Finite Group Databasebeta

← C2×#10593951 #11903839

Subgroups — C2×#10593951 #11903839

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#874C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63898C212yesmaximal, complemented
5C2×Dic3×D12C212yesmaximal, complemented
6C2×#63884C214yesmaximal, complemented
7C2×#63863C212yesmaximal, complemented
8C2×#63860C212yesmaximal, complemented
9#10593951C2116yesmaximal, direct product factor
10C2×#5713—31nomaximal
11C2×#5585—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2212yes—
14C22×C3×D12C2212yes—
15C22×C3×D12C2212yes—
16C22×C3×Dic6C2211yescharacteristic
17C22×D3×Dic3C2214yes—
18C2×C32×C42C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2212yes—
21C2×C4×C3⋊Dic3C2212yes—
22C4×#634C2218yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C3×#874C2218yes—
27C3×C4×Dic6C2218yescomplemented
28C2×(C2×D3)⋊Dic3C2214yes—
29C2×(C2×D3)⋊Dic3C2214yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31#63898C22116yescomplemented
32Dic3×D12C22116yescomplemented
33#63884C22132yescomplemented
34#63863C22116yescomplemented
35#63860C22116yescomplemented
36C2×C3×#127—31no—
37C2×C3×C4×Q8—31no—
38C2×#947—32no—
39C2×#936—32no—
40C2×#936—32no—
41C2×#935—34no—
42C2×D4×Dic3—32no—
43C2×D4×Dic3—32no—
44#5713—316no—
45#5585—316no—
46C2×#894—34no—
47C2×#893—32no—
48C2×#875—32no—
49C2×#874D311yescharacteristic
50C2×C4×D12—32no—
51C2×C4×Dic6—31no—
52C2×C4×Dic6—31no—
53C2×C4×Dic6—61no—
54C2×C4×Dic6D311yescharacteristic, complemented
55C23×C3×D3C2314yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
61C2×#634—24no—
62C2×#634C2314yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×D12—28no—
66C2×C3×D12—28no—
67C2×C3×D12—44no—
68C2×C3×D12C2318yes—
69C2×C3×D12C2318yes—
70C2×C3×D12C2318yes—
71C2×C3×Dic6—24no—
72C2×C3×Dic6C2314yes—
73C2×D3×Dic3—48no—
74C2×D3×Dic3C23116yes—
75C32×C42C2314yes—
76C4⋊(C3⋊Dic3)C2314yes—
77#3750C2318yes—
78C4×C3⋊Dic3C2318yes—
79C3×C4⋊Dic3C2314yes—
80C3×Dic3⋊C4C2318yes—
81C3×C4×Dic3C2318yes—
82(C2×D3)⋊Dic3C23116yes—
83(C2×D3)⋊Dic3C23116yes—
84(C2×D3)⋊Dic3C23116yes—
85C2×#559—91noSylow
86C22×C3×Q8—31no—
87C22×C3×D4—32no—
88C22×C3×D4—32no—
89C22×C3×D4—32no—
90C23×Dic3—34no—
91C22×D12C2×D312yes—
92C22×D12C2×D312yes—
93C22×D12C2×D312yes—
94C22×C4×D3—34no—
95C22×Dic6—31no—
96C22×Dic6—31no—
97C22×Dic6—61no—
98C22×Dic6C2×D311yescharacteristic
99C3×#127—38no—
100C3×C4×Q8—38no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C42—21no—
104C2×C3×C42—32no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×#217—34no—
108C2×#217—34no—
109C2×#217—34no—
110#947—316no—
111#936—316no—
112#936—316no—
113#935—332no—
114D4×Dic3—316no—
115D4×Dic3—316no—
116C2×(C2×D3)⋊C4—34no—
117C2×(C2×D3)⋊C4—34no—
118C2×(C2×D3)⋊C4—34no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—62no—
126C2×Dic3⋊C4C2×D312yes—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—62no—
130C2×C4×Dic3C2×D312yes—
131#894—332no—
132#893—316no—
133#875—316no—
134#874C2×D318yes—
135C4×D12—316no—
136C4×Dic6—38no—
137C4×Dic6—38no—
138C4×Dic6—68no—
139C4×Dic6C2×D318yescomplemented
140C23×C32C2411yescharacteristic
141C22×C3×D3—28no—
142C22×C3×D3—28no—
143C22×C3×D3—28no—
144C22×C3×D3C2418yes—
145C2×C32×C4—22no—
146C2×C32×C4#4114yes—
147C2×C32×C4#4114yes—
148C2×C32×C4C2412yes—
149C2×C32×C4C2412yes—
150C2×C32×C4C2412yes—
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3—24no—
153C2×C3⋊Dic3C2414yes—
154C2×C3⋊Dic3C2414yes—
155#634—28no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3—24no—
158C2×C3×Dic3C2414yes—
159C2×C3×Dic3C2414yes—
160C3×D12—216no—
161C3×D12—216no—
162C3×D12—48no—
163C3×Dic6—28no—
164D3×Dic3—416no—
165#559—916no—
166C2×#127—31no—
167C2×#124—92no—
168C2×#124—92no—
169C2×#123—94no—
170C2×C4×Q8—31no—
171C2×C4×Q8—91no—
172C2×C4×D4—92no—
173C2×C4×D4—92no—
174C24×C3—34no—
175C23×D3C22×D314yes—
176C2×C3×Q8—34no—
177C2×C3×Q8—64no—
178C2×C3×D4—38no—
179C2×C3×D4—38no—
180C2×C3×D4—38no—
181C2×C3×D4—68no—
182C2×C3×D4—68no—
183C2×C3×D4—124no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—316no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202C22×Dic3—128no—
203C22×Dic3C22×D312yes—
204C22×Dic3C22×D312yes—
205C2×D12—28no—
206C2×D12—28no—
207C2×D12—44no—
208C2×D12C22×D318yes—
209C2×D12C22×D318yes—
210C2×D12C22×D318yes—
211C2×C4×D3—316no—
212C2×C4×D3—128no—
213C2×Dic6—24no—
214C2×Dic6—34no—
215C2×Dic6—34no—
216C2×Dic6—64no—
217C2×Dic6—68no—
218C2×Dic6—64no—
219C2×Dic6—64no—
220C2×Dic6C22×D314yes—
221C3×C4⋊C4—34no—
222C3×C4⋊C4—38no—
223C3×C42—24no—
224C3×C42—38no—
225C3×C42C22×D314yes—
226C3×C42C22×D314yes—
227#217—316no—
228#217—316no—
229#217—316no—
230(C2×D3)⋊C4—316no—
231(C2×D3)⋊C4—316no—
232(C2×D3)⋊C4—316no—
233C4⋊Dic3—34no—
234C4⋊Dic3—34no—
235C4⋊Dic3—64no—
236C4⋊Dic3C22×D314yes—
237Dic3⋊C4—38no—
238Dic3⋊C4—38no—
239Dic3⋊C4—68no—
240Dic3⋊C4C22×D318yes—
241C4×Dic3—38no—
242C4×Dic3—38no—
243C4×Dic3—68no—
244C4×Dic3C22×D318yes—
245C22×C32C2×#4112yes—
246C22×C32C2×#4112yes—
247C22×C32H(5,𝔽2)12yes—
248C22×C32C2511yescharacteristic
249C2×C3×D3—28no—
250C2×C3×D3—28no—
251C2×C3×D3—28no—
252C2×C3×D3—416no—
253C32×C4—22no—
254C32×C4C2×#4114yes—
255C32×C4C2×#4114yes—
256C3⋊Dic3—24no—
257C3⋊Dic3—24no—
258C3×Dic3—24no—
259C3×Dic3—24no—
260C22×Q8—31no—
261C22×Q8—91no—
262C22×D4—32no—
263C22×D4—32no—
264C22×D4—32no—
265C23×C4—94no—
266#127—38no—
267#124—916no—
268#124—916no—
269#123—932no—
270C4×Q8—38no—
271C4×Q8—98no—
272C4×D4—916no—
273C4×D4—916no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—32no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—92no—
278C2×C22⋊C4—94no—
279C2×C22⋊C4—94no—
280C2×C22⋊C4—94no—
281C2×C42—32no—
282C2×C42—92no—
283C2×C42D3211yescharacteristic
284C23×C3—21no—
285C23×C3—38no—
286C23×C3—68no—
287C23×C3—68no—
288C23×C3—68no—
289C23×C3C23×D311yescharacteristic
290C23×C3C23×D311yescharacteristic
291C22×D3—28no—
292C22×D3—28no—
293C22×D3—28no—
294C22×D3C23×D318yes—
295C3×Q8—68no—
296C3×D4—616no—
297C3×D4—616no—
298C3×D4—128no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—34no—
307C2×C3×C4—34no—
308C2×C3×C4—42no—
309C2×C3×C4—64no—
310C2×C3×C4—64no—
311C2×C3×C4#23514yes—
312C2×C3×C4#23714yes—
313C2×C3×C4#23714yes—
314C2×C3×C4#23914yes—
315C2×C3×C4C23×D312yes—
316C2×C3×C4C23×D312yes—
317C2×C3×C4C23×D312yes—
318C2×C3×C4C23×D312yes—
319C2×C3×C4C23×D312yes—
320C2×C3×C4C23×D312yes—
321C2×Dic3—24no—
322C2×Dic3—24no—
323C2×Dic3—34no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—64no—
328C2×Dic3—64no—
329C2×Dic3—68no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3—64no—
333C2×Dic3—64no—
334C2×Dic3—124no—
335C2×Dic3—1216no—
336C2×Dic3C23×D314yes—
337C2×Dic3C23×D314yes—
338D12—216no—
339D12—216no—
340D12—48no—
341C4×D3—1216no—
342Dic6—28no—
343Dic6—616no—
344Dic6—68no—
345Dic6—68no—
346C2×C32#55914yescomplemented
347C2×C32C22×#4111yescharacteristic
348C2×C32C22×#4111yescharacteristic
349C2×C32C2×H(5,𝔽2)11yescharacteristic
350C3×D3—48no—
351C24—34no—
352C2×Q8—34no—
353C2×Q8—64no—
354C2×Q8—94no—
355C2×Q8—184no—
356C2×D4—38no—
357C2×D4—38no—
358C2×D4—38no—
359C2×D4—68no—
360C2×D4—68no—
361C2×D4—124no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—916no—
365C22×C4—92no—
366C22×C4—92no—
367C22×C4—368no—
368C22×C4C2×D3211yescharacteristic
369C22×C4C2×D3211yescharacteristic
370C22×C4C2×D3211yescharacteristic
371C4⋊C4—34no—
372C4⋊C4—38no—
373C4⋊C4—94no—
374C4⋊C4—98no—
375C22⋊C4—916no—
376C22⋊C4—916no—
377C22⋊C4—916no—
378C42—38no—
379C42—98no—
380C42C2×D3214yes—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—68no—
386C22×C3—68no—
387C22×C3—68no—
388C22×C3—1216no—
389C22×C3C2×#23512yes—
390C22×C3C2×#23712yes—
391C22×C3C2×#23712yes—
392C22×C3#100412yes—
393C22×C3C2×#23912yes—
394C22×C3#100912yes—
395C22×C3C24×D311yescharacteristic
396C22×C3C24×D311yescharacteristic
397C2×D3—28no—
398C2×D3—28no—
399C2×D3—28no—
400C2×D3—416no—
401C3×C4—22no—
402C3×C4—22no—
403C3×C4—24no—
404C3×C4—24no—
405C3×C4—42no—
406C3×C4—64no—
407C3×C4—64no—
408C3×C4C2×#23514yes—
409C3×C4C2×#23714yes—
410C3×C4C2×#23714yes—
411C3×C4C2×#23914yes—
412Dic3—24no—
413Dic3—24no—
414Dic3—68no—
415Dic3—64no—
416Dic3—64no—
417Dic3—64no—
418Dic3—64no—
419Dic3—124no—
420C32C2×#55911yescharacteristic, complemented, Sylow
421C23—38no—
422C23—68no—
423C23—68no—
424C23—68no—
425C23C22×D3211yescharacteristic
426Q8—68no—
427Q8—188no—
428D4—616no—
429D4—616no—
430D4—128no—
431C2×C4—22no—
432C2×C4—34no—
433C2×C4—34no—
434C2×C4—64no—
435C2×C4—64no—
436C2×C4—94no—
437C2×C4—94no—
438C2×C4—184no—
439C2×C4—184no—
440C2×C4—3616no—
441C2×C4#379514yes—
442C2×C4#379614yes—
443C2×C4C22×D3212yes—
444C2×C4C22×D3212yes—
445C2×C4C22×D3212yes—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—24no—
450C2×C3—128no—
451C2×C3#558514yescomplemented
452C2×C3#571314yescomplemented
453C2×C3C22×#23511yescharacteristic
454C2×C3C22×#23711yescharacteristic
455C2×C3C22×#23711yescharacteristic
456C2×C3C2×#100411yescharacteristic
457C2×C3C22×#23911yescharacteristic
458C2×C3C2×#100911yescharacteristic
459D3—48no—
460C22—68no—
461C22—68no—
462C22—68no—
463C22—1216no—
464C22C2×#379512yes—
465C22C2×#379612yes—
466C22#6430712yes—
467C22C23×D3211yescharacteristic
468C4—22no—
469C4—64no—
470C4—64no—
471C4—184no—
472C4—184no—
473C4C2×#379514yes—
474C4C2×#379614yes—
475C3—21no—
476C3C2×#558511yescharacteristic, complemented
477C3C2×#571311yescharacteristic, complemented
478C2—128no—
479C2#1059395114yesdirect product factor
480C2C22×#379511yescharacteristic
481C2C22×#379611yescharacteristic
482C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×C3×#874C2
hypercenterC2×C42D32
hypocenterC32C2×#559
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×#634C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63898C2semidirect
5. C2×Dic3×D12C2semidirect
6. C2×#63884C2semidirect
7. C2×#63863C2semidirect
8. C2×#63860C2semidirect
9. #10593951C2direct (N × H)
22. C4×#634C22semidirect
27. C3×C4×Dic6C22semidirect
31. #63898C22semidirect
32. Dic3×D12C22semidirect
33. #63884C22semidirect
34. #63863C22semidirect
35. #63860C22semidirect
54. C2×C4×Dic6D3semidirect
139. C4×Dic6C2×D3semidirect
346. C2×C32#559semidirect
420. C32C2×#559semidirect
451. C2×C3#5585semidirect
452. C2×C3#5713semidirect
476. C3C2×#5585semidirect
477. C3C2×#5713semidirect
479. C2#10593951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8742
C2×C3×C4×Dic62
C2×#638982
C2×Dic3×D122
C2×#638842
C2×#638632
C2×#638602
#105939512
C2×#57133
C2×#55853