Finite Group Databasebeta

← C2×#10593197 #11922092

Subgroups — C2×#10593197 #11922092

Order 1152.

681 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 681 conjugacy classes of subgroups — too many to draw. Only its 75 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×C3⋊(#41⋊C3)C211yesmaximal, characteristic
2C22×C3⋊#226C211yesmaximal, characteristic, complemented
3C2×C3×#859C211yesmaximal, characteristic, complemented
4#10593197C214yesmaximal, direct product factor
5C2×#5425—31nomaximal
6C2×#4808—31nomaximal
7C22×C3×SL(2,𝔽3)C2211yescharacteristic
8C2×C3⋊(#41⋊C3)—22no—
9C2×C3⋊(#41⋊C3)C2212yes—
10C2×C3⋊#226—22no—
11C2×C3⋊#226C2212yescomplemented
12C2×Dic3⋊Dic3—41nomaximal
13C3×#859C2212yescomplemented
14C22×#239D311yescharacteristic
15C22×#41⋊C3—31no—
16C22×#226—31no—
17C22×#226—61no—
18C22×#216—31no—
19C22×#204—31no—
20C2×#897—31no—
21#5425—34no—
22C2×#859D311yescharacteristic, complemented
23C2×C3×#103—31no—
24C2×(C2×D3)⋊C8—31no—
25C2×#809—31no—
26#4808—34no—
27#4808—34no—
28C22×C3⋊Dic3—41no—
29C22×C3×Dic3—41no—
30C22×C3×Dic3—41no—
31C2×C3×SL(2,𝔽3)D412yes—
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C3⋊(#41⋊C3)—22no—
34C3⋊#226—22no—
35Dic3⋊Dic3—44no—
36C2×#452—91noSylow
37C22×C3×Q8C2×D311yescharacteristic
38C2×#239—22no—
39C2×#239—32no—
40C2×#239—62no—
41C2×#239C2×D312yes—
42C22×D12—31no—
43C22×C4×D3—31no—
44C22×Dic6—31no—
45C2×#41⋊C3—32no—
46C2×#41⋊C3—62no—
47C22×SL(2,𝔽3)—21no—
48C22×SL(2,𝔽3)C2×D311yescharacteristic
49C2×#226—32no—
50C2×#226—62no—
51C2×#226—64no—
52C2×#226—62no—
53C22×C3×C8—31no—
54C2×C3×C4⋊C4—31no—
55C2×#216—32no—
56C2×#216—32no—
57C2×#216—62no—
58C2×#216—62no—
59C2×(C2×D3)⋊C4—61no—
60C2×C4⋊Dic3—61no—
61C2×Dic3⋊C4—121no—
62C22×C3⋊C8—31no—
63C2×#204—34no—
64C2×#204—64no—
65#897—34no—
66#897—62no—
67#859C2×D312yescomplemented
68C3×#103—32no—
69C3×#103—32no—
70(C2×D3)⋊C8—34no—
71#809—34no—
72C23×C32—41no—
73C2×C3⋊Dic3—42no—
74C2×C3⋊Dic3—82no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—44no—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—82no—
79C3×SL(2,𝔽3)C2×D411yescharacteristic
80C22×#41—31no—
81C22×Q16—91no—
82C22×SD16—91no—
83C2×C22⋊Q8—91no—
84#452—94no—
85#452—94no—
86C2×#103—31no—
87C2×#102—91no—
88C2×C22⋊C8—91no—
89C23×D3—31no—
90C2×C3×Q8—31no—
91C2×C3×Q8—32no—
92C2×C3×Q8#6712yes—
93C2×C3×Q8C22×D311yescharacteristic
94C22×C3×C4—31no—
95C22×C3×C4—61no—
96C22×C3×C4—121no—
97C22×Dic3—41no—
98C22×Dic3—61no—
99C22×Dic3—121no—
100C22×Dic3—241no—
101C22×Dic3S411yescharacteristic
102#239—22no—
103#239—64no—
104#239—62no—
105#239—64no—
106C2×D12—32no—
107C2×D12—34no—
108C2×D12—61no—
109C2×D12—62no—
110C2×C4×D3—32no—
111C2×C4×D3—32no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×Dic6—32no—
115C2×Dic6—62no—
116C2×Dic6—62no—
117C2×Dic6—61no—
118#41⋊C3—62no—
119C2×SL(2,𝔽3)—22no—
120C2×SL(2,𝔽3)—21no—
121C2×SL(2,𝔽3)D1212yes—
122C2×SL(2,𝔽3)C22×D311yescharacteristic
123#226—64no—
124#226—62no—
125C2×C3×C8—32no—
126C2×C3×C8—62no—
127C3×C4⋊C4—32no—
128C3×C4⋊C4—61no—
129#216—64no—
130#216—62no—
131#216—62no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—64no—
134Dic3⋊C4—124no—
135C2×C3⋊C8—32no—
136C2×C3⋊C8—62no—
137#204—68no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—42no—
141C22×C32—41no—
142C3⋊Dic3—82no—
143C3×Dic3—44no—
144C3×Dic3—82no—
145C2×#41—32no—
146C2×#41—62no—
147C2×#41—92no—
148C2×#41—182no—
149C22×Q8—91no—
150C22×Q8D3211yescharacteristic
151C22×D4—91no—
152C23×C4—91no—
153C2×Q16—92no—
154C2×Q16—92no—
155C2×Q16—182no—
156C2×Q16—182no—
157C2×SD16—94no—
158C2×SD16—184no—
159C22×C8—31no—
160C22×C8—91no—
161C22⋊Q8—94no—
162C22⋊Q8—182no—
163C2×C4⋊C4—31no—
164C2×C4⋊C4—181no—
165C2×C22⋊C4—181no—
166#103—32no—
167#103—32no—
168#102—94no—
169C22⋊C8—94no—
170C23×C3—41no—
171C23×C3—81no—
172C23×C3C2×S411yescharacteristic
173C22×D3—32no—
174C22×D3—62no—
175C22×D3—62no—
176C22×D3—62no—
177C3×Q8—32no—
178C3×Q8—31no—
179C3×Q8—61no—
180C3×Q8C2×#6711yescharacteristic
181C2×C3×C4—32no—
182C2×C3×C4—32no—
183C2×C3×C4—31no—
184C2×C3×C4—31no—
185C2×C3×C4—62no—
186C2×C3×C4—122no—
187C2×C3×C4—122no—
188C2×C3×C4—242no—
189C2×Dic3—22no—
190C2×Dic3—42no—
191C2×Dic3—44no—
192C2×Dic3—62no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C2×Dic3—242no—
196C2×Dic3—242no—
197C2×Dic3—244no—
198C2×Dic3C2×S412yes—
199D12—34no—
200D12—62no—
201D12—64no—
202C4×D3—62no—
203C4×D3—62no—
204C4×D3—64no—
205Dic6—62no—
206Dic6—62no—
207Dic6—122no—
208SL(2,𝔽3)—21no—
209SL(2,𝔽3)C2×D1211yescharacteristic
210C3×C8—62no—
211C3⋊C8—62no—
212C2×C32—41no—
213C2×C32—41no—
214C2×C32—41no—
215C2×C32—44no—
216C24—91no—
217#41—62no—
218#41—184no—
219#41—182no—
220#41—184no—
221C2×Q8—31no—
222C2×Q8—32no—
223C2×Q8—92no—
224C2×Q8—181no—
225C2×Q8—182no—
226C2×Q8—182no—
227C2×Q8#62612yes—
228C2×Q8C2×D3211yescharacteristic
229C2×D4—92no—
230C2×D4—94no—
231C2×D4—181no—
232C2×D4—182no—
233C22×C4—31no—
234C22×C4—31no—
235C22×C4—61no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—182no—
239C22×C4—182no—
240C22×C4—181no—
241Q16—184no—
242Q16—182no—
243Q16—182no—
244SD16—188no—
245C2×C8—32no—
246C2×C8—62no—
247C2×C8—92no—
248C2×C8—182no—
249C4⋊C4—32no—
250C4⋊C4—61no—
251C4⋊C4—184no—
252C22⋊C4—184no—
253C22×C3—41no—
254C22×C3—42no—
255C22×C3—42no—
256C22×C3—42no—
257C22×C3—81no—
258C22×C3—82no—
259C22×C3—82no—
260C22×C3—82no—
261C22×C3#98412yes—
262C22×C3#98512yes—
263C22×C3GL(2,ℤ/4)12yes—
264C22×C3C22×S411yescharacteristic
265C2×D3—62no—
266C2×D3—62no—
267C2×D3—62no—
268C2×D3—124no—
269C3×C4—31no—
270C3×C4—31no—
271C3×C4—32no—
272C3×C4—122no—
273C3×C4—242no—
274Dic3—22no—
275Dic3—44no—
276Dic3—122no—
277Dic3—242no—
278Dic3—244no—
279C32—41noSylow
280C23—92no—
281C23—182no—
282C23—182no—
283C23—182no—
284C23D3×S411yescharacteristic
285Q8—32no—
286Q8—31no—
287Q8—61no—
288Q8—182no—
289Q8—182no—
290Q8—362no—
291Q8C2×#62611yescharacteristic
292D4—94no—
293D4—182no—
294D4—184no—
295C2×C4—31no—
296C2×C4—31no—
297C2×C4—32no—
298C2×C4—32no—
299C2×C4—32no—
300C2×C4—62no—
301C2×C4—62no—
302C2×C4—122no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—184no—
306C2×C4—182no—
307C2×C4—362no—
308C8—62no—
309C8—182no—
310C2×C3—41no—
311C2×C3—41no—
312C2×C3—41no—
313C2×C3—44no—
314C2×C3—81no—
315C2×C3—81no—
316C2×C3—81no—
317C2×C3—84no—
318C2×C3#542514yescomplemented
319C2×C3C2×#98411yescharacteristic
320C2×C3C2×#98511yescharacteristic
321C2×C3C2×GL(2,ℤ/4)11yescharacteristic
322D3—122no—
323C22—182no—
324C22—182no—
325C22—182no—
326C22—364no—
327C22#6419612yes—
328C22#6419712yes—
329C22#6421012yes—
330C22C2×D3×S411yescharacteristic
331C4—31no—
332C4—31no—
333C4—32no—
334C4—62no—
335C4—122no—
336C4—362no—
337C3—41no—
338C3—81no—
339C3C2×#542511yescharacteristic, complemented
340C2—362no—
341C2#1059319714yesdirect product factor
342C2C2×#6419611yescharacteristic
343C2C2×#6419711yescharacteristic
344C2C2×#6421011yescharacteristic
subgroupG/H
center, hypercenterC23D3×S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C2×D3×S4
FittingC22×C3×Q8C2×D3
socleC23×C3C2×S4
prime radicalC22×C3⋊(#41⋊C3)C2
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊#226C2semidirect
3. C2×C3×#859C2semidirect
4. #10593197C2direct (N × H)
11. C2×C3⋊#226C22semidirect
13. C3×#859C22semidirect
22. C2×#859D3semidirect
67. #859C2×D3semidirect
318. C2×C3#5425semidirect
339. C3C2×#5425semidirect
341. C2#10593197direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3⋊(#41⋊C3)2
C22×C3⋊#2262
C2×C3×#8592
#105931972
C2×#54253
C2×#48083
C2×Dic3⋊Dic34