Finite Group Databasebeta

← #11798092

Subgroups — #11798092

Order 1152.

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

normal subgroups only

This group has 497 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×#63655C211yesmaximal, characteristic, complemented
3#10590832C211yesmaximal, characteristic
4C2×#63549C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7(C2×D3)⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
8#72063—31nomaximal
9#69223—31nomaximal
10C2×C3×D3×Q8—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×#3745C2211yescharacteristic
13C2×C3×#216—21no—
14C3×D3×Q16—22no—
15C3×D3×Q16—22no—
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18#63909—21no—
19#63655—22no—
20C2×C3⋊(C3⋊C16)C2211yescharacteristic
21C3×#818C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23#63564—21no—
24#63549—22no—
25C22×C3×Q16—31no—
26C2×D3×Q16D311yescharacteristic, complemented
27C2×#828—31no—
28C2×#828—31no—
29C2×#828—31no—
30C2×#828—61no—
31#5115—31no—
32C2×#800—31no—
33#4883—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×C4⋊(C3⋊D3)—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—
48C2×#626—41no—
49C32×Q16—21no—
50C32×Q16D412yescomplemented
51C2×C32×C8C2311yescharacteristic
52#3745—21no—
53#3745—21no—
54C3×#216—24no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C3×Dic12—21no—
58C3×Dic12D412yescomplemented
59C3×D3×C8—21no—
60C3×D3×C8—21no—
61#3722—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
74C22×C3×C8—31no—
75C2×#216—21no—
76#930—61no—
77D3×Q16—22no—
78D3×Q16—22no—
79C2×Dic12C2×D311yescharacteristic
80C2×D24—31no—
81C2×D24—31no—
82C2×D24—61no—
83C2×D3×C8C2×D311yescharacteristic
84#895—61no—
85C2×C3×C16—31no—
86C3×#107—31no—
87#828—62no—
88#828—64no—
89#828—62no—
90#828—62no—
91#821—61no—
92#818C2×D311yescharacteristic
93C2×C3⋊C16—31no—
94C2×C3⋊C16—31no—
95C2×C3⋊C16—61no—
96C2×C3⋊C16C2×D311yescharacteristic
97#809—61no—
98#800—62no—
99C22×C3⋊D3—41no—
100C22×C3×D3D811yescharacteristic
101C32×Q8—22no—
102C32×Q8—41no—
103C2×C32×C4—41no—
104C2×C32×C4C2×D411yescharacteristic
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—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—
116#626—82no—
117C32×C8C2×D411yescharacteristic
118C32×C8C2×D411yescharacteristic
119C3×C3⋊C8—21no—
120C22×Q16—31no—
121C2×SD32—91no—
122C2×SD32—91no—
123#466—91no—
124#358—31no—
125#358—91no—
126C22⋊C16—91no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×Q8—41no—
130C2×C3×Q8—64no—
131C2×C3×Q8—61no—
132C2×C3×Q8—121no—
133C2×C3×Q8—122no—
134C22×C3×C4—31no—
135C22×C3×C4—121no—
136C2×#67—121no—
137D3×Q8—24no—
138D3×Q8—42no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—121no—
142C2×D12—121no—
143C2×C4×D3—41no—
144C2×C4×D3#6711yescharacteristic
145C2×Dic6—21no—
146C2×Dic6—41no—
147C3×Q16—21no—
148C3×Q16—21no—
149C3×Q16—22no—
150C3×Q16—32no—
151C3×Q16—41no—
152C3×Q16—64no—
153C3×Q16—61no—
154C3×Q16D1212yescomplemented
155C3×Q16#6712yescomplemented
156C2×C3×C8—21no—
157C2×C3×C8—31no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C2×C3×C8C22×D311yescharacteristic
161C2×C3×C8C22×D311yescharacteristic
162C3×C4⋊C4—61no—
163#216—24no—
164(C2×D3)⋊C4—121no—
165(C2×D3)⋊C4—121no—
166C4⋊Dic3—21no—
167C2×C3⋊C8#6711yescharacteristic
168Dic12—21no—
169Dic12#6712yescomplemented
170D24—62no—
171D24—61no—
172D24—61no—
173D24—61no—
174D24—61no—
175D24—121no—
176D3×C8—21no—
177D3×C8—21no—
178C3×C16—61no—
179C3⋊C16—21no—
180C3⋊C16—62no—
181C3⋊C16—61no—
182C3⋊C16—61no—
183C22×C32C2×D811yescharacteristic
184C2×C3⋊D3—81no—
185C2×C3⋊D3—81no—
186C2×C3⋊D3—81no—
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3SD3212yescomplemented
190C32×C4—42no—
191C32×C4#12011yescharacteristic
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C3×Dic3—21no—
194C3×Dic3—42no—
195C3×Dic3—81no—
196C22×Q8—61no—
197C2×Q16—31no—
198C2×Q16—61no—
199C2×Q16—62no—
200C2×Q16—62no—
201C2×Q16D3211yescharacteristic
202C2×D8—91no—
203C22×C8—31no—
204#121—181no—
205SD32—182no—
206SD32—182no—
207C2×C16—31no—
208C2×C16—91no—
209#107—31no—
210#102—181no—
211C23×C3—31no—
212C22×D3—121no—
213C22×D3—121no—
214C22×D3—241no—
215C22×D3#21311yescharacteristic
216C3×Q8—22no—
217C3×Q8—22no—
218C3×Q8—42no—
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—62no—
222C3×Q8—81no—
223C3×Q8—124no—
224C3×Q8—121no—
225C2×C3×C4—21no—
226C2×C3×C4—31no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—81no—
232C2×C3×C4—124no—
233C2×C3×C4—121no—
234C2×C3×C4—121no—
235C2×C3×C4D3×D411yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237#67—242no—
238C2×Dic3—41no—
239C2×Dic3—41no—
240C2×Dic3#21311yescharacteristic
241D12—122no—
242D12—121no—
243D12—121no—
244D12—121no—
245D12—121no—
246D12—241no—
247D12—242no—
248C4×D3—21no—
249C4×D3—21no—
250C4×D3—44no—
251Dic6—22no—
252Dic6—44no—
253Dic6—41no—
254C3×C8—21no—
255C3×C8—21no—
256C3×C8—61no—
257C3×C8C2×D1211yescharacteristic
258C3×C8D3×D411yescharacteristic
259C3×C8C2×#6711yescharacteristic
260C3×C8C2×#6711yescharacteristic
261C3⋊C8—21no—
262C2×C32#44711yescharacteristic
263C2×C32C2×SD3211yescharacteristic
264C2×C32#51011yescharacteristic
265C3⋊D3—161no—
266C3×D3—22no—
267C2×Q8—21no—
268C2×Q8—64no—
269C2×Q8—61no—
270C2×Q8—121no—
271C2×Q8—122no—
272C2×D4—181no—
273C2×D4—361no—
274C22×C4—31no—
275C22×C4—121no—
276Q16—21no—
277Q16—32no—
278Q16—64no—
279Q16—61no—
280Q16#62612yescomplemented
281D8—181no—
282D8—181no—
283C2×C8—31no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8C2×D3211yescharacteristic
287C4⋊C4—61no—
288C22⋊C4—361no—
289C16—61no—
290C16—181no—
291C22×C3—21no—
292C22×C3—32no—
293C22×C3—61no—
294C22×C3—61no—
295C22×C3D3×D811yescharacteristic
296C22×C3C2×#21311yescharacteristic
297C2×D3—21no—
298C2×D3—21no—
299C2×D3—242no—
300C2×D3—241no—
301C2×D3—241no—
302C2×D3—241no—
303C2×D3—241no—
304C2×D3—241no—
305C2×D3—241no—
306C2×D3—481no—
307C2×D3—481no—
308C2×D3#82812yescomplemented
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—42no—
312C3×C4—42no—
313C3×C4—61no—
314C3×C4—82no—
315C3×C4—122no—
316C3×C4—241no—
317C3×C4#88211yescharacteristic
318C3×C4#91411yescharacteristic
319C3×C4#93211yescharacteristic
320C3×C4#95311yescharacteristic
321Dic3—21no—
322Dic3—42no—
323Dic3—81no—
324C32#218511yescharacteristic, complemented, Sylow
325C23—31no—
326C23—361no—
327Q8—22no—
328Q8—41no—
329Q8—62no—
330Q8—124no—
331Q8—121no—
332D4—361no—
333D4—361no—
334D4—722no—
335C2×C4—31no—
336C2×C4—41no—
337C2×C4—61no—
338C2×C4—61no—
339C2×C4—124no—
340C2×C4—121no—
341C2×C4—121no—
342C2×C4D3×#6711yescharacteristic
343C8—61no—
344C8C2×#62611yescharacteristic
345C8D3×#6711yescharacteristic
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—62no—
350C2×C3#477311yescharacteristic
351C2×C3D3×SD3211yescharacteristic
352C2×C3#491811yescharacteristic
353C2×C3C2×#82811yescharacteristic
354C2×C3#517911yescharacteristic
355C2×C3#521711yescharacteristic
356D3—22no—
357D3—482no—
358D3—481no—
359D3—481no—
360C22—32no—
361C22—61no—
362C22—61no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22D3×#21311yescharacteristic
367C4—42no—
368C4—61no—
369C4—122no—
370C4—241no—
371C4#6393411yescharacteristic
372C4#6397711yescharacteristic
373C3—21no—
374C3#6922311yescharacteristic, complemented
375C3#7206311yescharacteristic, complemented
376C2—62no—
377C2—1441no—
378C2D3×#82811yescharacteristic
379C2#1059104711yescharacteristic
380C2#1059144811yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radical#10590832C2
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×#63655C2semidirect
4. C2×#63549C2semidirect
5. C3×#4564C2semidirect
6. #10589117C2semidirect
7. (C2×D3)⋊(C3⋊C16)C2semidirect
26. C2×D3×Q16D3semidirect
36. #4564D3semidirect
50. C32×Q16D4semidirect
58. C3×Dic12D4semidirect
154. C3×Q16D12semidirect
155. C3×Q16#67semidirect
169. Dic12#67semidirect
189. C2×C3×D3SD32semidirect
280. Q16#626semidirect
308. C2×D3#828semidirect
324. C32#2185semidirect
374. C3#69223semidirect
375. 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×#636552
#105908322
C2×#635492
C3×#45642
#105891172
(C2×D3)⋊(C3⋊C16)2
#720633
#692233