Finite Group Databasebeta

← #11786588

Subgroups — #11786588

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C2×#63660C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4#10591139C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#71647—31nomaximal
7#69642—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C2×#3748C2212yes—
10C2×C3×#217—22no—
11C2×C3×#217—22no—
12C3×D4×Dic3—22no—
13C3×D4×Dic3—22no—
14C3×#926C2212yes—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17#63660C414yescomplemented
18#63576—22no—
19#63574—22no—
20C3×#518—31no—
21#5798D311yescharacteristic
22C3×#390—31no—
23#5221D311yescharacteristic
24C2×#833—31no—
25C2×#833—31no—
26C2×#833—61no—
27#4995—32no—
28#4964—32no—
29#4532—32no—
30#4523—32no—
31C24×C32D412yes—
32C2×C32×D4—22no—
33C2×C32×D4—22no—
34C2×C32×D4C2×C412yes—
35C2×C32×D4Q812yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3—21no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3—21no—
41#3748—22no—
42#3748C2×C414yescomplemented
43C2×C3⋊(C3⋊C8)—22no—
44C3×#217—24no—
45C3×#217—22no—
46C3×#217—44no—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3D412yes—
49C3×C4⋊Dic3D412yes—
50C3×C4×Dic3—22no—
51C3×C4×Dic3—22no—
52#1856—91noSylow
53C22×C3×D4—21no—
54C22×C3×D4C2×D311yescharacteristic
55C22×C3×D4C2×D311yescharacteristic
56C3×C4×D4—62no—
57C3×C4×D4—62no—
58C3×#117—32no—
59C2×C3×C4⋊C4—31no—
60C2×C3×C22⋊C4—62no—
61C2×C3×C22⋊C4—62no—
62C2×C3×C42—31no—
63C2×#217—22no—
64C2×#217—22no—
65D4×Dic3—22no—
66D4×Dic3—22no—
67#926C2×D312yes—
68C2×C4⋊Dic3C2×D311yescharacteristic
69C2×C4×Dic3C2×D311yescharacteristic
70C2×#208—32no—
71C2×#208—32no—
72C2×#208—62no—
73#833—34no—
74#833—34no—
75#833—64no—
76#808—62no—
77#808—62no—
78#807—62no—
79#807—62no—
80C23×C32—22no—
81C23×C32—22no—
82C23×C32—42no—
83C23×C32—42no—
84C23×C32C4⋊C414yes—
85C23×C32C2×D411yescharacteristic
86C32×D4—24no—
87C32×D4—24no—
88C2×C32×C4C22×C411yescharacteristic
89C2×C32×C4C2×D412yes—
90C2×C32×C4C2×Q811yescharacteristic
91C2×C32×C4#4112yes—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—22no—
94C2×C3×Dic3—22no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—82no—
100C2×C3×Dic3—82no—
101C3⋊(C3⋊C8)—24no—
102#518—31no—
103#428—92no—
104C2×#100—91no—
105#390—31no—
106#339—92no—
107C24×C3—22no—
108C24×C3#6712yes—
109C24×C3#6712yes—
110C2×C3×D4—22no—
111C2×C3×D4—22no—
112C2×C3×D4—22no—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—42no—
117C2×C3×D4—42no—
118C2×C3×D4Dic612yes—
119C2×C3×D4Dic612yes—
120C2×C3×D4C4×D312yes—
121C2×C3×D4C4×D312yes—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—62no—
125C22×C3×C4—62no—
126C22×C3×C4—61no—
127C22×C3×C4C22×D311yescharacteristic
128C22×C3×C4C22×D311yescharacteristic
129C22×Dic3—21no—
130C22×Dic3—22no—
131C22×Dic3—22no—
132C22×Dic3—21no—
133C3×C4⋊C4—32no—
134C3×C4⋊C4—32no—
135C3×C4⋊C4—62no—
136C3×C22⋊C4—64no—
137C3×C22⋊C4—62no—
138C3×C22⋊C4—124no—
139C3×C42—62no—
140C3×C42—62no—
141#217—24no—
142#217—22no—
143#217—44no—
144C4⋊Dic3—22no—
145C4⋊Dic3#6712yes—
146C4⋊Dic3#6712yes—
147C4×Dic3—22no—
148C4×Dic3—22no—
149#208—34no—
150#208—34no—
151#208—64no—
152#208—62no—
153#208—62no—
154#208—122no—
155C2×C3⋊C8—62no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—122no—
158C22×C32—21no—
159C22×C32—21no—
160C22×C32—24no—
161C22×C32—44no—
162C22×C32—42no—
163C22×C32—42no—
164C22×C32—82no—
165C22×C32C2×C4⋊C411yescharacteristic
166C22×C32#12011yescharacteristic
167C22×C32#12311yescharacteristic
168C32×C4C4×D412yes—
169C32×C4C22⋊Q812yes—
170C3×Dic3—42no—
171C3×Dic3—42no—
172C3×Dic3—42no—
173C3×Dic3—81no—
174C22×D4D3211yescharacteristic
175C2×M16—92no—
176C4×D4—62no—
177C4×D4—62no—
178#117—32no—
179C2×C4⋊C4—31no—
180C2×C22⋊C4—62no—
181C2×C22⋊C4—62no—
182C2×C42—31no—
183#107—182no—
184#106—182no—
185#100—94no—
186C23×C3—22no—
187C23×C3—22no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—24no—
191C23×C3—21no—
192C23×C3—42no—
193C23×C3—42no—
194C23×C3—42no—
195C23×C3—42no—
196C23×C3—42no—
197C23×C3—42no—
198C23×C3—82no—
199C23×C3—82no—
200C23×C3Dic3⋊C414yes—
201C23×C3Dic3⋊C414yes—
202C23×C3C2×#6711yescharacteristic
203C23×C3C2×#6711yescharacteristic
204C3×D4—24no—
205C3×D4—24no—
206C3×D4—24no—
207C3×D4—24no—
208C3×D4—44no—
209C3×D4—44no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—22no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—121no—
218C2×C3×C4—121no—
219C2×C3×C4—122no—
220C2×C3×C4—121no—
221C2×C3×C4—242no—
222C2×C3×C4—242no—
223C2×C3×C4C2×Dic611yescharacteristic
224C2×C3×C4C2×Dic611yescharacteristic
225C2×C3×C4C2×C4×D311yescharacteristic
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4#23512yes—
228C2×C3×C4D3×D412yes—
229C2×C3×C4#23712yes—
230C2×C3×C4C2×#6712yes—
231C2×Dic3—22no—
232C2×Dic3—22no—
233C2×Dic3—22no—
234C2×Dic3—41no—
235C2×Dic3—41no—
236C2×Dic3—42no—
237C2×Dic3—41no—
238C2×Dic3—82no—
239C2×Dic3—82no—
240C3⋊C8—64no—
241C3⋊C8—64no—
242C3⋊C8—124no—
243C2×C32—21no—
244C2×C32—21no—
245C2×C32—44no—
246C2×C32#38511yescharacteristic
247C2×C32#45311yescharacteristic
248C2×C32#45511yescharacteristic
249C24#62512yes—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4#62412yes—
253C2×D4#62712yes—
254C22×C4—61no—
255C22×C4—62no—
256C22×C4—62no—
257C22×C4—61no—
258C22×C4C2×D3211yescharacteristic
259M16—94no—
260M16—182no—
261C2×C8—182no—
262C4⋊C4—32no—
263C4⋊C4—32no—
264C4⋊C4—62no—
265C22⋊C4—64no—
266C22⋊C4—62no—
267C22⋊C4—124no—
268C42—62no—
269C42—62no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—24no—
275C22×C3—24no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—44no—
282C22×C3—44no—
283C22×C3—44no—
284C22×C3—42no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3—42no—
288C22×C3—82no—
289C22×C3—82no—
290C22×C3—84no—
291C22×C3—82no—
292C22×C3—82no—
293C22×C3—84no—
294C22×C3C2×Dic3⋊C411yescharacteristic
295C22×C3C2×Dic3⋊C411yescharacteristic
296C22×C3#92911yescharacteristic
297C22×C3#93511yescharacteristic
298C22×C3#93711yescharacteristic
299C22×C3#95311yescharacteristic
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—122no—
303C3×C4—122no—
304C3×C4—122no—
305C3×C4—241no—
306C3×C4#87812yes—
307C3×C4#67⋊C412yes—
308C3×C4#92412yes—
309C3×C4C4×#6712yes—
310Dic3—42no—
311Dic3—42no—
312Dic3—42no—
313Dic3—81no—
314C32#185611yescharacteristic, complemented, Sylow
315C23—22no—
316C23—22no—
317C23—42no—
318C23—42no—
319C23#372414yes—
320C23C2×#62511yescharacteristic
321D4—24no—
322D4—24no—
323C2×C4—62no—
324C2×C4—62no—
325C2×C4—62no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4—122no—
329C2×C4—121no—
330C2×C4—242no—
331C2×C4—242no—
332C2×C4#380412yes—
333C2×C4C2×#62411yescharacteristic
334C2×C4C2×#62711yescharacteristic
335C2×C4D3×#6712yes—
336C8—184no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—41no—
345C2×C3—41no—
346C2×C3—44no—
347C2×C3—44no—
348C2×C3—84no—
349C2×C3#494611yescharacteristic
350C2×C3#506111yescharacteristic
351C2×C3#507711yescharacteristic
352C2×C3#521011yescharacteristic
353C2×C3#524111yescharacteristic
354C2×C3#524211yescharacteristic
355C22—21no—
356C22—21no—
357C22—24no—
358C22—44no—
359C22—42no—
360C22—42no—
361C22—82no—
362C22#6396111yescharacteristic
363C22C2×#372411yescharacteristic
364C22#6397611yescharacteristic
365C4—122no—
366C4—122no—
367C4—122no—
368C4—241no—
369C4#6395212yes—
370C4#6396412yes—
371C3—21no—
372C3#6964211yescharacteristic, complemented
373C3#7164711yescharacteristic, complemented
374C2—21no—
375C2—21no—
376C2—44no—
377C2#1059150911yescharacteristic
378C2#1059151211yescharacteristic
379C2#1059169311yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1856
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591139C2semidirect
5. #10589161C2semidirect
17. #63660C4semidirect
42. #3748C2×C4semidirect
314. C32#1856semidirect
372. C3#69642semidirect
373. C3#71647semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C2×#636602
C3×#52212
#105911392
#105891612
#716473
#696423