Finite Group Databasebeta

← C2×#10593209 #11922115

Subgroups — C2×#10593209 #11922115

Order 1152.

745 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 745 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×D3×SL(2,𝔽3)C211yesmaximal, characteristic
2C2×C3⋊#859C211yesmaximal, characteristic, complemented
3C2×C3×#859C211yesmaximal, characteristic, complemented
4#10593209C214yesmaximal, direct product factor
5C2×#5420—31nomaximal
6C2×#4802—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×D3×SL(2,𝔽3)C414yescomplemented
9C2×D3×SL(2,𝔽3)C2212yes—
10C2×(C2×D3)⋊Dic3—41nomaximal
11C3⋊#859C2212yescomplemented
12C3×#859C2212yescomplemented
13C22×D3×Q8D311yescharacteristic
14C23×SL(2,𝔽3)—31no—
15C22×ΓL(1,𝔽25)—31no—
16C2×#892—31no—
17#5420—34no—
18C2×#859—31no—
19C2×#859—61no—
20C2×#859D311yescharacteristic, complemented
21C2×C3×#103—31no—
22C2×#835—31no—
23C2×#816—31no—
24C2×#810—31no—
25#4802—34no—
26#4802—34no—
27C23×C3×D3—41no—
28C22×C3⋊Dic3—41no—
29C22×C3×Dic3—41no—
30C2×C3×SL(2,𝔽3)C2×C412yes—
31C2×C3×SL(2,𝔽3)C2311yescharacteristic
32D3×SL(2,𝔽3)C2×C414yescomplemented
33(C2×D3)⋊Dic3—44no—
34C2×#419—91noSylow
35C22×C3×Q8C2×D311yescharacteristic
36C2×D3×Q8—34no—
37C2×D3×Q8—32no—
38C2×D3×Q8Dic314yescomplemented
39C2×D3×Q8C2×D312yes—
40C22×C4×D3—31no—
41C22×Dic6—31no—
42C22×SL(2,𝔽3)—21no—
43C22×SL(2,𝔽3)—34no—
44C22×SL(2,𝔽3)—32no—
45C22×SL(2,𝔽3)C2×D311yescharacteristic
46C22×C3×C8—31no—
47C2×C3×C4⋊C4—31no—
48C2×#217—121no—
49C2×(C2×D3)⋊C4—61no—
50C2×C4⋊Dic3—31no—
51C2×C4×Dic3—61no—
52C22×C3⋊C8—31no—
53C2×ΓL(1,𝔽25)—34no—
54C2×ΓL(1,𝔽25)—64no—
55#892—34no—
56#892—62no—
57#859—32no—
58#859—62no—
59#859C2×D312yescomplemented
60C3×#103—32no—
61C3×#103—32no—
62#835—32no—
63#835—32no—
64#816—34no—
65#810—34no—
66C23×C32—41no—
67C22×C3×D3—44no—
68C22×C3×D3—42no—
69C22×C3×D3—82no—
70C22×C3×D3—82no—
71C2×C3⋊Dic3—42no—
72C2×C3⋊Dic3—82no—
73C2×C3×Dic3—42no—
74C2×C3×Dic3—82no—
75C3×SL(2,𝔽3)C22×C411yescharacteristic
76C23×Q8—31no—
77C22×M16—91no—
78C2×#117—91no—
79#419—94no—
80#419—94no—
81C2×#103—31no—
82C2×#103—91no—
83C2×#103—91no—
84C2×#103—91no—
85C24×C3—121no—
86C23×D3S411yescharacteristic
87C2×C3×Q8—31no—
88C2×C3×Q8—32no—
89C2×C3×Q8C2×Dic312yes—
90C2×C3×Q8C22×D311yescharacteristic
91C22×C3×C4—31no—
92C22×C3×C4—61no—
93C22×Dic3—31no—
94C22×Dic3—41no—
95C22×Dic3—61no—
96C22×Dic3—121no—
97C22×Dic3—241no—
98D3×Q8—38no—
99D3×Q8—34no—
100D3×Q8—64no—
101D3×Q8C2×Dic314yescomplemented
102C2×C4×D3—34no—
103C2×C4×D3—34no—
104C2×C4×D3—32no—
105C2×C4×D3—32no—
106C2×Dic6—32no—
107C2×Dic6—34no—
108C2×Dic6—62no—
109C2×Dic6—61no—
110C2×SL(2,𝔽3)—22no—
111C2×SL(2,𝔽3)—21no—
112C2×SL(2,𝔽3)—34no—
113C2×SL(2,𝔽3)C4×D312yes—
114C2×SL(2,𝔽3)C22×D311yescharacteristic
115C2×C3×C8—32no—
116C2×C3×C8—62no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—61no—
119#217—124no—
120(C2×D3)⋊C4—64no—
121C4⋊Dic3—32no—
122C4⋊Dic3—61no—
123C4×Dic3—64no—
124C2×C3⋊C8—32no—
125C2×C3⋊C8—62no—
126ΓL(1,𝔽25)—68no—
127C22×C32—42no—
128C22×C32—42no—
129C22×C32—42no—
130C22×C32—41no—
131C2×C3×D3—44no—
132C2×C3×D3—82no—
133C2×C3×D3—82no—
134C2×C3×D3—88no—
135C3⋊Dic3—82no—
136C3×Dic3—82no—
137C22×Q8—34no—
138C22×Q8—32no—
139C22×Q8—91no—
140C22×Q8—92no—
141C22×Q8—94no—
142C22×Q8D3211yescharacteristic
143C23×C4—91no—
144C2×M16—94no—
145C2×M16—184no—
146C22×C8—31no—
147C22×C8—91no—
148#117—94no—
149#117—182no—
150C2×C4⋊C4—31no—
151C2×C4⋊C4—91no—
152C2×C22⋊C4—181no—
153C2×C42—181no—
154#103—32no—
155#103—32no—
156#103—94no—
157#103—94no—
158#103—92no—
159#103—92no—
160C23×C3—41no—
161C23×C3—81no—
162C23×C3—122no—
163C23×C3—124no—
164C23×C3—242no—
165C23×C3—242no—
166C23×C3C2×S411yescharacteristic
167C22×D3—22no—
168C22×D3—22no—
169C22×D3SL(2,ℤ/4)14yes—
170C22×D3C2×S412yes—
171C3×Q8—32no—
172C3×Q8—31no—
173C3×Q8—61no—
174C3×Q8C22×Dic311yescharacteristic
175C2×C3×C4—32no—
176C2×C3×C4—32no—
177C2×C3×C4—31no—
178C2×C3×C4—31no—
179C2×C3×C4—62no—
180C2×C3×C4—122no—
181C2×Dic3—34no—
182C2×Dic3—32no—
183C2×Dic3—42no—
184C2×Dic3—62no—
185C2×Dic3—82no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188C2×Dic3—242no—
189C2×Dic3—242no—
190C2×Dic3—244no—
191C4×D3—34no—
192C4×D3—34no—
193C4×D3—38no—
194Dic6—34no—
195Dic6—62no—
196Dic6—64no—
197SL(2,𝔽3)—21no—
198SL(2,𝔽3)C2×C4×D311yescharacteristic
199C3×C8—62no—
200C3⋊C8—62no—
201C2×C32—41no—
202C2×C32—41no—
203C2×C32—41no—
204C2×C32—44no—
205C3×D3—84no—
206C24—31no—
207C2×Q8—31no—
208C2×Q8—32no—
209C2×Q8—34no—
210C2×Q8—92no—
211C2×Q8—94no—
212C2×Q8—94no—
213C2×Q8—98no—
214C2×Q8—181no—
215C2×Q8—182no—
216C2×Q8—184no—
217C2×Q8D3×Dic312yes—
218C2×Q8C2×D3211yescharacteristic
219C22×C4—31no—
220C22×C4—61no—
221C22×C4—92no—
222C22×C4—92no—
223C22×C4—94no—
224C22×C4—94no—
225C22×C4—91no—
226C22×C4—181no—
227M16—188no—
228C2×C8—32no—
229C2×C8—62no—
230C2×C8—92no—
231C2×C8—182no—
232C4⋊C4—32no—
233C4⋊C4—61no—
234C4⋊C4—92no—
235C4⋊C4—181no—
236C22⋊C4—184no—
237C42—184no—
238C22×C3—41no—
239C22×C3—42no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—81no—
243C22×C3—82no—
244C22×C3—82no—
245C22×C3—82no—
246C22×C3—124no—
247C22×C3—242no—
248C22×C3—242no—
249C22×C3—248no—
250C22×C3#98312yes—
251C22×C3#98312yes—
252C22×C3C2×SL(2,ℤ/4)12yes—
253C22×C3C22×S411yescharacteristic
254C2×D3—22no—
255C2×D3—22no—
256C2×D3—28no—
257C2×D3C2×SL(2,ℤ/4)14yes—
258C3×C4—31no—
259C3×C4—31no—
260C3×C4—32no—
261C3×C4—122no—
262Dic3—34no—
263Dic3—82no—
264Dic3—122no—
265Dic3—242no—
266Dic3—244no—
267C32—41noSylow
268C23—32no—
269C23—34no—
270C23—62no—
271C23—62no—
272C23D3×S411yescharacteristic
273Q8—32no—
274Q8—31no—
275Q8—61no—
276Q8—94no—
277Q8—182no—
278Q8—184no—
279Q8C2×D3×Dic311yescharacteristic
280C2×C4—31no—
281C2×C4—31no—
282C2×C4—32no—
283C2×C4—32no—
284C2×C4—62no—
285C2×C4—94no—
286C2×C4—94no—
287C2×C4—98no—
288C2×C4—92no—
289C2×C4—94no—
290C2×C4—122no—
291C2×C4—182no—
292C2×C4—362no—
293C8—62no—
294C8—182no—
295C2×C3—41no—
296C2×C3—41no—
297C2×C3—41no—
298C2×C3—44no—
299C2×C3—81no—
300C2×C3—81no—
301C2×C3—81no—
302C2×C3—84no—
303C2×C3—244no—
304C2×C3#542014yescomplemented
305C2×C3C2×#98311yescharacteristic
306C2×C3C2×#98311yescharacteristic
307C2×C3C22×SL(2,ℤ/4)11yescharacteristic
308D3—24no—
309C22—34no—
310C22—62no—
311C22—62no—
312C22—68no—
313C22#6420112yes—
314C22#6420212yes—
315C22D3×SL(2,ℤ/4)12yes—
316C22C2×D3×S411yescharacteristic
317C4—31no—
318C4—31no—
319C4—32no—
320C4—94no—
321C4—122no—
322C4—362no—
323C3—41no—
324C3—81no—
325C3C2×#542011yescharacteristic, complemented
326C2—64no—
327C2#1059320914yesdirect product factor
328C2C2×#6420111yescharacteristic
329C2C2×#6420211yescharacteristic
330C2C2×D3×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, hypocenterC3×SL(2,𝔽3)C22×C4
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
prime radicalC22×D3×SL(2,𝔽3)C2
cosocleC2×C3×SL(2,𝔽3)C23
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊#859C2semidirect
3. C2×C3×#859C2semidirect
4. #10593209C2direct (N × H)
8. C2×D3×SL(2,𝔽3)C4semidirect
11. C3⋊#859C22semidirect
12. C3×#859C22semidirect
20. C2×#859D3semidirect
32. D3×SL(2,𝔽3)C2×C4semidirect
38. C2×D3×Q8Dic3semidirect
59. #859C2×D3semidirect
101. D3×Q8C2×Dic3semidirect
304. C2×C3#5420semidirect
325. C3C2×#5420semidirect
327. C2#10593209direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×SL(2,𝔽3)2
C2×C3⋊#8592
C2×C3×#8592
#105932092
C2×#54203
C2×#48023
C2×(C2×D3)⋊Dic34