Finite Group Databasebeta

← C2×#10592734 #11869413

Subgroups — C2×#10592734 #11869413

Order 1152.

1404 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C2×#64135C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5C2×#63657C211yesmaximal, characteristic, complemented
6#10592734C218yesmaximal, direct product factor
7C2×#63635C211yesmaximal, characteristic, complemented
8C2×#63634C211yesmaximal, characteristic, complemented
9C2×#5035—34nomaximal
10C22×C32×D4—21no—
11C22×C32×D4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C32×#121—22no—
14C32×#121C2214yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4—21no—
17C2×#3757—21no—
18#64135—22no—
19#64135C2214yescomplemented
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3—21no—
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#63659C2214yescomplemented
26#63659C2214yescomplemented
27#63657C2214yescomplemented
28#63635C2214yescomplemented
29#63634C2214yescomplemented
30C2×C3×#121D314yes—
31C2×#926—34no—
32C2×#832—34no—
33C2×#832—34no—
34C2×#830—34no—
35#5035—332no—
36C2×#808—34no—
37C2×#807—34no—
38C24×C32—21no—
39C24×C32D411yescharacteristic
40C2×C32×D4—24no—
41C2×C32×D4—21no—
42C2×C32×D4—22no—
43C2×C32×D4—22no—
44C2×C32×D4—44no—
45C2×C32×D4C2312yes—
46C22×C32×C4—22no—
47C22×C32×C4—22no—
48C22×C32×C4—21no—
49C22×C32×C4D411yescharacteristic
50C22×C32×C4D412yes—
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3⋊Dic3—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2312yes—
57C32×C22⋊C4—24no—
58#3757—24no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2312yes—
62C4⋊(C3⋊Dic3)C2312yes—
63C4×C3⋊Dic3—24no—
64C2×C3⋊(C3⋊C8)—22no—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C2×C3⋊(C3⋊C8)C2312yes—
68C2×#482—91noSylow
69C22×C3×D4—24no—
70C22×C3×D4C2×D314yes—
71C23×C3×C4C2×D314yes—
72C3×#121—28no—
73C3×#121C2×D3116yes—
74C2×C3×C4⋊C4C2×D314yes—
75C2×C3×C22⋊C4—24no—
76C2×#217—64no—
77#926—316no—
78#926—68no—
79C2×C4⋊Dic3—34no—
80C2×C4⋊Dic3—34no—
81C2×C4×Dic3—64no—
82C22×C3⋊C8—34no—
83C22×C3⋊C8—34no—
84#832—316no—
85#832—316no—
86#830—316no—
87#808—316no—
88#807—316no—
89C23×C32—22no—
90C23×C32—22no—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32—42no—
94C23×C32—42no—
95C23×C32—42no—
96C23×C32C2×D412yes—
97C23×C32C2×D411yescharacteristic
98C32×D4—22no—
99C32×D4—22no—
100C32×D4—48no—
101C32×D4—42no—
102C2×C32×C4—22no—
103C2×C32×C4—24no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—42no—
108C2×C32×C4C2×D412yes—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4112yes—
111C2×C32×C4#4112yes—
112C2×C32×C4C2411yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—42no—
116C2×C3⋊Dic3—42no—
117C3⋊(C3⋊C8)—22no—
118C3⋊(C3⋊C8)—22no—
119C2×#121C3⋊D311yescharacteristic
120C2×#117—91no—
121#482—98no—
122C2×#107—91no—
123C2×#106—91no—
124C2×#102—91no—
125C2×#102—91no—
126C2×C22⋊C8—91no—
127C24×C3—24no—
128C24×C3#6714yes—
129C2×C3×D4—216no—
130C2×C3×D4—28no—
131C2×C3×D4—28no—
132C2×C3×D4—24no—
133C2×C3×D4—416no—
134C2×C3×D4C22×D318yes—
135C22×C3×C4—28no—
136C22×C3×C4—28no—
137C22×C3×C4—24no—
138C22×C3×C4#6714yes—
139C22×C3×C4#6718yes—
140C22×C3×C4C22×D318yes—
141C22×C3×C4C22×D314yes—
142C22×Dic3—64no—
143C22×Dic3—64no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4C22×D318yes—
146C3×C22⋊C4—216no—
147#217—616no—
148C4⋊Dic3—38no—
149C4⋊Dic3—38no—
150C4⋊Dic3—64no—
151C4⋊Dic3—64no—
152C4×Dic3—616no—
153C2×C3⋊C8—38no—
154C2×C3⋊C8—38no—
155C2×C3⋊C8—68no—
156C2×C3⋊C8—68no—
157C22×C32—22no—
158C22×C32—22no—
159C22×C32—22no—
160C22×C32—44no—
161C22×C32—42no—
162C22×C32—42no—
163C22×C32—42no—
164C22×C32—84no—
165C22×C32#12312yes—
166C22×C32#13512yes—
167C22×C32AGL(1,ℤ/8)12yes—
168C22×C32C22×D411yescharacteristic
169C32×C4—22no—
170C32×C4—42no—
171C32×C4#12312yes—
172C32×C4C2×#4111yescharacteristic
173C32×C4C2×#4111yescharacteristic
174C3⋊Dic3—42no—
175C3⋊Dic3—42no—
176C22×D4—21no—
177C22×D4C2×C3⋊D311yescharacteristic
178C23×C4C2×C3⋊D311yescharacteristic
179C22×C8—91no—
180C22×C8—91no—
181#121—22no—
182#121C2×C3⋊D314yes—
183#117—94no—
184#117—182no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4C2×C3⋊D311yescharacteristic
188C2×C22⋊C4—21no—
189C2×C22⋊C4—181no—
190C2×C42—181no—
191#107—94no—
192#106—94no—
193#102—94no—
194#102—94no—
195C22⋊C8—94no—
196C23×C3—28no—
197C23×C3—28no—
198C23×C3—28no—
199C23×C3—28no—
200C23×C3—48no—
201C23×C3—48no—
202C23×C3—48no—
203C23×C3C2×#6718yes—
204C23×C3C2×#6714yes—
205C3×D4—28no—
206C3×D4—28no—
207C3×D4—432no—
208C3×D4—48no—
209C2×C3×C4—28no—
210C2×C3×C4—216no—
211C2×C3×C4—28no—
212C2×C3×C4—28no—
213C2×C3×C4—28no—
214C2×C3×C4—48no—
215C2×C3×C4#23718yes—
216C2×C3×C4#23718yes—
217C2×C3×C4C2×#6718yes—
218C2×C3×C4C2×#6714yes—
219C2×C3×C4C23×D314yes—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—128no—
223C2×Dic3—128no—
224C3⋊C8—68no—
225C3⋊C8—68no—
226C2×C32—42no—
227C2×C32—82no—
228C2×C32#48214yescomplemented
229C2×C32C2×#12311yescharacteristic
230C2×C32C2×#13511yescharacteristic
231C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
232C24—21no—
233C24#63811yescharacteristic
234C2×D4—24no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—21no—
238C2×D4—44no—
239C2×D4C22×C3⋊D312yes—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—181no—
244C22×C4—181no—
245C22×C4#63812yes—
246C22×C4#63811yescharacteristic
247C22×C4C22×C3⋊D312yes—
248C22×C4C22×C3⋊D311yescharacteristic
249C2×C8—92no—
250C2×C8—92no—
251C2×C8—182no—
252C2×C8—182no—
253C4⋊C4—21no—
254C4⋊C4—92no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4C22×C3⋊D312yes—
259C22⋊C4—24no—
260C22⋊C4—184no—
261C42—184no—
262C22×C3—28no—
263C22×C3—28no—
264C22×C3—28no—
265C22×C3—416no—
266C22×C3—48no—
267C22×C3—48no—
268C22×C3—48no—
269C22×C3—816no—
270C22×C3#93218yes—
271C22×C3#93518yes—
272C22×C3#95018yes—
273C22×C3C22×#6714yes—
274C3×C4—28no—
275C3×C4—48no—
276C3×C4#93518yes—
277C3×C4C2×#23714yes—
278C3×C4C2×#23714yes—
279Dic3—128no—
280Dic3—128no—
281C32C2×#48211yescharacteristic, complemented, Sylow
282C23—22no—
283C23—22no—
284C23—22no—
285C23—22no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23C2×#63812yes—
290C23C2×#63811yescharacteristic
291D4—22no—
292D4—22no—
293D4—48no—
294D4—42no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—24no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—182no—
302C2×C4—182no—
303C2×C4—362no—
304C2×C4—362no—
305C2×C4#383012yes—
306C2×C4#383012yes—
307C2×C4C2×#63812yes—
308C2×C4C2×#63811yescharacteristic
309C2×C4C23×C3⋊D311yescharacteristic
310C8—182no—
311C8—182no—
312C2×C3—48no—
313C2×C3—88no—
314C2×C3#5035116yescomplemented
315C2×C3C2×#93214yes—
316C2×C3C2×#93514yes—
317C2×C3C2×#95014yes—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—44no—
322C22—42no—
323C22—42no—
324C22—42no—
325C22—84no—
326C22#6414112yes—
327C22#6414412yes—
328C22#6415912yes—
329C22C22×#63811yescharacteristic
330C4—22no—
331C4—42no—
332C4—362no—
333C4—362no—
334C4#6414412yes—
335C4C2×#383011yescharacteristic
336C4C2×#383011yescharacteristic
337C3C2×#503514yescomplemented
338C2—42no—
339C2—82no—
340C2#1059273414yesdirect product factor
341C2C2×#6414111yescharacteristic
342C2C2×#6414411yescharacteristic
343C2C2×#6415911yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C2×D4
hypercenterC2×#121C3⋊D3
hypocenterC32C2×#482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#64135C2semidirect
3. C2×#63659C2semidirect
4. C2×#63659C2semidirect
5. C2×#63657C2semidirect
6. #10592734C2direct (N × H)
7. C2×#63635C2semidirect
8. C2×#63634C2semidirect
19. #64135C22semidirect
25. #63659C22semidirect
26. #63659C22semidirect
27. #63657C22semidirect
28. #63635C22semidirect
29. #63634C22semidirect
228. C2×C32#482semidirect
281. C32C2×#482semidirect
314. C2×C3#5035semidirect
337. C3C2×#5035semidirect
340. C2#10592734direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×#641352
C2×#636592
C2×#636572
#105927342
C2×#636352
C2×#636342
C2×#50353