#815—31no—
28C2×C4×C3⋊D3—41no—
29C3×#41⋊C3C2×C411yescharacteristic
30C3×#41⋊C3C2311yescharacteristic
31C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
32C3⋊GL(2,𝔽3)C2×C412yescomplemented
33C3⋊#226C2×C412yescomplemented
34C2×C32×C8—41no—
35C2×C3⋊(C3⋊C8)—41no—
36#3743—44no—
37C2×#444—91noSylow
38C2×C3×#41C2×D311yescharacteristic
39C2×#235—31no—
40C2×#41⋊C3C2×D313yes—
41#985—36no—
42#985—36no—
43C2×GL(2,𝔽3)—33no—
44C2×#226—33no—
45C3×#131—32no—
46C3×#131C2×D312yescomplemented
47C2×C3×M16—31no—
48C22×C3×C8—31no—
49#950—32no—
50#950—32no—
51#950—32no—
52#950—32no—
53C2×#216—31no—
54C2×#215—31no—
55C2×#214—31no—
56C2×#213—31no—
57C2×C4×Dic3—31no—
58C2×#208—31no—
59C22×C3⋊C8—31no—
60#901—34no—
61#901—62no—
62C2×ΓL(1,𝔽25)—61no—
63C2×ΓL(1,𝔽25)—123no—
64C2×D3×C8—61no—
65#131⋊C3C2×D316yescomplemented
66GU(2,𝔽3)—36no—
67#837—32no—
68#837—32no—
69#825—34no—
70#822—34no—
71#815—34no—
72C22×C3⋊D3—41no—
73C2×C32×C4—41no—
74C2×C3⋊Dic3—41no—
75C4×C3⋊D3—42no—
76C4×C3⋊D3—42no—
77C3×SL(2,𝔽3)C22×C411yescharacteristic
78C32×C8—42no—
79C3⋊(C3⋊C8)—42no—
80C2×#135—91no—
81C2×#131—91no—
82C2×#131C3⋊D311yescharacteristic, complemented
83#444—94no—
84#444—94no—
85C2×#108—91no—
86C2×#104—91no—
87C2×#104—91no—
88C2×#97—91no—
89C3×#41—31no—
90C3×#41—31no—
91C3×#41C4×D311yescharacteristic
92C3×#41C22×D311yescharacteristic
93C2×C3×Q8C4×D311yescharacteristic
94C2×C3×D4—31no—
95C22×C3×C4—31no—
96C2×#67—61no—
97C22×Dic3—61no—
98#235—32no—
99#235—32no—
100#235—61no—
101#235—61no—
102C2×D12—31no—
103C2×C4×D3—61no—
104C2×C4×D3—123no—
105C2×Dic6—31no—
106#41⋊C3C4×D313yes—
107#41⋊C3C22×D313yes—
108C2×SL(2,𝔽3)C4×D313yes—
109GL(2,𝔽3)—36no—
110#226—36no—
111C3×M16—32no—
112C3×M16—61no—
113C2×C3×C8—31no—
114C2×C3×C8—32no—
115C2×C3×C8—32no—
116C2×C3×C8—43no—
117C2×C3×C8S411yescharacteristic
118#216—32no—
119#216—32no—
120#215—32no—
121#215—32no—
122#214—32no—
123#214—32no—
124#213—32no—
125#213—32no—
126C4×Dic3—32no—
127C4×Dic3—61no—
128#208—32no—
129#208—61no—
130C2×C3⋊C8—32no—
131C2×C3⋊C8—31no—
132C2×C3⋊C8—31no—
133C2×C3⋊C8—32no—
134C2×C3⋊C8—61no—
135C2×C3⋊C8—123no—
136ΓL(1,𝔽25)—64no—
137ΓL(1,𝔽25)—1212no—
138D3×C8—64no—
139C22×C32—41no—
140C2×C3⋊D3—42no—
141C2×C3⋊D3—82no—
142C32×C4—41no—
143C32×C4—41no—
144C3⋊Dic3—42no—
145C2×#41—91no—
146C2×#41C2×C3⋊D311yescharacteristic
147#135—92no—
148#135—92no—
149#135—92no—
150#135—92no—
151C2×Q16—91no—
152C2×SD16—91no—
153C2×SD16—91no—
154C2×D8—91no—
155#131—32no—
156#131—94no—
157#131—182no—
158#131C2×C3⋊D312yescomplemented
159C2×M16—31no—
160C2×M16—91no—
161C2×M16—181no—
162C22×C8—31no—
163C22×C8—91no—
164C22×C8—181no—
165C2×C42—91no—
166#108—94no—
167#104—94no—
168#104—92no—
169#104—92no—
170#97—94no—
171C23×C3—31no—
172C22×D3—61no—
173C22×D3—123no—
174C3×Q8—31no—
175C3×Q8C2×C4×D311yescharacteristic
176C3×D4—31no—
177C3×D4—31no—
178C3×D4—61no—
179C2×C3×C4—31no—
180C2×C3×C4—31no—
181C2×C3×C4—31no—
182C2×C3×C4—31no—
183C2×C3×C4—31no—
184C2×C3×C4—43no—
185C2×C3×C4C2×S411yescharacteristic
186#67—62no—
187#67—62no—
188C2×Dic3—61no—
189C2×Dic3—62no—
190C2×Dic3—123no—
191C2×Dic3—122no—
192D12—32no—
193D12—61no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—126no—
197C4×D3—126no—
198Dic6—32no—
199Dic6—61no—
200SL(2,𝔽3)C2×C4×D313yes—
201C3×C8—32no—
202C3×C8—46no—
203C3×C8C2×S412yes—
204C3⋊C8—32no—
205C3⋊C8—32no—
206C3⋊C8—62no—
207C3⋊C8—126no—
208C2×C32—41no—
209C2×C32—42no—
210C3⋊D3—82no—
211#41—31no—
212#41—31no—
213#41—92no—
214#41—92no—
215#41—181no—
216#41—181no—
217#41C4×C3⋊D311yescharacteristic
218#41C22×C3⋊D311yescharacteristic
219C2×Q8—91no—
220C2×Q8C4×C3⋊D311yescharacteristic
221C2×D4—31no—
222C2×D4—91no—
223C2×D4—181no—
224C22×C4—31no—
225C22×C4—181no—
226C22×C4—181no—
227Q16—92no—
228Q16—92no—
229SD16—92no—
230SD16—92no—
231SD16—92no—
232SD16—92no—
233D8—92no—
234D8—92no—
235M16—32no—
236M16—61no—
237M16—92no—
238M16—181no—
239M16—184no—
240C2×C8—31no—
241C2×C8—32no—
242C2×C8—32no—
243C2×C8—92no—
244C2×C8—91no—
245C2×C8—91no—
246C2×C8—92no—
247C2×C8—184no—
248C2×C8—181no—
249C2×C8C3⋊S411yescharacteristic
250C42—92no—
251C42—181no—
252C22×C3—31no—
253C22×C3—31no—
254C22×C3—43no—
255C22×C3—62no—
256C22×C3C4×S411yescharacteristic
257C2×D3—62no—
258C2×D3—126no—
259C2×D3—122no—
260C2×D3—246no—
261C3×C4—31no—
262C3×C4—31no—
263C3×C4—43no—
264C3×C4—43no—
265C3×C4C4×S411yescharacteristic
266C3×C4C22×S411yescharacteristic
267Dic3—62no—
268Dic3—126no—
269Dic3—122no—
270C32—41noSylow
271C23—31no—
272C23—181no—
273Q8—31no—
274Q8—92no—
275Q8—181no—
276Q8C2×C4×C3⋊D311yescharacteristic
277D4—31no—
278D4—31no—
279D4—61no—
280D4—92no—
281D4—181no—
282D4—182no—
283D4—182no—
284C2×C4—31no—
285C2×C4—31no—
286C2×C4—31no—
287C2×C4—31no—
288C2×C4—31no—
289C2×C4—181no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—362no—
294C2×C4C2×C3⋊S411yescharacteristic
295C8—32no—
296C8—92no—
297C8—92no—
298C8—182no—
299C8C2×C3⋊S412yes—
300C2×C3—46no—
301C2×C3—43no—
302C2×C3—61no—
303C2×C3—61no—
304C2×C3#540512yescomplemented
305C2×C3C2×C4×S411yescharacteristic
306D3—122no—
307D3—246no—
308C22—31no—
309C22—31no—
310C22—62no—
311C22—182no—
312C22—362no—
313C22C4×C3⋊S411yescharacteristic
314C4—31no—
315C4—31no—
316C4—182no—
317C4—362no—
318C4C4×C3⋊S411yescharacteristic
319C4C22×C3⋊S411yescharacteristic
320C3—43no—
321C3C2×#540511yescharacteristic, complemented
322C2—61no—
323C2—61no—
324C2—362no—
325C2#1059363912yesdirect product factor
326C2C2×C4×C3⋊S411yescharacteristic
subgroupG/H
centerC2×C4C2×C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC4C22×C3⋊S4
FittingC2×C3×#131D3
socleC22×C3C4×S4
prime radicalC2×#64266C2
cosocleC3×#41⋊C3C23
hypercenterC2×C8C3⋊S4
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#131⋊C3C2semidirect
3. C2×C3⋊GU(2,𝔽3)C2semidirect
4. #10593639C2direct (N × H)
8. #64266C4semidirect
10. C2×C3⋊GL(2,𝔽3)C4semidirect
11. C2×C3⋊#226C4semidirect
13. C3×#131⋊C3C22semidirect
14. C3⋊GU(2,𝔽3)C22semidirect
16. C2×C3×#131D3semidirect
19. C2×#131⋊C3D3semidirect
32. C3⋊GL(2,𝔽3)C2×C4semidirect
33. C3⋊#226C2×C4semidirect
46. C3×#131C2×D3semidirect
65. #131⋊C3C2×D3semidirect
82. C2×#131C3⋊D3semidirect
158. #131C2×C3⋊D3semidirect
304. C2×C3#5405semidirect
321. C3C2×#5405semidirect
325. C2#10593639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642662
C2×C3×#131⋊C32
C2×C3⋊GU(2,𝔽3)2
#105936392
C2×#54053
C2×#51453
C2×#37434