Finite Group Databasebeta

← C2×#10588862 #11865623

Subgroups — C2×#10588862 #11865623

Order 1152.

720 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
1C22×C9×Q16C211yesmaximal, characteristic
2C2×Q8×Dic9C211yesmaximal, characteristic
3C2×#63506C211yesmaximal, characteristic
4C22×#3674C211yesmaximal, characteristic
5C2×#63395C211yesmaximal, characteristic
6#10588862C218yesmaximal, direct product factor
7C2×#63376C211yesmaximal, characteristic
8C2×Dic9⋊C8C211yesmaximal, characteristic
9C2×#5182—31nomaximal
10C22×Q8×C9C2211yescharacteristic
11C22×Q8×C9C2211yescharacteristic
12C22×Dic18C2211yescharacteristic
13C2×C9×Q16—24no—
14C2×C9×Q16C2214yes—
15C22×C8×C9C2211yescharacteristic
16Q8×Dic9—22no—
17Q8×Dic9C2214yes—
18#63506—22no—
19#63506C2214yes—
20C2×#3674—24no—
21C2×#3674C2214yes—
22C2×C4⋊Dic9—21no—
23C2×C4⋊Dic9C2211yescharacteristic
24C2×Dic9⋊C4—21no—
25C2×Dic9⋊C4—21no—
26C2×C4×Dic9—21no—
27C2×C4×Dic9C2211yescharacteristic
28C22×C9⋊C8C2211yescharacteristic
29#63395C2214yes—
30#63376C2214yes—
31Dic9⋊C8C2214yes—
32C22×C3×Q16D311yescharacteristic
33C2×Q8×Dic3—31no—
34C2×#944—31no—
35C22×#216—31no—
36C2×#835—31no—
37#5182—38no—
38C2×#816—31no—
39C2×Dic3⋊C8—31no—
40C2×Q8×C9—21no—
41C2×Q8×C9—21no—
42C2×Q8×C9—22no—
43C2×Q8×C9—22no—
44C2×Q8×C9—22no—
45C2×Q8×C9D414yes—
46C2×Q8×C9C2312yes—
47C2×Q8×C9C2312yes—
48C22×C4×C9—21no—
49C22×C4×C9—21no—
50C22×C4×C9C2311yescharacteristic
51C22×Dic9—21no—
52C22×Dic9—21no—
53C22×Dic9D411yescharacteristic
54C22×Dic9D411yescharacteristic
55C2×Dic18—22no—
56C2×Dic18—22no—
57C2×Dic18—21no—
58C2×Dic18C2312yes—
59C9×Q16—28no—
60C2×C8×C9—22no—
61C2×C8×C9C2312yes—
62#3674—28no—
63C4⋊Dic9—21no—
64C4⋊Dic9—24no—
65C4⋊Dic9C2312yes—
66Dic9⋊C4—24no—
67Dic9⋊C4—24no—
68C4×Dic9—24no—
69C4×Dic9D412yes—
70C4×Dic9C2312yes—
71C2×C9⋊C8—22no—
72C2×C9⋊C8C2312yes—
73C2×#462—91noSylow
74C22×C3×Q8C2×D311yescharacteristic
75C22×C3×Q8C2×D311yescharacteristic
76C22×Dic6—31no—
77C2×C3×Q16—24no—
78C2×C3×Q16C2×D314yes—
79C22×C3×C8C2×D311yescharacteristic
80Q8×Dic3—34no—
81Q8×Dic3—62no—
82#944—34no—
83#944—62no—
84C2×#216—34no—
85C2×#216—64no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×Dic3⋊C4—61no—
89C2×Dic3⋊C4—61no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—61no—
92C22×C3⋊C8—31no—
93#835—34no—
94#816—34no—
95Dic3⋊C8—34no—
96C23×C9C2×D411yescharacteristic
97Q8×C9—24no—
98Q8×C9—22no—
99Q8×C9—22no—
100Q8×C9—22no—
101Q8×C9—42no—
102Q8×C9C2×D414yes—
103C2×C4×C9—24no—
104C2×C4×C9—22no—
105C2×C4×C9—22no—
106C2×C4×C9—42no—
107C2×C4×C9C2×D411yescharacteristic
108C2×C4×C9C2×D412yes—
109C2×C4×C9#4112yes—
110C2×C4×C9C2411yescharacteristic
111C2×Dic9—22no—
112C2×Dic9—22no—
113C2×Dic9—22no—
114C2×Dic9—42no—
115C2×Dic9—42no—
116C2×Dic9Q1614yescomplemented
117C2×Dic9C2×D412yes—
118C2×Dic9C2×D412yes—
119Dic18—22no—
120Dic18—22no—
121Dic18—42no—
122C8×C9—22no—
123C9⋊C8—22no—
124C22×Q16—91no—
125C22×Q16D911yescharacteristic
126C2×C4⋊Q8—91no—
127C2×C4×Q8—91no—
128#462—98no—
129C2×C4⋊C8—91no—
130C2×#103—91no—
131C2×#103—91no—
132C2×C3×Q8—21no—
133C2×C3×Q8—21no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8#6714yes—
138C2×C3×Q8C22×D312yes—
139C2×C3×Q8C22×D312yes—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3—31no—
144C22×Dic3—31no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C2×Dic6—32no—
148C2×Dic6—62no—
149C2×Dic6—62no—
150C2×Dic6—61no—
151C3×Q16—28no—
152C2×C3×C8—22no—
153C2×C3×C8C22×D312yes—
154#216—68no—
155C4⋊Dic3—32no—
156C4⋊Dic3—64no—
157C4⋊Dic3—61no—
158Dic3⋊C4—64no—
159Dic3⋊C4—64no—
160C4×Dic3—32no—
161C4×Dic3—32no—
162C4×Dic3—64no—
163C2×C3⋊C8—32no—
164C2×C3⋊C8—62no—
165C22×C9#12112yes—
166C22×C9C2×Q1612yes—
167C22×C9#13712yes—
168C22×C9C22×D411yescharacteristic
169C4×C9—24no—
170C4×C9—42no—
171C4×C9#12112yes—
172C4×C9C22×D411yescharacteristic
173C4×C9C2×#4111yescharacteristic
174Dic9—22no—
175Dic9—42no—
176Dic9—42no—
177Dic9C2×Q1614yescomplemented
178C22×Q8—91no—
179C22×Q8C2×D911yescharacteristic
180C22×Q8C2×D911yescharacteristic
181C2×Q16—24no—
182C2×Q16—94no—
183C2×Q16—184no—
184C2×Q16C2×D914yes—
185C22×C8—91no—
186C22×C8C2×D911yescharacteristic
187C4⋊Q8—94no—
188C4⋊Q8—182no—
189C4×Q8—94no—
190C4×Q8—182no—
191C2×C4⋊C4—91no—
192C2×C4⋊C4—181no—
193C2×C4⋊C4—181no—
194C2×C4⋊C4—181no—
195C2×C42—91no—
196C2×C42—181no—
197C4⋊C8—94no—
198#103—94no—
199#103—94no—
200C23×C3D3×D411yescharacteristic
201C3×Q8—24no—
202C3×Q8—22no—
203C3×Q8—22no—
204C3×Q8—22no—
205C3×Q8—42no—
206C3×Q8C2×#6714yes—
207C2×C3×C4—24no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—42no—
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4#23712yes—
213C2×C3×C4C2×#6712yes—
214C2×C3×C4C23×D311yescharacteristic
215C2×Dic3—34no—
216C2×Dic3—32no—
217C2×Dic3—32no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223Dic6—62no—
224Dic6—62no—
225Dic6—122no—
226C3×C8—22no—
227C3⋊C8—62no—
228C2×C9#46214yescomplemented
229C2×C9C2×#12111yescharacteristic
230C2×C9C22×Q1611yescharacteristic
231C2×C9C2×#13711yescharacteristic
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—92no—
238C2×Q8—181no—
239C2×Q8—182no—
240C2×Q8—182no—
241C2×Q8#61114yes—
242C2×Q8C22×D912yes—
243C2×Q8C22×D912yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4C22×D911yescharacteristic
251Q16—28no—
252Q16—188no—
253C2×C8—22no—
254C2×C8—92no—
255C2×C8—182no—
256C2×C8C22×D912yes—
257C4⋊C4—92no—
258C4⋊C4—184no—
259C4⋊C4—184no—
260C4⋊C4—184no—
261C4⋊C4—181no—
262C42—92no—
263C42—92no—
264C42—184no—
265C22×C3D3×Q1612yes—
266C22×C3#91812yes—
267C22×C3#93912yes—
268C22×C3C2×D3×D411yescharacteristic
269C3×C4—24no—
270C3×C4—42no—
271C3×C4#93912yes—
272C3×C4C2×#23711yescharacteristic
273C3×C4C22×#6711yescharacteristic
274Dic3—34no—
275Dic3—62no—
276Dic3—122no—
277Dic3—122no—
278C9C2×#46211yescharacteristic, complemented, Sylow
279C23D4×D911yescharacteristic
280Q8—24no—
281Q8—22no—
282Q8—22no—
283Q8—22no—
284Q8—42no—
285Q8—182no—
286Q8—182no—
287Q8—362no—
288Q8C2×#61114yes—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—92no—
294C2×C4—94no—
295C2×C4—92no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—362no—
300C2×C4—362no—
301C2×C4D4×D911yescharacteristic
302C2×C4#369912yes—
303C2×C4C2×#61112yes—
304C2×C4C23×D911yescharacteristic
305C8—22no—
306C8—182no—
307C2×C3#518214yes—
308C2×C3C2×D3×Q1611yescharacteristic
309C2×C3C2×#91811yescharacteristic
310C2×C3C2×#93911yescharacteristic
311C22Q16×D912yes—
312C22#6348012yes—
313C22#6350112yes—
314C22C2×D4×D911yescharacteristic
315C4—24no—
316C4—42no—
317C4—94no—
318C4—182no—
319C4—362no—
320C4—362no—
321C4#6350112yes—
322C4C2×#369911yescharacteristic
323C4C22×#61111yescharacteristic
324C3C2×#518211yescharacteristic
325C2#1058886214yesdirect product factor
326C2C2×Q16×D911yescharacteristic
327C2C2×#6348011yescharacteristic
328C2C2×#6350111yescharacteristic
subgroupG/H
centerC23D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC22×C9×Q16C2
socle, prime radicalC23×C3D3×D4
hypercenterC22×Q16D9
hypocenterC9C2×#462
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
6. #10588862C2direct (N × H)
116. C2×Dic9Q16semidirect
177. Dic9C2×Q16semidirect
228. C2×C9#462semidirect
278. C9C2×#462semidirect
325. C2#10588862direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×Q162
C2×Q8×Dic92
C2×#635062
C22×#36742
C2×#633952
#105888622
C2×#633762
C2×Dic9⋊C82
C2×#51823