Finite Group Databasebeta

← C2×#10591084 #11857798

Subgroups — C2×#10591084 #11857798

Order 1152.

1749 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C2×#64135C211yesmaximal, characteristic, complemented
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63566C212yesmaximal, complemented
5#10591084C218yesmaximal, direct product factor
6C2×#63563C212yesmaximal, complemented
7C2×#5233—31nomaximal
8C2×#5113—31nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67—21no—
11C2×C3×#235—24no—
12C2×C3×#235—22no—
13C2×C3×#235C418yescomplemented
14C2×C3×#235C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3—21no—
17C22×C3×Dic6C2211yescharacteristic
18C2×#3757—21no—
19#64135—22no—
20#64135C2214yescomplemented
21C2×C4⋊(C3⋊Dic3)C2212yes—
22C2×C4×C3⋊Dic3—21no—
23C22×C3×C3⋊C8—24no—
24C22×C3×C3⋊C8C2212yes—
25C22×C3×C3⋊C8C2214yescomplemented
26#63566C2218yescomplemented
27#63563C2218yescomplemented
28C22×C3×#41—31no—
29C22×#235D311yescharacteristic
30C23×C3×C8—31no—
31C2×#926—31no—
32C2×#926—31no—
33C2×#926—61no—
34C23×C3⋊C8D311yescharacteristic, complemented
35#5233—38no—
36C2×#835—32no—
37C2×#832—32no—
38#5113—38no—
39C2×#821—32no—
40C2×#816—32no—
41C24×C32D411yescharacteristic
42C23×C3×D3—21no—
43C22×C32×C4C2×C414yes—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D412yes—
46C22×C32×C4D414yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2312yes—
49C22×C3⋊Dic3—22no—
50C2×C3×#67—28no—
51C2×C3×#67—24no—
52C22×C3×Dic3—21no—
53C3×#235—216no—
54C3×#235—28no—
55C3×#235C2×C4116yescomplemented
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—28no—
61C2×C3×C4×D3—24no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yes—
65C2×C3×Dic6C2312yes—
66#3757—24no—
67C4⋊(C3⋊Dic3)—22no—
68C4⋊(C3⋊Dic3)C2314yes—
69C4×C3⋊Dic3—24no—
70C2×C3×C3⋊C8—24no—
71C2×C3×C3⋊C8—28no—
72C2×C3×C3⋊C8C2314yes—
73C2×#416—91noSylow
74C2×C3×#41—38no—
75C2×C3×#41—34no—
76C2×C3×#41—62no—
77C2×C3×#41—64no—
78C22×C3×Q8—31no—
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4—61no—
83C23×C3×C4C2×D311yescharacteristic
84C23×C3×C4C2×D311yescharacteristic
85C22×#67—21no—
86C2×#235—24no—
87C2×#235—22no—
88C2×#235Dic318yescomplemented
89C2×#235C2×D314yes—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—21no—
92C22×Dic6C2×D311yescharacteristic
93C22×C3×C8—32no—
94C22×C3×C8—34no—
95C22×C3×C8—64no—
96C2×#217—62no—
97C2×#217—61no—
98C2×#217—61no—
99#926—34no—
100#926—34no—
101#926—64no—
102#926—64no—
103#926—62no—
104#926—62no—
105C2×C4⋊Dic3—32no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—62no—
108C2×C4×Dic3—62no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111C22×C3⋊C8—24no—
112C22×C3⋊C8C2×D312yes—
113C22×C3⋊C8C2×D314yescomplemented
114#835—38no—
115#832—38no—
116#821—38no—
117#816—38no—
118C23×C32—24no—
119C23×C32C22⋊C414yes—
120C23×C32C2×D412yes—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—44no—
125C2×C32×C4C22⋊C414yes—
126C2×C32×C4C22⋊C418yes—
127C2×C32×C4C22×C412yes—
128C2×C32×C4C22×C414yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×D414yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3⋊Dic3—24no—
135C2×C3⋊Dic3—44no—
136C3×#67—216no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—22no—
139C3×D12—24no—
140C3×D12—22no—
141C3×D12C22×C414yes—
142C3×C4×D3—216no—
143C3×Dic6—24no—
144C3×Dic6—22no—
145C3×Dic6C22×C414yes—
146C3×C3⋊C8—24no—
147C22×#41—31no—
148C23×C8—31no—
149C2×#117—91no—
150#416—98no—
151C2×#103—92no—
152C2×#102—92no—
153C24×C3—21no—
154C24×C3—61no—
155C24×C3D1211yescharacteristic
156C24×C3#6711yescharacteristic
157C23×D3—21no—
158C3×#41—316no—
159C3×#41—616no—
160C3×#41—68no—
161C2×C3×Q8—34no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—62no—
165C2×C3×D4—34no—
166C2×C3×D4—32no—
167C2×C3×D4—68no—
168C2×C3×D4—64no—
169C2×C3×D4—61no—
170C2×C3×D4—62no—
171C22×C3×C4—24no—
172C22×C3×C4—24no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—61no—
178C22×C3×C4—68no—
179C22×C3×C4—64no—
180C22×C3×C4C4×D314yes—
181C22×C3×C4D1212yes—
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4C2×Dic314yes—
184C22×C3×C4#6714yes—
185C22×C3×C4#6714yes—
186C22×C3×C4#6712yes—
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D312yes—
192C2×#67—28no—
193C2×#67—24no—
194C22×Dic3—21no—
195C22×Dic3—64no—
196C22×Dic3—62no—
197C22×Dic3—62no—
198#235—216no—
199#235—28no—
200#235C2×Dic3116yescomplemented
201C2×D12—22no—
202C2×D12—21no—
203C2×D12C2×Dic314yes—
204C2×D12C22×D312yes—
205C2×C4×D3—28no—
206C2×C4×D3—24no—
207C2×Dic6—22no—
208C2×Dic6—21no—
209C2×Dic6C2×Dic314yes—
210C2×Dic6C22×D312yes—
211C2×C3×C8—34no—
212C2×C3×C8—64no—
213C2×C3×C8—68no—
214#217—68no—
215#217—64no—
216#217—64no—
217C4⋊Dic3—34no—
218C4⋊Dic3—34no—
219C4⋊Dic3—64no—
220C4⋊Dic3—64no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223C4×Dic3—68no—
224C4×Dic3—64no—
225C4×Dic3—64no—
226C2×C3⋊C8—24no—
227C2×C3⋊C8—28no—
228C2×C3⋊C8C22×D314yes—
229C22×C32—24no—
230C22×C32—28no—
231C22×C32C2×C22⋊C414yes—
232C22×C32C2×C22⋊C412yes—
233C22×C32#13514yes—
234C22×C32C22×D411yescharacteristic
235C2×C3×D3—24no—
236C2×C3×D3—44no—
237C2×C3×D3—48no—
238C32×C4C2×C22⋊C412yes—
239C32×C4C2×C22⋊C414yes—
240C32×C4C23×C411yescharacteristic
241C32×C4C22×D411yescharacteristic
242C3⋊Dic3—44no—
243C3×Dic3—24no—
244C2×#41—38no—
245C2×#41—34no—
246C2×#41—64no—
247C2×#41—62no—
248C22×Q8—31no—
249C22×D4—31no—
250C22×D4—61no—
251C23×C4—61no—
252C23×C4D3211yescharacteristic
253C22×C8—32no—
254C22×C8—34no—
255C22×C8—64no—
256#117—94no—
257#117—182no—
258C2×C4⋊C4—92no—
259C2×C22⋊C4—181no—
260C2×C42—181no—
261#103—98no—
262#102—98no—
263C23×C3—24no—
264C23×C3—24no—
265C23×C3—24no—
266C23×C3—21no—
267C23×C3—22no—
268C23×C3—44no—
269C23×C3—64no—
270C23×C3—62no—
271C23×C3—124no—
272C23×C3(C2×D3)⋊C414yes—
273C23×C3#21714yes—
274C23×C3C2×D1212yes—
275C23×C3C2×D1211yescharacteristic
276C23×C3C2×#6712yes—
277C23×C3C2×#6711yescharacteristic
278C22×D3—24no—
279C22×D3—22no—
280C22×D3—44no—
281C3×Q8—34no—
282C3×Q8—64no—
283C3×Q8—62no—
284C3×D4—34no—
285C3×D4—616no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—21no—
289C2×C3×C4—24no—
290C2×C3×C4—28no—
291C2×C3×C4—22no—
292C2×C3×C4—24no—
293C2×C3×C4—22no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—64no—
298C2×C3×C4—62no—
299C2×C3×C4—616no—
300C2×C3×C4(C2×D3)⋊C414yes—
301C2×C3×C4(C2×D3)⋊C418yes—
302C2×C3×C4#21714yes—
303C2×C3×C4#21718yes—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×C4×D314yes—
306C2×C3×C4C2×D1212yes—
307C2×C3×C4C2×D1211yescharacteristic
308C2×C3×C4C22×Dic312yes—
309C2×C3×C4C22×Dic314yes—
310C2×C3×C4C2×#6712yes—
311C2×C3×C4C2×#6714yes—
312C2×C3×C4C2×#6712yes—
313C2×C3×C4C2×#6714yes—
314C2×C3×C4C2×#6712yes—
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C23×D311yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318#67—216no—
319C2×Dic3—24no—
320C2×Dic3—22no—
321C2×Dic3—68no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—128no—
325C2×Dic3—124no—
326C2×Dic3—124no—
327D12—24no—
328D12—22no—
329D12C22×Dic314yes—
330C4×D3—216no—
331Dic6—24no—
332Dic6—22no—
333Dic6C22×Dic314yes—
334C3×C8—64no—
335C3⋊C8—24no—
336C2×C32—24no—
337C2×C32#41614yescomplemented
338C2×C32C22×C22⋊C411yescharacteristic
339C2×C32C2×#13512yes—
340C3×D3—44no—
341C24—61no—
342C24#62611yescharacteristic
343#41—316no—
344#41—616no—
345#41—68no—
346C2×Q8—32no—
347C2×Q8—34no—
348C2×Q8—62no—
349C2×Q8—61no—
350C2×D4—32no—
351C2×D4—34no—
352C2×D4—68no—
353C2×D4—64no—
354C2×D4—62no—
355C2×D4—61no—
356C22×C4—61no—
357C22×C4—68no—
358C22×C4—64no—
359C22×C4—182no—
360C22×C4D3×Dic314yes—
361C22×C4#62514yes—
362C22×C4#62612yes—
363C22×C4#62611yescharacteristic
364C22×C4C2×D3211yescharacteristic
365C22×C4C2×D3212yes—
366C2×C8—34no—
367C2×C8—64no—
368C2×C8—68no—
369C4⋊C4—94no—
370C4⋊C4—182no—
371C22⋊C4—184no—
372C42—184no—
373C22×C3—24no—
374C22×C3—28no—
375C22×C3—24no—
376C22×C3—28no—
377C22×C3—21no—
378C22×C3—24no—
379C22×C3—22no—
380C22×C3—24no—
381C22×C3—48no—
382C22×C3—44no—
383C22×C3—64no—
384C22×C3—124no—
385C22×C3—128no—
386C22×C3#90414yes—
387C22×C3C2×(C2×D3)⋊C414yes—
388C22×C3C2×(C2×D3)⋊C412yes—
389C22×C3#95014yes—
390C22×C3C2×#21714yes—
391C22×C3C2×#21712yes—
392C22×C3C22×D1211yescharacteristic
393C22×C3C22×#6711yescharacteristic
394C2×D3—24no—
395C2×D3—48no—
396C2×D3—44no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—24no—
400C3×C4—22no—
401C3×C4—64no—
402C3×C4C2×(C2×D3)⋊C414yes—
403C3×C4C2×(C2×D3)⋊C412yes—
404C3×C4C2×#21712yes—
405C3×C4C2×#21714yes—
406C3×C4C22×C4×D311yescharacteristic
407C3×C4C23×Dic311yescharacteristic
408C3×C4C22×#6711yescharacteristic
409C3×C4C22×#6711yescharacteristic
410Dic3—24no—
411Dic3—128no—
412Dic3—124no—
413Dic3—124no—
414C32C2×#41611yescharacteristic, complemented, Sylow
415C23—24no—
416C23—62no—
417C23—64no—
418C23—124no—
419C23(C2×D3)⋊Dic314yes—
420C23C2×#62612yes—
421C23C2×#62611yescharacteristic
422Q8—34no—
423Q8—62no—
424Q8—64no—
425D4—34no—
426D4—616no—
427D4—62no—
428D4—64no—
429C2×C4—62no—
430C2×C4—64no—
431C2×C4—616no—
432C2×C4—184no—
433C2×C4—364no—
434C2×C4(C2×D3)⋊Dic314yes—
435C2×C4(C2×D3)⋊Dic318yes—
436C2×C4C2×D3×Dic312yes—
437C2×C4C2×D3×Dic314yes—
438C2×C4C2×#62512yes—
439C2×C4C2×#62514yes—
440C2×C4C2×#62612yes—
441C2×C4C2×#62611yescharacteristic
442C2×C4C22×D3211yescharacteristic
443C8—64no—
444C2×C3—24no—
445C2×C3—24no—
446C2×C3—24no—
447C2×C3—21no—
448C2×C3—22no—
449C2×C3—44no—
450C2×C3—124no—
451C2×C3#511314yescomplemented
452C2×C3#523314yescomplemented
453C2×C3C2×#90412yes—
454C2×C3C22×(C2×D3)⋊C411yescharacteristic
455C2×C3C2×#95012yes—
456C2×C3C22×#21711yescharacteristic
457D3—44no—
458C22—28no—
459C22—24no—
460C22—64no—
461C22—128no—
462C22—124no—
463C22#6382914yes—
464C22C2×(C2×D3)⋊Dic314yes—
465C22C2×(C2×D3)⋊Dic312yes—
466C22C22×#62611yescharacteristic
467C4—64no—
468C4—364no—
469C4C2×(C2×D3)⋊Dic314yes—
470C4C2×(C2×D3)⋊Dic312yes—
471C4C22×D3×Dic311yescharacteristic
472C4C22×#62511yescharacteristic
473C3—21no—
474C3C2×#511311yescharacteristic, complemented
475C3C2×#523311yescharacteristic, complemented
476C2—24no—
477C2—124no—
478C2#1059108414yesdirect product factor
479C2C2×#6382912yes—
480C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC22×C4#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×C3×#235C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64135C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. C2×#63566C2semidirect
5. #10591084C2direct (N × H)
6. C2×#63563C2semidirect
13. C2×C3×#235C4semidirect
20. #64135C22semidirect
25. C22×C3×C3⋊C8C22semidirect
26. #63566C22semidirect
27. #63563C22semidirect
34. C23×C3⋊C8D3semidirect
55. C3×#235C2×C4semidirect
88. C2×#235Dic3semidirect
113. C22×C3⋊C8C2×D3semidirect
200. #235C2×Dic3semidirect
337. C2×C32#416semidirect
414. C32C2×#416semidirect
451. C2×C3#5113semidirect
452. C2×C3#5233semidirect
474. C3C2×#5113semidirect
475. C3C2×#5233semidirect
478. C2#10591084direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#641352
C23×C3×C3⋊C82
C2×#635662
#105910842
C2×#635632
C2×#52333
C2×#51133