Finite Group Databasebeta

← #11791128

Subgroups — #11791128

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×C32×#97C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic
4C2×#63645C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6#10592638C211yesmaximal, characteristic
7#10592628C211yesmaximal, characteristic, complemented
8#69826—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3752—22no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3744—22no—
18C2×#3744—22no—
19C2×#3744C414yescomplemented
20C32×#97—22no—
21#63658—22no—
22#63648—22no—
23#63645—22no—
24#63643—22no—
25C22×#204—34no—
26C2×C3×#97D314yescomplemented
27C2×#821—34no—
28C2×#818—34no—
29C2×#816—34no—
30#4939—34no—
31#4929—34no—
32C23×C3⋊D3—21no—
33C22×C32×C4D412yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)C2×C412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8C2×C412yes—
53C2×C32×C8D412yes—
54C2×C32×C8D412yes—
55C2×C32×C8D412yes—
56C32×C42—21no—
57C32×C42—21no—
58#3752—44no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63#3744—28no—
64#1973—91noSylow
65C22×D12—34no—
66C22×Dic6—34no—
67C22×C3×C8C2×D314yes—
68C22×C3×C8C2×D314yes—
69C2×C3×C42C2×D314yes—
70C2×(C2×D3)⋊C4—68no—
71C2×C4⋊Dic3—34no—
72C2×C4⋊Dic3—34no—
73C2×#204—316no—
74C2×#204—68no—
75C2×#204—68no—
76C3×#97—28no—
77C3⋊#95—68no—
78#821—68no—
79#818—68no—
80#816—68no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—41no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3—42no—
86C22×C3⋊D3—42no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3—42no—
103C4⋊(C3⋊D3)—22no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107#634—22no—
108#634—22no—
109#634—41no—
110#634—41no—
111C32×C8—22no—
112C32×C8C22⋊C414yescomplemented
113C22×SD16—91no—
114C2×#107—91no—
115C2×#103—91no—
116C2×#102—91no—
117C2×#97C3⋊D311yescharacteristic, complemented
118#391—91no—
119#390—91no—
120C23×D3—64no—
121C22×C3×C4D1218yes—
122C22×C3×C4C22×D314yes—
123C22×Dic3—64no—
124C22×Dic3—64no—
125C22×Dic3—64no—
126C2×D12—38no—
127C2×D12—64no—
128C2×D12—64no—
129C2×D12—64no—
130C2×D12—64no—
131C2×D12—64no—
132C2×Dic6—38no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C2×Dic6—64no—
137C2×Dic6—64no—
138C2×C3×C8—24no—
139C2×C3×C8—24no—
140C2×C3×C8C4×D318yes—
141C2×C3×C8D1218yes—
142C2×C3×C8D1218yes—
143C2×C3×C8#6718yes—
144C3×C42—24no—
145C3×C42—24no—
146(C2×D3)⋊C4—1216no—
147C4⋊Dic3—64no—
148C4⋊Dic3—64no—
149C4⋊Dic3—64no—
150C4⋊Dic3—64no—
151#204—632no—
152C22×C32C4×D411yescharacteristic
153C22×C32#12111yescharacteristic
154C22×C32#12711yescharacteristic
155C22×C32AGL(1,ℤ/8)12yes—
156C22×C32#13712yes—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—44no—
159C2×C3⋊D3—82no—
160C2×C3⋊D3—81no—
161C2×C3⋊D3—81no—
162C32×C4—42no—
163C32×C4C2×C22⋊C411yescharacteristic
164C32×C4C4×D411yescharacteristic
165C32×C4#12111yescharacteristic
166C32×C4#12411yescharacteristic
167C3⋊Dic3—42no—
168C3⋊Dic3—81no—
169C3⋊Dic3—81no—
170C22×Q8—91no—
171C22×D4—91no—
172C2×SD16—94no—
173C2×SD16—182no—
174C2×SD16—182no—
175C22×C8C2×C3⋊D311yescharacteristic
176C22×C8C2×C3⋊D311yescharacteristic
177C2×C4⋊C4—91no—
178C2×C4⋊C4—91no—
179C2×C22⋊C4—182no—
180C2×C42C2×C3⋊D311yescharacteristic
181#107—182no—
182#103—182no—
183#102—182no—
184#97—22no—
185#95—182no—
186C23×C3C2×D1214yes—
187C22×D3—68no—
188C22×D3—124no—
189C22×D3—128no—
190C22×D3—128no—
191C22×D3—124no—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4—28no—
195C2×C3×C4C2×C4×D314yes—
196C2×C3×C4C2×D1214yes—
197C2×C3×C4C2×D1214yes—
198C2×C3×C4#23514yes—
199C2×C3×C4#23514yes—
200C2×C3×C4C2×#6714yes—
201C2×Dic3—68no—
202C2×Dic3—124no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3—124no—
206C2×Dic3—128no—
207C2×Dic3—128no—
208D12—68no—
209D12—68no—
210D12—124no—
211D12—124no—
212Dic6—68no—
213Dic6—68no—
214Dic6—124no—
215Dic6—124no—
216C3×C8—28no—
217C3×C8(C2×D3)⋊C4116yescomplemented
218C2×C32#39011yescharacteristic
219C2×C32#44012yes—
220C2×C32#46812yes—
221C2×C32#49611yescharacteristic
222C2×C32#49711yescharacteristic
223C3⋊D3—82no—
224C24—181no—
225C2×Q8—92no—
226C2×Q8—181no—
227C2×Q8—181no—
228C2×Q8—181no—
229C2×Q8—181no—
230C2×Q8—181no—
231C2×D4—92no—
232C2×D4—181no—
233C2×D4—181no—
234C2×D4—181no—
235C2×D4—181no—
236C2×D4—181no—
237C22×C4—181no—
238C22×C4—181no—
239C22×C4—181no—
240C22×C4C4⋊(C3⋊D3)12yes—
241C22×C4C22×C3⋊D311yescharacteristic
242SD16—188no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8C4×C3⋊D312yes—
246C2×C8C4⋊(C3⋊D3)12yes—
247C2×C8C4⋊(C3⋊D3)12yes—
248C2×C8#63812yes—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C22⋊C4—364no—
254C42—21no—
255C42—21no—
256C22×C3C4×D1214yes—
257C22×C3#87414yes—
258C22×C3#90818yes—
259C22×C3#90918yes—
260C22×C3#93014yes—
261C2×D3—128no—
262C2×D3—1216no—
263C2×D3—248no—
264C2×D3—244no—
265C2×D3—244no—
266C3×C4—48no—
267C3×C4C4×D1214yes—
268C3×C4#87514yes—
269C3×C4C2×(C2×D3)⋊C414yes—
270C3×C4#93014yes—
271Dic3—128no—
272Dic3—244no—
273Dic3—244no—
274C32#197311yescharacteristic, complemented, Sylow
275C23—182no—
276C23—361no—
277C23—362no—
278C23—362no—
279C23—361no—
280C23C2×C4⋊(C3⋊D3)11yescharacteristic
281Q8—182no—
282Q8—182no—
283Q8—361no—
284Q8—361no—
285D4—182no—
286D4—182no—
287D4—361no—
288D4—361no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—182no—
293C2×C4—361no—
294C2×C4—361no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4—362no—
298C2×C4—362no—
299C2×C4C2×C4×C3⋊D311yescharacteristic
300C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
301C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
302C2×C4#382811yescharacteristic
303C2×C4#382811yescharacteristic
304C2×C4C2×#63811yescharacteristic
305C8—22no—
306C8#375214yescomplemented
307C2×C3#471018yes—
308C2×C3#471214yes—
309C2×C3#471514yes—
310C2×C3#493914yes—
311C2×C3#513418yes—
312D3—248no—
313C22—362no—
314C22—364no—
315C22—722no—
316C22—721no—
317C22—721no—
318C22C4×C4⋊(C3⋊D3)11yescharacteristic
319C22#6408311yescharacteristic
320C22#6411712yes—
321C22#6411812yes—
322C22#6413911yescharacteristic
323C4—42no—
324C4—362no—
325C4—721no—
326C4—721no—
327C4C4×C4⋊(C3⋊D3)11yescharacteristic
328C4#6408411yescharacteristic
329C4C2×#375211yescharacteristic
330C4#6413911yescharacteristic
331C3#6982614yescomplemented
332C2—722no—
333C2#1059240912yes—
334C2#1059241111yescharacteristic
335C2#1059241411yescharacteristic
336C2#1059263811yescharacteristic
337C2#1059283312yes—
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#97C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×#97C3⋊D3
hypocenterC32#1973
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×C32×#97C2semidirect
4. C2×#63645C2semidirect
5. C2×#63643C2semidirect
7. #10592628C2semidirect
19. C2×#3744C4semidirect
26. C2×C3×#97D3semidirect
112. C32×C8C22⋊C4semidirect
117. C2×#97C3⋊D3semidirect
217. C3×C8(C2×D3)⋊C4semidirect
274. C32#1973semidirect
306. C8#3752semidirect
331. C3#69826semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C32×#972
C2×#636482
C2×#636452
C2×#636432
#105926382
#105926282
#698263