Finite Group Databasebeta

← C2×#10593224 #11922266

Subgroups — C2×#10593224 #11922266

Order 1152.

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

normal subgroups only

This group has 557 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
2C2×C3×#984C211yesmaximal, characteristic, complemented
3C2×C3⋊(#131⋊C3)C211yesmaximal, characteristic, complemented
4#10593224C214yesmaximal, direct product factor
5C2×#5406—31nomaximal
6C2×#5203—31nomaximal
7C2×C3×#41⋊C3C2211yescharacteristic
8#64267—21no—
9#64267C2212yes—
10C2×C3⋊GL(2,𝔽3)—21no—
11C3×#984—21no—
12C3×#984C2212yescomplemented
13C2×C3×#226—21no—
14C2×#3717—41nomaximal
15C3⋊(#131⋊C3)C2212yescomplemented
16C2×#986—31no—
17C2×#986—61no—
18C2×#984D311yescharacteristic, complemented
19C2×C3×#137—31no—
20C2×#949—31no—
21C2×#948D311yescharacteristic, complemented
22C22×#215—31no—
23C2×#131⋊C3—31no—
24#5406—34no—
25C2×#836—31no—
26#5203—34no—
27#5203—34no—
28C2×#823—31no—
29C2×#822—31no—
30C2×C4⋊(C3⋊D3)—41no—
31C2×C3×Dic6—41no—
32C3×#41⋊C3D411yescharacteristic
33C3×#41⋊C3C2311yescharacteristic
34C2×C3×SL(2,𝔽3)D411yescharacteristic
35C3⋊GL(2,𝔽3)—22no—
36C3×#226—22no—
37C2×C3×C3⋊C8—41no—
38#3717—44no—
39C2×#471—91noSylow
40C2×C3×#41C2×D311yescharacteristic
41C22×C3×Q8—31no—
42C22×D12—31no—
43C2×#41⋊C3—21no—
44C2×#41⋊C3C2×D311yescharacteristic
45#986—32no—
46#986—62no—
47#986—62no—
48#986—61no—
49#984—21no—
50#984C2×D312yescomplemented
51C2×GL(2,𝔽3)—62no—
52C2×GL(2,𝔽3)—61no—
53C2×#226—21no—
54C3×#137—32no—
55C3×#137—32no—
56C3×#137—61no—
57C3×#137—61no—
58C2×C3×Q16—61no—
59C2×C3×SD16—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—34no—
68C2×#215—61no—
69C2×#215—62no—
70C2×#215—61no—
71C2×#215—61no—
72C2×#213—61no—
73C2×#208—31no—
74C2×#208—31no—
75C22×C3⋊C8—31no—
76C2×#204—121no—
77#131⋊C3—32no—
78#836—34no—
79#823—34no—
80#822—34no—
81C22×C3⋊D3—81no—
82C2×C32×C4—41no—
83C4⋊(C3⋊D3)—42no—
84C4⋊(C3⋊D3)—81no—
85C2×C3×Dic3—81no—
86C3×Dic6—42no—
87C3×Dic6—81no—
88C3×SL(2,𝔽3)C2×D411yescharacteristic
89C3×C3⋊C8—42no—
90C2×#137—31no—
91C2×AGL(1,ℤ/8)—91no—
92C22×SD16—91no—
93C2×#131—31no—
94#471—94no—
95#471—94no—
96C2×#108—91no—
97C2×#101—91no—
98C2×#100—91no—
99C23×D3—61no—
100C3×#41—31no—
101C3×#41—31no—
102C3×#41D1211yescharacteristic
103C3×#41C22×D311yescharacteristic
104C2×C3×Q8—32no—
105C2×C3×Q8—61no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×C3×Q8—61no—
110C2×C3×Q8D1211yescharacteristic
111C2×C3×D4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—61no—
114C2×D12—32no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—61no—
120C2×D12—121no—
121C2×D12—241no—
122C2×Dic6—41no—
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)—64no—
130GL(2,𝔽3)—62no—
131#226—22no—
132C3×Q16—62no—
133C3×Q16—62no—
134C3×SD16—62no—
135C3×SD16—62no—
136C3×M16—32no—
137C3×M16—61no—
138C2×C3×C8—61no—
139C2×C3×C8—121no—
140#215—64no—
141#215—62no—
142#215—62no—
143#215—64no—
144#213—62no—
145#213—62no—
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
155#204—124no—
156C22×C32—41no—
157C2×C3⋊D3—82no—
158C2×C3⋊D3—162no—
159C32×C4—41no—
160C32×C4—41no—
161C3×Dic3—82no—
162C2×#41D3211yescharacteristic
163C22×Q8—31no—
164C22×D4—91no—
165#137—32no—
166#137—32no—
167#137—61no—
168#137—61no—
169AGL(1,ℤ/8)—92no—
170AGL(1,ℤ/8)—92no—
171AGL(1,ℤ/8)—181no—
172AGL(1,ℤ/8)—181no—
173C2×Q16—61no—
174C2×SD16—61no—
175C2×SD16—94no—
176C2×SD16—181no—
177C2×SD16—182no—
178C2×SD16—181no—
179C2×SD16—181no—
180C2×D8—181no—
181#131—32no—
182#131—92no—
183C2×M16—31no—
184C2×M16—91no—
185C2×M16—91no—
186C22×C8—91no—
187#108—94no—
188#101—94no—
189#100—94no—
190C23×C3—31no—
191C22×D3—62no—
192C22×D3—121no—
193C22×D3—121no—
194C22×D3—241no—
195C22×D3—242no—
196C22×D3—242no—
197C3×Q8—31no—
198C3×Q8—62no—
199C3×Q8—62no—
200C3×Q8—121no—
201C3×Q8—121no—
202C3×Q8C2×D1211yescharacteristic
203C3×D4—31no—
204C3×D4—31no—
205C3×D4—61no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—31no—
209C2×C3×C4—31no—
210C2×C3×C4—31no—
211C2×C3×C4—41no—
212C2×C3×C4—62no—
213C2×C3×C4—81no—
214C2×C3×C4—121no—
215C2×C3×C4—121no—
216C2×C3×C4C2×S411yescharacteristic
217C2×Dic3—81no—
218D12—62no—
219D12—62no—
220D12—122no—
221D12—121no—
222D12—121no—
223D12—242no—
224D12—241no—
225D12—242no—
226Dic6—42no—
227Dic6—81no—
228SL(2,𝔽3)—21no—
229SL(2,𝔽3)C2×#6711yescharacteristic
230C3×C8—62no—
231C3×C8—122no—
232C3⋊C8—32no—
233C3⋊C8—62no—
234C3⋊C8C2×S412yes—
235C2×C32—41no—
236C2×C32—42no—
237C3⋊D3—162no—
238C24—181no—
239#41—31no—
240#41—31no—
241#41#62611yescharacteristic
242#41C2×D3211yescharacteristic
243C2×Q8—32no—
244C2×Q8—61no—
245C2×Q8—61no—
246C2×Q8—61no—
247C2×Q8—61no—
248C2×Q8—61no—
249C2×Q8#62611yescharacteristic
250C2×D4—31no—
251C2×D4—92no—
252C2×D4—181no—
253C2×D4—181no—
254C2×D4—181no—
255C2×D4—181no—
256C2×D4—181no—
257C22×C4—31no—
258C22×C4—61no—
259Q16—62no—
260Q16—62no—
261SD16—62no—
262SD16—62no—
263SD16—184no—
264SD16—184no—
265SD16—182no—
266SD16—182no—
267D8—182no—
268D8—182no—
269M16—32no—
270M16—61no—
271M16—92no—
272M16—92no—
273M16—181no—
274M16—181no—
275C2×C8—31no—
276C2×C8—61no—
277C2×C8—92no—
278C2×C8—92no—
279C2×C8—91no—
280C2×C8—181no—
281C22×C3—31no—
282C22×C3—31no—
283C22×C3—41no—
284C22×C3—62no—
285C22×C3—81no—
286C22×C3C4⋊S411yescharacteristic
287C2×D3—122no—
288C2×D3—242no—
289C2×D3—244no—
290C2×D3—242no—
291C2×D3—242no—
292C2×D3—242no—
293C2×D3—482no—
294C2×D3—484no—
295C3×C4—31no—
296C3×C4—31no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—81no—
300C3×C4—81no—
301C3×C4—122no—
302C3×C4C4⋊S411yescharacteristic
303C3×C4C22×S411yescharacteristic
304Dic3—82no—
305C32—41noSylow
306C23—31no—
307C23—182no—
308C23—361no—
309C23—361no—
310C23—722no—
311Q8—31no—
312Q8—62no—
313Q8—62no—
314Q8—121no—
315Q8—121no—
316Q8C2×#62611yescharacteristic
317D4—31no—
318D4—31no—
319D4—61no—
320D4—182no—
321D4—182no—
322D4—361no—
323D4—361no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—31no—
329C2×C4—62no—
330C2×C4—121no—
331C2×C4—121no—
332C2×C4D3×S411yescharacteristic
333C8—32no—
334C8—62no—
335C8—92no—
336C8—182no—
337C2×C3—41no—
338C2×C3—42no—
339C2×C3—61no—
340C2×C3—61no—
341C2×C3—81no—
342C2×C3—82no—
343C2×C3#540612yescomplemented
344C2×C3C2×C4⋊S411yescharacteristic
345D3—242no—
346D3—482no—
347D3—484no—
348C22—31no—
349C22—31no—
350C22—62no—
351C22—362no—
352C22—722no—
353C22—722no—
354C22—722no—
355C22#6420711yescharacteristic
356C4—31no—
357C4—31no—
358C4—122no—
359C4#6420711yescharacteristic
360C4C2×D3×S411yescharacteristic
361C3—41no—
362C3—81no—
363C3C2×#540611yescharacteristic, complemented
364C2—61no—
365C2—61no—
366C2—722no—
367C2#1059322412yesdirect product factor
368C2C2×#6420711yescharacteristic
subgroupG/H
centerC22#64207
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC22×C3C4⋊S4
prime radicalC2×#64267C2
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
2. C2×C3×#984C2semidirect
3. C2×C3⋊(#131⋊C3)C2semidirect
4. #10593224C2direct (N × H)
12. C3×#984C22semidirect
15. C3⋊(#131⋊C3)C22semidirect
18. C2×#984D3semidirect
21. C2×#948D3semidirect
50. #984C2×D3semidirect
66. #948C2×D3semidirect
343. C2×C3#5406semidirect
363. C3C2×#5406semidirect
367. C2#10593224direct (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×#9842
C2×C3⋊(#131⋊C3)2
#105932242
C2×#54063
C2×#52033
C2×#37174