Finite Group Databasebeta

← #11798098

Subgroups — #11798098

Order 1152.

497 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 497 conjugacy classes of subgroups — too many to draw. Only its 86 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×D3×Dic12C211yesmaximal, characteristic, complemented
2C2×#63627C211yesmaximal, characteristic, complemented
3#10590832C211yesmaximal, characteristic
4C2×#63549C211yesmaximal, characteristic, complemented
5C3×(C2×D3)⋊C16C211yesmaximal, characteristic, complemented
6C3×#4503C211yesmaximal, characteristic, complemented
7#10589119C211yesmaximal, characteristic, complemented
8#69223—31nomaximal
9#69112—31nomaximal
10C2×D3×Dic6—21no—
11C2×#3746C2211yescharacteristic
12C2×#3745C2211yescharacteristic
13C2×C3×Dic12C2211yescharacteristic
14C2×C3×D3×C8C2211yescharacteristic
15#63909—21no—
16C2×#3719—21no—
17D3×Dic12—22no—
18D3×Dic12—22no—
19C2×C32×C16C2211yescharacteristic
20#63627—22no—
21C3×#818C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23#63564—21no—
24#63549—22no—
25C2×D3×Q16—31no—
26C22×Dic12—31no—
27C2×#828—31no—
28#5115—31no—
29C2×#800—31no—
30C2×#800—31no—
31C2×#800—31no—
32C2×#800—61no—
33#4883—31no—
34C3×#358—31no—
35C3×C22⋊C16—31no—
36(C2×D3)⋊C16D311yescharacteristic, complemented
37#4503—31no—
38#4503D311yescharacteristic, complemented
39#4492—31no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×#634—21no—
42C2×C3×C4×D3D411yescharacteristic
43C2×C3×Dic6—21no—
44C2×#627—41no—
45C2×#626—41no—
46C2×D3×Dic3—41no—
47D3×Dic6—24no—
48D3×Dic6—42no—
49C2×C32×C8C2311yescharacteristic
50#3746—21no—
51#3746D412yescomplemented
52#3745—21no—
53#3745—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C3×Dic12—21no—
57C3×Dic12D412yescomplemented
58C3×D3×C8—21no—
59C3×D3×C8—21no—
60#3722—41no—
61#3719—24no—
62C32×C16—21no—
63C3×C3⋊C16—21no—
64#2185—91noSylow
65C2×D3×Q8—61no—
66C22×Dic6—61no—
67C2×C3×Q16—31no—
68C22×C3×C8—31no—
69C2×#216—61no—
70#930—61no—
71D3×Q16—62no—
72D3×Q16—62no—
73C2×Dic12—31no—
74C2×Dic12—31no—
75C2×Dic12—61no—
76C2×Dic12—62no—
77C2×Dic12—61no—
78C2×Dic12—62no—
79C2×Dic12C2×D311yescharacteristic
80C2×D24—31no—
81C2×D24—31no—
82C2×D24—61no—
83C2×D3×C8C2×D311yescharacteristic
84#895—61no—
85C2×C3×C16—21no—
86C2×C3×C16—31no—
87C2×C3×C16C2×D311yescharacteristic
88C2×C3×C16C2×D311yescharacteristic
89C3×#107—31no—
90#828—62no—
91#821—61no—
92#818C2×D311yescharacteristic
93C2×C3⋊C16C2×D311yescharacteristic
94#809—61no—
95#800—62no—
96#800—62no—
97#800—64no—
98#800—62no—
99C22×C3⋊D3—41no—
100C22×C3×D3D811yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C3⋊Dic3—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105#634—22no—
106#634—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3D811yescharacteristic
110C3×C4×D3—21no—
111C3×C4×D3—21no—
112C3×Dic6—22no—
113C3×Dic6—41no—
114#627—44no—
115#626—82no—
116D3×Dic3—44no—
117C32×C8C2×D411yescharacteristic
118C32×C8C2×D411yescharacteristic
119C3×C3⋊C8—21no—
120C22×Q16—91no—
121C2×SD32—91no—
122C2×SD32—91no—
123#466—91no—
124#358—31no—
125#358—91no—
126C22⋊C16—31no—
127C2×C3×Q8—61no—
128C22×C3×C4—31no—
129C2×#67—121no—
130C22×Dic3—121no—
131D3×Q8—64no—
132D3×Q8—122no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—121no—
136C2×D12—121no—
137C2×C4×D3—121no—
138C2×C4×D3D1211yescharacteristic
139C2×Dic6—21no—
140C2×Dic6—64no—
141C2×Dic6—61no—
142C2×Dic6—61no—
143C2×Dic6—121no—
144C2×Dic6—122no—
145C2×Dic6—121no—
146C2×Dic6—121no—
147C3×Q16—32no—
148C3×Q16—61no—
149C2×C3×C8—21no—
150C2×C3×C8—31no—
151C2×C3×C8—61no—
152C2×C3×C8—61no—
153C2×C3×C8C22×D311yescharacteristic
154C2×C3×C8C22×D311yescharacteristic
155C3×C4⋊C4—61no—
156#216—64no—
157(C2×D3)⋊C4—121no—
158(C2×D3)⋊C4—121no—
159C4⋊Dic3—21no—
160C2×C3⋊C8D1211yescharacteristic
161Dic12—21no—
162Dic12—32no—
163Dic12—32no—
164Dic12—62no—
165Dic12—64no—
166Dic12—61no—
167Dic12—61no—
168Dic12—121no—
169Dic12D1212yescomplemented
170D24—62no—
171D24—61no—
172D24—61no—
173D24—61no—
174D24—61no—
175D24—121no—
176D3×C8—21no—
177D3×C8—21no—
178C3×C16—22no—
179C3×C16—21no—
180C3×C16—21no—
181C3×C16—61no—
182C3⋊C16—21no—
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#12011yescharacteristic
191C32×C4AGL(1,ℤ/8)11yescharacteristic
192C3⋊Dic3—42no—
193C3×Dic3—21no—
194C3×Dic3—42no—
195C3×Dic3—81no—
196C22×Q8—181no—
197C2×Q16—31no—
198C2×Q16—91no—
199C2×Q16—181no—
200C2×Q16—182no—
201C2×Q16—182no—
202C2×D8—91no—
203C22×C8—31no—
204#121—181no—
205SD32—182no—
206SD32—182no—
207C2×C16—31no—
208C2×C16D3211yescharacteristic
209#107—31no—
210#102—181no—
211C23×C3—31no—
212C22×D3—121no—
213C22×D3—121no—
214C22×D3—241no—
215C22×D3D2411yescharacteristic
216C3×Q8—62no—
217C3×Q8—121no—
218C2×C3×C4—21no—
219C2×C3×C4—31no—
220C2×C3×C4—61no—
221C2×C3×C4—61no—
222C2×C3×C4—121no—
223C2×C3×C4—121no—
224C2×C3×C4C2×D1211yescharacteristic
225C2×C3×C4D3×D411yescharacteristic
226#67—242no—
227C2×Dic3—41no—
228C2×Dic3—41no—
229C2×Dic3—124no—
230C2×Dic3—121no—
231C2×Dic3—121no—
232C2×Dic3—241no—
233C2×Dic3D2411yescharacteristic
234D12—122no—
235D12—121no—
236D12—121no—
237D12—121no—
238D12—121no—
239D12—241no—
240D12—242no—
241C4×D3—21no—
242C4×D3—21no—
243C4×D3—124no—
244Dic6—22no—
245Dic6—41no—
246Dic6—62no—
247Dic6—62no—
248Dic6—122no—
249Dic6—124no—
250Dic6—124no—
251Dic6—121no—
252Dic6—121no—
253Dic6—241no—
254C3×C8—21no—
255C3×C8—21no—
256C3×C8—61no—
257C3×C8C2×D1211yescharacteristic
258C3×C8D3×D411yescharacteristic
259C3×C8D3×D411yescharacteristic
260C3×C8D3×D411yescharacteristic
261C3⋊C8—21no—
262C2×C32#44711yescharacteristic
263C2×C32C2×SD3211yescharacteristic
264C2×C32#51011yescharacteristic
265C3⋊D3—161no—
266C3×D3—22no—
267C2×Q8—61no—
268C2×Q8—184no—
269C2×Q8—181no—
270C2×Q8—361no—
271C2×Q8—362no—
272C2×D4—181no—
273C2×D4—361no—
274C22×C4—31no—
275C22×C4—361no—
276Q16—32no—
277Q16—61no—
278Q16—92no—
279Q16—184no—
280Q16—181no—
281D8—181no—
282D8—181no—
283C2×C8—31no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8C2×D3211yescharacteristic
287C4⋊C4—61no—
288C22⋊C4—361no—
289C16—21no—
290C16—61no—
291C22×C3—21no—
292C22×C3—32no—
293C22×C3—61no—
294C22×C3—61no—
295C22×C3C2×D2411yescharacteristic
296C22×C3D3×D811yescharacteristic
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#80012yescomplemented
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—61no—
312C3×C4—122no—
313C3×C4—241no—
314C3×C4#88211yescharacteristic
315C3×C4#88211yescharacteristic
316C3×C4#90811yescharacteristic
317C3×C4#91411yescharacteristic
318Dic3—21no—
319Dic3—42no—
320Dic3—81no—
321Dic3—122no—
322Dic3—122no—
323Dic3—242no—
324C32#218511yescharacteristic, complemented, Sylow
325C23—31no—
326C23—361no—
327Q8—62no—
328Q8—121no—
329Q8—182no—
330Q8—364no—
331Q8—361no—
332D4—361no—
333D4—361no—
334D4—722no—
335C2×C4—31no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—121no—
339C2×C4—121no—
340C2×C4—364no—
341C2×C4—361no—
342C2×C4D3×D1211yescharacteristic
343C8—61no—
344C8D3×D1211yescharacteristic
345C8#381111yescharacteristic
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—62no—
350C2×C3#473211yescharacteristic
351C2×C3#477311yescharacteristic
352C2×C3C2×#80011yescharacteristic
353C2×C3#490911yescharacteristic
354C2×C3D3×SD3211yescharacteristic
355C2×C3#491811yescharacteristic
356D3—22no—
357D3—482no—
358D3—481no—
359D3—481no—
360C22—32no—
361C22—61no—
362C22—61no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22D3×D2411yescharacteristic
367C4—61no—
368C4—122no—
369C4—241no—
370C4—362no—
371C4#6379411yescharacteristic
372C4#6392311yescharacteristic
373C3—21no—
374C3#6911211yescharacteristic, complemented
375C3#6922311yescharacteristic, complemented
376C2—62no—
377C2—1441no—
378C2D3×#80011yescharacteristic
379C2#1059023811yescharacteristic
380C2#1059094711yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
prime radical#10590832C2
hypercenterC2×C16D32
hypocenterC32#2185
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×D3×Dic12C2semidirect
2. C2×#63627C2semidirect
4. C2×#63549C2semidirect
5. C3×(C2×D3)⋊C16C2semidirect
6. C3×#4503C2semidirect
7. #10589119C2semidirect
36. (C2×D3)⋊C16D3semidirect
38. #4503D3semidirect
51. #3746D4semidirect
57. C3×Dic12D4semidirect
169. Dic12D12semidirect
189. C2×C3×D3SD32semidirect
308. C2×D3#800semidirect
324. C32#2185semidirect
374. C3#69112semidirect
375. C3#69223semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
C2×#636272
#105908322
C2×#635492
C3×(C2×D3)⋊C162
C3×#45032
#105891192
#692233
#691123