Finite Group Databasebeta

← C2×#10593960 #11903280

Subgroups — C2×#10593960 #11903280

Order 1152.

2545 conjugacy classes of subgroups.

The subgroup lattice has 470 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×#63896C214yesmaximal, complemented
5C2×Dic3×D12C212yesmaximal
6C2×D3×C4⋊Dic3C212yesmaximal, complemented
7C2×#63869C212yesmaximal, complemented
8C2×#63856C212yesmaximal, complemented
9#10593960C2116yesmaximal, direct product factor
10C2×#5579—31nomaximal
11C2×#5543—31nomaximal
12C22×#634C2212yes—
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×C3×Dic6C2211yescharacteristic
16C22×D3×Dic3C2214yes—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2212yes—
19C2×C4⋊(C3⋊Dic3)C2212yes—
20#64078C2218yescomplemented
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C3×C4×D12C2218yes—
27C3×C4×Dic6C2218yescomplemented
28C2×#3724C2214yes—
29C2×Dic3⋊Dic3C2214yes—
30C2×(C2×D3)⋊Dic3C2214yes—
31#63896C22132yescomplemented
32Dic3×D12C22116yes—
33D3×C4⋊Dic3C22116yescomplemented
34#63869C22116yescomplemented
35#63856C22116yescomplemented
36C2×C3×C4×Q8—31no—
37C2×C3×C4×D4—31no—
38C2×#946—32no—
39C2×D4×Dic3—32no—
40C22×C4⋊Dic3—32no—
41C2×#924—32no—
42#5579—316no—
43#5543—316no—
44C2×#896—34no—
45C2×D3×C4⋊C4—32no—
46C2×#890—32no—
47C2×#878—34no—
48C2×C4×D12—32no—
49C2×C4×D12D311yescharacteristic
50C2×#870—32no—
51C2×#869—31no—
52C2×#869—31no—
53C2×#869—61no—
54C2×C4×Dic6D311yescharacteristic, complemented
55C23×C3×D3C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2314yes—
60C2×#634—44no—
61C2×#634C2318yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×D12Q818yescomplemented
66C2×C3×D12C2314yes—
67C2×C3×C4×D3—28no—
68C2×C3×C4×D3C2318yes—
69C2×C3×Dic6—24no—
70C2×C3×Dic6C2314yes—
71C2×D3×Dic3—48no—
72C2×D3×Dic3C23116yes—
73C32×C42C2314yes—
74C4⋊(C3⋊Dic3)C2318yes—
75C4⋊(C3⋊Dic3)C2318yes—
76C3×(C2×D3)⋊C4C2318yes—
77C3×C4⋊Dic3C2314yes—
78C3×C4⋊Dic3C2314yes—
79C3×Dic3⋊C4C2318yes—
80C3×C4×Dic3C2318yes—
81#3724C23116yes—
82Dic3⋊Dic3C23116yes—
83(C2×D3)⋊Dic3C23116yes—
84C2×#554—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C23×C3×C4—32no—
88C23×Dic3—34no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—34no—
91C22×C4×D3C2×D312yes—
92C22×Dic6—32no—
93C22×Dic6—32no—
94C22×Dic6—62no—
95C22×Dic6C2×D311yescharacteristic
96C3×C4×Q8—38no—
97C3×C4×D4—38no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C42—21no—
103C2×C3×C42—32no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106C2×#217—34no—
107#946—316no—
108D4×Dic3—316no—
109C2×(C2×D3)⋊C4—34no—
110C2×(C2×D3)⋊C4C2×D312yes—
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—32no—
115C2×C4⋊Dic3—34no—
116C2×C4⋊Dic3—316no—
117C2×C4⋊Dic3—62no—
118C2×C4⋊Dic3—62no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×C4⋊Dic3C2×D311yescharacteristic
121#924—316no—
122C2×Dic3⋊C4—34no—
123C2×Dic3⋊C4—34no—
124C2×Dic3⋊C4—34no—
125C2×Dic3⋊C4C2×D312yes—
126C2×C4×Dic3C2×D312yes—
127#896—332no—
128D3×C4⋊C4—316no—
129#890—316no—
130#878—332no—
131C4×D12—316no—
132C4×D12C2×D318yes—
133#870—316no—
134#869—38no—
135#869—38no—
136#869—68no—
137C4×Dic6C2×D318yescomplemented
138C23×C32C2411yescharacteristic
139C22×C3×D3—24no—
140C22×C3×D3—24no—
141C22×C3×D3C2×Q818yes—
142C22×C3×D3C2414yes—
143C2×C32×C4—22no—
144C2×C32×C4C2×Q814yes—
145C2×C32×C4#4114yes—
146C2×C32×C4C2412yes—
147C2×C32×C4C2412yes—
148C2×C32×C4C2412yes—
149C2×C3⋊Dic3—28no—
150C2×C3⋊Dic3C2418yes—
151#634—48no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3C2414yes—
156C2×C3×Dic3C2414yes—
157C2×C3×Dic3C2414yes—
158C3×D12C2×Q8116yescomplemented
159C3×C4×D3—216no—
160C3×Dic6—28no—
161D3×Dic3—416no—
162#554—916no—
163C2×C4⋊Q8—91no—
164C2×#125—92no—
165C2×C22⋊Q8—94no—
166C2×C22⋊Q8—92no—
167C2×C4×Q8—31no—
168C2×C4×D4—31no—
169C2×C4×D4—92no—
170C22×C4⋊C4—92no—
171C24×C3—32no—
172C23×D3C22×D312yes—
173C2×C3×Q8—34no—
174C2×C3×Q8—64no—
175C2×C3×D4—38no—
176C2×C3×D4—34no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4—38no—
184C22×C3×C4—68no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—34no—
192C22×Dic3—34no—
193C22×Dic3—316no—
194C22×Dic3—64no—
195C22×Dic3—128no—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C2×D12Dic618yescomplemented
200C2×D12C22×D314yes—
201C2×C4×D3—28no—
202C2×C4×D3—316no—
203C2×C4×D3—128no—
204C2×C4×D3C22×D318yes—
205C2×Dic6—24no—
206C2×Dic6—38no—
207C2×Dic6—38no—
208C2×Dic6—68no—
209C2×Dic6—124no—
210C2×Dic6—124no—
211C2×Dic6—128no—
212C2×Dic6C22×D314yes—
213C3×C4⋊C4—34no—
214C3×C4⋊C4—34no—
215C3×C4⋊C4—38no—
216C3×C22⋊C4—38no—
217C3×C42—24no—
218C3×C42—38no—
219C3×C42C22×D314yes—
220C3×C42C22×D314yes—
221#217—316no—
222(C2×D3)⋊C4—316no—
223(C2×D3)⋊C4C22×D318yes—
224C4⋊Dic3—38no—
225C4⋊Dic3—38no—
226C4⋊Dic3—38no—
227C4⋊Dic3—38no—
228C4⋊Dic3—316no—
229C4⋊Dic3—68no—
230C4⋊Dic3—68no—
231C4⋊Dic3C22×D314yes—
232C4⋊Dic3C22×D314yes—
233Dic3⋊C4—316no—
234Dic3⋊C4—316no—
235Dic3⋊C4—316no—
236Dic3⋊C4C22×D318yes—
237C4×Dic3C22×D318yes—
238C22×C32C22×Q812yes—
239C22×C32C2×#4112yes—
240C22×C32H(5,𝔽2)12yes—
241C22×C32C2511yescharacteristic
242C2×C3×D3—216no—
243C2×C3×D3—24no—
244C2×C3×D3—24no—
245C2×C3×D3C22×Q818yes—
246C32×C4—22no—
247C32×C4C22×Q814yes—
248C32×C4C2×#4114yes—
249C3⋊Dic3—28no—
250C3×Dic3—24no—
251C3×Dic3—24no—
252C3×Dic3—24no—
253C22×Q8—31no—
254C22×Q8—92no—
255C22×D4—31no—
256C23×C4—32no—
257C23×C4—94no—
258C4⋊Q8—98no—
259#125—916no—
260C22⋊Q8—932no—
261C22⋊Q8—916no—
262C4×Q8—38no—
263C4×D4—38no—
264C4×D4—916no—
265C2×C4⋊C4—31no—
266C2×C4⋊C4—31no—
267C2×C4⋊C4—32no—
268C2×C4⋊C4—916no—
269C2×C4⋊C4—94no—
270C2×C4⋊C4—94no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—92no—
273C2×C22⋊C4—32no—
274C2×C22⋊C4—94no—
275C2×C42—32no—
276C2×C42D3211yescharacteristic
277C23×C3—21no—
278C23×C3—38no—
279C23×C3—34no—
280C23×C3—64no—
281C23×C3—64no—
282C23×C3C23×D311yescharacteristic
283C23×C3C23×D311yescharacteristic
284C22×D3—24no—
285C22×D3—24no—
286C22×D3C2×Dic618yes—
287C22×D3C23×D314yes—
288C3×Q8—68no—
289C3×D4—316no—
290C2×C3×C4—24no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—34no—
301C2×C3×C4—64no—
302C2×C3×C4—64no—
303C2×C3×C4—64no—
304C2×C3×C4—616no—
305C2×C3×C4C2×Dic614yes—
306C2×C3×C4#23514yes—
307C2×C3×C4#23714yes—
308C2×C3×C4D3×Q814yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D312yes—
311C2×C3×C4C23×D312yes—
312C2×C3×C4C23×D312yes—
313C2×C3×C4C23×D312yes—
314C2×C3×C4C23×D312yes—
315C2×Dic3—24no—
316C2×Dic3—24no—
317C2×Dic3—24no—
318C2×Dic3—38no—
319C2×Dic3—38no—
320C2×Dic3—68no—
321C2×Dic3—68no—
322C2×Dic3—68no—
323C2×Dic3—128no—
324C2×Dic3—1216no—
325C2×Dic3C23×D314yes—
326C2×Dic3C23×D314yes—
327C2×Dic3C23×D314yes—
328D12C2×Dic6116yescomplemented
329C4×D3—216no—
330C4×D3—1216no—
331Dic6—28no—
332Dic6—128no—
333Dic6—128no—
334Dic6—1216no—
335C2×C32#55414yescomplemented
336C2×C32C23×Q811yescharacteristic
337C2×C32C22×#4111yescharacteristic
338C2×C32C2×H(5,𝔽2)11yescharacteristic
339C3×D3—28no—
340C24—32no—
341C2×Q8—34no—
342C2×Q8—64no—
343C2×Q8—98no—
344C2×Q8—364no—
345C2×D4—34no—
346C2×D4—38no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—32no—
350C22×C4—38no—
351C22×C4—68no—
352C22×C4—916no—
353C22×C4—94no—
354C22×C4—368no—
355C22×C4C2×D3211yescharacteristic
356C22×C4C2×D3211yescharacteristic
357C22×C4C2×D3211yescharacteristic
358C4⋊C4—34no—
359C4⋊C4—34no—
360C4⋊C4—38no—
361C4⋊C4—916no—
362C4⋊C4—916no—
363C4⋊C4—98no—
364C4⋊C4—98no—
365C22⋊C4—38no—
366C22⋊C4—916no—
367C42—38no—
368C42C2×D3214yes—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—38no—
374C22×C3—64no—
375C22×C3—64no—
376C22×C3—616no—
377C22×C3C22×Dic612yes—
378C22×C3C2×#23512yes—
379C22×C3C2×#23712yes—
380C22×C3C2×D3×Q812yes—
381C22×C3#100912yes—
382C22×C3#100912yes—
383C22×C3C24×D311yescharacteristic
384C22×C3C24×D311yescharacteristic
385C2×D3—24no—
386C2×D3—24no—
387C2×D3—216no—
388C2×D3C22×Dic618yes—
389C3×C4—24no—
390C3×C4—22no—
391C3×C4—22no—
392C3×C4—24no—
393C3×C4—24no—
394C3×C4—64no—
395C3×C4—64no—
396C3×C4—64no—
397C3×C4C22×Dic614yes—
398C3×C4C2×#23514yes—
399C3×C4C2×#23714yes—
400C3×C4C2×D3×Q814yes—
401Dic3—24no—
402Dic3—24no—
403Dic3—24no—
404Dic3—68no—
405Dic3—68no—
406Dic3—128no—
407C32C2×#55411yescharacteristic, complemented, Sylow
408C23—38no—
409C23—34no—
410C23—64no—
411C23—64no—
412C23C22×D3211yescharacteristic
413Q8—68no—
414Q8—368no—
415D4—316no—
416C2×C4—22no—
417C2×C4—34no—
418C2×C4—34no—
419C2×C4—34no—
420C2×C4—64no—
421C2×C4—64no—
422C2×C4—64no—
423C2×C4—616no—
424C2×C4—98no—
425C2×C4—188no—
426C2×C4—3616no—
427C2×C4D3×Dic614yes—
428C2×C4#379514yes—
429C2×C4C22×D3212yes—
430C2×C4C22×D3212yes—
431C2×C4C22×D3212yes—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—24no—
436C2×C3—68no—
437C2×C3#554314yescomplemented
438C2×C3#557914yescomplemented
439C2×C3C23×Dic611yescharacteristic
440C2×C3C22×#23511yescharacteristic
441C2×C3C22×#23711yescharacteristic
442C2×C3C22×D3×Q811yescharacteristic
443C2×C3C2×#100911yescharacteristic
444C2×C3C2×#100911yescharacteristic
445D3—28no—
446C22—38no—
447C22—64no—
448C22—64no—
449C22—616no—
450C22C2×D3×Dic612yes—
451C22C2×#379512yes—
452C22#6430812yes—
453C22C23×D3211yescharacteristic
454C4—22no—
455C4—64no—
456C4—64no—
457C4—64no—
458C4—188no—
459C4C2×D3×Dic614yes—
460C4C2×#379514yes—
461C3—21no—
462C3C2×#554311yescharacteristic, complemented
463C3C2×#557911yescharacteristic, complemented
464C2—68no—
465C2#1059396014yesdirect product factor
466C2C22×D3×Dic611yescharacteristic
467C2C22×#379511yescharacteristic
468C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#554
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×#63896C2semidirect
6. C2×D3×C4⋊Dic3C2semidirect
7. C2×#63869C2semidirect
8. C2×#63856C2semidirect
9. #10593960C2direct (N × H)
20. #64078C22semidirect
27. C3×C4×Dic6C22semidirect
31. #63896C22semidirect
33. D3×C4⋊Dic3C22semidirect
34. #63869C22semidirect
35. #63856C22semidirect
54. C2×C4×Dic6D3semidirect
65. C2×C3×D12Q8semidirect
137. C4×Dic6C2×D3semidirect
158. C3×D12C2×Q8semidirect
199. C2×D12Dic6semidirect
328. D12C2×Dic6semidirect
335. C2×C32#554semidirect
407. C32C2×#554semidirect
437. C2×C3#5543semidirect
438. C2×C3#5579semidirect
462. C3C2×#5543semidirect
463. C3C2×#5579semidirect
465. C2#10593960direct (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×#638962
C2×Dic3×D122
C2×D3×C4⋊Dic32
C2×#638692
C2×#638562
#105939602
C2×#55793
C2×#55433