Finite Group Databasebeta

← #11861711

Subgroups — #11861711

Order 1152.

841 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#10593980C211yesmaximal, characteristic
2C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#4690C212yesmaximal, complemented
4#10590906C212yesmaximal, complemented
5#10590788C211yesmaximal, characteristic, complemented
6#10590737C212yesmaximal, complemented
7#10590734C211yesmaximal, characteristic, complemented
8#10590718C211yesmaximal, characteristic, complemented
9#10590645C211yesmaximal, characteristic, complemented
10#10590319C212yesmaximal, complemented
11#10590299C211yesmaximal, characteristic, complemented
12#79366—32nomaximal
13C2×C8×C3⋊D3C2211yescharacteristic
14C2×C8×C3⋊D3C2211yescharacteristic
15C42×C3⋊D3C2211yescharacteristic
16C3×#872C2212yes—
17C4×#627C2211yescharacteristic
18#63915C411yescharacteristic
19#63912C411yescharacteristic
20C4×#626C2212yes—
21C4×#625C2211yescharacteristic
22#63870C411yescharacteristic
23#63865C411yescharacteristic
24#63862C412yes—
25#63853C412yes—
26C2×#3711C2212yes—
27C2×D3×C3⋊C8C2212yes—
28C32×C4×C8C2211yescharacteristic
29C8×C3⋊Dic3C2211yescharacteristic
30C8×C3⋊Dic3C2211yescharacteristic
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×(C2×D3)⋊C8C2212yes—
33C3×(C2×D3)⋊C8C2212yes—
34C3×Dic3⋊C8C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×#803C2212yes—
37#63572C2211yescharacteristic
38#63572C2211yescharacteristic
39#63557C2212yes—
40#63554C2212yes—
41Dic3×C3⋊C8C2212yes—
42#5528—32no—
43C3×#433—32no—
44#4997—32no—
45#4836—32no—
46#4834—32no—
47#4830—32no—
48#4828—32no—
49#4729—32no—
50#4728—32no—
51#67⋊C8—32no—
52#67⋊C8—32no—
53#4708—32no—
54#4705—32no—
55#4690D312yescomplemented
56C4×D3×C8—32no—
57C4×D3×C8—61no—
58C2×C4×C3⋊D3C2×C411yescharacteristic
59C2×C4×C3⋊D3C2×C411yescharacteristic
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C3×C4×D3C2312yes—
62C2×#627C2×C411yescharacteristic
63C2×#626C2×C412yes—
64C2×#625C2×C411yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2311yescharacteristic
67C32×C42C2311yescharacteristic
68C4×C3⋊Dic3C2×C411yescharacteristic
69C4×C3⋊Dic3C2×C411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C2×C3⋊(C3⋊C8)C2311yescharacteristic
72C2×C3⋊(C3⋊C8)C2311yescharacteristic
73C8×C3⋊D3—22no—
74C8×C3⋊D3—22no—
75C3×(C2×D3)⋊C4C2×C412yes—
76C3×(C2×D3)⋊C4C2×C412yes—
77C3×Dic3⋊C4C2×C412yes—
78C3×Dic3⋊C4C2×C412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3724C2×C411yescharacteristic
83#3724C2×C411yescharacteristic
84Dic3⋊Dic3C2×C412yes—
85Dic3⋊Dic3C2×C412yes—
86#3722C2×C412yes—
87(C2×D3)⋊Dic3C2×C412yes—
88(C2×D3)⋊Dic3C2×C412yes—
89#3711—24no—
90D3×C3⋊C8—24no—
91#2966—91noSylow
92C3×#117—32no—
93C4×#67—32no—
94C4×#67—32no—
95C2×#208—32no—
96C22×C3⋊C8—32no—
97C2×ΓL(1,𝔽25)—32no—
98C2×D3×C8—32no—
99C2×D3×C8—32no—
100C2×D3×C8—32no—
101C2×D3×C8—61no—
102C2×D3×C8—61no—
103#898—32no—
104#896—32no—
105#894—32no—
106#889—32no—
107#885—32no—
108#884—32no—
109#883—32no—
110#879—32no—
111C4×D12—32no—
112#872C2×D312yes—
113C42×D3—32no—
114C42×D3—61no—
115C4×Dic6—32no—
116C3×C4⋊C8—32no—
117C3×C4⋊C8—32no—
118C3×C22⋊C8—32no—
119C3×C22⋊C8—32no—
120C3×#97—32no—
121C3×C4×C8—21no—
122C3×C4×C8C2×D312yes—
123(C2×D3)⋊C8—32no—
124(C2×D3)⋊C8—32no—
125(C2×D3)⋊C8C2×D312yes—
126(C2×D3)⋊C8C2×D312yes—
127#815—32no—
128Dic3⋊C8—32no—
129Dic3⋊C8—32no—
130Dic3⋊C8C2×D312yes—
131Dic3⋊C8C2×D312yes—
132C8×Dic3—32no—
133C8×Dic3—32no—
134C8×Dic3—32no—
135C8×Dic3—61no—
136C8×Dic3—61no—
137#803—32no—
138#803C2×D312yes—
139C4×C3⋊C8—32no—
140C4×C3⋊C8—32no—
141C4×C3⋊C8—61no—
142C22×C3⋊D3C22×C411yescharacteristic
143C22×C3×D3C22×C412yes—
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C22×C411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3C22×C411yescharacteristic
148C2×C3⋊Dic3C22×C411yescharacteristic
149C2×C3⋊Dic3C22×C411yescharacteristic
150C4×C3⋊D3—22no—
151C4×C3⋊D3—21no—
152C4×C3⋊D3—21no—
153C4×C3⋊D3—22no—
154C2×C3×Dic3C22×C412yes—
155C2×C3×Dic3C22×C412yes—
156C2×C3×Dic3C22×C412yes—
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159#627—22no—
160#626—24no—
161#625—22no—
162C32×C8—21no—
163C32×C8—21no—
164C3⋊(C3⋊C8)#4112yes—
165C3⋊(C3⋊C8)#4112yes—
166C3×C3⋊C8—22no—
167C3×C3⋊C8—22no—
168#529—91no—
169#446—91no—
170C8×Q8—91no—
171#436—91no—
172#435—92no—
173C8×D4—91no—
174C8×D4—92no—
175#433—32no—
176#432—91no—
177#405—92no—
178C2×C4×C8—91no—
179C22×C3×C4—32no—
180C2×#67—32no—
181C2×#67—32no—
182C2×D12—32no—
183C2×C4×D3—32no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—61no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3C22×D312yes—
190C2×Dic6—32no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—32no—
194C2×C3×C8—32no—
195C2×C3×C8C22×D312yes—
196C2×C3×C8C22×D312yes—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—32no—
199C3×C22⋊C4—32no—
200C3×C22⋊C4—32no—
201C3×C42—21no—
202C3×C42—32no—
203C3×C42C22×D312yes—
204#217—32no—
205#217—32no—
206(C2×D3)⋊C4—32no—
207(C2×D3)⋊C4—32no—
208(C2×D3)⋊C4—32no—
209(C2×D3)⋊C4—32no—
210(C2×D3)⋊C4C4×D312yes—
211(C2×D3)⋊C4C4×D312yes—
212C4⋊Dic3—32no—
213C4⋊Dic3—32no—
214Dic3⋊C4—32no—
215Dic3⋊C4—32no—
216Dic3⋊C4—32no—
217Dic3⋊C4—32no—
218Dic3⋊C4C4×D312yes—
219Dic3⋊C4C4×D312yes—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C4×Dic3—61no—
226C4×Dic3C22×D312yes—
227#208—64no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—64no—
233C2×C3⋊C8C22×D312yes—
234C2×C3⋊C8C22×D312yes—
235ΓL(1,𝔽25)—64no—
236D3×C8—64no—
237D3×C8—64no—
238D3×C8—64no—
239D3×C8—64no—
240D3×C8—64no—
241C22×C32C23×C411yescharacteristic
242C2×C3⋊D3—21no—
243C2×C3⋊D3—21no—
244C2×C3⋊D3#13112yes—
245C2×C3×D3—22no—
246C2×C3×D3—22no—
247C2×C3×D3—22no—
248C32×C4—21no—
249C32×C4—21no—
250C32×C4C2×#4111yescharacteristic
251C32×C4C2×#4111yescharacteristic
252C3⋊Dic3—21no—
253C3⋊Dic3—21no—
254C3⋊Dic3#13112yes—
255C3×Dic3—22no—
256C3×Dic3—22no—
257C3×Dic3—22no—
258C2×M16—92no—
259C22×C8—92no—
260C22×C8—91no—
261C22×C8—91no—
262#126—92no—
263#125—91no—
264#124—91no—
265#123—92no—
266C22⋊Q8—91no—
267#121—91no—
268C4×Q8—91no—
269C4×D4—92no—
270C4×D4—91no—
271#117—32no—
272C2×C42—91no—
273C4⋊C8—32no—
274C4⋊C8—32no—
275C4⋊C8—91no—
276C4⋊C8—91no—
277C22⋊C8—32no—
278C22⋊C8—32no—
279C22⋊C8—92no—
280#97—32no—
281#97—92no—
282C4×C8—92no—
283C4×C8—91no—
284C4×C8—91no—
285C4×C8—91no—
286C4×C8D3211yescharacteristic
287C23×C3—32no—
288C22×D3—32no—
289C22×D3—61no—
290C22×D3C2×C4×D312yes—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4C2×C4×D312yes—
300C2×C3×C4C2×C4×D312yes—
301C2×C3×C4C23×D312yes—
302#67—64no—
303#67—64no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3C2×C4×D312yes—
311C2×Dic3C2×C4×D312yes—
312C2×Dic3C2×C4×D312yes—
313D12—64no—
314C4×D3—22no—
315C4×D3—22no—
316C4×D3—64no—
317C4×D3—64no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—64no—
321C4×D3—64no—
322C4×D3—62no—
323C4×D3—62no—
324Dic6—64no—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—22no—
328C3×C8—22no—
329C3×C8—62no—
330C3×C8—62no—
331C3⋊C8—22no—
332C3⋊C8—22no—
333C3⋊C8—34no—
334C3⋊C8—34no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C2×C32C4×#4111yescharacteristic
338C2×C32C2×#13111yescharacteristic
339C2×C32C2×#13111yescharacteristic
340C3⋊D3—22no—
341C3×D3—42no—
342C2×Q8—91no—
343C2×D4—92no—
344C2×D4—91no—
345C22×C4—32no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349M16—184no—
350C2×C8—32no—
351C2×C8—32no—
352C2×C8—91no—
353C2×C8—91no—
354C2×C8—182no—
355C2×C8—182no—
356C2×C8—184no—
357C2×C8C2×D3211yescharacteristic
358C2×C8C2×D3211yescharacteristic
359C4⋊C4—32no—
360C4⋊C4—32no—
361C4⋊C4—91no—
362C4⋊C4—92no—
363C4⋊C4—91no—
364C4⋊C4—92no—
365C22⋊C4—32no—
366C22⋊C4—32no—
367C22⋊C4—92no—
368C22⋊C4—92no—
369C22⋊C4—92no—
370C42—32no—
371C42—91no—
372C42—91no—
373C42—91no—
374C42C2×D3211yescharacteristic
375C22×C3—21no—
376C22×C3—62no—
377C22×C3—62no—
378C22×C3—62no—
379C22×C3C22×C4×D312yes—
380C2×D3—22no—
381C2×D3—22no—
382C2×D3—22no—
383C2×D3—34no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—62no—
387C2×D3—62no—
388C2×D3—62no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—62no—
396C3×C4—62no—
397C3×C4—62no—
398C3×C4D3×#4112yes—
399C3×C4D3×#4112yes—
400Dic3—22no—
401Dic3—22no—
402Dic3—22no—
403Dic3—34no—
404Dic3—62no—
405Dic3—62no—
406Dic3—62no—
407Dic3—62no—
408Dic3—62no—
409C32#296611yescharacteristic, complemented, Sylow
410C23—32no—
411C23—91no—
412Q8—182no—
413D4—184no—
414D4—182no—
415C2×C4—32no—
416C2×C4—32no—
417C2×C4—32no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—181no—
426C2×C4—181no—
427C2×C4C4×D3211yescharacteristic
428C2×C4C4×D3211yescharacteristic
429C2×C4C22×D3211yescharacteristic
430C8—21no—
431C8—21no—
432C8—62no—
433C8—62no—
434C8—92no—
435C8—92no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—122no—
440C2×C3#552212yes—
441C2×C3D3×#13112yes—
442C2×C3D3×#13112yes—
443D3—42no—
444D3—64no—
445D3—64no—
446C22—62no—
447C22—62no—
448C22—62no—
449C22—92no—
450C22—181no—
451C22—181no—
452C22C2×C4×D3211yescharacteristic
453C4—21no—
454C4—21no—
455C4—62no—
456C4—62no—
457C4—62no—
458C4—92no—
459C4—181no—
460C4—181no—
461C4#6430611yescharacteristic
462C4#6430611yescharacteristic
463C3—21no—
464C3#7936612yescomplemented
465C2—122no—
466C2—182no—
467C2#1059396611yescharacteristic
468C2#1059466911yescharacteristic
469C2#1059466911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×C8C22
prime radical#63912C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2966
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×C8×C3⋊D3C2semidirect
3. C3×#4690C2semidirect
4. #10590906C2semidirect
5. #10590788C2semidirect
6. #10590737C2semidirect
7. #10590734C2semidirect
8. #10590718C2semidirect
9. #10590645C2semidirect
10. #10590319C2semidirect
11. #10590299C2semidirect
55. #4690D3semidirect
409. C32#2966semidirect
464. C3#79366semidirect

Maximal subgroups

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

subgroupindex
#105939802
C4×C8×C3⋊D32
C3×#46902
#105909062
#105907882
#105907372
#105907342
#105907182
#105906452
#105903192
#105902992
#793663