Finite Group Databasebeta

← #11787909

Subgroups — #11787909

Order 1152.

743 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5516C211yesmaximal, characteristic, complemented
2C2×#63863C211yesmaximal, characteristic
3C3×#5001C211yesmaximal, characteristic
4#10591085C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71661—31nomaximal
9#70325—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#887—22no—
18C3×#877—22no—
19C3×C4×Dic6—22no—
20C2×(C2×D3)⋊Dic3—22no—
21#63863—22no—
22#63863C414yescomplemented
23C3×#809—22no—
24#63562—22no—
25#63560—22no—
26C3×#519—31no—
27C2×#947—31no—
28C2×#936—31no—
29#5516D311yescharacteristic, complemented
30C3×#418—31no—
31C2×#836—31no—
32#5215—31no—
33C2×#824—31no—
34#5001—31no—
35#5001D311yescharacteristic
36#4555—31no—
37#4532—31no—
38#4532—31no—
39#4532—31no—
40#4532—61no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3×Dic3D412yes—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12C2×C412yes—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6C2×C412yes—
56C2×C3×Dic6D412yes—
57C32×C4⋊C4D412yes—
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3C2×C412yes—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×C4⋊Dic3D412yes—
67C3×Dic3⋊C4—24no—
68C3×C4×Dic3—24no—
69C3×C4×Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—28no—
74#1888—91noSylow
75C22×C3×Q8—31no—
76C22×C3×D4—31no—
77C22×D12C2×D311yescharacteristic
78C22×Dic6C2×D311yescharacteristic
79C2×C3×M16—31no—
80C3×C4×Q8—62no—
81C3×C4×Q8—62no—
82C3×#117—21no—
83C3×#117—31no—
84C3×#117—62no—
85C3×#117C2×D311yescharacteristic
86C3×#117C2×D311yescharacteristic
87C2×#217—62no—
88#947—34no—
89#947—62no—
90#936—34no—
91#936—62no—
92C2×(C2×D3)⋊C4—62no—
93#926C2×D311yescharacteristic
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—61no—
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101#887—22no—
102#877—22no—
103C4×Dic6—22no—
104C3×#102—62no—
105#836—62no—
106#832—62no—
107#824—62no—
108#809—22no—
109#809—62no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—44no—
113C22×C3×D3—41no—
114C22×C3×D3—41no—
115C2×C32×C4—22no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—42no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3C22⋊C414yes—
128C3×D12—22no—
129C3×D12—22no—
130C3×D12—41no—
131C3×D12—41no—
132C3×Dic6—22no—
133C3×Dic6—22no—
134C3×Dic6—22no—
135C3×Dic6—22no—
136C3⋊(C3⋊C8)—41no—
137C3×C3⋊C8—41no—
138C2×#124—91no—
139#519—31no—
140#418—31no—
141#418—91no—
142C2×#101—91no—
143#339—91no—
144#339—91no—
145C24×C3—61no—
146C23×D3—21no—
147C2×C3×Q8—32no—
148C2×C3×Q8—32no—
149C2×C3×Q8—61no—
150C2×C3×Q8—61no—
151C2×C3×Q8—61no—
152C2×C3×Q8—61no—
153C2×C3×D4—32no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—32no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3#6712yes—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12C4×D312yes—
173C2×Dic6—21no—
174C2×Dic6—21no—
175C2×Dic6—21no—
176C2×Dic6—21no—
177C2×Dic6C4×D312yes—
178C2×Dic6D1212yes—
179C3×M16—61no—
180C3×M16—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—32no—
184C3×C4⋊C4—64no—
185C3×C4⋊C4#6712yes—
186C3×C4⋊C4#6712yes—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—61no—
191C3×C42—21no—
192C3×C42—21no—
193C3×C42—41no—
194C3×C42—64no—
195C3×C42—61no—
196#217—21no—
197#217—68no—
198(C2×D3)⋊C4—68no—
199C4⋊Dic3#6712yes—
200Dic3⋊C4—24no—
201C4×Dic3—24no—
202C4×Dic3—21no—
203C4×Dic3—32no—
204C4×Dic3—32no—
205C4×Dic3—62no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—121no—
209#208—21no—
210#208—21no—
211#208—62no—
212#208—61no—
213#208—61no—
214#208—61no—
215#208—61no—
216#208—121no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—121no—
221C22×C32—22no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32#12011yescharacteristic
224C22×C32#12311yescharacteristic
225C2×C3×D3—44no—
226C2×C3×D3—42no—
227C2×C3×D3—82no—
228C2×C3×D3—82no—
229C32×C4—42no—
230C32×C4C4×D411yescharacteristic
231C32×C4C4×D411yescharacteristic
232C32×C4#12111yescharacteristic
233C32×C4#12111yescharacteristic
234C3⋊Dic3—42no—
235C3×Dic3—24no—
236C3×Dic3—42no—
237C22×Q8—31no—
238C22×D4—31no—
239C2×M16—31no—
240C2×M16—91no—
241#124—94no—
242#124—182no—
243C4×Q8—62no—
244C4×Q8—62no—
245#117—31no—
246#117—62no—
247#117D3211yescharacteristic
248C2×C22⋊C4—182no—
249C2×C42—91no—
250#102—62no—
251#102—182no—
252#101—182no—
253C23×C3—21no—
254C23×C3—62no—
255C23×C3—124no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3D3×D411yescharacteristic
259C23×C3C2×#6711yescharacteristic
260C22×D3—22no—
261C22×D3—44no—
262C22×D3—41no—
263C22×D3—41no—
264C3×Q8—62no—
265C3×Q8—62no—
266C3×Q8—62no—
267C3×Q8—62no—
268C3×D4—62no—
269C3×D4—62no—
270C3×D4—121no—
271C3×D4—121no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—34no—
281C2×C3×C4—42no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4#23511yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4#23711yescharacteristic
294C2×C3×C4C2×#6711yescharacteristic
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C2×#6711yescharacteristic
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—124no—
306C2×Dic3(C2×D3)⋊C414yes—
307D12—22no—
308D12—22no—
309D12—41no—
310D12—41no—
311Dic6—22no—
312Dic6—22no—
313Dic6—22no—
314Dic6—22no—
315C3×C8—121no—
316C3⋊C8—41no—
317C3⋊C8—122no—
318C3⋊C8—121no—
319C3⋊C8—121no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#38611yescharacteristic
323C2×C32#45412yes—
324C3×D3—82no—
325C24—61no—
326C2×Q8—32no—
327C2×Q8—32no—
328C2×Q8—61no—
329C2×Q8—61no—
330C2×Q8—61no—
331C2×Q8—61no—
332C2×D4—32no—
333C2×D4—61no—
334C2×D4—61no—
335C2×D4—61no—
336C2×D4—61no—
337C2×D4—61no—
338C22×C4—32no—
339C22×C4—181no—
340C22×C4C2×D3211yescharacteristic
341M16—61no—
342M16—61no—
343M16—181no—
344M16—181no—
345C2×C8—61no—
346C2×C8—181no—
347C4⋊C4—32no—
348C4⋊C4—64no—
349C4⋊C4#62512yes—
350C22⋊C4—21no—
351C22⋊C4—61no—
352C22⋊C4—188no—
353C42—21no—
354C42—64no—
355C42—61no—
356C42—92no—
357C42—181no—
358C22×C3—22no—
359C22×C3—22no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—42no—
364C22×C3—124no—
365C22×C3—122no—
366C22×C3—242no—
367C22×C3—242no—
368C22×C3D3×C22⋊C411yescharacteristic
369C22×C3#88311yescharacteristic
370C22×C3C2×(C2×D3)⋊C411yescharacteristic
371C22×C3#92911yescharacteristic
372C22×C3#93711yescharacteristic
373C22×C3#95311yescharacteristic
374C2×D3—44no—
375C2×D3—42no—
376C2×D3—82no—
377C2×D3—82no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—42no—
383C3×C4—42no—
384C3×C4—64no—
385C3×C4—82no—
386C3×C4—122no—
387C3×C4#67⋊C411yescharacteristic
388C3×C4#88411yescharacteristic
389C3×C4C4×#6711yescharacteristic
390C3×C4C4×#6711yescharacteristic
391C3×C4C4×#6711yescharacteristic
392C3×C4#93011yescharacteristic
393C3×C4#93011yescharacteristic
394C3×C4#93811yescharacteristic
395Dic3—24no—
396Dic3—42no—
397Dic3—122no—
398Dic3—122no—
399Dic3—124no—
400C32#188811yescharacteristic, complemented, Sylow
401C23—62no—
402C23—124no—
403C23—121no—
404C23—121no—
405C23D3×#6711yescharacteristic
406Q8—62no—
407Q8—62no—
408Q8—62no—
409Q8—62no—
410D4—62no—
411D4—62no—
412D4—121no—
413D4—121no—
414C2×C4—22no—
415C2×C4—34no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4—182no—
420C2×C4—362no—
421C2×C4#379511yescharacteristic
422C2×C4#379811yescharacteristic
423C2×C4C4×D3211yescharacteristic
424C2×C4D3×D1211yescharacteristic
425C2×C4C2×#62511yescharacteristic
426C2×C4D3×#6711yescharacteristic
427C8—121no—
428C8—361no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—22no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—242no—
438C2×C3#495611yescharacteristic
439C2×C3#520112yes—
440C2×C3#521311yescharacteristic
441C2×C3#524512yes—
442D3—82no—
443C22—22no—
444C22—124no—
445C22—122no—
446C22—242no—
447C22—242no—
448C22#6390511yescharacteristic
449C22D3×(C2×D3)⋊C411yescharacteristic
450C22#6397611yescharacteristic
451C4—42no—
452C4—64no—
453C4—122no—
454C4—362no—
455C4#6387911yescharacteristic
456C4C4×#62511yescharacteristic
457C4#6390611yescharacteristic
458C4#6390811yescharacteristic
459C3—21no—
460C3#7032511yescharacteristic, complemented
461C3#7166111yescharacteristic, complemented
462C2—21no—
463C2—21no—
464C2—242no—
465C2#1059138111yescharacteristic
466C2#1059168412yes—
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1888
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5516C2semidirect
5. C2×#63560C2semidirect
6. #10589398C2semidirect
7. #10589160C2semidirect
22. #63863C4semidirect
29. #5516D3semidirect
400. C32#1888semidirect
460. C3#70325semidirect
461. C3#71661semidirect

Maximal subgroups

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

subgroupindex
C3×#55162
C2×#638632
C3×#50012
#105910852
C2×#635602
#105893982
#105891602
#716613
#703253