Finite Group Databasebeta

← C2×#10590909 #11857210

Subgroups — C2×#10590909 #11857210

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic
4C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C2×#63555C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590909C218yesmaximal, direct product factor
9C2×#5122—31nomaximal
10C2×#4708—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C418yescomplemented
19C2×C3×ΓL(1,𝔽25)C2214yes—
20C2×Dic3⋊Dic3C412yes—
21C2×(C2×D3)⋊Dic3C412yes—
22#63855C414yes—
23#63855C2214yes—
24C2×D3×C3⋊C8C418yescomplemented
25C2×D3×C3⋊C8C2214yes—
26C8×C3⋊Dic3C2214yescomplemented
27C3×#815C2214yescomplemented
28#63555C2214yescomplemented
29Dic3×C3⋊C8C2214yescomplemented
30C22×C3×M16—31no—
31C2×#926—31no—
32C23×C3⋊C8—31no—
33C22×ΓL(1,𝔽25)D311yescharacteristic
34C22×D3×C8—31no—
35C2×#872—31no—
36C2×C3×#97—31no—
37#5122—38no—
38C2×#815—31no—
39C2×#815—31no—
40C2×#815D311yescharacteristic, complemented
41C2×C8×Dic3—31no—
42C2×C8×Dic3—31no—
43C2×C8×Dic3—31no—
44C2×C8×Dic3—61no—
45C2×C4×C3⋊C8—31no—
46#4708—38no—
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2×C412yes—
50C22×C3×Dic3C2×C412yes—
51C22×C3×Dic3C2×C411yescharacteristic
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3C2×C414yes—
54C2×C3×C4×D3C2×C414yes—
55C2×C3×C4×D3C2312yes—
56C2×C32×C8C2×C414yes—
57C2×C32×C8C2312yes—
58C4×C3⋊Dic3C2×C412yes—
59C4×C3⋊Dic3C2312yes—
60C2×C3⋊(C3⋊C8)C2×C414yes—
61C2×C3⋊(C3⋊C8)C2312yes—
62C3×C4×Dic3C2×C412yes—
63C3×C4×Dic3C2312yes—
64C2×C3×C3⋊C8C2×C414yes—
65C2×C3×C3⋊C8C2×C414yes—
66C2×C3×C3⋊C8C2312yes—
67C2×C3×C3⋊C8C2312yes—
68C3×ΓL(1,𝔽25)C2×C4116yescomplemented
69Dic3⋊Dic3C2×C418yes—
70(C2×D3)⋊Dic3C2×C418yes—
71D3×C3⋊C8C2×C4116yescomplemented
72C2×#405—91noSylow
73C23×C3×C4—31no—
74C22×C4×D3C2×D311yescharacteristic
75C2×C3×M16—38no—
76C2×C3×M16—34no—
77C22×C3×C8—21no—
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C42—31no—
83C2×#217—32no—
84C2×(C2×D3)⋊C4—32no—
85#926—34no—
86#926—34no—
87C2×C4⋊Dic3—32no—
88C2×Dic3⋊C4—32no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—61no—
92C2×C4×Dic3C2×D311yescharacteristic
93C22×C3⋊C8—31no—
94C22×C3⋊C8—31no—
95C22×C3⋊C8—38no—
96C22×C3⋊C8—34no—
97C22×C3⋊C8—61no—
98C22×C3⋊C8C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100C2×ΓL(1,𝔽25)Dic318yescomplemented
101C2×ΓL(1,𝔽25)C2×D314yes—
102C2×D3×C8—38no—
103C2×D3×C8—34no—
104#872—34no—
105#872—34no—
106C3×#97—34no—
107#815—34no—
108#815—34no—
109#815C2×D314yescomplemented
110C8×Dic3—34no—
111C8×Dic3—34no—
112C8×Dic3—34no—
113C8×Dic3—64no—
114C4×C3⋊C8—34no—
115C23×C32C22×C411yescharacteristic
116C22×C3×D3—24no—
117C22×C3×D3C4214yes—
118C22×C3×D3C22×C412yes—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C22×C412yes—
121C2×C32×C4C22×C412yes—
122C2×C32×C4C2411yescharacteristic
123C2×C3⋊Dic3—24no—
124C2×C3⋊Dic3C22×C414yes—
125C2×C3×Dic3—24no—
126C2×C3×Dic3C4214yes—
127C2×C3×Dic3C22×C414yes—
128C2×C3×Dic3C22×C412yes—
129C3×C4×D3C4218yes—
130C3×C4×D3C22×C414yes—
131C3×C4×D3C22×C414yes—
132C32×C8C22×C414yes—
133C3⋊(C3⋊C8)C22×C414yes—
134C3×C3⋊C8C22×C414yes—
135C3×C3⋊C8C22×C414yes—
136C22×M16—31no—
137C23×C8—91no—
138C2×#117—91no—
139#405—98no—
140C2×#97—31no—
141C2×#97—91no—
142C2×C4×C8—91no—
143C2×C4×C8—91no—
144C24×C3—31no—
145C23×D3C4×D311yescharacteristic
146C22×C3×C4—21no—
147C22×C3×C4—31no—
148C22×C3×C4—34no—
149C22×C3×C4—32no—
150C22×C3×C4—34no—
151C22×C3×C4—32no—
152C22×C3×C4—32no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—62no—
158C22×Dic3C4×D312yes—
159C22×Dic3C4×D311yescharacteristic
160C2×C4×D3C4×D312yes—
161C2×C4×D3C4×D314yes—
162C2×C4×D3C2×Dic314yes—
163C2×C4×D3C22×D312yes—
164C3×M16—316no—
165C2×C3×C8—24no—
166C2×C3×C8—22no—
167C2×C3×C8—34no—
168C2×C3×C8—34no—
169C2×C3×C8—32no—
170C2×C3×C8—32no—
171C2×C3×C8C4×D314yes—
172C2×C3×C8C2×Dic314yes—
173C2×C3×C8C22×D312yes—
174C2×C3×C8C22×D312yes—
175C3×C42—32no—
176C3×C42—32no—
177#217—38no—
178(C2×D3)⋊C4—38no—
179C4⋊Dic3—38no—
180Dic3⋊C4—38no—
181C4×Dic3—32no—
182C4×Dic3—32no—
183C4×Dic3—32no—
184C4×Dic3—32no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3C4×D312yes—
188C4×Dic3C22×D312yes—
189C2×C3⋊C8—34no—
190C2×C3⋊C8—34no—
191C2×C3⋊C8—32no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—316no—
194C2×C3⋊C8—62no—
195C2×C3⋊C8—64no—
196C2×C3⋊C8C4×D314yes—
197C2×C3⋊C8C2×Dic314yes—
198C2×C3⋊C8C22×D312yes—
199C2×C3⋊C8C22×D312yes—
200ΓL(1,𝔽25)C2×Dic3116yescomplemented
201D3×C8—316no—
202C22×C32C2×C4212yes—
203C22×C32#13114yes—
204C22×C32C23×C411yescharacteristic
205C2×C3×D3—24no—
206C2×C3×D3—28no—
207C2×C3×D3C2×C4214yes—
208C32×C4C2×C4212yes—
209C32×C4C23×C411yescharacteristic
210C32×C4C23×C411yescharacteristic
211C3⋊Dic3—24no—
212C3×Dic3—24no—
213C3×Dic3C2×C4214yes—
214C23×C4—31no—
215C2×M16—38no—
216C2×M16—34no—
217C22×C8—31no—
218C22×C8—31no—
219C22×C8—94no—
220C22×C8—98no—
221C22×C8—91no—
222C22×C8D3211yescharacteristic
223#117—94no—
224#117—94no—
225C2×C4⋊C4—92no—
226C2×C22⋊C4—92no—
227C2×C42—31no—
228C2×C42—91no—
229#97—34no—
230#97—94no—
231C4×C8—94no—
232C4×C8—94no—
233C23×C3—21no—
234C23×C3—34no—
235C23×C3—32no—
236C23×C3—64no—
237C23×C3C2×C4×D311yescharacteristic
238C23×C3C2×C4×D311yescharacteristic
239C22×D3—24no—
240C22×D3C4×Dic314yes—
241C22×D3C2×C4×D312yes—
242C2×C3×C4—21no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—22no—
246C2×C3×C4—34no—
247C2×C3×C4—32no—
248C2×C3×C4—38no—
249C2×C3×C4—34no—
250C2×C3×C4—34no—
251C2×C3×C4—34no—
252C2×C3×C4—64no—
253C2×C3×C4C2×C4×D311yescharacteristic
254C2×C3×C4C2×C4×D312yes—
255C2×C3×C4C2×C4×D311yescharacteristic
256C2×C3×C4C2×C4×D312yes—
257C2×C3×C4C2×C4×D312yes—
258C2×C3×C4C22×Dic312yes—
259C2×C3×C4C23×D311yescharacteristic
260C2×C3×C4C23×D311yescharacteristic
261C2×Dic3—24no—
262C2×Dic3—34no—
263C2×Dic3—34no—
264C2×Dic3—64no—
265C2×Dic3—68no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C2×Dic3C4×Dic314yes—
269C2×Dic3C2×C4×D314yes—
270C2×Dic3C2×C4×D312yes—
271C4×D3C4×Dic318yes—
272C4×D3C2×C4×D314yes—
273C4×D3C22×Dic314yes—
274C3×C8—24no—
275C3×C8—34no—
276C3×C8—34no—
277C3×C8C2×C4×D314yes—
278C3×C8C22×Dic314yes—
279C3⋊C8—34no—
280C3⋊C8—34no—
281C3⋊C8—64no—
282C3⋊C8C2×C4×D314yes—
283C3⋊C8C22×Dic314yes—
284C2×C32#40514yescomplemented
285C2×C32C22×C4211yescharacteristic
286C2×C32C2×#13112yes—
287C3×D3—24no—
288C24—31no—
289C22×C4—31no—
290C22×C4—32no—
291C22×C4—32no—
292C22×C4—34no—
293C22×C4—34no—
294C22×C4—32no—
295C22×C4—92no—
296C22×C4C2×D3211yescharacteristic
297M16—316no—
298C2×C8—32no—
299C2×C8—32no—
300C2×C8—34no—
301C2×C8—34no—
302C2×C8—916no—
303C2×C8—92no—
304C2×C8—94no—
305C2×C8D3×Dic314yes—
306C2×C8C2×D3212yes—
307C4⋊C4—98no—
308C22⋊C4—98no—
309C42—32no—
310C42—32no—
311C42—92no—
312C42—92no—
313C22×C3—21no—
314C22×C3—24no—
315C22×C3—22no—
316C22×C3—34no—
317C22×C3—68no—
318C22×C3—64no—
319C22×C3C42×D312yes—
320C22×C3#90714yes—
321C22×C3#90714yes—
322C22×C3C2×C4×Dic312yes—
323C22×C3C22×C4×D311yescharacteristic
324C22×C3C22×C4×D311yescharacteristic
325C2×D3—28no—
326C2×D3—24no—
327C2×D3C2×C4×Dic314yes—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—22no—
331C3×C4—34no—
332C3×C4—64no—
333C3×C4C42×D312yes—
334C3×C4C2×C4×Dic312yes—
335C3×C4C22×C4×D311yescharacteristic
336C3×C4C22×C4×D311yescharacteristic
337C3×C4C22×C4×D311yescharacteristic
338C3×C4C23×Dic311yescharacteristic
339Dic3—24no—
340Dic3—68no—
341Dic3—64no—
342Dic3—64no—
343Dic3C2×C4×Dic314yes—
344C32C2×#40511yescharacteristic, complemented, Sylow
345C23—32no—
346C23—34no—
347C23—64no—
348C23C4×D3211yescharacteristic
349C2×C4—32no—
350C2×C4—34no—
351C2×C4—34no—
352C2×C4—34no—
353C2×C4—38no—
354C2×C4—34no—
355C2×C4—64no—
356C2×C4—94no—
357C2×C4—184no—
358C2×C4C4×D3212yes—
359C2×C4C4×D3211yescharacteristic
360C2×C4C2×D3×Dic312yes—
361C2×C4C22×D3211yescharacteristic
362C8—34no—
363C8—34no—
364C8—94no—
365C8C2×D3×Dic314yes—
366C2×C3—21no—
367C2×C3—22no—
368C2×C3—24no—
369C2×C3—64no—
370C2×C3#470814yescomplemented
371C2×C3#512214yescomplemented
372C2×C3C2×C42×D311yescharacteristic
373C2×C3C2×#90712yes—
374C2×C3C2×#90712yes—
375C2×C3C22×C4×Dic311yescharacteristic
376D3—24no—
377C22—34no—
378C22—64no—
379C22—68no—
380C22#6380514yes—
381C22C4×D3×Dic312yes—
382C22C2×C4×D3211yescharacteristic
383C4—34no—
384C4—64no—
385C4—184no—
386C4C4×D3×Dic312yes—
387C4C2×C4×D3211yescharacteristic
388C4C22×D3×Dic311yescharacteristic
389C3—21no—
390C3C2×#470811yescharacteristic, complemented
391C3C2×#512211yescharacteristic, complemented
392C2—64no—
393C2#1059090914yesdirect product factor
394C2C2×#6380512yes—
395C2C2×C4×D3×Dic311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#405
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C8×C3⋊Dic3C2semidirect
5. C2×C3×#815C2semidirect
6. C2×#63555C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590909C2direct (N × H)
18. C2×C3×ΓL(1,𝔽25)C4semidirect
24. C2×D3×C3⋊C8C4semidirect
26. C8×C3⋊Dic3C22semidirect
27. C3×#815C22semidirect
28. #63555C22semidirect
29. Dic3×C3⋊C8C22semidirect
40. C2×#815D3semidirect
68. C3×ΓL(1,𝔽25)C2×C4semidirect
71. D3×C3⋊C8C2×C4semidirect
100. C2×ΓL(1,𝔽25)Dic3semidirect
109. #815C2×D3semidirect
200. ΓL(1,𝔽25)C2×Dic3semidirect
284. C2×C32#405semidirect
344. C32C2×#405semidirect
370. C2×C3#4708semidirect
371. C2×C3#5122semidirect
390. C3C2×#4708semidirect
391. C3C2×#5122semidirect
393. C2#10590909direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
C2×#638552
C22×D3×C3⋊C82
C2×C8×C3⋊Dic32
C2×C3×#8152
C2×#635552
C2×Dic3×C3⋊C82
#105909092
C2×#51223
C2×#47083