Finite Group Databasebeta

← #11785126

Subgroups — #11785126

Order 1152.

885 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 885 conjugacy classes of subgroups — too many to draw. Only its 158 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#833C212yesmaximal
3#10591120C212yesmaximal, complemented
4#10589168C212yesmaximal, complemented
5#70063—32nomaximal
6C22×C32×D4C2211yescharacteristic
7C23×C3⋊Dic3C412yes—
8C2×#3757C412yes—
9D4×C3⋊Dic3—22no—
10D4×C3⋊Dic3—22no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×#208C2214yes—
14C3×#833—24no—
15#63572—22no—
16#63572—22no—
17C2×D4×Dic3—32no—
18C2×D4×Dic3—61no—
19C2×C3×#100—32no—
20C2×#833D312yes—
21#5118—34no—
22#4554—34no—
23C24×C32C2×C412yes—
24C2×C32×D4—22no—
25C2×C32×D4—22no—
26C2×C32×D4D412yes—
27C2×C32×D4Q812yes—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—22no—
30C22×C3⋊Dic3—22no—
31C22×C3⋊Dic3—44no—
32C22×C3⋊Dic3C2×C411yescharacteristic
33C22×C3⋊Dic3C2×C412yes—
34C22×C3⋊Dic3C2×C411yescharacteristic
35#3757—24no—
36C4⋊(C3⋊Dic3)—22no—
37C4×C3⋊Dic3D412yes—
38C4×C3⋊Dic3D412yes—
39C3×#208—24no—
40C3×#208—24no—
41C2×C3×C3⋊C8—24no—
42#1800—91noSylow
43C22×C3×D4—21no—
44C22×C3×D4C2×D312yes—
45C23×Dic3—34no—
46C23×Dic3—62no—
47C2×C3×M16—34no—
48C2×#217—34no—
49C2×#217—62no—
50D4×Dic3—64no—
51D4×Dic3—64no—
52D4×Dic3—64no—
53D4×Dic3—64no—
54C2×C4⋊Dic3—32no—
55C2×C4⋊Dic3—61no—
56C2×C4×Dic3—32no—
57C2×C4×Dic3—61no—
58C2×#208C2×D314yes—
59C3×#100—64no—
60#833—24no—
61Dic3⋊C8—64no—
62Dic3⋊C8—64no—
63C23×C32—22no—
64C23×C32—22no—
65C23×C32—42no—
66C23×C32—42no—
67C23×C32C4⋊C414yes—
68C23×C32C22×C411yescharacteristic
69C32×D4—24no—
70C32×D4—24no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×Q811yescharacteristic
74C2×C32×C4#4112yes—
75C2×C3⋊Dic3—22no—
76C2×C3⋊Dic3—22no—
77C2×C3⋊Dic3—41no—
78C2×C3⋊Dic3—44no—
79C2×C3⋊Dic3—44no—
80C2×C3⋊Dic3—42no—
81C2×C3⋊Dic3C22⋊C412yes—
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C3×C3⋊C8—44no—
85C2×C4×D4—91no—
86#423—92no—
87C2×#100—32no—
88#343—92no—
89C24×C3—22no—
90C24×C3C4×D314yes—
91C2×C3×D4—24no—
92C2×C3×D4—24no—
93C2×C3×D4—24no—
94C2×C3×D4—24no—
95C2×C3×D4—22no—
96C2×C3×D4—22no—
97C2×C3×D4Dic614yes—
98C2×C3×D4#6714yes—
99C22×C3×C4—21no—
100C22×C3×C4C22×D312yes—
101C22×Dic3—32no—
102C22×Dic3—32no—
103C22×Dic3—34no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—62no—
107C22×Dic3—64no—
108C22×Dic3—64no—
109C22×Dic3—64no—
110C22×Dic3—64no—
111C22×Dic3—128no—
112C22×Dic3—128no—
113C3×M16—64no—
114C3×M16—64no—
115C2×C3×C8—64no—
116#217—68no—
117#217—68no—
118C4⋊Dic3—64no—
119C4⋊Dic3—64no—
120C4×Dic3—34no—
121C4×Dic3—34no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124#208—24no—
125#208—24no—
126C2×C3⋊C8—24no—
127C22×C32—21no—
128C22×C32—21no—
129C22×C32—24no—
130C22×C32—44no—
131C22×C32—44no—
132C22×C32—42no—
133C22×C32—42no—
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32C2×C4⋊C411yescharacteristic
136C22×C32#11711yescharacteristic
137C32×C4#12112yes—
138C32×C4C22⋊Q812yes—
139C3⋊Dic3—21no—
140C3⋊Dic3—22no—
141C3⋊Dic3—42no—
142C3⋊Dic3#10012yescomplemented
143C22×D4D3211yescharacteristic
144C23×C4—92no—
145C2×M16—34no—
146C4×D4—182no—
147C4×D4—182no—
148C2×C4⋊C4—91no—
149C2×C22⋊C4—92no—
150C2×C42—91no—
151C4⋊C8—182no—
152C4⋊C8—182no—
153#100—64no—
154C23×C3—24no—
155C23×C3—24no—
156C23×C3—24no—
157C23×C3—24no—
158C23×C3—24no—
159C23×C3—21no—
160C23×C3—44no—
161C23×C3—44no—
162C23×C3—44no—
163C23×C3—44no—
164C23×C3Dic3⋊C418yes—
165C23×C3C2×C4×D312yes—
166C3×D4—28no—
167C3×D4—28no—
168C3×D4—28no—
169C3×D4—28no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—22no—
174C2×C3×C4C2×Dic612yes—
175C2×C3×C4D3×D414yes—
176C2×C3×C4#23714yes—
177C2×C3×C4C2×#6712yes—
178C2×Dic3—32no—
179C2×Dic3—34no—
180C2×Dic3—32no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—62no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186C2×Dic3—64no—
187C2×Dic3—64no—
188C2×Dic3—128no—
189C2×Dic3—122no—
190C2×Dic3—128no—
191C2×Dic3—128no—
192C2×Dic3—128no—
193C2×Dic3—122no—
194C2×Dic3—124no—
195C2×Dic3—124no—
196C3×C8—124no—
197C3⋊C8—44no—
198C2×C32—21no—
199C2×C32—21no—
200C2×C32—44no—
201C2×C32#38011yescharacteristic
202C2×C32C2×#10011yescharacteristic
203C2×C32#41311yescharacteristic
204C24#62412yes—
205C2×D4—22no—
206C2×D4—22no—
207C2×D4#62512yes—
208C2×D4#62712yes—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—92no—
212C22×C4—182no—
213C22×C4—182no—
214C22×C4—364no—
215C22×C4C2×D3211yescharacteristic
216M16—64no—
217M16—64no—
218C2×C8—64no—
219C4⋊C4—182no—
220C22⋊C4—184no—
221C42—92no—
222C42—92no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—28no—
228C22×C3—28no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—48no—
233C22×C3—44no—
234C22×C3—48no—
235C22×C3—48no—
236C22×C3—48no—
237C22×C3—44no—
238C22×C3—44no—
239C22×C3—44no—
240C22×C3#87712yes—
241C22×C3D3×C22⋊C412yes—
242C22×C3C2×Dic3⋊C412yes—
243C3×C4—22no—
244C3×C4—22no—
245C3×C4#87814yes—
246C3×C4#93914yes—
247Dic3—34no—
248Dic3—62no—
249Dic3—62no—
250Dic3—62no—
251Dic3—64no—
252Dic3—122no—
253Dic3—124no—
254Dic3—124no—
255C32#180011yescharacteristic, complemented, Sylow
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23#372414yes—
261C23C2×#62411yescharacteristic
262D4—24no—
263D4—24no—
264C2×C4—91no—
265C2×C4—92no—
266C2×C4—91no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—364no—
270C2×C4—361no—
271C2×C4—364no—
272C2×C4—362no—
273C2×C4#380512yes—
274C2×C4C2×#62511yescharacteristic
275C2×C4C2×#62711yescharacteristic
276C2×C4#381112yes—
277C8—124no—
278C2×C3—22no—
279C2×C3—22no—
280C2×C3—22no—
281C2×C3—22no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—48no—
286C2×C3—48no—
287C2×C3D3×#10012yes—
288C2×C3#474512yes—
289C2×C3#494212yes—
290C22—21no—
291C22—21no—
292C22—24no—
293C22—44no—
294C22—44no—
295C22—42no—
296C22—42no—
297C22#6395711yescharacteristic
298C22C2×#372411yescharacteristic
299C22#6397411yescharacteristic
300C4—92no—
301C4—181no—
302C4—182no—
303C4—362no—
304C4#6398012yes—
305C4#6398212yes—
306C3—21no—
307C3#7006312yescomplemented
308C2—21no—
309C2—21no—
310C2—44no—
311C2#1059150311yescharacteristic
312C2#1059150411yescharacteristic
313C2#1059172011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1800
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591120C2semidirect
4. #10589168C2semidirect
142. C3⋊Dic3#100semidirect
255. C32#1800semidirect
307. C3#70063semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#8332
#105911202
#105891682
#700633