Finite Group Databasebeta

← #11808864

Subgroups — #11808864

Order 1152.

1157 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 1157 conjugacy classes of subgroups — too many to draw. Only its 224 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
1C2×#64096C211yesmaximal, characteristic
2C2×#63838C211yesmaximal, characteristic
3C3×#4983C212yesmaximal
4#10591356C212yesmaximal
5#10591354C212yesmaximal
6#10591252C211yesmaximal, characteristic
7#10591241C214yesmaximal
8#10591195C212yesmaximal
9#77740—32nomaximal
10C22×#634C2211yescharacteristic
11C22×#627C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64096—24no—
17C2×C3×Dic3⋊C4C2214yes—
18C2×C3×Dic3⋊C4C2212yes—
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2214yes—
21C2×Dic32C2212yes—
22C2×Dic32C2212yes—
23#63838—24no—
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2212yes—
26#63579C2214yes—
27#63579C2212yes—
28C2×#887—32no—
29C2×#887—32no—
30C2×#887—61no—
31C3×#398—32no—
32#4983D312yes—
33#4979—34no—
34#4979—32no—
35Dic3×C4⋊C4—34no—
36#4657—34no—
37#4656—32no—
38#4649—34no—
39#4648—32no—
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C2×#634—22no—
46C2×#634—24no—
47C22×C3×Dic3C2312yes—
48C22×C3×Dic3C2314yes—
49C22×C3×Dic3C2312yes—
50C2×#627—22no—
51C2×#627—24no—
52C32×C4⋊C4—22no—
53#3750—24no—
54C4×C3⋊Dic3—24no—
55C4×C3⋊Dic3D414yes—
56C3×Dic3⋊C4—24no—
57C3×Dic3⋊C4—28no—
58#3724—22no—
59Dic3⋊Dic3—28no—
60Dic32—24no—
61Dic32Q818yescomplemented
62#2399—91noSylow
63C22×Dic6—32no—
64C22×Dic6—32no—
65C22×Dic6—61no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—34no—
68C2×C3×C4⋊C4—32no—
69C2×C3×C4⋊C4C2×D312yes—
70C2×C4⋊Dic3—34no—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—32no—
74C2×Dic3⋊C4—62no—
75C2×Dic3⋊C4C2×D314yes—
76C2×Dic3⋊C4C2×D312yes—
77C2×C4×Dic3—32no—
78C2×C4×Dic3—34no—
79C2×C4×Dic3—34no—
80C2×C4×Dic3—32no—
81C2×C4×Dic3—32no—
82C2×C4×Dic3—61no—
83C2×C4×Dic3—62no—
84#887—68no—
85#887—68no—
86#887—68no—
87C3×#95—32no—
88C3×#95—34no—
89C3⋊#95—34no—
90C3⋊#95—34no—
91C3⋊#95—34no—
92C3⋊#95C2×D312yes—
93C3⋊#95C2×D314yes—
94C23×C32C2411yescharacteristic
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—24no—
98C2×C32×C4C2×D412yes—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3C2×D412yes—
103C2×C3⋊Dic3C2×D412yes—
104C2×C3⋊Dic3C2×Q814yes—
105C2×C3⋊Dic3#4114yes—
106#634—28no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3C2×Q818yes—
114C2×C3×Dic3#4114yes—
115#627—28no—
116C2×C4×Q8—91no—
117C2×C4×Q8—91no—
118#398—32no—
119#398—92no—
120#395—92no—
121#395—92no—
122C4×C4⋊C4—94no—
123#376—91no—
124C22×C3×C4—21no—
125C22×C3×C4—22no—
126C22×C3×C4—34no—
127C22×C3×C4—32no—
128C22×C3×C4—32no—
129C22×C3×C4C22×D314yes—
130C22×C3×C4C22×D312yes—
131C22×Dic3—32no—
132C22×Dic3—32no—
133C22×Dic3—34no—
134C22×Dic3—61no—
135C22×Dic3—62no—
136C22×Dic3—61no—
137C22×Dic3C22×D312yes—
138C22×Dic3C22×D312yes—
139C22×Dic3C22×D314yes—
140C2×Dic6—64no—
141C2×Dic6—64no—
142C2×Dic6—68no—
143C2×Dic6—64no—
144C2×Dic6—68no—
145C2×Dic6—64no—
146C2×Dic6—64no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—24no—
149C3×C4⋊C4—68no—
150C3×C4⋊C4—64no—
151C4⋊Dic3—68no—
152Dic3⋊C4—24no—
153Dic3⋊C4—28no—
154Dic3⋊C4—64no—
155Dic3⋊C4—68no—
156Dic3⋊C4—68no—
157Dic3⋊C4—68no—
158C4×Dic3—38no—
159C4×Dic3—316no—
160C4×Dic3—64no—
161C4×Dic3—64no—
162C4×Dic3—64no—
163C4×Dic3—68no—
164C4×Dic3—68no—
165C22×C32C22×D411yescharacteristic
166C22×C32C22×Q812yes—
167C22×C32C2×#4112yes—
168C22×C32C2×#4112yes—
169C32×C4—22no—
170C32×C4—42no—
171C3⋊Dic3—24no—
172C3⋊Dic3—22no—
173C3⋊Dic3C4⋊Q814yes—
174C3×Dic3—24no—
175C3×Dic3—28no—
176C3×Dic3—42no—
177C22×Q8—91no—
178C22×Q8—91no—
179C4×Q8—184no—
180C4×Q8—184no—
181C2×C4⋊C4—32no—
182C2×C4⋊C4—34no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—94no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4D3211yescharacteristic
187C2×C42—92no—
188C2×C42—91no—
189C2×C42—92no—
190C2×C42—92no—
191#95—32no—
192#95—34no—
193#95—92no—
194#95—94no—
195C23×C3—21no—
196C23×C3C23×D312yes—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—22no—
204C2×C3×C4—38no—
205C2×C3×C4—34no—
206C2×C3×C4—44no—
207C2×C3×C4—62no—
208C2×C3×C4—62no—
209C2×C3×C4—64no—
210C2×C3×C4—64no—
211C2×C3×C4—62no—
212C2×C3×C4—64no—
213C2×C3×C4D3×D414yes—
214C2×Dic3—22no—
215C2×Dic3—24no—
216C2×Dic3—24no—
217C2×Dic3—22no—
218C2×Dic3—22no—
219C2×Dic3—24no—
220C2×Dic3—34no—
221C2×Dic3—38no—
222C2×Dic3—34no—
223C2×Dic3—38no—
224C2×Dic3—62no—
225C2×Dic3—64no—
226C2×Dic3—64no—
227C2×Dic3—62no—
228C2×Dic3—64no—
229C2×Dic3—64no—
230C2×Dic3—64no—
231C2×Dic3—62no—
232C2×Dic3—64no—
233C2×Dic3—62no—
234C2×Dic3—122no—
235C2×Dic3#23714yes—
236C2×Dic3D3×Q818yes—
237Dic6—616no—
238Dic6—616no—
239Dic6—616no—
240C2×C32#52511yescharacteristic
241C2×C32#52511yescharacteristic
242C2×C32C2×C4⋊Q811yescharacteristic
243C2×C32#53314yes—
244C2×Q8—184no—
245C2×Q8—184no—
246C2×Q8—182no—
247C2×Q8—182no—
248C22×C4—34no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—91no—
252C22×C4—92no—
253C22×C4—91no—
254C22×C4C2×D3212yes—
255C22×C4C2×D3211yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—68no—
258C4⋊C4—64no—
259C4⋊C4—184no—
260C4⋊C4—182no—
261C4⋊C4—188no—
262C42—98no—
263C42—94no—
264C42—184no—
265C42—184no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—21no—
270C22×C3C2×D3×D412yes—
271C22×C3C2×#23712yes—
272C22×C3C2×D3×Q814yes—
273C22×C3D3×#4114yes—
274C22×C3D3×#4112yes—
275C3×C4—24no—
276C3×C4—24no—
277C3×C4—44no—
278C3×C4—44no—
279C3×C4—68no—
280C3×C4—64no—
281C3×C4—122no—
282Dic3—24no—
283Dic3—28no—
284Dic3—38no—
285Dic3—42no—
286Dic3—64no—
287Dic3—68no—
288Dic3—68no—
289Dic3—64no—
290Dic3—122no—
291C32#239911yescharacteristic, complemented, Sylow
292C23C22×D3211yescharacteristic
293Q8—188no—
294Q8—188no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—34no—
299C2×C4—38no—
300C2×C4—64no—
301C2×C4—64no—
302C2×C4—62no—
303C2×C4—62no—
304C2×C4—64no—
305C2×C4—62no—
306C2×C4—94no—
307C2×C4—92no—
308C2×C4—94no—
309C2×C4—92no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4#381112yes—
314C2×C3—21no—
315C2×C3—24no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3#560612yes—
319C2×C3#562214yes—
320C2×C3#565612yes—
321C2×C3#568814yes—
322C2×C3D3×C4⋊Q812yes—
323C22#6430612yes—
324C22D3×#23712yes—
325C22D32×Q812yes—
326C22C2×#381111yescharacteristic
327C4—22no—
328C4—42no—
329C4—68no—
330C4—64no—
331C4—94no—
332C4—122no—
333C4—184no—
334C4—182no—
335C3—21no—
336C3#7774012yescomplemented
337C2#1059438814yes—
338C2#1059492011yescharacteristic
339C2#1059530611yescharacteristic
340C2#1059536511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
61. Dic32Q8semidirect
291. C32#2399semidirect
336. C3#77740semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638382
C3×#49832
#105913562
#105913542
#105912522
#105912412
#105911952
#777403