Finite Group Databasebeta

← #11777439

Subgroups — #11777439

Order 1152.

377 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#214C211yesmaximal, characteristic
2C3×D4×C3⋊C8C211yesmaximal, characteristic
3#10590258C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
5#10589097C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589078C211yesmaximal, characteristic, complemented
8#70895—31nomaximal
9#70842—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×C3×#214C411yescharacteristic
12C22×C3×C3⋊C8—21no—
13C3×C4×Dic6C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#832C411yescharacteristic
17C3×#830—21no—
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—
26C3×C8×D4—31no—
27#5024—31no—
28C4×#214D311yescharacteristic
29D4×C3⋊C8D311yescharacteristic
30#4679—31no—
31#4535—31no—
32D4⋊(C3⋊C8)—31no—
33D4⋊(C3⋊C8)—31no—
34D4⋊(C3⋊C8)—61no—
35#4484—31no—
36#4480—31no—
37#4457—31no—
38#4455—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)—21no—
48C3×#214—22no—
49C3×C4⋊Dic3C2×C411yescharacteristic
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—42no—
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1582—91noSylow
59C2×C3×SD16—31no—
60C22×C3×C8—61no—
61C3×C4×Q8—31no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C2×D311yescharacteristic
65C2×#214Dic311yescharacteristic
66C22×C3⋊C8—21no—
67C4×Dic6C2×D311yescharacteristic
68C3×#106—31no—
69C3×C4⋊C8—31no—
70C3×#103—31no—
71C3×#102—31no—
72C3×C22⋊C8—61no—
73C3×C4×C8—31no—
74C3×C4×C8—31no—
75#832Dic311yescharacteristic
76#830—21no—
77#815—61no—
78Dic3⋊C8—61no—
79#810Dic311yescharacteristic
80#808Dic311yescharacteristic
81C4⋊(C3⋊C8)—31no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—61no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86#803—61no—
87C4×C3⋊C8—31no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C23×C32—21no—
93C32×D4—21no—
94C32×D4M1612yes—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—21no—
102C2×C3×Dic3—21no—
103C3×Dic6—21no—
104C3×Dic6—21no—
105C3⋊(C3⋊C8)—41no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8SD1612yescomplemented
112#446—91no—
113C4×SD16—31no—
114C8×D4—31no—
115#334—91no—
116Q8⋊C8—91no—
117D4⋊C8—91no—
118#322—91no—
119C2×C3×Q8—31no—
120C2×C3×D4—21no—
121C2×C3×D4C4×D311yescharacteristic
122C2×C3×D4C2×Dic311yescharacteristic
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—41no—
126C2×Dic6C2×Dic311yescharacteristic
127C3×SD16—62no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—61no—
133C2×C3×C8—122no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4C4×D311yescharacteristic
138C3×C4⋊C4C2×Dic311yescharacteristic
139C3×C22⋊C4—21no—
140C3×C22⋊C4—21no—
141C3×C22⋊C4—41no—
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—42no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—121no—
157C2×C3⋊C8—121no—
158C2×C3⋊C8C2×Dic311yescharacteristic
159C2×C3⋊C8C2×Dic311yescharacteristic
160C2×C3⋊C8#6711yescharacteristic
161C2×C3⋊C8#6711yescharacteristic
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32C4×D411yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4C2×M1611yescharacteristic
169C32×C4#13111yescharacteristic
170C32×C4C2×SD1611yescharacteristic
171C32×C4#13511yescharacteristic
172C3×Dic3—41no—
173C3×Dic3—41no—
174C2×SD16—31no—
175C22×C8—61no—
176C4×Q8—31no—
177C4×D4D3211yescharacteristic
178#106—31no—
179C4⋊C8—31no—
180C4⋊C8—91no—
181C4⋊C8—181no—
182#103—31no—
183#102—31no—
184C22⋊C8—61no—
185#97—181no—
186C4×C8—31no—
187C4×C8—31no—
188C4×C8—91no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—41no—
192C3×Q8—61no—
193C3×Q8—61no—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—22no—
197C3×D4—41no—
198C3×D4ΓL(1,𝔽25)12yes—
199C3×D4#20812yes—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—81no—
213C2×C3×C4—81no—
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4#23511yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4#23711yescharacteristic
218C2×C3×C4C22×Dic311yescharacteristic
219C2×C3×C4C2×#6711yescharacteristic
220C2×Dic3—21no—
221C2×Dic3—21no—
222Dic6—21no—
223Dic6—21no—
224C3×C8—32no—
225C3×C8—61no—
226C3×C8—61no—
227C3×C8—61no—
228C3×C8—121no—
229C3⋊C8—21no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8—41no—
233C3⋊C8—121no—
234C3⋊C8—121no—
235C3⋊C8—122no—
236C3⋊C8—121no—
237C3⋊C8—121no—
238C3⋊C8—241no—
239C3⋊C8#21412yescomplemented
240C2×C32—42no—
241C2×C32#43511yescharacteristic
242C2×C32C4×SD1611yescharacteristic
243C2×C32#44411yescharacteristic
244C2×Q8—31no—
245C2×D4D3×Dic311yescharacteristic
246C22×C4—21no—
247SD16—62no—
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—31no—
251C2×C8—31no—
252C2×C8—61no—
253C2×C8—122no—
254C2×C8—181no—
255C2×C8—181no—
256C4⋊C4—31no—
257C4⋊C4—61no—
258C4⋊C4D3×Dic311yescharacteristic
259C22⋊C4—21no—
260C42—61no—
261C42C2×D3211yescharacteristic
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—21no—
265C22×C3—42no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—81no—
271C22×C3—81no—
272C22×C3C4×#6711yescharacteristic
273C22×C3D4×Dic311yescharacteristic
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—81no—
284C3×C4—121no—
285C3×C4—121no—
286C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
287C3×C4#90111yescharacteristic
288C3×C4D3×SD1611yescharacteristic
289C3×C4#91611yescharacteristic
290C3×C4C2×#20811yescharacteristic
291C3×C4C2×#21411yescharacteristic
292C3×C4#94811yescharacteristic
293C3×C4#95011yescharacteristic
294Dic3—41no—
295Dic3—41no—
296C32#158211yescharacteristic, complemented, Sylow
297C23—21no—
298Q8—61no—
299Q8—61no—
300D4—21no—
301D4#371112yes—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4C2×D3×Dic311yescharacteristic
308C2×C4#380411yescharacteristic
309C2×C4D3×#6711yescharacteristic
310C8—32no—
311C8—61no—
312C8—61no—
313C8—61no—
314C8—121no—
315C8—361no—
316C8—361no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—42no—
321C2×C3—42no—
322C2×C3—82no—
323C2×C3#501111yescharacteristic
324C2×C3C4×#21411yescharacteristic
325C2×C3#511111yescharacteristic
326C2×C3#514511yescharacteristic
327C2×C3Dic3×SD1611yescharacteristic
328C2×C3#519711yescharacteristic
329C22—22no—
330C22—41no—
331C22—41no—
332C22Dic3×#6711yescharacteristic
333C4—21no—
334C4—41no—
335C4—121no—
336C4—121no—
337C4#6381411yescharacteristic
338C4C2×#371111yescharacteristic
339C4D3×#21411yescharacteristic
340C4#6393511yescharacteristic
341C3—21no—
342C3#7084211yescharacteristic, complemented
343C3#7089511yescharacteristic, complemented
344C2—42no—
345C2#1059115511yescharacteristic
346C2Dic3×#21411yescharacteristic
347C2#1059167411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
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. #10590258C2semidirect
5. #10589097C2semidirect
6. #10589083C2semidirect
7. #10589078C2semidirect
111. C3×C3⋊C8SD16semidirect
239. C3⋊C8#214semidirect
296. C32#1582semidirect
342. C3#70842semidirect
343. C3#70895semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2142
C3×D4×C3⋊C82
#105902582
D4⋊(C3⋊(C3⋊C8))2
#105890972
#105890832
#105890782
#708953
#708423