Finite Group Databasebeta

← #11777544

Subgroups — #11777544

Order 1152.

337 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 337 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C4×#3718C211yesmaximal, characteristic
2#10590259C211yesmaximal, characteristic
3#10590250C211yesmaximal, characteristic
4#10589320C211yesmaximal, characteristic
5C3×#4456C211yesmaximal, characteristic
6C3×#4456C211yesmaximal, characteristic
7#10589100C211yesmaximal, characteristic
8#68219—31nomaximal
9#68218—31nomaximal
10C3×C4×Dic6C2211yescharacteristic
11C3×C4×Dic6C2211yescharacteristic
12C2×#3718C411yescharacteristic
13C32×C4×C8C2211yescharacteristic
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18#63576C411yescharacteristic
19Dic3⋊(C3⋊C8)—21no—
20Dic3⋊(C3⋊C8)—21no—
21#63565C411yescharacteristic
22#63565C411yescharacteristic
23#63554—21no—
24Dic3×C3⋊C8—21no—
25C4×#216—31no—
26C4×#216—31no—
27#5024—31no—
28Q8×C3⋊C8—31no—
29#4831—31no—
30#4830—31no—
31C3×Q8⋊C8—31no—
32C3×Q8⋊C8—31no—
33#4479—31no—
34#4479—31no—
35#4456D311yescharacteristic
36#4456D311yescharacteristic
37#4454—31no—
38#4454—31no—
39#4454—61no—
40C2×C3×Dic6C2×C411yescharacteristic
41C2×C3×Dic6C2×C411yescharacteristic
42C2×C32×C8—21no—
43C32×C42C2311yescharacteristic
44C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
45C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C3×C4⋊Dic3C2×C411yescharacteristic
49C3×C4⋊Dic3C2×C411yescharacteristic
50C3×Dic3⋊C4—21no—
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56#3718—22no—
57#1584—91noSylow
58C3×C4×Q8—31no—
59C3×C4×Q8—31no—
60C2×#216—31no—
61C2×#216—31no—
62C4×Dic6C2×D311yescharacteristic
63C4×Dic6C2×D311yescharacteristic
64C3×C4⋊C8—31no—
65C3×C4⋊C8—31no—
66C3×C4×C8—21no—
67C3×C4×C8C2×D311yescharacteristic
68C3×C4×C8C2×D311yescharacteristic
69#835—31no—
70#835—31no—
71#815—61no—
72Dic3⋊C8—61no—
73Dic3⋊C8—61no—
74C8×Dic3—61no—
75#810—31no—
76#810—31no—
77#807—31no—
78#807—31no—
79C4⋊(C3⋊C8)—61no—
80C4⋊(C3⋊C8)—61no—
81C4⋊(C3⋊C8)C2×D311yescharacteristic
82C4⋊(C3⋊C8)C2×D311yescharacteristic
83#803—61no—
84C4×C3⋊C8—31no—
85C4×C3⋊C8—31no—
86C4×C3⋊C8—31no—
87C4×C3⋊C8—31no—
88C4×C3⋊C8—61no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8—61no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C3×Dic3—21no—
95C2×C3×Dic3—21no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—21no—
98C3×Dic6—21no—
99C3×Dic6—21no—
100C3×Dic6—21no—
101C3×Dic6M1612yes—
102C32×C8—41no—
103C3⋊(C3⋊C8)—21no—
104C3⋊(C3⋊C8)—21no—
105C3⋊(C3⋊C8)—21no—
106C3⋊(C3⋊C8)Q1612yescomplemented
107C3×C3⋊C8—41no—
108C3×C3⋊C8—41no—
109#446—91no—
110C8×Q8—91no—
111C4×Q16—91no—
112#335—91no—
113Q8⋊C8—31no—
114Q8⋊C8—31no—
115#322—91no—
116C2×C3×Q8—31no—
117C2×C3×Q8—31no—
118C2×Dic6C4×D311yescharacteristic
119C2×Dic6C4×D311yescharacteristic
120C2×C3×C8—22no—
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C2×C3×C8—61no—
124C2×C3×C8—61no—
125C3×C4⋊C4—31no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C42—21no—
130C3×C42—61no—
131C3×C42—61no—
132C3×C42C22×D311yescharacteristic
133C3×C42C22×D311yescharacteristic
134#216—62no—
135#216—62no—
136C4⋊Dic3C4×D311yescharacteristic
137C4⋊Dic3C4×D311yescharacteristic
138Dic3⋊C4—21no—
139Dic3⋊C4—21no—
140C4×Dic3—21no—
141C4×Dic3—21no—
142C2×C3⋊C8—21no—
143C2×C3⋊C8—21no—
144C2×C3⋊C8—31no—
145C2×C3⋊C8—31no—
146C2×C3⋊C8—31no—
147C2×C3⋊C8—31no—
148C2×C3⋊C8—31no—
149C2×C3⋊C8—31no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C22×C32C4×D411yescharacteristic
157C32×C4—21no—
158C32×C4C2×M1611yescharacteristic
159C32×C4#13111yescharacteristic
160C32×C4C2×Q1611yescharacteristic
161C32×C4#13511yescharacteristic
162C3×Dic3—22no—
163C3×Dic3—41no—
164C3×Dic3—41no—
165C3×Dic3—41no—
166C2×Q16—91no—
167C4×Q8—31no—
168C4×Q8—31no—
169#107—91no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8—181no—
173C4⋊C8—181no—
174#103—91no—
175#103—91no—
176#97—181no—
177C4×C8—91no—
178C4×C8—91no—
179C4×C8—181no—
180C4×C8D3211yescharacteristic
181C3×Q8—32no—
182C3×Q8—61no—
183C3×Q8—61no—
184C3×Q8—61no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4—61no—
192C2×C3×C4C2×C4×D311yescharacteristic
193C2×C3×C4C2×C4×D311yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×C3×C4D3×D411yescharacteristic
196C2×C3×C4#23711yescharacteristic
197C2×C3×C4#23711yescharacteristic
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202Dic6—21no—
203Dic6—21no—
204Dic6—21no—
205Dic6ΓL(1,𝔽25)12yes—
206C3×C8—42no—
207C3×C8—41no—
208C3×C8—41no—
209C3×C8—121no—
210C3×C8—121no—
211C3⋊C8—32no—
212C3⋊C8—32no—
213C3⋊C8—41no—
214C3⋊C8—41no—
215C3⋊C8—62no—
216C3⋊C8—62no—
217C3⋊C8—61no—
218C3⋊C8—61no—
219C3⋊C8—61no—
220C3⋊C8—61no—
221C3⋊C8—61no—
222C3⋊C8—61no—
223C3⋊C8—121no—
224C3⋊C8—121no—
225C2×C32#43511yescharacteristic
226C2×C32C4×Q1611yescharacteristic
227C2×C32#44411yescharacteristic
228C2×Q8—31no—
229C2×Q8—31no—
230Q16—182no—
231C2×C8—21no—
232C2×C8—61no—
233C2×C8—61no—
234C2×C8—91no—
235C2×C8—91no—
236C2×C8—91no—
237C2×C8—91no—
238C4⋊C4—31no—
239C4⋊C4—31no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C42—61no—
243C42—61no—
244C42C2×D3211yescharacteristic
245C22×C3—21no—
246C22×C3#67⋊C411yescharacteristic
247C22×C3#67⋊C411yescharacteristic
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—21no—
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—62no—
256C3×C4—121no—
257C3×C4—121no—
258C3×C4—121no—
259C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
260C3×C4#90111yescharacteristic
261C3×C4D3×M1611yescharacteristic
262C3×C4#90711yescharacteristic
263C3×C4#91611yescharacteristic
264C3×C4#91611yescharacteristic
265C3×C4D3×Q1611yescharacteristic
266C3×C4D3×Q1611yescharacteristic
267Dic3—22no—
268Dic3—41no—
269Dic3—41no—
270Dic3—41no—
271C32#158411yescharacteristic, complemented, Sylow
272Q8—32no—
273Q8—61no—
274Q8—61no—
275Q8—61no—
276C2×C4—61no—
277C2×C4—61no—
278C2×C4—61no—
279C2×C4—61no—
280C2×C4C4×D3211yescharacteristic
281C2×C4#380211yescharacteristic
282C2×C4#380511yescharacteristic
283C8—41no—
284C8—92no—
285C8—121no—
286C8—121no—
287C8—181no—
288C8—181no—
289C8—181no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#472811yescharacteristic
294C2×C3#473011yescharacteristic
295C2×C3#479011yescharacteristic
296C2×C3#479011yescharacteristic
297C2×C3#482311yescharacteristic
298C2×C3#482311yescharacteristic
299C22#6390211yescharacteristic
300C4—21no—
301C4—62no—
302C4—121no—
303C4—121no—
304C4—121no—
305C4D3×ΓL(1,𝔽25)11yescharacteristic
306C4#6380211yescharacteristic
307C4#6380411yescharacteristic
308C4#6380911yescharacteristic
309C3—21no—
310C3#6821811yescharacteristic, complemented
311C3#6821911yescharacteristic, complemented
312C2#1059039011yescharacteristic
313C2#1059072511yescharacteristic
314C2#1059079011yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32C4×D4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1584
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
106. C3⋊(C3⋊C8)Q16semidirect
271. C32#1584semidirect
310. C3#68218semidirect
311. C3#68219semidirect

Maximal subgroups

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

subgroupindex
C4×#37182
#105902592
#105902502
#105893202
C3×#44562
#105891002
#682193
#682183