Finite Group Databasebeta

← #11807142

Subgroups — #11807142

Order 1152.

1137 conjugacy classes of subgroups; only the 284 normal subgroups are shown.

normal subgroups only

This group has 1137 conjugacy classes of subgroups — too many to draw. Only its 284 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×#64153C211yesmaximal, characteristic
2C3×#5229C212yesmaximal
3#10591273C212yesmaximal
4#10591264C214yesmaximal
5#10591257C212yesmaximal
6#10591243C214yesmaximal
7#76494—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10#64153C418yescomplemented
11C2×#3750C2214yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4×Dic3C2212yes—
15C2×#3724C2212yes—
16C2×#3724C2212yes—
17C2×#3724C2212yes—
18C2×Dic32C2214yes—
19C2×Dic32C2212yes—
20C3×C3⋊#95C2214yes—
21C3×C3⋊#95C2214yes—
22#63579C2214yes—
23C2×#944—32no—
24C2×#944—61no—
25C3×#391—32no—
26#5229D312yes—
27#4976—34no—
28C4×Dic3⋊C4—34no—
29#4649—34no—
30#4649—34no—
31#4647—34no—
32#4646—34no—
33C2×C32×Q8—41no—
34C2×C32×Q8—41no—
35C2×C32×Q8C2×C414yes—
36C22×C32×C4C2312yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2312yes—
40C2×#634—41no—
41C2×#634—41no—
42C2×#634C2×C414yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2314yes—
45#3750C2×C4116yes—
46C4×C3⋊Dic3C2×C414yes—
47C3×C4⋊Dic3—42no—
48C3×C4×Dic3—42no—
49#3724—24no—
50#3724—42no—
51#3724Q818yescomplemented
52Dic32—28no—
53Dic32—42no—
54#2369—91noSylow
55C22×C3×Q8—21no—
56C22×C3×Q8C2×D312yes—
57C22×Dic6—32no—
58C22×Dic6—61no—
59C2×C3×C4⋊C4—32no—
60C2×C3×C42—32no—
61#944—316no—
62#944—68no—
63C2×C4⋊Dic3C2×D312yes—
64C2×Dic3⋊C4—34no—
65C2×Dic3⋊C4—34no—
66C2×Dic3⋊C4—34no—
67C2×Dic3⋊C4—34no—
68C2×Dic3⋊C4—34no—
69C2×Dic3⋊C4—64no—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—34no—
72C2×C4×Dic3—34no—
73C2×C4×Dic3—34no—
74C2×C4×Dic3—61no—
75C2×C4×Dic3C2×D312yes—
76C3×#95—34no—
77C3×#95—34no—
78C3⋊#95—34no—
79C3⋊#95—34no—
80C3⋊#95C2×D314yes—
81C3⋊#95C2×D314yes—
82C23×C32C2411yescharacteristic
83C32×Q8—44no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4C22×C412yes—
89C2×C32×C4C22×C414yes—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3C22×C414yes—
93C2×C3⋊Dic3C22×C414yes—
94C2×C3⋊Dic3C2×Q814yes—
95C2×C3⋊Dic3#4114yes—
96#634—44no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—24no—
102C2×C3×Dic3C2×Q818yes—
103C2×C4⋊Q8—91no—
104#391—32no—
105#391—92no—
106#389—94no—
107C4×C4⋊C4—92no—
108C4×C4⋊C4—94no—
109C2×C3×Q8—24no—
110C2×C3×Q8—42no—
111C2×C3×Q8—42no—
112C2×C3×Q8—42no—
113C2×C3×Q8—42no—
114C2×C3×Q8C4×D318yes—
115C22×C3×C4—21no—
116C22×C3×C4—22no—
117C22×C3×C4—34no—
118C22×C3×C4—34no—
119C22×C3×C4C22×D312yes—
120C22×C3×C4C22×D312yes—
121C22×C3×C4C22×D312yes—
122C22×Dic3—34no—
123C22×Dic3—34no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3C22×D314yes—
127C22×Dic3C22×D314yes—
128C2×Dic6—38no—
129C2×Dic6—64no—
130C2×Dic6—122no—
131C2×Dic6—122no—
132C2×Dic6—122no—
133C2×Dic6—122no—
134C3×C4⋊C4—122no—
135C3×C42—122no—
136C4⋊Dic3—42no—
137Dic3⋊C4—316no—
138Dic3⋊C4—316no—
139Dic3⋊C4—316no—
140Dic3⋊C4—616no—
141Dic3⋊C4—68no—
142Dic3⋊C4—124no—
143C4×Dic3—38no—
144C4×Dic3—42no—
145C4×Dic3—64no—
146C4×Dic3—68no—
147C4×Dic3—68no—
148C4×Dic3—124no—
149C22×C32C23×C411yescharacteristic
150C22×C32C22×Q812yes—
151C22×C32C2×#4112yes—
152C22×C32H(5,𝔽2)11yescharacteristic
153C22×C32H(5,𝔽2)11yescharacteristic
154C32×C4—22no—
155C32×C4—24no—
156C3⋊Dic3—24no—
157C3⋊Dic3C4×Q818yes—
158C3×Dic3—28no—
159C3×Dic3—44no—
160C22×Q8—91no—
161C22×Q8D3211yescharacteristic
162C4⋊Q8—98no—
163C2×C4⋊C4—32no—
164C2×C4⋊C4—92no—
165C2×C4⋊C4—94no—
166C2×C4⋊C4—92no—
167C2×C4⋊C4—92no—
168C2×C42—32no—
169C2×C42—91no—
170C2×C42—94no—
171C2×C42—92no—
172#95—34no—
173#95—34no—
174#95—94no—
175C23×C3—21no—
176C23×C3C23×D312yes—
177C3×Q8—48no—
178C3×Q8—48no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—24no—
189C2×C3×C4—38no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—64no—
193C2×C3×C4—64no—
194C2×C3×C4—64no—
195C2×C3×C4—64no—
196C2×C3×C4—64no—
197C2×C3×C4C2×C4×D314yes—
198C2×C3×C4C2×C4×D314yes—
199C2×C3×C4C2×C4×D314yes—
200C2×Dic3—24no—
201C2×Dic3—24no—
202C2×Dic3—24no—
203C2×Dic3—24no—
204C2×Dic3—24no—
205C2×Dic3—38no—
206C2×Dic3—38no—
207C2×Dic3—38no—
208C2×Dic3—38no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—64no—
215C2×Dic3—122no—
216C2×Dic3—122no—
217C2×Dic3D3×Q818yes—
218Dic6—128no—
219Dic6—128no—
220C2×C32C2×C4×Q812yes—
221C2×C32#51811yescharacteristic
222C2×C32#55412yes—
223C2×C32#55511yescharacteristic
224C2×C32Q8211yescharacteristic
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—94no—
228C2×Q8—361no—
229C2×Q8—361no—
230C2×Q8#62414yes—
231C22×C4—34no—
232C22×C4—34no—
233C22×C4—92no—
234C22×C4—92no—
235C22×C4C2×D3211yescharacteristic
236C22×C4C2×D3212yes—
237C4⋊C4—98no—
238C4⋊C4—916no—
239C4⋊C4—122no—
240C4⋊C4—184no—
241C4⋊C4—362no—
242C42—94no—
243C42—122no—
244C42—188no—
245C42—362no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3C22×C4×D312yes—
252C22×C3#100412yes—
253C22×C3#100412yes—
254C22×C3C2×D3×Q814yes—
255C22×C3D3×#4114yes—
256C3×C4—24no—
257C3×C4—24no—
258C3×C4—24no—
259C3×C4—24no—
260C3×C4—44no—
261C3×C4—68no—
262C3×C4—124no—
263Dic3—28no—
264Dic3—316no—
265Dic3—44no—
266Dic3—68no—
267Dic3—68no—
268Dic3—124no—
269C32#236911yescharacteristic, complemented, Sylow
270C23C22×D3211yescharacteristic
271Q8—44no—
272Q8—364no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—38no—
278C2×C4—64no—
279C2×C4—64no—
280C2×C4—64no—
281C2×C4—64no—
282C2×C4—64no—
283C2×C4—94no—
284C2×C4—94no—
285C2×C4—94no—
286C2×C4—94no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4C2×#62412yes—
290C2×C4C2×#62414yes—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3#548612yes—
297C2×C3C4×D3×Q814yes—
298C2×C3#563614yes—
299C2×C3#567012yes—
300C2×C3#572212yes—
301C22D32×Q812yes—
302C22#6431912yes—
303C22C22×#62411yescharacteristic
304C22#6433011yescharacteristic
305C22#6433011yescharacteristic
306C4—22no—
307C4—24no—
308C4—68no—
309C4—98no—
310C4—124no—
311C4—184no—
312C3—21no—
313C3#7649412yescomplemented
314C2#1059537012yes—
315C2Q8×#62412yes—
316C2#1059539011yescharacteristic
317C2#1059542111yescharacteristic
318C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, prime radical, cosocleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
10. #64153C4semidirect
51. #3724Q8semidirect
269. C32#2369semidirect
313. C3#76494semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C3×#52292
#105912732
#105912642
#105912572
#105912432
#764943