Finite Group Databasebeta

← C2×#10590426 #11869397

Subgroups — C2×#10590426 #11869397

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×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C2×#63637C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
8#10590426C218yesmaximal, direct product factor
9C2×#4971—31nomaximal
10C2×#4862—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C22×C3×C4×D3C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×D3×C4⋊C4—22no—
21C3×D3×C4⋊C4C2214yes—
22C2×Dic3⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63857—22no—
25#63857C2214yes—
26#63637C2214yescomplemented
27C3×#808C2214yescomplemented
28#63574C2214yescomplemented
29#63567C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yes—
31C22×C3×C4⋊C4—31no—
32C2×#924—31no—
33C2×#897—31no—
34C2×D3×C4⋊C4D311yescharacteristic
35C2×C3×#106—31no—
36C2×#830—31no—
37C2×(C2×D3)⋊C8—31no—
38C2×#816—31no—
39#4971—38no—
40C2×#810—31no—
41C2×#810—31no—
42C2×#810—31no—
43C2×#810—61no—
44C2×#808—31no—
45C2×#808—31no—
46C2×#808D311yescharacteristic, complemented
47#4862—38no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
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×D3—24no—
62C2×C3×C4×D3—44no—
63C2×C3×C4×D3D412yes—
64C2×C3×C4×D3C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×Dic3⋊C4—24no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76Dic3⋊Dic3—24no—
77(C2×D3)⋊Dic3—24no—
78C2×#483—91noSylow
79C23×C3×C4—31no—
80C23×C3×C4—61no—
81C22×C4×D3—21no—
82C22×C4×D3C2×D311yescharacteristic
83C22×Dic6—31no—
84C22×Dic6—31no—
85C22×Dic6—61no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—34no—
91C2×C3×C4⋊C4—62no—
92C2×C3×C4⋊C4—61no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×#217—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100#924—34no—
101#924—62no—
102C2×Dic3⋊C4—21no—
103C2×Dic3⋊C4—61no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#897—34no—
109#897—62no—
110D3×C4⋊C4—22no—
111D3×C4⋊C4C2×D314yes—
112C3×#106—34no—
113#830—34no—
114(C2×D3)⋊C8—34no—
115#816—34no—
116#810—34no—
117#810—34no—
118#810—34no—
119#810—64no—
120#808—34no—
121#808—34no—
122#808C2×D314yescomplemented
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3SD1614yes—
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—
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—
148C3×C4×D3—48no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—22no—
151C2×C22⋊Q8—91no—
152C22×C4⋊C4—31no—
153#483—98no—
154C2×#106—31no—
155C2×#106—91no—
156C2×#103—91no—
157C2×#103—91no—
158C2×C22⋊C8—91no—
159C24×C3—31no—
160C23×D3#6711yescharacteristic
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—41no—
168C22×C3×C4—64no—
169C22×C3×C4—62no—
170C22×C3×C4—62no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—124no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—61no—
179C22×Dic3—61no—
180C22×Dic3—121no—
181C22×Dic3#6711yescharacteristic
182C2×C4×D3—22no—
183C2×C4×D3—22no—
184C2×C4×D3—24no—
185C2×C4×D3—44no—
186C2×C4×D3#6712yes—
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—32no—
201C2×C3×C8—62no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—41no—
208C3×C4⋊C4—64no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C22×D312yes—
213#217—64no—
214(C2×D3)⋊C4—64no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—64no—
218C4⋊Dic3C22×D312yes—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—24no—
221Dic3⋊C4—64no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—122no—
229C2×C3⋊C8C22×D312yes—
230C22×C32#12312yes—
231C22×C32C2×SD1612yes—
232C22×C32#13712yes—
233C22×C32C22×D411yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—28no—
237C2×C3×D3C2×SD1614yes—
238C32×C4—42no—
239C32×C4#12312yes—
240C32×C4C2×#4111yescharacteristic
241C32×C4C2×#4111yescharacteristic
242C3⋊Dic3—42no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—91no—
247C23×C4—31no—
248C23×C4—61no—
249C22×C8—31no—
250C22×C8—91no—
251C22⋊Q8—94no—
252C22⋊Q8—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—34no—
256C2×C4⋊C4—62no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4—181no—
259C2×C4⋊C4D3211yescharacteristic
260C2×C22⋊C4—181no—
261#106—34no—
262#106—94no—
263#103—94no—
264#103—94no—
265C22⋊C8—94no—
266C23×C3—21no—
267C23×C3—34no—
268C23×C3—32no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3D3×D411yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C22×D3—22no—
274C22×D3—22no—
275C22×D3#21414yes—
276C22×D3C2×#6712yes—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—32no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—64no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—82no—
294C2×C3×C4—128no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4#23512yes—
298C2×C3×C4#23512yes—
299C2×C3×C4#23512yes—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23912yes—
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×C3×C4C23×D311yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—122no—
313C2×Dic3—124no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3C2×#6712yes—
317C4×D3—24no—
318C4×D3—22no—
319C4×D3—22no—
320C4×D3—48no—
321Dic6—64no—
322Dic6—62no—
323Dic6—62no—
324Dic6—62no—
325Dic6—62no—
326Dic6—122no—
327Dic6—124no—
328Dic6—122no—
329Dic6—122no—
330C3×C8—62no—
331C3⋊C8—22no—
332C3⋊C8—62no—
333C3⋊C8—62no—
334C3⋊C8—122no—
335C2×C32#48314yescomplemented
336C2×C32C2×#12311yescharacteristic
337C2×C32C22×SD1611yescharacteristic
338C2×C32C2×#13711yescharacteristic
339C3×D3—24no—
340C24—31no—
341C2×Q8—92no—
342C2×Q8—181no—
343C2×Q8—182no—
344C2×Q8—182no—
345C22×C4—21no—
346C22×C4—31no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—64no—
350C22×C4—62no—
351C22×C4—62no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—124no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357C2×C8—32no—
358C2×C8—62no—
359C2×C8—92no—
360C2×C8—182no—
361C4⋊C4—21no—
362C4⋊C4—32no—
363C4⋊C4—32no—
364C4⋊C4—64no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—184no—
368C4⋊C4C2×D3212yes—
369C22⋊C4—184no—
370C22×C3—21no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—34no—
375C22×C3—62no—
376C22×C3—62no—
377C22×C3—68no—
378C22×C3#89412yes—
379C22×C3D3×SD1612yes—
380C22×C3#91512yes—
381C22×C3#92912yes—
382C22×C3C2×#21412yes—
383C22×C3#94212yes—
384C22×C3C2×D3×D411yescharacteristic
385C22×C3C22×#6711yescharacteristic
386C2×D3—28no—
387C2×D3—22no—
388C2×D3—22no—
389C2×D3C2×#21414yes—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—62no—
396C3×C4—82no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4#89412yes—
400C3×C4#92912yes—
401C3×C4C2×#23511yescharacteristic
402C3×C4C2×#23511yescharacteristic
403C3×C4C2×#23511yescharacteristic
404C3×C4C2×#23911yescharacteristic
405Dic3—22no—
406Dic3—42no—
407Dic3—42no—
408Dic3—124no—
409Dic3—122no—
410Dic3—122no—
411C32C2×#48311yescharacteristic, complemented, Sylow
412C23—32no—
413C23—34no—
414C23—62no—
415C23—62no—
416C23D3×#6711yescharacteristic
417Q8—182no—
418Q8—182no—
419Q8—362no—
420C2×C4—22no—
421C2×C4—32no—
422C2×C4—42no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—64no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—128no—
430C2×C4—122no—
431C2×C4—122no—
432C2×C4—182no—
433C2×C4—362no—
434C2×C4#379812yes—
435C2×C4#379912yes—
436C2×C4D3×#6711yescharacteristic
437C2×C4C22×D3211yescharacteristic
438C8—62no—
439C8—182no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—24no—
444C2×C3—64no—
445C2×C3#486214yescomplemented
446C2×C3#497114yescomplemented
447C2×C3C2×#89411yescharacteristic
448C2×C3C2×D3×SD1611yescharacteristic
449C2×C3C2×#91511yescharacteristic
450C2×C3C2×#92911yescharacteristic
451C2×C3C22×#21411yescharacteristic
452C2×C3C2×#94211yescharacteristic
453D3—24no—
454C22—34no—
455C22—62no—
456C22—62no—
457C22—68no—
458C22#6385012yes—
459C22D3×#21412yes—
460C22#6394612yes—
461C22C2×D3×#6711yescharacteristic
462C4—42no—
463C4—62no—
464C4—122no—
465C4—122no—
466C4—362no—
467C4#6385012yes—
468C4C2×#379811yescharacteristic
469C4C2×#379911yescharacteristic
470C3—21no—
471C3C2×#486211yescharacteristic, complemented
472C3C2×#497111yescharacteristic, complemented
473C2—64no—
474C2#1059042614yesdirect product factor
475C2C2×#6385011yescharacteristic
476C2C2×D3×#21411yescharacteristic
477C2C2×#6394611yescharacteristic
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×#483
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×#63637C2semidirect
4. C2×C3×#808C2semidirect
5. C2×#63574C2semidirect
6. C2×#63567C2semidirect
8. #10590426C2direct (N × H)
26. #63637C22semidirect
27. C3×#808C22semidirect
28. #63574C22semidirect
29. #63567C22semidirect
46. C2×#808D3semidirect
122. #808C2×D3semidirect
335. C2×C32#483semidirect
411. C32C2×#483semidirect
445. C2×C3#4862semidirect
446. C2×C3#4971semidirect
471. C3C2×#4862semidirect
472. C3C2×#4971semidirect
474. C2#10590426direct (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×#638572
C2×#636372
C2×C3×#8082
C2×#635742
C2×#635672
C2×(C2×D3)⋊(C3⋊C8)2
#105904262
C2×#49713
C2×#48623