Finite Group Databasebeta

← #11777596

Subgroups — #11777596

Order 1152.

371 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#215C211yesmaximal, characteristic
2C3×#5024C211yesmaximal, characteristic, complemented
3C3⋊C8×D12C211yesmaximal, characteristic
4#10589401C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589080C211yesmaximal, characteristic
7#10589079C211yesmaximal, characteristic, complemented
8#70954—31nomaximal
9#70897—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×C3×#215C411yescharacteristic
12C3×C4×D12C2211yescharacteristic
13C2×D3×C3⋊C8—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#835C411yescharacteristic
17C3×#809C411yescharacteristic
18C3×#808C411yescharacteristic
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×#803—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#446—31no—
26C3×C4×SD16—31no—
27C4×#215D311yescharacteristic
28#5024D311yescharacteristic, complemented
29D4×C3⋊C8—31no—
30C8×D12—31no—
31#4535—31no—
32#4535—31no—
33#4535—61no—
34D4⋊(C3⋊C8)—31no—
35#4483—31no—
36#4479—31no—
37#4458—31no—
38#4454—31no—
39#4454—31no—
40C2×C32×Q8C2×C411yescharacteristic
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C42—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C3×#215—22no—
50C3×(C2×D3)⋊C4—21no—
51C3×C4⋊Dic3C2×C411yescharacteristic
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8C2×C411yescharacteristic
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57D3×C3⋊C8—42no—
58#1585—91noSylow
59C2×C3×SD16—31no—
60C3×C4×Q8—21no—
61C3×C4×Q8C2×D311yescharacteristic
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×D4—31no—
64C2×#215Dic311yescharacteristic
65C22×C3⋊C8—61no—
66C2×D3×C8—61no—
67C4×D12C2×D311yescharacteristic
68C3×#106—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—61no—
71C3×#103—31no—
72C3×#102—31no—
73C3×#97—61no—
74C3×C4×C8—31no—
75C3×C4×C8—31no—
76#835Dic311yescharacteristic
77#830—61no—
78(C2×D3)⋊C8—61no—
79#809Dic311yescharacteristic
80#808Dic311yescharacteristic
81C4⋊(C3⋊C8)—21no—
82C4⋊(C3⋊C8)—31no—
83C4⋊(C3⋊C8)—31no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)C2×D311yescharacteristic
86#803—21no—
87C4×C3⋊C8—31no—
88C4×C3⋊C8—31no—
89C4×C3⋊C8—61no—
90C4×C3⋊C8C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C22×C3×D3—21no—
93C32×Q8—21no—
94C32×Q8—21no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3×Dic3—21no—
101C3×D12—21no—
102C3×D12M1612yes—
103C3×C4×D3—41no—
104C3×C4×D3—41no—
105C3⋊(C3⋊C8)—22no—
106C3⋊(C3⋊C8)—41no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—21no—
111C3×C3⋊C8—41no—
112#446—31no—
113C4×SD16—31no—
114C8×D4—91no—
115#335—91no—
116Q8⋊C8—91no—
117D4⋊C8—91no—
118#322—91no—
119C2×C3×Q8—21no—
120C2×C3×Q8C4×D311yescharacteristic
121C2×C3×Q8C2×Dic311yescharacteristic
122C2×C3×D4—31no—
123C22×C3×C4—61no—
124C2×D12C2×Dic311yescharacteristic
125C2×C4×D3—21no—
126C3×SD16—62no—
127C2×C3×C8—31no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—61no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—31no—
136C3×C4⋊C4—41no—
137C3×C4⋊C4C4×D311yescharacteristic
138C3×C4⋊C4C2×Dic311yescharacteristic
139C3×C22⋊C4—61no—
140C3×C42—21no—
141C3×C42—21no—
142C3×C42—21no—
143C3×C42—41no—
144C3×C42C22×D311yescharacteristic
145C3×C42C22×D311yescharacteristic
146#215—22no—
147(C2×D3)⋊C4—21no—
148C4⋊Dic3C2×Dic311yescharacteristic
149C2×C3⋊C8—21no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—121no—
155C2×C3⋊C8—121no—
156C2×C3⋊C8—122no—
157C2×C3⋊C8C2×Dic311yescharacteristic
158C2×C3⋊C8C2×Dic311yescharacteristic
159C2×C3⋊C8#6711yescharacteristic
160C2×C3⋊C8#6711yescharacteristic
161D3×C8—122no—
162C22×C32C4×D411yescharacteristic
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C32×C4—21no—
167C32×C4—41no—
168C32×C4—41no—
169C32×C4C2×M1611yescharacteristic
170C32×C4#13111yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C32×C4#13711yescharacteristic
173C3×Dic3—41no—
174C2×SD16—31no—
175C22×C8—181no—
176C4×Q8D3211yescharacteristic
177C4×D4—31no—
178#106—31no—
179C4⋊C8—31no—
180C4⋊C8—61no—
181C4⋊C8—91no—
182#103—31no—
183#102—31no—
184C22⋊C8—181no—
185#97—61no—
186C4×C8—31no—
187C4×C8—31no—
188C4×C8—91no—
189C23×C3—61no—
190C22×D3—21no—
191C3×Q8—22no—
192C3×Q8—21no—
193C3×Q8—21no—
194C3×Q8—21no—
195C3×Q8—21no—
196C3×Q8—41no—
197C3×D4—32no—
198C3×D4—61no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—61no—
209C2×C3×C4—121no—
210C2×C3×C4—121no—
211C2×C3×C4C2×C4×D311yescharacteristic
212C2×C3×C4#23511yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4#23711yescharacteristic
215C2×C3×C4C22×Dic311yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×Dic3—21no—
218D12—21no—
219D12#20812yes—
220C4×D3—41no—
221C4×D3—41no—
222C3×C8—61no—
223C3×C8—61no—
224C3×C8—61no—
225C3×C8—61no—
226C3×C8—121no—
227C3⋊C8—21no—
228C3⋊C8—21no—
229C3⋊C8—21no—
230C3⋊C8—21no—
231C3⋊C8—41no—
232C3⋊C8—62no—
233C3⋊C8—62no—
234C3⋊C8—122no—
235C3⋊C8—121no—
236C3⋊C8—121no—
237C3⋊C8—241no—
238C2×C32#43511yescharacteristic
239C2×C32#44011yescharacteristic
240C2×C32#44311yescharacteristic
241C3×D3—42no—
242C2×Q8D3×Dic311yescharacteristic
243C2×D4—31no—
244C22×C4—61no—
245SD16—62no—
246C2×C8—31no—
247C2×C8—31no—
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—61no—
251C2×C8—181no—
252C2×C8—181no—
253C2×C8—362no—
254C4⋊C4—21no—
255C4⋊C4—31no—
256C4⋊C4D3×Dic311yescharacteristic
257C22⋊C4—61no—
258C42—21no—
259C42C2×D3211yescharacteristic
260C22×C3—21no—
261C22×C3—62no—
262C22×C3—121no—
263C22×C3—121no—
264C22×C3C4×#6711yescharacteristic
265C22×C3D4×Dic311yescharacteristic
266C2×D3—22no—
267C2×D3—41no—
268C2×D3—41no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—41no—
276C3×C4—42no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—81no—
282C3×C4—121no—
283C3×C4D3×M1611yescharacteristic
284C3×C4#90711yescharacteristic
285C3×C4#91411yescharacteristic
286C3×C4#91511yescharacteristic
287C3×C4C2×#20811yescharacteristic
288C3×C4#94211yescharacteristic
289C3×C4#94811yescharacteristic
290C3×C4#94911yescharacteristic
291Dic3—41no—
292C32#158511yescharacteristic, complemented, Sylow
293C23—61no—
294Q8—21no—
295Q8—21no—
296D4—32no—
297D4—61no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—61no—
301C2×C4—121no—
302C2×C4—121no—
303C2×C4C2×D3×Dic311yescharacteristic
304C2×C4#380411yescharacteristic
305C2×C4D3×#6711yescharacteristic
306C8—61no—
307C8—61no—
308C8—61no—
309C8—61no—
310C8—121no—
311C8—182no—
312C8—361no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—122no—
317C2×C3#501111yescharacteristic
318C2×C3#502611yescharacteristic
319C2×C3#512711yescharacteristic
320C2×C3#514411yescharacteristic
321C2×C3#516411yescharacteristic
322C2×C3#519611yescharacteristic
323D3—42no—
324C22—62no—
325C22—121no—
326C22—121no—
327C22Dic3×#6711yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—121no—
332C4D3×#20811yescharacteristic
333C4#6381511yescharacteristic
334C4#6393911yescharacteristic
335C4#6394611yescharacteristic
336C3—21no—
337C3#7089711yescharacteristic, complemented
338C3#7095411yescharacteristic, complemented
339C2—122no—
340C2#1059114711yescharacteristic
341C2#1059156611yescharacteristic
342C2#1059167311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C4×D4
prime radicalC2×C3×D12C2×C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1585
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5024C2semidirect
4. #10589401C2semidirect
5. #10589099C2semidirect
7. #10589079C2semidirect
28. #5024D3semidirect
292. C32#1585semidirect
337. C3#70897semidirect
338. C3#70954semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2152
C3×#50242
C3⋊C8×D122
#105894012
#105890992
#105890802
#105890792
#709543
#708973