Finite Group Databasebeta

← C2×#10593969 #11900799

Subgroups — C2×#10593969 #11900799

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×#3799C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64084C211yesmaximal, characteristic, complemented
4C2×C3×#875C211yesmaximal, characteristic, complemented
5C2×C3×C42×D3C211yesmaximal, characteristic, complemented
6C2×#63911C211yesmaximal, characteristic, complemented
7C2×#63906C214yesmaximal, complemented
8C2×#63880C214yesmaximal, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10#10593969C2116yesmaximal, direct product factor
11C2×#5668—31nomaximal
12C2×#5477—31nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C22×#626C2212yes—
20C22×#626C2214yes—
21C22×#625C2212yes—
22C22×#624C2212yes—
23C22×D3×Dic3C2212yes—
24C2×#3799—28no—
25C2×#3799C2218yescomplemented
26C2×#3795—28no—
27C2×#3795C2218yescomplemented
28C2×C32×C42C2211yescharacteristic
29C2×#3752C2214yes—
30#64084C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2214yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2212yes—
34C3×#875C2218yescomplemented
35C3×C42×D3C2218yescomplemented
36C2×Dic3⋊Dic3C2214yes—
37#63911C2218yescomplemented
38#63906C22132yescomplemented
39#63880C22132yescomplemented
40#63866C2218yescomplemented
41C22×#239—31no—
42C22×#237—31no—
43C22×#235—31no—
44C22×#235—31no—
45C2×C3×#124—31no—
46C22×C3×C42—31no—
47C2×#944—31no—
48C2×#940—31no—
49C2×#930—34no—
50#5668—316no—
51C2×#884—34no—
52C2×#67⋊C4—34no—
53#5477—316no—
54C2×#875—31no—
55C2×#875—31no—
56C2×#875—61no—
57C2×#875D311yescharacteristic, complemented
58C2×#874—31no—
59C2×C4×D12—34no—
60C2×C42×D3D311yescharacteristic, complemented
61C2×#869—31no—
62C23×C3⋊D3C2312yes—
63C23×C3×D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C2×C4⋊(C3⋊D3)—24no—
69C2×C4⋊(C3⋊D3)C2314yes—
70C2×#634—24no—
71C2×#634C2314yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C2×C3×D12—24no—
76C2×C3×D12C2314yes—
77C2×C3×C4×D3—28no—
78C2×C3×C4×D3D418yescomplemented
79C2×C3×C4×D3C2318yes—
80C2×C3×C4×D3C2314yes—
81C2×C3×Dic6—24no—
82C2×C3×Dic6C2314yes—
83C2×#626—28no—
84C2×#626—216no—
85C2×#626C2318yes—
86C2×#626C23116yes—
87C2×#625—28no—
88C2×#625C2318yes—
89C2×#624—28no—
90C2×#624C2318yes—
91C2×D3×Dic3—28no—
92C2×D3×Dic3C2318yes—
93#3799—232no—
94#3795—232no—
95C32×C42C2314yes—
96#3752C23116yes—
97C3×(C2×D3)⋊C4C23116yes—
98C3×C4×Dic3C2314yes—
99C3×C4×Dic3C2318yes—
100Dic3⋊Dic3C23116yes—
101C2×#532—91noSylow
102C22×C3×Q8—31no—
103C22×C3×D4—31no—
104C23×C3×C4—31no—
105C23×C3×C4—32no—
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—32no—
109C22×#67—34no—
110C23×Dic3—32no—
111C2×#239—38no—
112C2×#239—68no—
113C2×#237—38no—
114C2×#237—68no—
115C2×#235—38no—
116C2×#235—38no—
117C2×#235—68no—
118C2×#235—68no—
119C22×D12—32no—
120C22×D12—34no—
121C22×D12—31no—
122C22×D12—31no—
123C22×D12—61no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3—32no—
126C22×C4×D3—32no—
127C22×C4×D3—32no—
128C22×C4×D3C2×D312yes—
129C22×C4×D3C2×D311yescharacteristic
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6—61no—
133C22×Dic6C2×D311yescharacteristic
134C3×#124—38no—
135C2×C3×C22⋊C4—34no—
136C2×C3×C42—21no—
137C2×C3×C42—31no—
138C2×C3×C42—32no—
139C2×C3×C42—38no—
140C2×C3×C42C2×D311yescharacteristic
141C2×C3×C42C2×D311yescharacteristic
142#944—38no—
143#940—38no—
144#930—332no—
145C2×(C2×D3)⋊C4—34no—
146C2×(C2×D3)⋊C4—34no—
147C2×(C2×D3)⋊C4—64no—
148C2×(C2×D3)⋊C4C2×D314yes—
149C2×C4⋊Dic3—34no—
150C2×Dic3⋊C4—34no—
151C2×C4×Dic3C2×D312yes—
152C2×C4×Dic3C2×D311yescharacteristic
153#884—332no—
154#67⋊C4—332no—
155#875—38no—
156#875—38no—
157#875—68no—
158#875C2×D318yescomplemented
159#874—38no—
160C4×D12—332no—
161C42×D3C2×D318yescomplemented
162#869—38no—
163C23×C32C2411yescharacteristic
164C22×C3⋊D3—24no—
165C22×C3⋊D3—28no—
166C22×C3⋊D3C2414yes—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3—28no—
170C22×C3×D3C2×D414yes—
171C22×C3×D3C2414yes—
172C22×C3×D3C2412yes—
173C2×C32×C4—24no—
174C2×C32×C4C2×D414yes—
175C2×C32×C4C2414yes—
176C2×C32×C4C2412yes—
177C2×C3⋊Dic3—24no—
178C2×C3⋊Dic3C2414yes—
179C4⋊(C3⋊D3)—28no—
180#634—28no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3C2×D414yes—
183C2×C3×Dic3#4118yescomplemented
184C2×C3×Dic3C2414yes—
185C2×C3×Dic3C2412yes—
186C2×C3×Dic3C2414yes—
187C3×D12—28no—
188C3×C4×D3—216no—
189C3×C4×D3C2×D4116yescomplemented
190C3×Dic6—28no—
191#626—216no—
192#626—232no—
193#625—216no—
194#624—216no—
195D3×Dic3—216no—
196C22×#41—91no—
197C22×#41—91no—
198#532—916no—
199C2×C4⋊Q8—91no—
200C2×#127—91no—
201C2×#124—31no—
202C2×#124—91no—
203C2×#121—94no—
204C2×C4×D4—94no—
205C22×C42—31no—
206C24×C3—31no—
207C24×C3—32no—
208C23×D3—32no—
209C23×D3—32no—
210C23×D3—62no—
211C23×D3C22×D312yes—
212C23×D3C22×D311yescharacteristic
213C2×C3×Q8—34no—
214C2×C3×Q8—64no—
215C2×C3×D4—34no—
216C2×C3×D4—64no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—38no—
222C22×C3×C4—34no—
223C22×C3×C4—32no—
224C22×C3×C4—38no—
225C22×C3×C4—68no—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—316no—
233C2×#67—38no—
234C2×#67—68no—
235C2×#67—68no—
236C2×#67—68no—
237C2×#67—616no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—38no—
241C22×Dic3—62no—
242C22×Dic3—68no—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D312yes—
246#239—632no—
247#237—632no—
248#235—632no—
249#235—632no—
250C2×D12—24no—
251C2×D12—316no—
252C2×D12—38no—
253C2×D12—34no—
254C2×D12—34no—
255C2×D12—64no—
256C2×D12—616no—
257C2×D12—68no—
258C2×D12—64no—
259C2×D12—64no—
260C2×D12—124no—
261C2×D12C22×D314yes—
262C2×C4×D3—28no—
263C2×C4×D3—38no—
264C2×C4×D3—38no—
265C2×C4×D3—38no—
266C2×C4×D3—68no—
267C2×C4×D3—68no—
268C2×C4×D3—68no—
269C2×C4×D3D1218yescomplemented
270C2×C4×D3C22×D318yes—
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×C22⋊C4—316no—
281C3×C42—24no—
282C3×C42—34no—
283C3×C42—38no—
284C3×C42C22×D314yes—
285C3×C42C22×D314yes—
286(C2×D3)⋊C4—316no—
287(C2×D3)⋊C4—316no—
288(C2×D3)⋊C4—616no—
289(C2×D3)⋊C4C22×D3116yes—
290C4⋊Dic3—316no—
291Dic3⋊C4—316no—
292C4×Dic3C22×D318yes—
293C4×Dic3C22×D314yes—
294C22×C32C22×D412yes—
295C22×C32C2×#4114yes—
296C22×C32C2511yescharacteristic
297C2×C3⋊D3—24no—
298C2×C3⋊D3—28no—
299C2×C3⋊D3—48no—
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×C4—24no—
307C32×C4C22×D414yes—
308C3⋊Dic3—24no—
309C3×Dic3—24no—
310C3×Dic3C22×D414yes—
311C3×Dic3C2×#4118yescomplemented
312C2×#41—98no—
313C2×#41—98no—
314C2×#41—188no—
315C2×#41—188no—
316C22×Q8—31no—
317C22×Q8—91no—
318C22×D4—31no—
319C22×D4—94no—
320C22×D4—92no—
321C22×D4—92no—
322C22×D4—91no—
323C23×C4—31no—
324C23×C4—32no—
325C23×C4—92no—
326C23×C4—92no—
327C4⋊Q8—98no—
328#127—98no—
329#124—38no—
330#124—98no—
331#121—932no—
332C4×D4—932no—
333C2×C4⋊C4—94no—
334C2×C22⋊C4—34no—
335C2×C22⋊C4—94no—
336C2×C42—32no—
337C2×C42—31no—
338C2×C42—38no—
339C2×C42D3211yescharacteristic
340C23×C3—21no—
341C23×C3—34no—
342C23×C3—32no—
343C23×C3—34no—
344C23×C3—64no—
345C23×C3—64no—
346C23×C3—68no—
347C23×C3C23×D311yescharacteristic
348C23×C3C23×D311yescharacteristic
349C22×D3—24no—
350C22×D3—24no—
351C22×D3—28no—
352C22×D3—34no—
353C22×D3—34no—
354C22×D3—64no—
355C22×D3—64no—
356C22×D3—68no—
357C22×D3—64no—
358C22×D3—68no—
359C22×D3—124no—
360C22×D3—128no—
361C22×D3C2×D1214yes—
362C22×D3C23×D314yes—
363C22×D3C23×D312yes—
364C3×Q8—68no—
365C3×D4—68no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—34no—
372C2×C3×C4—38no—
373C2×C3×C4—34no—
374C2×C3×C4—32no—
375C2×C3×C4—316no—
376C2×C3×C4—34no—
377C2×C3×C4—44no—
378C2×C3×C4—616no—
379C2×C3×C4—64no—
380C2×C3×C4C2×D1214yes—
381C2×C3×C4D3×D414yes—
382C2×C3×C4C23×D314yes—
383C2×C3×C4C23×D314yes—
384C2×C3×C4C23×D312yes—
385C2×C3×C4C23×D312yes—
386#67—616no—
387#67—616no—
388#67—616no—
389#67—632no—
390C2×Dic3—24no—
391C2×Dic3—34no—
392C2×Dic3—34no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—64no—
396C2×Dic3—616no—
397C2×Dic3—124no—
398C2×Dic3C2×D1214yes—
399C2×Dic3#23518yescomplemented
400C2×Dic3C23×D314yes—
401C2×Dic3C23×D312yes—
402C2×Dic3C23×D314yes—
403D12—28no—
404D12—632no—
405D12—616no—
406D12—68no—
407D12—68no—
408D12—128no—
409C4×D3—216no—
410C4×D3—616no—
411C4×D3—616no—
412C4×D3—616no—
413C4×D3C2×D12116yescomplemented
414Dic6—28no—
415Dic6—68no—
416Dic6—68no—
417Dic6—128no—
418C2×C32#53214yescomplemented
419C2×C32C23×D411yescharacteristic
420C2×C32C22×#4112yes—
421C3⋊D3—44no—
422C3×D3—24no—
423C3×D3—44no—
424C24—31no—
425C24—32no—
426C24—92no—
427#41—1832no—
428#41—1832no—
429C2×Q8—34no—
430C2×Q8—64no—
431C2×Q8—94no—
432C2×Q8—184no—
433C2×D4—34no—
434C2×D4—64no—
435C2×D4—916no—
436C2×D4—98no—
437C2×D4—98no—
438C2×D4—94no—
439C2×D4—1816no—
440C2×D4—188no—
441C2×D4—188no—
442C2×D4—184no—
443C22×C4—32no—
444C22×C4—31no—
445C22×C4—34no—
446C22×C4—38no—
447C22×C4—32no—
448C22×C4—38no—
449C22×C4—68no—
450C22×C4—98no—
451C22×C4—98no—
452C22×C4—92no—
453C22×C4—188no—
454C22×C4—188no—
455C22×C4C2×D3212yes—
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—916no—
458C22⋊C4—316no—
459C22⋊C4—916no—
460C42—38no—
461C42—34no—
462C42C2×D3214yes—
463C22×C3—22no—
464C22×C3—24no—
465C22×C3—21no—
466C22×C3—34no—
467C22×C3—68no—
468C22×C3—64no—
469C22×C3—64no—
470C22×C3—68no—
471C22×C3—128no—
472C22×C3C22×D1212yes—
473C22×C3C2×#23514yes—
474C22×C3C2×D3×D412yes—
475C22×C3D3×#4114yes—
476C22×C3C24×D311yescharacteristic
477C22×C3C24×D311yescharacteristic
478C2×D3—24no—
479C2×D3—28no—
480C2×D3—24no—
481C2×D3—28no—
482C2×D3—48no—
483C2×D3—64no—
484C2×D3—68no—
485C2×D3—64no—
486C2×D3—68no—
487C2×D3—124no—
488C2×D3—128no—
489C2×D3—128no—
490C2×D3—128no—
491C2×D3—248no—
492C2×D3C22×D1214yes—
493C3×C4—24no—
494C3×C4—24no—
495C3×C4—24no—
496C3×C4—34no—
497C3×C4—38no—
498C3×C4—44no—
499C3×C4—64no—
500C3×C4C22×D1214yes—
501C3×C4C2×D3×D414yes—
502Dic3—24no—
503Dic3—64no—
504Dic3—64no—
505Dic3—124no—
506Dic3C22×D1214yes—
507Dic3C2×#23518yescomplemented
508C32C2×#53211yescharacteristic, complemented, Sylow
509C23—34no—
510C23—32no—
511C23—34no—
512C23—64no—
513C23—64no—
514C23—68no—
515C23—94no—
516C23—184no—
517C23—188no—
518C23C22×D3211yescharacteristic
519Q8—68no—
520Q8—188no—
521D4—68no—
522D4—1832no—
523D4—1816no—
524D4—1816no—
525D4—188no—
526C2×C4—24no—
527C2×C4—34no—
528C2×C4—38no—
529C2×C4—34no—
530C2×C4—32no—
531C2×C4—316no—
532C2×C4—34no—
533C2×C4—616no—
534C2×C4—64no—
535C2×C4—94no—
536C2×C4—1816no—
537C2×C4—1816no—
538C2×C4—184no—
539C2×C4D3×D1214yes—
540C2×C4C22×D3214yes—
541C2×C4C22×D3212yes—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—24no—
545C2×C3—64no—
546C2×C3—124no—
547C2×C3#547714yescomplemented
548C2×C3#566814yescomplemented
549C2×C3C23×D1211yescharacteristic
550C2×C3C22×#23512yes—
551C2×C3C22×D3×D411yescharacteristic
552C2×C3C2×D3×#4112yes—
553D3—24no—
554D3—44no—
555D3—124no—
556D3—124no—
557D3—244no—
558C22—34no—
559C22—64no—
560C22—68no—
561C22—64no—
562C22—68no—
563C22—128no—
564C22—184no—
565C22—188no—
566C22—368no—
567C22C2×D3×D1212yes—
568C22D3×#23514yes—
569C22C23×D3211yescharacteristic
570C4—24no—
571C4—34no—
572C4—38no—
573C4—64no—
574C4—184no—
575C4C2×D3×D1214yes—
576C3—21no—
577C3C2×#547711yescharacteristic, complemented
578C3C2×#566811yescharacteristic, complemented
579C2—64no—
580C2—124no—
581C2—364no—
582C2#1059396914yesdirect product factor
583C2C22×D3×D1211yescharacteristic
584C2C2×D3×#23512yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C22×#3795C2semidirect
3. C2×#64084C2semidirect
4. C2×C3×#875C2semidirect
5. C2×C3×C42×D3C2semidirect
6. C2×#63911C2semidirect
7. C2×#63906C2semidirect
8. C2×#63880C2semidirect
9. C2×#63866C2semidirect
10. #10593969C2direct (N × H)
25. C2×#3799C22semidirect
27. C2×#3795C22semidirect
30. #64084C22semidirect
34. C3×#875C22semidirect
35. C3×C42×D3C22semidirect
37. #63911C22semidirect
38. #63906C22semidirect
39. #63880C22semidirect
40. #63866C22semidirect
57. C2×#875D3semidirect
60. C2×C42×D3D3semidirect
78. C2×C3×C4×D3D4semidirect
158. #875C2×D3semidirect
161. C42×D3C2×D3semidirect
183. C2×C3×Dic3#41semidirect
189. C3×C4×D3C2×D4semidirect
269. C2×C4×D3D12semidirect
311. C3×Dic3C2×#41semidirect
399. C2×Dic3#235semidirect
413. C4×D3C2×D12semidirect
418. C2×C32#532semidirect
507. Dic3C2×#235semidirect
508. C32C2×#532semidirect
547. C2×C3#5477semidirect
548. C2×C3#5668semidirect
577. C3C2×#5477semidirect
578. C3C2×#5668semidirect
582. C2#10593969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37952
C2×#640842
C2×C3×#8752
C2×C3×C42×D32
C2×#639112
C2×#639062
C2×#638802
C2×#638662
#105939692
C2×#56683
C2×#54773