Finite Group Databasebeta

← #11793861

Subgroups — #11793861

Order 1152.

595 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 595 conjugacy classes of subgroups — too many to draw. Only its 104 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#10594786C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic, complemented
3C3×#5132C212yesmaximal, complemented
4C2×#63568C212yesmaximal, complemented
5#10589159C211yesmaximal, characteristic, complemented
6#70144—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×M16C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×#3748C2211yescharacteristic
11C2×C3×#208C2212yes—
12#63827—22no—
13#63823—22no—
14#63822—22no—
15#63641—22no—
16C3×#824—22no—
17C3×#823—22no—
18#63568—22no—
19#63568—22no—
20#5822—32no—
21C3×#413—32no—
22C2×#837—32no—
23C2×#825—32no—
24#5132D312yescomplemented
25#5118—32no—
26#5118—61no—
27C3⋊#338—32no—
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3—21no—
30C2×C3×#67—22no—
31C3×#235—22no—
32C3×#235—22no—
33C3×#235—22no—
34C3×#235—22no—
35C2×C3×D12D412yes—
36C2×C3×C4×D3—22no—
37C2×C3×Dic6D412yes—
38C32×M16—22no—
39C2×C32×C8—21no—
40C4×C3⋊Dic3—21no—
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43#3748—22no—
44C2×C3⋊(C3⋊C8)D412yes—
45C3×#208—22no—
46C3×#208—22no—
47C2×C3×C3⋊C8—22no—
48#3718—22no—
49#3715—24no—
50#3713—22no—
51#2050—91noSylow
52C2×C3×#41—32no—
53C2×#235C2×D312yes—
54C2×C3×M16—21no—
55C2×C3×M16—32no—
56C2×C3×M16C2×D312yes—
57#951—62no—
58#950—64no—
59#949—62no—
60#942—62no—
61#932—62no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C2×#208—32no—
65C2×#208—61no—
66C2×#208C2×D312yes—
67C3×#101—62no—
68C3×#100—62no—
69#837—62no—
70#837—62no—
71#825—62no—
72#825—62no—
73#824—22no—
74#823—22no—
75Dic3⋊C8—64no—
76Dic3⋊C8—64no—
77C23×C32#4111yescharacteristic
78C22×C3×D3—22no—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D412yes—
82C2×C32×C4#4112yes—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—42no—
86C3×#67—42no—
87C3×#67—42no—
88C2×C3×Dic3—22no—
89C3×D12—22no—
90C3×D12—22no—
91C3×C4×D3—42no—
92C3×C4×D3—42no—
93C3×Dic6—22no—
94C3×Dic6—22no—
95C32×C8—41no—
96C3⋊(C3⋊C8)—22no—
97C3×C3⋊C8—42no—
98#575—91no—
99#423—91no—
100C2×#104—92no—
101#413—32no—
102#338—91no—
103C3×#41—62no—
104C3×#41—62no—
105C3×#41—62no—
106C3×#41—62no—
107C2×C3×Q8—32no—
108C2×C3×D4—32no—
109C2×C3×D4—62no—
110C22×C3×C4—21no—
111C22×C3×C4—62no—
112C22×C3×C4C22×D312yes—
113C2×#67—22no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116#235—22no—
117#235—22no—
118#235—22no—
119#235—22no—
120C2×D12#6712yes—
121C2×C4×D3—22no—
122C2×Dic6#6712yes—
123C3×M16—22no—
124C3×M16—22no—
125C3×M16—42no—
126C3×M16—62no—
127C3×M16—62no—
128C2×C3×C8—22no—
129C2×C3×C8—22no—
130C2×C3×C8—62no—
131#216—64no—
132#215—64no—
133#214—64no—
134#213—64no—
135C4×Dic3—32no—
136C4×Dic3—32no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—62no—
140C4×Dic3—62no—
141#208—22no—
142#208—22no—
143#208—62no—
144#208—62no—
145#208—122no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8—34no—
148C2×C3⋊C8—62no—
149C22×C32—41no—
150C22×C32#12111yescharacteristic
151C22×C32#12312yes—
152C2×C3×D3—42no—
153C2×C3×D3—82no—
154C32×C4#12011yescharacteristic
155C32×C4#12112yes—
156C32×C4#12411yescharacteristic
157C3⋊Dic3—22no—
158C3⋊Dic3—41no—
159C3×Dic3—42no—
160C2×#41—32no—
161#137—182no—
162AGL(1,ℤ/8)—182no—
163#135—182no—
164C2×M16—32no—
165C2×M16—91no—
166C2×M16D3211yescharacteristic
167C2×C42—91no—
168C4⋊C8—182no—
169#104—182no—
170#104—182no—
171#101—62no—
172#100—62no—
173C23×C3—21no—
174C23×C3—62no—
175C23×C3#23512yes—
176C22×D3—22no—
177C3×Q8—62no—
178C3×Q8—62no—
179C3×D4—62no—
180C3×D4—62no—
181C3×D4—122no—
182C3×D4—122no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—22no—
186C2×C3×C4—21no—
187C2×C3×C4—62no—
188C2×C3×C4—122no—
189C2×C3×C4—122no—
190C2×C3×C4#23512yes—
191C2×C3×C4D3×D412yes—
192C2×C3×C4D3×D412yes—
193C2×C3×C4D3×D412yes—
194C2×C3×C4#23712yes—
195C2×C3×C4C2×#6712yes—
196#67—42no—
197#67—42no—
198C2×Dic3—22no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205D12—22no—
206D12—22no—
207C4×D3—42no—
208C4×D3—42no—
209Dic6—22no—
210Dic6—22no—
211C3×C8—42no—
212C3×C8—42no—
213C3×C8—122no—
214C3⋊C8—42no—
215C3⋊C8—64no—
216C3⋊C8—122no—
217C2×C32—21no—
218C2×C32—22no—
219C2×C32#39411yescharacteristic
220C3×D3—82no—
221#41—62no—
222#41—62no—
223#41—62no—
224#41—62no—
225C2×Q8—32no—
226C2×D4—32no—
227C2×D4—62no—
228C22×C4—62no—
229C22×C4—181no—
230C22×C4C2×D3211yescharacteristic
231Q16—182no—
232SD16—184no—
233D8—182no—
234M16—22no—
235M16—62no—
236M16—62no—
237M16—182no—
238C2×C8—21no—
239C2×C8—62no—
240C2×C8—92no—
241C42—91no—
242C42—91no—
243C42—181no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—42no—
247C22×C3—42no—
248C22×C3—122no—
249C22×C3—242no—
250C22×C3#88312yes—
251C22×C3#88412yes—
252C22×C3#92912yes—
253C2×D3—42no—
254C2×D3—82no—
255C3×C4—22no—
256C3×C4—21no—
257C3×C4—21no—
258C3×C4—122no—
259C3×C4#88412yes—
260C3×C4#88512yes—
261C3×C4#93712yes—
262C3×C4#93912yes—
263Dic3—42no—
264Dic3—64no—
265Dic3—64no—
266Dic3—122no—
267Dic3—122no—
268C32#205011yescharacteristic, complemented, Sylow
269C23—62no—
270C23#379811yescharacteristic
271Q8—62no—
272Q8—62no—
273D4—62no—
274D4—62no—
275D4—122no—
276D4—122no—
277C2×C4—62no—
278C2×C4—122no—
279C2×C4—122no—
280C2×C4—181no—
281C2×C4—181no—
282C2×C4—362no—
283C2×C4#379512yes—
284C2×C4#380211yescharacteristic
285C2×C4D3×#6712yes—
286C2×C4#381111yescharacteristic
287C8—41no—
288C8—122no—
289C8—182no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—21no—
295C2×C3—42no—
296C2×C3—242no—
297C2×C3#495912yes—
298D3—82no—
299C22—41no—
300C22—122no—
301C22—242no—
302C22#6390512yes—
303C22#6391211yescharacteristic
304C4—122no—
305C4—182no—
306C4—361no—
307C4#6388512yes—
308C4#6391311yescharacteristic
309C4#6398311yescharacteristic
310C3—21no—
311C3#7014412yescomplemented
312C2—21no—
313C2—22no—
314C2—242no—
315C2#1059138811yescharacteristic
subgroupG/H
centerC4#63913
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#394
prime radical#10594786C2
hypercenterC2×M16D32
hypocenterC32#2050
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592817C2semidirect
3. C3×#5132C2semidirect
4. C2×#63568C2semidirect
5. #10589159C2semidirect
24. #5132D3semidirect
268. C32#2050semidirect
311. C3#70144semidirect

Maximal subgroups

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

subgroupindex
#105947862
#105928172
C3×#51322
C2×#635682
#105891592
#701443