Finite Group Databasebeta

← #11805604

Subgroups — #11805604

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic
2C2×#63838C212yesmaximal
3#10592348C211yesmaximal, characteristic
4C3×#4650C212yesmaximal
5#10591360C211yesmaximal, characteristic
6#10591328C212yesmaximal
7#10591242C212yesmaximal
8#10591234C214yesmaximal
9#74157—32nomaximal
10C22×#627C2211yescharacteristic
11C2×#3750C2212yes—
12C2×C4×C3⋊Dic3C2212yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic3⋊C4C2214yes—
15C2×C3×C4×Dic3C2212yes—
16C2×#3724C2212yes—
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3C2214yes—
19C2×Dic3⋊Dic3C2212yes—
20C2×Dic32C2214yes—
21C4×#627C418yescomplemented
22#63838—28no—
23C32×#95C2211yescharacteristic
24#63658C2211yescharacteristic
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2212yes—
27#63579C2212yes—
28C2×#887—34no—
29C2×C4×Dic6—32no—
30C3×#382—32no—
31#4972—34no—
32C4×C4⋊Dic3—32no—
33#4650—32no—
34#4650D312yes—
35#4649—32no—
36#4649—32no—
37#4649—61no—
38#4647—34no—
39#4647—34no—
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3×Dic3C2314yes—
46C22×C3×Dic3C2312yes—
47C22×C3×Dic3C2312yes—
48C2×#627C2×C414yes—
49C2×#627D414yes—
50C2×#627Q814yes—
51#3750—24no—
52C4×C3⋊Dic3—24no—
53C4×C3⋊Dic3C2×C414yes—
54C3×Dic3⋊C4—28no—
55C3×C4×Dic3C2×C418yes—
56#3724—24no—
57#3724C2×C414yes—
58Dic3⋊Dic3—28no—
59Dic3⋊Dic3C2×C418yes—
60Dic32—28no—
61#2351—91noSylow
62C22×Dic6—32no—
63C2×C3×C4⋊C4—34no—
64C2×C3×C42—32no—
65C2×C4⋊Dic3—32no—
66C2×C4⋊Dic3—34no—
67C2×Dic3⋊C4—32no—
68C2×Dic3⋊C4—32no—
69C2×Dic3⋊C4—34no—
70C2×Dic3⋊C4—34no—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—62no—
73C2×Dic3⋊C4C2×D314yes—
74C2×C4×Dic3—32no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3—34no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—61no—
79C2×C4×Dic3—62no—
80C2×C4×Dic3C2×D312yes—
81#887—616no—
82C4×Dic6—316no—
83C3×#95—21no—
84C3×#95—34no—
85C3×#95—32no—
86C3×#95C2×D312yes—
87C3⋊#95—32no—
88C3⋊#95—34no—
89C3⋊#95—61no—
90C3⋊#95C2×D314yes—
91C3⋊#95C2×D312yes—
92C23×C32C2411yescharacteristic
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4C22×C412yes—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C22×C412yes—
102C2×C3⋊Dic3C22×C412yes—
103C2×C3⋊Dic3C2×D412yes—
104C2×C3⋊Dic3C2×Q812yes—
105C2×C3⋊Dic3#4114yes—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—24no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3C22×C414yes—
111C2×C3×Dic3C22×C414yes—
112C2×C3×Dic3C2×D414yes—
113C2×C3×Dic3C2×Q814yes—
114#627C4⋊C4116yescomplemented
115C2×C4×Q8—91no—
116C2×C4×Q8—92no—
117#389—92no—
118#389—94no—
119#382—32no—
120#382—91no—
121C4×C4⋊C4—92no—
122C4×C4⋊C4—91no—
123C22×C3×C4—21no—
124C22×C3×C4—22no—
125C22×C3×C4—32no—
126C22×C3×C4—32no—
127C22×C3×C4—34no—
128C22×C3×C4C22×D314yes—
129C22×C3×C4C22×D312yes—
130C22×Dic3—32no—
131C22×Dic3—32no—
132C22×Dic3—34no—
133C22×Dic3—61no—
134C22×Dic3—61no—
135C22×Dic3—62no—
136C22×Dic3C22×D314yes—
137C22×Dic3C22×D312yes—
138C22×Dic3C22×D312yes—
139C2×Dic6—38no—
140C2×Dic6—38no—
141C2×Dic6—38no—
142C3×C4⋊C4—68no—
143C3×C42—38no—
144C4⋊Dic3—38no—
145C4⋊Dic3—68no—
146Dic3⋊C4—28no—
147Dic3⋊C4—38no—
148Dic3⋊C4—38no—
149Dic3⋊C4—68no—
150Dic3⋊C4—68no—
151Dic3⋊C4—68no—
152Dic3⋊C4—68no—
153C4×Dic3—38no—
154C4×Dic3—64no—
155C4×Dic3—68no—
156C4×Dic3—68no—
157C4×Dic3—68no—
158C4×Dic3—124no—
159C4×Dic3C4×D318yes—
160C22×C32C23×C411yescharacteristic
161C22×C32C22×D411yescharacteristic
162C22×C32C22×Q811yescharacteristic
163C22×C32C2×#4112yes—
164C22×C322−1+412yes—
165C32×C4—22no—
166C32×C4—42no—
167C3⋊Dic3—22no—
168C3⋊Dic3—24no—
169C3⋊Dic3C2×C4⋊C414yes—
170C3×Dic3—24no—
171C3×Dic3—44no—
172C3×Dic3C2×C4⋊C418yes—
173C22×Q8—91no—
174C4×Q8—98no—
175C4×Q8—188no—
176C2×C4⋊C4—34no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4—92no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—94no—
181C2×C4⋊C4—92no—
182C2×C42—32no—
183C2×C42—91no—
184C2×C42—94no—
185C2×C42—92no—
186#95—32no—
187#95—34no—
188#95—92no—
189#95—91no—
190#95D3211yescharacteristic
191C23×C3—21no—
192C23×C3C23×D312yes—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—22no—
199C2×C3×C4—34no—
200C2×C3×C4—34no—
201C2×C3×C4—34no—
202C2×C3×C4—34no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—64no—
207C2×C3×C4—64no—
208C2×C3×C4—64no—
209C2×C3×C4—64no—
210C2×C3×C4C2×C4×D314yes—
211C2×Dic3—24no—
212C2×Dic3—24no—
213C2×Dic3—24no—
214C2×Dic3—24no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—34no—
219C2×Dic3—38no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—64no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C2×Dic3C2×C4×D314yes—
232C2×Dic3C2×C4×D314yes—
233C2×Dic3D3×D414yes—
234C2×Dic3D3×Q814yes—
235Dic6—332no—
236C2×C32C22×C4⋊C411yescharacteristic
237C2×C32C4×#4111yescharacteristic
238C2×C32#51911yescharacteristic
239C2×C32#54812yes—
240C2×C32#55712yes—
241C2×Q8—94no—
242C2×Q8—94no—
243C2×Q8—94no—
244C22×C4—32no—
245C22×C4—32no—
246C22×C4—34no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—92no—
250C22×C4C2×D3212yes—
251C22×C4C2×D3211yescharacteristic
252C4⋊C4—68no—
253C4⋊C4—94no—
254C4⋊C4—98no—
255C4⋊C4—184no—
256C4⋊C4—184no—
257C4⋊C4—188no—
258C42—38no—
259C42—94no—
260C42—184no—
261C42—188no—
262C22×C3—21no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3C22×C4×D312yes—
268C22×C3C2×D3×D412yes—
269C22×C3C2×D3×Q812yes—
270C22×C3D3×#4114yes—
271C22×C3#101014yes—
272C3×C4—24no—
273C3×C4—38no—
274C3×C4—42no—
275C3×C4—44no—
276C3×C4—44no—
277C3×C4—64no—
278C3×C4—124no—
279Dic3—24no—
280Dic3—38no—
281Dic3—44no—
282Dic3—64no—
283Dic3—64no—
284Dic3—68no—
285Dic3—64no—
286Dic3—124no—
287Dic3D3×C4⋊C418yes—
288C32#235111yescharacteristic, complemented, Sylow
289C23C22×D3211yescharacteristic
290Q8—916no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—34no—
296C2×C4—34no—
297C2×C4—34no—
298C2×C4—34no—
299C2×C4—64no—
300C2×C4—64no—
301C2×C4—64no—
302C2×C4—64no—
303C2×C4—92no—
304C2×C4—92no—
305C2×C4—92no—
306C2×C4—92no—
307C2×C4—94no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4C4×D3212yes—
312C2×C3—22no—
313C2×C3—21no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3C2×D3×C4⋊C412yes—
318C2×C3#551612yes—
319C2×C3#552212yes—
320C2×C3#567714yes—
321C2×C3#568514yes—
322C22C2×C4×D3211yescharacteristic
323C22#6430612yes—
324C22#6430912yes—
325C22D32×D411yescharacteristic
326C22D32×Q811yescharacteristic
327C4—22no—
328C4—38no—
329C4—42no—
330C4—64no—
331C4—94no—
332C4—124no—
333C4—184no—
334C4—182no—
335C3—21no—
336C3#7415712yescomplemented
337C2#1059396611yescharacteristic
338C2#1059419112yes—
339C2#1059424511yescharacteristic
340C2#1059459712yes—
341C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
21. C4×#627C4semidirect
114. #627C4⋊C4semidirect
288. C32#2351semidirect
336. C3#74157semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#638382
#105923482
C3×#46502
#105913602
#105913282
#105912422
#105912342
#741573