Finite Group Databasebeta

← C2×#10590921 #11861017

Subgroups — C2×#10590921 #11861017

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 365 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C212yesmaximal, complemented
2C2×#63822C211yesmaximal, characteristic
3C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63568C212yesmaximal, complemented
6#10590921C218yesmaximal, direct product factor
7C2×#5144—32nomaximal
8C2×C3×#235C2212yes—
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×#208C2212yes—
13C3×#901—24no—
14C3×#901C2218yescomplemented
15C2×C3×ΓL(1,𝔽25)—22no—
16C2×C3×D3×C8—22no—
17C2×#3718C411yescharacteristic, complemented
18C2×#3715C412yescomplemented
19#63822C414yescomplemented
20#63822C2214yes—
21C2×#3713C411yescharacteristic, complemented
22C8×C3⋊Dic3C2214yescomplemented
23#63578C2214yescomplemented
24#63568C2218yescomplemented
25C2×C3×#131—32no—
26C2×#950—32no—
27C2×#901D312yescomplemented
28C2×#837—32no—
29#5144—316no—
30C2×#825—32no—
31C2×#822—32no—
32C2×C8×Dic3—32no—
33C2×C8×Dic3—61no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C2×C3×#67—22no—
37C3×#235—22no—
38C3×#235—22no—
39C3×#235C2×C414yes—
40C3×#235C2314yes—
41C2×C3×D12C2×C412yes—
42C2×C3×C4×D3—22no—
43C2×C3×Dic6C2×C412yes—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8D412yes—
47C2×C32×C8C2312yes—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3C2312yes—
50C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
51C2×C3⋊(C3⋊C8)C2×C412yes—
52C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
53C2×C3⋊(C3⋊C8)C2312yes—
54C3×#208—22no—
55C3×#208C2314yes—
56C2×C3×C3⋊C8—22no—
57C3×ΓL(1,𝔽25)—28no—
58C3×D3×C8—28no—
59#3718C2×C414yescomplemented
60#3715C2×C418yescomplemented
61#3713C2×C414yescomplemented
62C2×#443—91noSylow
63C2×C3×#41—32no—
64C2×#235C2×D312yes—
65C3×#131—38no—
66C3×#131—64no—
67C2×C3×M16—32no—
68C2×C3×M16—62no—
69C22×C3×C8—21no—
70C22×C3×C8—62no—
71C22×C3×C8C2×D312yes—
72#950—38no—
73#950—38no—
74C2×#216—32no—
75C2×#215—32no—
76C2×#214—32no—
77C2×#213—32no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—61no—
80C2×#208C2×D312yes—
81C22×C3⋊C8—32no—
82C22×C3⋊C8—61no—
83#901—24no—
84#901C2×D318yescomplemented
85C2×ΓL(1,𝔽25)—22no—
86C2×D3×C8—22no—
87#837—38no—
88#825—38no—
89#822—38no—
90C8×Dic3—38no—
91C8×Dic3—64no—
92C23×C32#4111yescharacteristic
93C22×C3×D3—22no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C32×C4C2411yescharacteristic
100C2×C3⋊Dic3—24no—
101C2×C3⋊Dic3—22no—
102C3×#67—24no—
103C3×#67—24no—
104C2×C3×Dic3—22no—
105C3×D12—22no—
106C3×D12C22×C414yes—
107C3×C4×D3—24no—
108C3×C4×D3—24no—
109C3×Dic6—22no—
110C3×Dic6C22×C414yes—
111C32×C8C2×D412yes—
112C32×C8C2×D412yes—
113C3⋊(C3⋊C8)C22×C412yes—
114C3⋊(C3⋊C8)C22×C412yes—
115C3×C3⋊C8—24no—
116C2×#135—91no—
117C2×#131—32no—
118#443—98no—
119C2×#108—91no—
120C2×#104—92no—
121C2×C4×C8—91no—
122C3×#41—34no—
123C3×#41—34no—
124C3×#41—62no—
125C3×#41—62no—
126C2×C3×Q8—32no—
127C2×C3×D4—32no—
128C2×C3×D4—62no—
129C22×C3×C4—21no—
130C22×C3×C4—62no—
131C22×C3×C4C22×D312yes—
132C2×#67—22no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135#235—22no—
136#235—22no—
137#235C4×D314yes—
138#235C22×D314yes—
139C2×D12C4×D312yes—
140C2×C4×D3—22no—
141C2×Dic6C4×D312yes—
142C3×M16—34no—
143C3×M16—62no—
144C3×M16—68no—
145C2×C3×C8—21no—
146C2×C3×C8—22no—
147C2×C3×C8—21no—
148C2×C3×C8—22no—
149C2×C3×C8—62no—
150C2×C3×C8—68no—
151C2×C3×C8#6712yes—
152C2×C3×C8#6714yes—
153C2×C3×C8#6712yes—
154C2×C3×C8C22×D314yes—
155#216—38no—
156#215—38no—
157#214—38no—
158#213—38no—
159C4×Dic3—34no—
160C4×Dic3—62no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163#208—22no—
164#208C22×D314yes—
165C2×C3⋊C8—22no—
166C2×C3⋊C8—32no—
167C2×C3⋊C8—32no—
168C2×C3⋊C8—34no—
169C2×C3⋊C8—34no—
170C2×C3⋊C8—62no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—62no—
174ΓL(1,𝔽25)—28no—
175D3×C8—28no—
176C22×C32—22no—
177C22×C32C4×D411yescharacteristic
178C22×C32C4×D411yescharacteristic
179C22×C32C2×#4111yescharacteristic
180C2×C3×D3—24no—
181C2×C3×D3—44no—
182C32×C4C4×D411yescharacteristic
183C32×C4C4×D411yescharacteristic
184C32×C4C23×C411yescharacteristic
185C32×C4C22×D411yescharacteristic
186C3⋊Dic3—24no—
187C3×Dic3—24no—
188C2×#41—32no—
189#135—94no—
190#135—94no—
191C2×Q16—91no—
192C2×SD16—92no—
193C2×D8—91no—
194#131—38no—
195#131—64no—
196C2×M16—32no—
197C2×M16—62no—
198C22×C8—62no—
199C22×C8—91no—
200C22×C8D3211yescharacteristic
201C2×C42—91no—
202#108—94no—
203#104—98no—
204C4×C8—94no—
205C23×C3—21no—
206C23×C3—62no—
207C23×C3#23512yes—
208C22×D3—22no—
209C3×Q8—34no—
210C3×Q8—62no—
211C3×D4—34no—
212C3×D4—64no—
213C3×D4—64no—
214C3×D4—62no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—62no—
222C2×C3×C4—64no—
223C2×C3×C4—64no—
224C2×C3×C4C2×C4×D312yes—
225C2×C3×C4C2×C4×D312yes—
226C2×C3×C4#23512yes—
227C2×C3×C4C2×#6712yes—
228C2×C3×C4C2×#6712yes—
229C2×C3×C4C23×D312yes—
230#67—24no—
231#67—24no—
232C2×Dic3—22no—
233C2×Dic3—64no—
234C2×Dic3—68no—
235C2×Dic3—68no—
236C2×Dic3—64no—
237D12—22no—
238D12C2×C4×D314yes—
239C4×D3—24no—
240C4×D3—24no—
241Dic6—22no—
242Dic6C2×C4×D314yes—
243C3×C8—22no—
244C3×C8—22no—
245C3×C8—64no—
246C3×C8C2×#6714yes—
247C3×C8C2×#6714yes—
248C3⋊C8—24no—
249C3⋊C8—34no—
250C3⋊C8—34no—
251C3⋊C8—62no—
252C3⋊C8—62no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32#44312yescomplemented
256C2×C32C2×C4×D411yescharacteristic
257C3×D3—44no—
258#41—34no—
259#41—34no—
260#41—62no—
261#41—62no—
262C2×Q8—32no—
263C2×D4—32no—
264C2×D4—62no—
265C22×C4—62no—
266C22×C4—181no—
267C22×C4C2×D3211yescharacteristic
268Q16—94no—
269SD16—98no—
270D8—94no—
271M16—34no—
272M16—62no—
273M16—68no—
274C2×C8—62no—
275C2×C8—68no—
276C2×C8—92no—
277C2×C8—91no—
278C2×C8—91no—
279C2×C8—92no—
280C2×C8#62511yescharacteristic
281C2×C8#62512yes—
282C2×C8#62511yescharacteristic
283C2×C8C2×D3212yes—
284C42—92no—
285C42—181no—
286C22×C3—24no—
287C22×C3—24no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—64no—
292C22×C3—124no—
293C22×C3C4×#6712yes—
294C22×C3C4×#6712yes—
295C22×C3C2×#23512yes—
296C2×D3—24no—
297C2×D3—44no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—64no—
303C3×C4C4×#6712yes—
304C3×C4C4×#6712yes—
305C3×C4C22×C4×D312yes—
306C3×C4C22×#6712yes—
307Dic3—24no—
308Dic3—68no—
309Dic3—68no—
310C32C2×#44311yescharacteristic, complemented, Sylow
311C23—62no—
312C23#379811yescharacteristic
313Q8—34no—
314Q8—62no—
315D4—34no—
316D4—64no—
317D4—64no—
318D4—62no—
319C2×C4—62no—
320C2×C4—64no—
321C2×C4—64no—
322C2×C4—184no—
323C2×C4—182no—
324C2×C4#379811yescharacteristic
325C2×C4C4×D3211yescharacteristic
326C2×C4C4×D3211yescharacteristic
327C2×C4C2×#62511yescharacteristic
328C2×C4C2×#62511yescharacteristic
329C2×C4C22×D3211yescharacteristic
330C8—64no—
331C8—92no—
332C8—92no—
333C8C2×#62512yes—
334C8C2×#62512yes—
335C2×C3—22no—
336C2×C3—22no—
337C2×C3—22no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—22no—
341C2×C3—124no—
342C2×C3#514414yescomplemented
343C2×C3C2×C4×#6712yes—
344D3—44no—
345C22—22no—
346C22—64no—
347C22—124no—
348C22C4×#62511yescharacteristic
349C22C4×#62511yescharacteristic
350C22C2×#379811yescharacteristic
351C4—64no—
352C4—184no—
353C4C4×#62511yescharacteristic
354C4C4×#62511yescharacteristic
355C4C2×C4×D3211yescharacteristic
356C4C22×#62511yescharacteristic
357C3—21no—
358C3C2×#514412yescomplemented
359C2—21no—
360C2—21no—
361C2—124no—
362C2#1059092112yesdirect product factor
363C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC2×C8#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C4×D4
prime radicalC2×#63822C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#443
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
3. C2×C8×C3⋊Dic3C2semidirect
4. C2×#63578C2semidirect
5. C2×#63568C2semidirect
6. #10590921C2direct (N × H)
14. C3×#901C22semidirect
17. C2×#3718C4semidirect
18. C2×#3715C4semidirect
19. #63822C4semidirect
21. C2×#3713C4semidirect
22. C8×C3⋊Dic3C22semidirect
23. #63578C22semidirect
24. #63568C22semidirect
27. C2×#901D3semidirect
59. #3718C2×C4semidirect
60. #3715C2×C4semidirect
61. #3713C2×C4semidirect
84. #901C2×D3semidirect
255. C2×C32#443semidirect
310. C32C2×#443semidirect
342. C2×C3#5144semidirect
358. C3C2×#5144semidirect
362. C2#10590921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C2×#638222
C2×C8×C3⋊Dic32
C2×#635782
C2×#635682
#105909212
C2×#51443