Finite Group Databasebeta

← #11788213

Subgroups — #11788213

Order 1152.

881 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5#10589162C212yesmaximal, complemented
6#71591—31nomaximal
7#69966—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3828C2211yescharacteristic
10#64162—21no—
11#64139C412yescomplemented
12#64138—21no—
13C4×#638—22no—
14#64135C2211yescharacteristic
15#64133C412yescomplemented
16C2×C3×#217—21no—
17C3×#926—24no—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×#208C2212yes—
21C3×#830—22no—
22#63570—24no—
23C2×C3×#117—31no—
24#5791—31no—
25#5791—31no—
26#5791—61no—
27C2×#926D311yescharacteristic, complemented
28C3×#407—31no—
29#5207D311yescharacteristic, complemented
30C2×#825—32no—
31C2×#805—32no—
32#4555—32no—
33#4523—32no—
34C24×C32D411yescharacteristic
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4C2×C412yes—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—22no—
42C2×#638—21no—
43#3828—22no—
44#3828—22no—
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C2×C4×C3⋊D3—21no—
47C2×#634C2×C411yescharacteristic
48C22×C3×Dic3—22no—
49#3757—22no—
50#3757—21no—
51#3752—22no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53#3750—22no—
54C4×C3⋊Dic3—21no—
55C3×#217—24no—
56C3×C4⋊Dic3—24no—
57C3×C4×Dic3—22no—
58C3×C4×Dic3D414yescomplemented
59C3×#208—22no—
60C3×#208—22no—
61C2×C3×C3⋊C8—22no—
62#1897—91noSylow
63C23×C3×C4—21no—
64C23×C3×C4C2×D311yescharacteristic
65C23×C3×C4C2×D311yescharacteristic
66C2×#235—31no—
67C2×#235—31no—
68C2×#235—61no—
69C2×C3×M16—32no—
70C3×#117—64no—
71C2×C3×C4⋊C4—61no—
72C2×C3×C22⋊C4—61no—
73C2×C3×C42—32no—
74#953—62no—
75#953—61no—
76#953—61no—
77C2×#217—21no—
78#930—32no—
79#930—32no—
80#930—62no—
81#929—62no—
82#929—61no—
83#929—61no—
84C4×#67—64no—
85C4×#67—62no—
86C4×#67—62no—
87#926—24no—
88#926—31no—
89#926—31no—
90#926—61no—
91C2×C4⋊Dic3—21no—
92#924—32no—
93#924—32no—
94#924—62no—
95C2×C4×Dic3C2×D312yes—
96C2×#208C2×D312yes—
97C3×C22⋊C8—62no—
98#830—22no—
99#825—64no—
100#805—64no—
101C23×C32—21no—
102C23×C32—21no—
103C23×C32—42no—
104C23×C32C22⋊C412yes—
105C23×C32C2×D411yescharacteristic
106C22×C3⋊D3—21no—
107C2×C32×C4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—24no—
110C2×C32×C4—24no—
111C2×C32×C4C22⋊C412yes—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4#4112yes—
116#638—44no—
117#638—41no—
118#638—41no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—21no—
121C4⋊(C3⋊D3)—22no—
122C4×C3⋊D3—42no—
123#634—22no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—44no—
126C3×C3⋊C8—42no—
127#525—91no—
128C2×#117—31no—
129C2×#104—92no—
130#407—31no—
131#339—92no—
132C24×C3—21no—
133C24×C3D1211yescharacteristic
134C24×C3#6711yescharacteristic
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—42no—
144C22×C3×C4—42no—
145C22×C3×C4—62no—
146C22×C3×C4C4×D312yes—
147C22×C3×C4C4×D312yes—
148C22×C3×C4D1211yescharacteristic
149C22×C3×C4D1212yes—
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4#6712yes—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—64no—
155C2×#67—62no—
156C2×#67—62no—
157C2×#67—62no—
158C2×#67—61no—
159C2×#67—61no—
160C22×Dic3—22no—
161#235—62no—
162#235—62no—
163#235—62no—
164#235—62no—
165#235—122no—
166#235—122no—
167C2×D12—31no—
168C2×D12—31no—
169C2×D12—61no—
170C2×C4×D3—62no—
171C2×C4×D3—61no—
172C2×C4×D3—61no—
173C2×Dic6—31no—
174C2×Dic6—31no—
175C2×Dic6—61no—
176C3×M16—62no—
177C3×M16—62no—
178C2×C3×C8—62no—
179C3×C4⋊C4—64no—
180C3×C22⋊C4—64no—
181C3×C42—34no—
182C3×C42—62no—
183#217—24no—
184#217—64no—
185#217—62no—
186#217—62no—
187#217—62no—
188#217—61no—
189#217—61no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—62no—
192(C2×D3)⋊C4—62no—
193C4⋊Dic3—24no—
194C4⋊Dic3—32no—
195C4⋊Dic3—32no—
196C4⋊Dic3—62no—
197Dic3⋊C4—64no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200C4×Dic3—22no—
201C4×Dic3—62no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3#6714yescomplemented
205#208—22no—
206#208—22no—
207C2×C3⋊C8—22no—
208C22×C32—22no—
209C22×C32—22no—
210C22×C32—22no—
211C22×C32—22no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32C2×C22⋊C411yescharacteristic
215C22×C32#12011yescharacteristic
216C22×C32#12311yescharacteristic
217C2×C3⋊D3—41no—
218C2×C3⋊D3—42no—
219C32×C4—22no—
220C32×C4C4×D412yes—
221C32×C4#12112yes—
222C3⋊Dic3—41no—
223C3⋊Dic3—42no—
224C3×Dic3—44no—
225C2×#41—91no—
226C23×C4D3211yescharacteristic
227C2×M16—32no—
228#123—181no—
229C22⋊Q8—92no—
230#121—92no—
231#120—181no—
232C4×D4—182no—
233#117—64no—
234#117—91no—
235C2×C4⋊C4—61no—
236C2×C22⋊C4—61no—
237C2×C42—32no—
238#104—184no—
239C22⋊C8—62no—
240C23×C3—21no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—41no—
247C23×C3—41no—
248C23×C3—42no—
249C23×C3—42no—
250C23×C3—44no—
251C23×C3(C2×D3)⋊C412yes—
252C23×C3(C2×D3)⋊C412yes—
253C23×C3C2×D1211yescharacteristic
254C23×C3C2×#6711yescharacteristic
255C22×D3—62no—
256C22×D3—61no—
257C22×D3—61no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—44no—
272C2×C3×C4—44no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—64no—
276C2×C3×C4—124no—
277C2×C3×C4(C2×D3)⋊C412yes—
278C2×C3×C4(C2×D3)⋊C412yes—
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4C2×D1211yescharacteristic
282C2×C3×C4#23512yes—
283C2×C3×C4D3×D412yes—
284C2×C3×C4#23712yes—
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×#6712yes—
287#67—122no—
288#67—122no—
289#67—128no—
290#67—124no—
291#67—124no—
292#67—121no—
293#67—121no—
294#67—121no—
295#67—121no—
296C2×Dic3—24no—
297C2×Dic3—44no—
298C2×Dic3—64no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304D12—62no—
305D12—62no—
306D12—122no—
307C4×D3—124no—
308C4×D3—122no—
309C4×D3—122no—
310Dic6—62no—
311Dic6—62no—
312Dic6—122no—
313C3×C8—122no—
314C3⋊C8—42no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32—42no—
318C2×C32#38611yescharacteristic
319C2×C32#42112yes—
320C3⋊D3—81no—
321C24#62611yescharacteristic
322#41—182no—
323#41—182no—
324C2×Q8—91no—
325C2×D4—91no—
326C2×D4—182no—
327C2×D4—181no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—62no—
331C22×C4—181no—
332C22×C4#62412yes—
333C22×C4#62611yescharacteristic
334C22×C4#62612yes—
335C22×C4C2×D3211yescharacteristic
336M16—62no—
337M16—62no—
338C2×C8—62no—
339C4⋊C4—64no—
340C4⋊C4—92no—
341C4⋊C4—182no—
342C22⋊C4—64no—
343C22⋊C4—182no—
344C22⋊C4—181no—
345C22⋊C4—182no—
346C42—34no—
347C42—62no—
348C42—181no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—24no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—42no—
365C22×C3—42no—
366C22×C3—42no—
367C22×C3—42no—
368C22×C3—44no—
369C22×C3—44no—
370C22×C3#88211yescharacteristic
371C22×C3#88611yescharacteristic
372C22×C3C2×(C2×D3)⋊C411yescharacteristic
373C22×C3C2×(C2×D3)⋊C411yescharacteristic
374C22×C3#92911yescharacteristic
375C22×C3#95311yescharacteristic
376C2×D3—122no—
377C2×D3—124no—
378C2×D3—122no—
379C2×D3—121no—
380C2×D3—121no—
381C2×D3—122no—
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—42no—
387C3×C4—124no—
388C3×C4#67⋊C412yes—
389C3×C4C4×#6712yes—
390C3×C4#93012yes—
391C3×C4#93912yes—
392Dic3—44no—
393Dic3—122no—
394Dic3—124no—
395Dic3—122no—
396Dic3—121no—
397Dic3—121no—
398Dic3—122no—
399C32#189711yescharacteristic, complemented, Sylow
400C23—21no—
401C23—21no—
402C23—42no—
403C23—181no—
404C23#372212yes—
405C23C2×#62611yescharacteristic
406Q8—182no—
407D4—182no—
408D4—364no—
409D4—361no—
410D4—361no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—64no—
416C2×C4—124no—
417C2×C4—182no—
418C2×C4—181no—
419C2×C4—362no—
420C2×C4#372212yes—
421C2×C4#380412yes—
422C2×C4C2×#62411yescharacteristic
423C2×C4C2×#62611yescharacteristic
424C2×C4D3×#6712yes—
425C8—122no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—44no—
435C2×C3—42no—
436C2×C3—42no—
437C2×C3#495811yescharacteristic
438C2×C3#500512yes—
439C2×C3#513912yes—
440C2×C3#521311yescharacteristic
441D3—242no—
442D3—241no—
443D3—241no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—42no—
449C22—42no—
450C22—362no—
451C22—361no—
452C22C2×#372211yescharacteristic
453C22#6396611yescharacteristic
454C22#6397711yescharacteristic
455C4—22no—
456C4—124no—
457C4—362no—
458C4—361no—
459C4#6395212yes—
460C4#6397812yes—
461C3—21no—
462C3#6996611yescharacteristic, complemented
463C3#7159111yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—42no—
467C2—721no—
468C2#1059111312yes—
469C2#1059171111yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C3×#5207C2semidirect
4. C2×#63570C2semidirect
5. #10589162C2semidirect
11. #64139C4semidirect
15. #64133C4semidirect
27. C2×#926D3semidirect
29. #5207D3semidirect
58. C3×C4×Dic3D4semidirect
204. C4×Dic3#67semidirect
399. C32#1897semidirect
462. C3#69966semidirect
463. C3#71591semidirect

Maximal subgroups

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

subgroupindex
#105962622
C2×C3×#9262
C3×#52072
C2×#635702
#105891622
#715913
#699663