Finite Group Databasebeta

← #11794283

Subgroups — #11794283

Order 1152.

563 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 563 conjugacy classes of subgroups — too many to draw. Only its 124 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#10595971C211yesmaximal, characteristic
2C3×#4977C211yesmaximal, characteristic
3#10591130C212yesmaximal
4C3×#4530C211yesmaximal, characteristic
5#10589162C212yesmaximal
6#69543—31nomaximal
7#68979—31nomaximal
8C2×C32×C4⋊C4C2211yescharacteristic
9#64135C2212yes—
10#64133—22no—
11#64099—22no—
12#64097—22no—
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2212yes—
16C3×C3⋊#95—22no—
17#63575—22no—
18#63573—22no—
19#5500—31no—
20#5500—31no—
21#5500—61no—
22C3×#382—31no—
23#5121—32no—
24#4977D311yescharacteristic
25#4964—32no—
26C3×#343—31no—
27#4555—32no—
28#4530D311yescharacteristic
29#4523—32no—
30C22×C32×C4D412yes—
31C22×C32×C4C2311yescharacteristic
32C2×#634—22no—
33C22×C3×Dic3—21no—
34C22×C3×Dic3—21no—
35C32×C4⋊C4—22no—
36#3757—22no—
37C4⋊(C3⋊Dic3)—22no—
38C4⋊(C3⋊Dic3)D412yes—
39C4⋊(C3⋊Dic3)D412yes—
40#3750—24no—
41C4×C3⋊Dic3—22no—
42C3×C4⋊Dic3—22no—
43C3×C4×Dic3—21no—
44C3×C4×Dic3Q812yescomplemented
45C3×#208—22no—
46C3×#208Q814yescomplemented
47C2×C3×C3⋊C8—22no—
48#2061—91noSylow
49C2×C3×M16—32no—
50C2×C3×C4⋊C4—21no—
51C2×C3×C4⋊C4—31no—
52C2×C3×C4⋊C4C2×D311yescharacteristic
53C2×C3×C4⋊C4C2×D311yescharacteristic
54C2×C3×C42—31no—
55#926—32no—
56#926—32no—
57#926—62no—
58C2×C4⋊Dic3C2×D311yescharacteristic
59#924—64no—
60#924—62no—
61#924—62no—
62C2×C4×Dic3C2×D311yescharacteristic
63C2×#208C2×D312yes—
64#890—62no—
65#890—62no—
66#890—64no—
67#888—62no—
68#888—62no—
69#888—64no—
70C3×#95—62no—
71C3⋊#95—22no—
72#818—62no—
73#817—62no—
74#808—62no—
75#807—62no—
76C23×C32C2×D411yescharacteristic
77C2×C32×C4—22no—
78C2×C32×C4—42no—
79C2×C32×C4C2×D412yes—
80C2×C32×C4C2×Q812yes—
81C2×C32×C4C2×Q811yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85#634—82no—
86C2×C3×Dic3—22no—
87C2×C3×Dic3—41no—
88C2×C3×Dic3—41no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—41no—
91C3×C3⋊C8—24no—
92#544—91no—
93#428—92no—
94#382—31no—
95#343—31no—
96#339—92no—
97C22×C3×C4—22no—
98C22×C3×C4—21no—
99C22×C3×C4—61no—
100C22×C3×C4—61no—
101C22×C3×C4D1212yes—
102C22×C3×C4#6712yes—
103C22×C3×C4C22×D311yescharacteristic
104C22×C3×C4C22×D311yescharacteristic
105C22×Dic3—21no—
106C22×Dic3—21no—
107C2×Dic6—64no—
108C2×Dic6—62no—
109C2×Dic6—62no—
110C3×M16—34no—
111C3×M16—62no—
112C2×C3×C8—62no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—62no—
117C3×C42—32no—
118C3×C42—61no—
119#217—64no—
120#217—62no—
121#217—62no—
122C4⋊Dic3—22no—
123C4⋊Dic3—32no—
124C4⋊Dic3—32no—
125C4⋊Dic3—32no—
126C4⋊Dic3—32no—
127C4⋊Dic3—62no—
128C4⋊Dic3—62no—
129C4⋊Dic3—64no—
130C4⋊Dic3—62no—
131C4⋊Dic3—62no—
132Dic3⋊C4—68no—
133Dic3⋊C4—64no—
134Dic3⋊C4—64no—
135C4×Dic3—21no—
136C4×Dic3—64no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C4×Dic3Dic612yescomplemented
140#208—22no—
141#208Dic614yescomplemented
142C2×C3⋊C8—22no—
143C22×C32—21no—
144C22×C32—21no—
145C22×C32#12011yescharacteristic
146C22×C32C22⋊Q811yescharacteristic
147C22×C32C4⋊Q811yescharacteristic
148C32×C4—42no—
149C32×C4C22⋊Q812yes—
150C32×C4C4⋊Q812yes—
151C3⋊Dic3—42no—
152C3⋊Dic3—42no—
153C3×Dic3—42no—
154C3×Dic3—81no—
155C2×M16—32no—
156C4⋊Q8—182no—
157#125—182no—
158C22⋊Q8—182no—
159#117—92no—
160C2×C4⋊C4—31no—
161C2×C4⋊C4D3211yescharacteristic
162C2×C42—31no—
163#107—182no—
164#106—182no—
165#95—62no—
166C23×C3—21no—
167C23×C3C2×D1211yescharacteristic
168C23×C3C2×#6711yescharacteristic
169C2×C3×C4—24no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—22no—
174C2×C3×C4—21no—
175C2×C3×C4—22no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4—62no—
179C2×C3×C4—82no—
180C2×C3×C4—121no—
181C2×C3×C4—121no—
182C2×C3×C4—122no—
183C2×C3×C4—121no—
184C2×C3×C4C2×Dic612yes—
185C2×C3×C4C2×Dic611yescharacteristic
186C2×C3×C4#23511yescharacteristic
187C2×C3×C4D3×D412yes—
188C2×C3×C4D3×D412yes—
189C2×C3×C4#23711yescharacteristic
190C2×C3×C4D3×Q811yescharacteristic
191C2×C3×C4D3×Q812yes—
192C2×Dic3—22no—
193C2×Dic3—41no—
194C2×Dic3—41no—
195C2×Dic3—42no—
196C2×Dic3—41no—
197C2×Dic3—64no—
198C2×Dic3—64no—
199C2×Dic3—62no—
200C2×Dic3—62no—
201C2×Dic3—62no—
202C2×Dic3—62no—
203Dic6—244no—
204Dic6—242no—
205Dic6—242no—
206C3×C8—64no—
207C3⋊C8—24no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32#39511yescharacteristic
211C2×C32#45411yescharacteristic
212C2×C32#45511yescharacteristic
213C2×Q8—182no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4#62612yes—
217C22×C4C2×D3211yescharacteristic
218M16—34no—
219M16—62no—
220C2×C8—62no—
221C4⋊C4—22no—
222C4⋊C4—62no—
223C4⋊C4—92no—
224C4⋊C4—92no—
225C4⋊C4—182no—
226C4⋊C4—184no—
227C22⋊C4—182no—
228C42—32no—
229C42—61no—
230C42—182no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—41no—
239C22×C3—41no—
240C22×C3#86911yescharacteristic
241C22×C3#88211yescharacteristic
242C22×C3#89711yescharacteristic
243C22×C3#92411yescharacteristic
244C22×C3#93711yescharacteristic
245C22×C3#94411yescharacteristic
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—44no—
249C3×C4—42no—
250C3×C4—42no—
251C3×C4—122no—
252C3×C4—241no—
253C3×C4#87812yes—
254C3×C4#88812yes—
255C3×C4#88812yes—
256C3×C4#89612yes—
257Dic3—42no—
258Dic3—81no—
259Dic3—124no—
260Dic3—124no—
261Dic3—122no—
262Dic3—122no—
263Dic3—122no—
264Dic3—122no—
265C32#206111yescharacteristic, complemented, Sylow
266C23C2×#62611yescharacteristic
267Q8—722no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—62no—
271C2×C4—121no—
272C2×C4—121no—
273C2×C4—122no—
274C2×C4—121no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4D3×Dic611yescharacteristic
278C2×C4D3×Dic612yes—
279C2×C4#379511yescharacteristic
280C2×C4#381112yes—
281C8—64no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—41no—
290C2×C3—41no—
291C2×C3#465611yescharacteristic
292C2×C3#474611yescharacteristic
293C2×C3#475311yescharacteristic
294C2×C3#497911yescharacteristic
295C2×C3#506111yescharacteristic
296C2×C3#506211yescharacteristic
297C22—21no—
298C22—21no—
299C22#6385711yescharacteristic
300C22#6386611yescharacteristic
301C22#6398111yescharacteristic
302C4—42no—
303C4—122no—
304C4—241no—
305C4—362no—
306C4—362no—
307C4#6384012yes—
308C4#6389612yes—
309C3—21no—
310C3#6897911yescharacteristic, complemented
311C3#6954311yescharacteristic, complemented
312C2—21no—
313C2—21no—
314C2#1059135411yescharacteristic
315C2#1059151411yescharacteristic
316C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32#2061
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
44. C3×C4×Dic3Q8semidirect
46. C3×#208Q8semidirect
139. C4×Dic3Dic6semidirect
141. #208Dic6semidirect
265. C32#2061semidirect
310. C3#68979semidirect
311. C3#69543semidirect

Maximal subgroups

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

subgroupindex
#105959712
C3×#49772
#105911302
C3×#45302
#105891622
#695433
#689793