Finite Group Databasebeta

← C2×#10590910 #11857211

Subgroups — C2×#10590910 #11857211

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3743C211yesmaximal, characteristic
2C2×#63874C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C2×C3×#815C211yesmaximal, characteristic, complemented
5C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
6C2×#63554C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590910C218yesmaximal, direct product factor
9C2×#4708—31nomaximal
10C2×#4689—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×#3743C418yescomplemented
15C2×#3743C2214yes—
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3724C412yes—
21C2×#3722C412yes—
22#63874C414yes—
23#63874C2214yes—
24C2×#3710C418yescomplemented
25C2×#3710C2214yes—
26C3×#815C2214yescomplemented
27C3×C8×Dic3C2214yescomplemented
28#63554C2214yescomplemented
29Dic3×C3⋊C8C2214yescomplemented
30C22×ΓL(1,𝔽25)—31no—
31C22×ΓL(1,𝔽25)—31no—
32C22×ΓL(1,𝔽25)—61no—
33C22×D3×C8—31no—
34C22×D3×C8—31no—
35C2×#872—31no—
36C2×#872—31no—
37C2×C3×#97—31no—
38C2×C3×C4×C8—31no—
39C2×#815—31no—
40C2×#815D311yescharacteristic, complemented
41C2×C8×Dic3—31no—
42C2×C8×Dic3D311yescharacteristic, complemented
43C2×#803—31no—
44C2×C4×C3⋊C8—31no—
45#4708—38no—
46#4689—38no—
47C23×C3⋊D3C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C2×C4×C3⋊D3C2×C412yes—
51C2×C4×C3⋊D3C2×C414yes—
52C2×C4×C3⋊D3C2×C414yes—
53C2×C4×C3⋊D3C2312yes—
54C22×C3×Dic3C2×C412yes—
55C22×C3×Dic3C2×C412yes—
56C2×C32×C8C2×C414yes—
57C2×C32×C8C2312yes—
58C2×C3⋊(C3⋊C8)C2×C414yes—
59C2×C3⋊(C3⋊C8)C2312yes—
60#3743C2×C4116yescomplemented
61C3×C4×Dic3C2×C412yes—
62C3×C4×Dic3C2×C412yes—
63C3×C4×Dic3C2312yes—
64C3×C4×Dic3C2312yes—
65C2×C3×C3⋊C8C2×C414yes—
66C2×C3×C3⋊C8C2×C414yes—
67C2×C3×C3⋊C8C2312yes—
68C2×C3×C3⋊C8C2312yes—
69#3724C2×C418yes—
70#3722C2×C418yes—
71#3710C2×C4116yescomplemented
72C2×#405—91noSylow
73C22×C4×D3—31no—
74C22×C4×D3—31no—
75C22×C4×D3—61no—
76C22×C3×C8—21no—
77C22×C3×C8—31no—
78C22×C3×C8—31no—
79C22×C3×C8C2×D311yescharacteristic
80C22×C3×C8C2×D311yescharacteristic
81C2×C3×C42—31no—
82C2×C3×C42—31no—
83C2×(C2×D3)⋊C4—32no—
84C2×(C2×D3)⋊C4—32no—
85C2×Dic3⋊C4—32no—
86C2×Dic3⋊C4—32no—
87C2×C4×Dic3C2×D311yescharacteristic
88C2×C4×Dic3C2×D311yescharacteristic
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94C2×ΓL(1,𝔽25)—38no—
95C2×ΓL(1,𝔽25)—38no—
96C2×ΓL(1,𝔽25)—34no—
97C2×ΓL(1,𝔽25)—34no—
98C2×ΓL(1,𝔽25)—68no—
99C2×ΓL(1,𝔽25)—64no—
100C2×D3×C8—38no—
101C2×D3×C8—38no—
102C2×D3×C8—34no—
103C2×D3×C8—34no—
104#872—34no—
105#872—34no—
106#872—34no—
107#872—34no—
108C3×#97—34no—
109C3×C4×C8—34no—
110#815—34no—
111#815C2×D314yescomplemented
112C8×Dic3—34no—
113C8×Dic3C2×D314yescomplemented
114#803—34no—
115C4×C3⋊C8—34no—
116C23×C32C22×C411yescharacteristic
117C22×C3⋊D3—24no—
118C22×C3⋊D3C4214yes—
119C22×C3⋊D3C22×C412yes—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3C4214yes—
125C2×C3⋊Dic3C22×C412yes—
126C4×C3⋊D3C4218yes—
127C4×C3⋊D3C22×C414yes—
128C4×C3⋊D3C22×C414yes—
129C2×C3×Dic3—24no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3C22×C414yes—
132C2×C3×Dic3C22×C414yes—
133C32×C8C22×C414yes—
134C3⋊(C3⋊C8)C22×C414yes—
135C3×C3⋊C8C22×C414yes—
136C3×C3⋊C8C22×C414yes—
137C22×M16—91no—
138C23×C8—91no—
139C2×#117—91no—
140#405—98no—
141C2×#97—31no—
142C2×#97—91no—
143C2×C4×C8—31no—
144C2×C4×C8—91no—
145C23×D3—31no—
146C23×D3—31no—
147C23×D3—61no—
148C22×C3×C4—21no—
149C22×C3×C4—32no—
150C22×C3×C4—32no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C22×Dic3—31no—
154C22×Dic3—31no—
155C22×Dic3—61no—
156C22×Dic3C4×D312yes—
157C22×Dic3C4×D312yes—
158C2×C4×D3—32no—
159C2×C4×D3—32no—
160C2×C4×D3—34no—
161C2×C4×D3—34no—
162C2×C4×D3—34no—
163C2×C4×D3—34no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—64no—
167C2×C4×D3—62no—
168C2×C4×D3—62no—
169C2×C4×D3—64no—
170C2×C3×C8—24no—
171C2×C3×C8—22no—
172C2×C3×C8—34no—
173C2×C3×C8—34no—
174C2×C3×C8—32no—
175C2×C3×C8—32no—
176C2×C3×C8C4×D314yes—
177C2×C3×C8C4×D314yes—
178C2×C3×C8C22×D312yes—
179C2×C3×C8C22×D312yes—
180C3×C42—32no—
181C3×C42—32no—
182C3×C42—32no—
183C3×C42—32no—
184(C2×D3)⋊C4—38no—
185(C2×D3)⋊C4—38no—
186Dic3⋊C4—38no—
187Dic3⋊C4—38no—
188C4×Dic3C4×D312yes—
189C4×Dic3C4×D312yes—
190C4×Dic3C22×D312yes—
191C4×Dic3C22×D312yes—
192C2×C3⋊C8—34no—
193C2×C3⋊C8—34no—
194C2×C3⋊C8—32no—
195C2×C3⋊C8—32no—
196C2×C3⋊C8—64no—
197C2×C3⋊C8—62no—
198C2×C3⋊C8C4×D314yes—
199C2×C3⋊C8C4×D314yes—
200C2×C3⋊C8C22×D312yes—
201C2×C3⋊C8C22×D312yes—
202ΓL(1,𝔽25)—316no—
203ΓL(1,𝔽25)—316no—
204ΓL(1,𝔽25)—616no—
205D3×C8—316no—
206D3×C8—316no—
207C22×C32C2×C4212yes—
208C22×C32#13114yes—
209C22×C32C23×C411yescharacteristic
210C2×C3⋊D3—24no—
211C2×C3⋊D3—28no—
212C2×C3⋊D3C2×C4214yes—
213C32×C4C2×C4212yes—
214C32×C4C23×C411yescharacteristic
215C32×C4C23×C411yescharacteristic
216C3⋊Dic3C2×C4214yes—
217C3×Dic3—24no—
218C3×Dic3—24no—
219C23×C4—91no—
220C2×M16—98no—
221C2×M16—94no—
222C22×C8—31no—
223C22×C8—31no—
224C22×C8—98no—
225C22×C8—94no—
226C22×C8—91no—
227C22×C8D3211yescharacteristic
228#117—94no—
229#117—94no—
230C2×C4⋊C4—92no—
231C2×C22⋊C4—92no—
232C2×C42—31no—
233C2×C42—31no—
234#97—34no—
235#97—94no—
236C4×C8—34no—
237C4×C8—94no—
238C23×C3—21no—
239C23×C3C2×C4×D311yescharacteristic
240C23×C3C2×C4×D311yescharacteristic
241C22×D3—34no—
242C22×D3—34no—
243C22×D3—32no—
244C22×D3—32no—
245C22×D3—64no—
246C22×D3—62no—
247C22×D3—64no—
248C22×D3—64no—
249C22×D3—124no—
250C2×C3×C4—21no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—34no—
255C2×C3×C4—34no—
256C2×C3×C4—64no—
257C2×C3×C4—64no—
258C2×C3×C4C2×C4×D311yescharacteristic
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×C4×D312yes—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4C2×C4×D312yes—
263C2×C3×C4C2×C4×D312yes—
264C2×C3×C4C23×D311yescharacteristic
265C2×C3×C4C23×D311yescharacteristic
266C2×Dic3—24no—
267C2×Dic3—24no—
268C2×Dic3—34no—
269C2×Dic3—34no—
270C2×Dic3—32no—
271C2×Dic3—32no—
272C2×Dic3—64no—
273C2×Dic3—62no—
274C2×Dic3C2×C4×D314yes—
275C2×Dic3C2×C4×D314yes—
276C4×D3—38no—
277C4×D3—38no—
278C4×D3—34no—
279C4×D3—34no—
280C4×D3—34no—
281C4×D3—34no—
282C4×D3—68no—
283C4×D3—64no—
284C4×D3—64no—
285C3×C8—24no—
286C3×C8—34no—
287C3×C8—34no—
288C3×C8C2×C4×D314yes—
289C3×C8C2×C4×D314yes—
290C3⋊C8—34no—
291C3⋊C8—34no—
292C3⋊C8—64no—
293C3⋊C8C2×C4×D314yes—
294C3⋊C8C2×C4×D314yes—
295C2×C32#40514yescomplemented
296C2×C32C22×C4211yescharacteristic
297C2×C32C2×#13112yes—
298C3⋊D3—24no—
299C24—91no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—91no—
303C22×C4—92no—
304C22×C4—92no—
305C22×C4—94no—
306C22×C4—94no—
307C22×C4C2×D3211yescharacteristic
308M16—916no—
309C2×C8—32no—
310C2×C8—32no—
311C2×C8—34no—
312C2×C8—34no—
313C2×C8—916no—
314C2×C8—92no—
315C2×C8—94no—
316C2×C8#62414yes—
317C2×C8C2×D3212yes—
318C4⋊C4—98no—
319C22⋊C4—98no—
320C42—32no—
321C42—32no—
322C42—32no—
323C42—32no—
324C22×C3—21no—
325C22×C3—24no—
326C22×C3—22no—
327C22×C3C42×D312yes—
328C22×C3C42×D312yes—
329C22×C3#90114yes—
330C22×C3#90714yes—
331C22×C3C22×C4×D311yescharacteristic
332C22×C3C22×C4×D311yescharacteristic
333C2×D3—34no—
334C2×D3—34no—
335C2×D3—64no—
336C2×D3—68no—
337C2×D3—68no—
338C2×D3—64no—
339C2×D3—64no—
340C2×D3—124no—
341C2×D3—128no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—22no—
345C3×C4—64no—
346C3×C4—64no—
347C3×C4C42×D312yes—
348C3×C4C42×D312yes—
349C3×C4C22×C4×D311yescharacteristic
350C3×C4C22×C4×D311yescharacteristic
351C3×C4C22×C4×D311yescharacteristic
352C3×C4C22×C4×D311yescharacteristic
353Dic3—24no—
354Dic3—24no—
355Dic3—34no—
356Dic3—34no—
357Dic3—64no—
358C32C2×#40511yescharacteristic, complemented, Sylow
359C23—92no—
360C23—94no—
361C23—184no—
362C23C4×D3211yescharacteristic
363C2×C4—34no—
364C2×C4—34no—
365C2×C4—64no—
366C2×C4—64no—
367C2×C4—92no—
368C2×C4—94no—
369C2×C4—94no—
370C2×C4—94no—
371C2×C4—98no—
372C2×C4C4×D3212yes—
373C2×C4C4×D3211yescharacteristic
374C2×C4C2×#62412yes—
375C2×C4C22×D3211yescharacteristic
376C8—34no—
377C8—34no—
378C8—94no—
379C8C2×#62414yes—
380C2×C3—21no—
381C2×C3—22no—
382C2×C3—24no—
383C2×C3#468914yescomplemented
384C2×C3#470814yescomplemented
385C2×C3C2×C42×D311yescharacteristic
386C2×C3C2×C42×D311yescharacteristic
387C2×C3C2×#90112yes—
388C2×C3C2×#90712yes—
389D3—64no—
390D3—64no—
391D3—124no—
392C22—94no—
393C22—184no—
394C22—188no—
395C22#6380414yes—
396C22C4×#62412yes—
397C22C2×C4×D3211yescharacteristic
398C4—64no—
399C4—64no—
400C4—94no—
401C4C4×#62412yes—
402C4C2×C4×D3211yescharacteristic
403C4C22×#62411yescharacteristic
404C3—21no—
405C3C2×#468911yescharacteristic, complemented
406C3C2×#470811yescharacteristic, complemented
407C2—184no—
408C2#1059091014yesdirect product factor
409C2C2×#6380412yes—
410C2C2×C4×#62411yescharacteristic
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×C3×#815C2semidirect
5. C2×C3×C8×Dic3C2semidirect
6. C2×#63554C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590910C2direct (N × H)
14. C2×#3743C4semidirect
24. C2×#3710C4semidirect
26. C3×#815C22semidirect
27. C3×C8×Dic3C22semidirect
28. #63554C22semidirect
29. Dic3×C3⋊C8C22semidirect
40. C2×#815D3semidirect
42. C2×C8×Dic3D3semidirect
60. #3743C2×C4semidirect
71. #3710C2×C4semidirect
111. #815C2×D3semidirect
113. C8×Dic3C2×D3semidirect
295. C2×C32#405semidirect
358. C32C2×#405semidirect
383. C2×C3#4689semidirect
384. C2×C3#4708semidirect
405. C3C2×#4689semidirect
406. C3C2×#4708semidirect
408. C2#10590910direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37432
C2×#638742
C22×#37102
C2×C3×#8152
C2×C3×C8×Dic32
C2×#635542
C2×Dic3×C3⋊C82
#105909102
C2×#47083
C2×#46893