Finite Group Databasebeta

← #11796558

Subgroups — #11796558

Order 1152.

691 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 691 conjugacy classes of subgroups — too many to draw. Only its 108 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
1#10596301C211yesmaximal, characteristic
2C3×#5237C212yesmaximal, complemented
3#10589183C214yesmaximal, complemented
4#70149—32nomaximal
5C2×C32×#41C2211yescharacteristic
6C22×C4⋊(C3⋊D3)C411yescharacteristic
7#64156C2212yes—
8#64149C412yes—
9#64146—22no—
10#64139—22no—
11#64135C411yescharacteristic
12C2×C3×#208—22no—
13C3×#836C2214yescomplemented
14C3×#833—22no—
15#5830—32no—
16#5830—61no—
17C3×#413—32no—
18#5237D312yescomplemented
19#4477—38no—
20C23×C3⋊D3—21no—
21C32×#41—42no—
22C2×C32×Q8C2311yescharacteristic
23C2×C32×D4C2×C411yescharacteristic
24C2×C32×D4D412yes—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4D412yes—
27C2×#638—24no—
28C2×C4⋊(C3⋊D3)—21no—
29C2×C4⋊(C3⋊D3)—42no—
30C2×C4⋊(C3⋊D3)C2×C412yes—
31#3757—21no—
32#3752—24no—
33C4⋊(C3⋊Dic3)—21no—
34C4×C3⋊Dic3C2×C412yes—
35C3×#208—24no—
36C3×#208—42no—
37C2×C3×C3⋊C8—42no—
38#2134—91noSylow
39C2×C3×#41—21no—
40C2×C3×#41C2×D312yes—
41C22×D12—32no—
42C22×D12—61no—
43C2×C3×M16—62no—
44#947—34no—
45#947—62no—
46#940—34no—
47#940—62no—
48#937—64no—
49#937—62no—
50#937—62no—
51#930—64no—
52#930—62no—
53#930—62no—
54#926—32no—
55#926—61no—
56C2×#208—22no—
57C3×#101—34no—
58C3×#100—62no—
59#836C2×D314yescomplemented
60#833—22no—
61C23×C32C22⋊C411yescharacteristic
62C23×C32C22⋊C412yes—
63C22×C3⋊D3—22no—
64C22×C3⋊D3—42no—
65C22×C3⋊D3—82no—
66C32×Q8—41no—
67C32×D4—41no—
68C32×D4—42no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22×C411yescharacteristic
74C2×C32×C4C2×D412yes—
75#638—84no—
76C2×C3⋊Dic3—22no—
77C4⋊(C3⋊D3)—42no—
78C4⋊(C3⋊D3)—42no—
79C3×C3⋊C8—44no—
80#535—91no—
81#413—32no—
82#355—94no—
83C23×D3—62no—
84C23×D3—62no—
85C3×#41—42no—
86C3×#41—42no—
87C3×#41—44no—
88C2×C3×Q8—21no—
89C2×C3×Q8C22×D312yes—
90C2×C3×D4—21no—
91C2×C3×D4—22no—
92C2×C3×D4C4×D312yes—
93C2×C3×D4D1212yes—
94C2×C3×D4#6712yes—
95C22×C3×C4—21no—
96C22×C3×C4—22no—
97C22×C3×C4C4×D312yes—
98C22×C3×C4D1212yes—
99C22×C3×C4#6712yes—
100C2×#67—68no—
101C2×#67—64no—
102C2×#67—64no—
103C2×D12—34no—
104C2×D12—62no—
105C2×D12—62no—
106C2×D12—62no—
107C2×D12—124no—
108C2×D12—122no—
109C2×D12—122no—
110C3×M16—64no—
111C3×M16—122no—
112C2×C3×C8—122no—
113#217—62no—
114#217—62no—
115(C2×D3)⋊C4—68no—
116(C2×D3)⋊C4—64no—
117(C2×D3)⋊C4—64no—
118C4⋊Dic3—62no—
119C4⋊Dic3—62no—
120C4×Dic3—34no—
121C4×Dic3—62no—
122#208—24no—
123#208—42no—
124C2×C3⋊C8—42no—
125C22×C32—21no—
126C22×C32—22no—
127C22×C32—42no—
128C22×C32—41no—
129C22×C32C2×C22⋊C411yescharacteristic
130C2×C3⋊D3—44no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—84no—
133C32×C4—21no—
134C32×C4—22no—
135C32×C4#9912yes—
136C3⋊Dic3—42no—
137C2×#41D3211yescharacteristic
138C22×D4—91no—
139C2×M16—62no—
140#127—92no—
141#124—92no—
142#121—182no—
143#120—182no—
144#117—91no—
145#101—34no—
146#100—62no—
147C23×C3—21no—
148C23×C3—22no—
149C23×C3(C2×D3)⋊C412yes—
150C23×C3(C2×D3)⋊C412yes—
151C23×C3(C2×D3)⋊C412yes—
152C22×D3—64no—
153C22×D3—64no—
154C22×D3—124no—
155C22×D3—124no—
156C22×D3—244no—
157C22×D3—244no—
158C3×Q8—42no—
159C3×Q8—42no—
160C3×D4—42no—
161C3×D4—42no—
162C3×D4—42no—
163C3×D4—42no—
164C3×D4—44no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—22no—
175C2×C3×C4—42no—
176C2×C3×C4—42no—
177C2×C3×C4(C2×D3)⋊C412yes—
178C2×C3×C4C2×C4×D312yes—
179C2×C3×C4C2×D1212yes—
180C2×C3×C4C2×#6712yes—
181#67—244no—
182#67—244no—
183#67—248no—
184C2×Dic3—64no—
185C2×Dic3—64no—
186D12—124no—
187D12—124no—
188D12—124no—
189D12—122no—
190D12—122no—
191C3×C8—124no—
192C3⋊C8—44no—
193C2×C32—21no—
194C2×C32—41no—
195C2×C32—42no—
196C2×C32C2×#9911yescharacteristic
197C3⋊D3—82no—
198C24—181no—
199#41—42no—
200C2×Q8C2×D3211yescharacteristic
201C2×D4—92no—
202C2×D4—184no—
203C2×D4—181no—
204C2×D4—362no—
205C2×D4#62411yescharacteristic
206C2×D4#62612yes—
207C22×C4#62411yescharacteristic
208C22×C4#62612yes—
209M16—64no—
210M16—122no—
211C2×C8—122no—
212C4⋊C4—181no—
213C22⋊C4—181no—
214C22⋊C4—184no—
215C42—92no—
216C22×C3—22no—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—22no—
220C22×C3—21no—
221C22×C3—42no—
222C22×C3—42no—
223C22×C3—42no—
224C22×C3—42no—
225C22×C3—42no—
226C22×C3—44no—
227C22×C3C2×(C2×D3)⋊C412yes—
228C2×D3—124no—
229C2×D3—128no—
230C2×D3—124no—
231C2×D3—124no—
232C2×D3—124no—
233C2×D3—248no—
234C2×D3—248no—
235C3×C4—22no—
236C3×C4—22no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—42no—
241C3×C4#80612yes—
242C3×C4#80612yes—
243Dic3—124no—
244Dic3—124no—
245C32#213411yescharacteristic, complemented, Sylow
246C23—182no—
247C23—362no—
248C23—722no—
249C23#372211yescharacteristic
250C23#372212yes—
251Q8—41no—
252D4—41no—
253D4—42no—
254D4—362no—
255D4—362no—
256D4—724no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—182no—
261C2×C4#372211yescharacteristic
262C2×C4C2×#62411yescharacteristic
263C2×C4C2×#62612yes—
264C8—124no—
265C2×C3—22no—
266C2×C3—22no—
267C2×C3—21no—
268C2×C3—42no—
269C2×C3—42no—
270C2×C3—42no—
271C2×C3—42no—
272C2×C3—82no—
273C2×C3C2×#80612yes—
274D3—244no—
275D3—244no—
276C22—21no—
277C22—22no—
278C22—42no—
279C22—41no—
280C22—364no—
281C22—362no—
282C22—724no—
283C22C2×#372211yescharacteristic
284C4—22no—
285C4—21no—
286C4—362no—
287C4#6358112yes—
288C3—21no—
289C3#7014912yescomplemented
290C2—21no—
291C2—41no—
292C2—42no—
293C2—722no—
294C2C2×#6358111yescharacteristic
subgroupG/H
centerC2C2×#63581
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC2×C32×#41C22
socleC2×C32C2×#99
prime radical#10596301C2
cosocleC2×C32×Q8C23
hypercenterC2×#41D32
hypocenterC32#2134
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5237C2semidirect
3. #10589183C2semidirect
13. C3×#836C22semidirect
18. #5237D3semidirect
59. #836C2×D3semidirect
245. C32#2134semidirect
289. C3#70149semidirect

Maximal subgroups

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

subgroupindex
#105963012
C3×#52372
#105891832
#701493