Finite Group Databasebeta

← #11790794

Subgroups — #11790794

Order 1152.

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

normal subgroups only

This group has 644 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#10594929C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3C2×#63741C214yesmaximal, complemented
4C4×Dic32C211yesmaximal, characteristic, complemented
5C2×#3805C2212yes—
6C2×#3792C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#930—21no—
9C2×C3×C4×Dic3—21no—
10#63980—21no—
11C2×Dic32—21no—
12C2×Dic32C2212yes—
13#63919C411yescharacteristic, complemented
14#63915C412yescomplemented
15#63914C411yescharacteristic, complemented
16#63902—21no—
17#63898—21no—
18#63779—21no—
19C4⋊#622—21no—
20#63741—28no—
21#5596—61no—
22C42×Dic3—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C3×#67—22no—
27C22×C3×Dic3—22no—
28C2×C3×D12—21no—
29C2×#627C2×C412yes—
30C2×#625—21no—
31C2×#625C2×C412yes—
32#3805—24no—
33#3805—24no—
34C2×D3×Dic3—22no—
35#3792—24no—
36C2×#622—22no—
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43C3×C4×Dic3—24no—
44#3724—21no—
45(C2×D3)⋊Dic3—22no—
46Dic32—24no—
47Dic32—22no—
48Dic32D414yescomplemented
49#1962—91nomaximal, Sylow
50C2×#237—62no—
51C3×#121—61no—
52C2×C3×C42—61no—
53#940—61no—
54#939—62no—
55D4×Dic3—61no—
56#930—21no—
57C2×C4×Dic3—21no—
58C2×C4×Dic3—62no—
59C2×C4×Dic3—61no—
60C2×C4×Dic3—61no—
61C2×C4×Dic3—62no—
62#893—61no—
63#888—61no—
64#885—62no—
65#67⋊C4—62no—
66C23×C32C2×D411yescharacteristic
67C22×C3×D3—22no—
68C2×C32×C4—22no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C22×C411yescharacteristic
75C2×C3⋊Dic3C2×D412yes—
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3#4112yes—
78C3×#67—44no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—24no—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—22no—
83C3×D12—42no—
84#627—24no—
85#625—24no—
86#625—42no—
87D3×Dic3—42no—
88D3×Dic3—42no—
89#622—42no—
90#532—91no—
91#423—91no—
92C2×#104—94no—
93C43—91no—
94C2×C3×D4—61no—
95C2×C3×D4—62no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
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—
107C22×Dic3—62no—
108#237—124no—
109#237—124no—
110C2×D12—21no—
111C2×C4×D3—62no—
112C2×Dic6—62no—
113C3×C4⋊C4—61no—
114C3×C22⋊C4—62no—
115C3×C42—64no—
116#217—62no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—62no—
119C4⋊Dic3—21no—
120Dic3⋊C4—62no—
121C4×Dic3—24no—
122C4×Dic3—64no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C4×Dic3—61no—
131C4×Dic3—64no—
132C4×Dic3—68no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32C2×C22⋊C411yescharacteristic
136C22×C32#12112yes—
137C2×C3×D3—42no—
138C2×C3×D3—42no—
139C2×C3×D3—42no—
140C32×C4—21no—
141C32×C4#10412yescomplemented
142C3⋊Dic3—21no—
143C3⋊Dic3#10412yescomplemented
144C3⋊Dic3C4×D412yes—
145C3⋊Dic3#12411yescharacteristic
146C3⋊Dic3#12711yescharacteristic
147C3×Dic3—28no—
148C3×Dic3—42no—
149C2×#41—92no—
150C2×M16—92no—
151C4⋊Q8—91no—
152#127—91no—
153#124—92no—
154#121—61no—
155#121—181no—
156C4×D4—181no—
157C4×D4—181no—
158C2×C42—61no—
159C2×C42—91no—
160C2×C42—92no—
161C2×C42—181no—
162C4⋊C8—181no—
163C4⋊C8—181no—
164#104—188no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—62no—
168C22×D3—22no—
169C3×D4—122no—
170C3×D4—124no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—42no—
178C2×C3×C4—64no—
179C2×C3×C4—64no—
180C2×C3×C4—64no—
181C2×C3×C4—62no—
182#67—44no—
183#67—124no—
184#67—124no—
185C2×Dic3—24no—
186C2×Dic3—24no—
187C2×Dic3—24no—
188C2×Dic3—22no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—62no—
196C2×Dic3—61no—
197C2×Dic3—62no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—61no—
201C2×Dic3—64no—
202C2×Dic3—122no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205D12—42no—
206C4×D3—122no—
207C4×D3—122no—
208Dic6—124no—
209C2×C32—22no—
210C2×C32#39011yescharacteristic
211C2×C32C2×#10411yescharacteristic
212C2×C32C2×#10411yescharacteristic
213C3×D3—82no—
214#41—184no—
215#41—184no—
216C2×Q8—92no—
217C2×D4—62no—
218C2×D4—61no—
219C2×D4—92no—
220C2×D4—181no—
221C22×C4—62no—
222C22×C4—91no—
223C22×C4—91no—
224C22×C4—182no—
225C22×C4GO+(4,𝔽2)11yescharacteristic
226M16—184no—
227C2×C8—182no—
228C4⋊C4—61no—
229C4⋊C4—181no—
230C22⋊C4—62no—
231C22⋊C4—182no—
232C42—64no—
233C42—94no—
234C42—91no—
235C42—91no—
236C42—91no—
237C42—91no—
238C42—182no—
239C42—184no—
240C22×C3—21no—
241C22×C3—22no—
242C22×C3—21no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—41no—
248C22×C3—41no—
249C22×C3—122no—
250C22×C3—122no—
251C22×C3—122no—
252C2×D3—42no—
253C2×D3—42no—
254C2×D3—42no—
255C3×C4—22no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—41no—
259C3×C4—68no—
260C3×C4—122no—
261Dic3—28no—
262Dic3—42no—
263Dic3—62no—
264Dic3—61no—
265Dic3—61no—
266Dic3—62no—
267Dic3—62no—
268Dic3—61no—
269Dic3—61no—
270Dic3—62no—
271Dic3—62no—
272Dic3—121no—
273C32#196211yescharacteristic, complemented, Sylow
274C23—62no—
275C23C2×GO+(4,𝔽2)11yescharacteristic
276Q8—184no—
277D4—124no—
278D4—122no—
279D4—184no—
280D4—362no—
281C2×C4—22no—
282C2×C4—64no—
283C2×C4—64no—
284C2×C4—64no—
285C2×C4—62no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—91no—
291C2×C4—91no—
292C2×C4—182no—
293C2×C4—362no—
294C2×C4—362no—
295C2×C4D32⋊C411yescharacteristic
296C2×C4D32⋊C411yescharacteristic
297C8—362no—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—42no—
307C2×C3—242no—
308D3—82no—
309C22—21no—
310C22—21no—
311C22—122no—
312C22—122no—
313C22—122no—
314C22#6423012yes—
315C22C2×D32⋊C411yescharacteristic
316C4—21no—
317C4—68no—
318C4—92no—
319C4—91no—
320C4—91no—
321C4—92no—
322C4—122no—
323C4—181no—
324C4#6374112yescomplemented
325C3—21no—
326C3—21no—
327C2—22no—
328C2—242no—
329C2#1059338011yescharacteristic
330C2#1059340511yescharacteristic
331C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1962
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
3. C2×#63741C2semidirect
4. C4×Dic32C2semidirect
13. #63919C4semidirect
14. #63915C4semidirect
15. #63914C4semidirect
48. Dic32D4semidirect
141. C32×C4#104semidirect
143. C3⋊Dic3#104semidirect
273. C32#1962semidirect
324. C4#63741semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938052
C2×#637412
C4×Dic322
#19629