Finite Group Databasebeta

← C2×#10590437 #11858486

Subgroups — C2×#10590437 #11858486

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×D3×C4⋊Dic3C211yesmaximal, characteristic
3C22×#3711C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic, complemented
5C2×C3×#808C211yesmaximal, characteristic, complemented
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590437C218yesmaximal, direct product factor
9C2×#4995—31nomaximal
10C2×#4861—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#892—22no—
22C3×#892C2214yes—
23C2×Dic3⋊Dic3—21no—
24D3×C4⋊Dic3—22no—
25D3×C4⋊Dic3C2214yes—
26C2×#3711C418yescomplemented
27C2×#3711C2214yes—
28#63635C2214yescomplemented
29C3×#808C2214yescomplemented
30#63576C2214yescomplemented
31#63575C2214yescomplemented
32C2×C3×#117—31no—
33C22×C4⋊Dic3—31no—
34C22×#208—31no—
35C22×ΓL(1,𝔽25)—31no—
36C2×#892D311yescharacteristic
37C2×D3×C4⋊C4—31no—
38C2×C3×#106—31no—
39C2×#818—31no—
40#4995—38no—
41C2×#808—31no—
42C2×#808—31no—
43C2×#808—61no—
44C2×#808D311yescharacteristic, complemented
45C2×#807—31no—
46C2×#807—31no—
47C2×#807—31no—
48#4861—38no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×C4×D3C2×C414yes—
57C2×C3×C4×D3D412yes—
58C2×C3×C4×D3Q814yes—
59C2×C3×C4×D3C2312yes—
60C2×D3×Dic3—24no—
61C2×D3×Dic3—44no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2312yes—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66C2×C3⋊(C3⋊C8)C2×C414yescomplemented
67C2×C3⋊(C3⋊C8)C2312yes—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3—24no—
74C2×C3×C3⋊C8C2×C414yescomplemented
75C2×C3×C3⋊C8C2312yes—
76Dic3⋊Dic3—24no—
77#3711C2×C4116yescomplemented
78C2×#428—91noSylow
79C23×C3×C4—31no—
80C23×Dic3—61no—
81C22×C4×D3—61no—
82C22×C4×D3C2×D311yescharacteristic
83C22×C3×C8—31no—
84C3×#117—34no—
85C3×#117—62no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C22⋊C4—61no—
92C2×C3×C42—61no—
93C2×(C2×D3)⋊C4—21no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—34no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3—62no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3—21no—
104C2×#208—38no—
105C2×#208—34no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×ΓL(1,𝔽25)—38no—
111C2×ΓL(1,𝔽25)—34no—
112#892—22no—
113#892C2×D314yes—
114D3×C4⋊C4—34no—
115D3×C4⋊C4—62no—
116C3×#106—34no—
117#818—34no—
118#808—34no—
119#808—34no—
120#808—64no—
121#808C2×D314yescomplemented
122#807—34no—
123#807—34no—
124#807—34no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3C4⋊C414yes—
129C22×C3×D3C2×D412yes—
130C2×C32×C4—22no—
131C2×C32×C4—42no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×Q812yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—42no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3C4⋊C414yes—
143C2×C3×Dic3C2×D412yes—
144C3×C4×D3C4⋊C418yes—
145C3×C4×D3C22×C414yes—
146C3×C4×D3C2×Q814yes—
147D3×Dic3—48no—
148C3⋊(C3⋊C8)C22×C414yescomplemented
149C3×C3⋊C8C22×C414yescomplemented
150C22×M16—91no—
151C2×#117—31no—
152C22×C4⋊C4—91no—
153#428—98no—
154C2×#107—91no—
155C2×#107—91no—
156C2×#106—31no—
157C2×#106—91no—
158C24×C3—31no—
159C23×D3#6711yescharacteristic
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—34no—
165C22×C3×C4—32no—
166C22×C3×C4—34no—
167C22×C3×C4—32no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—64no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—121no—
179C22×Dic3—124no—
180C22×Dic3#6711yescharacteristic
181C2×C4×D3—64no—
182C2×C4×D3—124no—
183C2×C4×D3Dic614yes—
184C2×C4×D3C4×D314yes—
185C2×C4×D3#6712yes—
186C2×C4×D3C22×D312yes—
187C2×C3×C8—34no—
188C2×C3×C8—32no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4C22×D312yes—
198C3×C4⋊C4C22×D312yes—
199C3×C22⋊C4—64no—
200C3×C42—64no—
201(C2×D3)⋊C4—24no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—32no—
205C4⋊Dic3—32no—
206C4⋊Dic3—62no—
207C4⋊Dic3—64no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—121no—
211C4⋊Dic3C22×D312yes—
212C4⋊Dic3C22×D312yes—
213Dic3⋊C4—64no—
214C4×Dic3—24no—
215#208—316no—
216C2×C3⋊C8—34no—
217C2×C3⋊C8—34no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—64no—
222C2×C3⋊C8C4×D314yescomplemented
223C2×C3⋊C8C22×D312yes—
224ΓL(1,𝔽25)—316no—
225C22×C32C2×C4⋊C412yes—
226C22×C32AGL(1,ℤ/8)12yes—
227C22×C32#13712yes—
228C22×C32C22×D411yescharacteristic
229C2×C3×D3—22no—
230C2×C3×D3—22no—
231C2×C3×D3—28no—
232C2×C3×D3C2×C4⋊C414yes—
233C32×C4—42no—
234C32×C4C2×C4⋊C412yes—
235C32×C4C23×C411yescharacteristic
236C32×C4C22×Q811yescharacteristic
237C3⋊Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C3×Dic3C2×C4⋊C414yes—
241C23×C4—31no—
242C23×C4—181no—
243C2×M16—98no—
244C2×M16—94no—
245C22×C8—31no—
246C22×C8—91no—
247#117—34no—
248#117—62no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—94no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—182no—
254C2×C4⋊C4—181no—
255C2×C4⋊C4D3211yescharacteristic
256C2×C22⋊C4—61no—
257C2×C42—61no—
258#107—94no—
259#107—94no—
260#106—34no—
261#106—94no—
262C23×C3—21no—
263C23×C3—34no—
264C23×C3—32no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—22no—
270C22×D3—22no—
271C22×D3Dic3⋊C414yes—
272C22×D3C2×#6712yes—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—34no—
280C2×C3×C4—32no—
281C2×C3×C4—38no—
282C2×C3×C4—34no—
283C2×C3×C4—34no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—82no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4C2×Dic612yes—
293C2×C3×C4C2×C4×D312yes—
294C2×C3×C4C2×C4×D312yes—
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×Q812yes—
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3—128no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—242no—
311C2×Dic3Dic3⋊C414yes—
312C2×Dic3C2×#6712yes—
313C4×D3—128no—
314C4×D3Dic3⋊C418yes—
315C4×D3C2×Dic614yes—
316C4×D3C2×C4×D314yes—
317C3×C8—34no—
318C3⋊C8—34no—
319C3⋊C8—34no—
320C3⋊C8—64no—
321C3⋊C8C2×C4×D314yescomplemented
322C2×C32#42814yescomplemented
323C2×C32C22×C4⋊C411yescharacteristic
324C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
325C2×C32C2×#13711yescharacteristic
326C3×D3—24no—
327C24—31no—
328C22×C4—21no—
329C22×C4—31no—
330C22×C4—32no—
331C22×C4—34no—
332C22×C4—34no—
333C22×C4—32no—
334C22×C4—61no—
335C22×C4—61no—
336C22×C4—184no—
337C22×C4—181no—
338C22×C4—364no—
339C22×C4C2×D3211yescharacteristic
340M16—916no—
341C2×C8—32no—
342C2×C8—34no—
343C2×C8—92no—
344C2×C8—94no—
345C4⋊C4—21no—
346C4⋊C4—32no—
347C4⋊C4—32no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—92no—
351C4⋊C4—184no—
352C4⋊C4—181no—
353C4⋊C4C2×D3212yes—
354C22⋊C4—64no—
355C42—64no—
356C22×C3—21no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—34no—
361C22×C3—62no—
362C22×C3—62no—
363C22×C3—68no—
364C22×C3D3×C4⋊C412yes—
365C22×C3#91412yes—
366C22×C3#91512yes—
367C22×C3C2×Dic3⋊C412yes—
368C22×C3#94912yes—
369C22×C3#95112yes—
370C22×C3C2×D3×D411yescharacteristic
371C22×C3C22×#6711yescharacteristic
372C2×D3—28no—
373C2×D3—22no—
374C2×D3—22no—
375C2×D3C2×Dic3⋊C414yes—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—22no—
379C3×C4—34no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—82no—
383C3×C4—122no—
384C3×C4—122no—
385C3×C4D3×C4⋊C412yes—
386C3×C4C2×Dic3⋊C412yes—
387C3×C4C22×Dic611yescharacteristic
388C3×C4C22×C4×D311yescharacteristic
389C3×C4C22×C4×D311yescharacteristic
390C3×C4C2×D3×Q811yescharacteristic
391Dic3—42no—
392Dic3—42no—
393Dic3—122no—
394Dic3—122no—
395Dic3—242no—
396Dic3C2×Dic3⋊C414yes—
397C32C2×#42811yescharacteristic, complemented, Sylow
398C23—32no—
399C23—34no—
400C23—62no—
401C23—62no—
402C23D3×#6711yescharacteristic
403C2×C4—22no—
404C2×C4—32no—
405C2×C4—34no—
406C2×C4—34no—
407C2×C4—34no—
408C2×C4—38no—
409C2×C4—42no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—122no—
413C2×C4—122no—
414C2×C4—182no—
415C2×C4—368no—
416C2×C4—362no—
417C2×C4D3×Dic612yes—
418C2×C4C4×D3212yes—
419C2×C4D3×#6711yescharacteristic
420C2×C4C22×D3211yescharacteristic
421C8—34no—
422C8—94no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—24no—
426C2×C3—21no—
427C2×C3—64no—
428C2×C3#486114yescomplemented
429C2×C3#499514yescomplemented
430C2×C3C2×D3×C4⋊C411yescharacteristic
431C2×C3C2×#91411yescharacteristic
432C2×C3C2×#91511yescharacteristic
433C2×C3C22×Dic3⋊C411yescharacteristic
434C2×C3C2×#94911yescharacteristic
435C2×C3C2×#95111yescharacteristic
436D3—24no—
437C22—34no—
438C22—62no—
439C22—68no—
440C22—62no—
441C22D3×Dic3⋊C412yes—
442C22#6392912yes—
443C22#6393912yes—
444C22C2×D3×#6711yescharacteristic
445C4—34no—
446C4—42no—
447C4—122no—
448C4—122no—
449C4—362no—
450C4D3×Dic3⋊C412yes—
451C4C2×D3×Dic611yescharacteristic
452C4C2×C4×D3211yescharacteristic
453C3—21no—
454C3C2×#486111yescharacteristic, complemented
455C3C2×#499511yescharacteristic, complemented
456C2—64no—
457C2#1059043714yesdirect product factor
458C2C2×D3×Dic3⋊C411yescharacteristic
459C2C2×#6392911yescharacteristic
460C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#428
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#63635C2semidirect
5. C2×C3×#808C2semidirect
6. C2×#63576C2semidirect
7. C2×#63575C2semidirect
8. #10590437C2direct (N × H)
26. C2×#3711C4semidirect
28. #63635C22semidirect
29. C3×#808C22semidirect
30. #63576C22semidirect
31. #63575C22semidirect
44. C2×#808D3semidirect
66. C2×C3⋊(C3⋊C8)C2×C4semidirect
74. C2×C3×C3⋊C8C2×C4semidirect
77. #3711C2×C4semidirect
121. #808C2×D3semidirect
148. C3⋊(C3⋊C8)C22×C4semidirect
149. C3×C3⋊C8C22×C4semidirect
222. C2×C3⋊C8C4×D3semidirect
321. C3⋊C8C2×C4×D3semidirect
322. C2×C32#428semidirect
397. C32C2×#428semidirect
428. C2×C3#4861semidirect
429. C2×C3#4995semidirect
454. C3C2×#4861semidirect
455. C3C2×#4995semidirect
457. C2#10590437direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×D3×C4⋊Dic32
C22×#37112
C2×#636352
C2×C3×#8082
C2×#635762
C2×#635752
#105904372
C2×#49953
C2×#48613