Finite Group Databasebeta

← C2×#10590860 #11865561

Subgroups — C2×#10590860 #11865561

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3C2×#63860C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590860C218yesmaximal, direct product factor
9C2×#4844—31nomaximal
10C2×#4787—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×#624—21no—
15C22×C32×C8C2211yescharacteristic
16C2×#3744—24no—
17C2×#3744C2214yescomplemented
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63894—22no—
25#63894C2214yescomplemented
26#63860—22no—
27#63860C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yes—
30C3×#821C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63567C2214yescomplemented
33C2×#936—31no—
34C22×#213—31no—
35C22×D24—31no—
36C22×#204—31no—
37C22×#204—31no—
38C22×#204—61no—
39C2×#893—31no—
40C2×#875—31no—
41C2×C4×D12—31no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#102—31no—
44C2×#821D311yescharacteristic, complemented
45C2×#816—31no—
46C2×Dic3⋊C8D311yescharacteristic, complemented
47C2×#810—31no—
48#4844—38no—
49#4787—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)D414yes—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×#624—24no—
70C2×#624—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73#3744—28no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80#3722—24no—
81(C2×D3)⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83#3714—28no—
84C2×#463—91noSylow
85C22×C3×D4—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—61no—
91C22×C4×D3—61no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C2×D311yescharacteristic
99C2×C3×C4⋊C4—31no—
100C2×C3×C42—31no—
101C2×#217—61no—
102C2×#217—61no—
103#936—34no—
104#936—62no—
105C2×#213—34no—
106C2×#213—64no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114C2×D24—34no—
115C2×D24—64no—
116C2×#204—34no—
117C2×#204—34no—
118C2×#204—64no—
119C2×#204—64no—
120C2×#204—64no—
121C2×#204—68no—
122#893—34no—
123#893—62no—
124#875—34no—
125#875—62no—
126C4×D12—34no—
127C4×D12—62no—
128C3×C4⋊C8—34no—
129C3×#102—34no—
130#821C2×D314yescomplemented
131#816—34no—
132Dic3⋊C8C2×D314yescomplemented
133#810—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—24no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149C4⋊(C3⋊D3)—24no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)C2×D414yes—
152#634—22no—
153#634—22no—
154#634—42no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D412yes—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—42no—
164#624—48no—
165C32×C8—22no—
166C3×C3⋊C8—22no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—91no—
170C2×C4×D4—91no—
171#463—98no—
172C2×C4⋊C8—31no—
173C2×#103—91no—
174C2×#102—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—62no—
183C2×C3×D4—62no—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194C22×Dic3D1211yescharacteristic
195C22×Dic3D1211yescharacteristic
196C2×D12—22no—
197C2×D12—22no—
198C2×D12—21no—
199C2×D12—34no—
200C2×D12—34no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—64no—
204C2×D12—62no—
205C2×D12—61no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—62no—
209C2×D12—122no—
210C2×D12—121no—
211C2×D12C22×D312yes—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×C4×D3—124no—
215C2×C4×D3—124no—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C2×Dic6—64no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6—122no—
228C2×C3×C8—24no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—32no—
233C2×C3×C8—62no—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C22×D312yes—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C42—32no—
239C3×C42—32no—
240#217—64no—
241#217—64no—
242#213—68no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—21no—
248C4⋊Dic3C22×D312yes—
249C4×Dic3D1212yes—
250C4×Dic3C22×D312yes—
251C2×C3⋊C8—22no—
252C2×C3⋊C8C22×D312yes—
253D24—68no—
254#204—68no—
255#204—68no—
256#204—616no—
257C22×C32#12112yes—
258C22×C32#13512yes—
259C22×C32AGL(1,ℤ/8)12yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—24no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—48no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—22no—
274C3×Dic3—22no—
275C3×Dic3—42no—
276C22×Q8—91no—
277C22×D4—31no—
278C22×D4—91no—
279C23×C4—181no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—94no—
283C2×D8—184no—
284C22×C8—31no—
285C22×C8D3211yescharacteristic
286#124—94no—
287#124—182no—
288C4×D4—94no—
289C4×D4—182no—
290C2×C4⋊C4—31no—
291C2×C22⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C42—31no—
295C4⋊C8—34no—
296#103—94no—
297#102—34no—
298C23×C3—21no—
299C23×C3—62no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3C2×D1211yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—122no—
314C22×D3—124no—
315C22×D3—122no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—242no—
320C22×D3—242no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—122no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—32no—
329C2×C3×C4—32no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—122no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4#23512yes—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D412yes—
338C2×C3×C4D3×D412yes—
339C2×C3×C4#23912yes—
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—42no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—122no—
349C2×Dic3—124no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3C2×D1212yes—
353C2×Dic3C2×D1212yes—
354D12—22no—
355D12—22no—
356D12—34no—
357D12—34no—
358D12—42no—
359D12—64no—
360D12—64no—
361D12—64no—
362D12—62no—
363D12—62no—
364D12—122no—
365D12—124no—
366C4×D3—128no—
367C4×D3—128no—
368Dic6—64no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—122no—
374Dic6—124no—
375Dic6—122no—
376Dic6—122no—
377C3×C8—24no—
378C3×C8—22no—
379C3×C8—22no—
380C3×C8—62no—
381C3⋊C8—22no—
382C2×C32#46314yescomplemented
383C2×C32C2×#12111yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C3⋊D3—44no—
387C3×D3—82no—
388C24—61no—
389C24—181no—
390C2×Q8—92no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—182no—
394C2×D4—32no—
395C2×D4—62no—
396C2×D4—61no—
397C2×D4—62no—
398C2×D4—92no—
399C2×D4—94no—
400C2×D4—182no—
401C2×D4—181no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—61no—
405C22×C4—184no—
406C22×C4—181no—
407C22×C4—364no—
408C22×C4C2×D3211yescharacteristic
409SD16—188no—
410D8—188no—
411C2×C8—22no—
412C2×C8—32no—
413C2×C8—62no—
414C2×C8C2×D3212yes—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C22⋊C4—184no—
418C22⋊C4—184no—
419C22⋊C4—184no—
420C42—32no—
421C42—32no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—244no—
430C22×C3#88412yes—
431C22×C3#89512yes—
432C22×C3#90412yes—
433C22×C3#90812yes—
434C22×C3#91112yes—
435C22×C3#91612yes—
436C22×C3C22×D1211yescharacteristic
437C22×C3C2×D3×D411yescharacteristic
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—84no—
444C2×D3—124no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—128no—
450C2×D3—128no—
451C2×D3—242no—
452C2×D3—242no—
453C2×D3—248no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—122no—
460C3×C4#88412yes—
461C3×C4#89512yes—
462C3×C4C2×#23511yescharacteristic
463C3×C4C2×D3×D411yescharacteristic
464C3×C4C2×D3×D411yescharacteristic
465C3×C4C2×#23911yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—42no—
469Dic3—124no—
470Dic3—122no—
471Dic3—122no—
472C32C2×#46311yescharacteristic, complemented, Sylow
473C23—62no—
474C23—122no—
475C23—122no—
476C23—122no—
477C23—182no—
478C23—184no—
479C23—362no—
480C23—362no—
481C23D3×D1211yescharacteristic
482Q8—182no—
483Q8—182no—
484Q8—362no—
485D4—62no—
486D4—62no—
487D4—94no—
488D4—122no—
489D4—182no—
490D4—184no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—122no—
497C2×C4—182no—
498C2×C4—368no—
499C2×C4—362no—
500C2×C4#379912yes—
501C2×C4D3×D1211yescharacteristic
502C2×C4#381112yes—
503C2×C4C22×D3211yescharacteristic
504C8—22no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—24no—
509C2×C3—21no—
510C2×C3—242no—
511C2×C3#478714yescomplemented
512C2×C3#484414yescomplemented
513C2×C3C2×#88411yescharacteristic
514C2×C3C2×#89511yescharacteristic
515C2×C3C2×#90411yescharacteristic
516C2×C3C2×#90811yescharacteristic
517C2×C3C2×#91111yescharacteristic
518C2×C3C2×#91611yescharacteristic
519D3—82no—
520D3—124no—
521D3—124no—
522D3—244no—
523C22—122no—
524C22—122no—
525C22—122no—
526C22—184no—
527C22—244no—
528C22—362no—
529C22—362no—
530C22—368no—
531C22#6379512yes—
532C22#6380612yes—
533C22#6391012yes—
534C22C2×D3×D1211yescharacteristic
535C4—62no—
536C4—62no—
537C4—122no—
538C4—362no—
539C4#6391012yes—
540C4C2×#379911yescharacteristic
541C4C2×#381111yescharacteristic
542C3—21no—
543C3C2×#478711yescharacteristic, complemented
544C3C2×#484411yescharacteristic, complemented
545C2—242no—
546C2—364no—
547C2#1059086014yesdirect product factor
548C2C2×#6379511yescharacteristic
549C2C2×#6380611yescharacteristic
550C2C2×#6391011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×C8D32
hypocenterC32C2×#463
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
1. C22×#3744C2semidirect
2. C2×#63894C2semidirect
3. C2×#63860C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×#63567C2semidirect
8. #10590860C2direct (N × H)
17. C2×#3744C22semidirect
25. #63894C22semidirect
27. #63860C22semidirect
30. C3×#821C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63567C22semidirect
44. C2×#821D3semidirect
46. C2×Dic3⋊C8D3semidirect
130. #821C2×D3semidirect
132. Dic3⋊C8C2×D3semidirect
382. C2×C32#463semidirect
472. C32C2×#463semidirect
511. C2×C3#4787semidirect
512. C2×C3#4844semidirect
543. C3C2×#4787semidirect
544. C3C2×#4844semidirect
547. C2#10590860direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#638942
C2×#638602
C22×#37142
C2×C3×#8212
C2×C3×Dic3⋊C82
C2×#635672
#105908602
C2×#48443
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