Finite Group Databasebeta

← #11798200

Subgroups — #11798200

Order 1152.

473 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic
2C2×#63656C211yesmaximal, characteristic, complemented
3#10590852C211yesmaximal, characteristic
4C2×#63551C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic
8#72064—31nomaximal
9#69225—31nomaximal
10C2×C3×D3×Q8—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×#3746C2211yescharacteristic
13C2×C3×#216—21no—
14C3×D3×Q16—22no—
15C3×D3×Q16—22no—
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18#63857—21no—
19#63656—22no—
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C3×#818C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23#63567—21no—
24#63551—22no—
25C22×C3×Q16—31no—
26C2×D3×Q16D311yescharacteristic
27C2×#829—31no—
28C2×#829—31no—
29C2×#829—31no—
30C2×#829—61no—
31#5116—31no—
32C2×Dic24—31no—
33#4887—31no—
34C3×#358—31no—
35#4564—31no—
36#4564D311yescharacteristic, complemented
37#4549—31no—
38(C2×D3)⋊C16—31no—
39#4492—31no—
40C2×C32×Q8—21no—
41C2×#634—21no—
42C3×D3×Q8—24no—
43C3×D3×Q8—42no—
44C2×C3×C4×D3—41no—
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C3×Dic6—41no—
48C32×Q16—21no—
49C32×Q16D412yes—
50C2×C32×C8C2311yescharacteristic
51#3746—21no—
52#3746—21no—
53C3×#216—24no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C3×Dic12—21no—
57C3×Dic12D412yes—
58C3×D3×C8—21no—
59C3×D3×C8—21no—
60Dic3⋊Dic3—41no—
61(C2×D3)⋊Dic3—41no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2188—91noSylow
65C22×C3×Q8—61no—
66C2×D3×Q8—21no—
67C2×C3×Q16—21no—
68C2×C3×Q16—31no—
69C2×C3×Q16—61no—
70C2×C3×Q16—62no—
71C2×C3×Q16—62no—
72C2×C3×Q16C2×D311yescharacteristic
73C2×C3×Q16C2×D311yescharacteristic
74C22×C3×C8—31no—
75C2×#216—21no—
76#924—61no—
77D3×Q16—22no—
78D3×Q16—22no—
79C2×Dic12—31no—
80C2×Dic12—31no—
81C2×Dic12—61no—
82C2×Dic12C2×D311yescharacteristic
83C2×D3×C8C2×D311yescharacteristic
84#897—61no—
85C2×C3×C16—31no—
86C3×#107—31no—
87#829—62no—
88#829—64no—
89#829—62no—
90#829—62no—
91#818C2×D311yescharacteristic
92#816—61no—
93C2×C3⋊C16—31no—
94C2×C3⋊C16—31no—
95C2×C3⋊C16—61no—
96C2×C3⋊C16C2×D311yescharacteristic
97#810—61no—
98Dic24—62no—
99C22×C3×D3D811yescharacteristic
100C32×Q8—22no—
101C32×Q8—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C3⋊Dic3—41no—
105#634—41no—
106#634—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3D811yescharacteristic
110C3×C4×D3—21no—
111C3×C4×D3—21no—
112C3×C4×D3—44no—
113C3×Dic6—22no—
114C3×Dic6—44no—
115C3×Dic6—41no—
116C32×C8C2×D411yescharacteristic
117C32×C8C2×D411yescharacteristic
118C3×C3⋊C8—21no—
119C22×Q16—31no—
120C2×Q32—91no—
121C2×Q32—91no—
122#467—91no—
123#358—31no—
124#358—91no—
125C22⋊C16—91no—
126C2×C3×Q8—21no—
127C2×C3×Q8—21no—
128C2×C3×Q8—41no—
129C2×C3×Q8—64no—
130C2×C3×Q8—61no—
131C2×C3×Q8—121no—
132C2×C3×Q8—122no—
133C22×C3×C4—31no—
134C22×C3×C4—121no—
135D3×Q8—24no—
136D3×Q8—42no—
137C2×C4×D3—41no—
138C2×C4×D3#6711yescharacteristic
139C2×Dic6—21no—
140C2×Dic6—41no—
141C2×Dic6—61no—
142C2×Dic6—61no—
143C2×Dic6—121no—
144C3×Q16—21no—
145C3×Q16—21no—
146C3×Q16—22no—
147C3×Q16—32no—
148C3×Q16—41no—
149C3×Q16—64no—
150C3×Q16—61no—
151C3×Q16D1212yes—
152C3×Q16#6712yes—
153C2×C3×C8—21no—
154C2×C3×C8—31no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C2×C3×C8C22×D311yescharacteristic
158C2×C3×C8C22×D311yescharacteristic
159C3×C4⋊C4—61no—
160#217—121no—
161#216—24no—
162(C2×D3)⋊C4—121no—
163C4⋊Dic3—21no—
164C4⋊Dic3—121no—
165Dic3⋊C4—121no—
166C2×C3⋊C8#6711yescharacteristic
167Dic12—21no—
168Dic12—62no—
169Dic12—61no—
170Dic12—61no—
171Dic12—61no—
172Dic12—61no—
173Dic12—121no—
174Dic12#6712yes—
175D3×C8—21no—
176D3×C8—21no—
177C3×C16—61no—
178C3⋊C16—21no—
179C3⋊C16—62no—
180C3⋊C16—61no—
181C3⋊C16—61no—
182C22×C32C2×D811yescharacteristic
183C2×C3×D3—21no—
184C2×C3×D3—21no—
185C2×C3×D3Q3212yescomplemented
186C32×C4—42no—
187C32×C4#12011yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C3⋊Dic3—81no—
190C3×Dic3—21no—
191C3×Dic3—42no—
192C3×Dic3—81no—
193C22×Q8—61no—
194C2×Q16—31no—
195C2×Q16—61no—
196C2×Q16—62no—
197C2×Q16—62no—
198C2×Q16—91no—
199C2×Q16D3211yescharacteristic
200C22×C8—31no—
201C22⋊Q8—181no—
202Q32—182no—
203Q32—182no—
204C2×C16—31no—
205C2×C16—91no—
206#107—31no—
207#103—181no—
208C23×C3—31no—
209C22×D3#21311yescharacteristic
210C3×Q8—22no—
211C3×Q8—22no—
212C3×Q8—42no—
213C3×Q8—41no—
214C3×Q8—41no—
215C3×Q8—62no—
216C3×Q8—81no—
217C3×Q8—124no—
218C3×Q8—121no—
219C2×C3×C4—21no—
220C2×C3×C4—31no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—61no—
224C2×C3×C4—61no—
225C2×C3×C4—81no—
226C2×C3×C4—124no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×Dic3—41no—
232C2×Dic3—41no—
233C2×Dic3—121no—
234C2×Dic3—121no—
235C2×Dic3—241no—
236C2×Dic3#21311yescharacteristic
237C4×D3—21no—
238C4×D3—21no—
239C4×D3—44no—
240Dic6—22no—
241Dic6—44no—
242Dic6—41no—
243Dic6—122no—
244Dic6—121no—
245Dic6—121no—
246Dic6—121no—
247Dic6—121no—
248Dic6—241no—
249C3×C8—21no—
250C3×C8—21no—
251C3×C8—61no—
252C3×C8C2×D1211yescharacteristic
253C3×C8D3×D411yescharacteristic
254C3×C8C2×#6711yescharacteristic
255C3×C8C2×#6711yescharacteristic
256C3⋊C8—21no—
257C2×C32#44711yescharacteristic
258C2×C32C2×Q3211yescharacteristic
259C2×C32#51011yescharacteristic
260C3×D3—22no—
261C2×Q8—21no—
262C2×Q8—64no—
263C2×Q8—61no—
264C2×Q8—121no—
265C2×Q8—122no—
266C2×Q8—181no—
267C22×C4—31no—
268C22×C4—121no—
269Q16—21no—
270Q16—32no—
271Q16—64no—
272Q16—61no—
273Q16—181no—
274Q16—181no—
275Q16#62612yes—
276C2×C8—31no—
277C2×C8—61no—
278C2×C8—61no—
279C2×C8C2×D3211yescharacteristic
280C4⋊C4—61no—
281C4⋊C4—361no—
282C22⋊C4—361no—
283C16—61no—
284C16—181no—
285C22×C3—21no—
286C22×C3—32no—
287C22×C3—61no—
288C22×C3—61no—
289C22×C3D3×D811yescharacteristic
290C22×C3C2×#21311yescharacteristic
291C2×D3—21no—
292C2×D3—21no—
293C2×D3#82912yescomplemented
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—42no—
297C3×C4—42no—
298C3×C4—61no—
299C3×C4—82no—
300C3×C4—122no—
301C3×C4—241no—
302C3×C4#88211yescharacteristic
303C3×C4#91411yescharacteristic
304C3×C4#93211yescharacteristic
305C3×C4#95311yescharacteristic
306Dic3—21no—
307Dic3—42no—
308Dic3—81no—
309Dic3—242no—
310Dic3—241no—
311Dic3—241no—
312C32#218811yescharacteristic, complemented, Sylow
313C23—31no—
314Q8—22no—
315Q8—41no—
316Q8—62no—
317Q8—124no—
318Q8—121no—
319Q8—361no—
320Q8—361no—
321C2×C4—31no—
322C2×C4—41no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—124no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4—361no—
329C2×C4D3×#6711yescharacteristic
330C8—61no—
331C8C2×#62611yescharacteristic
332C8D3×#6711yescharacteristic
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—62no—
337C2×C3#477311yescharacteristic
338C2×C3#491511yescharacteristic
339C2×C3D3×Q3211yescharacteristic
340C2×C3#517911yescharacteristic
341C2×C3C2×#82911yescharacteristic
342C2×C3#521711yescharacteristic
343D3—22no—
344C22—32no—
345C22—61no—
346C22—61no—
347C22D3×#21311yescharacteristic
348C4—42no—
349C4—61no—
350C4—122no—
351C4—241no—
352C4—721no—
353C4#6393411yescharacteristic
354C4#6397711yescharacteristic
355C3—21no—
356C3#6922511yescharacteristic, complemented
357C3#7206411yescharacteristic, complemented
358C2—62no—
359C2D3×#82911yescharacteristic
360C2#1059104511yescharacteristic
361C2#1059144811yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC22×C3×D3D8
hypercenterC2×Q16D32
hypocenterC32#2188
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#63656C2semidirect
4. C2×#63551C2semidirect
5. C3×#4564C2semidirect
6. #10589117C2semidirect
36. #4564D3semidirect
185. C2×C3×D3Q32semidirect
293. C2×D3#829semidirect
312. C32#2188semidirect
356. C3#69225semidirect
357. C3#72064semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
C2×#636562
#105908522
C2×#635512
C3×#45642
#105891172
(C2×D3)⋊(C3⋊C16)2
#720643
#692253