Finite Group Databasebeta

← C2×#10593879 #11903416

Subgroups — C2×#10593879 #11903416

Order 1152.

2369 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C2×#63861C214yesmaximal, complemented
5C2×#63860C212yesmaximal
6C2×#63856C212yesmaximal, complemented
7C2×#63844C212yesmaximal, complemented
8C2×#63841C212yesmaximal, complemented
9#10593879C2116yesmaximal, direct product factor
10C2×#5584—31nomaximal
11C2×#5542—31nomaximal
12C22×#634C2212yes—
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2212yes—
18C2×C4⋊(C3⋊Dic3)C2212yes—
19#64078C2218yescomplemented
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C3×C4×D12C2218yes—
26C3×C4×Dic6C2218yescomplemented
27C2×#3724C2214yes—
28C2×(C2×D3)⋊Dic3C2214yes—
29C2×(C2×D3)⋊Dic3C2214yes—
30C2×Dic32C2214yes—
31#63861C22132yescomplemented
32#63860C22116yes—
33#63856C22116yescomplemented
34#63844C22116yescomplemented
35#63841C22116yescomplemented
36C2×C3×C4×Q8—31no—
37C2×C3×C4×D4—31no—
38C2×#946—32no—
39C2×#936—32no—
40C2×#926—32no—
41C2×#924—32no—
42#5584—316no—
43#5542—316no—
44C2×#898—34no—
45C2×#892—32no—
46C2×#887—32no—
47C2×#879—34no—
48C2×#875—32no—
49C2×C4×D12D311yescharacteristic
50C2×#869—31no—
51C2×#869—31no—
52C2×#869—61no—
53C2×C4×Dic6—32no—
54C2×C4×Dic6D311yescharacteristic, complemented
55C23×C3×D3C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2314yes—
60C2×#634—28no—
61C2×#634C2318yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×D12—24no—
66C2×C3×D12C2314yes—
67C2×C3×C4×D3—28no—
68C2×C3×C4×D3C2318yes—
69C2×C3×Dic6—24no—
70C2×C3×Dic6C2314yes—
71C32×C42C2314yes—
72C4⋊(C3⋊Dic3)C2318yes—
73C4⋊(C3⋊Dic3)C2318yes—
74C3×(C2×D3)⋊C4C2318yes—
75C3×C4⋊Dic3C2314yes—
76C3×C4⋊Dic3C2314yes—
77C3×Dic3⋊C4C2318yes—
78C3×C4×Dic3C2318yes—
79#3724C23116yes—
80(C2×D3)⋊Dic3C23116yes—
81(C2×D3)⋊Dic3C23116yes—
82Dic32C23116yes—
83C2×#556—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C23×C3×C4—32no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3C2×D312yes—
89C22×Dic6—32no—
90C22×Dic6—32no—
91C22×Dic6—62no—
92C22×Dic6C2×D311yescharacteristic
93C3×C4×Q8—38no—
94C3×C4×D4—38no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C42—21no—
100C2×C3×C42—32no—
101C2×C3×C42C2×D311yescharacteristic
102C2×C3×C42C2×D311yescharacteristic
103C2×#217—34no—
104C2×#217—34no—
105#946—316no—
106#936—316no—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4—34no—
109C2×(C2×D3)⋊C4C2×D312yes—
110#926—316no—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—62no—
116C2×C4⋊Dic3—62no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119#924—316no—
120C2×Dic3⋊C4—34no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4C2×D312yes—
123C2×C4×Dic3—34no—
124C2×C4×Dic3—34no—
125C2×C4×Dic3C2×D312yes—
126#898—332no—
127#892—316no—
128#887—316no—
129#879—332no—
130#875—316no—
131C4×D12C2×D318yes—
132#869—38no—
133#869—38no—
134#869—68no—
135C4×Dic6—316no—
136C4×Dic6C2×D318yescomplemented
137C23×C32C2411yescharacteristic
138C22×C3×D3—24no—
139C22×C3×D3—24no—
140C22×C3×D3—24no—
141C22×C3×D3C2414yes—
142C2×C32×C4—22no—
143C2×C32×C4#4114yes—
144C2×C32×C4#4114yes—
145C2×C32×C4C2412yes—
146C2×C32×C4C2412yes—
147C2×C32×C4C2412yes—
148C2×C3⋊Dic3—28no—
149C2×C3⋊Dic3C2418yes—
150#634—216no—
151C2×C3×Dic3—24no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3C2414yes—
155C2×C3×Dic3C2414yes—
156C2×C3×Dic3C2414yes—
157C3×D12—28no—
158C3×C4×D3—216no—
159C3×Dic6—28no—
160#556—916no—
161C2×C4⋊Q8—91no—
162C2×#126—94no—
163C2×#124—92no—
164C2×C22⋊Q8—92no—
165C2×C4×Q8—31no—
166C2×C4×Q8—92no—
167C2×C4×D4—31no—
168C2×#117—92no—
169C24×C3—32no—
170C23×D3C22×D312yes—
171C2×C3×Q8—34no—
172C2×C3×Q8—64no—
173C2×C3×D4—34no—
174C2×C3×D4—64no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—38no—
182C22×C3×C4—68no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—34no—
190C22×Dic3—34no—
191C22×Dic3—64no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C2×D12—24no—
196C2×D12C22×D314yes—
197C2×C4×D3—28no—
198C2×C4×D3C22×D318yes—
199C2×Dic6—24no—
200C2×Dic6—38no—
201C2×Dic6—38no—
202C2×Dic6—68no—
203C2×Dic6—68no—
204C2×Dic6—68no—
205C2×Dic6—128no—
206C2×Dic6C22×D314yes—
207C3×C4⋊C4—34no—
208C3×C4⋊C4—34no—
209C3×C4⋊C4—38no—
210C3×C22⋊C4—38no—
211C3×C42—24no—
212C3×C42—38no—
213C3×C42C22×D314yes—
214C3×C42C22×D314yes—
215#217—316no—
216#217—316no—
217(C2×D3)⋊C4—316no—
218(C2×D3)⋊C4—316no—
219(C2×D3)⋊C4C22×D318yes—
220C4⋊Dic3—38no—
221C4⋊Dic3—38no—
222C4⋊Dic3—38no—
223C4⋊Dic3—38no—
224C4⋊Dic3—68no—
225C4⋊Dic3—68no—
226C4⋊Dic3C22×D314yes—
227C4⋊Dic3C22×D314yes—
228Dic3⋊C4—316no—
229Dic3⋊C4—316no—
230Dic3⋊C4C22×D318yes—
231C4×Dic3—316no—
232C4×Dic3—316no—
233C4×Dic3C22×D318yes—
234C22×C32C2×#4112yes—
235C22×C32C2×#4112yes—
236C22×C322−1+412yes—
237C22×C32C2511yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—24no—
240C2×C3×D3—24no—
241C2×C3×D3—48no—
242C32×C4—22no—
243C32×C4C2×#4114yes—
244C32×C4C2×#4114yes—
245C3⋊Dic3—28no—
246C3×Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—24no—
249C22×Q8—31no—
250C22×Q8—92no—
251C22×D4—31no—
252C23×C4—32no—
253C4⋊Q8—98no—
254#126—932no—
255#124—916no—
256C22⋊Q8—916no—
257C4×Q8—38no—
258C4×Q8—916no—
259C4×D4—38no—
260#117—916no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—32no—
264C2×C4⋊C4—94no—
265C2×C4⋊C4—92no—
266C2×C4⋊C4—92no—
267C2×C22⋊C4—32no—
268C2×C22⋊C4—94no—
269C2×C22⋊C4—94no—
270C2×C42—32no—
271C2×C42—94no—
272C2×C42D3211yescharacteristic
273C23×C3—21no—
274C23×C3—34no—
275C23×C3—64no—
276C23×C3—64no—
277C23×C3—64no—
278C23×C3C23×D311yescharacteristic
279C23×C3C23×D311yescharacteristic
280C22×D3—24no—
281C22×D3—24no—
282C22×D3—24no—
283C22×D3C23×D314yes—
284C3×Q8—68no—
285C3×D4—68no—
286C2×C3×C4—24no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—34no—
295C2×C3×C4—34no—
296C2×C3×C4—34no—
297C2×C3×C4—64no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4—616no—
301C2×C3×C4#23514yes—
302C2×C3×C4#23514yes—
303C2×C3×C4#23714yes—
304C2×C3×C4#23914yes—
305C2×C3×C4C23×D312yes—
306C2×C3×C4C23×D312yes—
307C2×C3×C4C23×D312yes—
308C2×C3×C4C23×D312yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D312yes—
311C2×Dic3—24no—
312C2×Dic3—24no—
313C2×Dic3—24no—
314C2×Dic3—38no—
315C2×Dic3—38no—
316C2×Dic3—68no—
317C2×Dic3—68no—
318C2×Dic3—68no—
319C2×Dic3—128no—
320C2×Dic3C23×D314yes—
321C2×Dic3C23×D314yes—
322C2×Dic3C23×D314yes—
323D12—28no—
324C4×D3—216no—
325Dic6—28no—
326Dic6—616no—
327Dic6—616no—
328Dic6—1216no—
329C2×C32#55614yescomplemented
330C2×C32C22×#4111yescharacteristic
331C2×C32C22×#4111yescharacteristic
332C2×C32C2×2−1+411yescharacteristic
333C3×D3—44no—
334C24—32no—
335C2×Q8—34no—
336C2×Q8—64no—
337C2×Q8—98no—
338C2×Q8—188no—
339C2×D4—34no—
340C2×D4—64no—
341C22×C4—32no—
342C22×C4—32no—
343C22×C4—32no—
344C22×C4—38no—
345C22×C4—68no—
346C22×C4—94no—
347C22×C4C2×D3211yescharacteristic
348C22×C4C2×D3211yescharacteristic
349C22×C4C2×D3211yescharacteristic
350C4⋊C4—34no—
351C4⋊C4—34no—
352C4⋊C4—38no—
353C4⋊C4—916no—
354C4⋊C4—98no—
355C4⋊C4—98no—
356C22⋊C4—38no—
357C22⋊C4—916no—
358C22⋊C4—916no—
359C42—38no—
360C42—916no—
361C42C2×D3214yes—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—64no—
367C22×C3—64no—
368C22×C3—64no—
369C22×C3—128no—
370C22×C3C2×#23512yes—
371C22×C3C2×#23512yes—
372C22×C3C2×#23712yes—
373C22×C3C2×#23912yes—
374C22×C3#101012yes—
375C22×C3#101012yes—
376C22×C3C24×D311yescharacteristic
377C22×C3C24×D311yescharacteristic
378C2×D3—24no—
379C2×D3—24no—
380C2×D3—24no—
381C2×D3—48no—
382C3×C4—24no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—24no—
386C3×C4—24no—
387C3×C4—64no—
388C3×C4—64no—
389C3×C4—64no—
390C3×C4C2×#23514yes—
391C3×C4C2×#23514yes—
392C3×C4C2×#23714yes—
393C3×C4C2×#23914yes—
394Dic3—24no—
395Dic3—24no—
396Dic3—24no—
397Dic3—68no—
398Dic3—68no—
399Dic3—128no—
400C32C2×#55611yescharacteristic, complemented, Sylow
401C23—34no—
402C23—64no—
403C23—64no—
404C23—64no—
405C23C22×D3211yescharacteristic
406Q8—68no—
407Q8—1816no—
408D4—68no—
409C2×C4—22no—
410C2×C4—34no—
411C2×C4—34no—
412C2×C4—34no—
413C2×C4—64no—
414C2×C4—64no—
415C2×C4—64no—
416C2×C4—616no—
417C2×C4—98no—
418C2×C4—188no—
419C2×C4#379514yes—
420C2×C4#379914yes—
421C2×C4C22×D3212yes—
422C2×C4C22×D3212yes—
423C2×C4C22×D3212yes—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—24no—
428C2×C3—124no—
429C2×C3#554214yescomplemented
430C2×C3#558414yescomplemented
431C2×C3C22×#23511yescharacteristic
432C2×C3C22×#23511yescharacteristic
433C2×C3C22×#23711yescharacteristic
434C2×C3C22×#23911yescharacteristic
435C2×C3C2×#101011yescharacteristic
436C2×C3C2×#101011yescharacteristic
437D3—44no—
438C22—64no—
439C22—64no—
440C22—64no—
441C22—128no—
442C22C2×#379512yes—
443C22#6429812yes—
444C22C2×#379912yes—
445C22C23×D3211yescharacteristic
446C4—22no—
447C4—64no—
448C4—64no—
449C4—64no—
450C4—188no—
451C4C2×#379514yes—
452C4C2×#379914yes—
453C3—21no—
454C3C2×#554211yescharacteristic, complemented
455C3C2×#558411yescharacteristic, complemented
456C2—124no—
457C2#1059387914yesdirect product factor
458C2C22×#379511yescharacteristic
459C2C2×#6429811yescharacteristic
460C2C22×#379911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#556
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64078C2semidirect
3. C2×C3×C4×Dic6C2semidirect
4. C2×#63861C2semidirect
6. C2×#63856C2semidirect
7. C2×#63844C2semidirect
8. C2×#63841C2semidirect
9. #10593879C2direct (N × H)
19. #64078C22semidirect
26. C3×C4×Dic6C22semidirect
31. #63861C22semidirect
33. #63856C22semidirect
34. #63844C22semidirect
35. #63841C22semidirect
54. C2×C4×Dic6D3semidirect
136. C4×Dic6C2×D3semidirect
329. C2×C32#556semidirect
400. C32C2×#556semidirect
429. C2×C3#5542semidirect
430. C2×C3#5584semidirect
454. C3C2×#5542semidirect
455. C3C2×#5584semidirect
457. C2#10593879direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640782
C2×C3×C4×D122
C2×C3×C4×Dic62
C2×#638612
C2×#638602
C2×#638562
C2×#638442
C2×#638412
#105938792
C2×#55843
C2×#55423