Finite Group Databasebeta

← C2×#10590956 #11857802

Subgroups — C2×#10590956 #11857802

Order 1152.

1753 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C22×C8×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590956C218yesmaximal, direct product factor
9C2×#4804—31nomaximal
10C2×#4772—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C22×D3×Dic3—21no—
16C2×#3796—22no—
17C2×#3796—24no—
18C2×#3796C418yescomplemented
19C2×#3796C2214yes—
20C22×C32×C8C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C8×C3⋊D3—24no—
23C2×C8×C3⋊D3C2214yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×#3722—21no—
27C2×Dic32—21no—
28#63849—22no—
29#63849C2214yescomplemented
30C3×#821C2214yescomplemented
31C3×#816C2214yescomplemented
32#63565C2214yescomplemented
33#63562C2214yescomplemented
34C22×#239—31no—
35C22×#237—31no—
36C22×D3×C8—31no—
37C22×D3×C8—31no—
38C22×D3×C8—61no—
39C2×#892—31no—
40C2×#892—31no—
41C2×C3×#103—31no—
42C2×C3×#102—31no—
43C2×#835—31no—
44C2×#832—31no—
45C2×#821D311yescharacteristic, complemented
46C2×#816D311yescharacteristic, complemented
47C2×#810—31no—
48C2×#809—31no—
49#4804—38no—
50#4772—38no—
51C23×C3⋊D3D411yescharacteristic
52C23×C3×D3—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C2×C4×C3⋊D3C2×C414yes—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3D414yes—
58C2×C4×C3⋊D3C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yes—
65C2×C3×D12C2312yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2×C414yes—
69C2×C3×Dic6C2312yes—
70C2×#626—28no—
71C2×#626—24no—
72C2×D3×Dic3—28no—
73C2×D3×Dic3—24no—
74#3796—216no—
75#3796—28no—
76#3796C2×C4116yescomplemented
77C2×C32×C8—22no—
78C2×C32×C8C2312yes—
79C2×C3⋊(C3⋊C8)—22no—
80C2×C3⋊(C3⋊C8)C2312yes—
81C8×C3⋊D3—28no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×C4⋊Dic3C2312yes—
86#3722—24no—
87Dic32—24no—
88C2×#416—91noSylow
89C22×C3×Q8—31no—
90C22×C3×D4—31no—
91C22×#67—61no—
92C23×Dic3—61no—
93C2×#239—38no—
94C2×#239—34no—
95C2×#239—62no—
96C2×#239—64no—
97C2×#237—38no—
98C2×#237—34no—
99C2×#237—62no—
100C2×#237—64no—
101C22×D12—61no—
102C22×D12C2×D311yescharacteristic
103C22×C4×D3—31no—
104C22×C4×D3—31no—
105C22×C4×D3—61no—
106C22×C4×D3—61no—
107C22×Dic6C2×D311yescharacteristic
108C22×C3×C8—21no—
109C22×C3×C8C2×D311yescharacteristic
110C22×C3×C8C2×D311yescharacteristic
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—31no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4×Dic3—61no—
118C2×C4×Dic3—61no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C2×D3×C8—34no—
123C2×D3×C8—34no—
124C2×D3×C8—64no—
125C2×D3×C8—64no—
126C2×D3×C8—64no—
127C2×D3×C8—68no—
128#892—34no—
129#892—34no—
130#892—62no—
131#892—62no—
132C3×#103—34no—
133C3×#102—34no—
134#835—34no—
135#832—34no—
136#821C2×D314yescomplemented
137#816C2×D314yescomplemented
138#810—34no—
139#809—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3C22⋊C414yes—
144C22×C3⋊D3C2×D412yes—
145C22×C3×D3—24no—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3C22⋊C414yes—
154C2×C3⋊Dic3C2×D412yes—
155C4×C3⋊D3C22⋊C418yes—
156C4×C3⋊D3C22×C414yes—
157C4×C3⋊D3C2×D414yes—
158C2×C3×Dic3—24no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—42no—
164C3×D12—24no—
165C3×D12—22no—
166C3×D12C22×C414yes—
167C3×Dic6—24no—
168C3×Dic6—22no—
169C3×Dic6C22×C414yes—
170#626—216no—
171D3×Dic3—216no—
172C32×C8—22no—
173C3⋊(C3⋊C8)—22no—
174C22×#41—91no—
175C23×C8—91no—
176C2×#117—91no—
177#416—98no—
178C2×#103—31no—
179C2×#103—91no—
180C2×#102—31no—
181C2×#102—91no—
182C24×C3—61no—
183C23×D3—21no—
184C23×D3—31no—
185C23×D3—31no—
186C23×D3—61no—
187C2×C3×Q8—34no—
188C2×C3×Q8—32no—
189C2×C3×Q8—61no—
190C2×C3×Q8—62no—
191C2×C3×D4—34no—
192C2×C3×D4—32no—
193C2×C3×D4—61no—
194C2×C3×D4—62no—
195C22×C3×C4—21no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—68no—
202C2×#67—64no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—31no—
207C22×Dic3—31no—
208C22×Dic3—61no—
209C22×Dic3—68no—
210C22×Dic3—64no—
211#239—316no—
212#239—616no—
213#239—68no—
214#237—316no—
215#237—616no—
216#237—68no—
217C2×D12—21no—
218C2×D12—22no—
219C2×D12—68no—
220C2×D12—64no—
221C2×D12C4×D314yes—
222C2×D12C22×D312yes—
223C2×C4×D3—34no—
224C2×C4×D3—34no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—34no—
228C2×C4×D3—34no—
229C2×C4×D3—32no—
230C2×C4×D3—32no—
231C2×C4×D3—64no—
232C2×C4×D3—62no—
233C2×C4×D3—64no—
234C2×C4×D3—62no—
235C2×C4×D3—68no—
236C2×C4×D3—64no—
237C2×Dic6—21no—
238C2×Dic6—22no—
239C2×Dic6C4×D314yes—
240C2×Dic6C22×D312yes—
241C2×C3×C8—24no—
242C2×C3×C8—22no—
243C2×C3×C8—22no—
244C2×C3×C8—22no—
245C2×C3×C8C22×D312yes—
246C2×C3×C8C22×D312yes—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3C22×D312yes—
256C4⋊Dic3C22×D312yes—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8—64no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—62no—
265D3×C8—68no—
266D3×C8—68no—
267D3×C8—616no—
268C22×C32C2×C22⋊C412yes—
269C22×C32#13512yes—
270C22×C32#13512yes—
271C22×C32C22×D411yescharacteristic
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—28no—
275C2×C3⋊D3C2×C22⋊C414yes—
276C2×C3×D3—24no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—48no—
280C32×C4C2×C22⋊C412yes—
281C32×C4C23×C411yescharacteristic
282C32×C4C22×D411yescharacteristic
283C3⋊Dic3C2×C22⋊C414yes—
284C3×Dic3—24no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C2×#41—94no—
288C2×#41—98no—
289C2×#41—182no—
290C2×#41—184no—
291C22×Q8—31no—
292C22×D4—31no—
293C22×D4—181no—
294C23×C4—91no—
295C23×C4—181no—
296C22×C8—91no—
297C22×C8—94no—
298C22×C8—184no—
299C22×C8D3211yescharacteristic
300#117—94no—
301#117—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—31no—
304C2×C22⋊C4—181no—
305C2×C42—181no—
306#103—34no—
307#103—94no—
308#102—34no—
309#102—94no—
310C23×C3—21no—
311C23×C3—64no—
312C23×C3—62no—
313C23×C3—122no—
314C23×C3—122no—
315C23×C3D3×D411yescharacteristic
316C23×C3D3×D411yescharacteristic
317C22×D3—24no—
318C22×D3—22no—
319C22×D3—34no—
320C22×D3—34no—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3—64no—
326C22×D3—62no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C3×Q8—34no—
334C3×Q8—64no—
335C3×Q8—62no—
336C3×D4—34no—
337C3×D4—64no—
338C3×D4—62no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—64no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4—122no—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D412yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—616no—
358C2×Dic3—24no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—34no—
363C2×Dic3—34no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—42no—
367C2×Dic3—42no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—616no—
371D12—24no—
372D12—22no—
373D12—616no—
374D12C2×C4×D314yes—
375C4×D3—38no—
376C4×D3—38no—
377C4×D3—34no—
378C4×D3—34no—
379C4×D3—34no—
380C4×D3—34no—
381C4×D3—68no—
382C4×D3—64no—
383C4×D3—64no—
384C4×D3—616no—
385Dic6—24no—
386Dic6—22no—
387Dic6C2×C4×D314yes—
388C3×C8—24no—
389C3×C8—22no—
390C3×C8—22no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32#41614yescomplemented
395C2×C32C22×C22⋊C411yescharacteristic
396C2×C32C2×#13511yescharacteristic
397C2×C32C2×#13511yescharacteristic
398C3⋊D3—24no—
399C3×D3—44no—
400C24—61no—
401C24—91no—
402#41—916no—
403#41—188no—
404#41—1816no—
405C2×Q8—32no—
406C2×Q8—34no—
407C2×Q8—61no—
408C2×Q8—62no—
409C2×D4—32no—
410C2×D4—34no—
411C2×D4—61no—
412C2×D4—62no—
413C2×D4—184no—
414C2×D4—188no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—91no—
419C22×C4—92no—
420C22×C4—94no—
421C22×C4—92no—
422C22×C4—94no—
423C22×C4—184no—
424C22×C4—188no—
425C22×C4C2×D3211yescharacteristic
426C2×C8—22no—
427C2×C8—92no—
428C2×C8—188no—
429C2×C8—182no—
430C2×C8C2×D3212yes—
431C4⋊C4—32no—
432C4⋊C4—32no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C22⋊C4—184no—
436C42—184no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—64no—
442C22×C3—122no—
443C22×C3—122no—
444C22×C3—128no—
445C22×C3D3×C22⋊C412yes—
446C22×C3D3×C22⋊C412yes—
447C22×C3#91212yes—
448C22×C3#91612yes—
449C22×C3#91612yes—
450C22×C3#91912yes—
451C22×C3C2×D3×D411yescharacteristic
452C22×C3C2×D3×D411yescharacteristic
453C2×D3—24no—
454C2×D3—34no—
455C2×D3—34no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—48no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—616no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—62no—
467C2×D3—68no—
468C2×D3—68no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—64no—
473C3×C4—122no—
474C3×C4—122no—
475C3×C4D3×C22⋊C412yes—
476C3×C4D3×C22⋊C412yes—
477C3×C4C22×C4×D311yescharacteristic
478C3×C4C22×C4×D311yescharacteristic
479C3×C4C2×D3×D411yescharacteristic
480C3×C4C2×D3×D411yescharacteristic
481Dic3—24no—
482Dic3—34no—
483Dic3—34no—
484Dic3—42no—
485Dic3—42no—
486Dic3—64no—
487C32C2×#41611yescharacteristic, complemented, Sylow
488C23—62no—
489C23—64no—
490C23—92no—
491C23—94no—
492C23—122no—
493C23—122no—
494C23—182no—
495C23—182no—
496C23#380211yescharacteristic
497Q8—34no—
498Q8—62no—
499Q8—64no—
500D4—34no—
501D4—62no—
502D4—64no—
503D4—1816no—
504C2×C4—62no—
505C2×C4—64no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—92no—
509C2×C4—94no—
510C2×C4—94no—
511C2×C4—94no—
512C2×C4—98no—
513C2×C4—122no—
514C2×C4—122no—
515C2×C4—1816no—
516C2×C4C4×D3212yes—
517C2×C4#380211yescharacteristic
518C2×C4#381112yes—
519C2×C4C22×D3211yescharacteristic
520C8—22no—
521C8—182no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—24no—
525C2×C3—21no—
526C2×C3—124no—
527C2×C3#477214yescomplemented
528C2×C3#480414yescomplemented
529C2×C3C2×D3×C22⋊C411yescharacteristic
530C2×C3C2×D3×C22⋊C411yescharacteristic
531C2×C3C2×#91211yescharacteristic
532C2×C3C2×#91611yescharacteristic
533C2×C3C2×#91611yescharacteristic
534C2×C3C2×#91911yescharacteristic
535D3—44no—
536D3—68no—
537D3—64no—
538D3—64no—
539C22—64no—
540C22—94no—
541C22—122no—
542C22—122no—
543C22—128no—
544C22—182no—
545C22—182no—
546C22—188no—
547C22#6380912yes—
548C22#6381012yes—
549C22#6392112yes—
550C22C2×#380211yescharacteristic
551C4—64no—
552C4—94no—
553C4—122no—
554C4—122no—
555C4#6392112yes—
556C4C2×C4×D3211yescharacteristic
557C4C2×#381111yescharacteristic
558C3—21no—
559C3C2×#477211yescharacteristic, complemented
560C3C2×#480411yescharacteristic, complemented
561C2—124no—
562C2—184no—
563C2#1059095614yesdirect product factor
564C2C2×#6380911yescharacteristic
565C2C2×#6381011yescharacteristic
566C2C2×#6392111yescharacteristic
subgroupG/H
centerC23#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3796C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#416
LCSG ▷ 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
2. C22×C8×C3⋊D3C2semidirect
3. C2×#63849C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63565C2semidirect
7. C2×#63562C2semidirect
8. #10590956C2direct (N × H)
18. C2×#3796C4semidirect
23. C2×C8×C3⋊D3C22semidirect
29. #63849C22semidirect
30. C3×#821C22semidirect
31. C3×#816C22semidirect
32. #63565C22semidirect
33. #63562C22semidirect
45. C2×#821D3semidirect
46. C2×#816D3semidirect
76. #3796C2×C4semidirect
136. #821C2×D3semidirect
137. #816C2×D3semidirect
394. C2×C32#416semidirect
487. C32C2×#416semidirect
527. C2×C3#4772semidirect
528. C2×C3#4804semidirect
559. C3C2×#4772semidirect
560. C3C2×#4804semidirect
563. C2#10590956direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C22×C8×C3⋊D32
C2×#638492
C2×C3×#8212
C2×C3×#8162
C2×#635652
C2×#635622
#105909562
C2×#48043
C2×#47723