Finite Group Databasebeta

← #11786586

Subgroups — #11786586

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2#10592920C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4#10591131C212yesmaximal, complemented
5#10589160C212yesmaximal, complemented
6#71647—31nomaximal
7#70068—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C2×#3757—22no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×#217—22no—
13C3×D4×Dic3—22no—
14C3×D4×Dic3—22no—
15C3×#926C2212yes—
16C2×C3×#208C2212yes—
17C3×#833C414yescomplemented
18#63575—22no—
19#63573—22no—
20C3×#518—31no—
21#5798D311yescharacteristic
22C2×C3×#100—31no—
23#5221—31no—
24#5221—31no—
25#5221—61no—
26C2×#833D311yescharacteristic
27#5121—32no—
28#4995—32no—
29#4555—32no—
30#4532—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—21no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3—22no—
41#3757—44no—
42C4⋊(C3⋊Dic3)—22no—
43C4×C3⋊Dic3—22no—
44C3×#217—24no—
45C3×#217—22no—
46C3×C4⋊Dic3D412yes—
47C3×C4⋊Dic3D412yes—
48C3×C4×Dic3—22no—
49C3×#208—22no—
50C3×#208C2×C414yescomplemented
51C2×C3×C3⋊C8—22no—
52#1856—91noSylow
53C22×C3×D4—21no—
54C22×C3×D4C2×D311yescharacteristic
55C22×C3×D4C2×D311yescharacteristic
56C2×C3×M16—32no—
57C3×C4×D4—62no—
58C3×C4×D4—62no—
59C3×#117—32no—
60C2×C3×C22⋊C4—62no—
61C2×#217—22no—
62C2×#217—64no—
63C2×#217—62no—
64C2×#217—62no—
65D4×Dic3—22no—
66D4×Dic3—22no—
67#926C2×D312yes—
68C2×C4⋊Dic3—31no—
69C2×C4⋊Dic3—31no—
70C2×C4⋊Dic3—61no—
71C2×C4×Dic3—31no—
72C2×C4×Dic3—31no—
73C2×C4×Dic3—61no—
74C2×#208C2×D312yes—
75C3×#100—34no—
76#833Dic314yescomplemented
77#818—62no—
78#817—62no—
79#808—62no—
80#807—62no—
81C23×C32—22no—
82C23×C32—22no—
83C23×C32—42no—
84C23×C32—42no—
85C23×C32C4⋊C414yes—
86C23×C32C2×D411yescharacteristic
87C32×D4—24no—
88C32×D4—24no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D412yes—
91C2×C32×C4C2×Q811yescharacteristic
92C2×C32×C4#4112yes—
93C2×C3⋊Dic3—22no—
94C2×C3⋊Dic3—41no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—41no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—82no—
101C2×C3×Dic3—82no—
102C3×C3⋊C8—24no—
103#518—31no—
104#428—92no—
105C2×#100—31no—
106#390—91no—
107#339—92no—
108C24×C3—22no—
109C24×C3D1212yes—
110C24×C3#6712yes—
111C2×C3×D4—22no—
112C2×C3×D4—22no—
113C2×C3×D4—22no—
114C2×C3×D4—22no—
115C2×C3×D4—22no—
116C2×C3×D4—22no—
117C2×C3×D4—42no—
118C2×C3×D4—42no—
119C2×C3×D4Dic612yes—
120C2×C3×D4Dic612yes—
121C2×C3×D4C4×D312yes—
122C2×C3×D4C2×Dic312yes—
123C22×C3×C4—21no—
124C22×C3×C4—62no—
125C22×C3×C4—62no—
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C22×Dic3—22no—
129C22×Dic3—22no—
130C22×Dic3—62no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136C3×M16—34no—
137C3×M16—62no—
138C2×C3×C8—62no—
139C3×C4⋊C4—32no—
140C3×C4⋊C4—32no—
141C3×C22⋊C4—64no—
142C3×C22⋊C4—62no—
143C3×C42—62no—
144#217—24no—
145#217—22no—
146#217—124no—
147#217—124no—
148#217—128no—
149C4⋊Dic3—62no—
150C4⋊Dic3—62no—
151C4⋊Dic3—122no—
152C4⋊Dic3#6712yes—
153C4⋊Dic3#6712yes—
154C4×Dic3—22no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157C4×Dic3—122no—
158#208—22no—
159#208C2×Dic314yescomplemented
160C2×C3⋊C8—22no—
161C22×C32—21no—
162C22×C32—21no—
163C22×C32—24no—
164C22×C32—44no—
165C22×C32—42no—
166C22×C32—42no—
167C22×C32—82no—
168C22×C32C2×C4⋊C411yescharacteristic
169C22×C32#12011yescharacteristic
170C22×C32#12311yescharacteristic
171C32×C4C4×D412yes—
172C32×C4C22⋊Q812yes—
173C3⋊Dic3—42no—
174C3⋊Dic3—81no—
175C3×Dic3—42no—
176C3×Dic3—42no—
177C22×D4D3211yescharacteristic
178C2×M16—32no—
179C4×D4—62no—
180C4×D4—62no—
181#117—32no—
182C2×C4⋊C4—91no—
183C2×C22⋊C4—62no—
184C2×C22⋊C4—182no—
185C2×C42—91no—
186#107—182no—
187#106—182no—
188#100—34no—
189C23×C3—22no—
190C23×C3—22no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—24no—
194C23×C3—21no—
195C23×C3—42no—
196C23×C3—42no—
197C23×C3—42no—
198C23×C3—42no—
199C23×C3—42no—
200C23×C3—42no—
201C23×C3—44no—
202C23×C3—44no—
203C23×C3Dic3⋊C414yes—
204C23×C3C4⋊Dic314yes—
205C23×C3C2×D1211yescharacteristic
206C23×C3C2×#6711yescharacteristic
207C3×D4—24no—
208C3×D4—24no—
209C3×D4—24no—
210C3×D4—24no—
211C3×D4—44no—
212C3×D4—44no—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—22no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—242no—
220C2×C3×C4—242no—
221C2×C3×C4C2×Dic611yescharacteristic
222C2×C3×C4C2×Dic611yescharacteristic
223C2×C3×C4C2×C4×D311yescharacteristic
224C2×C3×C4#23512yes—
225C2×C3×C4D3×D412yes—
226C2×C3×C4#23712yes—
227C2×C3×C4C22×Dic311yescharacteristic
228C2×C3×C4C2×#6712yes—
229C2×Dic3—22no—
230C2×Dic3—22no—
231C2×Dic3—64no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—82no—
235C2×Dic3—82no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C2×Dic3—121no—
239C2×Dic3—121no—
240C2×Dic3—121no—
241C2×Dic3—121no—
242C2×Dic3—122no—
243C2×Dic3—124no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248C3×C8—64no—
249C3⋊C8—24no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—44no—
253C2×C32#38511yescharacteristic
254C2×C32#45311yescharacteristic
255C2×C32#45511yescharacteristic
256C24#62612yes—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4D3×Dic312yes—
260C2×D4#62712yes—
261C22×C4—62no—
262C22×C4—62no—
263C22×C4—181no—
264C22×C4—181no—
265C22×C4C2×D3211yescharacteristic
266M16—34no—
267M16—62no—
268C2×C8—62no—
269C4⋊C4—32no—
270C4⋊C4—32no—
271C4⋊C4—182no—
272C22⋊C4—64no—
273C22⋊C4—62no—
274C22⋊C4—364no—
275C42—62no—
276C42—182no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—24no—
284C22×C3—24no—
285C22×C3—21no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—44no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3—48no—
292C22×C3—42no—
293C22×C3—42no—
294C22×C3—42no—
295C22×C3—42no—
296C22×C3—82no—
297C22×C3—82no—
298C22×C3—82no—
299C22×C3—82no—
300C22×C3—84no—
301C22×C3#88211yescharacteristic
302C22×C3#88611yescharacteristic
303C22×C3C2×Dic3⋊C411yescharacteristic
304C22×C3C2×C4⋊Dic311yescharacteristic
305C22×C3#92911yescharacteristic
306C22×C3#95311yescharacteristic
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—122no—
310C3×C4—122no—
311C3×C4#87812yes—
312C3×C4#92412yes—
313C3×C4C4×#6712yes—
314C3×C4D4×Dic312yes—
315Dic3—42no—
316Dic3—42no—
317Dic3—124no—
318Dic3—122no—
319Dic3—122no—
320Dic3—242no—
321Dic3—241no—
322Dic3—241no—
323C32#185611yescharacteristic, complemented, Sylow
324C23—22no—
325C23—22no—
326C23—42no—
327C23—42no—
328C23Dic3⋊Dic314yes—
329C23C2×#62611yescharacteristic
330D4—24no—
331D4—24no—
332C2×C4—62no—
333C2×C4—62no—
334C2×C4—182no—
335C2×C4—242no—
336C2×C4—242no—
337C2×C4—361no—
338C2×C4—361no—
339C2×C4—362no—
340C2×C4—361no—
341C2×C4C2×D3×Dic311yescharacteristic
342C2×C4#380412yes—
343C2×C4C2×#62711yescharacteristic
344C2×C4D3×#6712yes—
345C8—64no—
346C2×C3—22no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—44no—
356C2×C3—44no—
357C2×C3—84no—
358C2×C3#474611yescharacteristic
359C2×C3#474711yescharacteristic
360C2×C3#495011yescharacteristic
361C2×C3#521011yescharacteristic
362C2×C3#524111yescharacteristic
363C2×C3#524211yescharacteristic
364C22—21no—
365C22—21no—
366C22—24no—
367C22—44no—
368C22—42no—
369C22—42no—
370C22—82no—
371C22C2×Dic3⋊Dic311yescharacteristic
372C22#6396611yescharacteristic
373C22#6397711yescharacteristic
374C4—122no—
375C4—122no—
376C4—362no—
377C4—721no—
378C4#6396412yes—
379C4Dic3×#6712yes—
380C3—21no—
381C3#7006811yescharacteristic, complemented
382C3#7164711yescharacteristic, complemented
383C2—21no—
384C2—21no—
385C2—44no—
386C2#1059151011yescharacteristic
387C2#1059151311yescharacteristic
388C2#1059171811yescharacteristic
subgroupG/H
centerC22#63977
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. #10591131C2semidirect
5. #10589160C2semidirect
17. C3×#833C4semidirect
50. C3×#208C2×C4semidirect
76. #833Dic3semidirect
159. #208C2×Dic3semidirect
323. C32#1856semidirect
381. C3#70068semidirect
382. C3#71647semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
#105929202
C2×C3×#8332
#105911312
#105891602
#716473
#700683