Finite Group Databasebeta

← C2×#10591478 #11873443

Subgroups — C2×#10591478 #11873443

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic
2C2×#63869C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5#10591478C218yesmaximal, direct product factor
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5056—31nomaximal
10C2×#4768—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C2×C3×#217—21no—
17C3×#936—22no—
18C3×#936C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3724—21no—
23C2×Dic3⋊Dic3—21no—
24#63869—22no—
25#63869C2214yescomplemented
26#63659C2214yes—
27C3×#832C2214yes—
28#63566C2214yescomplemented
29#63565C2214yescomplemented
30Dic3×C3⋊C8C2214yescomplemented
31C2×C3×#124—31no—
32C2×#936D311yescharacteristic
33C2×#890—31no—
34C2×#870—31no—
35C2×C3×#102—31no—
36C2×#835—31no—
37C2×#835—31no—
38C2×#832—31no—
39C2×#832—31no—
40C2×#832—61no—
41C2×#832D311yescharacteristic
42C2×#816—31no—
43C2×C8×Dic3—31no—
44#5056—38no—
45C2×#810—31no—
46C2×C4×C3⋊C8—31no—
47#4768—38no—
48C24×C32—21no—
49C2×C32×D4—21no—
50C2×C32×D4—22no—
51C2×C32×D4—22no—
52C2×C32×D4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×#217—24no—
68C3×#217—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75#3724—24no—
76Dic3⋊Dic3—24no—
77C2×#488—91noSylow
78C22×C3×Q8—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2×D311yescharacteristic
81C22×C3×D4C2×D311yescharacteristic
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—31no—
84C3×#124—34no—
85C3×#124—62no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C22⋊C4—61no—
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—31no—
90C2×#217—21no—
91C2×#217—21no—
92#936—22no—
93#936C2×D314yes—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107#890—34no—
108#890—62no—
109#870—34no—
110#870—62no—
111C3×#102—34no—
112#835—34no—
113#835—34no—
114#832—34no—
115#832—34no—
116#832—64no—
117#832C2×D314yes—
118#816—34no—
119C8×Dic3—34no—
120#810—34no—
121C4×C3⋊C8—34no—
122C23×C32—22no—
123C23×C32—42no—
124C23×C32—42no—
125C23×C32—42no—
126C23×C32C2×D411yescharacteristic
127C32×D4—22no—
128C32×D4—22no—
129C32×D4—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—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3C2×D412yes—
143C2×C3×Dic3C2×D412yes—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C3⋊(C3⋊C8)—22no—
148C3×C3⋊C8—22no—
149C2×#125—91no—
150C2×#124—31no—
151#488—98no—
152C2×#103—91no—
153C2×#103—91no—
154C2×#102—31no—
155C2×#102—91no—
156C2×C4×C8—91no—
157C24×C3—21no—
158C24×C3—21no—
159C24×C3—41no—
160C2×C3×Q8—32no—
161C2×C3×Q8—61no—
162C2×C3×Q8—62no—
163C2×C3×Q8—62no—
164C2×C3×D4—24no—
165C2×C3×D4—22no—
166C2×C3×D4—21no—
167C2×C3×D4—22no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4—21no—
171C2×C3×D4—22no—
172C2×C3×D4—42no—
173C2×C3×D4—41no—
174C2×C3×D4C22×D312yes—
175C2×C3×D4C22×D312yes—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—121no—
188C22×Dic3#6711yescharacteristic
189C22×Dic3#6711yescharacteristic
190C2×Dic6—22no—
191C2×Dic6—22no—
192C2×Dic6—21no—
193C2×Dic6C22×D312yes—
194C2×C3×C8—32no—
195C2×C3×C8—62no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—61no—
198C3×C22⋊C4—64no—
199C3×C22⋊C4—64no—
200C3×C42—32no—
201C3×C42—32no—
202#217—24no—
203#217—24no—
204C4⋊Dic3—21no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—62no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—64no—
211C4⋊Dic3—121no—
212C4⋊Dic3C22×D312yes—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216C4×Dic3#6712yes—
217C4×Dic3C22×D312yes—
218C2×C3⋊C8—22no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—122no—
225C2×C3⋊C8C22×D312yes—
226C22×C32—42no—
227C22×C32—42no—
228C22×C32—42no—
229C22×C32—84no—
230C22×C32#12412yes—
231C22×C32#13512yes—
232C22×C32#13512yes—
233C22×C32C22×D411yescharacteristic
234C32×C4#12412yes—
235C32×C4C2×#4111yescharacteristic
236C32×C4C2×#4111yescharacteristic
237C3⋊Dic3—42no—
238C3×Dic3—22no—
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—31no—
243C22×D4D3211yescharacteristic
244C22×C8—31no—
245C22×C8—91no—
246#125—94no—
247#125—182no—
248#124—34no—
249#124—62no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—181no—
253C2×C4⋊C4—181no—
254C2×C22⋊C4—61no—
255C2×C22⋊C4—61no—
256C2×C42—31no—
257#103—94no—
258#103—94no—
259#102—34no—
260#102—94no—
261C4×C8—94no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—21no—
265C23×C3—42no—
266C23×C3—44no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—42no—
270C23×C3—42no—
271C23×C3—42no—
272C23×C3—42no—
273C23×C3—82no—
274C23×C3—82no—
275C23×C3D3×D411yescharacteristic
276C23×C3C2×#6711yescharacteristic
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—122no—
280C3×D4—24no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—42no—
286C3×D4—44no—
287C3×D4—42no—
288C3×D4—42no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—32no—
294C2×C3×C4—32no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—122no—
300C2×C3×C4—122no—
301C2×C3×C4#23512yes—
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23712yes—
304C2×C3×C4#23712yes—
305C2×C3×C4#23712yes—
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×C3×C4C23×D311yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—42no—
314C2×Dic3—42no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C2×Dic3—242no—
321C2×Dic3C2×#6712yes—
322C2×Dic3C2×#6712yes—
323Dic6—22no—
324Dic6—22no—
325Dic6—42no—
326C3×C8—62no—
327C3⋊C8—22no—
328C3⋊C8—62no—
329C3⋊C8—62no—
330C3⋊C8—122no—
331C2×C32—82no—
332C2×C32#48814yescomplemented
333C2×C32C2×#12411yescharacteristic
334C2×C32C2×#13511yescharacteristic
335C2×C32C2×#13511yescharacteristic
336C24—21no—
337C2×Q8—32no—
338C2×Q8—61no—
339C2×Q8—62no—
340C2×Q8—62no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4C2×D3212yes—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—181no—
350C22×C4C2×D3211yescharacteristic
351C2×C8—32no—
352C2×C8—62no—
353C2×C8—92no—
354C2×C8—182no—
355C4⋊C4—32no—
356C4⋊C4—61no—
357C4⋊C4—92no—
358C4⋊C4—184no—
359C4⋊C4—184no—
360C4⋊C4—181no—
361C22⋊C4—64no—
362C22⋊C4—64no—
363C42—32no—
364C42—32no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—44no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—42no—
376C22×C3—82no—
377C22×C3—82no—
378C22×C3—88no—
379C22×C3—84no—
380C22×C3—84no—
381C22×C3#88512yes—
382C22×C3#91212yes—
383C22×C3#91612yes—
384C22×C3#93612yes—
385C22×C3#95012yes—
386C22×C3#95012yes—
387C22×C3C2×D3×D411yescharacteristic
388C22×C3C22×#6711yescharacteristic
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—62no—
393C3×C4—62no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4#88512yes—
397C3×C4#93612yes—
398C3×C4C2×#23511yescharacteristic
399C3×C4C2×#23711yescharacteristic
400C3×C4C2×#23711yescharacteristic
401C3×C4C2×#23711yescharacteristic
402Dic3—22no—
403Dic3—22no—
404Dic3—42no—
405Dic3—42no—
406Dic3—122no—
407Dic3—122no—
408Dic3—242no—
409C32C2×#48811yescharacteristic, complemented, Sylow
410C23—22no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23D3×#6711yescharacteristic
415Q8—62no—
416Q8—62no—
417Q8—122no—
418D4—22no—
419D4—22no—
420D4—42no—
421C2×C4—32no—
422C2×C4—32no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4—182no—
430C2×C4—362no—
431C2×C4#380412yes—
432C2×C4#380512yes—
433C2×C4D3×#6711yescharacteristic
434C2×C4C22×D3211yescharacteristic
435C8—62no—
436C8—182no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—24no—
441C2×C3—84no—
442C2×C3—82no—
443C2×C3—82no—
444C2×C3#476814yescomplemented
445C2×C3#505614yescomplemented
446C2×C3C2×#88511yescharacteristic
447C2×C3C2×#91211yescharacteristic
448C2×C3C2×#91611yescharacteristic
449C2×C3C2×#93611yescharacteristic
450C2×C3C2×#95011yescharacteristic
451C2×C3C2×#95011yescharacteristic
452C22—42no—
453C22—42no—
454C22—42no—
455C22—84no—
456C22#6393312yes—
457C22#6393512yes—
458C22#6395912yes—
459C22C2×D3×#6711yescharacteristic
460C4—62no—
461C4—62no—
462C4—122no—
463C4—122no—
464C4—362no—
465C4#6395912yes—
466C4C2×#380411yescharacteristic
467C4C2×#380511yescharacteristic
468C3—21no—
469C3C2×#476811yescharacteristic, complemented
470C3C2×#505611yescharacteristic, complemented
471C2—82no—
472C2#1059147814yesdirect product factor
473C2C2×#6393311yescharacteristic
474C2C2×#6393511yescharacteristic
475C2C2×#6395911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63869C2semidirect
5. #10591478C2direct (N × H)
6. C2×#63566C2semidirect
7. C2×#63565C2semidirect
8. C2×Dic3×C3⋊C8C2semidirect
25. #63869C22semidirect
28. #63566C22semidirect
29. #63565C22semidirect
30. Dic3×C3⋊C8C22semidirect
332. C2×C32#488semidirect
409. C32C2×#488semidirect
444. C2×C3#4768semidirect
445. C2×C3#5056semidirect
469. C3C2×#4768semidirect
470. C3C2×#5056semidirect
472. C2#10591478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C2×#638692
C2×#636592
C2×C3×#8322
#105914782
C2×#635662
C2×#635652
C2×Dic3×C3⋊C82
C2×#50563
C2×#47683