Finite Group Databasebeta

← #11780607

Subgroups — #11780607

Order 1152.

427 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 427 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×#5672C211yesmaximal, characteristic
2C3×#5060C211yesmaximal, characteristic
3#10590315C212yesmaximal, complemented
4#10589406C211yesmaximal, characteristic
5#10589088C212yesmaximal, complemented
6#71956—31nomaximal
7#71330—31nomaximal
8C32×#124C2211yescharacteristic
9C3×#944—21no—
10C2×C3×#216—21no—
11C3×#935—21no—
12C2×C3×#214—21no—
13C3×#879—22no—
14C3×#878—22no—
15C3×#870C2212yes—
16C3×#869C2211yescharacteristic
17#63630C2212yes—
18C3×#803C2211yescharacteristic
19#63576—22no—
20#63574—22no—
21C3×#563—31no—
22#5672D311yescharacteristic
23C3×#497—31no—
24#5081—32no—
25#5064—32no—
26#5060D311yescharacteristic
27#4543—32no—
28#4540—31no—
29#4540—31no—
30#4540—61no—
31#4465—32no—
32C2×C32×Q8D411yescharacteristic
33C2×C32×D4D411yescharacteristic
34C22×C3×Dic3—21no—
35C2×C3×Dic6—21no—
36C2×C3×Dic6—21no—
37C32×C22⋊C4—22no—
38C32×C42C2311yescharacteristic
39C2×C3⋊(C3⋊C8)—22no—
40C3×#217—22no—
41C3×#217—21no—
42C3×#216—42no—
43C3×#214—42no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3D412yes—
46C3×C4⋊Dic3D412yes—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C3×Dic3⋊C4—22no—
50C3×C4×Dic3—21no—
51C2×C3×C3⋊C8—21no—
52#1660—91noSylow
53C2×C3×Q16—61no—
54C2×C3×SD16—61no—
55C3×C4⋊Q8—31no—
56C3×C4⋊Q8—61no—
57C3×#126—62no—
58C3×#125—32no—
59C3×#124—21no—
60C3×#124C2×D311yescharacteristic
61C3×#124C2×D311yescharacteristic
62C3×#123—61no—
63C3×C22⋊Q8—62no—
64#944—21no—
65C2×#216—21no—
66#935—21no—
67C2×#214—21no—
68#879—22no—
69#878—22no—
70#870C2×D312yes—
71#869C2×D311yescharacteristic
72C3×#97—31no—
73#808—62no—
74#808—62no—
75#807—62no—
76#807—62no—
77#803—32no—
78#803—32no—
79#803—62no—
80#803C2×D311yescharacteristic
81C23×C32—21no—
82C32×Q8—41no—
83C32×D4—41no—
84C2×C32×C4—21no—
85C2×C32×C4C2×D412yes—
86C2×C32×C4C2×D411yescharacteristic
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—81no—
91C3×Dic6—41no—
92C3×Dic6—41no—
93C3×Dic6—81no—
94C3⋊(C3⋊C8)—24no—
95C3×C3⋊C8—22no—
96#563—31no—
97#501—92no—
98#497—31no—
99#330—92no—
100#329—91no—
101C2×C3×Q8—21no—
102C2×C3×Q8—61no—
103C2×C3×Q8—61no—
104C2×C3×Q8#6711yescharacteristic
105C2×C3×Q8#6711yescharacteristic
106C2×C3×D4—21no—
107C2×C3×D4#6711yescharacteristic
108C2×C3×D4#6711yescharacteristic
109C22×C3×C4—61no—
110C22×Dic3—21no—
111C2×Dic6—21no—
112C2×Dic6—21no—
113C3×Q16—122no—
114C3×SD16—122no—
115C2×C3×C8—61no—
116C3×C4⋊C4—32no—
117C3×C4⋊C4—32no—
118C3×C4⋊C4—62no—
119C3×C4⋊C4—62no—
120C3×C4⋊C4—62no—
121C3×C4⋊C4—62no—
122C3×C22⋊C4—22no—
123C3×C22⋊C4—22no—
124C3×C22⋊C4—42no—
125C3×C22⋊C4—62no—
126C3×C22⋊C4—61no—
127C3×C42—21no—
128C3×C42—61no—
129C3×C42C22×D311yescharacteristic
130C3×C42C22×D311yescharacteristic
131#217—22no—
132#217—21no—
133#216—42no—
134#214—42no—
135C4⋊Dic3—22no—
136C4⋊Dic3#6712yes—
137C4⋊Dic3#6712yes—
138Dic3⋊C4—22no—
139Dic3⋊C4—22no—
140Dic3⋊C4—22no—
141C4×Dic3—21no—
142C2×C3⋊C8—21no—
143C2×C3⋊C8—62no—
144C2×C3⋊C8—62no—
145C2×C3⋊C8—122no—
146C22×C32—41no—
147C22×C32—42no—
148C22×C32#12011yescharacteristic
149C32×C4—21no—
150C32×C4—22no—
151C32×C4—41no—
152C3×Dic3—42no—
153C3×Dic3—42no—
154C3×Dic3—81no—
155C2×Q16—61no—
156C2×SD16—61no—
157C4⋊Q8—31no—
158C4⋊Q8—61no—
159#126—62no—
160#125—32no—
161#124D3211yescharacteristic
162#123—61no—
163C22⋊Q8—62no—
164#107—182no—
165#106—182no—
166#97—31no—
167#97—92no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—41no—
171C3×Q8—41no—
172C3×Q8—41no—
173C3×Q8—81no—
174C3×Q8—121no—
175C3×Q8—121no—
176C3×Q8—241no—
177C3×D4—41no—
178C3×D4—41no—
179C3×D4—81no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—22no—
184C2×C3×C4—41no—
185C2×C3×C4—62no—
186C2×C3×C4—62no—
187C2×C3×C4—121no—
188C2×C3×C4—241no—
189C2×C3×C4D3×D412yes—
190C2×C3×C4C2×#6711yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×C3×C4C2×#6712yes—
193C2×Dic3—22no—
194C2×Dic3—22no—
195C2×Dic3—41no—
196C2×Dic3—81no—
197Dic6—41no—
198Dic6—41no—
199Dic6—81no—
200C3×C8—62no—
201C3⋊C8—22no—
202C3⋊C8—64no—
203C3⋊C8—64no—
204C3⋊C8—124no—
205C2×C32—81no—
206C2×C32#45311yescharacteristic
207C2×C32#45612yes—
208C2×Q8—61no—
209C2×Q8—61no—
210C2×Q8#62511yescharacteristic
211C2×D4#62511yescharacteristic
212C22×C4—61no—
213Q16—122no—
214SD16—122no—
215C2×C8—61no—
216C2×C8—182no—
217C4⋊C4—32no—
218C4⋊C4—32no—
219C4⋊C4—62no—
220C4⋊C4—62no—
221C4⋊C4—62no—
222C4⋊C4—62no—
223C22⋊C4—22no—
224C22⋊C4—62no—
225C22⋊C4—61no—
226C42—61no—
227C42C2×D3211yescharacteristic
228C22×C3—21no—
229C22×C3—42no—
230C22×C3—41no—
231C22×C3—42no—
232C22×C3—41no—
233C22×C3—81no—
234C22×C3—82no—
235C22×C3#93711yescharacteristic
236C22×C3#95311yescharacteristic
237C3×C4—22no—
238C3×C4—21no—
239C3×C4—22no—
240C3×C4—21no—
241C3×C4—42no—
242C3×C4—41no—
243C3×C4—41no—
244C3×C4—41no—
245C3×C4—81no—
246C3×C4—122no—
247C3×C4—122no—
248C3×C4—241no—
249Dic3—42no—
250Dic3—42no—
251Dic3—81no—
252C32#166011yescharacteristic, complemented, Sylow
253C23—21no—
254Q8—41no—
255Q8—121no—
256Q8—121no—
257Q8—241no—
258D4—41no—
259C2×C4—21no—
260C2×C4—62no—
261C2×C4—62no—
262C2×C4—121no—
263C2×C4—241no—
264C2×C4C2×#62511yescharacteristic
265C2×C4D3×#6712yes—
266C8—62no—
267C8—184no—
268C2×C3—21no—
269C2×C3—22no—
270C2×C3—81no—
271C2×C3—81no—
272C2×C3—161no—
273C2×C3#507711yescharacteristic
274C2×C3#520512yes—
275C2×C3#524111yescharacteristic
276C2×C3#524612yes—
277C22—41no—
278C22—42no—
279C22#6397611yescharacteristic
280C4—21no—
281C4—22no—
282C4—41no—
283C4—122no—
284C4—122no—
285C4—241no—
286C3—21no—
287C3#7133011yescharacteristic, complemented
288C3#7195611yescharacteristic, complemented
289C2—81no—
290C2#1059150911yescharacteristic
291C2#1059168712yes—
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#124D32
hypocenterC32#1660
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #10590315C2semidirect
5. #10589088C2semidirect
252. C32#1660semidirect
287. C3#71330semidirect
288. C3#71956semidirect

Maximal subgroups

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

subgroupindex
C3×#56722
C3×#50602
#105903152
#105894062
#105890882
#719563
#713303