Finite Group Databasebeta

← C2×#10595152 #11900795

Subgroups — C2×#10595152 #11900795

Order 1152.

3621 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64145C211yesmaximal, characteristic, complemented
4C2×C3×#940C211yesmaximal, characteristic, complemented
5C2×Dic3×#67C214yesmaximal, complemented
6C2×#63970C214yesmaximal, complemented
7#10595152C2116yesmaximal, direct product factor
8C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10C2×#63863C211yesmaximal, characteristic, complemented
11C2×#5832—31nomaximal
12C2×#5716—31nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C22×C3×#67C2214yes—
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2212yes—
18C2×C3×#237—28no—
19C2×C3×#237C2218yescomplemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#625C2212yes—
24C22×D3×Dic3C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3795—28no—
27C2×#3795C2218yescomplemented
28C2×#3757C2214yes—
29#64145C2218yescomplemented
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C3×#940C2218yescomplemented
32C2×C3×C4×Dic3C2211yescharacteristic
33Dic3×#67C22132yescomplemented
34#63970C22132yescomplemented
35C2×Dic3⋊Dic3C2214yes—
36C2×(C2×D3)⋊Dic3C2214yes—
37C2×Dic32C2212yes—
38C4×D3×Dic3C2218yescomplemented
39#63866C2218yescomplemented
40#63863C2218yescomplemented
41C22×C3×#41—31no—
42C22×#237—31no—
43C22×#237D311yescharacteristic, complemented
44C22×#235—31no—
45C2×C3×#127—31no—
46#5832—316no—
47C2×#947—31no—
48C2×#944—31no—
49C2×#940D311yescharacteristic, complemented
50C2×#939—34no—
51C2×#938—34no—
52C2×#936—31no—
53C2×#936—31no—
54C2×#936—31no—
55C2×#936—61no—
56C2×D4×Dic3—34no—
57C2×C4×#67—34no—
58C22×C4×Dic3—31no—
59#5716—316no—
60C2×C42×D3—31no—
61C2×#869—31no—
62C24×C32C2312yes—
63C23×C3×D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×D4—24no—
66C2×C32×D4C2314yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C2×#634—24no—
71C2×#634C2314yes—
72C2×C3×#67—28no—
73C2×C3×#67—216no—
74C2×C3×#67C23116yes—
75C2×C3×#67C2318yes—
76C22×C3×Dic3—28no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2318yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C3×#237—232no—
82C2×C3×D12—24no—
83C2×C3×D12C2314yes—
84C2×C3×C4×D3D418yescomplemented
85C2×C3×C4×D3C2314yes—
86C2×C3×Dic6—24no—
87C2×C3×Dic6C2314yes—
88C2×#625—28no—
89C2×#625C2318yes—
90C2×D3×Dic3—28no—
91C2×D3×Dic3—28no—
92C2×D3×Dic3C2318yes—
93C2×D3×Dic3C2318yes—
94#3795—232no—
95#3757C23116yes—
96C4×C3⋊Dic3C2314yes—
97C3×C4×Dic3C2314yes—
98Dic3⋊Dic3C23116yes—
99(C2×D3)⋊Dic3C23116yes—
100Dic32C2318yes—
101C2×#532—91noSylow
102C2×C3×#41—38no—
103C2×C3×#41—68no—
104C22×C3×Q8—31no—
105C22×C3×D4—21no—
106C22×C3×D4—32no—
107C22×C3×D4—34no—
108C22×C3×D4—31no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C2×D311yescharacteristic
111C23×C3×C4—31no—
112C23×C3×C4—32no—
113C22×#67—32no—
114C22×#67—32no—
115C22×#67C2×D312yes—
116C22×#67C2×D314yes—
117C23×Dic3—32no—
118C23×Dic3—32no—
119C23×Dic3C2×D312yes—
120C2×#237—28no—
121C2×#237—38no—
122C2×#237—68no—
123C2×#237C2×D318yescomplemented
124C2×#235—38no—
125C2×#235—68no—
126C22×D12C2×D311yescharacteristic
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3C2×D311yescharacteristic
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6—61no—
133C22×Dic6C2×D311yescharacteristic
134C3×#127—38no—
135C2×C3×C42—31no—
136C2×#217—34no—
137C2×#217—34no—
138C2×#217—34no—
139C2×#217—64no—
140#947—38no—
141#944—38no—
142#940C2×D318yescomplemented
143#939—332no—
144#938—332no—
145#936—38no—
146#936—38no—
147#936—38no—
148#936—68no—
149D4×Dic3—332no—
150C4×#67—332no—
151C2×(C2×D3)⋊C4—34no—
152C2×C4⋊Dic3—34no—
153C2×Dic3⋊C4—34no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3—38no—
159C2×C4×Dic3—61no—
160C2×C4×Dic3C2×D311yescharacteristic
161C42×D3—38no—
162#869—38no—
163C23×C32—24no—
164C23×C32—28no—
165C23×C32C2414yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3—28no—
170C22×C3×D3C2×D414yes—
171C22×C3×D3C2414yes—
172C22×C3×D3C2412yes—
173C32×D4—28no—
174C2×C32×C4C2×D414yes—
175C2×C32×C4C2412yes—
176C2×C3⋊Dic3—24no—
177C2×C3⋊Dic3—24no—
178C2×C3⋊Dic3C2414yes—
179C2×C3⋊Dic3C2414yes—
180#634—28no—
181C3×#67—216no—
182C3×#67—232no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—216no—
185C2×C3×Dic3C2×D414yes—
186C2×C3×Dic3#4118yescomplemented
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2412yes—
189C2×C3×Dic3C2414yes—
190C3×D12—28no—
191C3×C4×D3C2×D4116yescomplemented
192C3×Dic6—28no—
193#625—216no—
194D3×Dic3—216no—
195D3×Dic3—216no—
196C22×#41—31no—
197C22×#41—91no—
198#532—916no—
199C2×C4⋊Q8—91no—
200C2×#127—31no—
201C2×#124—91no—
202C2×#124—91no—
203C2×#121—94no—
204C2×C4×D4—94no—
205C22×C42—91no—
206C24×C3—22no—
207C24×C3—31no—
208C24×C3—32no—
209C24×C3C22×D312yes—
210C24×C3C22×D312yes—
211C23×D3C22×D312yes—
212C23×D3C22×D311yescharacteristic
213C3×#41—632no—
214C2×C3×Q8—34no—
215C2×C3×Q8—64no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—24no—
219C2×C3×D4—316no—
220C2×C3×D4—38no—
221C2×C3×D4—34no—
222C2×C3×D4—44no—
223C2×C3×D4—616no—
224C2×C3×D4—68no—
225C2×C3×D4—64no—
226C2×C3×D4C22×D314yes—
227C2×C3×D4C22×D314yes—
228C22×C3×C4—21no—
229C22×C3×C4—31no—
230C22×C3×C4—32no—
231C22×C3×C4—38no—
232C22×C3×C4—34no—
233C22×C3×C4—32no—
234C22×C3×C4—38no—
235C22×C3×C4—68no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—28no—
239C2×#67—216no—
240C2×#67—38no—
241C2×#67—38no—
242C2×#67—68no—
243C2×#67—68no—
244C2×#67C22×D3116yes—
245C2×#67C22×D318yes—
246C22×Dic3—28no—
247C22×Dic3—32no—
248C22×Dic3—32no—
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—38no—
252C22×Dic3—38no—
253C22×Dic3—62no—
254C22×Dic3—62no—
255C22×Dic3—68no—
256C22×Dic3—68no—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D318yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D311yescharacteristic
261#237—232no—
262#237—632no—
263#235—632no—
264C2×D12—24no—
265C2×D12C22×D314yes—
266C2×C4×D3—38no—
267C2×C4×D3—38no—
268C2×C4×D3—68no—
269C2×C4×D3—68no—
270C2×C4×D3#6718yescomplemented
271C2×C4×D3C22×D314yes—
272C2×Dic6—24no—
273C2×Dic6—34no—
274C2×Dic6—34no—
275C2×Dic6—64no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6—124no—
279C2×Dic6C22×D314yes—
280C3×C42—34no—
281#217—316no—
282#217—316no—
283#217—316no—
284#217—616no—
285(C2×D3)⋊C4—316no—
286C4⋊Dic3—316no—
287Dic3⋊C4—316no—
288C4×Dic3—34no—
289C4×Dic3—34no—
290C4×Dic3—38no—
291C4×Dic3—38no—
292C4×Dic3—64no—
293C4×Dic3C22×D314yes—
294C22×C32—24no—
295C22×C32—28no—
296C22×C32—48no—
297C22×C32C22×D412yes—
298C22×C32C2×#4114yes—
299C22×C32C2511yescharacteristic
300C2×C3×D3—28no—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3—28no—
304C2×C3×D3—48no—
305C2×C3×D3C22×D414yes—
306C32×C4C22×D414yes—
307C3⋊Dic3—24no—
308C3⋊Dic3—24no—
309C3×Dic3—24no—
310C3×Dic3C22×D414yes—
311C3×Dic3C2×#4118yescomplemented
312C2×#41—38no—
313C2×#41—68no—
314C2×#41—98no—
315C2×#41—188no—
316C22×Q8—31no—
317C22×Q8—91no—
318C22×D4—34no—
319C22×D4—32no—
320C22×D4—31no—
321C22×D4—92no—
322C22×D4D3211yescharacteristic
323C23×C4—31no—
324C23×C4—32no—
325C23×C4—92no—
326C23×C4—92no—
327C4⋊Q8—98no—
328#127—38no—
329#124—98no—
330#124—98no—
331#121—932no—
332C4×D4—932no—
333C2×C4⋊C4—94no—
334C2×C22⋊C4—94no—
335C2×C22⋊C4—94no—
336C2×C42—31no—
337C2×C42—98no—
338C2×C42—92no—
339C2×C42—91no—
340C23×C3—24no—
341C23×C3—28no—
342C23×C3—28no—
343C23×C3—24no—
344C23×C3—24no—
345C23×C3—21no—
346C23×C3—34no—
347C23×C3—32no—
348C23×C3—34no—
349C23×C3—44no—
350C23×C3—48no—
351C23×C3—64no—
352C23×C3—68no—
353C23×C3—64no—
354C23×C3C23×D314yes—
355C23×C3C23×D314yes—
356C23×C3C23×D311yescharacteristic
357C23×C3C23×D311yescharacteristic
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—28no—
361C22×D3C2×#6714yes—
362C22×D3C23×D314yes—
363C22×D3C23×D312yes—
364C3×Q8—68no—
365C3×D4—28no—
366C3×D4—28no—
367C3×D4—48no—
368C3×D4—632no—
369C3×D4—616no—
370C3×D4—68no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4—34no—
374C2×C3×C4—38no—
375C2×C3×C4—32no—
376C2×C3×C4—34no—
377C2×C3×C4—316no—
378C2×C3×C4—34no—
379C2×C3×C4—616no—
380C2×C3×C4—64no—
381C2×C3×C4D3×D414yes—
382C2×C3×C4C2×#6714yes—
383C2×C3×C4C23×D312yes—
384C2×C3×C4C23×D312yes—
385#67—216no—
386#67—232no—
387#67—616no—
388#67—616no—
389C2×Dic3—24no—
390C2×Dic3—216no—
391C2×Dic3—34no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—64no—
396C2×Dic3—64no—
397C2×Dic3—64no—
398C2×Dic3—64no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—616no—
402C2×Dic3—616no—
403C2×Dic3—124no—
404C2×Dic3—124no—
405C2×Dic3#23718yescomplemented
406C2×Dic3C2×#6714yes—
407C2×Dic3C23×D314yes—
408C2×Dic3C23×D314yes—
409C2×Dic3C23×D312yes—
410D12—28no—
411C4×D3—616no—
412C4×D3—616no—
413C4×D3C2×#67116yescomplemented
414Dic6—28no—
415Dic6—68no—
416Dic6—68no—
417Dic6—128no—
418C2×C32—44no—
419C2×C32#53214yescomplemented
420C2×C32C23×D411yescharacteristic
421C2×C32C22×#4112yes—
422C3×D3—24no—
423C3×D3—44no—
424C24—31no—
425C24—32no—
426C24C2×D3212yes—
427#41—632no—
428#41—1832no—
429C2×Q8—34no—
430C2×Q8—64no—
431C2×Q8—94no—
432C2×Q8—184no—
433C2×D4—24no—
434C2×D4—316no—
435C2×D4—38no—
436C2×D4—34no—
437C2×D4—616no—
438C2×D4—68no—
439C2×D4—64no—
440C2×D4—98no—
441C2×D4—188no—
442C2×D4C2×D3214yes—
443C22×C4—32no—
444C22×C4—31no—
445C22×C4—34no—
446C22×C4—38no—
447C22×C4—38no—
448C22×C4—32no—
449C22×C4—68no—
450C22×C4—98no—
451C22×C4—98no—
452C22×C4—92no—
453C22×C4—92no—
454C22×C4—188no—
455C22×C4—188no—
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—916no—
458C22⋊C4—916no—
459C22⋊C4—916no—
460C42—34no—
461C42—98no—
462C42—94no—
463C22×C3—24no—
464C22×C3—28no—
465C22×C3—28no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3—34no—
471C22×C3—44no—
472C22×C3—48no—
473C22×C3—48no—
474C22×C3—48no—
475C22×C3—64no—
476C22×C3—68no—
477C22×C3—68no—
478C22×C3—64no—
479C22×C3—88no—
480C22×C3—128no—
481C22×C3C2×D3×D412yes—
482C22×C3C2×#23714yes—
483C22×C3D3×#4114yes—
484C22×C3C22×#6712yes—
485C22×C3C24×D311yescharacteristic
486C22×C3C24×D311yescharacteristic
487C2×D3—24no—
488C2×D3—28no—
489C2×D3—24no—
490C2×D3—28no—
491C2×D3—48no—
492C2×D3C22×#6714yes—
493C3×C4—24no—
494C3×C4—34no—
495C3×C4—38no—
496C3×C4—64no—
497C3×C4C2×D3×D414yes—
498C3×C4C22×#6714yes—
499Dic3—24no—
500Dic3—64no—
501Dic3—64no—
502Dic3—64no—
503Dic3—64no—
504Dic3—124no—
505Dic3—124no—
506Dic3C2×#23718yescomplemented
507Dic3C22×#6714yes—
508C32C2×#53211yescharacteristic, complemented, Sylow
509C23—28no—
510C23—24no—
511C23—34no—
512C23—32no—
513C23—34no—
514C23—64no—
515C23—68no—
516C23—64no—
517C23C22×D3214yes—
518C23C22×D3211yescharacteristic
519Q8—68no—
520Q8—188no—
521D4—28no—
522D4—632no—
523D4—616no—
524D4—68no—
525D4—1816no—
526C2×C4—38no—
527C2×C4—34no—
528C2×C4—34no—
529C2×C4—32no—
530C2×C4—316no—
531C2×C4—34no—
532C2×C4—616no—
533C2×C4—64no—
534C2×C4—94no—
535C2×C4—94no—
536C2×C4—1816no—
537C2×C4—1816no—
538C2×C4—184no—
539C2×C4—184no—
540C2×C4D3×#6714yes—
541C2×C4C22×D3212yes—
542C2×C3—22no—
543C2×C3—24no—
544C2×C3—21no—
545C2×C3—44no—
546C2×C3—44no—
547C2×C3—64no—
548C2×C3—84no—
549C2×C3—124no—
550C2×C3#571614yescomplemented
551C2×C3#583214yescomplemented
552C2×C3C22×D3×D411yescharacteristic
553C2×C3C22×#23712yes—
554C2×C3C2×D3×#4112yes—
555C2×C3C23×#6711yescharacteristic
556D3—24no—
557D3—44no—
558C22—28no—
559C22—24no—
560C22—34no—
561C22—48no—
562C22—64no—
563C22—68no—
564C22—68no—
565C22—64no—
566C22—128no—
567C22D3×#23714yes—
568C22C2×D3×#6712yes—
569C22C23×D3211yescharacteristic
570C4—38no—
571C4—34no—
572C4—64no—
573C4—184no—
574C4—184no—
575C4C2×D3×#6714yes—
576C3—21no—
577C3C2×#571611yescharacteristic, complemented
578C3C2×#583211yescharacteristic, complemented
579C2—44no—
580C2—64no—
581C2—124no—
582C2#1059515214yesdirect product factor
583C2C2×D3×#23712yes—
584C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×#3795C2semidirect
3. C2×#64145C2semidirect
4. C2×C3×#940C2semidirect
5. C2×Dic3×#67C2semidirect
6. C2×#63970C2semidirect
7. #10595152C2direct (N × H)
8. C2×C4×D3×Dic3C2semidirect
9. C2×#63866C2semidirect
10. C2×#63863C2semidirect
19. C2×C3×#237C22semidirect
27. C2×#3795C22semidirect
29. #64145C22semidirect
31. C3×#940C22semidirect
33. Dic3×#67C22semidirect
34. #63970C22semidirect
38. C4×D3×Dic3C22semidirect
39. #63866C22semidirect
40. #63863C22semidirect
43. C22×#237D3semidirect
49. C2×#940D3semidirect
84. C2×C3×C4×D3D4semidirect
123. C2×#237C2×D3semidirect
142. #940C2×D3semidirect
186. C2×C3×Dic3#41semidirect
191. C3×C4×D3C2×D4semidirect
270. C2×C4×D3#67semidirect
311. C3×Dic3C2×#41semidirect
405. C2×Dic3#237semidirect
413. C4×D3C2×#67semidirect
419. C2×C32#532semidirect
506. Dic3C2×#237semidirect
508. C32C2×#532semidirect
550. C2×C3#5716semidirect
551. C2×C3#5832semidirect
577. C3C2×#5716semidirect
578. C3C2×#5832semidirect
582. C2#10595152direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×#37952
C2×#641452
C2×C3×#9402
C2×Dic3×#672
C2×#639702
#105951522
C2×C4×D3×Dic32
C2×#638662
C2×#638632
C2×#58323
C2×#57163