Finite Group Databasebeta

← #11791092

Subgroups — #11791092

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic, complemented
5C2×#63635C211yesmaximal, characteristic, complemented
6#10592638C211yesmaximal, characteristic, complemented
7C2×#63630C211yesmaximal, characteristic, complemented
8#69648—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4—22no—
13C2×C32×C42C2211yescharacteristic
14C2×#3753—22no—
15C2×#3753—22no—
16C2×#3753C414yescomplemented
17C2×#3752—22no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21#63659—22no—
22#63636—22no—
23#63635—22no—
24#63630—22no—
25C22×#213—34no—
26C3×#390D314yescomplemented
27C2×#832—34no—
28C2×#809—34no—
29C2×#808—34no—
30#4939—34no—
31C2×#803—34no—
32C24×C32—21no—
33C23×C3⋊D3—21no—
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4C2×C412yes—
40C22×C32×C4—21no—
41C22×C32×C4D412yes—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C22⋊C4—44no—
53C32×C42—21no—
54C32×C42—21no—
55#3753—28no—
56#3752—44no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)C2×C412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63C2×C3⋊(C3⋊C8)D412yes—
64C2×C3⋊(C3⋊C8)D412yes—
65#1972—91noSylow
66C22×C3×D4C2×D314yes—
67C22×D12—34no—
68C2×C3×C4⋊C4C2×D314yes—
69C2×C3×C22⋊C4—28no—
70C2×C3×C42C2×D314yes—
71C2×#213—316no—
72C2×#213—68no—
73C2×#213—68no—
74C2×(C2×D3)⋊C4—68no—
75C2×C4⋊Dic3—34no—
76C22×C3⋊C8—34no—
77C22×C3⋊C8—34no—
78#832—68no—
79#809—68no—
80#808—68no—
81#803—68no—
82C23×C32—22no—
83C23×C32—41no—
84C23×C32—41no—
85C23×C32—42no—
86C23×C32—42no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—42no—
92C22×C3⋊D3—42no—
93C32×D4—22no—
94C32×D4—22no—
95C32×D4—41no—
96C32×D4—41no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4—42no—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—42no—
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C3⋊(C3⋊C8)—22no—
115C3⋊(C3⋊C8)C22⋊C414yescomplemented
116C22×D8—91no—
117C2×#106—91no—
118C2×#102—91no—
119C2×#102—91no—
120C2×#97—91no—
121#390—91no—
122#390C3⋊D311yescharacteristic, complemented
123C24×C3—24no—
124C23×D3—64no—
125C2×C3×D4—24no—
126C2×C3×D4—24no—
127C2×C3×D4—24no—
128C2×C3×D4—24no—
129C2×C3×D4—24no—
130C2×C3×D4C4×D318yes—
131C22×C3×C4—24no—
132C22×C3×C4#6718yes—
133C22×C3×C4C22×D314yes—
134C22×Dic3—64no—
135C2×D12—38no—
136C2×D12—64no—
137C2×D12—64no—
138C2×D12—64no—
139C2×D12—64no—
140C2×D12—64no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143C3×C22⋊C4—416no—
144C3×C42—24no—
145C3×C42—24no—
146#213—632no—
147(C2×D3)⋊C4—1216no—
148C4⋊Dic3—64no—
149C4⋊Dic3—64no—
150C2×C3⋊C8—38no—
151C2×C3⋊C8—38no—
152C2×C3⋊C8—38no—
153C2×C3⋊C8—38no—
154C2×C3⋊C8—64no—
155C2×C3⋊C8—64no—
156C22×C32—42no—
157C22×C32—44no—
158C22×C32—82no—
159C22×C32—81no—
160C22×C32—81no—
161C22×C32C4×D411yescharacteristic
162C22×C32#12111yescharacteristic
163C22×C32#12711yescharacteristic
164C22×C32AGL(1,ℤ/8)12yes—
165C22×C32AGL(1,ℤ/8)12yes—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—44no—
168C2×C3⋊D3—82no—
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C32×C4—42no—
172C32×C4—81no—
173C32×C4C2×C22⋊C411yescharacteristic
174C32×C4C4×D411yescharacteristic
175C32×C4#12111yescharacteristic
176C32×C4#12411yescharacteristic
177C3⋊Dic3—81no—
178C22×D4—91no—
179C22×D4C2×C3⋊D311yescharacteristic
180C2×D8—94no—
181C2×D8—182no—
182C2×D8—182no—
183C22×C8—91no—
184C22×C8—91no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4C2×C3⋊D311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—182no—
189C2×C42C2×C3⋊D311yescharacteristic
190#106—182no—
191#102—182no—
192#102—182no—
193#97—182no—
194C23×C3—28no—
195C23×C3—48no—
196C23×C3—44no—
197C23×C3—44no—
198C23×C3—48no—
199C23×C3C2×#6714yes—
200C22×D3—68no—
201C22×D3—128no—
202C22×D3—124no—
203C22×D3—124no—
204C22×D3—128no—
205C3×D4—28no—
206C3×D4—28no—
207C3×D4—44no—
208C3×D4—44no—
209C2×C3×C4—28no—
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4—48no—
213C2×C3×C4—44no—
214C2×C3×C4C2×C4×D314yes—
215C2×C3×C4#23514yes—
216C2×C3×C4D3×D414yes—
217C2×C3×C4D3×D414yes—
218C2×C3×C4D3×D414yes—
219C2×C3×C4#23714yes—
220C2×Dic3—124no—
221C2×Dic3—128no—
222D12—68no—
223D12—68no—
224D12—124no—
225D12—124no—
226C3⋊C8—316no—
227C3⋊C8—68no—
228C2×C32—82no—
229C2×C32#39011yescharacteristic
230C2×C32#44212yes—
231C2×C32#46912yes—
232C2×C32#49611yescharacteristic
233C2×C32#49611yescharacteristic
234C3⋊D3—82no—
235C24—21no—
236C24—181no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—92no—
243C2×D4—181no—
244C2×D4—181no—
245C2×D4—181no—
246C2×D4—181no—
247C2×D4—181no—
248C2×D4C4×C3⋊D312yes—
249C22×C4—21no—
250C22×C4—181no—
251C22×C4#63812yes—
252C22×C4C22×C3⋊D311yescharacteristic
253D8—188no—
254C2×C8—92no—
255C2×C8—92no—
256C2×C8—92no—
257C2×C8—92no—
258C2×C8—181no—
259C2×C8—181no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C22⋊C4—44no—
265C22⋊C4—364no—
266C42—21no—
267C42—21no—
268C22×C3—48no—
269C22×C3—416no—
270C22×C3—88no—
271C22×C3—84no—
272C22×C3—84no—
273C22×C3C4×#6714yes—
274C22×C3#93218yes—
275C22×C3#93914yes—
276C22×C3#94014yes—
277C22×C3#94918yes—
278C2×D3—128no—
279C2×D3—1216no—
280C2×D3—248no—
281C2×D3—244no—
282C2×D3—244no—
283C3×C4—48no—
284C3×C4—84no—
285C3×C4D3×C22⋊C414yes—
286C3×C4#67⋊C414yes—
287C3×C4#88414yes—
288C3×C4#88514yes—
289Dic3—244no—
290C32#197211yescharacteristic, complemented, Sylow
291C23—22no—
292C23—42no—
293C23—41no—
294C23—41no—
295C23—42no—
296C23—182no—
297C23—362no—
298C23—361no—
299C23—361no—
300C23—362no—
301C23C2×#63811yescharacteristic
302D4—22no—
303D4—22no—
304D4—41no—
305D4—41no—
306D4—182no—
307D4—182no—
308D4—361no—
309D4—361no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—361no—
316C2×C4—362no—
317C2×C4C2×C4×C3⋊D311yescharacteristic
318C2×C4#382811yescharacteristic
319C2×C4D4×C3⋊D311yescharacteristic
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4D4×C3⋊D311yescharacteristic
322C2×C4#383011yescharacteristic
323C8—94no—
324C8—182no—
325C2×C3—88no—
326C2×C3#495714yes—
327C2×C3#501418yes—
328C2×C3#503918yes—
329C2×C3#505814yes—
330C2×C3#507414yes—
331D3—248no—
332C22—42no—
333C22—44no—
334C22—81no—
335C22—82no—
336C22—81no—
337C22—362no—
338C22—364no—
339C22—721no—
340C22—722no—
341C22—721no—
342C22C4×#63811yescharacteristic
343C22#6414112yes—
344C22#6414811yescharacteristic
345C22#6414911yescharacteristic
346C22#6415812yes—
347C4—42no—
348C4—81no—
349C4—721no—
350C4C22⋊C4×C3⋊D311yescharacteristic
351C4#6409011yescharacteristic
352C4#6409311yescharacteristic
353C4#6409411yescharacteristic
354C3#6964814yescomplemented
355C2—82no—
356C2—722no—
357C2#1059265611yescharacteristic
358C2#1059271312yes—
359C2#1059273812yes—
360C2#1059275711yescharacteristic
361C2#1059277311yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×#3753C2
cosocleC22×C32×C4C23
hypercenter#390C3⋊D3
hypocenterC32#1972
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C32×#390C2semidirect
3. C2×#63659C2semidirect
4. C2×#63636C2semidirect
5. C2×#63635C2semidirect
6. #10592638C2semidirect
7. C2×#63630C2semidirect
16. C2×#3753C4semidirect
26. C3×#390D3semidirect
115. C3⋊(C3⋊C8)C22⋊C4semidirect
122. #390C3⋊D3semidirect
290. C32#1972semidirect
354. C3#69648semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C32×#3902
C2×#636592
C2×#636362
C2×#636352
#105926382
C2×#636302
#696483