Finite Group Databasebeta

← #11798094

Subgroups — #11798094

Order 1152.

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

normal subgroups only

This group has 481 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, complemented
2C2×C3×#828C211yesmaximal, characteristic, complemented
3#10590831C211yesmaximal, characteristic
4C2×#63547C211yesmaximal, characteristic, complemented
5#10589430C211yesmaximal, characteristic, complemented
6#10589118C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
8#72063—31nomaximal
9#71483—31nomaximal
10C2×C3×D3×Q8—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×C3×#216—21no—
13C3×D3×Q16—22no—
14C3×D3×Q16—22no—
15C2×C3×Dic12C2211yescharacteristic
16C2×C3×D24C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18#63908—21no—
19#63645C2211yescharacteristic
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C3×#828—22no—
22C2×C3×C3⋊C16C2211yescharacteristic
23#63563—21no—
24#63547—22no—
25C22×C3×Q16—31no—
26C2×D3×Q16D311yescharacteristic, complemented
27C2×C3×SD32—31no—
28C2×#828—31no—
29C2×#828D311yescharacteristic, complemented
30#5157—31no—
31C2×#827—31no—
32#5115—31no—
33#4564—31no—
34#4564—31no—
35#4564—31no—
36#4564—61no—
37#4549—31no—
38(C2×D3)⋊C16—31no—
39#4503—31no—
40C2×C32×Q8—21no—
41C3×D3×Q8—24no—
42C3×D3×Q8—42no—
43C2×C3×D12—21no—
44C2×C3×C4×D3—41no—
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C3×Dic6—41no—
48C2×#625—41no—
49C32×Q16—21no—
50C32×Q16D412yescomplemented
51C2×C32×C8C2311yescharacteristic
52C4⋊(C3⋊Dic3)—21no—
53C3×#216—24no—
54C2×C3×C3⋊C8D411yescharacteristic
55C3×Dic12—21no—
56C3×Dic12D412yescomplemented
57C3×D24—21no—
58C3×D24—21no—
59C3×D3×C8—21no—
60C3×D3×C8—21no—
61(C2×D3)⋊Dic3—41no—
62C3⋊(C3⋊C16)—21no—
63C3×C3⋊C16—21no—
64#2185—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
74C2×C3×D8—31no—
75C22×C3×C8—31no—
76C2×#216—21no—
77#938—61no—
78#930—61no—
79D3×Q16—22no—
80D3×Q16—22no—
81C2×Dic12C2×D311yescharacteristic
82C2×D24C2×D311yescharacteristic
83C2×D3×C8C2×D311yescharacteristic
84C3×SD32—62no—
85C2×C3×C16—31no—
86#832—61no—
87#828—22no—
88#828—62no—
89#827—62no—
90#821—61no—
91#818—31no—
92#818—31no—
93#818—61no—
94C2×C3⋊C16—31no—
95C2×C3⋊C16—31no—
96C2×C3⋊C16—61no—
97C2×C3⋊C16C2×D311yescharacteristic
98C22×C3×D3—41no—
99C22×C3×D3D811yescharacteristic
100C32×Q8—22no—
101C32×Q8—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C3⋊Dic3—41no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3D811yescharacteristic
107C3×D12—41no—
108C3×D12—41no—
109C3×C4×D3—21no—
110C3×C4×D3—21no—
111C3×C4×D3—44no—
112C3×Dic6—22no—
113C3×Dic6—44no—
114C3×Dic6—41no—
115#625—82no—
116C32×C8C2×D411yescharacteristic
117C32×C8C2×D411yescharacteristic
118C3×C3⋊C8—21no—
119C22×Q16—31no—
120C2×SD32—31no—
121C2×SD32—91no—
122#466—91no—
123#358—91no—
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—
133C2×C3×D4—61no—
134C22×C3×C4—31no—
135C22×C3×C4—121no—
136C2×#67—121no—
137C2×#67—121no—
138D3×Q8—24no—
139D3×Q8—42no—
140C2×D12—21no—
141C2×C4×D3—41no—
142C2×C4×D3#6711yescharacteristic
143C2×Dic6—21no—
144C2×Dic6—41no—
145C3×Q16—21no—
146C3×Q16—21no—
147C3×Q16—22no—
148C3×Q16—32no—
149C3×Q16—41no—
150C3×Q16—64no—
151C3×Q16—61no—
152C3×Q16#6712yescomplemented
153C3×Q16#6712yescomplemented
154C3×D8—61no—
155C3×D8—61no—
156C2×C3×C8—21no—
157C2×C3×C8—31no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8C22×D311yescharacteristic
161C2×C3×C8C22×D311yescharacteristic
162#217—121no—
163#216—24no—
164(C2×D3)⋊C4—121no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—121no—
168C2×C3⋊C8#6711yescharacteristic
169Dic12—21no—
170Dic12#6712yescomplemented
171D24—21no—
172D24—21no—
173D3×C8—21no—
174D3×C8—21no—
175C3×C16—61no—
176C3⋊C16—21no—
177C3⋊C16—61no—
178C3⋊C16—61no—
179C3⋊C16—121no—
180C22×C32C2×D811yescharacteristic
181C2×C3×D3—21no—
182C2×C3×D3—21no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C2×C3×D3SD3212yescomplemented
187C32×C4—42no—
188C32×C4#12011yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C3⋊Dic3—81no—
191C3×Dic3—21no—
192C3×Dic3—42no—
193C22×Q8—61no—
194C2×Q16—31no—
195C2×Q16—61no—
196C2×Q16—62no—
197C2×Q16—62no—
198C2×Q16D3211yescharacteristic
199C2×D8—31no—
200C22×C8—31no—
201#121—181no—
202SD32—62no—
203SD32—182no—
204C2×C16—31no—
205C2×C16—91no—
206#107—91no—
207#102—181no—
208C23×C3—31no—
209C23×C3—121no—
210C22×D3—41no—
211C22×D3#21311yescharacteristic
212C3×Q8—22no—
213C3×Q8—22no—
214C3×Q8—42no—
215C3×Q8—41no—
216C3×Q8—41no—
217C3×Q8—62no—
218C3×Q8—81no—
219C3×Q8—124no—
220C3×Q8—121no—
221C3×D4—121no—
222C3×D4—121no—
223C2×C3×C4—21no—
224C2×C3×C4—31no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—81no—
230C2×C3×C4—124no—
231C2×C3×C4—121no—
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234#67—242no—
235#67—242no—
236C2×Dic3—41no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239C2×Dic3—241no—
240C2×Dic3#21311yescharacteristic
241D12—41no—
242D12—41no—
243C4×D3—21no—
244C4×D3—21no—
245C4×D3—44no—
246Dic6—22no—
247Dic6—44no—
248Dic6—41no—
249C3×C8—21no—
250C3×C8—21no—
251C3×C8—61no—
252C3×C8D3×D411yescharacteristic
253C3×C8C2×#6711yescharacteristic
254C3×C8C2×#6711yescharacteristic
255C3×C8C2×#6711yescharacteristic
256C3⋊C8—21no—
257C2×C32#44711yescharacteristic
258C2×C32C2×SD3211yescharacteristic
259C2×C32#51011yescharacteristic
260C3×D3—22no—
261C3×D3—161no—
262C2×Q8—21no—
263C2×Q8—64no—
264C2×Q8—61no—
265C2×Q8—121no—
266C2×Q8—122no—
267C2×D4—61no—
268C2×D4—361no—
269C22×C4—31no—
270C22×C4—121no—
271Q16—21no—
272Q16—32no—
273Q16—64no—
274Q16—61no—
275Q16#62512yescomplemented
276D8—61no—
277D8—61no—
278C2×C8—31no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8C2×D3211yescharacteristic
282C4⋊C4—181no—
283C22⋊C4—361no—
284C16—61no—
285C16—181no—
286C22×C3—21no—
287C22×C3—32no—
288C22×C3—61no—
289C22×C3—61no—
290C22×C3—241no—
291C22×C3—241no—
292C22×C3—241no—
293C22×C3D3×D811yescharacteristic
294C22×C3C2×#21311yescharacteristic
295C2×D3—21no—
296C2×D3—21no—
297C2×D3—81no—
298C2×D3—81no—
299C2×D3—81no—
300C2×D3#82812yescomplemented
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—42no—
304C3×C4—42no—
305C3×C4—61no—
306C3×C4—82no—
307C3×C4—122no—
308C3×C4#91111yescharacteristic
309C3×C4#93211yescharacteristic
310C3×C4#93711yescharacteristic
311C3×C4#95311yescharacteristic
312Dic3—21no—
313Dic3—42no—
314Dic3—241no—
315Dic3—241no—
316Dic3—481no—
317C32#218511yescharacteristic, complemented, Sylow
318C23—31no—
319C23—121no—
320Q8—22no—
321Q8—41no—
322Q8—62no—
323Q8—124no—
324Q8—121no—
325D4—121no—
326D4—121no—
327D4—722no—
328C2×C4—31no—
329C2×C4—41no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—124no—
333C2×C4—121no—
334C2×C4—361no—
335C2×C4D3×#6711yescharacteristic
336C8—61no—
337C8C2×#62511yescharacteristic
338C8D3×#6711yescharacteristic
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—62no—
343C2×C3—481no—
344C2×C3D3×SD3211yescharacteristic
345C2×C3#491511yescharacteristic
346C2×C3#515611yescharacteristic
347C2×C3C2×#82811yescharacteristic
348C2×C3#517911yescharacteristic
349C2×C3#521711yescharacteristic
350D3—22no—
351D3—161no—
352C22—32no—
353C22—61no—
354C22—61no—
355C22—241no—
356C22—241no—
357C22—241no—
358C22D3×#21311yescharacteristic
359C4—42no—
360C4—61no—
361C4—122no—
362C4—721no—
363C4#6393211yescharacteristic
364C4#6397611yescharacteristic
365C3—21no—
366C3#7148311yescharacteristic, complemented
367C3#7206311yescharacteristic, complemented
368C2—62no—
369C2—481no—
370C2D3×#82811yescharacteristic
371C2#1059104511yescharacteristic
372C2#1059144711yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radical#10590831C2
hypercenterC2×Q16D32
hypocenterC32#2185
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
1. C2×C3×D3×Q16C2semidirect
2. C2×C3×#828C2semidirect
4. C2×#63547C2semidirect
5. #10589430C2semidirect
6. #10589118C2semidirect
7. (C2×D3)⋊(C3⋊C16)C2semidirect
26. C2×D3×Q16D3semidirect
29. C2×#828D3semidirect
50. C32×Q16D4semidirect
56. C3×Dic12D4semidirect
152. C3×Q16#67semidirect
153. C3×Q16#67semidirect
170. Dic12#67semidirect
186. C2×C3×D3SD32semidirect
275. Q16#625semidirect
300. C2×D3#828semidirect
317. C32#2185semidirect
366. C3#71483semidirect
367. C3#72063semidirect

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×C3×#8282
#105908312
C2×#635472
#105894302
#105891182
(C2×D3)⋊(C3⋊C16)2
#720633
#714833