Finite Group Databasebeta

← C2×#10592452 #11864862

Subgroups — C2×#10592452 #11864862

Order 1152.

2184 conjugacy classes of subgroups; only the 313 normal subgroups are shown.

normal subgroups only

This group has 2184 conjugacy classes of subgroups — too many to draw. Only its 313 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C2×#64156C211yesmaximal, characteristic, complemented
3C2×#64117C212yesmaximal, complemented
4C2×C32×#101C211yesmaximal, characteristic, complemented
5C2×#63652C212yesmaximal, complemented
6#10592452C218yesmaximal, direct product factor
7C2×#4753—34nomaximal
8C22×C32×Q8C2211yescharacteristic
9#64364—22no—
10#64364—24no—
11#64364C2214yescomplemented
12C2×#3832—22no—
13C2×Q8×C3⋊D3—22no—
14C2×#3828—22no—
15C2×#3828C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×M16C2212yes—
18#64156—22no—
19#64156C2214yescomplemented
20C2×#3752—22no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64117—24no—
23#64117C2218yescomplemented
24C2×#3745—22no—
25C2×#3744—22no—
26C32×#101C2214yescomplemented
27#63652C2218yescomplemented
28C2×#1007—34no—
29C2×#947—34no—
30C2×#908—38no—
31C2×C3×#101D314yescomplemented
32C2×#825—38no—
33#4753—332no—
34C23×C3⋊D3—21no—
35C2×C32×Q8—22no—
36C2×C32×Q8—22no—
37C2×C32×Q8D412yes—
38C2×C32×Q8C2312yes—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—22no—
42C22×C3⋊Dic3—21no—
43#3832—28no—
44#3832—28no—
45Q8×C3⋊D3—28no—
46Q8×C3⋊D3—28no—
47#3828—28no—
48#3828—28no—
49#3828—22no—
50#3828—22no—
51#3828D414yes—
52#3828C2314yes—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)D412yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—24no—
60C2×C4×C3⋊D3—22no—
61C2×#634—22no—
62C2×#634D412yes—
63C32×M16—22no—
64C32×M16C2314yes—
65C2×C32×C8—22no—
66#3752—28no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3C2312yes—
69#3745—28no—
70#3744—28no—
71C2×#454—91noSylow
72C22×C3×Q8C2×D314yes—
73#1007—316no—
74#1007—616no—
75#1007—68no—
76C2×#239—68no—
77C2×D3×Q8—68no—
78C2×#235—38no—
79C2×#235—68no—
80C22×D12—34no—
81C2×C3×M16C2×D318yes—
82#947—316no—
83#947—68no—
84C2×(C2×D3)⋊C4—68no—
85C2×C4×Dic3—34no—
86#908—332no—
87#908—616no—
88C2×D24—68no—
89C2×#204—68no—
90C3×#101C2×D3116yescomplemented
91#825—332no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—44no—
96C22×C3⋊D3—41no—
97C22×C3⋊D3—41no—
98C32×Q8—24no—
99C32×Q8—24no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4C2×D414yes—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D412yes—
105C2×C32×C4C2×D412yes—
106C2×C32×C4C2411yescharacteristic
107#638—24no—
108#638—24no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—42no—
112C4⋊(C3⋊D3)—28no—
113C4⋊(C3⋊D3)—22no—
114C4⋊(C3⋊D3)—24no—
115C4⋊(C3⋊D3)—42no—
116C4⋊(C3⋊D3)C2×D414yes—
117C4×C3⋊D3—216no—
118C4×C3⋊D3—24no—
119C4×C3⋊D3—24no—
120#634—28no—
121#634—22no—
122#634C2×D414yes—
123C32×C8—24no—
124C2×2−1+4—91no—
125C2×AGL(1,ℤ/8)—92no—
126C2×#124—91no—
127#454—98no—
128C2×#104—92no—
129C2×#101C3⋊D311yescharacteristic, complemented
130C23×D3—64no—
131C2×C3×Q8—28no—
132C2×C3×Q8—28no—
133C2×C3×Q8D1218yes—
134C2×C3×Q8C22×D318yes—
135C22×C3×C4D1218yes—
136C22×C3×C4C22×D314yes—
137C2×#67—68no—
138C22×Dic3—64no—
139#239—632no—
140#239—632no—
141D3×Q8—632no—
142D3×Q8—632no—
143#235—316no—
144#235—316no—
145#235—632no—
146#235—68no—
147#235—632no—
148#235—68no—
149C2×D12—38no—
150C2×D12—38no—
151C2×D12—68no—
152C2×D12—68no—
153C2×D12—68no—
154C2×D12—64no—
155C2×C4×D3—616no—
156C2×C4×D3—68no—
157C2×Dic6—38no—
158C2×Dic6—68no—
159C3×M16—28no—
160C3×M16C22×D3116yes—
161C2×C3×C8—28no—
162(C2×D3)⋊C4—632no—
163C4×Dic3—38no—
164C4×Dic3—64no—
165D24—632no—
166#204—632no—
167C22×C32—22no—
168C22×C32#12011yescharacteristic
169C22×C32#12011yescharacteristic
170C22×C32C22×D411yescharacteristic
171C2×C3⋊D3—24no—
172C2×C3⋊D3—44no—
173C2×C3⋊D3—44no—
174C2×C3⋊D3—42no—
175C2×C3⋊D3—82no—
176C2×C3⋊D3—82no—
177C32×C4—24no—
178C32×C4#12012yes—
179C32×C4C22×D412yes—
180C3⋊Dic3—24no—
181C3⋊Dic3—42no—
1822−1+4—94no—
1832−1+4—184no—
1842−1+4—182no—
185C2×#41—92no—
186C2×#41—182no—
187C2×#41—182no—
188C22×Q8—182no—
189C22×Q8C2×C3⋊D311yescharacteristic
190C22×D4—91no—
191AGL(1,ℤ/8)—98no—
192AGL(1,ℤ/8)—184no—
193C2×SD16—182no—
194C2×D8—182no—
195C2×M16C2×C3⋊D312yes—
196#124—94no—
197#124—182no—
198C2×C22⋊C4—182no—
199C2×C42—91no—
200#104—98no—
201#101C2×C3⋊D314yescomplemented
202C23×C3C2×D1214yes—
203C22×D3—68no—
204C22×D3—68no—
205C22×D3—1216no—
206C22×D3—124no—
207C22×D3—124no—
208C3×Q8—216no—
209C3×Q8—216no—
210C2×C3×C4—28no—
211C2×C3×C4—28no—
212C2×C3×C4C2×D12116yes—
213C2×C3×C4C2×D1214yes—
214C2×C3×C4D3×D418yes—
215C2×C3×C4D3×D418yes—
216C2×C3×C4C23×D314yes—
217#67—616no—
218#67—616no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—128no—
222D12—316no—
223D12—632no—
224D12—68no—
225D12—616no—
226D12—128no—
227C4×D3—664no—
228C4×D3—616no—
229C4×D3—616no—
230Dic6—316no—
231Dic6—632no—
232Dic6—68no—
233C3×C8—216no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32#45412yescomplemented
237C2×C32C2×#12011yescharacteristic
238C3⋊D3—44no—
239C3⋊D3—82no—
240C24—181no—
241#41—94no—
242#41—94no—
243#41—188no—
244#41—188no—
245#41—188no—
246#41—182no—
247#41—188no—
248#41—182no—
249C2×Q8—22no—
250C2×Q8—22no—
251C2×Q8—92no—
252C2×Q8—182no—
253C2×Q8—188no—
254C2×Q8—188no—
255C2×Q8C4⋊(C3⋊D3)12yes—
256C2×Q8C22×C3⋊D312yes—
257C2×D4—92no—
258C2×D4—92no—
259C2×D4—182no—
260C2×D4—182no—
261C2×D4—181no—
262C2×D4—182no—
263C2×D4—182no—
264C22×C4—184no—
265C22×C4—182no—
266C22×C4—181no—
267C22×C4C4⋊(C3⋊D3)12yes—
268C22×C4C22×C3⋊D311yescharacteristic
269SD16—188no—
270D8—188no—
271M16—22no—
272M16C22×C3⋊D314yes—
273C2×C8—22no—
274C22⋊C4—188no—
275C42—92no—
276C42—181no—
277C22×C3—28no—
278C22×C3#88214yes—
279C22×C3#88214yes—
280C22×C3C22×D1214yes—
281C2×D3—616no—
282C2×D3—1216no—
283C2×D3—1216no—
284C2×D3—128no—
285C2×D3—248no—
286C2×D3—248no—
287C3×C4—216no—
288C3×C4#88218yes—
289C3×C4C2×D3×D418yes—
290Dic3—616no—
291Dic3—128no—
292C32C2×#45411yescharacteristic, complemented, Sylow
293C23—182no—
294C23—182no—
295C23—364no—
296C23—361no—
297C23—361no—
298C23C2×C4⋊(C3⋊D3)11yescharacteristic
299Q8—24no—
300Q8—24no—
301Q8—94no—
302Q8—188no—
303Q8—182no—
304D4—94no—
305D4—188no—
306D4—184no—
307D4—184no—
308D4—182no—
309D4—184no—
310D4—362no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—1816no—
314C2×C4—182no—
315C2×C4—184no—
316C2×C4—184no—
317C2×C4—182no—
318C2×C4—362no—
319C2×C4C2×C4⋊(C3⋊D3)14yes—
320C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
321C2×C4D4×C3⋊D312yes—
322C2×C4D4×C3⋊D312yes—
323C2×C4C23×C3⋊D311yescharacteristic
324C8—24no—
325C2×C3—24no—
326C2×C3—24no—
327C2×C3#475318yescomplemented
328C2×C3C2×#88214yes—
329D3—1216no—
330D3—248no—
331C22—22no—
332C22—184no—
333C22—364no—
334C22—364no—
335C22—362no—
336C22—722no—
337C22—722no—
338C22#6409111yescharacteristic
339C22#6409111yescharacteristic
340C22C22×C4⋊(C3⋊D3)11yescharacteristic
341C4—24no—
342C4—184no—
343C4—362no—
344C4#6409112yes—
345C4C2×D4×C3⋊D312yes—
346C3C2×#475314yescomplemented
347C2—21no—
348C2—21no—
349C2—364no—
350C2—722no—
351C2#1059245212yesdirect product factor
352C2C2×#6409111yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#101C2
socleC22×C32#120
hypercenterC2×#101C3⋊D3
hypocenterC32C2×#454
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#64364C2semidirect
2. C2×#64156C2semidirect
3. C2×#64117C2semidirect
4. C2×C32×#101C2semidirect
5. C2×#63652C2semidirect
6. #10592452C2direct (N × H)
11. #64364C22semidirect
19. #64156C22semidirect
23. #64117C22semidirect
26. C32×#101C22semidirect
27. #63652C22semidirect
31. C2×C3×#101D3semidirect
90. C3×#101C2×D3semidirect
129. C2×#101C3⋊D3semidirect
201. #101C2×C3⋊D3semidirect
236. C2×C32#454semidirect
292. C32C2×#454semidirect
327. C2×C3#4753semidirect
346. C3C2×#4753semidirect
351. C2#10592452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643642
C2×#641562
C2×#641172
C2×C32×#1012
C2×#636522
#105924522
C2×#47533