Finite Group Databasebeta

← C2×#10590684 #11869617

Subgroups — C2×#10590684 #11869617

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
5C2×C3×#818C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590684C218yesmaximal, direct product factor
9C2×#4884—31nomaximal
10C2×#4722—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×D3×Dic3—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22D3×C4⋊Dic3—22no—
23D3×C4⋊Dic3C2214yes—
24#63857—22no—
25#63857C2214yes—
26#63643C2214yescomplemented
27C3×(C2×D3)⋊C8C2214yes—
28C3×#818C2214yescomplemented
29#63575C2214yescomplemented
30#63567C2214yescomplemented
31C22×C4⋊Dic3—31no—
32C2×#924—31no—
33C2×#897—31no—
34C2×D3×C4⋊C4—31no—
35C2×C3×#107—31no—
36C2×C3×C22⋊C8—31no—
37C2×(C2×D3)⋊C8D311yescharacteristic
38C2×#818—31no—
39C2×#818D311yescharacteristic, complemented
40C2×#816—31no—
41C2×#816—31no—
42C2×#816—31no—
43C2×#816—61no—
44C2×#810—31no—
45C2×#807—31no—
46#4884—38no—
47#4722—38no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C2×#634—22no—
53C2×#634—22no—
54C2×#634—21no—
55C2×#634C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3D412yes—
62C2×C3×C4×D3C2312yes—
63C2×D3×Dic3—24no—
64C2×D3×Dic3—44no—
65C2×C32×C8—22no—
66C2×C32×C8C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75Dic3⋊Dic3—24no—
76Dic3⋊Dic3—24no—
77(C2×D3)⋊Dic3—24no—
78C2×#484—91noSylow
79C23×C3×C4—31no—
80C23×Dic3—61no—
81C22×C4×D3—61no—
82C22×C4×D3C2×D311yescharacteristic
83C22×Dic6—31no—
84C22×Dic6—31no—
85C22×Dic6—61no—
86C22×C3×C8—21no—
87C22×C3×C8—31no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×#217—61no—
93C2×(C2×D3)⋊C4—61no—
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⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103#924—34no—
104#924—62no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#897—34no—
109#897—62no—
110D3×C4⋊C4—34no—
111D3×C4⋊C4—62no—
112C3×#107—34no—
113C3×C22⋊C8—34no—
114(C2×D3)⋊C8C2×D314yes—
115#818—34no—
116#818C2×D314yescomplemented
117#816—34no—
118#816—34no—
119#816—34no—
120#816—64no—
121#810—34no—
122#807—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3Q1614yes—
127C22×C3×D3C2×D412yes—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4112yes—
130C2×C32×C4#4112yes—
131C2×C32×C4C2411yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—42no—
135C2×C3⋊Dic3—42no—
136#634—22no—
137#634—22no—
138#634—42no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3C2×D412yes—
145C3×C4×D3—24no—
146C3×C4×D3—22no—
147C3×C4×D3—22no—
148D3×Dic3—48no—
149C32×C8—22no—
150C3×C3⋊C8—22no—
151C2×C22⋊Q8—91no—
152C22×C4⋊C4—91no—
153#484—98no—
154C2×#107—31no—
155C2×#107—91no—
156C2×#103—91no—
157C2×#103—91no—
158C2×C22⋊C8—31no—
159C24×C3—31no—
160C23×D3D1211yescharacteristic
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—32no—
164C22×C3×C4—32no—
165C22×C3×C4—62no—
166C22×C3×C4—62no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—64no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—121no—
179C22×Dic3—121no—
180C22×Dic3—124no—
181C22×Dic3D1211yescharacteristic
182C2×C4×D3—22no—
183C2×C4×D3—22no—
184C2×C4×D3—64no—
185C2×C4×D3—124no—
186C2×C4×D3D1212yes—
187C2×C4×D3C22×D312yes—
188C2×Dic6—32no—
189C2×Dic6—32no—
190C2×Dic6—62no—
191C2×Dic6—64no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—62no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—121no—
199C2×Dic6—122no—
200C2×C3×C8—22no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—32no—
204C2×C3×C8—42no—
205C2×C3×C8—62no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212#217—64no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—32no—
217C4⋊Dic3—32no—
218C4⋊Dic3—62no—
219C4⋊Dic3—64no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—64no—
223C4⋊Dic3—121no—
224C4⋊Dic3C22×D312yes—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—64no—
227Dic3⋊C4—64no—
228C2×C3⋊C8—22no—
229C2×C3⋊C8C22×D312yes—
230C22×C32#12312yes—
231C22×C32C2×Q1612yes—
232C22×C32AGL(1,ℤ/8)12yes—
233C22×C32C22×D411yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—28no—
237C2×C3×D3C2×Q1614yes—
238C32×C4#12312yes—
239C32×C4C2×#4111yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3⋊Dic3—42no—
242C3⋊Dic3—42no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—91no—
247C23×C4—31no—
248C23×C4—181no—
249C22×C8—31no—
250C22×C8D3211yescharacteristic
251C22⋊Q8—94no—
252C22⋊Q8—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—94no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—182no—
258C2×C4⋊C4—181no—
259C2×C4⋊C4—181no—
260C2×C22⋊C4—181no—
261#107—34no—
262#107—94no—
263#103—94no—
264#103—94no—
265C22⋊C8—34no—
266C23×C3—21no—
267C23×C3—34no—
268C23×C3—32no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3C2×D1211yescharacteristic
272C23×C3D3×D411yescharacteristic
273C22×D3—22no—
274C22×D3—22no—
275C22×D3Dic1214yes—
276C22×D3C2×D1212yes—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—32no—
282C2×C3×C4—62no—
283C2×C3×C4—64no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—122no—
289C2×C3×C4—122no—
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4#23512yes—
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4#23712yes—
294C2×C3×C4#23712yes—
295C2×C3×C4#23912yes—
296C2×C3×C4C23×D311yescharacteristic
297C2×C3×C4C23×D311yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—42no—
302C2×Dic3—42no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—122no—
308C2×Dic3—122no—
309C2×Dic3—128no—
310C2×Dic3—124no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—242no—
316C2×Dic3C2×D1212yes—
317C4×D3—24no—
318C4×D3—22no—
319C4×D3—22no—
320C4×D3—128no—
321Dic6—64no—
322Dic6—62no—
323Dic6—62no—
324Dic6—62no—
325Dic6—62no—
326Dic6—122no—
327Dic6—124no—
328Dic6—122no—
329Dic6—122no—
330C3×C8—22no—
331C3×C8—22no—
332C3×C8—42no—
333C3×C8—62no—
334C3⋊C8—22no—
335C2×C32#48414yescomplemented
336C2×C32C2×#12311yescharacteristic
337C2×C32C22×Q1611yescharacteristic
338C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
339C3×D3—24no—
340C24—31no—
341C2×Q8—92no—
342C2×Q8—181no—
343C2×Q8—182no—
344C2×Q8—182no—
345C22×C4—31no—
346C22×C4—32no—
347C22×C4—32no—
348C22×C4—62no—
349C22×C4—62no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—184no—
353C22×C4—181no—
354C22×C4—181no—
355C22×C4—364no—
356C22×C4C2×D3211yescharacteristic
357C2×C8—22no—
358C2×C8—32no—
359C2×C8—62no—
360C2×C8C2×D3212yes—
361C4⋊C4—32no—
362C4⋊C4—32no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—92no—
366C4⋊C4—184no—
367C4⋊C4—184no—
368C4⋊C4—181no—
369C22⋊C4—184no—
370C22×C3—21no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—34no—
375C22×C3—68no—
376C22×C3—62no—
377C22×C3—62no—
378C22×C3#88612yes—
379C22×C3#89412yes—
380C22×C3C2×Dic1212yes—
381C22×C3#90812yes—
382C22×C3#91112yes—
383C22×C3D3×Q1612yes—
384C22×C3C22×D1211yescharacteristic
385C22×C3C2×D3×D411yescharacteristic
386C2×D3—28no—
387C2×D3—22no—
388C2×D3—22no—
389C2×D3C2×Dic1214yes—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—62no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4#88612yes—
397C3×C4#89412yes—
398C3×C4C2×#23511yescharacteristic
399C3×C4C2×#23711yescharacteristic
400C3×C4C2×#23711yescharacteristic
401C3×C4C2×#23911yescharacteristic
402Dic3—22no—
403Dic3—42no—
404Dic3—42no—
405Dic3—124no—
406Dic3—122no—
407Dic3—122no—
408Dic3—122no—
409Dic3—122no—
410Dic3—242no—
411C32C2×#48411yescharacteristic, complemented, Sylow
412C23—32no—
413C23—34no—
414C23—62no—
415C23—62no—
416C23D3×D1211yescharacteristic
417Q8—182no—
418Q8—182no—
419Q8—362no—
420C2×C4—32no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—64no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—368no—
432C2×C4—362no—
433C2×C4—362no—
434C2×C4#379612yes—
435C2×C4D3×D1211yescharacteristic
436C2×C4#380412yes—
437C2×C4C22×D3211yescharacteristic
438C8—22no—
439C8—62no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—24no—
444C2×C3—64no—
445C2×C3#472214yescomplemented
446C2×C3#488414yescomplemented
447C2×C3C2×#88611yescharacteristic
448C2×C3C2×#89411yescharacteristic
449C2×C3C22×Dic1211yescharacteristic
450C2×C3C2×#90811yescharacteristic
451C2×C3C2×#91111yescharacteristic
452C2×C3C2×D3×Q1611yescharacteristic
453D3—24no—
454C22—34no—
455C22—62no—
456C22—62no—
457C22—68no—
458C22#6379512yes—
459C22D3×Dic1212yes—
460C22#6389012yes—
461C22C2×D3×D1211yescharacteristic
462C4—62no—
463C4—122no—
464C4—122no—
465C4—362no—
466C4—362no—
467C4#6389012yes—
468C4C2×#379611yescharacteristic
469C4C2×#380411yescharacteristic
470C3—21no—
471C3C2×#472211yescharacteristic, complemented
472C3C2×#488411yescharacteristic, complemented
473C2—64no—
474C2#1059068414yesdirect product factor
475C2C2×#6379511yescharacteristic
476C2C2×D3×Dic1211yescharacteristic
477C2C2×#6389011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×C8D32
hypocenterC32C2×#484
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
3. C2×#63643C2semidirect
5. C2×C3×#818C2semidirect
6. C2×#63575C2semidirect
7. C2×#63567C2semidirect
8. #10590684C2direct (N × H)
26. #63643C22semidirect
28. C3×#818C22semidirect
29. #63575C22semidirect
30. #63567C22semidirect
39. C2×#818D3semidirect
116. #818C2×D3semidirect
335. C2×C32#484semidirect
411. C32C2×#484semidirect
445. C2×C3#4722semidirect
446. C2×C3#4884semidirect
471. C3C2×#4722semidirect
472. C3C2×#4884semidirect
474. C2#10590684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×#638572
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×C3×#8182
C2×#635752
C2×#635672
#105906842
C2×#48843
C2×#47223