Finite Group Databasebeta

← C2×#10593655 #11923054

Subgroups — C2×#10593655 #11923054

Order 1152.

1144 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C23×C3×SL(2,𝔽3)C211yesmaximal, characteristic, complemented
2C22×C3⋊GL(2,𝔽3)C211yesmaximal, characteristic, complemented
3#10593655C214yesmaximal, direct product factor
4C2×C3⋊#859C211yesmaximal, characteristic, complemented
5C2×#5421—33nomaximal
6C2×#5227—31nomaximal
7C22×#638—41nomaximal
8C22×C3×SL(2,𝔽3)—22no—
9C22×C3×SL(2,𝔽3)C2211yescharacteristic
10C22×C3×SL(2,𝔽3)C2212yescomplemented
11C2×C3⋊GL(2,𝔽3)—22no—
12C2×C3⋊GL(2,𝔽3)C2212yescomplemented
13C3⋊#859C2212yescomplemented
14C23×C3×Q8D311yescharacteristic, complemented
15C23×SL(2,𝔽3)D313yescomplemented
16C22×GL(2,𝔽3)—33no—
17C22×#215—31no—
18C22×#215—31no—
19C2×#930—31no—
20#5421—312no—
21C2×#859—33no—
22#5227—34no—
23#5227—34no—
24C2×#835—31no—
25C2×#835—31no—
26C2×#830—31no—
27C24×C32—41no—
28C23×C3⋊D3—41no—
29C2×#638—44no—
30C2×#638—48no—
31C22×C3⋊Dic3—41no—
32C2×C3×SL(2,𝔽3)—22no—
33C2×C3×SL(2,𝔽3)D412yescomplemented
34C2×C3×SL(2,𝔽3)C2311yescharacteristic
35C3⋊GL(2,𝔽3)—22no—
36C2×#448—91noSylow
37C22×C3×Q8—22no—
38C22×C3×Q8—31no—
39C22×C3×Q8—32no—
40C22×C3×Q8—62no—
41C22×C3×Q8C2×D311yescharacteristic
42C22×C3×Q8C2×D312yescomplemented
43C23×C3×C4—31no—
44C22×#67—61no—
45C22×#67—123no—
46C22×D12—31no—
47C22×SL(2,𝔽3)—26no—
48C22×SL(2,𝔽3)C2×D313yes—
49C22×SL(2,𝔽3)C2×D316yescomplemented
50C2×GL(2,𝔽3)—36no—
51C2×GL(2,𝔽3)—66no—
52C2×#215—32no—
53C2×#215—34no—
54C2×#215—32no—
55C2×#215—62no—
56C2×#215—64no—
57C2×#215—62no—
58#930—34no—
59#930—62no—
60C2×(C2×D3)⋊C4—61no—
61C2×C4⋊Dic3—31no—
62C22×C3⋊C8—31no—
63C22×C3⋊C8—31no—
64#859—36no—
65#835—32no—
66#835—34no—
67#835—32no—
68#830—34no—
69C23×C32—44no—
70C23×C32—41no—
71C23×C32—42no—
72C23×C32—82no—
73C23×C32—82no—
74C22×C3⋊D3—42no—
75C22×C3⋊D3—44no—
76C22×C3⋊D3—82no—
77C22×C3⋊D3—82no—
78#638—416no—
79C2×C3⋊Dic3—42no—
80C2×C3⋊Dic3—44no—
81C3×SL(2,𝔽3)C2×D411yescharacteristic, complemented
82C23×Q8C3⋊D311yescharacteristic, complemented
83C22×SD16—91no—
84C22×SD16—91no—
85C2×#121—91no—
86#448—94no—
87#448—94no—
88C2×#103—91no—
89C2×#103—91no—
90C2×C22⋊C8—91no—
91C24×C3—43no—
92C24×C3S411yescharacteristic
93C23×D3—61no—
94C23×D3—123no—
95C2×C3×Q8—22no—
96C2×C3×Q8—31no—
97C2×C3×Q8—32no—
98C2×C3×Q8—32no—
99C2×C3×Q8—34no—
100C2×C3×Q8—61no—
101C2×C3×Q8—62no—
102C2×C3×Q8—64no—
103C2×C3×Q8—62no—
104C2×C3×Q8—64no—
105C2×C3×Q8#6712yescomplemented
106C2×C3×Q8C22×D311yescharacteristic
107C22×C3×C4—31no—
108C22×C3×C4—32no—
109C22×C3×C4—31no—
110C22×C3×C4—32no—
111C22×C3×C4—62no—
112C22×C3×C4—62no—
113C2×#67—64no—
114C2×#67—1212no—
115C2×#67—1224no—
116C2×#67—124no—
117C22×Dic3—61no—
118C22×Dic3—123no—
119C2×D12—32no—
120C2×D12—62no—
121C2×D12—62no—
122C2×D12—61no—
123C2×SL(2,𝔽3)—26no—
124C2×SL(2,𝔽3)#6716yescomplemented
125C2×SL(2,𝔽3)C22×D313yes—
126GL(2,𝔽3)—66no—
127#215—64no—
128#215—62no—
129#215—68no—
130#215—62no—
131(C2×D3)⋊C4—64no—
132C4⋊Dic3—32no—
133C4⋊Dic3—61no—
134C2×C3⋊C8—32no—
135C2×C3⋊C8—32no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138C22×C32—42no—
139C22×C32—44no—
140C22×C32—42no—
141C22×C32—42no—
142C22×C32—41no—
143C22×C32—82no—
144C22×C32—88no—
145C22×C32—82no—
146C2×C3⋊D3—44no—
147C2×C3⋊D3—82no—
148C2×C3⋊D3—82no—
149C2×C3⋊D3—88no—
150C3⋊Dic3—44no—
151C22×Q8—22no—
152C22×Q8—31no—
153C22×Q8—32no—
154C22×Q8—62no—
155C22×Q8C2×C3⋊D311yescharacteristic
156C22×Q8C2×C3⋊D312yescomplemented
157C22×D4—91no—
158C22×D4—181no—
159C23×C4—31no—
160C2×SD16—92no—
161C2×SD16—94no—
162C2×SD16—92no—
163C2×SD16—182no—
164C2×SD16—184no—
165C2×SD16—182no—
166C22×C8—91no—
167C22×C8—91no—
168#121—94no—
169#121—182no—
170C2×C4⋊C4—91no—
171C2×C22⋊C4—181no—
172#103—92no—
173#103—94no—
174#103—92no—
175C22⋊C8—94no—
176C23×C3—22no—
177C23×C3—22no—
178C23×C3—46no—
179C23×C3—43no—
180C23×C3—412no—
181C23×C3—86no—
182C23×C3—86no—
183C23×C3GL(2,𝔽3)14yescomplemented
184C23×C3C2×S412yes—
185C23×C3C2×S411yescharacteristic
186C22×D3—62no—
187C22×D3—126no—
188C22×D3—1212no—
189C22×D3—122no—
190C22×D3—122no—
191C22×D3—122no—
192C22×D3—246no—
193C22×D3—246no—
194C3×Q8—32no—
195C3×Q8—31no—
196C3×Q8—34no—
197C3×Q8—61no—
198C3×Q8—62no—
199C3×Q8—64no—
200C3×Q8C2×#6711yescharacteristic, complemented
201C2×C3×C4—32no—
202C2×C3×C4—32no—
203C2×C3×C4—31no—
204C2×C3×C4—31no—
205C2×C3×C4—32no—
206C2×C3×C4—62no—
207C2×C3×C4—62no—
208C2×C3×C4—64no—
209C2×C3×C4—62no—
210#67—1248no—
211#67—128no—
212C2×Dic3—62no—
213C2×Dic3—126no—
214C2×Dic3—1212no—
215C2×Dic3—122no—
216D12—62no—
217D12—62no—
218D12—122no—
219SL(2,𝔽3)C2×#6713yescomplemented
220C3⋊C8—62no—
221C3⋊C8—62no—
222C2×C32—41no—
223C2×C32—41no—
224C2×C32—41no—
225C2×C32—44no—
226C2×C32—84no—
227C3⋊D3—84no—
228C24—181no—
229C24C3⋊S411yescharacteristic
230C2×Q8—22no—
231C2×Q8—31no—
232C2×Q8—32no—
233C2×Q8—32no—
234C2×Q8—34no—
235C2×Q8—61no—
236C2×Q8—62no—
237C2×Q8—64no—
238C2×Q8—62no—
239C2×Q8—64no—
240C2×Q8#63812yescomplemented
241C2×Q8C22×C3⋊D311yescharacteristic
242C2×D4—92no—
243C2×D4—182no—
244C2×D4—182no—
245C2×D4—181no—
246C2×D4—184no—
247C2×D4—364no—
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—31no—
252C22×C4—62no—
253C22×C4—62no—
254C22×C4—181no—
255SD16—184no—
256SD16—182no—
257SD16—188no—
258SD16—182no—
259C2×C8—92no—
260C2×C8—92no—
261C2×C8—182no—
262C2×C8—182no—
263C4⋊C4—92no—
264C4⋊C4—181no—
265C22⋊C4—184no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—28no—
269C22×C3—46no—
270C22×C3—412no—
271C22×C3—46no—
272C22×C3—46no—
273C22×C3—43no—
274C22×C3—824no—
275C22×C3—86no—
276C22×C3—86no—
277C22×C3C2×GL(2,𝔽3)12yes—
278C22×C3C2×GL(2,𝔽3)14yescomplemented
279C22×C3#98312yes—
280C22×C3GL(2,ℤ/4)12yes—
281C22×C3C22×S411yescharacteristic
282C2×D3—1212no—
283C2×D3—122no—
284C2×D3—122no—
285C2×D3—122no—
286C2×D3—246no—
287C2×D3—246no—
288C2×D3—2424no—
289C2×D3—244no—
290C3×C4—31no—
291C3×C4—31no—
292C3×C4—32no—
293C3×C4—62no—
294Dic3—1212no—
295Dic3—122no—
296C32—41noSylow
297C23—22no—
298C23—22no—
299C23—182no—
300C23—362no—
301C23—362no—
302C23—362no—
303C23C3⋊GL(2,𝔽3)14yescomplemented
304C23C2×C3⋊S412yes—
305C23C2×C3⋊S411yescharacteristic
306Q8—32no—
307Q8—31no—
308Q8—34no—
309Q8—61no—
310Q8—62no—
311Q8—64no—
312Q8C2×#63811yescharacteristic, complemented
313D4—182no—
314D4—182no—
315D4—362no—
316D4—368no—
317C2×C4—32no—
318C2×C4—32no—
319C2×C4—31no—
320C2×C4—31no—
321C2×C4—32no—
322C2×C4—62no—
323C2×C4—62no—
324C2×C4—64no—
325C2×C4—62no—
326C2×C4—182no—
327C2×C4—362no—
328C8—182no—
329C8—182no—
330C2×C3—24no—
331C2×C3—412no—
332C2×C3—43no—
333C2×C3—43no—
334C2×C3—43no—
335C2×C3—812no—
336C2×C3#542114yescomplemented
337C2×C3C22×GL(2,𝔽3)11yescharacteristic
338C2×C3C2×#98311yescharacteristic
339C2×C3C2×GL(2,ℤ/4)11yescharacteristic
340D3—2412no—
341D3—242no—
342C22—28no—
343C22—22no—
344C22—22no—
345C22—362no—
346C22—362no—
347C22—362no—
348C22—724no—
349C22C2×C3⋊GL(2,𝔽3)12yes—
350C22C2×C3⋊GL(2,𝔽3)14yescomplemented
351C22#6426412yes—
352C22#6426912yes—
353C22C22×C3⋊S411yescharacteristic
354C4—31no—
355C4—31no—
356C4—32no—
357C4—62no—
358C4—362no—
359C3—43no—
360C3C2×#542111yescharacteristic, complemented
361C2—24no—
362C2—722no—
363C2#1059365514yesdirect product factor
364C2C22×C3⋊GL(2,𝔽3)11yescharacteristic
365C2C2×#6426411yescharacteristic
366C2C2×#6426911yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C22×C3⋊S4
FittingC23×C3×Q8D3
socleC23×C3C2×S4
hypercenterC24C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C23×C3×SL(2,𝔽3)C2semidirect
2. C22×C3⋊GL(2,𝔽3)C2semidirect
3. #10593655C2direct (N × H)
4. C2×C3⋊#859C2semidirect
10. C22×C3×SL(2,𝔽3)C22semidirect
12. C2×C3⋊GL(2,𝔽3)C22semidirect
13. C3⋊#859C22semidirect
14. C23×C3×Q8D3semidirect
15. C23×SL(2,𝔽3)D3semidirect
33. C2×C3×SL(2,𝔽3)D4semidirect
42. C22×C3×Q8C2×D3semidirect
49. C22×SL(2,𝔽3)C2×D3semidirect
81. C3×SL(2,𝔽3)C2×D4semidirect
82. C23×Q8C3⋊D3semidirect
105. C2×C3×Q8#67semidirect
124. C2×SL(2,𝔽3)#67semidirect
156. C22×Q8C2×C3⋊D3semidirect
183. C23×C3GL(2,𝔽3)semidirect
200. C3×Q8C2×#67semidirect
219. SL(2,𝔽3)C2×#67semidirect
240. C2×Q8#638semidirect
278. C22×C3C2×GL(2,𝔽3)semidirect
303. C23C3⋊GL(2,𝔽3)semidirect
312. Q8C2×#638semidirect
336. C2×C3#5421semidirect
350. C22C2×C3⋊GL(2,𝔽3)semidirect
360. C3C2×#5421semidirect
363. C2#10593655direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×SL(2,𝔽3)2
C22×C3⋊GL(2,𝔽3)2
#105936552
C2×C3⋊#8592
C2×#54213
C2×#52273
C22×#6384