Finite Group Databasebeta

← C2×#10591479 #11868356

Subgroups — C2×#10591479 #11868356

Order 1152.

1109 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×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5#10591479C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×#63572C211yesmaximal, characteristic, complemented
9C2×#4763—31nomaximal
10C2×#4766—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C23×C3⋊Dic3—21no—
13C2×#3757—21no—
14D4×C3⋊Dic3—22no—
15D4×C3⋊Dic3C2214yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×Dic3⋊Dic3—21no—
24#63872—22no—
25#63872C2214yescomplemented
26C3×#832C2214yes—
27C3×#832C2214yes—
28#63575C2214yescomplemented
29#63573C2214yescomplemented
30#63572C2214yescomplemented
31C2×D4×Dic3—31no—
32C2×D4×Dic3—31no—
33C2×D4×Dic3—61no—
34C2×#890—31no—
35C2×#890—31no—
36C2×C3×#102—31no—
37C2×C3×#102—31no—
38C2×#832D311yescharacteristic
39C2×#832D311yescharacteristic
40C2×#818—31no—
41C2×#817—31no—
42C2×Dic3⋊C8—31no—
43C2×Dic3⋊C8—31no—
44C2×#808—31no—
45C2×#807—31no—
46#4766—38no—
47#4763—38no—
48C24×C32—21no—
49C2×C32×D4—21no—
50C2×C32×D4—22no—
51C2×C32×D4Q814yes—
52C2×C32×D4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—24no—
56C22×C3⋊Dic3—44no—
57C22×C3⋊Dic3D411yescharacteristic
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61#3757—24no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)C2312yes—
64C4×C3⋊Dic3D412yes—
65C4×C3⋊Dic3C2312yes—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2312yes—
70C2×C3×C3⋊C8—22no—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73C2×C3×C3⋊C8C2312yes—
74Dic3⋊Dic3—24no—
75Dic3⋊Dic3—24no—
76C2×#478—91noSylow
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C23×Dic3—61no—
81C23×Dic3—61no—
82C23×Dic3—62no—
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×#217—61no—
88C2×#217—61no—
89C2×#217—62no—
90D4×Dic3—34no—
91D4×Dic3—34no—
92D4×Dic3—64no—
93D4×Dic3—62no—
94D4×Dic3—62no—
95D4×Dic3—64no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110#890—34no—
111#890—34no—
112#890—62no—
113#890—62no—
114C3×#102—34no—
115C3×#102—34no—
116#832C2×D314yes—
117#832C2×D314yes—
118#818—34no—
119#817—34no—
120Dic3⋊C8—34no—
121Dic3⋊C8—34no—
122#808—34no—
123#807—34no—
124C23×C32—24no—
125C23×C32—22no—
126C23×C32—42no—
127C23×C32—42no—
128C23×C32C2×D411yescharacteristic
129C32×D4—24no—
130C32×D4—22no—
131C32×D4C2×Q814yes—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×Q812yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—48no—
140C2×C3⋊Dic3—42no—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D412yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—22no—
149C2×#125—91no—
150C2×C4×D4—91no—
151#478—98no—
152C2×#107—91no—
153C2×#106—91no—
154C2×C4⋊C8—91no—
155C2×#102—31no—
156C2×#102—31no—
157C24×C3—22no—
158C24×C3—21no—
159C24×C3—21no—
160C2×C3×D4—22no—
161C2×C3×D4—24no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—22no—
165C2×C3×D4—22no—
166C2×C3×D4—24no—
167C2×C3×D4—22no—
168C2×C3×D4Dic614yes—
169C2×C3×D4Dic614yes—
170C2×C3×D4C22×D312yes—
171C2×C3×D4C22×D312yes—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—64no—
186C22×Dic3—64no—
187C22×Dic3—62no—
188C22×Dic3—68no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—128no—
192C22×Dic3—124no—
193C22×Dic3—124no—
194C2×C3×C8—32no—
195C2×C3×C8—32no—
196C2×C3×C8—62no—
197C2×C3×C8—62no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202#217—64no—
203#217—64no—
204#217—68no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—32no—
208C4⋊Dic3—32no—
209C4⋊Dic3—62no—
210C4⋊Dic3—64no—
211C4⋊Dic3—64no—
212C4⋊Dic3—62no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3C22×D312yes—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C2×C3⋊C8—22no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8C22×D312yes—
228C2×C3⋊C8C22×D312yes—
229C22×C32—24no—
230C22×C32—42no—
231C22×C32—42no—
232C22×C32—48no—
233C22×C32C22⋊Q812yes—
234C22×C32#13512yes—
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32C22×D411yescharacteristic
237C32×C4C22⋊Q812yes—
238C32×C4C22×Q811yescharacteristic
239C32×C4C2×#4111yescharacteristic
240C3⋊Dic3—22no—
241C3⋊Dic3—22no—
242C3⋊Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C22×D4D3211yescharacteristic
246C23×C4—181no—
247C22×C8—31no—
248C22×C8—31no—
249#125—94no—
250#125—182no—
251C4×D4—94no—
252C4×D4—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—181no—
257C2×C4⋊C4—181no—
258C2×C22⋊C4—181no—
259C2×C42—91no—
260#107—94no—
261#106—94no—
262C4⋊C8—94no—
263#102—34no—
264#102—34no—
265C23×C3—24no—
266C23×C3—28no—
267C23×C3—24no—
268C23×C3—24no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—44no—
273C23×C3—44no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—42no—
277C23×C3—42no—
278C23×C3D3×D411yescharacteristic
279C23×C3D3×D411yescharacteristic
280C3×D4—24no—
281C3×D4—28no—
282C3×D4—24no—
283C3×D4—24no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—24no—
287C3×D4C2×Dic614yes—
288C3×D4C2×Dic614yes—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4C2×Dic612yes—
298C2×C3×C4C2×Dic612yes—
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23712yes—
302C2×C3×C4#23712yes—
303C2×C3×C4C23×D311yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—32no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—64no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—122no—
324C2×Dic3—1216no—
325C2×Dic3—128no—
326C2×Dic3—128no—
327C2×Dic3—124no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C3×C8—62no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—22no—
334C2×C32—44no—
335C2×C32#47814yescomplemented
336C2×C32C2×C22⋊Q811yescharacteristic
337C2×C32C2×#13511yescharacteristic
338C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
339C24—21no—
340C2×D4—22no—
341C2×D4—21no—
342C2×D4#62714yes—
343C2×D4C2×D3212yes—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—184no—
349C22×C4—181no—
350C22×C4—364no—
351C22×C4C2×D3211yescharacteristic
352C2×C8—32no—
353C2×C8—32no—
354C2×C8—62no—
355C2×C8—62no—
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—92no—
361C4⋊C4—184no—
362C4⋊C4—184no—
363C4⋊C4—181no—
364C22⋊C4—184no—
365C42—92no—
366C42—92no—
367C22×C3—28no—
368C22×C3—24no—
369C22×C3—24no—
370C22×C3—21no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—416no—
377C22×C3—42no—
378C22×C3—42no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—48no—
382C22×C3—48no—
383C22×C3#87812yes—
384C22×C3#87812yes—
385C22×C3#91112yes—
386C22×C3#91212yes—
387C22×C3#91412yes—
388C22×C3#91612yes—
389C22×C3C2×D3×D411yescharacteristic
390C22×C3C2×D3×D411yescharacteristic
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—22no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4#87812yes—
397C3×C4#87812yes—
398C3×C4C22×Dic611yescharacteristic
399C3×C4C22×Dic611yescharacteristic
400C3×C4C2×#23711yescharacteristic
401C3×C4C2×#23711yescharacteristic
402Dic3—42no—
403Dic3—42no—
404Dic3—64no—
405Dic3—62no—
406Dic3—62no—
407Dic3—62no—
408Dic3—62no—
409Dic3—122no—
410Dic3—124no—
411Dic3—122no—
412Dic3—122no—
413C32C2×#47811yescharacteristic, complemented, Sylow
414C23—22no—
415C23—24no—
416C23—42no—
417C23—42no—
418C23#381111yescharacteristic
419D4—22no—
420D4—24no—
421D4C2×#62714yes—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—92no—
425C2×C4—92no—
426C2×C4—122no—
427C2×C4—122no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—368no—
432C2×C4—362no—
433C2×C4#380512yes—
434C2×C4C2×#62712yes—
435C2×C4#381111yescharacteristic
436C2×C4C22×D3211yescharacteristic
437C8—62no—
438C8—62no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—24no—
443C2×C3—48no—
444C2×C3—44no—
445C2×C3—44no—
446C2×C3#476314yescomplemented
447C2×C3#476614yescomplemented
448C2×C3C2×#87811yescharacteristic
449C2×C3C2×#87811yescharacteristic
450C2×C3C2×#91111yescharacteristic
451C2×C3C2×#91211yescharacteristic
452C2×C3C2×#91411yescharacteristic
453C2×C3C2×#91611yescharacteristic
454C22—24no—
455C22—42no—
456C22—42no—
457C22—48no—
458C22#6393612yes—
459C22#6393712yes—
460C22#6398212yes—
461C22C2×#381111yescharacteristic
462C4—122no—
463C4—122no—
464C4—182no—
465C4—182no—
466C4—362no—
467C4#6398212yes—
468C4C2×#380511yescharacteristic
469C4C22×#62711yescharacteristic
470C3—21no—
471C3C2×#476611yescharacteristic, complemented
472C3C2×#476311yescharacteristic, complemented
473C2—44no—
474C2#1059147914yesdirect product factor
475C2C2×#6393611yescharacteristic
476C2C2×#6393711yescharacteristic
477C2C2×#6398211yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#478
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×#63872C2semidirect
5. #10591479C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63573C2semidirect
8. C2×#63572C2semidirect
25. #63872C22semidirect
28. #63575C22semidirect
29. #63573C22semidirect
30. #63572C22semidirect
335. C2×C32#478semidirect
413. C32C2×#478semidirect
446. C2×C3#4763semidirect
447. C2×C3#4766semidirect
471. C3C2×#4766semidirect
472. C3C2×#4763semidirect
474. C2#10591479direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×#638722
C2×C3×#8322
#105914792
C2×#635752
C2×#635732
C2×#635722
C2×#47633
C2×#47663