Finite Group Databasebeta

← #11787910

Subgroups — #11787910

Order 1152.

761 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 761 conjugacy classes of subgroups — too many to draw. Only its 164 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×#947C211yesmaximal, characteristic
2C3×#5812C211yesmaximal, characteristic, complemented
3C2×#63663C211yesmaximal, characteristic, complemented
4#10591085C212yesmaximal
5#10589161C212yesmaximal, complemented
6#71724—31nomaximal
7#71661—31nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×C3×D12C2211yescharacteristic
10C2×#3748C2212yes—
11C3×#947—22no—
12C3×#947C414yescomplemented
13C3×Q8×Dic3—24no—
14C2×C3×(C2×D3)⋊C4—22no—
15C3×#926—22no—
16C3×#926C2212yes—
17C2×C3×C4×Dic3C2211yescharacteristic
18#63663—22no—
19#63562—24no—
20C2×C3×#124—31no—
21C3×#519—31no—
22C2×#947D311yescharacteristic
23#5812D311yescharacteristic, complemented
24C2×#836—31no—
25C2×#836—31no—
26C2×#836—61no—
27#5215—32no—
28#5001—32no—
29#4532—32no—
30#4523—32no—
31C23×C3×D3—21no—
32C2×C32×Q8—22no—
33C2×C32×Q8—22no—
34C2×C32×Q8C2×C412yes—
35C2×C32×Q8D412yes—
36C22×C32×C4D412yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—21no—
39C2×C3×D12—22no—
40C2×C3×D12—22no—
41C2×C3×D12—21no—
42C2×C3×D12C2×C412yes—
43#3748—22no—
44#3748—22no—
45C2×C3⋊(C3⋊C8)—22no—
46C3×#217—22no—
47C3×(C2×D3)⋊C4—28no—
48C3×C4⋊Dic3—24no—
49C3×C4⋊Dic3D414yes—
50C3×C4×Dic3—24no—
51C3×C4×Dic3—21no—
52C3×C4×Dic3—22no—
53C3×C4×Dic3C2×C412yes—
54#1888—91noSylow
55C22×C3×Q8—21no—
56C22×C3×Q8C2×D311yescharacteristic
57C22×C3×Q8C2×D311yescharacteristic
58C22×C3×D4—31no—
59C22×D12C2×D311yescharacteristic
60C3×#124—34no—
61C3×#124—62no—
62C3×C4×Q8—64no—
63C3×#117—32no—
64C3×#117—62no—
65C2×C3×C22⋊C4—62no—
66C2×C3×C42—31no—
67#947—22no—
68#947Dic314yescomplemented
69Q8×Dic3—24no—
70C2×(C2×D3)⋊C4—22no—
71#926—22no—
72#926C2×D312yes—
73C2×C4×Dic3C2×D311yescharacteristic
74C2×#208—32no—
75C2×#208—32no—
76C2×#208—62no—
77#836—64no—
78#836—62no—
79#836—62no—
80#832—64no—
81#809—64no—
82C23×C32C2×D411yescharacteristic
83C22×C3×D3—22no—
84C22×C3×D3—44no—
85C22×C3×D3—41no—
86C22×C3×D3—41no—
87C32×Q8—24no—
88C32×Q8—24no—
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4C22⋊C414yes—
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4#4112yes—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—42no—
99C3×D12—24no—
100C3×D12—42no—
101C3⋊(C3⋊C8)—42no—
102C2×#124—31no—
103#519—31no—
104#418—92no—
105C2×#101—91no—
106#339—92no—
107C24×C3—61no—
108C23×D3—21no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—22no—
114C2×C3×Q8—22no—
115C2×C3×Q8—42no—
116C2×C3×Q8—42no—
117C2×C3×Q8C4×D312yes—
118C2×C3×Q8D1212yes—
119C2×C3×Q8C2×Dic312yes—
120C2×C3×Q8#6712yes—
121C2×C3×D4—32no—
122C2×C3×D4—61no—
123C2×C3×D4—62no—
124C2×C3×D4—62no—
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4—61no—
128C22×C3×C4#6712yes—
129C22×C3×C4#6712yes—
130C22×C3×C4C22×D311yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C22×Dic3—21no—
133C2×D12—22no—
134C2×D12—22no—
135C2×D12—21no—
136C2×D12C2×Dic312yes—
137C3×C4⋊C4—34no—
138C3×C4⋊C4—64no—
139C3×C22⋊C4—62no—
140C3×C22⋊C4—68no—
141C3×C42—32no—
142C3×C42—64no—
143C3×C42—61no—
144C3×C42—62no—
145#217—22no—
146(C2×D3)⋊C4—28no—
147C4⋊Dic3—24no—
148C4⋊Dic3#6714yes—
149C4×Dic3—24no—
150C4×Dic3—21no—
151C4×Dic3—22no—
152C4×Dic3C2×Dic312yes—
153#208—64no—
154#208—62no—
155#208—62no—
156#208—62no—
157#208—62no—
158#208—122no—
159C2×C3⋊C8—62no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—122no—
162C22×C32—22no—
163C22×C32C2×C22⋊C411yescharacteristic
164C22×C32#12011yescharacteristic
165C22×C32#12311yescharacteristic
166C2×C3×D3—44no—
167C2×C3×D3—42no—
168C2×C3×D3—82no—
169C2×C3×D3—82no—
170C32×C4—24no—
171C32×C4C4×D412yes—
172C32×C4#12112yes—
173C3×Dic3—42no—
174C3×Dic3—44no—
175C22×Q8D3211yescharacteristic
176C22×D4—31no—
177C2×M16—92no—
178#124—34no—
179#124—62no—
180C4×Q8—64no—
181#117—32no—
182#117—62no—
183C2×C22⋊C4—62no—
184C2×C42—31no—
185#102—184no—
186#101—182no—
187C23×C3—21no—
188C23×C3—62no—
189C23×C3—124no—
190C23×C3—121no—
191C23×C3—121no—
192C23×C3C2×#6711yescharacteristic
193C23×C3C2×#6711yescharacteristic
194C22×D3—22no—
195C22×D3—44no—
196C22×D3—41no—
197C22×D3—41no—
198C3×Q8—24no—
199C3×Q8—24no—
200C3×Q8—24no—
201C3×Q8—24no—
202C3×Q8—44no—
203C3×Q8—44no—
204C3×D4—64no—
205C3×D4—122no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—24no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—62no—
218C2×C3×C4—64no—
219C2×C3×C4—122no—
220C2×C3×C4(C2×D3)⋊C414yes—
221C2×C3×C4#21714yes—
222C2×C3×C4C2×C4×D311yescharacteristic
223C2×C3×C4C2×D1211yescharacteristic
224C2×C3×C4#23512yes—
225C2×C3×C4D3×D412yes—
226C2×C3×C4#23712yes—
227C2×C3×C4C22×Dic311yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×C3×C4C2×#6712yes—
230C2×Dic3—22no—
231C2×Dic3—24no—
232C2×Dic3—42no—
233D12—24no—
234D12—42no—
235C3⋊C8—124no—
236C3⋊C8—122no—
237C3⋊C8—122no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32#38611yescharacteristic
241C2×C32#45412yes—
242C3×D3—82no—
243C24—61no—
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8D3×Dic312yes—
247C2×Q8#62612yes—
248C2×D4—32no—
249C2×D4—62no—
250C2×D4—61no—
251C2×D4—62no—
252C22×C4—61no—
253C22×C4#62512yes—
254C22×C4C2×D3211yescharacteristic
255M16—182no—
256M16—182no—
257C2×C8—182no—
258C4⋊C4—34no—
259C4⋊C4—64no—
260C22⋊C4—62no—
261C22⋊C4—68no—
262C42—32no—
263C42—64no—
264C42—61no—
265C42—62no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—124no—
273C22×C3—122no—
274C22×C3—242no—
275C22×C3—242no—
276C22×C3C2×(C2×D3)⋊C411yescharacteristic
277C22×C3#92911yescharacteristic
278C22×C3#93511yescharacteristic
279C22×C3#93711yescharacteristic
280C22×C3C2×#21711yescharacteristic
281C22×C3#95311yescharacteristic
282C2×D3—44no—
283C2×D3—42no—
284C2×D3—82no—
285C2×D3—82no—
286C3×C4—24no—
287C3×C4—24no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—44no—
291C3×C4—122no—
292C3×C4—124no—
293C3×C4C4×#6712yes—
294C3×C4#93012yes—
295C3×C4D4×Dic312yes—
296C3×C4#93912yes—
297Dic3—42no—
298Dic3—44no—
299C32#188811yescharacteristic, complemented, Sylow
300C23—62no—
301C23—124no—
302C23—121no—
303C23—121no—
304C23C2×#62511yescharacteristic
305Q8—24no—
306Q8—24no—
307D4—64no—
308D4—122no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—62no—
312C2×C4—64no—
313C2×C4—122no—
314C2×C4(C2×D3)⋊Dic314yes—
315C2×C4C2×D3×Dic311yescharacteristic
316C2×C4#380412yes—
317C2×C4C2×#62611yescharacteristic
318C2×C4D3×#6712yes—
319C8—362no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—22no—
325C2×C3—21no—
326C2×C3—41no—
327C2×C3—41no—
328C2×C3—242no—
329C2×C3#506212yes—
330C2×C3#521311yescharacteristic
331C2×C3#522011yescharacteristic
332C2×C3#524512yes—
333D3—82no—
334C22—22no—
335C22—124no—
336C22—122no—
337C22—242no—
338C22—242no—
339C22C2×(C2×D3)⋊Dic311yescharacteristic
340C22#6396111yescharacteristic
341C22#6397611yescharacteristic
342C4—24no—
343C4—122no—
344C4—124no—
345C4Dic3×#6712yes—
346C4#6397812yes—
347C3—21no—
348C3#7166111yescharacteristic, complemented
349C3#7172411yescharacteristic, complemented
350C2—21no—
351C2—21no—
352C2—242no—
353C2#1059164512yes—
354C2#1059171011yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1888
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5812C2semidirect
3. C2×#63663C2semidirect
5. #10589161C2semidirect
12. C3×#947C4semidirect
23. #5812D3semidirect
68. #947Dic3semidirect
299. C32#1888semidirect
348. C3#71661semidirect
349. C3#71724semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C3×#58122
C2×#636632
#105910852
#105891612
#717243
#716613