Finite Group Databasebeta

← #11800182

Subgroups — #11800182

Order 1152.

293 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 293 conjugacy classes of subgroups — too many to draw. Only its 80 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×#5183C211yesmaximal, characteristic
2#10590873C211yesmaximal, characteristic
3#10589430C211yesmaximal, characteristic
4C3×#4564C211yesmaximal, characteristic
5#10589118C211yesmaximal, characteristic
6#10589117C211yesmaximal, characteristic
7#10589103C211yesmaximal, characteristic
8#71311—31nomaximal
9#69218—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11C3×#944—21no—
12C2×C3×#216—21no—
13C2×C3×Dic12C2211yescharacteristic
14#63869—21no—
15#63645C2211yescharacteristic
16C2×C3⋊(C3⋊C16)C2211yescharacteristic
17C3×#818C2211yescharacteristic
18C3×C8×Dic3C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20#63573—21no—
21C3×#494—31no—
22#5183D311yescharacteristic
23#4878—31no—
24#4683—31no—
25C3×#358—31no—
26#4564—31no—
27#4564—31no—
28#4564—31no—
29#4564—31no—
30#4564—61no—
31#4564D311yescharacteristic
32#4503—31no—
33#4502—31no—
34#4492—31no—
35#4461—31no—
36C2×C32×Q8—21no—
37C2×C3×Dic6—21no—
38C32×Q16—21no—
39C32×Q16—21no—
40C2×C32×C8C2311yescharacteristic
41C4⋊(C3⋊Dic3)—21no—
42C3×#216—42no—
43C3×C4⋊Dic3—21no—
44C3×Dic3⋊C4—41no—
45C3×Dic3⋊C4—41no—
46C3×C4×Dic3D411yescharacteristic
47C2×C3×C3⋊C8D411yescharacteristic
48C3×Dic12—21no—
49C3×Dic12—21no—
50#3724—41no—
51Dic3⋊Dic3—41no—
52C3⋊(C3⋊C16)—21no—
53C3×C3⋊C16—21no—
54#2245—91noSylow
55C2×C3×Q16—21no—
56C2×C3×Q16—31no—
57C2×C3×Q16—61no—
58C2×C3×Q16C2×D311yescharacteristic
59C2×C3×Q16C2×D311yescharacteristic
60C3×C4⋊Q8—61no—
61#944—21no—
62C2×#216—21no—
63C2×Dic12C2×D311yescharacteristic
64#890—61no—
65#870—61no—
66C2×C3×C16—31no—
67C3×#107—31no—
68C3×C4×C8—31no—
69#818—31no—
70#818—31no—
71#818—61no—
72#818C2×D311yescharacteristic
73#817—61no—
74C8×Dic3C2×D311yescharacteristic
75C2×C3⋊C16—31no—
76C2×C3⋊C16—31no—
77C2×C3⋊C16—61no—
78C2×C3⋊C16C2×D311yescharacteristic
79#808—61no—
80C32×Q8—41no—
81C32×Q8—41no—
82C2×C32×C4—41no—
83C2×C32×C4C2×D411yescharacteristic
84C2×C3⋊Dic3—41no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3—41no—
87C2×C3×Dic3D811yescharacteristic
88C2×C3×Dic3D811yescharacteristic
89C3×Dic6—41no—
90C3×Dic6—41no—
91C32×C8#4111yescharacteristic
92C32×C8#4111yescharacteristic
93C3×C3⋊C8SD1612yes—
94#499—91no—
95#494—31no—
96#358—31no—
97#358—91no—
98#358—91no—
99#358—91no—
100#346—91no—
101C2×C3×Q8—21no—
102C2×C3×Q8—21no—
103C2×C3×Q8—41no—
104C2×C3×Q8—61no—
105C2×Dic6—21no—
106C3×Q16—22no—
107C3×Q16—21no—
108C3×Q16—21no—
109C3×Q16—21no—
110C3×Q16—21no—
111C3×Q16—41no—
112C3×Q16—61no—
113C3×Q16—61no—
114C3×Q16—122no—
115C2×C3×C8—21no—
116C2×C3×C8—31no—
117C2×C3×C8C22×D311yescharacteristic
118C2×C3×C8C22×D311yescharacteristic
119C3×C4⋊C4—61no—
120C3×C4⋊C4—121no—
121C3×C4⋊C4—121no—
122C3×C42—31no—
123#216—42no—
124C4⋊Dic3—21no—
125C4⋊Dic3—61no—
126C4⋊Dic3—61no—
127C4⋊Dic3—121no—
128C4⋊Dic3—121no—
129Dic3⋊C4—41no—
130Dic3⋊C4—41no—
131Dic3⋊C4—121no—
132Dic3⋊C4—121no—
133Dic3⋊C4—121no—
134C4×Dic3#6711yescharacteristic
135C2×C3⋊C8#6711yescharacteristic
136Dic12—21no—
137Dic12—21no—
138C3×C16—61no—
139C3⋊C16—21no—
140C3⋊C16—61no—
141C3⋊C16—61no—
142C3⋊C16—121no—
143C22×C32C2×D811yescharacteristic
144C32×C4—81no—
145C32×C4#12411yescharacteristic
146C32×C4C2×SD1611yescharacteristic
147C3⋊Dic3—81no—
148C3×Dic3—21no—
149C3×Dic3—21no—
150C3×Dic3—81no—
151C3×Dic3—81no—
152C2×Q16—31no—
153C2×Q16—61no—
154C2×Q16D3211yescharacteristic
155C4⋊Q8—61no—
156#125—181no—
157C2×C16—31no—
158C2×C16—91no—
159#107—31no—
160#107—91no—
161#106—181no—
162C4×C8—31no—
163C3×Q8—42no—
164C3×Q8—41no—
165C3×Q8—41no—
166C3×Q8—41no—
167C3×Q8—41no—
168C3×Q8—81no—
169C3×Q8—121no—
170C3×Q8—121no—
171C2×C3×C4—21no—
172C2×C3×C4—31no—
173C2×C3×C4—31no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4—81no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×C3×C4D3×D411yescharacteristic
180C2×C3×C4C2×#6711yescharacteristic
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—121no—
184C2×Dic3—121no—
185C2×Dic3—241no—
186C2×Dic3#21311yescharacteristic
187C2×Dic3#21311yescharacteristic
188Dic6—41no—
189Dic6—41no—
190C3×C8—21no—
191C3×C8—21no—
192C3×C8—32no—
193C3×C8#23511yescharacteristic
194C3×C8#23711yescharacteristic
195C3×C8#23711yescharacteristic
196C3×C8#23711yescharacteristic
197C3⋊C8#21412yes—
198C2×C32#48611yescharacteristic
199C2×C32#51011yescharacteristic
200C2×C32#51011yescharacteristic
201C2×Q8—21no—
202C2×Q8—61no—
203Q16—21no—
204Q16—21no—
205Q16—61no—
206Q16—61no—
207Q16—122no—
208C2×C8—31no—
209C2×C8C2×D3211yescharacteristic
210C4⋊C4—61no—
211C4⋊C4—121no—
212C4⋊C4—121no—
213C4⋊C4—181no—
214C4⋊C4—361no—
215C4⋊C4—361no—
216C42—31no—
217C16—61no—
218C16—181no—
219C22×C3—21no—
220C22×C3D3×D811yescharacteristic
221C22×C3C2×#21311yescharacteristic
222C3×C4—21no—
223C3×C4—21no—
224C3×C4—61no—
225C3×C4—61no—
226C3×C4—82no—
227C3×C4—81no—
228C3×C4—81no—
229C3×C4—241no—
230C3×C4—241no—
231C3×C4#88511yescharacteristic
232C3×C4D3×SD1611yescharacteristic
233C3×C4C2×#21411yescharacteristic
234C3×C4#93611yescharacteristic
235Dic3—21no—
236Dic3—21no—
237Dic3—81no—
238Dic3—81no—
239Dic3—241no—
240Dic3—241no—
241Dic3—481no—
242C32#224511yescharacteristic, complemented, Sylow
243Q8—41no—
244Q8—41no—
245Q8—121no—
246Q8—121no—
247C2×C4—31no—
248C2×C4—31no—
249C2×C4—41no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—361no—
253C2×C4D3×#6711yescharacteristic
254C8—32no—
255C8#380411yescharacteristic
256C8#380511yescharacteristic
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3#476011yescharacteristic
261C2×C3#491511yescharacteristic
262C2×C3#491811yescharacteristic
263C2×C3#507011yescharacteristic
264C2×C3#517911yescharacteristic
265C2×C3#517911yescharacteristic
266C22D3×#21311yescharacteristic
267C4—61no—
268C4—61no—
269C4—81no—
270C4—241no—
271C4—241no—
272C4—721no—
273C4D3×#21411yescharacteristic
274C4#6395911yescharacteristic
275C3—21no—
276C3#6921811yescharacteristic, complemented
277C3#7131111yescharacteristic, complemented
278C2#1059104511yescharacteristic
279C2#1059104711yescharacteristic
280C2#1059148711yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socle, prime radicalC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32#2245
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
242. C32#2245semidirect
276. C3#69218semidirect
277. C3#71311semidirect

Maximal subgroups

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

subgroupindex
C3×#51832
#105908732
#105894302
C3×#45642
#105891182
#105891172
#105891032
#713113
#692183