Finite Group Databasebeta

← #11777440

Subgroups — #11777440

Order 1152.

403 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×C4×#214C211yesmaximal, characteristic
3#10590259C211yesmaximal, characteristic, complemented
4C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
5#10589097C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589079C211yesmaximal, characteristic, complemented
8#70895—31nomaximal
9#68154—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)—21no—
12C2×C3×#214C411yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63657—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#832C411yescharacteristic
18C3×#810C411yescharacteristic
19C3×#808C411yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23Dic3⋊(C3⋊C8)—21no—
24#63554—21no—
25C3×C4×SD16—31no—
26#5024—31no—
27C4×#214D311yescharacteristic
28D4×C3⋊C8—31no—
29D4×C3⋊C8—31no—
30D4×C3⋊C8—61no—
31#4831—31no—
32C3×D4⋊C8—31no—
33#4535—31no—
34D4⋊(C3⋊C8)D311yescharacteristic
35#4480—31no—
36#4457—31no—
37#4456—31no—
38#4454—31no—
39#4454—31no—
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×Dic6C2×C411yescharacteristic
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C22⋊C4—21no—
45C32×C42C2311yescharacteristic
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—42no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C3×#214—22no—
51C3×C4⋊Dic3C2×C411yescharacteristic
52C3×Dic3⋊C4—21no—
53C3×C4×Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8C2×C411yescharacteristic
57C2×C3×C3⋊C8C2×C411yescharacteristic
58#1582—91noSylow
59C2×C3×SD16—31no—
60C3×C4×Q8—31no—
61C3×C4×D4—21no—
62C3×C4×D4C2×D311yescharacteristic
63C3×C4×D4C2×D311yescharacteristic
64C2×#214Dic311yescharacteristic
65C22×C3⋊C8—61no—
66C22×C3⋊C8—61no—
67C22×C3⋊C8—62no—
68C4×Dic6C2×D311yescharacteristic
69C3×#106—31no—
70C3×C4⋊C8—31no—
71C3×#103—31no—
72C3×#102—31no—
73C3×C4×C8—31no—
74C3×C4×C8—31no—
75#832Dic311yescharacteristic
76#830—61no—
77#830—61no—
78#830—62no—
79#815—61no—
80Dic3⋊C8—61no—
81#810Dic311yescharacteristic
82#808Dic311yescharacteristic
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—31no—
85C4⋊(C3⋊C8)—61no—
86C4⋊(C3⋊C8)—61no—
87C4⋊(C3⋊C8)C2×D311yescharacteristic
88#803—61no—
89C4×C3⋊C8—31no—
90C4×C3⋊C8—31no—
91C4×C3⋊C8—61no—
92C4×C3⋊C8C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C23×C32—21no—
95C32×D4—21no—
96C32×D4M1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—21no—
104C2×C3×Dic3—21no—
105C3×Dic6—21no—
106C3×Dic6—21no—
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)—41no—
109C3⋊(C3⋊C8)SD1612yescomplemented
110C3×C3⋊C8—21no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#446—91no—
115C4×SD16—31no—
116C8×D4—91no—
117#334—91no—
118Q8⋊C8—91no—
119D4⋊C8—31no—
120#322—91no—
121C2×C3×Q8—31no—
122C2×C3×D4—21no—
123C2×C3×D4C4×D311yescharacteristic
124C2×C3×D4C2×Dic311yescharacteristic
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C2×Dic6C2×Dic311yescharacteristic
129C3×SD16—62no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4C4×D311yescharacteristic
138C3×C4⋊C4C2×Dic311yescharacteristic
139C3×C22⋊C4—22no—
140C3×C22⋊C4—21no—
141C3×C22⋊C4—21no—
142C3×C42—21no—
143C3×C42—61no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#214—22no—
147C4⋊Dic3C2×Dic311yescharacteristic
148Dic3⋊C4—21no—
149C4×Dic3—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—21no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—62no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—61no—
161C2×C3⋊C8—122no—
162C2×C3⋊C8—122no—
163C2×C3⋊C8—124no—
164C2×C3⋊C8C2×Dic311yescharacteristic
165C2×C3⋊C8C2×Dic311yescharacteristic
166C22×C32—22no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32C4×D411yescharacteristic
170C32×C4—21no—
171C32×C4—41no—
172C32×C4C2×M1611yescharacteristic
173C32×C4#13111yescharacteristic
174C32×C4C2×SD1611yescharacteristic
175C32×C4#13511yescharacteristic
176C3×Dic3—41no—
177C3×Dic3—41no—
178C2×SD16—31no—
179C22×C8—181no—
180C4×Q8—31no—
181C4×D4D3211yescharacteristic
182#106—31no—
183C4⋊C8—31no—
184C4⋊C8—91no—
185C4⋊C8—181no—
186#103—31no—
187#102—31no—
188C22⋊C8—181no—
189#97—181no—
190C4×C8—31no—
191C4×C8—31no—
192C4×C8—91no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—21no—
196C3×Q8—61no—
197C3×Q8—61no—
198C3×D4—22no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—22no—
202C3×D4ΓL(1,𝔽25)12yes—
203C3×D4#20812yes—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—42no—
211C2×C3×C4—42no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—61no—
217C2×C3×C4—61no—
218C2×C3×C4C2×C4×D311yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4#23711yescharacteristic
222C2×C3×C4#23711yescharacteristic
223C2×C3×C4C22×Dic311yescharacteristic
224C2×Dic3—21no—
225C2×Dic3—21no—
226Dic6—21no—
227Dic6—21no—
228C3×C8—61no—
229C3×C8—61no—
230C3×C8—121no—
231C3×C8—121no—
232C3⋊C8—21no—
233C3⋊C8—21no—
234C3⋊C8—32no—
235C3⋊C8—32no—
236C3⋊C8—41no—
237C3⋊C8—41no—
238C3⋊C8—62no—
239C3⋊C8—61no—
240C3⋊C8—61no—
241C3⋊C8—121no—
242C3⋊C8—122no—
243C3⋊C8—121no—
244C3⋊C8—121no—
245C2×C32—42no—
246C2×C32#43511yescharacteristic
247C2×C32C4×SD1611yescharacteristic
248C2×C32#44411yescharacteristic
249C2×Q8—31no—
250C2×D4D3×Dic311yescharacteristic
251C22×C4—21no—
252SD16—62no—
253C2×C8—31no—
254C2×C8—31no—
255C2×C8—61no—
256C2×C8—61no—
257C2×C8—91no—
258C2×C8—91no—
259C2×C8—181no—
260C2×C8—362no—
261C4⋊C4—31no—
262C4⋊C4—61no—
263C4⋊C4D3×Dic311yescharacteristic
264C22⋊C4—21no—
265C42—61no—
266C42C2×D3211yescharacteristic
267C22×C3—24no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3#67⋊C411yescharacteristic
278C22×C3D4×Dic311yescharacteristic
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—42no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—121no—
290C3×C4—121no—
291C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
292C3×C4#90711yescharacteristic
293C3×C4#91211yescharacteristic
294C3×C4D3×SD1611yescharacteristic
295C3×C4D3×SD1611yescharacteristic
296C3×C4#91611yescharacteristic
297C3×C4C2×#20811yescharacteristic
298C3×C4#94811yescharacteristic
299Dic3—41no—
300Dic3—41no—
301C32#158211yescharacteristic, complemented, Sylow
302C23—21no—
303Q8—61no—
304Q8—61no—
305D4—21no—
306D4#371112yes—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4C2×D3×Dic311yescharacteristic
313C2×C4#380511yescharacteristic
314C2×C4#381111yescharacteristic
315C8—61no—
316C8—61no—
317C8—92no—
318C8—121no—
319C8—121no—
320C8—181no—
321C8—361no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—44no—
326C2×C3—42no—
327C2×C3—42no—
328C2×C3#473011yescharacteristic
329C2×C3#475811yescharacteristic
330C2×C3#482311yescharacteristic
331C2×C3#501111yescharacteristic
332C2×C3Dic3×SD1611yescharacteristic
333C2×C3#519711yescharacteristic
334C22—22no—
335C22—41no—
336C22—41no—
337C22#67⋊Dic311yescharacteristic
338C4—21no—
339C4—41no—
340C4—121no—
341C4—121no—
342C4#6381511yescharacteristic
343C4C2×#371111yescharacteristic
344C4#6393011yescharacteristic
345C4#6393611yescharacteristic
346C3—21no—
347C3#6815411yescharacteristic, complemented
348C3#7089511yescharacteristic, complemented
349C2—42no—
350C2#1059115811yescharacteristic
351C2#1059144511yescharacteristic
352C2#1059167611yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C4×D4
prime radicalC2×C32×D4C2×C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1582
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590259C2semidirect
5. #10589097C2semidirect
6. #10589084C2semidirect
7. #10589079C2semidirect
109. C3⋊(C3⋊C8)SD16semidirect
301. C32#1582semidirect
347. C3#68154semidirect
348. C3#70895semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊C8)2
C3×C4×#2142
#105902592
C3×D4⋊(C3⋊C8)2
#105890972
#105890842
#105890792
#708953
#681543