Finite Group Databasebeta

← #11774778

Subgroups — #11774778

Order 1152.

545 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 108 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#10593882C211yesmaximal, characteristic
2C4×C8×C3⋊D3C211yesmaximal, characteristic
3#10590340C211yesmaximal, characteristic
4C3×#4456C212yesmaximal, complemented
5#10589083C212yesmaximal, complemented
6#68240—32nomaximal
7C2×C8×C3⋊D3—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×Dic6C2212yes—
10#63919C411yescharacteristic
11C4×#627—21no—
12#63874—21no—
13#63873C411yescharacteristic
14#63871C412yes—
15#63870—21no—
16#63865—21no—
17C2×#3712—21no—
18C32×C4×C8C2211yescharacteristic
19C8×C3⋊Dic3—21no—
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2212yes—
22#63572—21no—
23#5578—32no—
24#4837—32no—
25C4×D3×C8—32no—
26C4×D3×C8—61no—
27C3×Q8⋊C8—32no—
28#4535—32no—
29#4484—32no—
30#4456D312yescomplemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C3×Dic6C2×C412yes—
35C2×#627—21no—
36C2×C32×C8—21no—
37C32×C42C2311yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C2×C3⋊(C3⋊C8)—21no—
42C8×C3⋊D3—24no—
43C3×C4⋊Dic3C2×C412yes—
44C3×Dic3⋊C4—22no—
45C3×C4×Dic3—22no—
46C2×C3×C3⋊C8—22no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50Dic3⋊Dic3—22no—
51#3722—22no—
52#3712—42no—
53#1493—91noSylow
54C3×C4×Q8—32no—
55#946—32no—
56#944—32no—
57C2×ΓL(1,𝔽25)—62no—
58C2×D3×C8—62no—
59C2×D3×C8—62no—
60#897—32no—
61#896—62no—
62#889—62no—
63#888—32no—
64#872—62no—
65C42×D3—32no—
66C42×D3—61no—
67C4×Dic6—62no—
68C4×Dic6C2×D312yes—
69C3×C4⋊C8—32no—
70C3×C4×C8—21no—
71C3×C4×C8C2×D312yes—
72Dic3⋊C8—62no—
73C8×Dic3—62no—
74C8×Dic3—62no—
75C4⋊(C3⋊C8)C2×D312yes—
76C4×C3⋊C8—32no—
77C4×C3⋊C8—61no—
78C22×C3⋊D3C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C3⋊Dic3C22⋊C411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4×C3⋊D3—21no—
86C4×C3⋊D3—21no—
87C4×C3⋊D3—22no—
88C4×C3⋊D3SD1612yes—
89C4×C3⋊D3Q1612yes—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—22no—
92C3×Dic6—22no—
93C3×Dic6—22no—
94#627—42no—
95C32×C8—22no—
96C3⋊(C3⋊C8)—22no—
97C3×C3⋊C8—42no—
98#533—91no—
99#423—91no—
100C2×C4×C8—91no—
101Q8⋊C8—32no—
102Q8⋊C8—92no—
103C2×C3×Q8—32no—
104C2×C4×D3—32no—
105C2×C4×D3—32no—
106C2×C4×D3—32no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—61no—
110C2×Dic6—62no—
111C2×Dic6C4×D312yes—
112C2×C3×C8—22no—
113C2×C3×C8—22no—
114C2×C3×C8—62no—
115C3×C4⋊C4—32no—
116C3×C4⋊C4—62no—
117C3×C42—21no—
118C3×C42—62no—
119C3×C42C22×D312yes—
120(C2×D3)⋊C4—62no—
121(C2×D3)⋊C4—62no—
122C4⋊Dic3—62no—
123C4⋊Dic3C4×D312yes—
124Dic3⋊C4—22no—
125Dic3⋊C4—62no—
126Dic3⋊C4—62no—
127Dic3⋊C4—62no—
128Dic3⋊C4—62no—
129C4×Dic3—22no—
130C4×Dic3—32no—
131C4×Dic3—32no—
132C4×Dic3—32no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C4×Dic3—61no—
136C2×C3⋊C8—22no—
137C2×C3⋊C8—62no—
138C2×C3⋊C8—62no—
139ΓL(1,𝔽25)—124no—
140D3×C8—68no—
141D3×C8—68no—
142C22×C32C2×C22⋊C411yescharacteristic
143C2×C3⋊D3—21no—
144C2×C3⋊D3—21no—
145C2×C3⋊D3#10312yes—
146C32×C4—21no—
147C32×C4#13111yescharacteristic
148C32×C4#13111yescharacteristic
149C32×C4C2×SD1611yescharacteristic
150C32×C4C2×Q1611yescharacteristic
151C3⋊Dic3—21no—
152C3⋊Dic3#10312yes—
153C3⋊Dic3#10412yes—
154C3×Dic3—42no—
155C3×Dic3—42no—
156C2×M16—181no—
157C22×C8—181no—
158C4⋊Q8—91no—
159C4⋊Q8—91no—
160#125—181no—
161C22⋊Q8—92no—
162C22⋊Q8—181no—
163C4×Q8—32no—
164C4×Q8—181no—
165#117—181no—
166C2×C42—91no—
167C4⋊C8—32no—
168C4⋊C8—181no—
169C4×C8—91no—
170C4×C8—181no—
171C4×C8D3211yescharacteristic
172C22×D3—32no—
173C22×D3—61no—
174C3×Q8—62no—
175C3×Q8—62no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—62no—
180C2×C3×C4—62no—
181C2×C3×C4C2×C4×D312yes—
182C2×C3×C4D3×D412yes—
183C2×C3×C4D3×D412yes—
184C2×Dic3—22no—
185C2×Dic3—22no—
186C2×Dic3—32no—
187C2×Dic3—32no—
188C2×Dic3—32no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C4×D3—34no—
193C4×D3—34no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—64no—
197C4×D3—64no—
198C4×D3—62no—
199C4×D3—62no—
200C4×D3—62no—
201C4×D3—62no—
202Dic6—22no—
203Dic6—22no—
204Dic6—124no—
205C3×C8—24no—
206C3×C8—24no—
207C3×C8—122no—
208C3⋊C8—42no—
209C3⋊C8—64no—
210C3⋊C8—64no—
211C2×C32#40811yescharacteristic
212C2×C32C2×#10311yescharacteristic
213C2×C32C2×#10411yescharacteristic
214C3⋊D3—22no—
215C2×Q8—32no—
216C2×Q8—181no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—91no—
220M16—362no—
221C2×C8—21no—
222C2×C8—62no—
223C2×C8—184no—
224C2×C8—181no—
225C4⋊C4—32no—
226C4⋊C4—62no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4—182no—
230C4⋊C4—181no—
231C22⋊C4—182no—
232C42—62no—
233C42—91no—
234C42—91no—
235C42—91no—
236C42C2×D3211yescharacteristic
237C22×C3—21no—
238C22×C3D3×C22⋊C412yes—
239C2×D3—34no—
240C2×D3—62no—
241C2×D3—62no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—62no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—122no—
252C3×C4—122no—
253C3×C4#90112yes—
254C3×C4#90712yes—
255C3×C4D3×SD1612yes—
256C3×C4D3×Q1612yes—
257Dic3—34no—
258Dic3—34no—
259Dic3—42no—
260Dic3—42no—
261Dic3—62no—
262Dic3—62no—
263Dic3—62no—
264Dic3—62no—
265C32#149311yescharacteristic, complemented, Sylow
266C23—91no—
267Q8—62no—
268Q8—62no—
269Q8—362no—
270C2×C4—62no—
271C2×C4—62no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—92no—
275C2×C4—92no—
276C2×C4—91no—
277C2×C4—182no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4C4×D3211yescharacteristic
281C2×C4#380211yescharacteristic
282C2×C4#381111yescharacteristic
283C8—22no—
284C8—122no—
285C8—182no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#472712yes—
290C2×C3D3×#10312yes—
291C2×C3D3×#10412yes—
292D3—64no—
293D3—64no—
294C22—92no—
295C22—181no—
296C22—181no—
297C22#6392111yescharacteristic
298C4—21no—
299C4—92no—
300C4—92no—
301C4—122no—
302C4—122no—
303C4—181no—
304C4#6379611yescharacteristic
305C4#6380211yescharacteristic
306C4#6380311yescharacteristic
307C4#6380511yescharacteristic
308C3—21no—
309C3#6824012yescomplemented
310C2—182no—
311C2#1059039311yescharacteristic
312C2#1059067211yescharacteristic
313C2#1059095811yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1493
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. C3×#4456C2semidirect
5. #10589083C2semidirect
30. #4456D3semidirect
265. C32#1493semidirect
309. C3#68240semidirect

Maximal subgroups

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

subgroupindex
#105938822
C4×C8×C3⋊D32
#105903402
C3×#44562
#105890832
#682403