Finite Group Databasebeta

← C2×#10593659 #11923065

Subgroups — C2×#10593659 #11923065

Order 1152.

784 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 97 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⋊C3C211yesmaximal, characteristic
2C22×C3⋊#226C211yesmaximal, characteristic, complemented
3#10593659C214yesmaximal, direct product factor
4C2×C3⋊#859C211yesmaximal, characteristic, complemented
5C2×#5425—33nomaximal
6C2×#5239—31nomaximal
7C2×C3×#41⋊C3—22no—
8C2×C3×#41⋊C3C2212yes—
9C22×C3×SL(2,𝔽3)C2211yescharacteristic
10C2×C3⋊#226—22no—
11C2×C3⋊#226C2212yescomplemented
12C2×#3750—41nomaximal
13C3⋊#859C2212yescomplemented
14C22×C3×#41D311yescharacteristic
15C22×#41⋊C3D313yes—
16C22×#226—33no—
17C22×#216—31no—
18C22×#214—31no—
19C2×#924—31no—
20#5425—312no—
21C2×#859—33no—
22#5239—34no—
23#5239—34no—
24C2×#835—31no—
25C2×#832—31no—
26C2×#830—31no—
27C22×C32×C4—41no—
28C22×C3⋊Dic3—41no—
29C22×C3⋊Dic3—41no—
30C3×#41⋊C3—22no—
31C2×C3×SL(2,𝔽3)D412yes—
32C2×C3×SL(2,𝔽3)C2311yescharacteristic
33C3⋊#226—22no—
34#3750—44no—
35C2×#452—91noSylow
36C2×C3×#41—22no—
37C2×C3×#41—32no—
38C2×C3×#41—62no—
39C2×C3×#41C2×D312yes—
40C22×C3×Q8C2×D311yescharacteristic
41C22×C3×D4—31no—
42C23×C3×C4—31no—
43C22×Dic6—31no—
44C2×#41⋊C3—26no—
45C2×#41⋊C3C2×D316yes—
46C22×SL(2,𝔽3)C2×D313yes—
47C2×#226—36no—
48C2×#226—66no—
49C2×#217—61no—
50C2×#216—32no—
51C2×#216—32no—
52C2×#216—62no—
53C2×#216—62no—
54C2×#214—34no—
55C2×#214—64no—
56C2×C4⋊Dic3—31no—
57#924—34no—
58#924—62no—
59C2×Dic3⋊C4—61no—
60C2×Dic3⋊C4—123no—
61C22×C3⋊C8—31no—
62C22×C3⋊C8—31no—
63#859—36no—
64#835—32no—
65#835—32no—
66#832—34no—
67#830—34no—
68C23×C32—41no—
69C2×C32×C4—42no—
70C2×C32×C4—82no—
71C2×C3⋊Dic3—42no—
72C2×C3⋊Dic3—42no—
73C2×C3⋊Dic3—44no—
74C2×C3⋊Dic3—82no—
75C3×SL(2,𝔽3)C2×D411yescharacteristic
76C22×#41C3⋊D311yescharacteristic
77C22×Q16—91no—
78C22×SD16—91no—
79C2×C22⋊Q8—91no—
80#452—94no—
81#452—94no—
82C2×#103—91no—
83C2×#102—91no—
84C2×C22⋊C8—91no—
85C24×C3—31no—
86C3×#41—22no—
87C3×#41—64no—
88C3×#41—62no—
89C3×#41—64no—
90C2×C3×Q8—31no—
91C2×C3×Q8—32no—
92C2×C3×Q8#6712yes—
93C2×C3×Q8C22×D311yescharacteristic
94C2×C3×D4—32no—
95C2×C3×D4—34no—
96C2×C3×D4—61no—
97C2×C3×D4—62no—
98C22×C3×C4—31no—
99C22×C3×C4—32no—
100C22×C3×C4—32no—
101C22×C3×C4—43no—
102C22×C3×C4—62no—
103C22×C3×C4—62no—
104C22×C3×C4S411yescharacteristic
105C22×Dic3—61no—
106C22×Dic3—61no—
107C22×Dic3—123no—
108C22×Dic3—123no—
109C2×Dic6—32no—
110C2×Dic6—62no—
111C2×Dic6—62no—
112C2×Dic6—61no—
113#41⋊C3—26no—
114C2×SL(2,𝔽3)#6716yes—
115C2×SL(2,𝔽3)C22×D313yes—
116#226—66no—
117#217—64no—
118#216—64no—
119#216—62no—
120#216—62no—
121#214—68no—
122C4⋊Dic3—32no—
123C4⋊Dic3—61no—
124Dic3⋊C4—64no—
125Dic3⋊C4—1212no—
126C2×C3⋊C8—32no—
127C2×C3⋊C8—32no—
128C2×C3⋊C8—62no—
129C2×C3⋊C8—62no—
130C22×C32—42no—
131C22×C32—42no—
132C22×C32—42no—
133C22×C32—41no—
134C32×C4—82no—
135C3⋊Dic3—44no—
136C3⋊Dic3—82no—
137C2×#41—22no—
138C2×#41—32no—
139C2×#41—62no—
140C2×#41C2×C3⋊D312yes—
141C22×Q8—91no—
142C22×Q8C2×C3⋊D311yescharacteristic
143C22×D4—31no—
144C23×C4—31no—
145C2×Q16—92no—
146C2×Q16—92no—
147C2×Q16—182no—
148C2×Q16—182no—
149C2×SD16—94no—
150C2×SD16—184no—
151C22×C8—91no—
152C22×C8—91no—
153C22⋊Q8—94no—
154C22⋊Q8—182no—
155C2×C4⋊C4—91no—
156C2×C4⋊C4—181no—
157C2×C22⋊C4—181no—
158#103—92no—
159#103—92no—
160#102—94no—
161C22⋊C8—94no—
162C23×C3—32no—
163C23×C3—43no—
164C23×C3—62no—
165C23×C3—62no—
166C23×C3—62no—
167C23×C3C2×S411yescharacteristic
168C3×Q8—32no—
169C3×Q8—31no—
170C3×Q8—61no—
171C3×Q8C2×#6711yescharacteristic
172C3×D4—34no—
173C3×D4—62no—
174C3×D4—64no—
175C2×C3×C4—22no—
176C2×C3×C4—32no—
177C2×C3×C4—32no—
178C2×C3×C4—31no—
179C2×C3×C4—31no—
180C2×C3×C4—46no—
181C2×C3×C4—62no—
182C2×C3×C4—62no—
183C2×C3×C4—64no—
184C2×C3×C4—86no—
185C2×C3×C4C2×S412yes—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—126no—
189C2×Dic3—126no—
190C2×Dic3—1212no—
191C2×Dic3—122no—
192C2×Dic3—122no—
193C2×Dic3—246no—
194Dic6—62no—
195Dic6—62no—
196Dic6—122no—
197SL(2,𝔽3)C2×#6713yes—
198C3⋊C8—62no—
199C3⋊C8—62no—
200C2×C32—41no—
201C2×C32—41no—
202C2×C32—41no—
203C2×C32—44no—
204C24—31no—
205#41—22no—
206#41—64no—
207#41—62no—
208#41—64no—
209C2×Q8—31no—
210C2×Q8—32no—
211C2×Q8—92no—
212C2×Q8—181no—
213C2×Q8—182no—
214C2×Q8—182no—
215C2×Q8#63812yes—
216C2×Q8C22×C3⋊D311yescharacteristic
217C2×D4—32no—
218C2×D4—34no—
219C2×D4—61no—
220C2×D4—62no—
221C22×C4—31no—
222C22×C4—32no—
223C22×C4—32no—
224C22×C4—62no—
225C22×C4—62no—
226C22×C4—181no—
227C22×C4—181no—
228C22×C4C3⋊S411yescharacteristic
229Q16—184no—
230Q16—182no—
231Q16—182no—
232SD16—188no—
233C2×C8—92no—
234C2×C8—92no—
235C2×C8—182no—
236C2×C8—182no—
237C4⋊C4—92no—
238C4⋊C4—181no—
239C4⋊C4—184no—
240C22⋊C4—184no—
241C22×C3—46no—
242C22×C3—46no—
243C22×C3—46no—
244C22×C3—43no—
245C22×C3—62no—
246C22×C3—62no—
247C22×C3—62no—
248C22×C3—124no—
249C22×C3#98412yes—
250C22×C3#98512yes—
251C22×C3GL(2,ℤ/4)12yes—
252C22×C3C22×S411yescharacteristic
253C3×C4—22no—
254C3×C4—31no—
255C3×C4—31no—
256C3×C4—32no—
257C3×C4—86no—
258Dic3—1212no—
259Dic3—122no—
260Dic3—122no—
261Dic3—246no—
262C32—41noSylow
263C23—32no—
264C23—62no—
265C23—62no—
266C23—62no—
267C23C2×C3⋊S411yescharacteristic
268Q8—32no—
269Q8—31no—
270Q8—61no—
271Q8—182no—
272Q8—182no—
273Q8—362no—
274Q8C2×#63811yescharacteristic
275D4—34no—
276D4—62no—
277D4—64no—
278C2×C4—22no—
279C2×C4—32no—
280C2×C4—32no—
281C2×C4—31no—
282C2×C4—31no—
283C2×C4—62no—
284C2×C4—62no—
285C2×C4—64no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—362no—
289C2×C4—362no—
290C2×C4C2×C3⋊S412yes—
291C8—182no—
292C8—182no—
293C2×C3—412no—
294C2×C3—43no—
295C2×C3—43no—
296C2×C3—43no—
297C2×C3—122no—
298C2×C3#542514yescomplemented
299C2×C3C2×#98411yescharacteristic
300C2×C3C2×#98511yescharacteristic
301C2×C3C2×GL(2,ℤ/4)11yescharacteristic
302C22—62no—
303C22—62no—
304C22—62no—
305C22—124no—
306C22#6426512yes—
307C22#6426612yes—
308C22#6426912yes—
309C22C22×C3⋊S411yescharacteristic
310C4—22no—
311C4—31no—
312C4—31no—
313C4—32no—
314C4—362no—
315C4—362no—
316C3—43no—
317C3C2×#542511yescharacteristic, complemented
318C2—122no—
319C2#1059365914yesdirect product factor
320C2C2×#6426511yescharacteristic
321C2C2×#6426611yescharacteristic
322C2C2×#6426911yescharacteristic
subgroupG/H
centerC23C2×C3⋊S4
commutator, cosocleC2×C3×SL(2,𝔽3)C23
FrattiniC22C22×C3⋊S4
FittingC22×C3×#41D3
socleC23×C3C2×S4
prime radicalC22×C3×#41⋊C3C2
hypercenterC22×C4C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3⋊#226C2semidirect
3. #10593659C2direct (N × H)
4. C2×C3⋊#859C2semidirect
11. C2×C3⋊#226C22semidirect
13. C3⋊#859C22semidirect
298. C2×C3#5425semidirect
317. C3C2×#5425semidirect
319. C2#10593659direct (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⋊C32
C22×C3⋊#2262
#105936592
C2×C3⋊#8592
C2×#54253
C2×#52393
C2×#37504