Finite Group Databasebeta

← #11789794

Subgroups — #11789794

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×C8C211yesmaximal, characteristic, complemented
2C2×#63648C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic
4#10592638C211yesmaximal, characteristic
5#10592627C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589417C211yesmaximal, characteristic, complemented
8#69768—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3752—21no—
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750—21no—
19C32×C4×C8—22no—
20#63658—21no—
21#63648—22no—
22#63648C414yescomplemented
23C2×C3×C4×C8D314yescomplemented
24C2×#821—34no—
25C2×#821—34no—
26#4939—34no—
27#4928—34no—
28#4551—34no—
29#4551—34no—
30C23×C3⋊D3—21no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×C4⋊(C3⋊D3)—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)C2×C412yes—
43C2×C32×C8—21no—
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C2×C32×C8C2×C412yes—
48C2×C32×C8D412yes—
49C32×C42—21no—
50C32×C42—21no—
51#3752—42no—
52#3752—42no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)C2×C412yes—
59#3750—42no—
60#1934—91noSylow
61C22×D12—34no—
62C22×C3×C8C2×D314yes—
63C22×C3×C8C2×D314yes—
64C2×C3×C42C2×D314yes—
65C2×(C2×D3)⋊C4—64no—
66C2×(C2×D3)⋊C4—64no—
67C2×C4⋊Dic3—34no—
68C2×C4⋊Dic3—34no—
69C2×C4⋊Dic3—34no—
70C2×Dic3⋊C4—64no—
71C3×C4×C8—28no—
72C3⋊#95—64no—
73#821—316no—
74#821—68no—
75C23×C32C2×D411yescharacteristic
76C22×C3⋊D3—22no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3—41no—
80C22×C3⋊D3—41no—
81C22×C3⋊D3—41no—
82C22×C3⋊D3—41no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4D812yes—
88C2×C32×C4SD1612yes—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C32×C4#4111yescharacteristic
92C2×C32×C4#4111yescharacteristic
93C2×C32×C4#4111yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—22no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C32×C8—22no—
109C32×C8—22no—
110C2×#102—91no—
111C2×#102—91no—
112C2×C4×C8C3⋊D311yescharacteristic, complemented
113#390—91no—
114#389—91no—
115#340—91no—
116#340—91no—
117C23×D3—64no—
118C22×C3×C4D1214yes—
119C22×C3×C4D1214yes—
120C22×C3×C4C22×D314yes—
121C22×Dic3—64no—
122C22×Dic3—64no—
123C22×Dic3—64no—
124C2×D12—38no—
125C2×D12—64no—
126C2×D12—64no—
127C2×D12—64no—
128C2×D12—64no—
129C2×D12—64no—
130C2×C3×C8—24no—
131C2×C3×C8—24no—
132C2×C3×C8—24no—
133C2×C3×C8—24no—
134C2×C3×C8C4×D318yes—
135C2×C3×C8#6718yes—
136C3×C42—24no—
137C3×C42—24no—
138(C2×D3)⋊C4—128no—
139(C2×D3)⋊C4—128no—
140C4⋊Dic3—38no—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143C4⋊Dic3—64no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146Dic3⋊C4—128no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12111yescharacteristic
149C22×C32#12411yescharacteristic
150C22×C32C2×D811yescharacteristic
151C22×C32C2×SD1611yescharacteristic
152C22×C32#13511yescharacteristic
153C22×C32#13511yescharacteristic
154C2×C3⋊D3—42no—
155C2×C3⋊D3—42no—
156C2×C3⋊D3—42no—
157C2×C3⋊D3—81no—
158C2×C3⋊D3—81no—
159C2×C3⋊D3—81no—
160C2×C3⋊D3—81no—
161C32×C4—22no—
162C32×C4—22no—
163C32×C4#11711yescharacteristic
164C32×C4C4×D411yescharacteristic
165C32×C4#12311yescharacteristic
166C32×C4#12611yescharacteristic
167C3⋊Dic3—42no—
168C3⋊Dic3—81no—
169C3⋊Dic3—81no—
170C22×D4—91no—
171C22×C8C2×C3⋊D311yescharacteristic
172C22×C8C2×C3⋊D311yescharacteristic
173C2×C4⋊C4—91no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—181no—
177C2×C22⋊C4—181no—
178C2×C22⋊C4—181no—
179C2×C42C2×C3⋊D311yescharacteristic
180#102—94no—
181#102—182no—
182C4×C8—22no—
183#95—181no—
184C23×C3C2×D1214yes—
185C22×D3—68no—
186C22×D3—124no—
187C22×D3—124no—
188C22×D3—124no—
189C22×D3—124no—
190C22×D3—124no—
191C22×D3—124no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4#20418yes—
197C2×C3×C4D2418yes—
198C2×C3×C4C2×C4×D314yes—
199C2×C3×C4#23514yes—
200C2×C3×C4#23514yes—
201C2×C3×C4#23514yes—
202C2×C3×C4#23514yes—
203C2×C3×C4C2×#6714yes—
204C2×Dic3—68no—
205C2×Dic3—124no—
206C2×Dic3—124no—
207C2×Dic3—124no—
208C2×Dic3—124no—
209C2×Dic3—124no—
210C2×Dic3—124no—
211C2×Dic3—124no—
212C2×Dic3—124no—
213D12—68no—
214D12—68no—
215D12—124no—
216D12—124no—
217C3×C8—28no—
218C3×C8—28no—
219C2×C32#38811yescharacteristic
220C2×C32C4×D811yescharacteristic
221C2×C32C4×SD1611yescharacteristic
222C2×C32#46511yescharacteristic
223C2×C32#46611yescharacteristic
224C2×C32#48611yescharacteristic
225C2×C32#48811yescharacteristic
226C3⋊D3—82no—
227C24—181no—
228C2×D4—92no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4—181no—
232C2×D4—181no—
233C2×D4—181no—
234C22×C4—181no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4C4⋊(C3⋊D3)11yescharacteristic
238C22×C4C4⋊(C3⋊D3)11yescharacteristic
239C22×C4C22×C3⋊D311yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8C4×C3⋊D312yes—
245C2×C8#63812yes—
246C4⋊C4—92no—
247C4⋊C4—181no—
248C4⋊C4—181no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—362no—
253C22⋊C4—362no—
254C22⋊C4—362no—
255C42—21no—
256C42—21no—
257C22×C3C4×D1214yes—
258C22×C3#87514yes—
259C22×C3C2×#20414yes—
260C22×C3C2×D2414yes—
261C22×C3#90414yes—
262C22×C3#90414yes—
263C22×C3#93014yes—
264C2×D3—128no—
265C2×D3—128no—
266C2×D3—128no—
267C2×D3—244no—
268C2×D3—244no—
269C2×D3—244no—
270C2×D3—244no—
271C3×C4—28no—
272C3×C4—28no—
273C3×C4#87214yes—
274C3×C4#87614yes—
275C3×C4C4×#6714yes—
276C3×C4#92914yes—
277Dic3—128no—
278Dic3—244no—
279Dic3—244no—
280C32#193411yescharacteristic, complemented, Sylow
281C23—182no—
282C23—361no—
283C23—361no—
284C23—361no—
285C23—361no—
286C23—361no—
287C23—361no—
288C23C2×C4⋊(C3⋊D3)11yescharacteristic
289D4—182no—
290D4—182no—
291D4—361no—
292D4—361no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—182no—
298C2×C4—361no—
299C2×C4—361no—
300C2×C4—361no—
301C2×C4—361no—
302C2×C4—361no—
303C2×C4—361no—
304C2×C4—361no—
305C2×C4—361no—
306C2×C4#374412yes—
307C2×C4#374512yes—
308C2×C4C2×C4×C3⋊D311yescharacteristic
309C2×C4#382811yescharacteristic
310C2×C4#382811yescharacteristic
311C2×C4#382811yescharacteristic
312C2×C4#382811yescharacteristic
313C2×C4C2×#63811yescharacteristic
314C8—22no—
315C8—22no—
316C2×C3C4×#20414yes—
317C2×C3C4×D2414yes—
318C2×C3#469414yes—
319C2×C3#469714yes—
320C2×C3#494014yes—
321C2×C3#511414yes—
322C2×C3#511514yes—
323D3—248no—
324C22—362no—
325C22—362no—
326C22—362no—
327C22—721no—
328C22—721no—
329C22—721no—
330C22—721no—
331C22C4×C4⋊(C3⋊D3)11yescharacteristic
332C22#6408411yescharacteristic
333C22C2×#374411yescharacteristic
334C22C2×#374511yescharacteristic
335C22#6411311yescharacteristic
336C22#6411311yescharacteristic
337C22#6413911yescharacteristic
338C4—22no—
339C4—22no—
340C4—362no—
341C4—721no—
342C4—721no—
343C4#6408111yescharacteristic
344C4#6408511yescharacteristic
345C4C4×#63811yescharacteristic
346C4#6413811yescharacteristic
347C3#6976814yescomplemented
348C2—722no—
349C2C4×#374411yescharacteristic
350C2C4×#374511yescharacteristic
351C2#1059239311yescharacteristic
352C2#1059239611yescharacteristic
353C2#1059263911yescharacteristic
354C2#1059281311yescharacteristic
355C2#1059281411yescharacteristic
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4×C8C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4×C8C3⋊D3
hypocenterC32#1934
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×C8C2semidirect
5. #10592627C2semidirect
6. #10589417C2semidirect
7. #10589417C2semidirect
22. #63648C4semidirect
23. C2×C3×C4×C8D3semidirect
112. C2×C4×C8C3⋊D3semidirect
280. C32#1934semidirect
347. C3#69768semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×C82
C2×#636482
#105926382
#105926272
#105894172
#697683