Finite Group Databasebeta

← #11775066

Subgroups — #11775066

Order 1152.

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

normal subgroups only

This group has 536 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
3C4×#3724C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C2×C3×#235—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C2×C3×C4×Dic3—21no—
8#63980—21no—
9#63980C2212yes—
10C2×#3724—21no—
11#63914C411yescharacteristic, complemented
12C4×#625—21no—
13C4×#625C412yescomplemented
14#63873C411yescharacteristic, complemented
15#63863—21no—
16C22⋊#622C2212yes—
17C4⋊#622—21no—
18C4×#622—21no—
19#63579C2212yes—
20#5832—61no—
21C4×Dic3⋊C4—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C3×#67—22no—
26C22×C3×Dic3—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⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C3×C4×Dic3—42no—
40#3724—24no—
41#3724—21no—
42#3724C2×C412yes—
43(C2×D3)⋊Dic3—22no—
44(C2×D3)⋊Dic3—22no—
45#1502—91nomaximal, Sylow
46C2×C3×#41—61no—
47C2×#235—21no—
48C2×C3×C42—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×Dic3⋊C4—62no—
58C2×C4×Dic3—21no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61C3⋊#95—62no—
62C23×C32C2×D411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4D812yes—
67C2×C32×C4SD1612yes—
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—42no—
75C3×#67—42no—
76C2×C3×Dic3—24no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C3×D12—42no—
81C3×C4×D3—44no—
82C3×Dic6—42no—
83#625—42no—
84#625—42no—
85#622—42no—
86#532—91no—
87#431—91no—
88C4×C4⋊C4—91no—
89#327—94no—
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—
98C22×C3×C4—62no—
99C2×#67—22no—
100C2×#67—62no—
101C2×#67—62no—
102C22×Dic3—22no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—61no—
107#235—42no—
108#235—42no—
109C2×D12—21no—
110C2×C4×D3—22no—
111C2×Dic6—21no—
112C3×C42—122no—
113#217—62no—
114#217—62no—
115(C2×D3)⋊C4—62no—
116(C2×D3)⋊C4—62no—
117Dic3⋊C4—62no—
118Dic3⋊C4—68no—
119Dic3⋊C4—62no—
120C4×Dic3—42no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×C22⋊C411yescharacteristic
132C22×C32C2×D811yescharacteristic
133C22×C32C2×SD1611yescharacteristic
134C2×C3×D3—42no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137C32×C4#10212yes—
138C32×C4#10212yes—
139C3⋊Dic3—21no—
140C3⋊Dic3—21no—
141C3⋊Dic3—21no—
142C3⋊Dic3#10412yes—
143C3×Dic3—44no—
144C3×Dic3—42no—
145C2×#41—61no—
146C4⋊Q8—91no—
147#127—91no—
148#124—181no—
149#121—92no—
150#121—181no—
151C4×D4—92no—
152C4×D4—181no—
153C2×C4⋊C4—181no—
154C2×C42—61no—
155C2×C42—91no—
156C4⋊C8—181no—
157C22⋊C8—92no—
158C4×C8—181no—
159#95—92no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—62no—
163C22×D3—22no—
164C3×Q8—122no—
165C3×D4—122no—
166C3×D4—122no—
167C3×D4—122no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—62no—
177C2×C3×C4—64no—
178C2×C3×C4—124no—
179C2×C3×C4—122no—
180C2×C3×C4—122no—
181#67—42no—
182#67—42no—
183#67—124no—
184#67—124no—
185C2×Dic3—22no—
186C2×Dic3—24no—
187C2×Dic3—42no—
188C2×Dic3—42no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C2×Dic3—64no—
198C2×Dic3—122no—
199C2×Dic3—122no—
200C2×Dic3—122no—
201D12—42no—
202C4×D3—44no—
203Dic6—42no—
204C2×C32—21no—
205C2×C32—21no—
206C2×C32#41011yescharacteristic
207C2×C32C2×#10211yescharacteristic
208C2×C32C2×#10411yescharacteristic
209C3×D3—82no—
210#41—122no—
211#41—122no—
212C2×Q8—61no—
213C2×D4—62no—
214C2×D4—61no—
215C2×D4—92no—
216C2×D4—181no—
217C22×C4—62no—
218C22×C4—62no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4GO+(4,𝔽2)11yescharacteristic
222C2×C8—182no—
223C4⋊C4—92no—
224C4⋊C4—181no—
225C4⋊C4—184no—
226C22⋊C4—182no—
227C22⋊C4—182no—
228C42—91no—
229C42—91no—
230C42—91no—
231C42—91no—
232C42—122no—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—41no—
242C22×C3—41no—
243C22×C3—122no—
244C22×C3—122no—
245C22×C3—122no—
246C2×D3—42no—
247C2×D3—42no—
248C2×D3—42no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—22no—
253C3×C4—122no—
254C3×C4—124no—
255Dic3—42no—
256Dic3—44no—
257Dic3—62no—
258Dic3—62no—
259Dic3—62no—
260Dic3—62no—
261Dic3—121no—
262Dic3—121no—
263Dic3—121no—
264Dic3—121no—
265C32#150211yescharacteristic, complemented, Sylow
266C23—62no—
267C23C2×GO+(4,𝔽2)11yescharacteristic
268Q8—122no—
269D4—122no—
270D4—122no—
271D4—122no—
272D4—362no—
273D4—362no—
274C2×C4—64no—
275C2×C4—62no—
276C2×C4—91no—
277C2×C4—91no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—122no—
281C2×C4—122no—
282C2×C4—124no—
283C2×C4—182no—
284C2×C4—361no—
285C2×C4D32⋊C411yescharacteristic
286C2×C4D32⋊C411yescharacteristic
287C2×C4#377412yes—
288C2×C4#377512yes—
289C8—362no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—41no—
299C2×C3—41no—
300C2×C3—242no—
301D3—82no—
302C22—21no—
303C22—21no—
304C22—122no—
305C22—122no—
306C22—122no—
307C22C2×D32⋊C411yescharacteristic
308C22C2×#377411yescharacteristic
309C22C2×#377511yescharacteristic
310C4—92no—
311C4—124no—
312C4—122no—
313C4—181no—
314C4—181no—
315C4—181no—
316C4#6373912yes—
317C4#6373912yes—
318C3—21no—
319C3—21no—
320C2—21no—
321C2—21no—
322C2—242no—
323C2#1059334511yescharacteristic
324C2#1059338011yescharacteristic
325C2C2×#6373911yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1502
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. C4×#3724C2semidirect
4. #10590071C2semidirect
11. #63914C4semidirect
13. C4×#625C4semidirect
14. #63873C4semidirect
265. C32#1502semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105937952
C4×#37242
#105900712
#15029