Finite Group Databasebeta

← #11774771

Subgroups — #11774771

Order 1152.

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

normal subgroups only

This group has 527 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
2#10592536C211yesmaximal, characteristic
3C4×#3710C211yesmaximal, characteristic
4C3×#4484C212yesmaximal, complemented
5#10589084C212yesmaximal, complemented
6#68240—32nomaximal
7C2×#3743—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×#3710—21no—
18C32×C4⋊C8C2211yescharacteristic
19#63641—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C3×C4×C3⋊C8C2212yes—
22#63553—21no—
23#5578—32no—
24#4837—32no—
25#4837—61no—
26C4×D3×C8—32no—
27C3×Q8⋊C8—32no—
28#4535—32no—
29#4484D312yescomplemented
30#4456—32no—
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—
42#3743—42no—
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#3710—24no—
53#1493—91noSylow
54C3×C4×Q8—32no—
55#946—32no—
56#944—32no—
57C2×ΓL(1,𝔽25)—62no—
58C2×ΓL(1,𝔽25)—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—21no—
70C3×C4⋊C8C2×D312yes—
71C3×C4×C8—32no—
72Dic3⋊C8—62no—
73Dic3⋊C8—62no—
74C8×Dic3—62no—
75C4⋊(C3⋊C8)—32no—
76C4⋊(C3⋊C8)—61no—
77C4×C3⋊C8C2×D312yes—
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—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3SD1612yes—
88C4×C3⋊D3Q1612yes—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C3×Dic6—22no—
92C3×Dic6—22no—
93#627—42no—
94C32×C8—41no—
95C3⋊(C3⋊C8)—41no—
96C3×C3⋊C8—24no—
97#533—91no—
98#423—91no—
99C2×C4×C8—91no—
100Q8⋊C8—32no—
101Q8⋊C8—92no—
102C2×C3×Q8—32no—
103C2×C4×D3—32no—
104C2×C4×D3—32no—
105C2×C4×D3—32no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×Dic6—62no—
110C2×Dic6C4×D312yes—
111C2×C3×C8—22no—
112C2×C3×C8—22no—
113C2×C3×C8—62no—
114C3×C4⋊C4—32no—
115C3×C4⋊C4—62no—
116C3×C42—21no—
117C3×C42—62no—
118C3×C42C22×D312yes—
119(C2×D3)⋊C4—62no—
120(C2×D3)⋊C4—62no—
121C4⋊Dic3—62no—
122C4⋊Dic3C4×D312yes—
123Dic3⋊C4—22no—
124Dic3⋊C4—62no—
125Dic3⋊C4—62no—
126Dic3⋊C4—62no—
127Dic3⋊C4—62no—
128C4×Dic3—22no—
129C4×Dic3—32no—
130C4×Dic3—32no—
131C4×Dic3—32no—
132C4×Dic3—61no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—62no—
138ΓL(1,𝔽25)—124no—
139ΓL(1,𝔽25)—124no—
140D3×C8—68no—
141C22×C32C2×C22⋊C411yescharacteristic
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3⋊D3#10312yes—
145C32×C4—21no—
146C32×C4#13112yes—
147C32×C4C2×SD1611yescharacteristic
148C32×C4C2×Q1611yescharacteristic
149C3⋊Dic3—21no—
150C3⋊Dic3#10312yes—
151C3⋊Dic3#10412yes—
152C3×Dic3—42no—
153C3×Dic3—42no—
154C2×M16—181no—
155C22×C8—181no—
156C4⋊Q8—91no—
157C4⋊Q8—91no—
158#125—181no—
159C22⋊Q8—92no—
160C22⋊Q8—181no—
161C4×Q8—32no—
162C4×Q8—181no—
163#117—181no—
164C2×C42—91no—
165C4⋊C8—91no—
166C4⋊C8—181no—
167C4⋊C8D3211yescharacteristic
168C4×C8—32no—
169C4×C8—181no—
170C22×D3—32no—
171C22×D3—61no—
172C3×Q8—62no—
173C3×Q8—62no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—62no—
178C2×C3×C4—62no—
179C2×C3×C4C2×C4×D312yes—
180C2×C3×C4D3×D412yes—
181C2×C3×C4D3×D412yes—
182C2×Dic3—22no—
183C2×Dic3—22no—
184C2×Dic3—32no—
185C2×Dic3—32no—
186C2×Dic3—32no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C4×D3—34no—
191C4×D3—34no—
192C4×D3—62no—
193C4×D3—62no—
194C4×D3—64no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—122no—
198C4×D3—122no—
199Dic6—22no—
200Dic6—22no—
201Dic6—124no—
202C3×C8—42no—
203C3×C8—42no—
204C3×C8—64no—
205C3⋊C8—24no—
206C3⋊C8—122no—
207C3⋊C8—122no—
208C2×C32#40811yescharacteristic
209C2×C32C2×#10311yescharacteristic
210C2×C32C2×#10411yescharacteristic
211C3⋊D3—22no—
212C2×Q8—32no—
213C2×Q8—181no—
214C22×C4—91no—
215C22×C4—91no—
216C22×C4—91no—
217M16—362no—
218C2×C8—21no—
219C2×C8—62no—
220C2×C8—184no—
221C2×C8—181no—
222C4⋊C4—32no—
223C4⋊C4—62no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—182no—
227C4⋊C4—181no—
228C22⋊C4—182no—
229C42—62no—
230C42—91no—
231C42—91no—
232C42—91no—
233C42C2×D3211yescharacteristic
234C22×C3—21no—
235C22×C3D3×C22⋊C412yes—
236C2×D3—34no—
237C2×D3—62no—
238C2×D3—62no—
239C2×D3—62no—
240C2×D3—121no—
241C2×D3—121no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—41no—
247C3×C4—122no—
248C3×C4—122no—
249C3×C4#90112yes—
250C3×C4#90712yes—
251C3×C4D3×SD1612yes—
252C3×C4D3×Q1612yes—
253Dic3—34no—
254Dic3—34no—
255Dic3—42no—
256Dic3—42no—
257Dic3—62no—
258Dic3—62no—
259Dic3—62no—
260Dic3—121no—
261C32#149311yescharacteristic, complemented, Sylow
262C23—91no—
263Q8—62no—
264Q8—62no—
265Q8—362no—
266C2×C4—62no—
267C2×C4—62no—
268C2×C4—91no—
269C2×C4—91no—
270C2×C4—92no—
271C2×C4—92no—
272C2×C4—91no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4C4×D3211yescharacteristic
276C2×C4#380211yescharacteristic
277C2×C4#381111yescharacteristic
278C8—41no—
279C8—64no—
280C8—361no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3#472712yes—
285C2×C3D3×#10312yes—
286C2×C3D3×#10412yes—
287D3—64no—
288D3—122no—
289C22—92no—
290C22—181no—
291C22—181no—
292C22#6392111yescharacteristic
293C4—21no—
294C4—92no—
295C4—92no—
296C4—122no—
297C4—122no—
298C4—181no—
299C4#6380412yes—
300C4#6393011yescharacteristic
301C4#6394411yescharacteristic
302C3—21no—
303C3#6824012yescomplemented
304C2—182no—
305C2#1059060111yescharacteristic
306C2#1059095911yescharacteristic
307C2#1059100811yescharacteristic
subgroupG/H
centerC2×C4#3811
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×#4484C2semidirect
5. #10589084C2semidirect
29. #4484D3semidirect
261. C32#1493semidirect
303. C3#68240semidirect

Maximal subgroups

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

subgroupindex
#105938822
#105925362
C4×#37102
C3×#44842
#105890842
#682403