Finite Group Databasebeta

← C4×#63870 #11802494

Subgroups — C4×#63870 #11802494

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63870C211yesmaximal, characteristic
2C42×C3⋊Dic3C211yesmaximal, characteristic
3C3×C4×Dic3⋊C4C212yesmaximal
4#10591360C211yesmaximal, characteristic
5#10591337C211yesmaximal, characteristic
6C4×#3724C211yesmaximal, characteristic
7C4×#3724C211yesmaximal, characteristic
8#10591334C212yesmaximal
9C4×Dic3⋊Dic3C212yesmaximal
10#10591328C211yesmaximal, characteristic
11#10591192C212yesmaximal
12C4×#889—32nomaximal
13C2×C32×C42C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30#63870C418yesdirect product factor
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#889—32no—
38C3×C4×C4⋊C4—32no—
39#4980—32no—
40#4978—32no—
41#4976—32no—
42C4×C4⋊Dic3—32no—
43C4×Dic3⋊C4—32no—
44C4×Dic3⋊C4—32no—
45C4×Dic3⋊C4—32no—
46C4×Dic3⋊C4D312yes—
47C42×Dic3—32no—
48C42×Dic3—61no—
49#4653—32no—
50#4652—32no—
51#4650—32no—
52#4647—32no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C32×C42—22no—
65C4×C3⋊Dic3—22no—
66C4×C3⋊Dic3—22no—
67C4×C3⋊Dic3—22no—
68C4×C3⋊Dic3—22no—
69C4×C3⋊Dic3C2×C414yes—
70C4×C3⋊Dic3Q814yes—
71C3×Dic3⋊C4—24no—
72C3×Dic3⋊C4C2×C418yes—
73C3×C4×Dic3—24no—
74C3×C4×Dic3—24no—
75#3724—22no—
76#3724—22no—
77#3724C2×C414yes—
78#3724C2×C414yes—
79Dic3⋊Dic3—24no—
80Dic3⋊Dic3C2×C418yes—
81C4×#125—91noSylow
82C2×C3×C4⋊C4—32no—
83C2×C3×C4⋊C4—32no—
84C2×C3×C42—21no—
85C2×C3×C42—32no—
86C2×C3×C42—32no—
87C2×C3×C42C2×D312yes—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—32no—
93C2×Dic3⋊C4—32no—
94C2×Dic3⋊C4—32no—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4C2×D312yes—
97C2×Dic3⋊C4C2×D312yes—
98C2×C4×Dic3—32no—
99C2×C4×Dic3—32no—
100C2×C4×Dic3—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—32no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3C2×D312yes—
111C2×C4×Dic3C2×D312yes—
112#889—316no—
113C3×#95—32no—
114C3×#95—32no—
115C3⋊#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95C2×D312yes—
124C3⋊#95C2×D312yes—
125C23×C32C2411yescharacteristic
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4C22×C412yes—
131C2×C32×C4C2×Q812yes—
132C2×C32×C4#4112yes—
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3C22×C412yes—
142C2×C3⋊Dic3C22×C412yes—
143C2×C3⋊Dic3C2×Q812yes—
144C2×C3⋊Dic3C2×Q812yes—
145C2×C3⋊Dic3#4112yes—
146C2×C3⋊Dic3#4112yes—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3C22×C414yes—
158C2×C3×Dic3C22×C414yes—
159C2×#125—91no—
160#389—91no—
161#389—91no—
162#387—92no—
163#387—92no—
164#382—91no—
165C4×C4⋊C4—32no—
166C4×C4⋊C4—91no—
167C4×C4⋊C4—91no—
168C4×C4⋊C4—92no—
169C43—91no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4C22×D312yes—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3C22×D312yes—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C22×Dic3C22×D312yes—
192C3×C4⋊C4—38no—
193C3×C4⋊C4—64no—
194C3×C42—24no—
195C3×C42—24no—
196C3×C42—64no—
197C3×C42—64no—
198C4⋊Dic3—38no—
199C4⋊Dic3—64no—
200Dic3⋊C4—24no—
201Dic3⋊C4—38no—
202Dic3⋊C4—38no—
203Dic3⋊C4—38no—
204Dic3⋊C4—64no—
205Dic3⋊C4—64no—
206Dic3⋊C4—64no—
207Dic3⋊C4C4×D318yes—
208C4×Dic3—24no—
209C4×Dic3—24no—
210C4×Dic3—38no—
211C4×Dic3—38no—
212C4×Dic3—64no—
213C4×Dic3—64no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—64no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C22×C32C23×C411yescharacteristic
223C22×C32C22×Q811yescharacteristic
224C22×C32C2×#4111yescharacteristic
225C22×C32C2×#4111yescharacteristic
226C22×C32C2×#4111yescharacteristic
227C22×C32C2×#4111yescharacteristic
228C22×C32C2×#4111yescharacteristic
229C32×C4—22no—
230C32×C4—22no—
231C32×C4#12514yescomplemented
232C3⋊Dic3—22no—
233C3⋊Dic3—22no—
234C3⋊Dic3—22no—
235C3⋊Dic3C4×Q814yes—
236C3×Dic3—24no—
237C3×Dic3—24no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240#125—98no—
241C2×C4⋊C4—32no—
242C2×C4⋊C4—32no—
243C2×C4⋊C4—92no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—92no—
249C2×C42—32no—
250C2×C42—32no—
251C2×C42—91no—
252C2×C42—91no—
253C2×C42—91no—
254C2×C42—91no—
255C2×C42—91no—
256C2×C42—91no—
257C2×C42D3211yescharacteristic
258#95—32no—
259#95—32no—
260#95—92no—
261#95—92no—
262#95—92no—
263#95—92no—
264C23×C3—21no—
265C23×C3C23×D312yes—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—34no—
280C2×C3×C4—34no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4C2×C4×D314yes—
292C2×C3×C4#23514yes—
293C2×C3×C4#23514yes—
294C2×C3×C4#23714yes—
295C2×C3×C4D3×Q814yes—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—34no—
307C2×Dic3—34no—
308C2×Dic3—34no—
309C2×Dic3—34no—
310C2×Dic3—34no—
311C2×Dic3—34no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3C2×C4×D314yes—
331C2×Dic3C2×C4×D314yes—
332C2×C32C2×C4×Q811yescharacteristic
333C2×C32C4×#4111yescharacteristic
334C2×C32C4×#4111yescharacteristic
335C2×C32C2×#12511yescharacteristic
336C2×C32#52911yescharacteristic
337C2×C32#52911yescharacteristic
338C2×C32#53311yescharacteristic
339C22×C4—32no—
340C22×C4—32no—
341C22×C4—32no—
342C22×C4—32no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4C2×D3211yescharacteristic
348C22×C4C2×D3211yescharacteristic
349C22×C4C2×D3211yescharacteristic
350C4⋊C4—38no—
351C4⋊C4—64no—
352C4⋊C4—94no—
353C4⋊C4—94no—
354C4⋊C4—98no—
355C4⋊C4—182no—
356C4⋊C4—182no—
357C4⋊C4—184no—
358C42—22no—
359C42—64no—
360C42—64no—
361C42—94no—
362C42—94no—
363C42—182no—
364C42—182no—
365C42—182no—
366C42—182no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3C22×C4×D312yes—
375C22×C3C2×#23512yes—
376C22×C3C2×#23512yes—
377C22×C3C2×#23712yes—
378C22×C3C2×D3×Q812yes—
379C22×C3D3×#4112yes—
380C22×C3D3×#4112yes—
381C3×C4—24no—
382C3×C4—24no—
383C3×C4—24no—
384C3×C4—24no—
385C3×C4—24no—
386C3×C4—64no—
387C3×C4—64no—
388C3×C4—122no—
389C3×C4—122no—
390C3×C4#88918yescomplemented
391Dic3—24no—
392Dic3—24no—
393Dic3—38no—
394Dic3—42no—
395Dic3—42no—
396Dic3—64no—
397Dic3—64no—
398Dic3—64no—
399Dic3—64no—
400Dic3—64no—
401Dic3—64no—
402Dic3—64no—
403C32C4×#12511yescharacteristic, complemented, Sylow
404C23C22×D3211yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—34no—
410C2×C4—34no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—92no—
422C2×C4—92no—
423C2×C4—92no—
424C2×C4—92no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—181no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4—181no—
432C2×C4—181no—
433C2×C4#379712yes—
434C2×C4#379812yes—
435C2×C4#379812yes—
436C2×C4C4×D3212yes—
437C2×C4#380512yes—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3C4×#23512yes—
446C2×C3C2×#88912yes—
447C2×C3#552812yes—
448C2×C3C4×#23712yes—
449C2×C3#553812yes—
450C2×C3C4×D3×Q812yes—
451C2×C3#557812yes—
452C22C2×#379711yescharacteristic
453C22C2×#379811yescharacteristic
454C22C2×#379811yescharacteristic
455C22C2×C4×D3211yescharacteristic
456C22#6430611yescharacteristic
457C22#6430611yescharacteristic
458C22C2×#380511yescharacteristic
459C4—22no—
460C4—22no—
461C4—64no—
462C4—64no—
463C4—94no—
464C4—122no—
465C4—122no—
466C4—182no—
467C4—182no—
468C4—182no—
469C4#6387014yesdirect product factor
470C3—21no—
471C3C4×#88912yescomplemented
472C2#1059388211yescharacteristic
473C2C4×#379711yescharacteristic
474C2C4×#379811yescharacteristic
475C2#1059398011yescharacteristic
476C2C2×#6387011yescharacteristic
477C2C4×#380511yescharacteristic
478C2#1059503311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C4×#125
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
30. #63870C4direct (N × H)
231. C32×C4#125semidirect
390. C3×C4#889semidirect
403. C32C4×#125semidirect
469. C4#63870direct (N × H)
471. C3C4×#889semidirect

Maximal subgroups

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

subgroupindex
C2×#638702
C42×C3⋊Dic32
C3×C4×Dic3⋊C42
#105913602
#105913372
C4×#37242
#105913342
C4×Dic3⋊Dic32
#105913282
#105911922
C4×#8893