Finite Group Databasebeta

← C2×#10590920 #11861069

Subgroups — C2×#10590920 #11861069

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2C2×#63815C212yesmaximal, complemented
3C2×#63642C211yesmaximal, characteristic, complemented
4C2×C3×#819C211yesmaximal, characteristic, complemented
5C2×#63568C212yesmaximal, complemented
6#10590920C218yesmaximal, direct product factor
7C2×#5197—31nomaximal
8C2×#4894—31nomaximal
9C2×C3×#235C2212yes—
10C22×C32×C8C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#208C2212yes—
14C2×C3×Dic12C411yescharacteristic, complemented
15C3×#904C414yescomplemented
16C3×#904C2214yes—
17C2×C3×D24C411yescharacteristic, complemented
18C2×C3×#204C412yescomplemented
19C2×#3711—22no—
20#63815—24no—
21#63815C2218yescomplemented
22C2×D3×C3⋊C8—22no—
23#63642C2214yescomplemented
24C3×#819C2214yescomplemented
25#63568C2218yescomplemented
26C2×C3×#135—31no—
27C2×#948—32no—
28C2×#907—32no—
29C2×#904D311yescharacteristic
30C2×C3×#108—31no—
31C2×#837—32no—
32#5197—38no—
33C2×#825—32no—
34C2×#819D311yescharacteristic, complemented
35C2×#815—31no—
36C2×#815—31no—
37C2×#815—61no—
38#4894—38no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
41C2×C3×#67—22no—
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—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3C2312yes—
55C2×C3⋊(C3⋊C8)D412yes—
56C2×C3⋊(C3⋊C8)D412yes—
57C2×C3⋊(C3⋊C8)C2312yes—
58C3×#208—22no—
59C3×#208C2314yes—
60C2×C3×C3⋊C8—22no—
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—
74C2×C3×M16—32no—
75C22×C3×C8—21no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C2×D311yescharacteristic
78#948—38no—
79#948—64no—
80C2×C4×Dic3—31no—
81C2×C4×Dic3—31no—
82C2×C4×Dic3—61no—
83C2×#208—62no—
84C2×#208C2×D312yes—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—31no—
87C22×C3⋊C8—61no—
88C22×C3⋊C8—62no—
89#907—38no—
90#907—64no—
91C2×Dic12Dic311yescharacteristic, complemented
92#904Dic314yescomplemented
93#904C2×D314yes—
94C2×D24Dic311yescharacteristic, complemented
95C2×#204Dic312yescomplemented
96C2×ΓL(1,𝔽25)—62no—
97C2×D3×C8—62no—
98C3×#108—34no—
99#837—38no—
100#825—38no—
101#819C2×D314yescomplemented
102#815—34no—
103#815—34no—
104#815—64no—
105C23×C32#4111yescharacteristic
106C22×C3×D3—22no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4C2411yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C3×#67—24no—
116C3×#67—24no—
117C2×C3×Dic3—22no—
118C3×D12—22no—
119C3×D12C22×C414yes—
120C3×C4×D3—24no—
121C3×C4×D3—24no—
122C3×Dic6—22no—
123C3×Dic6C22×C414yes—
124C32×C8C22×C412yes—
125C32×C8C22×C412yes—
126C3⋊(C3⋊C8)C2×D414yes—
127C3×C3⋊C8—24no—
128C2×#135—31no—
129C2×#131—92no—
130#444—98no—
131C2×#108—31no—
132C2×#104—92no—
133C2×#97—91no—
134C3×#41—34no—
135C3×#41—34no—
136C3×#41—62no—
137C3×#41—62no—
138C2×C3×Q8—32no—
139C2×C3×D4—32no—
140C2×C3×D4—62no—
141C22×C3×C4—21no—
142C22×C3×C4—62no—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—22no—
146C22×Dic3—62no—
147C22×Dic3—61no—
148C22×Dic3—61no—
149#235—22no—
150#235—22no—
151#235C2×Dic314yes—
152#235C22×D314yes—
153C2×D12C2×Dic312yes—
154C2×C4×D3—22no—
155C2×Dic6C2×Dic312yes—
156C3×Q16—34no—
157C3×SD16—38no—
158C3×D8—34no—
159C3×M16—34no—
160C3×M16—62no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—22no—
164C2×C3×C8—22no—
165C2×C3×C8—62no—
166C2×C3×C8C4×D311yescharacteristic
167C2×C3×C8C4×D311yescharacteristic
168C2×C3×C8C4×D312yes—
169C2×C3×C8C2×Dic311yescharacteristic
170C2×C3×C8C2×Dic311yescharacteristic
171C2×C3×C8C2×Dic312yes—
172C2×C3×C8C22×D312yes—
173C2×C3×C8C22×D312yes—
174C4×Dic3—32no—
175C4×Dic3—32no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180#208—22no—
181#208—68no—
182#208C22×D314yes—
183C2×C3⋊C8—22no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—32no—
186C2×C3⋊C8—32no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—62no—
193C2×C3⋊C8—68no—
194Dic12C2×Dic314yescomplemented
195D24C2×Dic314yescomplemented
196#204C2×Dic318yescomplemented
197ΓL(1,𝔽25)—68no—
198D3×C8—68no—
199C22×C32—22no—
200C22×C32C4×D411yescharacteristic
201C22×C32C4×D411yescharacteristic
202C22×C32C2×#4111yescharacteristic
203C2×C3×D3—24no—
204C2×C3×D3—44no—
205C32×C4C4×D411yescharacteristic
206C32×C4C4×D411yescharacteristic
207C32×C4C23×C411yescharacteristic
208C32×C4C22×D411yescharacteristic
209C3⋊Dic3—42no—
210C3×Dic3—24no—
211C2×#41—32no—
212#135—34no—
213#135—34no—
214C2×Q16—31no—
215C2×SD16—32no—
216C2×D8—31no—
217#131—98no—
218#131—184no—
219C2×M16—32no—
220C2×M16—182no—
221C22×C8—91no—
222C22×C8—182no—
223C22×C8D3211yescharacteristic
224C2×C42—91no—
225#108—34no—
226#104—98no—
227#97—94no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3#23711yescharacteristic
231C23×C3#23911yescharacteristic
232C22×D3—22no—
233C3×Q8—34no—
234C3×Q8—62no—
235C3×D4—34no—
236C3×D4—64no—
237C3×D4—64no—
238C3×D4—62no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—62no—
246C2×C3×C4—64no—
247C2×C3×C4—64no—
248C2×C3×C4C2×C4×D311yescharacteristic
249C2×C3×C4C2×C4×D311yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4#23711yescharacteristic
255C2×C3×C4#23911yescharacteristic
256C2×C3×C4C22×Dic311yescharacteristic
257C2×C3×C4C22×Dic311yescharacteristic
258C2×C3×C4C23×D311yescharacteristic
259C2×C3×C4C23×D311yescharacteristic
260#67—24no—
261#67—24no—
262C2×Dic3—22no—
263C2×Dic3—64no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—124no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269D12—22no—
270D12C22×Dic314yes—
271C4×D3—24no—
272C4×D3—24no—
273Dic6—22no—
274Dic6C22×Dic314yes—
275C3×C8—22no—
276C3×C8—22no—
277C3×C8—64no—
278C3×C8C2×C4×D312yes—
279C3×C8C2×C4×D312yes—
280C3×C8C22×Dic312yes—
281C3×C8C22×Dic312yes—
282C3⋊C8—24no—
283C3⋊C8—34no—
284C3⋊C8—34no—
285C3⋊C8—64no—
286C2×C32—21no—
287C2×C32—21no—
288C2×C32#44412yescomplemented
289C2×C32C2×C4×D411yescharacteristic
290C3×D3—44no—
291#41—34no—
292#41—34no—
293#41—62no—
294#41—62no—
295C2×Q8—32no—
296C2×D4—32no—
297C2×D4—62no—
298C22×C4—62no—
299C22×C4—181no—
300C22×C4C2×D3211yescharacteristic
301Q16—34no—
302SD16—38no—
303D8—34no—
304M16—34no—
305M16—62no—
306M16—188no—
307C2×C8—62no—
308C2×C8—92no—
309C2×C8—92no—
310C2×C8—92no—
311C2×C8—188no—
312C2×C8D3×Dic311yescharacteristic
313C2×C8D3×Dic311yescharacteristic
314C2×C8D3×Dic312yes—
315C2×C8C2×D3212yes—
316C42—92no—
317C42—181no—
318C22×C3—24no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—64no—
325C22×C3—124no—
326C22×C3#89311yescharacteristic
327C22×C3#89311yescharacteristic
328C22×C3D4×Dic311yescharacteristic
329C22×C3D4×Dic311yescharacteristic
330C22×C3C2×#23711yescharacteristic
331C22×C3C2×#23911yescharacteristic
332C2×D3—24no—
333C2×D3—44no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—64no—
339C3×C4#89311yescharacteristic
340C3×C4#89311yescharacteristic
341C3×C4D4×Dic311yescharacteristic
342C3×C4D4×Dic311yescharacteristic
343C3×C4C22×C4×D311yescharacteristic
344C3×C4C2×D3×D411yescharacteristic
345C3×C4C2×D3×D411yescharacteristic
346C3×C4C23×Dic311yescharacteristic
347Dic3—24no—
348Dic3—124no—
349Dic3—122no—
350Dic3—122no—
351C32C2×#44411yescharacteristic, complemented, Sylow
352C23—62no—
353C23#379611yescharacteristic
354Q8—34no—
355Q8—62no—
356D4—34no—
357D4—64no—
358D4—64no—
359D4—62no—
360C2×C4—62no—
361C2×C4—64no—
362C2×C4—64no—
363C2×C4—182no—
364C2×C4—362no—
365C2×C4#379611yescharacteristic
366C2×C4#380211yescharacteristic
367C2×C4#380211yescharacteristic
368C2×C4C2×D3×Dic311yescharacteristic
369C2×C4C2×D3×Dic311yescharacteristic
370C2×C4C22×D3211yescharacteristic
371C8—64no—
372C8—94no—
373C8C2×D3×Dic312yes—
374C8C2×D3×Dic312yes—
375C2×C3—22no—
376C2×C3—22no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—22no—
383C2×C3—124no—
384C2×C3#489412yescomplemented
385C2×C3#519712yescomplemented
386C2×C3C2×#89311yescharacteristic
387C2×C3C2×D4×Dic311yescharacteristic
388D3—44no—
389C22—22no—
390C22—64no—
391C22—124no—
392C22#6389811yescharacteristic
393C22#6389811yescharacteristic
394C22C2×#379611yescharacteristic
395C4—64no—
396C4—362no—
397C4#6389811yescharacteristic
398C4#6389811yescharacteristic
399C4C2×#380211yescharacteristic
400C4C22×D3×Dic311yescharacteristic
401C3—21no—
402C3C2×#489411yescharacteristic, complemented
403C3C2×#519711yescharacteristic, complemented
404C2—21no—
405C2—21no—
406C2—124no—
407C2#1059092012yesdirect product factor
408C2C2×#6389811yescharacteristic
subgroupG/H
centerC2×C4#3802
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×#63815C2semidirect
3. C2×#63642C2semidirect
4. C2×C3×#819C2semidirect
5. C2×#63568C2semidirect
6. #10590920C2direct (N × H)
14. C2×C3×Dic12C4semidirect
15. C3×#904C4semidirect
17. C2×C3×D24C4semidirect
18. C2×C3×#204C4semidirect
21. #63815C22semidirect
23. #63642C22semidirect
24. C3×#819C22semidirect
25. #63568C22semidirect
34. C2×#819D3semidirect
61. C3×Dic12C2×C4semidirect
62. C3×D24C2×C4semidirect
63. C3×#204C2×C4semidirect
91. C2×Dic12Dic3semidirect
92. #904Dic3semidirect
94. C2×D24Dic3semidirect
95. C2×#204Dic3semidirect
101. #819C2×D3semidirect
194. Dic12C2×Dic3semidirect
195. D24C2×Dic3semidirect
196. #204C2×Dic3semidirect
288. C2×C32#444semidirect
351. C32C2×#444semidirect
384. C2×C3#4894semidirect
385. C2×C3#5197semidirect
402. C3C2×#4894semidirect
403. C3C2×#5197semidirect
407. C2#10590920direct (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×#638152
C2×#636422
C2×C3×#8192
C2×#635682
#105909202
C2×#51973
C2×#48943