Finite Group Databasebeta

← #11790353

Subgroups — #11790353

Order 1152.

446 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 99 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⋊#622C211yesmaximal, characteristic
2C2×#63742C212yesmaximal
3#10591359C211yesmaximal, characteristic
4C4×#3724C211yesmaximal, characteristic
5#10590075C212yesmaximal
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×C3×C4×Dic3—21no—
10C2×#3724—21no—
11C2×#3724C2212yes—
12C2×#3724C2211yescharacteristic
13C2×#3724C2211yescharacteristic
14C4⋊#622C414yescomplemented
15#63742—24no—
16#63579—21no—
17#4975—61no—
18C4×Dic3⋊C4—61no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C22×C3×Dic3—21no—
23C22×C3×Dic3—21no—
24C22×C3×Dic3—22no—
25C2×#622—22no—
26C2×#622—22no—
27C2×#622C2×C414yes—
28C4×C3⋊Dic3C2×C412yes—
29C4×C3⋊Dic3Q812yes—
30C3×C4⋊Dic3—42no—
31C3×C4×Dic3—42no—
32#3724—21no—
33#3724—21no—
34#3724—22no—
35#3724—22no—
36#3724—42no—
37#3724D412yes—
38#3724Q812yes—
39#1948—91nomaximal, Sylow
40C2×C3×C4⋊C4—61no—
41C2×C3×C42—61no—
42C2×C4⋊Dic3—21no—
43C2×Dic3⋊C4—61no—
44C2×Dic3⋊C4—61no—
45C2×Dic3⋊C4—62no—
46C2×Dic3⋊C4—62no—
47C2×C4×Dic3—21no—
48C2×C4×Dic3—61no—
49C2×C4×Dic3—61no—
50C3⋊#95—61no—
51C3⋊#95—61no—
52C23×C32C2×D411yescharacteristic
53C2×C32×C4C4⋊C412yes—
54C2×C32×C4SD1612yes—
55C2×C32×C4SD1612yes—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3C4⋊C412yes—
59C2×C3⋊Dic3C22×C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×Q811yescharacteristic
62C2×C3⋊Dic3C2×Q811yescharacteristic
63C2×C3⋊Dic3#4111yescharacteristic
64C2×C3⋊Dic3#4111yescharacteristic
65C2×C3×Dic3—22no—
66C2×C3×Dic3—22no—
67C2×C3×Dic3—41no—
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C2×C3×Dic3—41no—
71C2×C3×Dic3—42no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74#622—24no—
75C2×#106—92no—
76C2×C4⋊C8—91no—
77#384—91no—
78C4×C4⋊C4—91no—
79#340—92no—
80C22×C3×C4—21no—
81C22×C3×C4—21no—
82C22×C3×C4—61no—
83C22×C3×C4—61no—
84C22×C3×C4—62no—
85C22×Dic3—21no—
86C22×Dic3—21no—
87C22×Dic3—22no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C3×C4⋊C4—122no—
93C3×C42—122no—
94C4⋊Dic3—42no—
95Dic3⋊C4—62no—
96Dic3⋊C4—62no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99Dic3⋊C4—122no—
100Dic3⋊C4—122no—
101Dic3⋊C4—124no—
102C4×Dic3—42no—
103C4×Dic3—62no—
104C4×Dic3—62no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C22×C32C2×C4⋊C411yescharacteristic
108C22×C32#12111yescharacteristic
109C22×C32C22⋊Q811yescharacteristic
110C22×C32C2×SD1611yescharacteristic
111C22×C32C2×SD1611yescharacteristic
112C22×C32AGL(1,ℤ/8)11yescharacteristic
113C22×C32#13711yescharacteristic
114C32×C4#10614yescomplemented
115C3⋊Dic3—22no—
116C3⋊Dic3C4×D411yescharacteristic
117C3⋊Dic3C4×Q811yescharacteristic
118C3⋊Dic3#12511yescharacteristic
119C3⋊Dic3C4⋊Q811yescharacteristic
120C3×Dic3—42no—
121C3×Dic3—42no—
122C3×Dic3—82no—
123C22×C8—92no—
124C2×C4⋊C4—61no—
125C2×C4⋊C4—91no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4—92no—
128C2×C4⋊C4—181no—
129C2×C42—61no—
130C2×C42—91no—
131#106—184no—
132C4⋊C8—94no—
133#95—181no—
134C23×C3—21no—
135C23×C3—21no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—22no—
142C2×C3×C4—62no—
143C2×C3×C4—62no—
144C2×C3×C4—121no—
145C2×C3×C4—121no—
146C2×C3×C4—121no—
147C2×C3×C4—121no—
148C2×C3×C4—122no—
149C2×C3×C4—122no—
150C2×C3×C4—122no—
151C2×Dic3—22no—
152C2×Dic3—22no—
153C2×Dic3—41no—
154C2×Dic3—41no—
155C2×Dic3—41no—
156C2×Dic3—41no—
157C2×Dic3—42no—
158C2×Dic3—42no—
159C2×Dic3—42no—
160C2×Dic3—62no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—121no—
177C2×Dic3—121no—
178C2×C32#38911yescharacteristic
179C2×C32C2×#10611yescharacteristic
180C2×C32#42811yescharacteristic
181C2×C32#46011yescharacteristic
182C2×C32#46111yescharacteristic
183C2×C32#47511yescharacteristic
184C2×C32#47611yescharacteristic
185C22×C4—61no—
186C22×C4—61no—
187C22×C4—62no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4GO+(4,𝔽2)11yescharacteristic
191C2×C8—94no—
192C2×C8—182no—
193C2×C8—182no—
194C4⋊C4—92no—
195C4⋊C4—92no—
196C4⋊C4—122no—
197C4⋊C4—181no—
198C4⋊C4—181no—
199C4⋊C4—182no—
200C4⋊C4—182no—
201C4⋊C4—362no—
202C42—92no—
203C42—92no—
204C42—122no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—122no—
222C3×C4—122no—
223C3×C4—242no—
224Dic3—42no—
225Dic3—42no—
226Dic3—61no—
227Dic3—61no—
228Dic3—61no—
229Dic3—61no—
230Dic3—61no—
231Dic3—61no—
232Dic3—61no—
233Dic3—61no—
234Dic3—64no—
235Dic3—82no—
236Dic3—122no—
237C32#194811yescharacteristic, complemented, Sylow
238C23C2×GO+(4,𝔽2)11yescharacteristic
239C2×C4—62no—
240C2×C4—62no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—91no—
247C2×C4—92no—
248C2×C4—121no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—122no—
253C2×C4—122no—
254C2×C4—122no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4#377312yes—
258C2×C4#377512yes—
259C2×C4#377512yes—
260C8—184no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C22D32⋊Q811yescharacteristic
276C22#6422411yescharacteristic
277C22#6422611yescharacteristic
278C22#6423011yescharacteristic
279C22C2×#377311yescharacteristic
280C22C2×#377511yescharacteristic
281C22C2×#377511yescharacteristic
282C4—91no—
283C4—91no—
284C4—91no—
285C4—91no—
286C4—122no—
287C4—122no—
288C4—182no—
289C4—242no—
290C4#6374214yescomplemented
291C3—21no—
292C3—21no—
293C2#1059335911yescharacteristic
294C2#1059337611yescharacteristic
295C2#1059339411yescharacteristic
296C2#1059341211yescharacteristic
297C2#1059343711yescharacteristic
298C2#1059343911yescharacteristic
299C2C2×#6374211yescharacteristic
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#1948
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⋊#622C4semidirect
114. C32×C4#106semidirect
237. C32#1948semidirect
290. C4#63742semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#6222
C2×#637422
#105913592
C4×#37242
#105900752
#19489