Finite Group Databasebeta

← C2×#10591443 #11865696

Subgroups — C2×#10591443 #11865696

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64145C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C2×#63843C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic
6#10591443C218yesmaximal, direct product factor
7C2×#63572C211yesmaximal, characteristic, complemented
8C2×#63567C211yesmaximal, characteristic, complemented
9C2×#5166—31nomaximal
10C2×#4767—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3757—21no—
15C2×#3757—21no—
16#64145—22no—
17#64145C2214yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#214—24no—
20C2×C3×#214C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×Dic32—21no—
26#63843—22no—
27#63843C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C3×#832C2214yes—
31#63572C2214yescomplemented
32#63567C2214yescomplemented
33C22×C3×SD16—31no—
34C2×Q8×Dic3—31no—
35C22×#216—31no—
36C2×#936—31no—
37C2×#936—31no—
38C2×#936—61no—
39C22×#214D311yescharacteristic
40C22×Dic12—31no—
41C2×#887—31no—
42C2×C3×#102—31no—
43C2×#832D311yescharacteristic
44#5166—38no—
45C2×#816—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—31no—
48C2×#810—31no—
49#4767—38no—
50C24×C32—21no—
51C2×C32×D4—22no—
52C2×C32×D4—21no—
53C2×C32×D4—22no—
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3D411yescharacteristic
58C22×C3⋊Dic3D411yescharacteristic
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yes—
68C2×C3×Dic6C2312yes—
69#3757—24no—
70#3757—24no—
71C4×C3⋊Dic3D412yes—
72C4×C3⋊Dic3C2312yes—
73C3×#214—28no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81Dic32—24no—
82#3719—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6C2×D311yescharacteristic
92C2×C3×SD16—34no—
93C2×C3×SD16—64no—
94C22×C3×C8—31no—
95C22×C3×C8—31no—
96C2×C3×C4⋊C4—31no—
97C2×#217—61no—
98C2×#217—61no—
99C2×#217—61no—
100C2×#217—61no—
101C2×#217—62no—
102C2×#217—62no—
103Q8×Dic3—34no—
104Q8×Dic3—62no—
105C2×#216—34no—
106C2×#216—64no—
107#936—34no—
108#936—34no—
109#936—64no—
110#936—62no—
111#936—62no—
112#936—64no—
113C2×#214—24no—
114C2×#214C2×D314yes—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×Dic3⋊C4—61no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—61no—
121C2×C4×Dic3—61no—
122C2×C4×Dic3—61no—
123C22×C3⋊C8C2×D311yescharacteristic
124C22×C3⋊C8C2×D311yescharacteristic
125C2×Dic12—34no—
126C2×Dic12—64no—
127#887—34no—
128#887—62no—
129C3×#102—34no—
130#832C2×D314yes—
131#816—34no—
132Dic3⋊C8—34no—
133Dic3⋊C8—34no—
134#810—34no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32C2×D411yescharacteristic
140C32×D4—22no—
141C32×D4—22no—
142C32×D4—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151C2×C3⋊Dic3C2×D412yes—
152C2×C3⋊Dic3C2×D412yes—
153#634—22no—
154#634—22no—
155#634—42no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C3×Dic6—24no—
161C3×Dic6—22no—
162C3×Dic6C2×D414yes—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—22no—
165C22×Q16—91no—
166C22×SD16—31no—
167C2×#124—91no—
168C2×C4×Q8—91no—
169#464—98no—
170C2×C4⋊C8—91no—
171C2×#103—91no—
172C2×#102—31no—
173C24×C3—22no—
174C24×C3—21no—
175C24×C3—21no—
176C2×C3×Q8—34no—
177C2×C3×Q8—32no—
178C2×C3×Q8—62no—
179C2×C3×Q8—61no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—42no—
189C2×C3×D4—42no—
190C2×C3×D4C22×D312yes—
191C2×C3×D4C22×D312yes—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—31no—
200C22×Dic3—31no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—61no—
204C22×Dic3—61no—
205C22×Dic3—62no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C2×Dic6—21no—
209C2×Dic6—22no—
210C2×Dic6—32no—
211C2×Dic6—32no—
212C2×Dic6—62no—
213C2×Dic6—62no—
214C2×Dic6—62no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—122no—
221C2×Dic6—122no—
222C2×Dic6#6714yes—
223C2×Dic6C22×D312yes—
224C3×SD16—68no—
225C2×C3×C8—32no—
226C2×C3×C8—32no—
227C2×C3×C8—62no—
228C2×C3×C8—62no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—61no—
231#217—64no—
232#217—64no—
233#217—64no—
234#217—64no—
235#217—68no—
236#217—68no—
237#216—68no—
238#214—28no—
239C4⋊Dic3—21no—
240C4⋊Dic3—64no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—64no—
243C4×Dic3—32no—
244C4×Dic3—32no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—62no—
248C4×Dic3—62no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8—22no—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255Dic12—68no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—84no—
260C22×C32#12112yes—
261C22×C32#13512yes—
262C22×C32#13712yes—
263C22×C32C22×D411yescharacteristic
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—22no—
268C3⋊Dic3—22no—
269C3⋊Dic3—42no—
270C3×Dic3—24no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8—91no—
274C22×D4D3211yescharacteristic
275C2×Q16—94no—
276C2×Q16—184no—
277C2×SD16—34no—
278C2×SD16—64no—
279C22×C8—31no—
280C22×C8—31no—
281#124—94no—
282#124—182no—
283C4×Q8—94no—
284C4×Q8—182no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4—181no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C42—91no—
290C2×C42—181no—
291C4⋊C8—94no—
292#103—94no—
293#102—34no—
294C23×C3—24no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—44no—
299C23×C3—44no—
300C23×C3—44no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3D3×D411yescharacteristic
308C23×C3D3×D411yescharacteristic
309C3×Q8—34no—
310C3×Q8—64no—
311C3×Q8—62no—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—42no—
317C3×D4—42no—
318C3×D4—44no—
319C3×D4—42no—
320C3×D4—42no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—64no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—122no—
329C2×C3×C4#23512yes—
330C2×C3×C4D3×D412yes—
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23712yes—
334C2×C3×C4C2×#6712yes—
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337C2×Dic3—24no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—42no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—64no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—124no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359Dic6—24no—
360Dic6—22no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—62no—
365Dic6—122no—
366Dic6—122no—
367Dic6—124no—
368Dic6—122no—
369Dic6—122no—
370Dic6C2×#6714yes—
371C3×C8—62no—
372C3×C8—62no—
373C3⋊C8—22no—
374C3⋊C8—22no—
375C2×C32—82no—
376C2×C32#46414yescomplemented
377C2×C32C2×#12111yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32C2×#13711yescharacteristic
380C24—21no—
381C2×Q8—32no—
382C2×Q8—34no—
383C2×Q8—62no—
384C2×Q8—61no—
385C2×Q8—92no—
386C2×Q8—181no—
387C2×Q8—182no—
388C2×Q8—182no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4C2×D3212yes—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399Q16—188no—
400SD16—68no—
401C2×C8—32no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8—62no—
405C4⋊C4—32no—
406C4⋊C4—61no—
407C4⋊C4—184no—
408C22⋊C4—184no—
409C22⋊C4—184no—
410C42—92no—
411C42—92no—
412C42—184no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—88no—
427C22×C3—84no—
428C22×C3—84no—
429C22×C3#88412yes—
430C22×C3#91212yes—
431C22×C3#91512yes—
432C22×C3#91512yes—
433C22×C3#91612yes—
434C22×C3#93912yes—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—64no—
441C3×C4—122no—
442C3×C4#88412yes—
443C3×C4#93912yes—
444C3×C4C2×#23511yescharacteristic
445C3×C4C2×D3×D411yescharacteristic
446C3×C4C2×#23711yescharacteristic
447C3×C4C22×#6711yescharacteristic
448Dic3—24no—
449Dic3—42no—
450Dic3—62no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—122no—
455Dic3—122no—
456Dic3—124no—
457Dic3—122no—
458Dic3—122no—
459C32C2×#46411yescharacteristic, complemented, Sylow
460C23—22no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23#381111yescharacteristic
465Q8—34no—
466Q8—62no—
467Q8—64no—
468Q8—182no—
469Q8—182no—
470Q8—362no—
471D4—22no—
472D4—22no—
473D4—42no—
474C2×C4—62no—
475C2×C4—64no—
476C2×C4—62no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—122no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—362no—
484C2×C4#380412yes—
485C2×C4D3×#6712yes—
486C2×C4#381111yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—62no—
489C8—62no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—24no—
494C2×C3—84no—
495C2×C3—82no—
496C2×C3—82no—
497C2×C3#476714yescomplemented
498C2×C3#516614yescomplemented
499C2×C3C2×#88411yescharacteristic
500C2×C3C2×#91211yescharacteristic
501C2×C3C2×#91511yescharacteristic
502C2×C3C2×#91511yescharacteristic
503C2×C3C2×#91611yescharacteristic
504C2×C3C2×#93911yescharacteristic
505C22—42no—
506C22—42no—
507C22—42no—
508C22—84no—
509C22#6393112yes—
510C22#6393612yes—
511C22#6397112yes—
512C22C2×#381111yescharacteristic
513C4—64no—
514C4—122no—
515C4—182no—
516C4—182no—
517C4—362no—
518C4#6397112yes—
519C4C2×#380411yescharacteristic
520C4C2×D3×#6711yescharacteristic
521C3—21no—
522C3C2×#476711yescharacteristic, complemented
523C3C2×#516611yescharacteristic, complemented
524C2—82no—
525C2#1059144314yesdirect product factor
526C2C2×#6393111yescharacteristic
527C2C2×#6393611yescharacteristic
528C2C2×#6397111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#464
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
3. C2×#63843C2semidirect
4. C22×#3719C2semidirect
6. #10591443C2direct (N × H)
7. C2×#63572C2semidirect
8. C2×#63567C2semidirect
27. #63843C22semidirect
29. C2×#3719C22semidirect
31. #63572C22semidirect
32. #63567C22semidirect
376. C2×C32#464semidirect
459. C32C2×#464semidirect
497. C2×C3#4767semidirect
498. C2×C3#5166semidirect
522. C3C2×#4767semidirect
523. C3C2×#5166semidirect
525. C2#10591443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C22×C3×#2142
C2×#638432
C22×#37192
C2×C3×#8322
#105914432
C2×#635722
C2×#635672
C2×#51663
C2×#47673