Finite Group Databasebeta

← #11776149

Subgroups — #11776149

Order 1152.

480 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 73 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#10595032C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic, complemented
3C2×#63572C211yesmaximal, characteristic, complemented
4#10590038C212yesmaximal, complemented
5#10590037C212yesmaximal, complemented
6C2×C3×#235—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C22×C3×C3⋊C8—21no—
9#63980—21no—
10#63980C412yes—
11#63914C2211yescharacteristic
12C4×#625—21no—
13C4×#625C412yes—
14#63873C2211yescharacteristic
15#63863—21no—
16C22⋊#622—21no—
17C4⋊#622C2212yes—
18C4×#622—21no—
19#63572—21no—
20#63572C2212yes—
21#5832—61no—
22C2×Dic3⋊C8—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C3×#67—22no—
27C3×#235—42no—
28C3×#235—42no—
29C2×C3×D12—21no—
30C2×C3×C4×D3—22no—
31C2×C3×Dic6—21no—
32C2×#625—21no—
33C2×#625C2×C412yes—
34C2×#622—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8—42no—
41#3724—21no—
42#3724C2×C412yes—
43(C2×D3)⋊Dic3—22no—
44(C2×D3)⋊Dic3—22no—
45#1540—91nomaximal, Sylow
46C2×C3×#41—61no—
47C2×#235—21no—
48C22×C3×C8—61no—
49#947—61no—
50#944—61no—
51#940—61no—
52#939—62no—
53#939—62no—
54#936—61no—
55C4×#67—62no—
56C4×#67—62no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—61no—
59C22×C3⋊C8—21no—
60Dic3⋊C8—62no—
61Dic3⋊C8—62no—
62C23×C32C22⋊C411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4D812yes—
66C2×C32×C4SD1612yes—
67C2×C32×C4C2×D411yescharacteristic
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C3×#67—44no—
75C2×C3×Dic3—22no—
76C3×D12—41no—
77C3×D12—41no—
78C3×C4×D3—44no—
79C3×Dic6—41no—
80C3×Dic6—41no—
81#625—42no—
82#625—42no—
83#622—42no—
84C3×C3⋊C8—42no—
85#532—91no—
86#431—91no—
87C2×C4⋊C8—91no—
88#332—92no—
89#331—92no—
90C3×#41—122no—
91C3×#41—122no—
92C2×C3×Q8—61no—
93C2×C3×D4—61no—
94C2×C3×D4—62no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—62no—
98C2×#67—22no—
99C2×#67—62no—
100C2×#67—62no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105#235—42no—
106#235—42no—
107C2×D12—21no—
108C2×C4×D3—22no—
109C2×Dic6—21no—
110C2×C3×C8—62no—
111C2×C3×C8—122no—
112#217—62no—
113#217—62no—
114(C2×D3)⋊C4—62no—
115(C2×D3)⋊C4—62no—
116Dic3⋊C4—62no—
117Dic3⋊C4—62no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C2×C3⋊C8—22no—
127C2×C3⋊C8—42no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32#10212yes—
131C22×C32C2×C22⋊C411yescharacteristic
132C2×C3×D3—42no—
133C2×C3×D3—42no—
134C2×C3×D3—42no—
135C32×C4#10212yes—
136C32×C4C2×D811yescharacteristic
137C32×C4C2×SD1611yescharacteristic
138C3⋊Dic3—21no—
139C3⋊Dic3—21no—
140C3⋊Dic3—21no—
141C3⋊Dic3#13512yes—
142C3×Dic3—42no—
143C2×#41—61no—
144C22×C8—61no—
145C4⋊Q8—91no—
146#127—91no—
147#124—181no—
148#121—92no—
149#121—181no—
150C4×D4—92no—
151C4×D4—181no—
152C2×C42—91no—
153C4⋊C8—92no—
154C4⋊C8—92no—
155C4⋊C8—181no—
156C22⋊C8—181no—
157C4×C8—181no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—62no—
161C22×D3—22no—
162C3×Q8—121no—
163C3×Q8—121no—
164C3×D4—121no—
165C3×D4—121no—
166C3×D4—124no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—62no—
176C2×C3×C4—124no—
177#67—44no—
178#67—124no—
179#67—124no—
180C2×Dic3—22no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—64no—
190C2×Dic3—122no—
191C2×Dic3—122no—
192C2×Dic3—122no—
193D12—41no—
194D12—41no—
195C4×D3—44no—
196Dic6—41no—
197Dic6—41no—
198C3×C8—122no—
199C3⋊C8—42no—
200C2×C32—22no—
201C2×C32#41311yescharacteristic
202C2×C32C2×#10211yescharacteristic
203C2×C32#41611yescharacteristic
204C3×D3—82no—
205#41—122no—
206#41—122no—
207C2×Q8—61no—
208C2×D4—62no—
209C2×D4—61no—
210C2×D4—92no—
211C2×D4—181no—
212C22×C4—62no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4GO+(4,𝔽2)11yescharacteristic
216C2×C8—62no—
217C2×C8—122no—
218C2×C8—182no—
219C4⋊C4—92no—
220C4⋊C4—181no—
221C22⋊C4—182no—
222C22⋊C4—182no—
223C42—91no—
224C42—91no—
225C42—91no—
226C42—91no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—22no—
232C22×C3—22no—
233C22×C3—41no—
234C22×C3—41no—
235C22×C3—122no—
236C22×C3—122no—
237C22×C3—122no—
238C2×D3—42no—
239C2×D3—42no—
240C2×D3—42no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—122no—
248Dic3—42no—
249Dic3—62no—
250Dic3—62no—
251Dic3—62no—
252Dic3—62no—
253Dic3—121no—
254Dic3—121no—
255Dic3—121no—
256Dic3—121no—
257C32#154011yescharacteristic, complemented, Sylow
258C23—62no—
259C23D32⋊C411yescharacteristic
260Q8—121no—
261Q8—121no—
262D4—124no—
263D4—121no—
264D4—121no—
265D4—362no—
266D4—362no—
267C2×C4—62no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—124no—
273C2×C4—182no—
274C2×C4—361no—
275C2×C4D32⋊C411yescharacteristic
276C2×C4#377412yes—
277C2×C4#377512yes—
278C2×C4C2×GO+(4,𝔽2)11yescharacteristic
279C8—122no—
280C8—362no—
281C2×C3—24no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—42no—
289C2×C3—242no—
290D3—82no—
291C22—21no—
292C22—21no—
293C22—122no—
294C22—122no—
295C22—122no—
296C22#6373912yes—
297C22C2×D32⋊C411yescharacteristic
298C4—92no—
299C4—122no—
300C4—181no—
301C4—181no—
302C4—181no—
303C4#6373912yes—
304C4C2×#377411yescharacteristic
305C4C2×#377511yescharacteristic
306C3—21no—
307C3—21no—
308C2—22no—
309C2—242no—
310C2#1059331111yescharacteristic
311C2#1059331711yescharacteristic
312C2C2×#6373911yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1540
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593795C2semidirect
3. C2×#63572C2semidirect
4. #10590038C2semidirect
5. #10590037C2semidirect
257. C32#1540semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105937952
C2×#635722
#105900382
#105900372
#15409