Finite Group Databasebeta

← #11785293

Subgroups — #11785293

Order 1152.

518 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×#627C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic
3C2×#63740C212yesmaximal
4#10591360C211yesmaximal, characteristic
5#10590075C212yesmaximal
6C22×#627C2211yescharacteristic
7C22×#622C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×C4×Dic3—21no—
10C2×#3724C2212yes—
11C2×#3724C2211yescharacteristic
12C2×Dic3⋊Dic3—21no—
13C4×#627—22no—
14C4×#627C414yescomplemented
15#63779—22no—
16#63740—24no—
17C3×C3⋊#95—21no—
18#63579—21no—
19C2×C4×Dic6—61no—
20#4650—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C22×C3×Dic3—21no—
25C22×C3×Dic3—21no—
26C22×C3×Dic3—22no—
27C2×#627—21no—
28C2×#627—21no—
29C2×#627—21no—
30C2×#627C2×C412yes—
31C2×#627D412yes—
32C2×#627Q812yes—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622—22no—
36C4×C3⋊Dic3C2×C412yes—
37C4×C3⋊Dic3D412yes—
38C3×C4×Dic3—24no—
39#3724—21no—
40#3724—22no—
41#3724—22no—
42#3724C2×C412yes—
43Dic3⋊Dic3—24no—
44#1805—91nomaximal, Sylow
45C22×Dic6—61no—
46C2×C3×C42—61no—
47C2×C4⋊Dic3—61no—
48C2×Dic3⋊C4—61no—
49C2×Dic3⋊C4—62no—
50C2×Dic3⋊C4—61no—
51C2×C4×Dic3—21no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54C4×Dic6—64no—
55C4×Dic6—64no—
56C3×#95—61no—
57C3⋊#95—21no—
58C3⋊#95—62no—
59C23×C32C2×D411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4C22⋊C412yes—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3C2×Q811yescharacteristic
68C2×C3⋊Dic3#4111yescharacteristic
69C2×C3⋊Dic3#4111yescharacteristic
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—42no—
78#627—22no—
79#627—22no—
80#627—22no—
81#627C4⋊C414yes—
82#622—42no—
83C2×C4×Q8—91no—
84C2×C4⋊C8—91no—
85C2×#103—92no—
86#382—91no—
87#340—92no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—61no—
91C22×C3×C4—61no—
92C22×C3×C4—62no—
93C22×Dic3—21no—
94C22×Dic3—21no—
95C22×Dic3—22no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C2×Dic6—62no—
101C2×Dic6—62no—
102C2×Dic6—62no—
103C2×Dic6—62no—
104C2×Dic6—62no—
105C2×Dic6—62no—
106C3×C42—64no—
107C4⋊Dic3—64no—
108Dic3⋊C4—62no—
109Dic3⋊C4—64no—
110Dic3⋊C4—62no—
111Dic3⋊C4—122no—
112Dic3⋊C4—122no—
113C4×Dic3—24no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C22×C32C2×C22⋊C411yescharacteristic
119C22×C32#12111yescharacteristic
120C22×C32C22⋊Q811yescharacteristic
121C22×C32#13512yes—
122C22×C32#13712yes—
123C32×C4—22no—
124C3⋊Dic3—22no—
125C3⋊Dic3C2×C4⋊C411yescharacteristic
126C3⋊Dic3#11711yescharacteristic
127C3⋊Dic3#12111yescharacteristic
128C3⋊Dic3C22⋊Q811yescharacteristic
129C3×Dic3—24no—
130C3×Dic3—42no—
131C3×Dic3—82no—
132C22×Q8—91no—
133C22×C8—92no—
134C4×Q8—94no—
135C4×Q8—182no—
136C2×C4⋊C4—91no—
137C2×C4⋊C4—92no—
138C2×C4⋊C4—181no—
139C2×C42—61no—
140C2×C42—91no—
141C4⋊C8—182no—
142#103—184no—
143#95—61no—
144#95—181no—
145C23×C3—21no—
146C23×C3—21no—
147C2×C3×C4—24no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—42no—
151C2×C3×C4—62no—
152C2×C3×C4—62no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×C3×C4—122no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158C2×C3×C4—122no—
159C2×Dic3—22no—
160C2×Dic3—22no—
161C2×Dic3—22no—
162C2×Dic3—22no—
163C2×Dic3—42no—
164C2×Dic3—42no—
165C2×Dic3—42no—
166C2×Dic3—42no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—122no—
182C2×Dic3—122no—
183Dic6—64no—
184Dic6—64no—
185Dic6—64no—
186Dic6—64no—
187C2×C32#38011yescharacteristic
188C2×C32#41611yescharacteristic
189C2×C32#41911yescharacteristic
190C2×C32#46412yes—
191C2×C32#47912yes—
192C2×Q8—92no—
193C2×Q8—92no—
194C2×Q8—92no—
195C2×Q8—181no—
196C2×Q8—181no—
197C2×Q8—181no—
198C22×C4—61no—
199C22×C4—61no—
200C22×C4—62no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4GO+(4,𝔽2)11yescharacteristic
204C2×C8—182no—
205C2×C8—182no—
206C2×C8—182no—
207C4⋊C4—92no—
208C4⋊C4—181no—
209C4⋊C4—184no—
210C4⋊C4—182no—
211C4⋊C4—182no—
212C42—64no—
213C42—92no—
214C42—92no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—22no—
224C22×C3—22no—
225C3×C4—24no—
226C3×C4—42no—
227C3×C4—64no—
228C3×C4—122no—
229C3×C4—242no—
230Dic3—24no—
231Dic3—42no—
232Dic3—61no—
233Dic3—61no—
234Dic3—61no—
235Dic3—61no—
236Dic3—61no—
237Dic3—61no—
238Dic3—61no—
239Dic3—61no—
240Dic3—82no—
241Dic3—122no—
242Dic3—122no—
243C32#180511yescharacteristic, complemented, Sylow
244C23C2×GO+(4,𝔽2)11yescharacteristic
245Q8—94no—
246Q8—182no—
247Q8—182no—
248Q8—182no—
249C2×C4—22no—
250C2×C4—62no—
251C2×C4—62no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—92no—
261C2×C4—122no—
262C2×C4—122no—
263C2×C4—122no—
264C2×C4—122no—
265C2×C4—182no—
266C2×C4D32⋊C412yes—
267C8—362no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C22D32⋊Q811yescharacteristic
279C22#6422312yes—
280C22#6423011yescharacteristic
281C22C2×D32⋊C411yescharacteristic
282C22#6423912yes—
283C4—22no—
284C4—64no—
285C4—91no—
286C4—91no—
287C4—91no—
288C4—91no—
289C4—122no—
290C4—182no—
291C4—242no—
292C3—21no—
293C3—21no—
294C2#1059334911yescharacteristic
295C2#1059335212yes—
296C2#1059338212yes—
297C2#1059340311yescharacteristic
298C2#1059350311yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1805
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
14. C4×#627C4semidirect
243. C32#1805semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#637792
C2×#637402
#105913602
#105900752
#18059