Finite Group Databasebeta

← C2×#10593665 #11923081

Subgroups — C2×#10593665 #11923081

Order 1152.

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

normal subgroups only

This group has 752 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×C3×2−1+4⋊C3C211yesmaximal, characteristic, complemented
2C2×#64267C211yesmaximal, characteristic, complemented
3#10593665C214yesmaximal, direct product factor
4C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×#5431—33nomaximal
6C2×#5245—31nomaximal
7C3×2−1+4⋊C3—21no—
8C3×2−1+4⋊C3C2212yescomplemented
9C2×C3×#41⋊C3C2211yescharacteristic
10C22×C3×SL(2,𝔽3)—21no—
11#64267—21no—
12#64267C2212yescomplemented
13C2×C3⋊GL(2,𝔽3)—21no—
14C2×#3753—41nomaximal
15C3⋊GU(2,𝔽3)C2212yescomplemented
16C2×C3×2−1+4D311yescharacteristic, complemented
17C2×2−1+4⋊C3D313yescomplemented
18C2×#986—33no—
19C2×#949—31no—
20C2×#949—31no—
21C2×#947—31no—
22#5431—312no—
23C2×GU(2,𝔽3)—33no—
24#5245—34no—
25#5245—34no—
26C2×#837—31no—
27C2×#837—31no—
28C2×#836—31no—
29C2×C32×D4—41no—
30C2×C4⋊(C3⋊D3)—41no—
31C3×#41⋊C3D411yescharacteristic
32C3×#41⋊C3C2311yescharacteristic
33C2×C3×SL(2,𝔽3)—22no—
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35C3⋊GL(2,𝔽3)—22no—
36#3753—44no—
37C2×C3⋊(C3⋊C8)—41no—
38C2×#454—91noSylow
39C3×2−1+4—21no—
40C3×2−1+4—32no—
41C3×2−1+4—61no—
42C3×2−1+4C2×D312yescomplemented
43C2×C3×#41—31no—
44C2×C3×#41—61no—
45C2×C3×#41C2×D311yescharacteristic
46C22×C3×Q8—21no—
47C22×C3×Q8—31no—
48C22×D12—31no—
492−1+4⋊C3—23no—
502−1+4⋊C3C2×D316yescomplemented
51C2×#41⋊C3C2×D313yes—
52C22×SL(2,𝔽3)—23no—
53#986—36no—
54#986—63no—
55C2×GL(2,𝔽3)—63no—
56#949—32no—
57#949—34no—
58#949—32no—
59#949—61no—
60#949—62no—
61#949—61no—
62#947—34no—
63#947—62no—
64C2×#215—61no—
65C2×#215—61no—
66C2×#213—61no—
67C2×#213—61no—
68C2×#213—123no—
69C2×(C2×D3)⋊C4—62no—
70C2×C4×Dic3—31no—
71C2×#208—31no—
72C2×#208—31no—
73GU(2,𝔽3)—36no—
74#837—32no—
75#837—34no—
76#837—32no—
77#836—34no—
78C23×C32—81no—
79C22×C3⋊D3—81no—
80C32×D4—42no—
81C32×D4—81no—
82C2×C32×C4—41no—
83C4⋊(C3⋊D3)—42no—
84C4⋊(C3⋊D3)—81no—
85C3×SL(2,𝔽3)C2×D411yescharacteristic
86C3⋊(C3⋊C8)—42no—
87C2×2−1+4C3⋊D311yescharacteristic, complemented
88C2×AGL(1,ℤ/8)—91no—
89C2×AGL(1,ℤ/8)—91no—
90C2×#124—91no—
91#454—94no—
92#454—94no—
93C2×#104—91no—
94C2×#104—91no—
95C2×#101—91no—
96C23×D3—61no—
97C3×#41—31no—
98C3×#41—31no—
99C3×#41—32no—
100C3×#41—32no—
101C3×#41—62no—
102C3×#41—61no—
103C3×#41—61no—
104C3×#41—64no—
105C3×#41—62no—
106C3×#41#6711yescharacteristic
107C3×#41C22×D311yescharacteristic
108C2×C3×Q8—22no—
109C2×C3×Q8—32no—
110C2×C3×Q8—32no—
111C2×C3×Q8—31no—
112C2×C3×Q8—61no—
113C2×C3×Q8—61no—
114C2×C3×Q8—61no—
115C2×C3×Q8—62no—
116C2×C3×Q8#6711yescharacteristic
117C2×C3×D4—31no—
118C2×C3×D4—43no—
119C2×C3×D4—61no—
120C2×C3×D4S411yescharacteristic
121C22×C3×C4—31no—
122C22×C3×C4—32no—
123C22×C3×C4—61no—
124C22×Dic3—61no—
125C2×D12—32no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—123no—
132#41⋊C3#6713yes—
133#41⋊C3C22×D313yes—
134C2×SL(2,𝔽3)—26no—
135C2×SL(2,𝔽3)#6713yes—
136GL(2,𝔽3)—66no—
137#215—62no—
138#215—64no—
139#215—62no—
140#213—62no—
141#213—62no—
142#213—64no—
143#213—1212no—
144(C2×D3)⋊C4—68no—
145C4×Dic3—32no—
146C4×Dic3—61no—
147#208—32no—
148#208—32no—
149#208—61no—
150#208—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—123no—
154C22×C32—41no—
155C22×C32—82no—
156C22×C32—162no—
157C2×C3⋊D3—82no—
158C2×C3⋊D3—162no—
159C32×C4—41no—
160C32×C4—41no—
1612−1+4—21no—
1622−1+4—32no—
1632−1+4—61no—
1642−1+4C2×C3⋊D312yescomplemented
165C2×#41—31no—
166C2×#41—61no—
167C2×#41C2×C3⋊D311yescharacteristic
168C22×Q8—21no—
169C22×Q8—31no—
170C22×D4—91no—
171AGL(1,ℤ/8)—92no—
172AGL(1,ℤ/8)—94no—
173AGL(1,ℤ/8)—92no—
174AGL(1,ℤ/8)—181no—
175AGL(1,ℤ/8)—182no—
176AGL(1,ℤ/8)—181no—
177C2×SD16—181no—
178C2×SD16—181no—
179C2×D8—181no—
180C2×D8—181no—
181C2×M16—91no—
182C2×M16—91no—
183#124—94no—
184#124—182no—
185C2×C22⋊C4—182no—
186C2×C42—91no—
187#104—92no—
188#104—94no—
189#104—92no—
190#101—94no—
191C23×C3—21no—
192C23×C3—31no—
193C23×C3—83no—
194C22×D3—62no—
195C22×D3—121no—
196C22×D3—124no—
197C22×D3—121no—
198C22×D3—243no—
199C3×Q8—31no—
200C3×Q8—32no—
201C3×Q8—62no—
202C3×Q8—62no—
203C3×Q8—61no—
204C3×Q8C2×#6711yescharacteristic
205C3×D4—21no—
206C3×D4—31no—
207C3×D4—31no—
208C3×D4—46no—
209C3×D4—61no—
210C3×D4—62no—
211C3×D4—62no—
212C3×D4—83no—
213C3×D4C2×S412yes—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—34no—
220C2×C3×C4—43no—
221C2×C3×C4—62no—
222C2×C3×C4—62no—
223C2×C3×C4—62no—
224C2×C3×C4—61no—
225C2×C3×C4C2×S411yescharacteristic
226C2×Dic3—62no—
227C2×Dic3—122no—
228D12—62no—
229D12—62no—
230D12—126no—
231D12—121no—
232D12—121no—
233D12—243no—
234SL(2,𝔽3)C2×#6713yes—
235C3⋊C8—62no—
236C3⋊C8—62no—
237C3⋊C8—126no—
238C2×C32—41no—
239C2×C32—42no—
240C2×C32—162no—
241C3⋊D3—162no—
242C24—181no—
243#41—31no—
244#41—31no—
245#41—32no—
246#41—32no—
247#41—62no—
248#41—61no—
249#41—61no—
250#41—64no—
251#41—62no—
252#41#63811yescharacteristic
253#41C22×C3⋊D311yescharacteristic
254C2×Q8—22no—
255C2×Q8—32no—
256C2×Q8—32no—
257C2×Q8—31no—
258C2×Q8—61no—
259C2×Q8—61no—
260C2×Q8—61no—
261C2×Q8—62no—
262C2×Q8#63811yescharacteristic
263C2×D4—31no—
264C2×D4—61no—
265C2×D4—92no—
266C2×D4—181no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4C3⋊S411yescharacteristic
272C22×C4—31no—
273C22×C4—32no—
274C22×C4—61no—
275C22×C4—181no—
276SD16—182no—
277SD16—184no—
278SD16—182no—
279D8—182no—
280D8—182no—
281D8—184no—
282M16—92no—
283M16—92no—
284M16—181no—
285M16—181no—
286C2×C8—181no—
287C2×C8—181no—
288C22⋊C4—188no—
289C42—92no—
290C42—181no—
291C22×C3—22no—
292C22×C3—31no—
293C22×C3—31no—
294C22×C3—42no—
295C22×C3—43no—
296C22×C3—62no—
297C22×C3—86no—
298C22×C3—166no—
299C22×C3GL(2,ℤ/4)11yescharacteristic
300C2×D3—124no—
301C2×D3—122no—
302C2×D3—246no—
303C2×D3—242no—
304C2×D3—242no—
305C2×D3—486no—
306C3×C4—31no—
307C3×C4—31no—
308C3×C4—43no—
309C3×C4—43no—
310C3×C4—62no—
311C3×C4GL(2,ℤ/4)11yescharacteristic
312C3×C4C22×S411yescharacteristic
313Dic3—122no—
314C32—41noSylow
315C23—21no—
316C23—31no—
317C23—182no—
318C23—361no—
319C23—364no—
320C23—361no—
321Q8—31no—
322Q8—32no—
323Q8—62no—
324Q8—62no—
325Q8—61no—
326Q8C2×#63811yescharacteristic
327D4—21no—
328D4—31no—
329D4—31no—
330D4—61no—
331D4—62no—
332D4—62no—
333D4—182no—
334D4—182no—
335D4—361no—
336D4—361no—
337D4C2×C3⋊S412yes—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—34no—
344C2×C4—62no—
345C2×C4—62no—
346C2×C4—62no—
347C2×C4—61no—
348C2×C4—182no—
349C2×C4—362no—
350C2×C4C2×C3⋊S411yescharacteristic
351C8—182no—
352C8—182no—
353C2×C3—42no—
354C2×C3—46no—
355C2×C3—43no—
356C2×C3—61no—
357C2×C3—61no—
358C2×C3—166no—
359C2×C3#543112yescomplemented
360C2×C3C2×GL(2,ℤ/4)11yescharacteristic
361D3—242no—
362D3—486no—
363C22—22no—
364C22—31no—
365C22—31no—
366C22—42no—
367C22—62no—
368C22—364no—
369C22—362no—
370C22—722no—
371C22—722no—
372C22#6426911yescharacteristic
373C4—31no—
374C4—31no—
375C4—62no—
376C4—362no—
377C4#6426911yescharacteristic
378C4C22×C3⋊S411yescharacteristic
379C3—43no—
380C3C2×#543111yescharacteristic, complemented
381C2—42no—
382C2—61no—
383C2—61no—
384C2—722no—
385C2#1059366512yesdirect product factor
386C2C2×#6426911yescharacteristic
subgroupG/H
centerC22#64269
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC2×C3×2−1+4D3
socleC22×C3GL(2,ℤ/4)
hypercenterC2×D4C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×2−1+4⋊C3C2semidirect
2. C2×#64267C2semidirect
3. #10593665C2direct (N × H)
4. C2×C3⋊GU(2,𝔽3)C2semidirect
8. C3×2−1+4⋊C3C22semidirect
12. #64267C22semidirect
15. C3⋊GU(2,𝔽3)C22semidirect
16. C2×C3×2−1+4D3semidirect
17. C2×2−1+4⋊C3D3semidirect
42. C3×2−1+4C2×D3semidirect
50. 2−1+4⋊C3C2×D3semidirect
87. C2×2−1+4C3⋊D3semidirect
164. 2−1+4C2×C3⋊D3semidirect
359. C2×C3#5431semidirect
380. C3C2×#5431semidirect
385. C2#10593665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×2−1+4⋊C32
C2×#642672
#105936652
C2×C3⋊GU(2,𝔽3)2
C2×#54313
C2×#52453
C2×#37534