Finite Group Databasebeta

← C2×#10590517 #11869613

Subgroups — C2×#10590517 #11869613

Order 1152.

985 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#63856C211yesmaximal, characteristic
3C2×#63634C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
8#10590517C218yesmaximal, direct product factor
9C2×#4970—31nomaximal
10C2×#4811—31nomaximal
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×D3×C4⋊C4—22no—
21C3×D3×C4⋊C4C2214yes—
22C2×#3724—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63856—22no—
25#63856C2214yes—
26#63634C2214yescomplemented
27C3×#810C2214yescomplemented
28#63575C2214yescomplemented
29#63565C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yes—
31C22×C3×C4⋊C4—31no—
32C2×#946—31no—
33C2×#924—31no—
34C2×D3×C4⋊C4D311yescharacteristic
35C2×C3×#103—31no—
36C2×#835—31no—
37C2×#830—31no—
38C2×(C2×D3)⋊C8—31no—
39C2×#818—31no—
40#4970—38no—
41C2×#810—31no—
42C2×#810D311yescharacteristic, complemented
43C2×#807—31no—
44C2×#807—31no—
45C2×#807—31no—
46C2×#807—61no—
47#4811—38no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—24no—
58C2×C3×C4×D3—44no—
59C2×C3×C4×D3D412yes—
60C2×C3×C4×D3C2312yes—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×Dic3⋊C4—24no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76#3724—24no—
77(C2×D3)⋊Dic3—24no—
78C2×#484—91noSylow
79C22×C3×Q8—31no—
80C23×C3×C4—31no—
81C23×C3×C4—61no—
82C22×C4×D3—21no—
83C22×C4×D3C2×D311yescharacteristic
84C22×Dic6C2×D311yescharacteristic
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—34no—
89C2×C3×C4⋊C4—62no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×#217—61no—
94#946—34no—
95#946—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101#924—34no—
102#924—62no—
103C2×Dic3⋊C4—21no—
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—61no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110D3×C4⋊C4—22no—
111D3×C4⋊C4C2×D314yes—
112C3×#103—34no—
113#835—34no—
114#830—34no—
115(C2×D3)⋊C8—34no—
116#818—34no—
117#810—34no—
118#810C2×D314yescomplemented
119#807—34no—
120#807—34no—
121#807—34no—
122#807—64no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3Q1614yes—
127C22×C3×D3C2×D412yes—
128C2×C32×C4—22no—
129C2×C32×C4—42no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4112yes—
132C2×C32×C4#4112yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—42no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3C2×D412yes—
142C3×C4×D3—24no—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C3×C4×D3—48no—
146C3×Dic6—22no—
147C3×Dic6—22no—
148C3×Dic6—42no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—22no—
151C2×C22⋊Q8—91no—
152C22×C4⋊C4—31no—
153#484—98no—
154C2×#107—91no—
155C2×#107—91no—
156C2×#103—31no—
157C2×#103—91no—
158C2×C22⋊C8—91no—
159C24×C3—31no—
160C23×D3#6711yescharacteristic
161C2×C3×Q8—32no—
162C2×C3×Q8—61no—
163C2×C3×Q8—62no—
164C2×C3×Q8—62no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4—41no—
172C22×C3×C4—64no—
173C22×C3×C4—62no—
174C22×C3×C4—62no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—124no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—121no—
185C22×Dic3#6711yescharacteristic
186C2×C4×D3—22no—
187C2×C4×D3—22no—
188C2×C4×D3—24no—
189C2×C4×D3—44no—
190C2×C4×D3#6712yes—
191C2×C4×D3C22×D312yes—
192C2×Dic6—22no—
193C2×Dic6—22no—
194C2×Dic6—21no—
195C2×Dic6C22×D312yes—
196C2×C3×C8—32no—
197C2×C3×C8—62no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—32no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—64no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4C22×D312yes—
206C3×C4⋊C4C22×D312yes—
207#217—64no—
208(C2×D3)⋊C4—64no—
209C4⋊Dic3—21no—
210C4⋊Dic3—32no—
211C4⋊Dic3—32no—
212C4⋊Dic3—62no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—24no—
218Dic3⋊C4—64no—
219Dic3⋊C4—64no—
220C2×C3⋊C8—22no—
221C2×C3⋊C8—32no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—64no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8C22×D312yes—
228C22×C32#12312yes—
229C22×C32C2×Q1612yes—
230C22×C32AGL(1,ℤ/8)12yes—
231C22×C32C22×D411yescharacteristic
232C2×C3×D3—22no—
233C2×C3×D3—22no—
234C2×C3×D3—28no—
235C2×C3×D3C2×Q1614yes—
236C32×C4—42no—
237C32×C4#12312yes—
238C32×C4C2×#4111yescharacteristic
239C32×C4C2×#4111yescharacteristic
240C3⋊Dic3—42no—
241C3×Dic3—22no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C22×Q8—31no—
245C23×C4—31no—
246C23×C4—61no—
247C22×C8—31no—
248C22×C8—91no—
249C22⋊Q8—94no—
250C22⋊Q8—182no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—34no—
253C2×C4⋊C4—62no—
254C2×C4⋊C4—61no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—181no—
257C2×C4⋊C4D3211yescharacteristic
258C2×C22⋊C4—181no—
259#107—94no—
260#107—94no—
261#103—34no—
262#103—94no—
263C22⋊C8—94no—
264C23×C3—21no—
265C23×C3—34no—
266C23×C3—32no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3D3×D411yescharacteristic
270C23×C3C2×#6711yescharacteristic
271C22×D3—22no—
272C22×D3—22no—
273C22×D3#21614yes—
274C22×D3C2×#6712yes—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×Q8—122no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—32no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—62no—
289C2×C3×C4—64no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—82no—
295C2×C3×C4—128no—
296C2×C3×C4—122no—
297C2×C3×C4—122no—
298C2×C3×C4#23512yes—
299C2×C3×C4#23512yes—
300C2×C3×C4#23512yes—
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4#23712yes—
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—42no—
310C2×Dic3—42no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—242no—
317C2×Dic3C2×#6712yes—
318C4×D3—24no—
319C4×D3—22no—
320C4×D3—22no—
321C4×D3—48no—
322Dic6—22no—
323Dic6—22no—
324Dic6—42no—
325C3×C8—62no—
326C3⋊C8—22no—
327C3⋊C8—64no—
328C3⋊C8—62no—
329C3⋊C8—62no—
330C2×C32#48414yescomplemented
331C2×C32C2×#12311yescharacteristic
332C2×C32C22×Q1611yescharacteristic
333C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
334C3×D3—24no—
335C24—31no—
336C2×Q8—32no—
337C2×Q8—61no—
338C2×Q8—62no—
339C2×Q8—62no—
340C22×C4—21no—
341C22×C4—31no—
342C22×C4—32no—
343C22×C4—32no—
344C22×C4—64no—
345C22×C4—62no—
346C22×C4—62no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—124no—
350C22×C4—181no—
351C22×C4C2×D3211yescharacteristic
352C2×C8—32no—
353C2×C8—62no—
354C2×C8—92no—
355C2×C8—182no—
356C4⋊C4—21no—
357C4⋊C4—32no—
358C4⋊C4—64no—
359C4⋊C4—61no—
360C4⋊C4—92no—
361C4⋊C4—184no—
362C4⋊C4—181no—
363C4⋊C4C2×D3212yes—
364C22⋊C4—184no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—34no—
370C22×C3—62no—
371C22×C3—62no—
372C22×C3—68no—
373C22×C3#88312yes—
374C22×C3#91412yes—
375C22×C3D3×Q1612yes—
376C22×C3#92912yes—
377C22×C3#93212yes—
378C22×C3C2×#21612yes—
379C22×C3C2×D3×D411yescharacteristic
380C22×C3C22×#6711yescharacteristic
381C2×D3—28no—
382C2×D3—22no—
383C2×D3—22no—
384C2×D3C2×#21614yes—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—22no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—62no—
391C3×C4—82no—
392C3×C4—122no—
393C3×C4—122no—
394C3×C4#88312yes—
395C3×C4#92912yes—
396C3×C4C2×#23511yescharacteristic
397C3×C4C2×#23511yescharacteristic
398C3×C4C2×#23511yescharacteristic
399C3×C4C2×#23711yescharacteristic
400Dic3—22no—
401Dic3—42no—
402Dic3—42no—
403Dic3—122no—
404Dic3—122no—
405Dic3—242no—
406C32C2×#48411yescharacteristic, complemented, Sylow
407C23—32no—
408C23—34no—
409C23—62no—
410C23—62no—
411C23D3×#6711yescharacteristic
412Q8—62no—
413Q8—62no—
414Q8—122no—
415C2×C4—22no—
416C2×C4—32no—
417C2×C4—42no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—64no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—128no—
425C2×C4—122no—
426C2×C4—122no—
427C2×C4—182no—
428C2×C4—362no—
429C2×C4#379512yes—
430C2×C4#379812yes—
431C2×C4D3×#6711yescharacteristic
432C2×C4C22×D3211yescharacteristic
433C8—62no—
434C8—182no—
435C2×C3—21no—
436C2×C3—24no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—64no—
440C2×C3#481114yescomplemented
441C2×C3#497014yescomplemented
442C2×C3C2×#88311yescharacteristic
443C2×C3C2×#91411yescharacteristic
444C2×C3C2×D3×Q1611yescharacteristic
445C2×C3C2×#92911yescharacteristic
446C2×C3C2×#93211yescharacteristic
447C2×C3C22×#21611yescharacteristic
448D3—24no—
449C22—34no—
450C22—62no—
451C22—68no—
452C22—62no—
453C22#6390512yes—
454C22#6393412yes—
455C22D3×#21612yes—
456C22C2×D3×#6711yescharacteristic
457C4—42no—
458C4—62no—
459C4—122no—
460C4—122no—
461C4—362no—
462C4#6390512yes—
463C4C2×#379511yescharacteristic
464C4C2×#379811yescharacteristic
465C3—21no—
466C3C2×#481111yescharacteristic, complemented
467C3C2×#497011yescharacteristic, complemented
468C2—64no—
469C2#1059051714yesdirect product factor
470C2C2×#6390511yescharacteristic
471C2C2×#6393411yescharacteristic
472C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#484
LCSG ▷ C2×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
3. C2×#63634C2semidirect
4. C2×C3×#810C2semidirect
5. C2×#63575C2semidirect
6. C2×#63565C2semidirect
8. #10590517C2direct (N × H)
26. #63634C22semidirect
27. C3×#810C22semidirect
28. #63575C22semidirect
29. #63565C22semidirect
42. C2×#810D3semidirect
118. #810C2×D3semidirect
330. C2×C32#484semidirect
406. C32C2×#484semidirect
440. C2×C3#4811semidirect
441. C2×C3#4970semidirect
466. C3C2×#4811semidirect
467. C3C2×#4970semidirect
469. C2#10590517direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×#638562
C2×#636342
C2×C3×#8102
C2×#635752
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
#105905172
C2×#49703
C2×#48113