Finite Group Databasebeta

← C2×#10590916 #11861070

Subgroups — C2×#10590916 #11861070

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×#63814C212yesmaximal, complemented
3C2×#63646C211yesmaximal, characteristic, complemented
4C2×C3×#815C211yesmaximal, characteristic, complemented
5C2×#63569C212yesmaximal, complemented
6#10590916C218yesmaximal, direct product factor
7C2×#5197—31nomaximal
8C2×#4717—31nomaximal
9C2×C3×#235C2212yes—
10C22×C32×C8C2211yescharacteristic
11C2×#3748C2212yes—
12C2×C3×C4×Dic3C2211yescharacteristic
13C22×C3×C3⋊C8C2211yescharacteristic
14C2×C3×Dic12C411yescharacteristic, complemented
15C3×#904C414yescomplemented
16C3×#904C2214yes—
17C2×C3×D24C411yescharacteristic, complemented
18C2×C3×#204C412yescomplemented
19C2×#3711—22no—
20#63814—24no—
21#63814C2218yescomplemented
22C2×D3×C3⋊C8—22no—
23#63646C2214yescomplemented
24C3×#815C2214yescomplemented
25#63569C2218yescomplemented
26C2×C3×#135—31no—
27C2×#948—32no—
28C2×#904D311yescharacteristic
29C2×#901—32no—
30C2×C3×#97—31no—
31C2×#837—32no—
32#5197—38no—
33C2×#819—31no—
34C2×#819—31no—
35C2×#819—61no—
36C2×#815D311yescharacteristic, complemented
37C2×#805—32no—
38#4717—38no—
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—22no—
41C22×C3×Dic3—21no—
42C3×#235—22no—
43C3×#235—22no—
44C3×#235C2×C414yes—
45C3×#235C2314yes—
46C2×C3×D12C2×C412yes—
47C2×C3×C4×D3—22no—
48C2×C3×Dic6C2×C412yes—
49C2×C32×C8C2×C411yescharacteristic
50C2×C32×C8C2×C411yescharacteristic
51C2×C32×C8C2×C412yes—
52C2×C32×C8C2312yes—
53#3748—22no—
54#3748C2314yes—
55C2×C3⋊(C3⋊C8)—22no—
56C3×C4×Dic3—21no—
57C3×C4×Dic3C2312yes—
58C2×C3×C3⋊C8D412yes—
59C2×C3×C3⋊C8D412yes—
60C2×C3×C3⋊C8C2312yes—
61C3×Dic12C2×C414yescomplemented
62C3×D24C2×C414yescomplemented
63C3×#204C2×C418yescomplemented
64#3711—28no—
65D3×C3⋊C8—28no—
66C2×#444—91noSylow
67C2×C3×#41—32no—
68C2×#235C2×D312yes—
69C3×#135—34no—
70C3×#135—34no—
71C2×C3×Q16—31no—
72C2×C3×SD16—32no—
73C2×C3×D8—31no—
74C22×C3×C8—21no—
75C22×C3×C8—31no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C2×D311yescharacteristic
78C2×C3×C42—31no—
79#948—38no—
80#948—64no—
81C2×C4×Dic3C2×D311yescharacteristic
82C2×#208—32no—
83C2×#208—32no—
84C2×#208—62no—
85C2×#208—62no—
86C22×C3⋊C8—62no—
87C22×C3⋊C8C2×D311yescharacteristic
88C2×Dic12Dic311yescharacteristic, complemented
89#904Dic314yescomplemented
90#904C2×D314yes—
91C2×D24Dic311yescharacteristic, complemented
92C2×#204Dic312yescomplemented
93#901—38no—
94#901—64no—
95C2×ΓL(1,𝔽25)—62no—
96C2×D3×C8—62no—
97C3×#97—34no—
98#837—38no—
99#819—34no—
100#819—34no—
101#819—64no—
102#815C2×D314yescomplemented
103#805—38no—
104C23×C32#4111yescharacteristic
105C22×C3×D3—22no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4C2411yescharacteristic
112C3×#67—24no—
113C3×#67—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×D12C22×C414yes—
119C3×C4×D3—24no—
120C3×C4×D3—24no—
121C3×Dic6—22no—
122C3×Dic6C22×C414yes—
123C32×C8C22×C412yes—
124C32×C8C22×C412yes—
125C3⋊(C3⋊C8)—24no—
126C3×C3⋊C8C2×D414yes—
127C2×#135—31no—
128C2×#131—92no—
129#444—98no—
130C2×#108—91no—
131C2×#104—92no—
132C2×#97—31no—
133C3×#41—34no—
134C3×#41—34no—
135C3×#41—62no—
136C3×#41—62no—
137C2×C3×Q8—32no—
138C2×C3×D4—32no—
139C2×C3×D4—62no—
140C22×C3×C4—21no—
141C22×C3×C4—62no—
142C22×C3×C4—61no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—22no—
146C22×Dic3—21no—
147#235—22no—
148#235—22no—
149#235C2×Dic314yes—
150#235C22×D314yes—
151C2×D12C2×Dic312yes—
152C2×C4×D3—22no—
153C2×Dic6C2×Dic312yes—
154C3×Q16—34no—
155C3×SD16—38no—
156C3×D8—34no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—22no—
160C2×C3×C8—22no—
161C2×C3×C8—32no—
162C2×C3×C8—32no—
163C2×C3×C8—32no—
164C2×C3×C8C4×D311yescharacteristic
165C2×C3×C8C4×D311yescharacteristic
166C2×C3×C8C4×D312yes—
167C2×C3×C8C2×Dic311yescharacteristic
168C2×C3×C8C2×Dic311yescharacteristic
169C2×C3×C8C2×Dic312yes—
170C2×C3×C8C22×D312yes—
171C2×C3×C8C22×D312yes—
172C3×C42—32no—
173C3×C42—61no—
174C4×Dic3—21no—
175C4×Dic3C22×D312yes—
176#208—34no—
177#208—34no—
178#208—64no—
179#208—62no—
180#208—62no—
181#208—68no—
182#208—122no—
183C2×C3⋊C8—62no—
184C2×C3⋊C8—62no—
185C2×C3⋊C8—68no—
186C2×C3⋊C8—122no—
187C2×C3⋊C8D1212yes—
188C2×C3⋊C8D1212yes—
189C2×C3⋊C8C22×D312yes—
190Dic12C2×Dic314yescomplemented
191D24C2×Dic314yescomplemented
192#204C2×Dic318yescomplemented
193ΓL(1,𝔽25)—68no—
194D3×C8—68no—
195C22×C32—22no—
196C22×C32C4×D411yescharacteristic
197C22×C32C4×D411yescharacteristic
198C22×C32C2×#4111yescharacteristic
199C2×C3×D3—24no—
200C2×C3×D3—44no—
201C32×C4C4×D411yescharacteristic
202C32×C4C4×D411yescharacteristic
203C32×C4C23×C411yescharacteristic
204C32×C4C22×D411yescharacteristic
205C3×Dic3—24no—
206C3×Dic3—42no—
207C2×#41—32no—
208#135—34no—
209#135—34no—
210C2×Q16—31no—
211C2×SD16—32no—
212C2×D8—31no—
213#131—98no—
214#131—184no—
215C2×M16—92no—
216C2×M16—182no—
217C22×C8—31no—
218C22×C8—182no—
219C22×C8D3211yescharacteristic
220C2×C42—31no—
221#108—94no—
222#104—98no—
223#97—34no—
224C23×C3—21no—
225C23×C3—62no—
226C23×C3#23511yescharacteristic
227C23×C3#23711yescharacteristic
228C22×D3—22no—
229C3×Q8—34no—
230C3×Q8—62no—
231C3×D4—34no—
232C3×D4—64no—
233C3×D4—64no—
234C3×D4—62no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—62no—
242C2×C3×C4—64no—
243C2×C3×C4—64no—
244C2×C3×C4—62no—
245C2×C3×C4—122no—
246C2×C3×C4C2×C4×D311yescharacteristic
247C2×C3×C4C2×C4×D311yescharacteristic
248C2×C3×C4C2×D1211yescharacteristic
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4#23511yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4#23711yescharacteristic
254C2×C3×C4C22×Dic311yescharacteristic
255C2×C3×C4C22×Dic311yescharacteristic
256C2×C3×C4C23×D311yescharacteristic
257C2×C3×C4C23×D311yescharacteristic
258#67—24no—
259#67—24no—
260C2×Dic3—22no—
261C2×Dic3—22no—
262C2×Dic3—42no—
263D12—22no—
264D12C22×Dic314yes—
265C4×D3—24no—
266C4×D3—24no—
267Dic6—22no—
268Dic6C22×Dic314yes—
269C3×C8—22no—
270C3×C8—22no—
271C3×C8—34no—
272C3×C8C2×C4×D312yes—
273C3×C8C2×C4×D312yes—
274C3×C8C22×Dic312yes—
275C3×C8C22×Dic312yes—
276C3⋊C8—64no—
277C3⋊C8—64no—
278C3⋊C8—124no—
279C3⋊C8C2×D1214yes—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32#44412yescomplemented
283C2×C32C2×C4×D411yescharacteristic
284C3×D3—44no—
285#41—34no—
286#41—34no—
287#41—62no—
288#41—62no—
289C2×Q8—32no—
290C2×D4—32no—
291C2×D4—62no—
292C22×C4—62no—
293C22×C4—61no—
294C22×C4C2×D3211yescharacteristic
295Q16—34no—
296SD16—38no—
297D8—34no—
298M16—94no—
299M16—188no—
300M16—182no—
301C2×C8—32no—
302C2×C8—32no—
303C2×C8—32no—
304C2×C8—188no—
305C2×C8—182no—
306C2×C8D3×Dic311yescharacteristic
307C2×C8D3×Dic311yescharacteristic
308C2×C8D3×Dic312yes—
309C2×C8C2×D3212yes—
310C42—32no—
311C42—61no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—42no—
318C22×C3—64no—
319C22×C3—124no—
320C22×C3C4×D1211yescharacteristic
321C22×C3C4×D1211yescharacteristic
322C22×C3D4×Dic311yescharacteristic
323C22×C3D4×Dic311yescharacteristic
324C22×C3C2×#23511yescharacteristic
325C22×C3C2×#23711yescharacteristic
326C2×D3—24no—
327C2×D3—44no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—64no—
333C3×C4—122no—
334C3×C4C4×D1211yescharacteristic
335C3×C4C4×D1211yescharacteristic
336C3×C4D4×Dic311yescharacteristic
337C3×C4D4×Dic311yescharacteristic
338C3×C4C22×C4×D311yescharacteristic
339C3×C4C22×D1211yescharacteristic
340C3×C4C2×D3×D411yescharacteristic
341C3×C4C23×Dic311yescharacteristic
342Dic3—24no—
343Dic3—42no—
344C32C2×#44411yescharacteristic, complemented, Sylow
345C23—62no—
346C23#379511yescharacteristic
347Q8—34no—
348Q8—62no—
349D4—34no—
350D4—64no—
351D4—64no—
352D4—62no—
353C2×C4—62no—
354C2×C4—64no—
355C2×C4—64no—
356C2×C4—62no—
357C2×C4—122no—
358C2×C4#379511yescharacteristic
359C2×C4D3×D1211yescharacteristic
360C2×C4D3×D1211yescharacteristic
361C2×C4C2×D3×Dic311yescharacteristic
362C2×C4C2×D3×Dic311yescharacteristic
363C2×C4C22×D3211yescharacteristic
364C8—34no—
365C8—184no—
366C8C2×D3×Dic312yes—
367C8C2×D3×Dic312yes—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—22no—
374C2×C3—41no—
375C2×C3—41no—
376C2×C3—124no—
377C2×C3#471712yescomplemented
378C2×C3#519712yescomplemented
379C2×C3C2×C4×D1211yescharacteristic
380C2×C3C2×D4×Dic311yescharacteristic
381D3—44no—
382C22—22no—
383C22—64no—
384C22—124no—
385C22Dic3×D1211yescharacteristic
386C22Dic3×D1211yescharacteristic
387C22C2×#379511yescharacteristic
388C4—64no—
389C4—122no—
390C4Dic3×D1211yescharacteristic
391C4Dic3×D1211yescharacteristic
392C4C2×D3×D1211yescharacteristic
393C4C22×D3×Dic311yescharacteristic
394C3—21no—
395C3C2×#471711yescharacteristic, complemented
396C3C2×#519711yescharacteristic, complemented
397C2—21no—
398C2—21no—
399C2—124no—
400C2#1059091612yesdirect product factor
401C2C2×Dic3×D1211yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×C3×#904C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63814C2semidirect
3. C2×#63646C2semidirect
4. C2×C3×#815C2semidirect
5. C2×#63569C2semidirect
6. #10590916C2direct (N × H)
14. C2×C3×Dic12C4semidirect
15. C3×#904C4semidirect
17. C2×C3×D24C4semidirect
18. C2×C3×#204C4semidirect
21. #63814C22semidirect
23. #63646C22semidirect
24. C3×#815C22semidirect
25. #63569C22semidirect
36. C2×#815D3semidirect
61. C3×Dic12C2×C4semidirect
62. C3×D24C2×C4semidirect
63. C3×#204C2×C4semidirect
88. C2×Dic12Dic3semidirect
89. #904Dic3semidirect
91. C2×D24Dic3semidirect
92. C2×#204Dic3semidirect
102. #815C2×D3semidirect
190. Dic12C2×Dic3semidirect
191. D24C2×Dic3semidirect
192. #204C2×Dic3semidirect
282. C2×C32#444semidirect
344. C32C2×#444semidirect
377. C2×C3#4717semidirect
378. C2×C3#5197semidirect
395. C3C2×#4717semidirect
396. C3C2×#5197semidirect
400. C2#10590916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×#638142
C2×#636462
C2×C3×#8152
C2×#635692
#105909162
C2×#51973
C2×#47173