Finite Group Databasebeta

← #11778797

Subgroups — #11778797

Order 1152.

460 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 45 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
1#10595044C211yesmaximal, characteristic
2#10593497C212yesmaximal, complemented
3#10591218C211yesmaximal, characteristic, complemented
4#10590202C211yesmaximal, characteristic, complemented
5#10590071C212yesmaximal, complemented
6C2×C3×#235—21no—
7C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
8#63980—21no—
9#63980C2212yes—
10C2×#3724C2211yescharacteristic
11#63908—22no—
12#63856—22no—
13C22⋊#622C2212yes—
14#63742—22no—
15#63739—22no—
16C3×C3⋊#95—21no—
17#63579—21no—
18#63579C2211yescharacteristic
19#5833—61no—
20#4660—61no—
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3D411yescharacteristic
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C3×#67—22no—
25C22×C3×Dic3—21no—
26C22×C3×Dic3—21no—
27C3×#235—42no—
28C3×#235—42no—
29C2×C3×D12—21no—
30C2×C3×C4×D3—22no—
31C2×C3×Dic6—21no—
32C2×#625—21no—
33C2×#625D412yes—
34C2×#622—22no—
35C4⋊(C3⋊Dic3)—22no—
36#3724—21no—
37#3724—22no—
38#3724D412yes—
39(C2×D3)⋊Dic3—22no—
40(C2×D3)⋊Dic3—22no—
41#1616—91nomaximal, Sylow
42C2×C3×#41—61no—
43C2×#235—21no—
44#946—62no—
45#939—62no—
46#939—62no—
47#938—62no—
48#930—62no—
49C2×C4⋊Dic3—61no—
50C2×C4⋊Dic3—61no—
51#924—62no—
52C2×Dic3⋊C4—61no—
53C3×#95—61no—
54C3⋊#95—21no—
55C3⋊#95—61no—
56C3⋊#95—61no—
57C3⋊#95—61no—
58C23×C32C2×D411yescharacteristic
59C22×C3×D3—22no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4SD1612yes—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3C2×D412yes—
67C3×#67—42no—
68C3×#67—42no—
69C2×C3×Dic3—22no—
70C2×C3×Dic3—41no—
71C2×C3×Dic3—41no—
72C2×C3×Dic3—41no—
73C2×C3×Dic3—41no—
74C2×C3×Dic3—41no—
75C2×C3×Dic3—41no—
76C3×D12—42no—
77C3×C4×D3—44no—
78C3×Dic6—42no—
79#625—42no—
80#625—81no—
81#622—42no—
82#537—91no—
83#481—92no—
84#400—91no—
85#327—92no—
86#324—91no—
87C3×#41—122no—
88C3×#41—122no—
89C2×C3×Q8—61no—
90C2×C3×D4—61no—
91C2×C3×D4—62no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—62no—
95C22×C3×C4—61no—
96C22×C3×C4—61no—
97C2×#67—22no—
98C2×#67—62no—
99C2×#67—62no—
100C22×Dic3—21no—
101C22×Dic3—21no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106#235—42no—
107#235—42no—
108C2×D12—21no—
109C2×C4×D3—22no—
110C2×Dic6—21no—
111#217—62no—
112#217—62no—
113(C2×D3)⋊C4—62no—
114(C2×D3)⋊C4—62no—
115C4⋊Dic3—62no—
116C4⋊Dic3—62no—
117C4⋊Dic3—122no—
118Dic3⋊C4—62no—
119Dic3⋊C4—62no—
120Dic3⋊C4—122no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32#12011yescharacteristic
124C22×C32C2×SD1611yescharacteristic
125C22×C32AGL(1,ℤ/8)11yescharacteristic
126C2×C3×D3—42no—
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129C32×C4—22no—
130C3⋊Dic3—22no—
131C3⋊Dic3—41no—
132C3×Dic3—42no—
133C3×Dic3—81no—
134C3×Dic3—81no—
135C2×#41—61no—
136C22⋊Q8—182no—
137#121—92no—
138#121—182no—
139#121—181no—
140C2×C4⋊C4—91no—
141C2×C4⋊C4—91no—
142#106—182no—
143#102—182no—
144C22⋊C8—92no—
145#95—61no—
146#95—91no—
147#95—181no—
148C23×C3—21no—
149C23×C3—21no—
150C23×C3—62no—
151C22×D3—22no—
152C3×Q8—122no—
153C3×D4—122no—
154C3×D4—122no—
155C3×D4—122no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—41no—
162C2×C3×C4—41no—
163C2×C3×C4—62no—
164C2×C3×C4—124no—
165C2×C3×C4—121no—
166C2×C3×C4—121no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×C3×C4—121no—
170C2×C3×C4—121no—
171#67—42no—
172#67—42no—
173#67—242no—
174#67—242no—
175C2×Dic3—22no—
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—41no—
179C2×Dic3—41no—
180C2×Dic3—41no—
181C2×Dic3—41no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—121no—
186C2×Dic3—121no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—241no—
191C2×Dic3—241no—
192D12—42no—
193C4×D3—44no—
194Dic6—42no—
195C2×C32—21no—
196C2×C32—21no—
197C2×C32#45011yescharacteristic
198C2×C32#45411yescharacteristic
199C2×C32#45811yescharacteristic
200C3×D3—82no—
201#41—122no—
202#41—122no—
203C2×Q8—61no—
204C2×D4—61no—
205C2×D4—62no—
206C2×D4—92no—
207C2×D4—181no—
208C22×C4—62no—
209C22×C4—61no—
210C22×C4—61no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4GO+(4,𝔽2)11yescharacteristic
214C2×C8—182no—
215C4⋊C4—92no—
216C4⋊C4—182no—
217C4⋊C4—181no—
218C4⋊C4—182no—
219C22⋊C4—182no—
220C22⋊C4—182no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—41no—
232C22×C3—41no—
233C22×C3—122no—
234C22×C3—122no—
235C22×C3—122no—
236C2×D3—42no—
237C2×D3—42no—
238C2×D3—42no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—42no—
242C3×C4—122no—
243C3×C4—241no—
244C3×C4—241no—
245Dic3—42no—
246Dic3—81no—
247Dic3—81no—
248Dic3—122no—
249Dic3—122no—
250Dic3—122no—
251Dic3—241no—
252C32#161611yescharacteristic, complemented, Sylow
253C23—62no—
254C23C2×GO+(4,𝔽2)11yescharacteristic
255Q8—122no—
256D4—122no—
257D4—122no—
258D4—122no—
259D4—362no—
260D4—721no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—62no—
264C2×C4—92no—
265C2×C4—124no—
266C2×C4—121no—
267C2×C4—121no—
268C2×C4—121no—
269C2×C4—121no—
270C2×C4—121no—
271C2×C4—121no—
272C2×C4—181no—
273C2×C4—361no—
274C2×C4—361no—
275C2×C4#377512yes—
276C8—362no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—41no—
288C2×C3—41no—
289C2×C3—242no—
290D3—82no—
291C22—21no—
292C22—21no—
293C22—122no—
294C22—122no—
295C22—122no—
296C22#6423611yescharacteristic
297C22C2×#377511yescharacteristic
298C22#6424111yescharacteristic
299C4—22no—
300C4—122no—
301C4—182no—
302C4—241no—
303C4—241no—
304C4—361no—
305C3—21no—
306C3—21no—
307C2—21no—
308C2—21no—
309C2—242no—
310C2#1059341511yescharacteristic
311C2#1059345111yescharacteristic
312C2#1059352311yescharacteristic
subgroupG/H
centerC22#64241
commutator, cosocleC22×C3⋊Dic3C23
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#120
prime radical#10595044C2
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1616
LCSG ▷ C22×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593497C2semidirect
3. #10591218C2semidirect
4. #10590202C2semidirect
5. #10590071C2semidirect
252. C32#1616semidirect

Maximal subgroups

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

subgroupindex
#105950442
#105934972
#105912182
#105902022
#105900712
#16169