Finite Group Databasebeta

← C2×#10593987 #11903339

Subgroups — C2×#10593987 #11903339

Order 1152.

2693 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63916C212yesmaximal, complemented
5C2×#63909C212yesmaximal, complemented
6C2×#63907C214yesmaximal, complemented
7C2×#63849C212yesmaximal, complemented
8C2×#63841C212yesmaximal, complemented
9#10593987C2116yesmaximal, direct product factor
10C2×#5734—31nomaximal
11C2×#5563—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2212yes—
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×Dic6C2212yes—
17C22×#626C2214yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2218yescomplemented
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C3×C4×D12C2218yescomplemented
27C3×#869C2218yescomplemented
28C2×#3722C2214yes—
29C2×(C2×D3)⋊Dic3C2214yes—
30C2×Dic32C2214yes—
31#63916C22116yescomplemented
32#63909C22116yescomplemented
33#63907C22132yescomplemented
34#63849C22116yescomplemented
35#63841C22116yescomplemented
36C2×C3×C4⋊Q8—31no—
37C2×C3×C4×D4—31no—
38C2×#947—34no—
39C2×#938—32no—
40C2×#930—32no—
41C2×#926—32no—
42#5734—316no—
43#5563—316no—
44C2×#895—32no—
45C2×#895—32no—
46C2×#892—32no—
47C2×#892—32no—
48C2×#892—32no—
49C2×#885—34no—
50C2×C4×D12—31no—
51C2×C4×D12—31no—
52C2×C4×D12—61no—
53C2×C4×D12D311yescharacteristic, complemented
54C2×#869D311yescharacteristic, complemented
55C23×C3⋊D3C2312yes—
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2312yes—
61C2×C4⋊(C3⋊D3)—24no—
62C2×C4⋊(C3⋊D3)C2314yes—
63C2×C4×C3⋊D3—28no—
64C2×C4×C3⋊D3C2318yes—
65C22×C3×Dic3C2314yes—
66C22×C3×Dic3C2312yes—
67C2×C3×D12—24no—
68C2×C3×D12C2314yes—
69C2×C3×C4×D3—28no—
70C2×C3×C4×D3C2318yes—
71C2×C3×Dic6—44no—
72C2×C3×Dic6C2318yes—
73C2×#626—48no—
74C2×#626C23116yes—
75C32×C42C2314yes—
76#3752C2318yes—
77C4⋊(C3⋊Dic3)C2314yes—
78C3×(C2×D3)⋊C4C2318yes—
79C3×C4⋊Dic3C2318yes—
80C3×C4⋊Dic3C2314yes—
81C3×C4⋊Dic3C2318yes—
82#3722C23116yes—
83(C2×D3)⋊Dic3C23116yes—
84Dic32C23116yes—
85C2×#555—91noSylow
86C22×C3×Q8—32no—
87C22×C3×D4—31no—
88C23×C3×C4—32no—
89C22×#67—34no—
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—34no—
93C22×D12—61no—
94C22×D12C2×D311yescharacteristic
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—62no—
98C22×C4×D3C2×D312yes—
99C22×Dic6C2×D312yes—
100C3×C4⋊Q8—38no—
101C3×C4×D4—38no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C42—21no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109C2×#217—34no—
110#947—332no—
111#938—316no—
112#930—316no—
113C2×(C2×D3)⋊C4—34no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—34no—
117C2×(C2×D3)⋊C4—34no—
118C2×(C2×D3)⋊C4—62no—
119C2×(C2×D3)⋊C4C2×D312yes—
120#926—316no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3C2×D312yes—
125C2×C4⋊Dic3C2×D312yes—
126C2×C4⋊Dic3C2×D311yescharacteristic
127C2×C4×Dic3—34no—
128C2×C4×Dic3—34no—
129#895—316no—
130#895—316no—
131#892—316no—
132#892—316no—
133#892—316no—
134#885—332no—
135C4×D12—38no—
136C4×D12—38no—
137C4×D12—68no—
138C4×D12C2×D318yescomplemented
139#869C2×D318yescomplemented
140C23×C32C2411yescharacteristic
141C22×C3⋊D3—24no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3—24no—
144C22×C3⋊D3C2414yes—
145C22×C3×D3—24no—
146C22×C3×D3—24no—
147C22×C3×D3—24no—
148C22×C3×D3C2414yes—
149C2×C32×C4—22no—
150C2×C32×C4#4114yes—
151C2×C32×C4#4114yes—
152C2×C32×C4C2412yes—
153C2×C32×C4C2412yes—
154C2×C32×C4C2412yes—
155C2×C3⋊Dic3—24no—
156C2×C3⋊Dic3C2414yes—
157C4⋊(C3⋊D3)—28no—
158C4×C3⋊D3—216no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3—28no—
161C2×C3×Dic3C2414yes—
162C2×C3×Dic3C2418yes—
163C3×D12—28no—
164C3×C4×D3—216no—
165C3×Dic6—48no—
166#626—416no—
167#555—916no—
168C2×C4⋊Q8—31no—
169C2×#124—94no—
170C2×#121—92no—
171C2×#121—92no—
172C2×C4×D4—31no—
173C2×C4×D4—91no—
174C2×#117—92no—
175C2×#117—92no—
176C24×C3—32no—
177C23×D3—32no—
178C23×D3—32no—
179C23×D3—62no—
180C23×D3C22×D312yes—
181C2×C3×Q8—38no—
182C2×C3×Q8—124no—
183C2×C3×D4—34no—
184C2×C3×D4—64no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—32no—
189C22×C3×C4—34no—
190C22×C3×C4—38no—
191C22×C3×C4—68no—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—316no—
199C2×#67—128no—
200C22×Dic3—32no—
201C22×Dic3—32no—
202C22×Dic3—62no—
203C22×Dic3C22×D312yes—
204C22×Dic3C22×D314yes—
205C2×D12—24no—
206C2×D12—34no—
207C2×D12—34no—
208C2×D12—316no—
209C2×D12—64no—
210C2×D12—68no—
211C2×D12—64no—
212C2×D12—64no—
213C2×D12—128no—
214C2×D12C22×D314yes—
215C2×C4×D3—28no—
216C2×C4×D3—38no—
217C2×C4×D3—38no—
218C2×C4×D3—68no—
219C2×C4×D3—68no—
220C2×C4×D3—68no—
221C2×C4×D3—128no—
222C2×C4×D3C22×D318yes—
223C2×Dic6—44no—
224C2×Dic6C22×D318yes—
225C3×C4⋊C4—34no—
226C3×C4⋊C4—38no—
227C3×C4⋊C4—38no—
228C3×C22⋊C4—38no—
229C3×C42—24no—
230C3×C42C22×D314yes—
231C3×C42C22×D314yes—
232#217—316no—
233(C2×D3)⋊C4—316no—
234(C2×D3)⋊C4—38no—
235(C2×D3)⋊C4—38no—
236(C2×D3)⋊C4—316no—
237(C2×D3)⋊C4—316no—
238(C2×D3)⋊C4—68no—
239(C2×D3)⋊C4C22×D318yes—
240C4⋊Dic3—34no—
241C4⋊Dic3—34no—
242C4⋊Dic3—64no—
243C4⋊Dic3C22×D318yes—
244C4⋊Dic3C22×D318yes—
245C4⋊Dic3C22×D314yes—
246C4×Dic3—316no—
247C4×Dic3—316no—
248C22×C32C2×#4112yes—
249C22×C32C2×#4112yes—
250C22×C32H(5,𝔽2)12yes—
251C22×C32C2511yescharacteristic
252C2×C3⋊D3—24no—
253C2×C3⋊D3—24no—
254C2×C3⋊D3—24no—
255C2×C3⋊D3—48no—
256C2×C3×D3—24no—
257C2×C3×D3—24no—
258C2×C3×D3—24no—
259C2×C3×D3—48no—
260C32×C4—22no—
261C32×C4C2×#4114yes—
262C32×C4C2×#4114yes—
263C3⋊Dic3—24no—
264C3×Dic3—24no—
265C3×Dic3—28no—
266C22×Q8—32no—
267C22×D4—31no—
268C22×D4—94no—
269C22×D4—91no—
270C23×C4—32no—
271C23×C4—92no—
272C4⋊Q8—38no—
273#124—932no—
274#121—916no—
275#121—916no—
276C4×D4—38no—
277C4×D4—98no—
278#117—916no—
279#117—916no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—32no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—91no—
284C2×C22⋊C4—32no—
285C2×C22⋊C4—94no—
286C2×C22⋊C4—94no—
287C2×C22⋊C4—92no—
288C2×C42—94no—
289C2×C42D3211yescharacteristic
290C23×C3—21no—
291C23×C3—34no—
292C23×C3—64no—
293C23×C3—64no—
294C23×C3—64no—
295C23×C3C23×D311yescharacteristic
296C23×C3C23×D311yescharacteristic
297C22×D3—24no—
298C22×D3—24no—
299C22×D3—24no—
300C22×D3—34no—
301C22×D3—34no—
302C22×D3—64no—
303C22×D3—68no—
304C22×D3—64no—
305C22×D3—64no—
306C22×D3—64no—
307C22×D3—64no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—124no—
311C22×D3—124no—
312C22×D3C23×D314yes—
313C3×Q8—128no—
314C3×D4—68no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—34no—
323C2×C3×C4—38no—
324C2×C3×C4—42no—
325C2×C3×C4—64no—
326C2×C3×C4—68no—
327C2×C3×C4—616no—
328C2×C3×C4#23514yes—
329C2×C3×C4#23714yes—
330C2×C3×C4#23914yes—
331C2×C3×C4#23914yes—
332C2×C3×C4C23×D312yes—
333C2×C3×C4C23×D312yes—
334C2×C3×C4C23×D312yes—
335C2×C3×C4C23×D312yes—
336C2×C3×C4C23×D312yes—
337C2×C3×C4C23×D312yes—
338#67—1216no—
339C2×Dic3—24no—
340C2×Dic3—28no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—64no—
344C2×Dic3—64no—
345C2×Dic3—64no—
346C2×Dic3—124no—
347C2×Dic3C23×D314yes—
348C2×Dic3C23×D318yes—
349D12—28no—
350D12—616no—
351D12—68no—
352D12—68no—
353D12—1216no—
354C4×D3—216no—
355C4×D3—616no—
356C4×D3—616no—
357C4×D3—1216no—
358Dic6—48no—
359C2×C32#55514yescomplemented
360C2×C32C22×#4111yescharacteristic
361C2×C32C22×#4111yescharacteristic
362C2×C32C2×H(5,𝔽2)11yescharacteristic
363C3⋊D3—44no—
364C3×D3—44no—
365C24—32no—
366C24—92no—
367C2×Q8—38no—
368C2×Q8—124no—
369C2×D4—34no—
370C2×D4—64no—
371C2×D4—916no—
372C2×D4—94no—
373C2×D4—184no—
374C2×D4—368no—
375C22×C4—32no—
376C22×C4—34no—
377C22×C4—38no—
378C22×C4—68no—
379C22×C4—92no—
380C22×C4—98no—
381C22×C4—188no—
382C22×C4C2×D3211yescharacteristic
383C22×C4C2×D3211yescharacteristic
384C22×C4C2×D3211yescharacteristic
385C4⋊C4—34no—
386C4⋊C4—38no—
387C4⋊C4—38no—
388C4⋊C4—94no—
389C22⋊C4—38no—
390C22⋊C4—916no—
391C22⋊C4—916no—
392C22⋊C4—98no—
393C42—916no—
394C42C2×D3214yes—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—21no—
399C22×C3—64no—
400C22×C3—64no—
401C22×C3—64no—
402C22×C3—128no—
403C22×C3C2×#23512yes—
404C22×C3C2×#23712yes—
405C22×C3#100412yes—
406C22×C3C2×#23912yes—
407C22×C3C2×#23912yes—
408C22×C3#100912yes—
409C22×C3C24×D311yescharacteristic
410C22×C3C24×D311yescharacteristic
411C2×D3—24no—
412C2×D3—24no—
413C2×D3—24no—
414C2×D3—48no—
415C2×D3—68no—
416C2×D3—64no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—64no—
422C2×D3—124no—
423C2×D3—124no—
424C2×D3—1216no—
425C2×D3—128no—
426C2×D3—128no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—24no—
430C3×C4—24no—
431C3×C4—42no—
432C3×C4—64no—
433C3×C4—68no—
434C3×C4C2×#23514yes—
435C3×C4C2×#23714yes—
436C3×C4C2×#23914yes—
437C3×C4C2×#23914yes—
438Dic3—24no—
439Dic3—28no—
440Dic3—64no—
441Dic3—64no—
442Dic3—124no—
443C32C2×#55511yescharacteristic, complemented, Sylow
444C23—34no—
445C23—64no—
446C23—64no—
447C23—64no—
448C23—94no—
449C23—184no—
450C23—184no—
451C23—184no—
452C23C22×D3211yescharacteristic
453Q8—128no—
454D4—68no—
455D4—188no—
456D4—3616no—
457C2×C4—22no—
458C2×C4—34no—
459C2×C4—38no—
460C2×C4—64no—
461C2×C4—68no—
462C2×C4—616no—
463C2×C4—94no—
464C2×C4—184no—
465C2×C4—1816no—
466C2×C4#379614yes—
467C2×C4#379914yes—
468C2×C4C22×D3212yes—
469C2×C4C22×D3212yes—
470C2×C4C22×D3212yes—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—24no—
475C2×C3—124no—
476C2×C3#556314yescomplemented
477C2×C3#573414yescomplemented
478C2×C3C22×#23511yescharacteristic
479C2×C3C22×#23711yescharacteristic
480C2×C3C2×#100411yescharacteristic
481C2×C3C22×#23911yescharacteristic
482C2×C3C22×#23911yescharacteristic
483C2×C3C2×#100911yescharacteristic
484D3—44no—
485D3—128no—
486D3—124no—
487D3—124no—
488C22—64no—
489C22—64no—
490C22—64no—
491C22—128no—
492C22—184no—
493C22—184no—
494C22—184no—
495C22—368no—
496C22C2×#379612yes—
497C22C2×#379912yes—
498C22#6430712yes—
499C22C23×D3211yescharacteristic
500C4—22no—
501C4—64no—
502C4—68no—
503C4—184no—
504C4C2×#379614yes—
505C4C2×#379914yes—
506C3—21no—
507C3C2×#556311yescharacteristic, complemented
508C3C2×#573411yescharacteristic, complemented
509C2—124no—
510C2—364no—
511C2#1059398714yesdirect product factor
512C2C22×#379611yescharacteristic
513C2C22×#379911yescharacteristic
514C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#555
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C3×#869C2semidirect
4. C2×#63916C2semidirect
5. C2×#63909C2semidirect
6. C2×#63907C2semidirect
7. C2×#63849C2semidirect
8. C2×#63841C2semidirect
9. #10593987C2direct (N × H)
21. C4×C4⋊(C3⋊D3)C22semidirect
26. C3×C4×D12C22semidirect
27. C3×#869C22semidirect
31. #63916C22semidirect
32. #63909C22semidirect
33. #63907C22semidirect
34. #63849C22semidirect
35. #63841C22semidirect
53. C2×C4×D12D3semidirect
54. C2×#869D3semidirect
138. C4×D12C2×D3semidirect
139. #869C2×D3semidirect
359. C2×C32#555semidirect
443. C32C2×#555semidirect
476. C2×C3#5563semidirect
477. C2×C3#5734semidirect
507. C3C2×#5563semidirect
508. C3C2×#5734semidirect
511. C2#10593987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×D122
C2×C3×#8692
C2×#639162
C2×#639092
C2×#639072
C2×#638492
C2×#638412
#105939872
C2×#57343
C2×#55633