Finite Group Databasebeta

← C2×#10590858 #11867019

Subgroups — C2×#10590858 #11867019

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic
2C22×C3×Dic12C211yesmaximal, characteristic, complemented
3C2×#63871C212yesmaximal
4C2×C3×#817C211yesmaximal, characteristic, complemented
5C2×#63565C212yesmaximal, complemented
6#10590858C218yesmaximal, direct product factor
7C2×#5189—31nomaximal
8C2×#4867—31nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×C3×Dic6C2212yes—
11C22×C32×C8C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×#3743—24no—
14C2×#3743C2214yes—
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic12—24no—
17C2×C3×Dic12C2214yescomplemented
18C2×Dic3⋊Dic3—22no—
19C2×#3722—22no—
20#63871—24no—
21#63871C2218yes—
22C3×#817C2214yescomplemented
23#63565C2218yescomplemented
24C22×C3×Q16—31no—
25C2×#946—32no—
26C22×Dic12D311yescharacteristic, complemented
27C22×ΓL(1,𝔽25)—31no—
28C22×ΓL(1,𝔽25)—31no—
29C22×ΓL(1,𝔽25)—61no—
30C2×#897—32no—
31C2×C3×#106—31no—
32C2×#835—32no—
33#5189—38no—
34C2×#817D311yescharacteristic, complemented
35C2×#810—32no—
36#4867—38no—
37C23×C3⋊D3D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3C2312yes—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—22no—
46C2×C3×Dic6—24no—
47C2×C3×Dic6—24no—
48C2×C3×Dic6—22no—
49C2×C3×Dic6C2314yes—
50C2×C32×C8D414yes—
51C2×C32×C8C2312yes—
52C2×C3⋊(C3⋊C8)—22no—
53C2×C3⋊(C3⋊C8)C2312yes—
54#3743—28no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3C2314yes—
57C3×Dic12—28no—
58Dic3⋊Dic3—28no—
59#3722—28no—
60C2×#470—91noSylow
61C22×C3×Q8—32no—
62C22×C4×D3—31no—
63C22×C4×D3—31no—
64C22×C4×D3—61no—
65C22×Dic6C2×D312yes—
66C2×C3×Q16—34no—
67C2×C3×Q16—64no—
68C22×C3×C8—21no—
69C22×C3×C8C2×D311yescharacteristic
70C22×C3×C8C2×D311yescharacteristic
71C2×C3×C4⋊C4—32no—
72#946—38no—
73#946—64no—
74C2×(C2×D3)⋊C4—62no—
75C2×(C2×D3)⋊C4—62no—
76C2×C4⋊Dic3—62no—
77C2×C4⋊Dic3C2×D312yes—
78C2×Dic3⋊C4—62no—
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—61no—
82C2×Dic12—24no—
83C2×Dic12C2×D314yescomplemented
84C2×ΓL(1,𝔽25)—34no—
85C2×ΓL(1,𝔽25)—34no—
86C2×ΓL(1,𝔽25)—64no—
87C2×ΓL(1,𝔽25)—68no—
88C2×ΓL(1,𝔽25)—64no—
89C2×ΓL(1,𝔽25)—64no—
90#897—38no—
91#897—64no—
92C3×#106—34no—
93#835—38no—
94#817C2×D314yescomplemented
95#810—38no—
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—22no—
98C22×C3⋊D3—24no—
99C22×C3⋊D3C2×D412yes—
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4112yes—
103C2×C32×C4C2411yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3C2×D412yes—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—44no—
112C2×C3×Dic3—44no—
113C3×Dic6—24no—
114C3×Dic6—24no—
115C3×Dic6—44no—
116C32×C8C2×D414yes—
117C3⋊(C3⋊C8)—22no—
118C22×Q16—31no—
119C22×M16—91no—
120C2×C22⋊Q8—92no—
121#470—98no—
122C2×#106—31no—
123C2×#103—92no—
124C23×D3—31no—
125C23×D3—31no—
126C23×D3—61no—
127C2×C3×Q8—34no—
128C2×C3×Q8—62no—
129C2×C3×Q8—64no—
130C2×C3×Q8—64no—
131C22×C3×C4—21no—
132C22×C3×C4—62no—
133C22×C3×C4—62no—
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C22×Dic3—22no—
137C22×Dic3—22no—
138C22×Dic3—31no—
139C22×Dic3—31no—
140C22×Dic3—61no—
141C2×C4×D3—32no—
142C2×C4×D3—32no—
143C2×C4×D3—32no—
144C2×C4×D3—32no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×C4×D3—64no—
148C2×C4×D3—64no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×Dic6—24no—
154C2×Dic6—24no—
155C2×Dic6—22no—
156C2×Dic6C22×D314yes—
157C3×Q16—68no—
158C2×C3×C8—24no—
159C2×C3×C8—22no—
160C2×C3×C8D1214yes—
161C2×C3×C8#6714yes—
162C2×C3×C8C22×D312yes—
163C2×C3×C8C22×D312yes—
164C3×C4⋊C4—34no—
165C3×C4⋊C4—62no—
166(C2×D3)⋊C4—68no—
167(C2×D3)⋊C4—68no—
168C4⋊Dic3—22no—
169C4⋊Dic3—68no—
170C4⋊Dic3C22×D314yes—
171Dic3⋊C4—68no—
172C2×C3⋊C8—32no—
173C2×C3⋊C8—32no—
174C2×C3⋊C8—62no—
175C2×C3⋊C8—64no—
176C2×C3⋊C8—62no—
177C2×C3⋊C8—62no—
178Dic12—28no—
179ΓL(1,𝔽25)—616no—
180ΓL(1,𝔽25)—68no—
181ΓL(1,𝔽25)—68no—
182C22×C32#12112yes—
183C22×C32#13714yes—
184C22×C32C22×D411yescharacteristic
185C2×C3⋊D3—22no—
186C2×C3⋊D3—24no—
187C2×C3⋊D3—44no—
188C32×C4#12112yes—
189C32×C4C22×D411yescharacteristic
190C32×C4C2×#4111yescharacteristic
191C3⋊Dic3—22no—
192C3×Dic3—44no—
193C3×Dic3—44no—
194C22×Q8—32no—
195C23×C4—91no—
196C2×Q16—34no—
197C2×Q16—64no—
198C2×M16—94no—
199C2×M16—184no—
200C22×C8—91no—
201C22×C8D3211yescharacteristic
202C22⋊Q8—98no—
203C22⋊Q8—184no—
204C2×C4⋊C4—32no—
205C2×C4⋊C4—182no—
206C2×C22⋊C4—182no—
207#106—34no—
208#103—98no—
209C23×C3—21no—
210C23×C3D3×D411yescharacteristic
211C23×C3D3×D411yescharacteristic
212C22×D3—32no—
213C22×D3—32no—
214C22×D3—62no—
215C22×D3—64no—
216C22×D3—62no—
217C22×D3—64no—
218C22×D3—64no—
219C22×D3—62no—
220C22×D3—124no—
221C3×Q8—64no—
222C3×Q8—64no—
223C3×Q8—124no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—22no—
228C2×C3×C4—64no—
229C2×C3×C4—64no—
230C2×C3×C4—124no—
231C2×C3×C4—124no—
232C2×C3×C4C2×D1212yes—
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4#23712yes—
236C2×C3×C4#23912yes—
237C2×C3×C4C2×#6712yes—
238C2×C3×C4C23×D311yescharacteristic
239C2×C3×C4C23×D311yescharacteristic
240C2×Dic3—24no—
241C2×Dic3—24no—
242C2×Dic3—32no—
243C2×Dic3—32no—
244C2×Dic3—44no—
245C2×Dic3—44no—
246C2×Dic3—62no—
247C2×Dic3—64no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C4×D3—64no—
251C4×D3—64no—
252C4×D3—68no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—62no—
256C4×D3—62no—
257C4×D3—62no—
258C4×D3—62no—
259Dic6—24no—
260Dic6—24no—
261Dic6—44no—
262C3×C8—24no—
263C3×C8C2×D1214yes—
264C3×C8C2×#6714yes—
265C3⋊C8—64no—
266C3⋊C8—62no—
267C3⋊C8—62no—
268C2×C32#47014yescomplemented
269C2×C32C2×#12111yescharacteristic
270C2×C32C2×#13712yes—
271C3⋊D3—42no—
272C24—91no—
273C2×Q8—34no—
274C2×Q8—62no—
275C2×Q8—64no—
276C2×Q8—64no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—91no—
280C22×C4—92no—
281C22×C4—92no—
282C22×C4—182no—
283C22×C4—182no—
284C22×C4C2×D3211yescharacteristic
285Q16—68no—
286M16—188no—
287C2×C8—92no—
288C2×C8—182no—
289C2×C8#62614yes—
290C2×C8C2×D3212yes—
291C4⋊C4—34no—
292C4⋊C4—62no—
293C4⋊C4—188no—
294C22⋊C4—188no—
295C22×C3—21no—
296C22×C3—24no—
297C22×C3—22no—
298C22×C3#89512yes—
299C22×C3#91514yes—
300C22×C3#91814yes—
301C22×C3#93812yes—
302C22×C3C2×D3×D411yescharacteristic
303C22×C3C2×D3×D411yescharacteristic
304C2×D3—64no—
305C2×D3—64no—
306C2×D3—62no—
307C2×D3—64no—
308C2×D3—62no—
309C2×D3—124no—
310C2×D3—128no—
311C2×D3—124no—
312C2×D3—124no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—22no—
316C3×C4—124no—
317C3×C4—124no—
318C3×C4#89512yes—
319C3×C4#93812yes—
320C3×C4C22×D1211yescharacteristic
321C3×C4C2×#23711yescharacteristic
322C3×C4C2×#23911yescharacteristic
323C3×C4C22×#6711yescharacteristic
324Dic3—44no—
325Dic3—44no—
326Dic3—64no—
327Dic3—62no—
328Dic3—62no—
329C32C2×#47011yescharacteristic, complemented, Sylow
330C23—92no—
331C23—184no—
332C23—182no—
333C23#380211yescharacteristic
334Q8—64no—
335Q8—64no—
336Q8—124no—
337C2×C4—64no—
338C2×C4—64no—
339C2×C4—92no—
340C2×C4—124no—
341C2×C4—124no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—184no—
346C2×C4#379612yes—
347C2×C4#380211yescharacteristic
348C2×C4C2×#62612yes—
349C2×C4C22×D3211yescharacteristic
350C8—182no—
351C8C2×#62614yes—
352C2×C3—24no—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3#486714yescomplemented
356C2×C3#518914yescomplemented
357C2×C3C2×#89511yescharacteristic
358C2×C3C2×#91512yes—
359C2×C3C2×#91812yes—
360C2×C3C2×#93811yescharacteristic
361D3—124no—
362D3—122no—
363D3—122no—
364C22—184no—
365C22—182no—
366C22—364no—
367C22#6381114yes—
368C22#6391612yes—
369C22C2×#380211yescharacteristic
370C4—124no—
371C4—124no—
372C4—182no—
373C4#6391612yes—
374C4C2×#379611yescharacteristic
375C4C22×#62611yescharacteristic
376C3—21no—
377C3C2×#486711yescharacteristic, complemented
378C3C2×#518911yescharacteristic, complemented
379C2—362no—
380C2#1059085814yesdirect product factor
381C2C2×#6381112yes—
382C2C2×#6391611yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C8D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×Dic12C2semidirect
4. C2×C3×#817C2semidirect
5. C2×#63565C2semidirect
6. #10590858C2direct (N × H)
17. C2×C3×Dic12C22semidirect
22. C3×#817C22semidirect
23. #63565C22semidirect
26. C22×Dic12D3semidirect
34. C2×#817D3semidirect
83. C2×Dic12C2×D3semidirect
94. #817C2×D3semidirect
268. C2×C32#470semidirect
329. C32C2×#470semidirect
355. C2×C3#4867semidirect
356. C2×C3#5189semidirect
377. C3C2×#4867semidirect
378. C3C2×#5189semidirect
380. C2#10590858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37432
C22×C3×Dic122
C2×#638712
C2×C3×#8172
C2×#635652
#105908582
C2×#51893
C2×#48673