Finite Group Databasebeta

← C2×#10593663 #11923074

Subgroups — C2×#10593663 #11923074

Order 1152.

812 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 81 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×#994C211yesmaximal, characteristic, complemented
2C2×#64267C211yesmaximal, characteristic, complemented
3#10593663C214yesmaximal, direct product factor
4C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×#5429—33nomaximal
6C2×#5241—31nomaximal
7C3×#994—21no—
8C3×#994C2212yescomplemented
9C2×C3×#41⋊C3—21no—
10C2×C3×#41⋊C3C2211yescharacteristic
11#64267—21no—
12#64267C2212yescomplemented
13C2×C3⋊GL(2,𝔽3)—21no—
14C2×#3755—41nomaximal
15C3⋊GU(2,𝔽3)C2212yescomplemented
16C2×C3×H(5,𝔽2)D311yescharacteristic, complemented
17C2×#994D313yescomplemented
18C2×#986—33no—
19C2×#949—31no—
20C2×#949—31no—
21C2×#940—31no—
22#5429—312no—
23C2×GU(2,𝔽3)—33no—
24#5241—34no—
25#5241—34no—
26C2×#837—31no—
27C2×#837—31no—
28C2×#833—31no—
29C2×C32×Q8—41no—
30C2×C4⋊(C3⋊D3)—41no—
31C3×#41⋊C3—22no—
32C3×#41⋊C3D411yescharacteristic, complemented
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic, complemented
35C3⋊GL(2,𝔽3)—22no—
36#3755—44no—
37C2×C3⋊(C3⋊C8)—41no—
38C2×#453—91noSylow
39C3×H(5,𝔽2)—21no—
40C3×H(5,𝔽2)—32no—
41C3×H(5,𝔽2)—61no—
42C3×H(5,𝔽2)C2×D312yescomplemented
43C2×C3×#41—21no—
44C2×C3×#41—31no—
45C2×C3×#41C2×D311yescharacteristic
46C22×C3×D4—31no—
47C22×C3×D4—61no—
48C22×#67—62no—
49C22×D12—31no—
50#994—23no—
51#994C2×D316yescomplemented
52C2×#41⋊C3—23no—
53C2×#41⋊C3C2×D313yes—
54#986—36no—
55#986—63no—
56C2×GL(2,𝔽3)—63no—
57#949—32no—
58#949—34no—
59#949—32no—
60#949—61no—
61#949—62no—
62#949—61no—
63C2×#215—61no—
64C2×#215—61no—
65C2×#215—123no—
66#940—34no—
67#940—62no—
68C2×#213—61no—
69C2×#213—61no—
70C2×C4×Dic3—31no—
71C2×#208—31no—
72C2×#208—31no—
73GU(2,𝔽3)—36no—
74#837—32no—
75#837—34no—
76#837—32no—
77#833—34no—
78C22×C3⋊D3—81no—
79C32×Q8—42no—
80C32×Q8—81no—
81C2×C32×C4—41no—
82C2×C32×C4—81no—
83C4⋊(C3⋊D3)—42no—
84C4⋊(C3⋊D3)—81no—
85C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
86C3⋊(C3⋊C8)—42no—
87C2×H(5,𝔽2)C3⋊D311yescharacteristic, complemented
88C2×AGL(1,ℤ/8)—91no—
89C2×AGL(1,ℤ/8)—91no—
90C2×#127—91no—
91#453—94no—
92#453—94no—
93C2×#104—91no—
94C2×#104—91no—
95C2×#100—91no—
96C24×C3—32no—
97C23×D3—61no—
98C3×#41—22no—
99C3×#41—31no—
100C3×#41—31no—
101C3×#41—32no—
102C3×#41—32no—
103C3×#41—61no—
104C3×#41—61no—
105C3×#41—62no—
106C3×#41#6711yescharacteristic
107C3×#41C22×D311yescharacteristic
108C2×C3×Q8—43no—
109C2×C3×Q8#6711yescharacteristic
110C2×C3×Q8S411yescharacteristic
111C2×C3×D4—31no—
112C2×C3×D4—32no—
113C2×C3×D4—32no—
114C2×C3×D4—31no—
115C2×C3×D4—61no—
116C2×C3×D4—61no—
117C2×C3×D4—61no—
118C2×C3×D4—61no—
119C2×C3×D4—62no—
120C2×C3×D4—62no—
121C2×C3×D4—64no—
122C22×C3×C4—31no—
123C22×C3×C4—61no—
124C2×#67—68no—
125C2×#67—128no—
126C22×Dic3—61no—
127C2×D12—32no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—123no—
134#41⋊C3—26no—
135#41⋊C3#6713yescomplemented
136#41⋊C3C22×D313yes—
137C2×SL(2,𝔽3)#6713yescomplemented
138GL(2,𝔽3)—66no—
139#215—62no—
140#215—62no—
141#215—64no—
142#215—1212no—
143#213—62no—
144#213—62no—
145#213—64no—
146C4×Dic3—32no—
147C4×Dic3—61no—
148#208—32no—
149#208—32no—
150#208—61no—
151#208—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—123no—
155C22×C32—41no—
156C2×C3⋊D3—82no—
157C2×C3⋊D3—162no—
158C32×C4—41no—
159C32×C4—41no—
160C32×C4—82no—
161H(5,𝔽2)—21no—
162H(5,𝔽2)—32no—
163H(5,𝔽2)—61no—
164H(5,𝔽2)C2×C3⋊D312yescomplemented
165C2×#41—21no—
166C2×#41—31no—
167C2×#41C2×C3⋊D311yescharacteristic
168C22×D4—31no—
169C22×D4—61no—
170C22×D4—91no—
171C22×D4—182no—
172AGL(1,ℤ/8)—92no—
173AGL(1,ℤ/8)—94no—
174AGL(1,ℤ/8)—92no—
175AGL(1,ℤ/8)—181no—
176AGL(1,ℤ/8)—182no—
177AGL(1,ℤ/8)—181no—
178C2×SD16—181no—
179C2×SD16—181no—
180C2×D8—181no—
181C2×D8—181no—
182C2×M16—91no—
183C2×M16—91no—
184#127—94no—
185#127—182no—
186C2×C42—91no—
187#104—92no—
188#104—94no—
189#104—92no—
190#100—94no—
191C23×C3—31no—
192C23×C3—34no—
193C23×C3—62no—
194C23×C3—61no—
195C23×C3—124no—
196C22×D3—62no—
197C22×D3—121no—
198C22×D3—124no—
199C22×D3—121no—
200C22×D3—243no—
201C3×Q8—21no—
202C3×Q8—31no—
203C3×Q8—46no—
204C3×Q8—83no—
205C3×Q8C2×#6711yescharacteristic
206C3×Q8C2×S412yes—
207C3×D4—31no—
208C3×D4—31no—
209C3×D4—32no—
210C3×D4—62no—
211C3×D4—62no—
212C3×D4—61no—
213C3×D4—62no—
214C3×D4—62no—
215C3×D4—61no—
216C2×C3×C4—21no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—31no—
220C2×C3×C4—31no—
221C2×C3×C4—31no—
222C2×C3×C4—43no—
223C2×C3×C4—62no—
224C2×C3×C4—62no—
225C2×C3×C4—83no—
226C2×C3×C4C2×S411yescharacteristic
227#67—1216no—
228C2×Dic3—62no—
229C2×Dic3—64no—
230D12—62no—
231D12—62no—
232D12—126no—
233D12—121no—
234D12—121no—
235D12—243no—
236SL(2,𝔽3)C2×#6713yescomplemented
237C3⋊C8—62no—
238C3⋊C8—62no—
239C3⋊C8—126no—
240C2×C32—41no—
241C2×C32—42no—
242C3⋊D3—162no—
243C24—32no—
244C24—181no—
245#41—22no—
246#41—31no—
247#41—31no—
248#41—32no—
249#41—32no—
250#41—61no—
251#41—61no—
252#41—62no—
253#41#63811yescharacteristic
254#41C22×C3⋊D311yescharacteristic
255C2×Q8#63811yescharacteristic
256C2×Q8C3⋊S411yescharacteristic
257C2×D4—31no—
258C2×D4—32no—
259C2×D4—32no—
260C2×D4—31no—
261C2×D4—61no—
262C2×D4—61no—
263C2×D4—61no—
264C2×D4—61no—
265C2×D4—62no—
266C2×D4—62no—
267C2×D4—64no—
268C2×D4—92no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—181no—
272C2×D4—181no—
273C2×D4—188no—
274C2×D4—181no—
275C2×D4—368no—
276C22×C4—31no—
277C22×C4—61no—
278C22×C4—181no—
279SD16—182no—
280SD16—184no—
281SD16—182no—
282D8—182no—
283D8—182no—
284D8—184no—
285M16—92no—
286M16—92no—
287M16—181no—
288M16—181no—
289C2×C8—181no—
290C2×C8—181no—
291C42—92no—
292C42—181no—
293C22×C3—31no—
294C22×C3—31no—
295C22×C3—43no—
296C22×C3—62no—
297C22×C3—62no—
298C22×C3—124no—
299C22×C3—122no—
300C22×C3—242no—
301C22×C3GL(2,ℤ/4)11yescharacteristic
302C2×D3—124no—
303C2×D3—122no—
304C2×D3—246no—
305C2×D3—242no—
306C2×D3—242no—
307C2×D3—486no—
308C3×C4—22no—
309C3×C4—31no—
310C3×C4—31no—
311C3×C4—43no—
312C3×C4—43no—
313C3×C4—86no—
314C3×C4GL(2,ℤ/4)11yescharacteristic
315C3×C4C22×S411yescharacteristic
316Dic3—64no—
317C32—41noSylow
318C23—31no—
319C23—34no—
320C23—62no—
321C23—61no—
322C23—124no—
323C23—182no—
324C23—361no—
325C23—364no—
326C23—361no—
327Q8—21no—
328Q8—31no—
329Q8C2×#63811yescharacteristic
330Q8C2×C3⋊S412yes—
331D4—31no—
332D4—31no—
333D4—32no—
334D4—62no—
335D4—62no—
336D4—61no—
337D4—62no—
338D4—62no—
339D4—61no—
340D4—182no—
341D4—182no—
342D4—361no—
343D4—3616no—
344D4—361no—
345C2×C4—21no—
346C2×C4—31no—
347C2×C4—31no—
348C2×C4—31no—
349C2×C4—31no—
350C2×C4—31no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—182no—
354C2×C4—184no—
355C2×C4C2×C3⋊S411yescharacteristic
356C8—182no—
357C8—182no—
358C2×C3—46no—
359C2×C3—43no—
360C2×C3—61no—
361C2×C3—61no—
362C2×C3—122no—
363C2×C3#542912yescomplemented
364C2×C3C2×GL(2,ℤ/4)11yescharacteristic
365D3—242no—
366D3—486no—
367C22—31no—
368C22—31no—
369C22—62no—
370C22—62no—
371C22—124no—
372C22—122no—
373C22—242no—
374C22—364no—
375C22—362no—
376C22—722no—
377C22—722no—
378C22#6426911yescharacteristic
379C4—22no—
380C4—31no—
381C4—31no—
382C4—184no—
383C4#6426911yescharacteristic
384C4C22×C3⋊S411yescharacteristic
385C3—43no—
386C3C2×#542911yescharacteristic, complemented
387C2—61no—
388C2—61no—
389C2—122no—
390C2—722no—
391C2#1059366312yesdirect product factor
392C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC2×C3×H(5,𝔽2)D3
socleC22×C3GL(2,ℤ/4)
hypercenterC2×Q8C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#994C2semidirect
2. C2×#64267C2semidirect
3. #10593663C2direct (N × H)
4. C2×C3⋊GU(2,𝔽3)C2semidirect
8. C3×#994C22semidirect
12. #64267C22semidirect
15. C3⋊GU(2,𝔽3)C22semidirect
16. C2×C3×H(5,𝔽2)D3semidirect
17. C2×#994D3semidirect
32. C3×#41⋊C3D4semidirect
34. C2×C3×SL(2,𝔽3)D4semidirect
42. C3×H(5,𝔽2)C2×D3semidirect
51. #994C2×D3semidirect
85. C3×SL(2,𝔽3)C2×D4semidirect
87. C2×H(5,𝔽2)C3⋊D3semidirect
135. #41⋊C3#67semidirect
137. C2×SL(2,𝔽3)#67semidirect
164. H(5,𝔽2)C2×C3⋊D3semidirect
236. SL(2,𝔽3)C2×#67semidirect
363. C2×C3#5429semidirect
386. C3C2×#5429semidirect
391. C2#10593663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9942
C2×#642672
#105936632
C2×C3⋊GU(2,𝔽3)2
C2×#54293
C2×#52413
C2×#37554