Finite Group Databasebeta

← #11791416

Subgroups — #11791416

Order 1152.

588 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C4×#3792C211yesmaximal, characteristic, complemented
3C2×#63741C214yesmaximal, complemented
4#10591257C211yesmaximal, characteristic, complemented
5C2×#3805C2212yes—
6C2×#3792C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#930—21no—
9#63980—21no—
10C2×#3724—21no—
11C2×Dic32C2212yes—
12#63919C411yescharacteristic, complemented
13#63915C412yescomplemented
14#63914C411yescharacteristic, complemented
15#63902—21no—
16#63898—21no—
17#63777—21no—
18C4×#622—21no—
19#63741—28no—
20C3×C3⋊#95—21no—
21#5596—61no—
22#4649—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—22no—
36#3792D414yescomplemented
37C2×#622—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C3×(C2×D3)⋊C4—22no—
43C3×C4⋊Dic3—21no—
44#3724—24no—
45#3724—21no—
46(C2×D3)⋊Dic3—22no—
47Dic32—24no—
48#1980—91nomaximal, Sylow
49C2×#237—62no—
50C3×#121—61no—
51#940—61no—
52#939—62no—
53D4×Dic3—61no—
54#930—21no—
55C2×Dic3⋊C4—62no—
56C2×C4×Dic3—61no—
57C2×C4×Dic3—61no—
58C2×C4×Dic3—62no—
59#893—61no—
60#888—61no—
61#885—62no—
62#67⋊C4—62no—
63C3×#95—61no—
64C3⋊#95—21no—
65C23×C32C2×D411yescharacteristic
66C22×C3×D3—22no—
67C2×C32×C4—41no—
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3#4112yes—
77C3×#67—42no—
78C3×#67—42no—
79C2×C3×Dic3—24no—
80C2×C3×Dic3—22no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C3×D12—42no—
84#627—24no—
85#625—24no—
86#625—42no—
87D3×Dic3—44no—
88#622—24no—
89#532—91no—
90C2×#104—94no—
91C4×M16—91no—
92C4×C4⋊C4—91no—
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—22no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—61no—
106C22×Dic3—62no—
107#237—124no—
108#237—124no—
109C2×D12—21no—
110C2×C4×D3—62no—
111C2×Dic6—62no—
112C3×C4⋊C4—61no—
113C3×C22⋊C4—62no—
114#217—62no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—62no—
117C4⋊Dic3—21no—
118Dic3⋊C4—62no—
119Dic3⋊C4—68no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—124no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×C22⋊C411yescharacteristic
132C22×C32#12411yescharacteristic
133C22×C32#12711yescharacteristic
134C2×C3×D3—42no—
135C2×C3×D3—42no—
136C2×C3×D3—42no—
137C32×C4—21no—
138C32×C4—21no—
139C3⋊Dic3—21no—
140C3⋊Dic3#10412yescomplemented
141C3⋊Dic3C4×D412yes—
142C3⋊Dic3#12112yes—
143C3×Dic3—44no—
144C3×Dic3—42no—
145C2×#41—92no—
146C2×M16—92no—
147C4⋊Q8—91no—
148#127—91no—
149#124—92no—
150#121—61no—
151#121—181no—
152C4×D4—181no—
153C4×D4—181no—
154C2×C4⋊C4—181no—
155C2×C42—91no—
156C2×C42—92no—
157#104—188no—
158#97—181no—
159C4×C8—181no—
160#95—61no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—62no—
164C22×D3—22no—
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—42no—
173C2×C3×C4—42no—
174C2×C3×C4—64no—
175C2×C3×C4—62no—
176C2×C3×C4—122no—
177C2×C3×C4—122no—
178#67—42no—
179#67—42no—
180#67—124no—
181#67—124no—
182C2×Dic3—24no—
183C2×Dic3—22no—
184C2×Dic3—42no—
185C2×Dic3—42no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—61no—
198C2×Dic3—64no—
199C2×Dic3—122no—
200C2×Dic3—124no—
201D12—42no—
202C4×D3—124no—
203Dic6—124no—
204C2×C32—21no—
205C2×C32—21no—
206C2×C32#39011yescharacteristic
207C2×C32C2×#10411yescharacteristic
208C2×C32#42111yescharacteristic
209C3×D3—82no—
210#41—184no—
211#41—184no—
212C2×Q8—92no—
213C2×D4—62no—
214C2×D4—61no—
215C2×D4—92no—
216C2×D4—181no—
217C22×C4—62no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—182no—
221C22×C4GO+(4,𝔽2)11yescharacteristic
222M16—94no—
223M16—182no—
224C2×C8—182no—
225C4⋊C4—61no—
226C4⋊C4—181no—
227C4⋊C4—184no—
228C22⋊C4—62no—
229C22⋊C4—182no—
230C42—91no—
231C42—91no—
232C42—91no—
233C42—91no—
234C42—184no—
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—41no—
244C22×C3—41no—
245C22×C3—122no—
246C22×C3—122no—
247C22×C3—122no—
248C2×D3—42no—
249C2×D3—42no—
250C2×D3—42no—
251C3×C4—22no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4—41no—
255C3×C4—122no—
256C3×C4—124no—
257Dic3—42no—
258Dic3—44no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—62no—
264Dic3—62no—
265Dic3—62no—
266Dic3—121no—
267C32#198011yescharacteristic, complemented, Sylow
268C23—62no—
269C23C2×GO+(4,𝔽2)11yescharacteristic
270Q8—184no—
271D4—122no—
272D4—122no—
273D4—122no—
274D4—184no—
275D4—362no—
276C2×C4—41no—
277C2×C4—64no—
278C2×C4—62no—
279C2×C4—92no—
280C2×C4—92no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—122no—
286C2×C4—122no—
287C2×C4—182no—
288C2×C4—364no—
289C2×C4D32⋊C411yescharacteristic
290C2×C4D32⋊C411yescharacteristic
291C8—184no—
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—41no—
301C2×C3—41no—
302C2×C3—242no—
303D3—82no—
304C22—21no—
305C22—21no—
306C22—122no—
307C22—122no—
308C22—122no—
309C22#6422111yescharacteristic
310C22#6423111yescharacteristic
311C22C2×D32⋊C411yescharacteristic
312C4—21no—
313C4—21no—
314C4—92no—
315C4—92no—
316C4—92no—
317C4—124no—
318C4—122no—
319C4—181no—
320C3—21no—
321C3—21no—
322C2—21no—
323C2—21no—
324C2—242no—
325C2#1059338011yescharacteristic
326C2#1059340711yescharacteristic
327C2#1059350611yescharacteristic
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#1980
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. C4×#3792C2semidirect
3. C2×#63741C2semidirect
4. #10591257C2semidirect
12. #63919C4semidirect
13. #63915C4semidirect
14. #63914C4semidirect
36. #3792D4semidirect
140. C3⋊Dic3#104semidirect
267. C32#1980semidirect

Maximal subgroups

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

subgroupindex
#105949292
C4×#37922
C2×#637412
#105912572
#19809