Finite Group Databasebeta

← C2×#10593225 #11922267

Subgroups — C2×#10593225 #11922267

Order 1152.

585 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 585 conjugacy classes of subgroups — too many to draw. Only its 59 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×#64267C211yesmaximal, characteristic, complemented
2C2×C3×#986C211yesmaximal, characteristic, complemented
3C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
4#10593225C214yesmaximal, direct product factor
5C2×#5407—31nomaximal
6C2×#5199—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#64267—21no—
9#64267C2212yescomplemented
10C2×C3⋊GL(2,𝔽3)—21no—
11C3×#986—21no—
12C3×#986C2212yescomplemented
13C2×C3×GL(2,𝔽3)—21no—
14C2×#3714—41nomaximal
15C3⋊(#131⋊C3)C2212yescomplemented
16C2×#986—31no—
17C2×#986—61no—
18C2×#986D311yescharacteristic, complemented
19C2×C3×AGL(1,ℤ/8)—31no—
20C2×#949—31no—
21C2×#948D311yescharacteristic, complemented
22C22×#213—31no—
23C2×#131⋊C3—31no—
24#5407—34no—
25C2×#833—31no—
26#5199—34no—
27#5199—34no—
28C2×#823—31no—
29C2×#822—31no—
30C2×C4⋊(C3⋊D3)—41no—
31C2×C3×D12—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35C3⋊GL(2,𝔽3)—22no—
36C3×GL(2,𝔽3)—22no—
37C2×C3×C3⋊C8—41no—
38#3714—44no—
39C2×#472—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×D4—31no—
42C22×D12—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#986—21no—
46#986—32no—
47#986—62no—
48#986—62no—
49#986—61no—
50#986C2×D312yescomplemented
51C2×GL(2,𝔽3)—21no—
52C2×GL(2,𝔽3)—62no—
53C2×GL(2,𝔽3)—61no—
54C3×AGL(1,ℤ/8)—32no—
55C3×AGL(1,ℤ/8)—32no—
56C3×AGL(1,ℤ/8)—61no—
57C3×AGL(1,ℤ/8)—61no—
58C2×C3×SD16—61no—
59C2×C3×D8—61no—
60C2×C3×M16—31no—
61#949—32no—
62#949—32no—
63#949—61no—
64#949—61no—
65#948—32no—
66#948C2×D312yescomplemented
67C2×#215—61no—
68C2×#213—34no—
69C2×#213—61no—
70C2×#213—62no—
71C2×#213—61no—
72C2×#213—61no—
73C2×#208—31no—
74C2×#208—31no—
75C22×C3⋊C8—31no—
76C2×D24—121no—
77#131⋊C3—32no—
78#833—34no—
79#823—34no—
80#822—34no—
81C22×C3⋊D3—81no—
82C22×C3×D3—81no—
83C2×C32×C4—41no—
84C4⋊(C3⋊D3)—42no—
85C4⋊(C3⋊D3)—81no—
86C3×D12—42no—
87C3×D12—81no—
88C3×SL(2,𝔽3)C2×D411yescharacteristic
89C3×C3⋊C8—42no—
90C2×AGL(1,ℤ/8)—31no—
91C2×AGL(1,ℤ/8)—91no—
92C22×D8—91no—
93C2×#131—31no—
94#472—94no—
95#472—94no—
96C2×#108—91no—
97C2×#100—91no—
98C2×#100—91no—
99C24×C3—61no—
100C23×D3—61no—
101C3×#41—31no—
102C3×#41—31no—
103C3×#41D1211yescharacteristic
104C3×#41C22×D311yescharacteristic
105C2×C3×Q8D1211yescharacteristic
106C2×C3×D4—31no—
107C2×C3×D4—32no—
108C2×C3×D4—61no—
109C2×C3×D4—61no—
110C2×C3×D4—61no—
111C2×C3×D4—61no—
112C2×C3×D4—61no—
113C22×C3×C4—31no—
114C2×D12—32no—
115C2×D12—41no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—61no—
120C2×D12—61no—
121C2×D12—121no—
122C2×D12—241no—
123#41⋊C3—21no—
124#41⋊C3—21no—
125#41⋊C3#6711yescharacteristic
126#41⋊C3C22×D311yescharacteristic
127C2×SL(2,𝔽3)—21no—
128C2×SL(2,𝔽3)#6711yescharacteristic
129GL(2,𝔽3)—22no—
130GL(2,𝔽3)—64no—
131GL(2,𝔽3)—62no—
132C3×SD16—62no—
133C3×SD16—62no—
134C3×D8—62no—
135C3×D8—62no—
136C3×M16—32no—
137C3×M16—61no—
138C2×C3×C8—61no—
139C2×C3×C8—121no—
140#215—62no—
141#215—62no—
142#213—64no—
143#213—62no—
144#213—62no—
145#213—64no—
146#208—32no—
147#208—32no—
148#208—61no—
149#208—61no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—32no—
152C2×C3⋊C8—32no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8S411yescharacteristic
155D24—124no—
156C22×C32—41no—
157C2×C3⋊D3—82no—
158C2×C3⋊D3—162no—
159C2×C3×D3—82no—
160C2×C3×D3—162no—
161C32×C4—41no—
162C32×C4—41no—
163C2×#41D3211yescharacteristic
164C22×D4—31no—
165C22×D4—91no—
166AGL(1,ℤ/8)—32no—
167AGL(1,ℤ/8)—32no—
168AGL(1,ℤ/8)—61no—
169AGL(1,ℤ/8)—61no—
170AGL(1,ℤ/8)—92no—
171AGL(1,ℤ/8)—92no—
172AGL(1,ℤ/8)—181no—
173AGL(1,ℤ/8)—181no—
174C2×SD16—61no—
175C2×SD16—181no—
176C2×D8—61no—
177C2×D8—94no—
178C2×D8—181no—
179C2×D8—182no—
180C2×D8—181no—
181C2×D8—181no—
182#131—32no—
183#131—92no—
184C2×M16—31no—
185C2×M16—91no—
186C2×M16—91no—
187C22×C8—91no—
188#108—94no—
189#100—94no—
190#100—94no—
191C23×C3—31no—
192C23×C3—62no—
193C23×C3—121no—
194C23×C3—121no—
195C23×C3—242no—
196C22×D3—62no—
197C22×D3—81no—
198C22×D3—121no—
199C22×D3—121no—
200C22×D3—241no—
201C22×D3—242no—
202C22×D3—242no—
203C3×Q8—31no—
204C3×Q8C2×D1211yescharacteristic
205C3×D4—31no—
206C3×D4—31no—
207C3×D4—61no—
208C3×D4—62no—
209C3×D4—62no—
210C3×D4—121no—
211C3×D4—121no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—41no—
218C2×C3×C4—81no—
219C2×C3×C4C2×S411yescharacteristic
220D12—42no—
221D12—62no—
222D12—62no—
223D12—81no—
224D12—122no—
225D12—121no—
226D12—121no—
227D12—242no—
228D12—241no—
229D12—242no—
230SL(2,𝔽3)—21no—
231SL(2,𝔽3)C2×#6711yescharacteristic
232C3×C8—62no—
233C3×C8—122no—
234C3⋊C8—32no—
235C3⋊C8—62no—
236C3⋊C8C2×S412yes—
237C2×C32—41no—
238C2×C32—42no—
239C3⋊D3—162no—
240C3×D3—162no—
241C24—61no—
242C24—181no—
243#41—31no—
244#41—31no—
245#41#62611yescharacteristic
246#41C2×D3211yescharacteristic
247C2×Q8#62611yescharacteristic
248C2×D4—31no—
249C2×D4—32no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—61no—
255C2×D4—92no—
256C2×D4—181no—
257C2×D4—181no—
258C2×D4—181no—
259C2×D4—181no—
260C2×D4—181no—
261C22×C4—31no—
262SD16—62no—
263SD16—62no—
264SD16—182no—
265SD16—182no—
266D8—62no—
267D8—62no—
268D8—184no—
269D8—184no—
270D8—182no—
271D8—182no—
272M16—32no—
273M16—61no—
274M16—92no—
275M16—92no—
276M16—181no—
277M16—181no—
278C2×C8—31no—
279C2×C8—61no—
280C2×C8—92no—
281C2×C8—92no—
282C2×C8—91no—
283C2×C8—181no—
284C22×C3—31no—
285C22×C3—31no—
286C22×C3—41no—
287C22×C3—62no—
288C22×C3—81no—
289C22×C3—122no—
290C22×C3—242no—
291C22×C3—242no—
292C22×C3—242no—
293C22×C3C4⋊S411yescharacteristic
294C2×D3—82no—
295C2×D3—122no—
296C2×D3—162no—
297C2×D3—242no—
298C2×D3—244no—
299C2×D3—242no—
300C2×D3—242no—
301C2×D3—242no—
302C2×D3—482no—
303C2×D3—484no—
304C3×C4—31no—
305C3×C4—31no—
306C3×C4—41no—
307C3×C4—41no—
308C3×C4—81no—
309C3×C4—81no—
310C3×C4C4⋊S411yescharacteristic
311C3×C4C22×S411yescharacteristic
312C32—41noSylow
313C23—31no—
314C23—62no—
315C23—121no—
316C23—121no—
317C23—182no—
318C23—242no—
319C23—361no—
320C23—361no—
321C23—722no—
322Q8—31no—
323Q8C2×#62611yescharacteristic
324D4—31no—
325D4—31no—
326D4—61no—
327D4—62no—
328D4—62no—
329D4—121no—
330D4—121no—
331D4—182no—
332D4—182no—
333D4—361no—
334D4—361no—
335C2×C4—31no—
336C2×C4—31no—
337C2×C4—31no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4D3×S411yescharacteristic
341C8—32no—
342C8—62no—
343C8—92no—
344C8—182no—
345C2×C3—41no—
346C2×C3—42no—
347C2×C3—61no—
348C2×C3—61no—
349C2×C3—81no—
350C2×C3—82no—
351C2×C3—242no—
352C2×C3#540712yescomplemented
353C2×C3C2×C4⋊S411yescharacteristic
354D3—162no—
355D3—242no—
356D3—482no—
357D3—484no—
358C22—31no—
359C22—31no—
360C22—62no—
361C22—122no—
362C22—242no—
363C22—242no—
364C22—242no—
365C22—362no—
366C22—722no—
367C22—722no—
368C22—722no—
369C22#6420711yescharacteristic
370C4—31no—
371C4—31no—
372C4#6420711yescharacteristic
373C4C2×D3×S411yescharacteristic
374C3—41no—
375C3—81no—
376C3C2×#540711yescharacteristic, complemented
377C2—61no—
378C2—61no—
379C2—242no—
380C2—722no—
381C2#1059322512yesdirect product factor
382C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64267C2semidirect
2. C2×C3×#986C2semidirect
3. C2×C3⋊(#131⋊C3)C2semidirect
4. #10593225C2direct (N × H)
9. #64267C22semidirect
12. C3×#986C22semidirect
15. C3⋊(#131⋊C3)C22semidirect
18. C2×#986D3semidirect
21. C2×#948D3semidirect
50. #986C2×D3semidirect
66. #948C2×D3semidirect
352. C2×C3#5407semidirect
376. C3C2×#5407semidirect
381. C2#10593225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642672
C2×C3×#9862
C2×C3⋊(#131⋊C3)2
#105932252
C2×#54073
C2×#51993
C2×#37144