Finite Group Databasebeta

← #11787009

Subgroups — #11787009

Order 1152.

810 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic
3#10592932C211yesmaximal, characteristic
4C2×#63649C211yesmaximal, characteristic, complemented
5#10592818C211yesmaximal, characteristic, complemented
6#10589390C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#70376—34nomaximal
9C2×C32×#41C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64157—22no—
13#64157—22no—
14#64135C2211yescharacteristic
15C2×#3748—21no—
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)—21no—
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C32×#104—22no—
21#63662C411yescharacteristic, complemented
22#63662C411yescharacteristic, complemented
23#63659C411yescharacteristic, complemented
24#63659C411yescharacteristic, complemented
25#63649—22no—
26#63641—21no—
27#63641—21no—
28C2×#948—34no—
29C2×C3×#104D314yes—
30#5233—34no—
31C2×#822—34no—
32#5119—34no—
33#4524—34no—
34#4523—34no—
35C32×#41—21no—
36C32×#41—21no—
37C32×#41D412yes—
38C32×#41Q812yes—
39C2×C32×Q8C2×C411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4C2×C411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C32×M16—21no—
46C32×M16—21no—
47C2×C32×C8—21no—
48C32×C42—21no—
49C32×C42—21no—
50#3757—21no—
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52C4⋊(C3⋊Dic3)C2×C411yescharacteristic
53C4×C3⋊Dic3—21no—
54#3748—24no—
55#3748—21no—
56#3748D412yes—
57C2×C3⋊(C3⋊C8)—24no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
64C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
65C2×C3⋊(C3⋊C8)D411yescharacteristic
66C2×C3⋊(C3⋊C8)D411yescharacteristic
67#1866—91noSylow
68C2×C3×#41C2×D314yes—
69C2×C3×M16C2×D314yes—
70C2×C3×C42C2×D314yes—
71#948—68no—
72#948—68no—
73#926—34no—
74C2×#208—34no—
75C2×#208—64no—
76C22×C3⋊C8—34no—
77C22×C3⋊C8—34no—
78C22×C3⋊C8—64no—
79C3×#104—28no—
80#835—34no—
81#835—34no—
82#832—34no—
83#832—34no—
84#822—68no—
85Dic3⋊C8—64no—
86Dic3⋊C8—64no—
87C23×C32—21no—
88C23×C32#4111yescharacteristic
89C32×Q8—21no—
90C32×Q8C4⋊C412yes—
91C32×D4—22no—
92C32×D4—22no—
93C32×D4—21no—
94C32×D4C4⋊C412yes—
95C2×C32×C4—21no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×Q811yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109C32×C8—41no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—21no—
112C3⋊(C3⋊C8)—21no—
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)—21no—
115C2×#131—91no—
116C2×#108—91no—
117#424—91no—
118C2×#104C3⋊D311yescharacteristic
119#416—91no—
120#339—91no—
121#336—91no—
122C3×#41—24no—
123C3×#41—24no—
124C3×#41Dic618yes—
125C3×#41#6718yes—
126C2×C3×Q8C4×D314yes—
127C2×C3×D4—24no—
128C2×C3×D4C4×D314yes—
129C22×C3×C4—24no—
130C22×C3×C4—24no—
131C22×C3×C4C22×D314yes—
132C3×M16—24no—
133C3×M16—24no—
134C2×C3×C8—24no—
135C3×C42—24no—
136C3×C42—24no—
137#217—64no—
138C4⋊Dic3—34no—
139C4⋊Dic3—34no—
140C4×Dic3—64no—
141#208—38no—
142#208—616no—
143#208—64no—
144C2×C3⋊C8—34no—
145C2×C3⋊C8—34no—
146C2×C3⋊C8—34no—
147C2×C3⋊C8—34no—
148C2×C3⋊C8—616no—
149C2×C3⋊C8—64no—
150C2×C3⋊C8—64no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—64no—
153C2×C3⋊C8—64no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32—22no—
157C22×C32—41no—
158C22×C32—41no—
159C22×C32C4×D411yescharacteristic
160C22×C32C22⋊Q811yescharacteristic
161C22×C32#12311yescharacteristic
162C32×C4—22no—
163C32×C4—42no—
164C32×C4C2×C4⋊C411yescharacteristic
165C32×C4C4×D411yescharacteristic
166C32×C4#12011yescharacteristic
167C32×C4C22⋊Q811yescharacteristic
168C3⋊Dic3—41no—
169C3⋊Dic3—41no—
170C2×#41C2×C3⋊D311yescharacteristic
171#131—182no—
172#131—182no—
173C2×M16—91no—
174C2×M16—181no—
175C2×M16C2×C3⋊D311yescharacteristic
176C22×C8—91no—
177C22×C8—91no—
178C22×C8—181no—
179#117—91no—
180C2×C42C2×C3⋊D311yescharacteristic
181#108—182no—
182C4⋊C8—181no—
183C4⋊C8—181no—
184#104—22no—
185#103—91no—
186#103—91no—
187#102—91no—
188#102—91no—
189C23×C3—24no—
190C23×C3#23714yes—
191C3×Q8—24no—
192C3×Q8Dic3⋊C418yes—
193C3×D4—28no—
194C3×D4—28no—
195C3×D4—24no—
196C3×D4Dic3⋊C418yes—
197C2×C3×C4—24no—
198C2×C3×C4—28no—
199C2×C3×C4—28no—
200C2×C3×C4—28no—
201C2×C3×C4—44no—
202C2×C3×C4—44no—
203C2×C3×C4C2×Dic614yes—
204C2×C3×C4C2×C4×D314yes—
205C2×C3×C4D3×D414yes—
206C2×C3×C4D3×D414yes—
207C2×C3×C4#23714yes—
208C2×C3×C4C2×#6714yes—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C3×C8—44no—
212C3⋊C8—64no—
213C3⋊C8—64no—
214C3⋊C8—64no—
215C3⋊C8—64no—
216C3⋊C8—68no—
217C2×C32—21no—
218C2×C32—21no—
219C2×C32—42no—
220C2×C32#38511yescharacteristic
221C2×C32#44311yescharacteristic
222C2×C32#44411yescharacteristic
223#41—21no—
224#41—21no—
225#41#63412yes—
226#41#63812yes—
227C2×Q8C4×C3⋊D311yescharacteristic
228C2×D4—21no—
229C2×D4C4×C3⋊D311yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22×C3⋊D311yescharacteristic
233M16—21no—
234M16—21no—
235M16—92no—
236M16—184no—
237M16—181no—
238C2×C8—21no—
239C2×C8—91no—
240C2×C8—91no—
241C2×C8—91no—
242C2×C8—91no—
243C2×C8—184no—
244C2×C8—181no—
245C2×C8—181no—
246C2×C8—181no—
247C2×C8—181no—
248C2×C8—181no—
249C4⋊C4—91no—
250C4⋊C4—91no—
251C22⋊C4—181no—
252C42—21no—
253C42—21no—
254C42—181no—
255C22×C3—24no—
256C22×C3—24no—
257C22×C3—28no—
258C22×C3—44no—
259C22×C3—44no—
260C22×C3#87814yes—
261C22×C3#67⋊C414yes—
262C22×C3#93514yes—
263C3×C4—28no—
264C3×C4—48no—
265C3×C4#87814yes—
266C3×C4#67⋊C414yes—
267C3×C4C2×Dic3⋊C414yes—
268C3×C4#93714yes—
269Dic3—124no—
270Dic3—124no—
271C32#186611yescharacteristic, complemented, Sylow
272C23—21no—
273C23#383011yescharacteristic
274Q8—21no—
275Q8#375012yes—
276D4—22no—
277D4—22no—
278D4—21no—
279D4#375012yes—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4C2×#63411yescharacteristic
289C2×C4C2×C4×C3⋊D311yescharacteristic
290C2×C4D4×C3⋊D311yescharacteristic
291C2×C4D4×C3⋊D311yescharacteristic
292C2×C4#383011yescharacteristic
293C2×C4C2×#63811yescharacteristic
294C8—41no—
295C8—181no—
296C8—181no—
297C8—181no—
298C8—181no—
299C8—182no—
300C2×C3—24no—
301C2×C3—24no—
302C2×C3—48no—
303C2×C3#482314yes—
304C2×C3#482414yes—
305C2×C3#494614yes—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—41no—
310C22—41no—
311C22#6408711yescharacteristic
312C22#6409011yescharacteristic
313C22#6414411yescharacteristic
314C4—22no—
315C4—42no—
316C4—361no—
317C4—361no—
318C4#6408711yescharacteristic
319C4#6409011yescharacteristic
320C4C2×#375011yescharacteristic
321C4#6414611yescharacteristic
322C3#7037614yescomplemented
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1059252211yescharacteristic
327C2#1059252311yescharacteristic
328C2#1059264511yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#104C2
socleC22×C32C4×D4
prime radicalC2×C32×#41C22
cosocleC22×C32×C4C23
hypercenterC2×#104C3⋊D3
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
4. C2×#63649C2semidirect
5. #10592818C2semidirect
6. #10589390C2semidirect
7. #10589389C2semidirect
21. #63662C4semidirect
22. #63662C4semidirect
23. #63659C4semidirect
24. #63659C4semidirect
271. C32#1866semidirect
322. C3#70376semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C32×#1042
#105929322
C2×#636492
#105928182
#105893902
#105893892
#703763