Finite Group Databasebeta

← C2×#10590686 #11869402

Subgroups — C2×#10590686 #11869402

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic
3C2×#63647C211yesmaximal, characteristic
4C2×C3×#817C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63574C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590686C218yesmaximal, direct product factor
9C2×#4862—31nomaximal
10C2×#4805—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#624—21no—
14C22×C32×C8C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×#3724—21no—
20C2×Dic3⋊Dic3—21no—
21C2×#3722—21no—
22#63900—22no—
23#63900C2214yes—
24#63871—22no—
25#63871C2214yes—
26#63647C2214yes—
27C3×#817C2214yescomplemented
28C3×#816C2214yescomplemented
29#63574C2214yescomplemented
30#63565C2214yescomplemented
31C2×#946—31no—
32C2×#897—31no—
33C2×D3×C4⋊C4—31no—
34C2×D3×C4⋊C4—31no—
35C2×C3×#106—31no—
36C2×C3×#103—31no—
37C2×#835—31no—
38C2×(C2×D3)⋊C8—31no—
39C2×(C2×D3)⋊C8—31no—
40C2×(C2×D3)⋊C8—61no—
41C2×#817D311yescharacteristic, complemented
42C2×#816D311yescharacteristic, complemented
43C2×#810—31no—
44C2×#808—31no—
45C2×#808—31no—
46#4862—38no—
47#4805—38no—
48C23×C3⋊D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3D412yes—
54C2×C4×C3⋊D3C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×#624—24no—
64C2×#624—44no—
65C2×C32×C8—22no—
66C2×C32×C8C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75#3724—24no—
76Dic3⋊Dic3—24no—
77#3722—24no—
78C2×#483—91noSylow
79C22×C3×Q8—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3—61no—
83C22×C4×D3—61no—
84C22×C4×D3—61no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—21no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92#946—34no—
93#946—62no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106#897—34no—
107#897—62no—
108D3×C4⋊C4—34no—
109D3×C4⋊C4—34no—
110D3×C4⋊C4—62no—
111D3×C4⋊C4—62no—
112C3×#106—34no—
113C3×#103—34no—
114#835—34no—
115(C2×D3)⋊C8—34no—
116(C2×D3)⋊C8—34no—
117(C2×D3)⋊C8—64no—
118#817C2×D314yescomplemented
119#816C2×D314yescomplemented
120#810—34no—
121#808—34no—
122#808—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3SD1614yes—
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⋊Dic3C2×D412yes—
134C4×C3⋊D3—24no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3—42no—
145C3×Dic6—22no—
146C3×Dic6—22no—
147C3×Dic6—42no—
148#624—48no—
149C32×C8—22no—
150C3⋊(C3⋊C8)—22no—
151C2×C22⋊Q8—91no—
152C22×C4⋊C4—91no—
153#483—98no—
154C2×#106—31no—
155C2×#106—91no—
156C2×#103—31no—
157C2×#103—91no—
158C2×C22⋊C8—91no—
159C23×D3—31no—
160C23×D3—31no—
161C23×D3—61no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—62no—
165C2×C3×Q8—62no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—61no—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—32no—
183C2×C4×D3—32no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×C4×D3—64no—
191C2×C4×D3—64no—
192C2×C4×D3—122no—
193C2×C4×D3—122no—
194C2×C4×D3—124no—
195C2×C4×D3—124no—
196C2×Dic6—22no—
197C2×Dic6—22no—
198C2×Dic6—21no—
199C2×Dic6C22×D312yes—
200C2×C3×C8—22no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—42no—
204C2×C3×C8C22×D312yes—
205C2×C3×C8C22×D312yes—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—64no—
218C4⋊Dic3C22×D312yes—
219C4⋊Dic3C22×D312yes—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223Dic3⋊C4—64no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—32no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—122no—
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#12312yes—
239C32×C4C2×#4111yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3⋊Dic3—22no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—31no—
247C23×C4—91no—
248C23×C4—181no—
249C22×C8—91no—
250C22×C8D3211yescharacteristic
251C22⋊Q8—94no—
252C22⋊Q8—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—94no—
257C2×C4⋊C4—182no—
258C2×C4⋊C4—181no—
259C2×C4⋊C4—181no—
260C2×C22⋊C4—181no—
261#106—34no—
262#106—94no—
263#103—34no—
264#103—94no—
265C22⋊C8—94no—
266C23×C3—21no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—34no—
270C22×D3—34no—
271C22×D3—32no—
272C22×D3—32no—
273C22×D3—64no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—122no—
280C22×D3—122no—
281C3×Q8—62no—
282C3×Q8—62no—
283C3×Q8—122no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—22no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—122no—
293C2×C3×C4—122no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4#23512yes—
297C2×C3×C4#23512yes—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23712yes—
301C2×C3×C4#23912yes—
302C2×C3×C4C23×D311yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318C4×D3—64no—
319C4×D3—64no—
320C4×D3—62no—
321C4×D3—62no—
322C4×D3—62no—
323C4×D3—62no—
324C4×D3—122no—
325C4×D3—122no—
326C4×D3—124no—
327C4×D3—128no—
328C4×D3—128no—
329Dic6—22no—
330Dic6—22no—
331Dic6—42no—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—42no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—122no—
338C2×C32#48314yescomplemented
339C2×C32C2×#12311yescharacteristic
340C2×C32C22×SD1611yescharacteristic
341C2×C32C2×#13711yescharacteristic
342C3⋊D3—24no—
343C24—91no—
344C2×Q8—32no—
345C2×Q8—61no—
346C2×Q8—62no—
347C2×Q8—62no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—91no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—184no—
356C22×C4—182no—
357C22×C4—182no—
358C22×C4—364no—
359C22×C4C2×D3211yescharacteristic
360C2×C8—22no—
361C2×C8—92no—
362C2×C8—182no—
363C2×C8C2×D3212yes—
364C4⋊C4—32no—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—184no—
371C4⋊C4—184no—
372C22⋊C4—184no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3#88312yes—
378C22×C3#89412yes—
379C22×C3D3×SD1612yes—
380C22×C3D3×SD1612yes—
381C22×C3#91512yes—
382C22×C3#91812yes—
383C22×C3C2×D3×D411yescharacteristic
384C22×C3C2×D3×D411yescharacteristic
385C2×D3—34no—
386C2×D3—34no—
387C2×D3—64no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—68no—
393C2×D3—68no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—128no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—22no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4—122no—
404C3×C4#88312yes—
405C3×C4#89412yes—
406C3×C4C2×#23511yescharacteristic
407C3×C4C2×#23511yescharacteristic
408C3×C4C2×#23711yescharacteristic
409C3×C4C2×#23911yescharacteristic
410Dic3—42no—
411Dic3—42no—
412Dic3—42no—
413Dic3—42no—
414Dic3—62no—
415Dic3—62no—
416Dic3—122no—
417C32C2×#48311yescharacteristic, complemented, Sylow
418C23—92no—
419C23—94no—
420C23—182no—
421C23—182no—
422C23#380211yescharacteristic
423Q8—62no—
424Q8—62no—
425Q8—122no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—92no—
431C2×C4—122no—
432C2×C4—122no—
433C2×C4—122no—
434C2×C4—122no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—184no—
439C2×C4—368no—
440C2×C4#379912yes—
441C2×C4#380211yescharacteristic
442C2×C4#380412yes—
443C2×C4C22×D3211yescharacteristic
444C8—22no—
445C8—182no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—24no—
450C2×C3#480514yescomplemented
451C2×C3#486214yescomplemented
452C2×C3C2×#88311yescharacteristic
453C2×C3C2×#89411yescharacteristic
454C2×C3C2×D3×SD1611yescharacteristic
455C2×C3C2×D3×SD1611yescharacteristic
456C2×C3C2×#91511yescharacteristic
457C2×C3C2×#91811yescharacteristic
458D3—64no—
459D3—64no—
460D3—124no—
461C22—94no—
462C22—182no—
463C22—182no—
464C22—188no—
465C22#6379612yes—
466C22#6381112yes—
467C22#6385412yes—
468C22C2×#380211yescharacteristic
469C4—122no—
470C4—122no—
471C4—122no—
472C4—122no—
473C4—182no—
474C4#6385412yes—
475C4C2×#379911yescharacteristic
476C4C2×#380411yescharacteristic
477C3—21no—
478C3C2×#480511yescharacteristic, complemented
479C3C2×#486211yescharacteristic, complemented
480C2—184no—
481C2#1059068614yesdirect product factor
482C2C2×#6379611yescharacteristic
483C2C2×#6381111yescharacteristic
484C2C2×#6385411yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×C8D32
hypocenterC32C2×#483
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
4. C2×C3×#817C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63574C2semidirect
7. C2×#63565C2semidirect
8. #10590686C2direct (N × H)
27. C3×#817C22semidirect
28. C3×#816C22semidirect
29. #63574C22semidirect
30. #63565C22semidirect
41. C2×#817D3semidirect
42. C2×#816D3semidirect
118. #817C2×D3semidirect
119. #816C2×D3semidirect
338. C2×C32#483semidirect
417. C32C2×#483semidirect
450. C2×C3#4805semidirect
451. C2×C3#4862semidirect
478. C3C2×#4805semidirect
479. C3C2×#4862semidirect
481. C2#10590686direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638712
C2×#636472
C2×C3×#8172
C2×C3×#8162
C2×#635742
C2×#635652
#105906862
C2×#48623
C2×#48053