Finite Group Databasebeta

← #11788921

Subgroups — #11788921

Order 1152.

691 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5825C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic
3#10592936C211yesmaximal, characteristic
4C2×#63560C212yesmaximal, complemented
5#10589170C212yesmaximal, complemented
6#72031—31nomaximal
7#71866—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×#3748C2212yes—
11C3×#948—24no—
12C3×#944—21no—
13C3×#936—21no—
14C3×#935C414yes—
15C3×#926C2211yescharacteristic
16C3×#924—22no—
17C2×C3×#208—22no—
18C2×C3×#208C2212yes—
19#63663—21no—
20#63660—21no—
21#63560—24no—
22C3×#568—31no—
23C3×#536—31no—
24#5825D311yescharacteristic
25#5819D311yescharacteristic
26#5237—31no—
27#5237—31no—
28#5237—61no—
29C2×#836—32no—
30C2×#824—32no—
31#4559—32no—
32#4533—32no—
33C32×#41—22no—
34C32×#41—22no—
35C2×C32×Q8D411yescharacteristic
36C2×C32×D4C2×C412yes—
37C2×C32×D4D411yescharacteristic
38C22×C32×C4D412yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3C2×C412yes—
41C2×C3×Dic6—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—22no—
45#3748—22no—
46#3748—22no—
47C2×C3⋊(C3⋊C8)—22no—
48C3×#217—24no—
49C3×#217C2×C412yes—
50C3×C4⋊Dic3—21no—
51C3×Dic3⋊C4—24no—
52C3×C4×Dic3—21no—
53C3×#208—24no—
54C3×#208—22no—
55C3×#208D414yes—
56C2×C3×C3⋊C8—24no—
57C2×C3×C3⋊C8—22no—
58#1915—91noSylow
59C2×C3×#41—21no—
60C2×C3×#41C2×D311yescharacteristic
61C2×C3×#41C2×D311yescharacteristic
62C22×C3×Q8—31no—
63C22×Dic6C2×D311yescharacteristic
64C3×#131—64no—
65C2×C3×M16—32no—
66C2×C3×M16—62no—
67C3×C4⋊Q8—61no—
68C3×#124—61no—
69C3×#123—34no—
70C3×C22⋊Q8—62no—
71C3×#117—31no—
72#948—24no—
73#944—21no—
74#936—21no—
75#935Dic314yes—
76#926C2×D311yescharacteristic
77#924—22no—
78C2×#208—22no—
79C2×#208—32no—
80C2×#208—32no—
81C2×#208—62no—
82C2×#208C2×D312yes—
83#836—62no—
84#836—61no—
85#836—61no—
86#836—64no—
87#833—62no—
88#833—61no—
89#833—61no—
90#824—64no—
91C23×C32C22⋊C412yes—
92C23×C32C22×C411yescharacteristic
93C32×Q8—22no—
94C32×D4—24no—
95C32×D4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4C22⋊C412yes—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4112yes—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—24no—
106C3×Dic6—41no—
107C3×Dic6—42no—
108C3×Dic6—41no—
109C3⋊(C3⋊C8)—42no—
110C3×C3⋊C8—24no—
111#568—31no—
112#536—31no—
113#413—91no—
114C2×#101—92no—
115#344—92no—
116C3×#41—22no—
117C3×#41—22no—
118C3×#41—22no—
119C3×#41—22no—
120C3×#41—42no—
121C3×#41—42no—
122C2×C3×Q8—21no—
123C2×C3×Q8—61no—
124C2×C3×Q8—62no—
125C2×C3×Q8—62no—
126C2×C3×Q8—61no—
127C2×C3×Q8D1211yescharacteristic
128C2×C3×Q8#6711yescharacteristic
129C2×C3×D4—22no—
130C2×C3×D4—21no—
131C2×C3×D4C4×D312yes—
132C2×C3×D4D1211yescharacteristic
133C2×C3×D4C2×Dic312yes—
134C2×C3×D4#6711yescharacteristic
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—32no—
138C22×C3×C4#6712yes—
139C22×C3×C4#6712yes—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×Dic3C2×Dic312yes—
143C2×Dic6—22no—
144C2×Dic6—22no—
145C2×Dic6—21no—
146C2×Dic6—21no—
147C3×M16—34no—
148C3×M16—64no—
149C3×M16—62no—
150C2×C3×C8—64no—
151C2×C3×C8—62no—
152C3×C4⋊C4—64no—
153C3×C4⋊C4—61no—
154C3×C22⋊C4—32no—
155C3×C22⋊C4—64no—
156C3×C42—61no—
157#217—24no—
158#217C2×Dic312yes—
159C4⋊Dic3—21no—
160Dic3⋊C4—24no—
161C4×Dic3—21no—
162#208—24no—
163#208—22no—
164#208—64no—
165#208—62no—
166#208—62no—
167#208—62no—
168#208—62no—
169#208—122no—
170#208#6714yes—
171C2×C3⋊C8—24no—
172C2×C3⋊C8—22no—
173C2×C3⋊C8—62no—
174C2×C3⋊C8—62no—
175C2×C3⋊C8—122no—
176C22×C32—22no—
177C22×C32—41no—
178C22×C32—42no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32C4×D412yes—
181C32×C4—22no—
182C32×C4#12011yescharacteristic
183C32×C4#12112yes—
184C32×C4#12311yescharacteristic
185C3×Dic3—42no—
186C3×Dic3—42no—
187C2×#41D3211yescharacteristic
188C22×Q8—31no—
189#131—64no—
190C2×M16—32no—
191C2×M16—62no—
192C2×M16—92no—
193C4⋊Q8—61no—
194#124—61no—
195#123—34no—
196C22⋊Q8—62no—
197#117—31no—
198#101—184no—
199#101—181no—
200#100—181no—
201C23×C3—22no—
202C23×C3—21no—
203C23×C3(C2×D3)⋊C412yes—
204C23×C3#21712yes—
205C23×C3C2×C4×D311yescharacteristic
206C23×C3C22×Dic311yescharacteristic
207C3×Q8—22no—
208C3×Q8—22no—
209C3×Q8—42no—
210C3×Q8—121no—
211C3×Q8—122no—
212C3×Q8—121no—
213C3×D4—24no—
214C3×D4—24no—
215C3×D4—22no—
216C3×D4—22no—
217C3×D4—42no—
218C3×D4—44no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—22no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—64no—
233C2×C3×C4(C2×D3)⋊C412yes—
234C2×C3×C4#21712yes—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4#23512yes—
237C2×C3×C4D3×D412yes—
238C2×C3×C4#23712yes—
239C2×C3×C4C2×#6711yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×#6712yes—
243C2×Dic3—24no—
244C2×Dic3—22no—
245C2×Dic3—22no—
246Dic6—41no—
247Dic6—41no—
248Dic6—42no—
249C3×C8—64no—
250C3⋊C8—24no—
251C3⋊C8—124no—
252C3⋊C8—122no—
253C3⋊C8—122no—
254C2×C32—21no—
255C2×C32—22no—
256C2×C32—42no—
257C2×C32#38611yescharacteristic
258#41—22no—
259#41—22no—
260C2×Q8—62no—
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8—62no—
264C2×Q8#62611yescharacteristic
265C2×D4D3×Dic312yes—
266C2×D4#62611yescharacteristic
267C22×C4—32no—
268C22×C4#62512yes—
269C22×C4C2×D3211yescharacteristic
270M16—34no—
271M16—64no—
272M16—62no—
273M16—182no—
274M16—182no—
275C2×C8—64no—
276C2×C8—62no—
277C2×C8—182no—
278C4⋊C4—64no—
279C4⋊C4—61no—
280C22⋊C4—32no—
281C22⋊C4—64no—
282C42—61no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3—21no—
286C22×C3—22no—
287C22×C3—42no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—42no—
291C22×C3—42no—
292C22×C3—81no—
293C22×C3—82no—
294C22×C3C2×(C2×D3)⋊C411yescharacteristic
295C22×C3C4×#6712yes—
296C22×C3D4×Dic312yes—
297C22×C3C2×#21711yescharacteristic
298C3×C4—22no—
299C3×C4—22no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—22no—
303C3×C4—42no—
304C3×C4—122no—
305C3×C4—122no—
306C3×C4#92911yescharacteristic
307C3×C4#93012yes—
308C3×C4#93511yescharacteristic
309C3×C4#93711yescharacteristic
310C3×C4#93912yes—
311C3×C4#95311yescharacteristic
312Dic3—42no—
313Dic3—42no—
314C32#191511yescharacteristic, complemented, Sylow
315C23(C2×D3)⋊Dic312yes—
316C23C2×D3×Dic311yescharacteristic
317Q8—22no—
318Q8—121no—
319Q8—121no—
320Q8—122no—
321D4—24no—
322D4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—62no—
326C2×C4—62no—
327C2×C4—64no—
328C2×C4(C2×D3)⋊Dic312yes—
329C2×C4#380412yes—
330C2×C4C2×#62511yescharacteristic
331C2×C4C2×#62611yescharacteristic
332C2×C4D3×#6712yes—
333C8—64no—
334C8—362no—
335C2×C3—21no—
336C2×C3—22no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—21no—
340C2×C3—41no—
341C2×C3—42no—
342C2×C3—42no—
343C2×C3—42no—
344C2×C3—82no—
345C2×C3#521311yescharacteristic
346C2×C3#522011yescharacteristic
347C22—22no—
348C22—41no—
349C22—42no—
350C22C2×(C2×D3)⋊Dic311yescharacteristic
351C22Dic3×#6712yes—
352C4—22no—
353C4—122no—
354C4—122no—
355C4#6396111yescharacteristic
356C4#6397611yescharacteristic
357C4#6397812yes—
358C3—21no—
359C3#7186611yescharacteristic, complemented
360C3#7203111yescharacteristic, complemented
361C2—21no—
362C2—22no—
363C2—42no—
364C2#1059171011yescharacteristic
subgroupG/H
centerC2#10591710
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#386
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1915
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63560C2semidirect
5. #10589170C2semidirect
314. C32#1915semidirect
359. C3#71866semidirect
360. C3#72031semidirect

Maximal subgroups

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

subgroupindex
C3×#58252
C3×#58192
#105929362
C2×#635602
#105891702
#720313
#718663