Finite Group Databasebeta

← C2×#10590841 #11866708

Subgroups — C2×#10590841 #11866708

Order 1152.

1297 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×#63871C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63574C211yesmaximal, characteristic, complemented
8#10590841C218yesmaximal, direct product factor
9C2×#4807—31nomaximal
10C2×#4778—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C22×C32×C8C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C8×C3⋊D3—24no—
18C2×C8×C3⋊D3C2214yescomplemented
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C2×#3722—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63916—22no—
25#63916C2214yes—
26#63871—22no—
27#63871C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30C3×#821C2214yescomplemented
31C3×#816C2214yescomplemented
32#63574C2214yescomplemented
33C2×#946—31no—
34C22×#215—31no—
35C2×#938—31no—
36C22×#214—31no—
37C22×D3×C8—31no—
38C22×D3×C8—31no—
39C22×D3×C8—61no—
40C2×#897—31no—
41C2×#895—31no—
42C2×C3×#103—31no—
43C2×C3×#102—31no—
44C2×#821D311yescharacteristic, complemented
45C2×#816D311yescharacteristic, complemented
46C2×#808—31no—
47C2×#808—31no—
48#4807—38no—
49#4778—38no—
50C23×C3⋊D3D411yescharacteristic
51C23×C3×D3—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×#626—24no—
70C2×#626—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73C2×C3⋊(C3⋊C8)D414yescomplemented
74C2×C3⋊(C3⋊C8)C2312yes—
75C8×C3⋊D3—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×C4⋊Dic3C2312yes—
80Dic3⋊Dic3—24no—
81#3722—24no—
82(C2×D3)⋊Dic3—24no—
83#3715—28no—
84C2×#465—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×#67—61no—
88C22×D12—61no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—31no—
91C22×C4×D3—31no—
92C22×C4×D3—61no—
93C22×Dic6C2×D311yescharacteristic
94C22×C3×C8—21no—
95C22×C3×C8C2×D311yescharacteristic
96C22×C3×C8C2×D311yescharacteristic
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×#217—61no—
100#946—34no—
101#946—62no—
102C2×#215—34no—
103C2×#215—64no—
104#938—34no—
105#938—62no—
106C2×#214—34no—
107C2×#214—64no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×Dic3⋊C4—61no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—61no—
118C2×D3×C8—34no—
119C2×D3×C8—34no—
120C2×D3×C8—64no—
121C2×D3×C8—64no—
122C2×D3×C8—64no—
123C2×D3×C8—68no—
124#897—34no—
125#897—62no—
126#895—34no—
127#895—62no—
128C3×#103—34no—
129C3×#102—34no—
130#821C2×D314yescomplemented
131#816C2×D314yescomplemented
132#808—34no—
133#808—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3SD1614yescomplemented
138C22×C3⋊D3C2×D412yes—
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⋊Dic3C2×D412yes—
149C4×C3⋊D3—24no—
150C4×C3⋊D3—22no—
151C4×C3⋊D3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3—42no—
157C2×C3×Dic3—42no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—42no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164#626—48no—
165C32×C8—22no—
166C3⋊(C3⋊C8)C2×D414yescomplemented
167C22×SD16—91no—
168C23×C8—91no—
169C2×C22⋊Q8—91no—
170C2×#121—91no—
171#465—98no—
172C2×#106—91no—
173C2×#103—31no—
174C2×#102—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—31no—
178C23×D3—31no—
179C23×D3—61no—
180C2×C3×Q8—32no—
181C2×C3×Q8—61no—
182C2×C3×Q8—62no—
183C2×C3×Q8—62no—
184C2×C3×D4—32no—
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C2×#67—64no—
195C2×#67—124no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—31no—
200C22×Dic3—31no—
201C22×Dic3—61no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12—21no—
205C2×D12—64no—
206C2×D12—124no—
207C2×D12C22×D312yes—
208C2×C4×D3—32no—
209C2×C4×D3—32no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×Dic6—22no—
221C2×Dic6—22no—
222C2×Dic6—21no—
223C2×Dic6C22×D312yes—
224C2×C3×C8—24no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8C22×D312yes—
229C2×C3×C8C22×D312yes—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234#217—64no—
235#215—68no—
236#214—68no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—64no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—64no—
243C4⋊Dic3C22×D312yes—
244C4⋊Dic3C22×D312yes—
245Dic3⋊C4—64no—
246C2×C3⋊C8—34no—
247C2×C3⋊C8—34no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—64no—
251C2×C3⋊C8—62no—
252D3×C8—68no—
253D3×C8—68no—
254D3×C8—616no—
255C22×C32#12112yes—
256C22×C32C2×SD1612yes—
257C22×C32#13512yes—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—22no—
260C2×C3⋊D3—22no—
261C2×C3⋊D3—28no—
262C2×C3⋊D3C2×SD1614yescomplemented
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—84no—
267C32×C4#12112yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C2×#4111yescharacteristic
270C3⋊Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×D4—31no—
276C22×D4—181no—
277C23×C4—91no—
278C2×SD16—94no—
279C2×SD16—184no—
280C22×C8—91no—
281C22×C8—94no—
282C22×C8—184no—
283C22×C8D3211yescharacteristic
284C22⋊Q8—94no—
285C22⋊Q8—182no—
286#121—94no—
287#121—182no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—181no—
291C2×C22⋊C4—181no—
292C2×C22⋊C4—181no—
293#106—94no—
294#103—34no—
295#102—34no—
296C23×C3—21no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3D3×D411yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—22no—
304C22×D3—34no—
305C22×D3—34no—
306C22×D3—32no—
307C22×D3—32no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—64no—
312C22×D3—62no—
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—62no—
318C22×D3—62no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×Q8—122no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—122no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4—122no—
334C2×C3×C4—122no—
335C2×C3×C4#23512yes—
336C2×C3×C4#23512yes—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D412yes—
340C2×C3×C4D3×D412yes—
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—128no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3—42no—
352C2×Dic3—62no—
353C2×Dic3—64no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356D12—22no—
357D12—22no—
358D12—42no—
359D12—128no—
360C4×D3—64no—
361C4×D3—64no—
362C4×D3—68no—
363C4×D3—64no—
364C4×D3—64no—
365C4×D3—62no—
366C4×D3—62no—
367C4×D3—62no—
368C4×D3—62no—
369Dic6—22no—
370Dic6—22no—
371Dic6—42no—
372C3×C8—24no—
373C3×C8—22no—
374C3×C8—22no—
375C3⋊C8—34no—
376C3⋊C8—34no—
377C3⋊C8—64no—
378C2×C32#46514yescomplemented
379C2×C32C2×#12111yescharacteristic
380C2×C32C22×SD1611yescharacteristic
381C2×C32C2×#13511yescharacteristic
382C3⋊D3—24no—
383C3×D3—82no—
384C24—61no—
385C24—91no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—62no—
389C2×Q8—62no—
390C2×D4—32no—
391C2×D4—62no—
392C2×D4—61no—
393C2×D4—62no—
394C2×D4—184no—
395C2×D4—364no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4—91no—
400C22×C4—92no—
401C22×C4—92no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4C2×D3211yescharacteristic
405SD16—188no—
406C2×C8—22no—
407C2×C8—92no—
408C2×C8—94no—
409C2×C8—188no—
410C2×C8C2×D3212yes—
411C4⋊C4—32no—
412C4⋊C4—32no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—184no—
416C22⋊C4—184no—
417C22⋊C4—184no—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—244no—
426C22×C3#88412yes—
427C22×C3#88412yes—
428C22×C3#91212yes—
429C22×C3D3×SD1612yes—
430C22×C3D3×SD1612yes—
431C22×C3#91912yes—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—34no—
435C2×D3—34no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—64no—
440C2×D3—64no—
441C2×D3—616no—
442C2×D3—64no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—68no—
448C2×D3—68no—
449C2×D3—84no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—122no—
454C3×C4—122no—
455C3×C4—122no—
456C3×C4#88412yes—
457C3×C4#88412yes—
458C3×C4C2×#23511yescharacteristic
459C3×C4C2×#23511yescharacteristic
460C3×C4C2×D3×D411yescharacteristic
461C3×C4C2×D3×D411yescharacteristic
462Dic3—42no—
463Dic3—42no—
464Dic3—42no—
465Dic3—64no—
466Dic3—62no—
467Dic3—62no—
468C32C2×#46511yescharacteristic, complemented, Sylow
469C23—62no—
470C23—92no—
471C23—94no—
472C23—122no—
473C23—122no—
474C23—122no—
475C23—182no—
476C23—182no—
477C23#380211yescharacteristic
478Q8—62no—
479Q8—62no—
480Q8—122no—
481D4—62no—
482D4—62no—
483D4—122no—
484D4—368no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—92no—
489C2×C4—122no—
490C2×C4—122no—
491C2×C4—122no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—184no—
496C2×C4#379812yes—
497C2×C4#380211yescharacteristic
498C2×C4#381112yes—
499C2×C4C22×D3211yescharacteristic
500C8—22no—
501C8—94no—
502C2×C3—24no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—242no—
507C2×C3#477814yescomplemented
508C2×C3#480714yescomplemented
509C2×C3C2×#88411yescharacteristic
510C2×C3C2×#88411yescharacteristic
511C2×C3C2×#91211yescharacteristic
512C2×C3C2×D3×SD1611yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3C2×#91911yescharacteristic
515D3—68no—
516D3—64no—
517D3—64no—
518D3—82no—
519C22—94no—
520C22—122no—
521C22—122no—
522C22—122no—
523C22—188no—
524C22—182no—
525C22—182no—
526C22—244no—
527C22#6379612yes—
528C22#6381012yes—
529C22#6391212yes—
530C22C2×#380211yescharacteristic
531C4—122no—
532C4—122no—
533C4—122no—
534C4—182no—
535C4#6391212yes—
536C4C2×#379811yescharacteristic
537C4C2×#381111yescharacteristic
538C3—21no—
539C3C2×#477811yescharacteristic, complemented
540C3C2×#480711yescharacteristic, complemented
541C2—184no—
542C2—242no—
543C2#1059084114yesdirect product factor
544C2C2×#6379611yescharacteristic
545C2C2×#6381011yescharacteristic
546C2C2×#6391211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC22×C8D32
hypocenterC32C2×#465
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×C8×C3⋊D3C2semidirect
3. C2×#63871C2semidirect
4. C22×#3715C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63574C2semidirect
8. #10590841C2direct (N × H)
18. C2×C8×C3⋊D3C22semidirect
27. #63871C22semidirect
29. C2×#3715C22semidirect
30. C3×#821C22semidirect
31. C3×#816C22semidirect
32. #63574C22semidirect
44. C2×#821D3semidirect
45. C2×#816D3semidirect
73. C2×C3⋊(C3⋊C8)D4semidirect
130. #821C2×D3semidirect
131. #816C2×D3semidirect
137. C22×C3⋊D3SD16semidirect
166. C3⋊(C3⋊C8)C2×D4semidirect
262. C2×C3⋊D3C2×SD16semidirect
378. C2×C32#465semidirect
468. C32C2×#465semidirect
507. C2×C3#4778semidirect
508. C2×C3#4807semidirect
539. C3C2×#4778semidirect
540. C3C2×#4807semidirect
543. C2#10590841direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
C2×#639162
C2×#638712
C22×#37152
C2×C3×#8212
C2×C3×#8162
C2×#635742
#105908412
C2×#48073
C2×#47783