Finite Group Databasebeta

← #11874417

Subgroups — #11874417

Order 1152.

1692 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic, complemented
2#10596303C212yesmaximal, complemented
3C2×#64159C212yesmaximal, complemented
4C2×#64113C211yesmaximal, characteristic, complemented
5#10592889C212yesmaximal, complemented
6#10592875C212yesmaximal, complemented
7#10592866C212yesmaximal, complemented
8#10592853C212yesmaximal, complemented
9C2×#63642C211yesmaximal, characteristic, complemented
10#83904—34nomaximal
11C2×C32×#41C2212yes—
12C2×#3828C2212yes—
13C32×#135—24no—
14C2×C32×Q16C2211yescharacteristic
15C2×C32×SD16C2212yes—
16C2×C32×D8C2211yescharacteristic
17C22×C32×C8C2211yescharacteristic
18#64159—28no—
19#64156C2212yes—
20#64153C2212yes—
21C2×#3756C2212yes—
22C2×#3755C2212yes—
23#64149C2212yes—
24#64148—24no—
25#64145C2212yes—
26C2×#3754C2212yes—
27C2×#3753C2212yes—
28C4×#638—24no—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C22×C3⋊(C3⋊C8)C2211yescharacteristic
31C2×#3746C2211yescharacteristic
32#64113—24no—
33C2×#3745C2211yescharacteristic
34C2×#3744C2212yes—
35#63642C2212yes—
36#63642C2212yes—
37C2×C3×#135D314yescomplemented
38#5832—38no—
39C2×#950—38no—
40C2×#904—34no—
41#5190—38no—
42#5176—38no—
43#5167—38no—
44#5154—38no—
45C2×#815—34no—
46C32×#41—24no—
47C32×#41—24no—
48C2×C32×Q8C2312yes—
49C2×C32×D4—22no—
50C2×C32×D4C2312yes—
51C22×C32×C4—22no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—22no—
54C2×#638—24no—
55C22×C3⋊Dic3D412yes—
56#3828—24no—
57#3828—24no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—22no—
60C2×#634C2312yes—
61C32×Q16—22no—
62C32×SD16—24no—
63C32×D8—22no—
64C2×C32×C8D414yescomplemented
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2311yescharacteristic
67#3757—24no—
68#3756—24no—
69#3755—24no—
70#3754—24no—
71#3753—24no—
72#3752—24no—
73#3750—24no—
74C4×C3⋊Dic3D412yes—
75C4×C3⋊Dic3C2312yes—
76C2×C3⋊(C3⋊C8)D414yescomplemented
77C2×C3⋊(C3⋊C8)C2312yes—
78#3746—22no—
79#3745—22no—
80#3744—24no—
81#3150—91noSylow
82C2×C3×#41C2×D318yes—
83C2×#235—38no—
84C3×#135—216no—
85C2×C3×Q16C2×D314yes—
86C2×C3×SD16C2×D318yes—
87C2×C3×D8C2×D314yes—
88C22×C3×C8C2×D314yes—
89#950—632no—
90#947—38no—
91#944—38no—
92C2×#216—38no—
93C2×#215—38no—
94#940—38no—
95#939—616no—
96#936—38no—
97C2×#214—38no—
98C2×#213—38no—
99C4×#67—616no—
100C2×C4×Dic3—34no—
101C22×C3⋊C8—34no—
102C2×Dic12—34no—
103#904—616no—
104C2×D24—34no—
105C2×#204—38no—
106#815—38no—
107#815—38no—
108C23×C32—22no—
109C23×C32C2×D411yescharacteristic
110C22×C3⋊D3—22no—
111C32×Q8—22no—
112C32×Q8—22no—
113C32×D4—22no—
114C32×D4—22no—
115C32×D4—44no—
116C2×C32×C4—22no—
117C2×C32×C4—44no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2411yescharacteristic
122#638—48no—
123#638—44no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—42no—
126C2×C3⋊Dic3C2×D414yes—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4×C3⋊D3—44no—
130#634—22no—
131#634—22no—
132C32×C8C2×D412yes—
133C32×C8C2×D412yes—
134C3⋊(C3⋊C8)C2×D414yes—
135C2×#135—92no—
136C2×#135—91no—
137C2×#135C3⋊D311yescharacteristic, complemented
138#532—92no—
139#497—92no—
140#497—92no—
141#496—92no—
142#496—92no—
143C2×#97—91no—
144C3×#41—216no—
145C3×#41—216no—
146C2×C3×Q8C22×D318yes—
147C2×C3×D4—28no—
148C2×C3×D4C22×D318yes—
149C22×C3×C4—28no—
150C22×C3×C4C22×D314yes—
151C2×#67—616no—
152C2×#67—68no—
153C22×Dic3—38no—
154#235—616no—
155#235—616no—
156C2×D12—38no—
157C2×C4×D3—68no—
158C2×Dic6—38no—
159C3×Q16—28no—
160C3×SD16—216no—
161C3×D8—28no—
162C2×C3×C8#67116yescomplemented
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165#217—616no—
166#216—616no—
167#215—616no—
168#214—616no—
169#213—616no—
170(C2×D3)⋊C4—616no—
171Dic3⋊C4—616no—
172C4×Dic3—38no—
173C4×Dic3—38no—
174C2×C3⋊C8—316no—
175C2×C3⋊C8—38no—
176Dic12—68no—
177D24—68no—
178#204—616no—
179C22×C32—22no—
180C22×C32—42no—
181C22×C32—44no—
182C22×C32#12712yes—
183C22×C32C22×D411yescharacteristic
184C2×C3⋊D3—42no—
185C2×C3⋊D3—44no—
186C32×C4—42no—
187C32×C4#12712yes—
188C32×C4C22×D411yescharacteristic
189C32×C4C22×D411yescharacteristic
190C3⋊Dic3—24no—
191C3⋊Dic3—42no—
192C2×#41—92no—
193C2×#41C2×C3⋊D312yes—
194#135—24no—
195#135—188no—
196#135—184no—
197C2×Q16—92no—
198C2×Q16—91no—
199C2×Q16C2×C3⋊D311yescharacteristic
200C2×SD16—92no—
201C2×SD16—92no—
202C2×SD16—92no—
203C2×SD16C2×C3⋊D312yes—
204C2×D8—92no—
205C2×D8—91no—
206C2×D8C2×C3⋊D311yescharacteristic
207C22×C8—91no—
208C22×C8C2×C3⋊D311yescharacteristic
209C4⋊Q8—92no—
210#127—92no—
211#124—92no—
212#124—92no—
213#121—184no—
214C4×D4—184no—
215C2×C42—91no—
216#97—92no—
217#97—92no—
218C23×C3—28no—
219C23×C3D3×D414yes—
220C22×D3—68no—
221C3×Q8—28no—
222C3×Q8—28no—
223C3×D4—28no—
224C3×D4—28no—
225C3×D4—416no—
226C2×C3×C4—28no—
227C2×C3×C4—416no—
228C2×C3×C4D3×D418yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4C2×#6718yes—
231C2×C3×C4C23×D314yes—
232#67—1232no—
233#67—1216no—
234C2×Dic3—316no—
235C2×Dic3—68no—
236C2×Dic3—128no—
237D12—68no—
238D12—68no—
239C4×D3—1216no—
240Dic6—68no—
241Dic6—68no—
242C3×C8C2×#6718yes—
243C3×C8C2×#6718yes—
244C3⋊C8—316no—
245C2×C32—22no—
246C2×C32—82no—
247C2×C32C2×#12711yescharacteristic
248C2×C32#57512yes—
249C3⋊D3—82no—
250#41—24no—
251#41—24no—
252#41—184no—
253#41—184no—
254C2×Q8—92no—
255C2×Q8C22×C3⋊D312yes—
256C2×D4—22no—
257C2×D4—92no—
258C2×D4—184no—
259C2×D4—182no—
260C2×D4C22×C3⋊D312yes—
261C22×C4—22no—
262C22×C4—92no—
263C22×C4—182no—
264C22×C4C22×C3⋊D311yescharacteristic
265Q16—22no—
266Q16—184no—
267Q16—182no—
268SD16—24no—
269SD16—184no—
270SD16—184no—
271SD16—184no—
272D8—22no—
273D8—184no—
274D8—182no—
275C2×C8—92no—
276C2×C8—94no—
277C2×C8#63814yescomplemented
278C2×C8C22×C3⋊D311yescharacteristic
279C2×C8C22×C3⋊D311yescharacteristic
280C4⋊C4—184no—
281C22⋊C4—184no—
282C22⋊C4—184no—
283C42—92no—
284C42—92no—
285C22×C3—28no—
286C22×C3—416no—
287C22×C3—48no—
288C22×C3#94018yes—
289C22×C3C2×D3×D414yes—
290C2×D3—1216no—
291C2×D3—128no—
292C3×C4—48no—
293C3×C4#94018yes—
294C3×C4C2×D3×D414yes—
295C3×C4C22×#6714yes—
296Dic3—616no—
297Dic3—128no—
298C32#315011yescharacteristic, complemented, Sylow
299C23—22no—
300C23—182no—
301C23D4×C3⋊D311yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—182no—
305Q8—182no—
306D4—22no—
307D4—22no—
308D4—44no—
309D4—182no—
310D4—182no—
311D4—368no—
312D4—364no—
313C2×C4—22no—
314C2×C4—44no—
315C2×C4—94no—
316C2×C4—182no—
317C2×C4—362no—
318C2×C4—364no—
319C2×C4D4×C3⋊D312yes—
320C2×C4D4×C3⋊D311yescharacteristic
321C2×C4C2×#63812yes—
322C2×C4C23×C3⋊D311yescharacteristic
323C8—94no—
324C8C2×#63812yes—
325C8C2×#63812yes—
326C2×C3—28no—
327C2×C3—88no—
328C2×C3#576818yes—
329C2×C3C2×#94014yes—
330D3—248no—
331C22—22no—
332C22—44no—
333C22—42no—
334C22—364no—
335C22—362no—
336C22#6414912yes—
337C22C2×D4×C3⋊D311yescharacteristic
338C4—42no—
339C4—184no—
340C4—362no—
341C4#6414912yes—
342C4C2×D4×C3⋊D311yescharacteristic
343C4C22×#63811yescharacteristic
344C3#8390414yescomplemented
345C2—22no—
346C2—82no—
347C2—722no—
348C2#1059623912yes—
349C2C2×#6414911yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×#135C3⋊D3
hypocenterC32#3150
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. #10596303C2semidirect
3. C2×#64159C2semidirect
4. C2×#64113C2semidirect
5. #10592889C2semidirect
6. #10592875C2semidirect
7. #10592866C2semidirect
8. #10592853C2semidirect
9. C2×#63642C2semidirect
37. C2×C3×#135D3semidirect
64. C2×C32×C8D4semidirect
76. C2×C3⋊(C3⋊C8)D4semidirect
137. C2×#135C3⋊D3semidirect
162. C2×C3×C8#67semidirect
277. C2×C8#638semidirect
298. C32#3150semidirect
344. C3#83904semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1352
#105963032
C2×#641592
C2×#641132
#105928892
#105928752
#105928662
#105928532
C2×#636422
#839043