Finite Group Databasebeta

← #11791374

Subgroups — #11791374

Order 1152.

617 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 617 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C22×#3718C211yesmaximal, characteristic
2#10592821C211yesmaximal, characteristic
3C2×C3×#824C212yesmaximal
4C2×#63578C211yesmaximal, characteristic
5#10591100C212yesmaximal
6#70108—32nomaximal
7C22×C3×Dic6C2212yes—
8C2×C32×M16C2211yescharacteristic
9#64135C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C2×C3×#208C2212yes—
12C2×#3718—22no—
13C2×#3718—21no—
14C2×#3718—21no—
15C2×#3718C414yescomplemented
16#63642—21no—
17C8×C3⋊Dic3—21no—
18C3×#824—24no—
19#63578—22no—
20#63566—24no—
21C22×#216—32no—
22C2×C3×#101—32no—
23#5225—32no—
24C2×#824D312yes—
25C2×#822—32no—
26#5122—32no—
27#5122—61no—
28#5120—32no—
29C22×C32×C4C2311yescharacteristic
30C22×C3×Dic3—22no—
31C2×C3×Dic6—22no—
32C2×C3×Dic6—22no—
33C2×C3×Dic6—22no—
34C2×C3×Dic6—22no—
35C2×C3×Dic6—22no—
36C2×C3×Dic6C2×C414yes—
37C32×M16—21no—
38C32×M16D412yes—
39C2×C32×C8—21no—
40#3757—21no—
41C4⋊(C3⋊Dic3)D412yes—
42C4×C3⋊Dic3—21no—
43C2×C3⋊(C3⋊C8)C2×C412yes—
44C2×C3⋊(C3⋊C8)D412yes—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C3×#208—22no—
48C3×#208—22no—
49C2×C3×C3⋊C8—22no—
50#3718—24no—
51#3718—24no—
52#1979—91noSylow
53C22×C3×Q8—32no—
54C22×Dic6C2×D312yes—
55C2×C3×M16—21no—
56C2×C3×M16—32no—
57C2×C3×M16C2×D312yes—
58C2×#216—38no—
59C2×#216—62no—
60C2×#216—62no—
61C2×#216—64no—
62#926—32no—
63#926—61no—
64C2×#208C2×D312yes—
65C22×C3⋊C8—32no—
66C22×C3⋊C8—61no—
67C3×#101—64no—
68#835—64no—
69#824—24no—
70#822—64no—
71#816—64no—
72#815—62no—
73#815—62no—
74C8×Dic3—62no—
75C8×Dic3—62no—
76C23×C32#4111yescharacteristic
77C2×C32×C4C22×C411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—42no—
86C2×C3×Dic3—42no—
87C3×Dic6—24no—
88C3×Dic6—24no—
89C3×Dic6—42no—
90C3×Dic6—42no—
91C32×C8—22no—
92C3⋊(C3⋊C8)C22⋊C412yes—
93C3⋊(C3⋊C8)C22⋊C412yes—
94C3×C3⋊C8—42no—
95C22×Q16—91no—
96C2×#108—91no—
97#419—92no—
98C2×#101—32no—
99#405—91no—
100C2×C3×Q8—34no—
101C2×C3×Q8—62no—
102C2×C3×Q8—62no—
103C2×C3×Q8—62no—
104C2×C3×Q8—62no—
105C2×C3×Q8—62no—
106C22×C3×C4—21no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C22×Dic3—22no—
110C2×Dic6—22no—
111C2×Dic6—22no—
112C2×Dic6—22no—
113C2×Dic6—22no—
114C2×Dic6—22no—
115C2×Dic6C4×D314yes—
116C3×M16—22no—
117C3×M16—22no—
118C3×M16—22no—
119C3×M16—62no—
120C3×M16—62no—
121C3×M16#6714yes—
122C2×C3×C8—22no—
123C2×C3×C8—22no—
124C2×C3×C8—62no—
125#217—62no—
126#217—62no—
127#216—68no—
128#216—68no—
129C4⋊Dic3—34no—
130C4⋊Dic3—62no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133#208—22no—
134#208—22no—
135C2×C3⋊C8—22no—
136C2×C3⋊C8—34no—
137C2×C3⋊C8—32no—
138C2×C3⋊C8—32no—
139C2×C3⋊C8—34no—
140C2×C3⋊C8—61no—
141C2×C3⋊C8—61no—
142C2×C3⋊C8—62no—
143C2×C3⋊C8—62no—
144C22×C32—22no—
145C22×C32C4×D411yescharacteristic
146C22×C32#12111yescharacteristic
147C22×C32#12411yescharacteristic
148C32×C4C2×C22⋊C411yescharacteristic
149C32×C4C4×D411yescharacteristic
150C32×C4#12111yescharacteristic
151C32×C4#12711yescharacteristic
152C3⋊Dic3—42no—
153C3×Dic3—44no—
154C22×Q8—32no—
155C2×Q16—94no—
156C2×Q16—182no—
157C2×Q16—181no—
158C2×Q16—181no—
159C2×M16—32no—
160C2×M16D3211yescharacteristic
161C22×C8—91no—
162#117—91no—
163#108—182no—
164#103—184no—
165#101—64no—
166#97—181no—
167C4×C8—181no—
168C23×C3—21no—
169C23×C3#23512yes—
170C3×Q8—64no—
171C3×Q8—64no—
172C3×Q8—122no—
173C3×Q8—122no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—64no—
181C2×C3×C4—122no—
182C2×C3×C4—122no—
183C2×C3×C4C2×C4×D312yes—
184C2×C3×C4D3×D412yes—
185C2×C3×C4D3×D412yes—
186C2×C3×C4D3×D412yes—
187C2×C3×C4#23712yes—
188C2×C3×C4C2×#6712yes—
189C2×Dic3—24no—
190C2×Dic3—42no—
191C2×Dic3—42no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194Dic6—24no—
195Dic6—24no—
196Dic6—42no—
197Dic6—42no—
198C3×C8—24no—
199C3×C8—24no—
200C3×C8—122no—
201C3⋊C8—34no—
202C3⋊C8—34no—
203C3⋊C8—42no—
204C3⋊C8—62no—
205C3⋊C8—62no—
206C2×C32—21no—
207C2×C32—21no—
208C2×C32#39011yescharacteristic
209C2×C32#47312yes—
210C2×Q8—34no—
211C2×Q8—62no—
212C2×Q8—62no—
213C2×Q8—62no—
214C2×Q8—62no—
215C2×Q8—62no—
216C22×C4—62no—
217C22×C4C2×D3211yescharacteristic
218Q16—184no—
219Q16—184no—
220M16—21no—
221M16—62no—
222M16—62no—
223M16#62512yes—
224C2×C8—21no—
225C2×C8—62no—
226C2×C8—92no—
227C2×C8—92no—
228C2×C8—91no—
229C2×C8—91no—
230C4⋊C4—92no—
231C22⋊C4—181no—
232C42—181no—
233C22×C3—24no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—42no—
238C22×C3#88412yes—
239C22×C3#88512yes—
240C22×C3C4×#6712yes—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—124no—
246C3×C4D3×C22⋊C412yes—
247C3×C4#67⋊C412yes—
248C3×C4#93912yes—
249C3×C4#94012yes—
250Dic3—44no—
251Dic3—124no—
252Dic3—124no—
253C32#197911yescharacteristic, complemented, Sylow
254C23#379811yescharacteristic
255Q8—64no—
256Q8—64no—
257Q8—122no—
258Q8—122no—
259C2×C4—64no—
260C2×C4—122no—
261C2×C4—122no—
262C2×C4—182no—
263C2×C4C4×D3211yescharacteristic
264C2×C4#380211yescharacteristic
265C2×C4#380211yescharacteristic
266C2×C4#380511yescharacteristic
267C2×C4C2×#62511yescharacteristic
268C2×C4#381111yescharacteristic
269C8—22no—
270C8—92no—
271C8—92no—
272C8—122no—
273C2×C3—22no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—21no—
277C2×C3—41no—
278C2×C3—41no—
279C2×C3#475514yes—
280C2×C3#495712yes—
281C22—22no—
282C22C4×#62511yescharacteristic
283C22#6391211yescharacteristic
284C22#6391511yescharacteristic
285C4—124no—
286C4—362no—
287C4#6390211yescharacteristic
288C4#6391411yescharacteristic
289C4#6392111yescharacteristic
290C4#6398011yescharacteristic
291C3—21no—
292C3#7010812yescomplemented
293C2—21no—
294C2—21no—
295C2#1059099312yes—
296C2#1059138511yescharacteristic
subgroupG/H
centerC22#63912
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC23×C32#41
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1979
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
15. C2×#3718C4semidirect
253. C32#1979semidirect
292. C3#70108semidirect

Maximal subgroups

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

subgroupindex
C22×#37182
#105928212
C2×C3×#8242
C2×#635782
#105911002
#701083