Finite Group Databasebeta

← C2×#10592494 #11865627

Subgroups — C2×#10592494 #11865627

Order 1152.

1440 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic
3C22×#3746C211yesmaximal, characteristic
4C2×#64096C211yesmaximal, characteristic
5C2×C32×#103C211yesmaximal, characteristic
6C2×#63641C211yesmaximal, characteristic
7C2×#63637C211yesmaximal, characteristic
8#10592494C218yesmaximal, direct product factor
9C2×#4795—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15#64153—22no—
16#64153C2214yes—
17C2×#3756—24no—
18C2×#3756C2214yes—
19C2×#3750—21no—
20C2×#3750—21no—
21C2×#3750—21no—
22C2×C4×C3⋊Dic3—21no—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×#3746—24no—
26C2×#3746C2214yes—
27#64096—22no—
28#64096C2214yes—
29C32×#103C2214yes—
30#63641C2214yes—
31#63637C2214yes—
32C2×#944—34no—
33C22×#216—34no—
34C22×Dic12—34no—
35C2×#887—34no—
36C2×C3×#103D314yes—
37C2×Dic3⋊C8—34no—
38C2×#810—34no—
39#4795—332no—
40C2×C32×Q8—21no—
41C2×C32×Q8—22no—
42C2×C32×Q8—22no—
43C2×C32×Q8C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×#634—21no—
52C2×#634—22no—
53C2×#634—22no—
54C2×#634—22no—
55C2×#634—21no—
56C2×#634D414yes—
57C2×#634C2312yes—
58C2×#634C2312yes—
59C2×C32×C8—22no—
60C2×C32×C8C2312yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2312yes—
63#3756—28no—
64#3750—24no—
65#3750—24no—
66#3750—24no—
67C4×C3⋊Dic3—24no—
68C4×C3⋊Dic3D412yes—
69C4×C3⋊Dic3C2312yes—
70C2×C3⋊(C3⋊C8)—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72#3746—28no—
73C2×#462—91noSylow
74C22×C3×Q8C2×D314yes—
75C22×Dic6—34no—
76C22×Dic6—34no—
77C22×C3×C8C2×D314yes—
78C2×C3×C4⋊C4C2×D314yes—
79#944—316no—
80#944—68no—
81C2×#216—316no—
82C2×#216—616no—
83C2×Dic3⋊C4—64no—
84C2×Dic3⋊C4—64no—
85C2×Dic3⋊C4—64no—
86C2×C4×Dic3—34no—
87C2×C4×Dic3—64no—
88C22×C3⋊C8—34no—
89C2×Dic12—316no—
90C2×Dic12—616no—
91#887—316no—
92#887—68no—
93C3×#103C2×D3116yes—
94Dic3⋊C8—316no—
95#810—316no—
96C23×C32C2×D411yescharacteristic
97C32×Q8—22no—
98C32×Q8—22no—
99C32×Q8—42no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—42no—
103C2×C32×C4—42no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D412yes—
106C2×C32×C4#4112yes—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—24no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3Q1614yescomplemented
114C2×C3⋊Dic3C2×D412yes—
115C2×C3⋊Dic3C2×D412yes—
116#634—24no—
117#634—22no—
118#634—22no—
119#634—22no—
120#634—42no—
121#634C2×D414yes—
122C32×C8—22no—
123C3⋊(C3⋊C8)—22no—
124C22×Q16—91no—
125C22×Q16—91no—
126C2×C4⋊Q8—91no—
127C2×C4×Q8—91no—
128#462—98no—
129C2×C4⋊C8—91no—
130C2×#103—91no—
131C2×#103C3⋊D311yescharacteristic
132C2×C3×Q8—24no—
133C2×C3×Q8—28no—
134C2×C3×Q8—28no—
135C2×C3×Q8C22×D318yes—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4C22×D314yes—
139C22×Dic3—34no—
140C22×Dic3—34no—
141C22×Dic3—64no—
142C22×Dic3—64no—
143C2×Dic6—316no—
144C2×Dic6—38no—
145C2×Dic6—38no—
146C2×Dic6—68no—
147C2×Dic6—64no—
148C2×Dic6—68no—
149C2×Dic6—68no—
150C2×Dic6—64no—
151C2×C3×C8—28no—
152C2×C3×C8C22×D318yes—
153C3×C4⋊C4—24no—
154C3×C4⋊C4C22×D318yes—
155#216—632no—
156Dic3⋊C4—616no—
157Dic3⋊C4—616no—
158Dic3⋊C4—616no—
159C4×Dic3—38no—
160C4×Dic3—38no—
161C4×Dic3—616no—
162C2×C3⋊C8—38no—
163C2×C3⋊C8—68no—
164Dic12—632no—
165C22×C32#12112yes—
166C22×C32C2×Q1612yes—
167C22×C32#13712yes—
168C22×C32C22×D411yescharacteristic
169C32×C4—42no—
170C32×C4—42no—
171C32×C4#12112yes—
172C32×C4C22×D411yescharacteristic
173C32×C4C2×#4111yescharacteristic
174C3⋊Dic3—24no—
175C3⋊Dic3—22no—
176C3⋊Dic3—42no—
177C3⋊Dic3C2×Q1614yescomplemented
178C22×Q8—91no—
179C22×Q8—91no—
180C22×Q8C2×C3⋊D311yescharacteristic
181C2×Q16—94no—
182C2×Q16—94no—
183C2×Q16—184no—
184C2×Q16—184no—
185C22×C8—91no—
186C22×C8C2×C3⋊D311yescharacteristic
187C4⋊Q8—94no—
188C4⋊Q8—182no—
189C4×Q8—94no—
190C4×Q8—182no—
191C2×C4⋊C4—181no—
192C2×C4⋊C4—181no—
193C2×C4⋊C4—181no—
194C2×C4⋊C4C2×C3⋊D311yescharacteristic
195C2×C42—91no—
196C2×C42—181no—
197C4⋊C8—94no—
198#103—94no—
199#103C2×C3⋊D314yes—
200C23×C3D3×D414yes—
201C3×Q8—28no—
202C3×Q8—28no—
203C3×Q8—48no—
204C2×C3×C4—28no—
205C2×C3×C4—28no—
206C2×C3×C4—48no—
207C2×C3×C4—48no—
208C2×C3×C4#23518yes—
209C2×C3×C4D3×D414yes—
210C2×C3×C4D3×D418yes—
211C2×C3×C4C23×D314yes—
212C2×Dic3—316no—
213C2×Dic3—38no—
214C2×Dic3—38no—
215C2×Dic3—616no—
216C2×Dic3—68no—
217C2×Dic3—68no—
218C2×Dic3—68no—
219C2×Dic3—128no—
220Dic6—316no—
221Dic6—616no—
222Dic6—68no—
223Dic6—68no—
224Dic6—68no—
225Dic6—128no—
226C3×C8—28no—
227C3⋊C8—68no—
228C2×C32#46214yescomplemented
229C2×C32C2×#12111yescharacteristic
230C2×C32C22×Q1611yescharacteristic
231C2×C32C2×#13711yescharacteristic
232C2×Q8—21no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—92no—
236C2×Q8—92no—
237C2×Q8—94no—
238C2×Q8—182no—
239C2×Q8—181no—
240C2×Q8—181no—
241C2×Q8—182no—
242C2×Q8—182no—
243C2×Q8C22×C3⋊D312yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4C22×C3⋊D311yescharacteristic
251Q16—188no—
252Q16—188no—
253C2×C8—22no—
254C2×C8—92no—
255C2×C8—182no—
256C2×C8C22×C3⋊D312yes—
257C4⋊C4—21no—
258C4⋊C4—184no—
259C4⋊C4—184no—
260C4⋊C4—184no—
261C4⋊C4C22×C3⋊D312yes—
262C42—92no—
263C42—92no—
264C42—184no—
265C22×C3#88418yes—
266C22×C3#91518yes—
267C22×C3D3×Q1618yes—
268C22×C3C2×D3×D414yes—
269C3×C4—48no—
270C3×C4—48no—
271C3×C4#88418yes—
272C3×C4C2×#23514yes—
273C3×C4C2×D3×D414yes—
274Dic3—316no—
275Dic3—616no—
276Dic3—68no—
277Dic3—128no—
278C32C2×#46211yescharacteristic, complemented, Sylow
279C23D4×C3⋊D311yescharacteristic
280Q8—22no—
281Q8—22no—
282Q8—42no—
283Q8—94no—
284Q8—184no—
285Q8—182no—
286Q8—182no—
287Q8—182no—
288Q8—362no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—92no—
294C2×C4—94no—
295C2×C4—92no—
296C2×C4—184no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—362no—
301C2×C4#382812yes—
302C2×C4D4×C3⋊D311yescharacteristic
303C2×C4D4×C3⋊D312yes—
304C2×C4C23×C3⋊D311yescharacteristic
305C8—22no—
306C8—182no—
307C2×C3#4795116yescomplemented
308C2×C3C2×#88414yes—
309C2×C3C2×#91514yes—
310C2×C3C2×D3×Q1614yes—
311C22#6409312yes—
312C22#6412412yes—
313C22Q16×C3⋊D312yes—
314C22C2×D4×C3⋊D311yescharacteristic
315C4—42no—
316C4—42no—
317C4—94no—
318C4—184no—
319C4—182no—
320C4—362no—
321C4#6409312yes—
322C4C2×#382811yescharacteristic
323C4C2×D4×C3⋊D311yescharacteristic
324C3C2×#479514yescomplemented
325C2#1059249414yesdirect product factor
326C2C2×#6409311yescharacteristic
327C2C2×#6412411yescharacteristic
328C2C2×Q16×C3⋊D311yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
hypercenterC2×#103C3⋊D3
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
8. #10592494C2direct (N × H)
113. C2×C3⋊Dic3Q16semidirect
177. C3⋊Dic3C2×Q16semidirect
228. C2×C32#462semidirect
278. C32C2×#462semidirect
307. C2×C3#4795semidirect
324. C3C2×#4795semidirect
325. C2#10592494direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C22×#37562
C22×#37462
C2×#640962
C2×C32×#1032
C2×#636412
C2×#636372
#105924942
C2×#47953