Finite Group Databasebeta

← #11778794

Subgroups — #11778794

Order 1152.

559 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 559 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#10594930C211yesmaximal, characteristic
2#10592358C211yesmaximal, characteristic, complemented
3#10591092C212yesmaximal, complemented
4C3×#4451C212yesmaximal, complemented
5#10589148C211yesmaximal, characteristic, complemented
6#68299—32nomaximal
7C2×#3805—21no—
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×#3750C2211yescharacteristic
10C3×#930C2212yes—
11#63980—21no—
12#63899—22no—
13#63885—22no—
14C32×#95C2211yescharacteristic
15#63658—21no—
16#63658—21no—
17C3×#830C2212yes—
18#63573—22no—
19#63563—22no—
20#5597—32no—
21#5034—32no—
22#4735—32no—
23#4659—32no—
24#4659—61no—
25C3×#327—32no—
26#4469—32no—
27#4451D312yescomplemented
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C3×#67—22no—
34C2×C3×D12D412yes—
35C2×#627—21no—
36C2×#625—21no—
37C2×#625—21no—
38#3805—42no—
39#3805—42no—
40C2×D3×Dic3—22no—
41C4⋊(C3⋊Dic3)—22no—
42#3750—22no—
43C3×(C2×D3)⋊C4—22no—
44C3×C4⋊Dic3D412yes—
45C2×C3×C3⋊C8—22no—
46#3724—21no—
47(C2×D3)⋊Dic3—22no—
48#1616—91noSylow
49C2×#237—62no—
50C3×#121—32no—
51#939—62no—
52#939—62no—
53#930C2×D312yes—
54C2×C4⋊Dic3—32no—
55C2×C4⋊Dic3—61no—
56C2×Dic3⋊C4—32no—
57C2×Dic3⋊C4—61no—
58#896—62no—
59#884—62no—
60#878—62no—
61C3×C22⋊C8—32no—
62C3×#95—21no—
63C3×#95C2×D312yes—
64#832—62no—
65C3⋊#95—62no—
66C3⋊#95—62no—
67C3⋊#95—62no—
68C3⋊#95—62no—
69#830C2×D312yes—
70#821—62no—
71#817—62no—
72#808—62no—
73C23×C32C2×D411yescharacteristic
74C22×C3×D3—22no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4C2×D412yes—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3SD1612yes—
87C3×#67—42no—
88C3×#67—42no—
89C2×C3×Dic3—22no—
90C3×D12—42no—
91#627—42no—
92#625—42no—
93#625—81no—
94D3×Dic3—44no—
95C3×C3⋊C8—42no—
96#537—91no—
97#481—92no—
98#400—91no—
99#327—32no—
100#324—91no—
101C2×C3×D4—32no—
102C2×C3×D4—62no—
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—21no—
106C22×C3×C4C22×D312yes—
107C2×#67—22no—
108C2×#67—62no—
109C2×#67—62no—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—61no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117#237—124no—
118#237—124no—
119C2×D12D1212yes—
120C2×C4×D3—62no—
121C2×Dic6—62no—
122C2×C3×C8—62no—
123C3×C4⋊C4—32no—
124C3×C22⋊C4—62no—
125#217—62no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—62no—
128C4⋊Dic3—62no—
129C4⋊Dic3—62no—
130C4⋊Dic3—122no—
131C4⋊Dic3D1212yes—
132Dic3⋊C4—62no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135Dic3⋊C4—122no—
136C2×C3⋊C8—22no—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32#12011yescharacteristic
140C22×C32C2×SD1611yescharacteristic
141C22×C32AGL(1,ℤ/8)11yescharacteristic
142C2×C3×D3—42no—
143C2×C3×D3—42no—
144C2×C3×D3—42no—
145C32×C4—22no—
146C32×C4—81no—
147C3⋊Dic3—22no—
148C3⋊Dic3—41no—
149C3⋊Dic3—81no—
150C3×Dic3—42no—
151C2×#41—181no—
152C22⋊Q8—182no—
153#121—32no—
154#121—182no—
155#121—181no—
156C2×C4⋊C4—91no—
157C2×C4⋊C4—91no—
158#106—182no—
159#102—182no—
160C22⋊C8—32no—
161#95—181no—
162#95—181no—
163#95D3211yescharacteristic
164C23×C3—21no—
165C23×C3—62no—
166C23×C3D3×D412yes—
167C22×D3—22no—
168C3×D4—122no—
169C3×D4—122no—
170C3×D4—122no—
171C2×C3×C4—22no—
172C2×C3×C4—42no—
173C2×C3×C4—42no—
174C2×C3×C4—42no—
175C2×C3×C4—42no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—42no—
179C2×C3×C4—42no—
180C2×C3×C4—62no—
181C2×C3×C4C2×D1212yes—
182C2×C3×C4D3×D412yes—
183#67—42no—
184#67—42no—
185#67—124no—
186#67—242no—
187C2×Dic3—22no—
188C2×Dic3—34no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—62no—
193C2×Dic3—121no—
194C2×Dic3—121no—
195C2×Dic3—121no—
196C2×Dic3—124no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199C2×Dic3—122no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202C2×Dic3—122no—
203D12—42no—
204C4×D3—124no—
205Dic6—124no—
206C3×C8—122no—
207C3⋊C8—42no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32#45011yescharacteristic
211C2×C32#45411yescharacteristic
212C2×C32#45811yescharacteristic
213C3×D3—82no—
214#41—362no—
215#41—362no—
216C2×Q8—181no—
217C2×D4—32no—
218C2×D4—62no—
219C2×D4—181no—
220C2×D4—181no—
221C22×C4—21no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—182no—
225C22×C4—181no—
226C22×C4C2×D3211yescharacteristic
227C2×C8—62no—
228C4⋊C4—32no—
229C4⋊C4—181no—
230C4⋊C4—182no—
231C4⋊C4—182no—
232C22⋊C4—62no—
233C22⋊C4—182no—
234C22×C3—22no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—122no—
242C22×C3—122no—
243C22×C3—122no—
244C22×C3#88212yes—
245C22×C3#91112yes—
246C22×C3D3×SD1612yes—
247C2×D3—42no—
248C2×D3—42no—
249C2×D3—42no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—42no—
253C3×C4—82no—
254C3×C4—82no—
255C3×C4—122no—
256Dic3—42no—
257Dic3—64no—
258Dic3—122no—
259Dic3—122no—
260Dic3—241no—
261Dic3—242no—
262Dic3—242no—
263C32#161611yescharacteristic, complemented, Sylow
264C23—62no—
265C23#381111yescharacteristic
266Q8—362no—
267D4—122no—
268D4—122no—
269D4—122no—
270D4—362no—
271D4—721no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—62no—
277C2×C4—92no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4—364no—
282C2×C4—361no—
283C2×C4—362no—
284C2×C4—361no—
285C2×C4D3×D1212yes—
286C8—122no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—242no—
295C2×C3#474212yes—
296C2×C3#477612yes—
297C2×C3#482712yes—
298D3—82no—
299C22—21no—
300C22—21no—
301C22—122no—
302C22—122no—
303C22—122no—
304C22#6392311yescharacteristic
305C22#6392711yescharacteristic
306C22#6394011yescharacteristic
307C4—22no—
308C4—81no—
309C4—122no—
310C4—182no—
311C4—361no—
312C4—721no—
313C3—21no—
314C3#6829912yescomplemented
315C2—21no—
316C2—21no—
317C2—242no—
318C2#1059040211yescharacteristic
319C2#1059040911yescharacteristic
320C2#1059059711yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#95C22
socleC22×C32#120
prime radical#10594930C2
hypercenter#95D32
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592358C2semidirect
3. #10591092C2semidirect
4. C3×#4451C2semidirect
5. #10589148C2semidirect
27. #4451D3semidirect
263. C32#1616semidirect
314. C3#68299semidirect

Maximal subgroups

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

subgroupindex
#105949302
#105923582
#105910922
C3×#44512
#105891482
#682993