Finite Group Databasebeta

← #16784546

Subgroups — #16784546

Order 3328.

558 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 126 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#13130751C211yesmaximal, characteristic
2C4×#88110C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal
4C2×Q8⋊#1057C212yesmaximal
5#13117405C211yesmaximal, characteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×#88198C411yescharacteristic
8C2×#88141C2211yescharacteristic
9C2×#88110—22no—
10C2×C4⋊#1057C2212yes—
11C2×C4×#1057C2212yes—
12C13×#391C411yescharacteristic
13#11718637C411yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718590C411yescharacteristic
16#11718310—22no—
17#11718308—22no—
18Q8⋊#1057—24no—
19#11718290—22no—
20#11718244—24no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×Dic26C2×C411yescharacteristic
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27Q8×Dic13—22no—
28Q8×Dic13—22no—
29#88198—22no—
30#88198—22no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—22no—
34C2×#6101—22no—
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D412yes—
40C2×C4×Dic13D412yes—
41C2×C4×Dic13C2311yescharacteristic
42#88141—22no—
43#88141—22no—
44#88110—28no—
45C4⋊#1057—22no—
46C4⋊#1057—22no—
47C4×#1057—22no—
48C4×#1057D414yes—
49C13×#95—22no—
50#88071—22no—
51#9647—131nomaximal, Sylow
52C2×Q8×C13—21no—
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13M1612yes—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13C22⋊C412yes—
63C22×Dic13C2×D411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C2×Dic26—22no—
66C2×Dic26—22no—
67C2×Dic26—21no—
68C2×Dic26M1612yes—
69C2×#1057—28no—
70C2×#1057—24no—
71C2×#1057—42no—
72C2×#1057—44no—
73C13×C4⋊C4—22no—
74C42×C13—22no—
75C4⋊Dic13—22no—
76C4⋊Dic13—42no—
77#6101—28no—
78#6101—44no—
79#6101—42no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—24no—
83C4×Dic13—24no—
84C4×Dic13—41no—
85C4×Dic13—41no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C4×Dic13C2×D412yes—
89C4×Dic13#4112yes—
90C4×C4⋊Q8—131no—
91#1831—131no—
92C4×#97—131no—
93C2×Q8⋊C8—132no—
94C2×Q8⋊C8—132no—
95C23×C13C2×C22⋊C411yescharacteristic
96Q8×C13—24no—
97Q8×C13—42no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13C4×D412yes—
107C2×C4×C13C2×M1611yescharacteristic
108C2×C4×C13C2×M1611yescharacteristic
109C2×C4×C13#13112yes—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—42no—
118C2×Dic13#10414yes—
119C2×Dic13#12112yes—
120C2×Dic13#12411yescharacteristic
121C2×Dic13#12711yescharacteristic
122C2×Dic13#13714yes—
123Dic26—24no—
124Dic26—42no—
125#1057—28no—
126#1057—82no—
127C2×C4⋊Q8—131no—
128C2×C4×Q8—131no—
129C2×C4×Q8—131no—
130C2×C4⋊C8—132no—
131C2×#97—262no—
132C2×C4×C8—132no—
133#391—131no—
134#391#26111yescharacteristic
135#389—262no—
136#384—131no—
137C4×C4⋊C4—262no—
138C43—131no—
139#336—262no—
140Q8⋊C8—264no—
141Q8⋊C8—264no—
142C22×C13#39011yescharacteristic
143C22×C13#40711yescharacteristic
144C22×C13#40811yescharacteristic
145C22×C13#41912yes—
146C22×C13C2×#10412yes—
147C4×C13—42no—
148C4×C13—42no—
149C4×C13—81no—
150C4×C13#43512yes—
151C4×C13#43512yes—
152Dic13—22no—
153Dic13—24no—
154Dic13—42no—
155Dic13—81no—
156Dic13#49112yes—
157Dic13#49712yes—
158C22×Q8—131no—
159C22×Q8C2×#26111yescharacteristic
160C22×C8—262no—
161C22×C8—262no—
162C4⋊Q8—262no—
163C4⋊Q8—262no—
164C4×Q8—262no—
165C4×Q8—262no—
166C4×Q8—262no—
167C4×Q8—262no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—262no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—262no—
173C2×C4⋊C4C2×#26111yescharacteristic
174C2×C42—131no—
175C2×C42—132no—
176C2×C42—132no—
177C2×C42—131no—
178C2×C42—261no—
179C2×C42—261no—
180C2×C42C2×#26111yescharacteristic
181C4⋊C8—262no—
182C4⋊C8—262no—
183#97—268no—
184C4×C8—134no—
185C4×C8—262no—
186#95—22no—
187#95—262no—
188C2×C13#148512yes—
189C2×C13#149112yes—
190C2×C13#195511yescharacteristic
191C2×C13#196011yescharacteristic
192C2×C13#196211yescharacteristic
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—132no—
197C2×Q8—261no—
198C2×Q8—262no—
199C2×Q8—262no—
200C2×Q8#611812yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—132no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4C22⋊#26112yes—
209C22×C4C22×#26111yescharacteristic
210C2×C8—264no—
211C2×C8—268no—
212C2×C8—522no—
213C2×C8—524no—
214C4⋊C4—22no—
215C4⋊C4—268no—
216C4⋊C4—262no—
217C4⋊C4—522no—
218C4⋊C4—522no—
219C4⋊C4—524no—
220C42—22no—
221C42—132no—
222C42—132no—
223C42—264no—
224C42—264no—
225C42—261no—
226C42—261no—
227C42—521no—
228C42—521no—
229C42—521no—
230C42—521no—
231C13#964711yescharacteristic, complemented, Sylow
232C23C2×C22⋊#26111yescharacteristic
233Q8—24no—
234Q8—42no—
235Q8—264no—
236Q8—522no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—131no—
246C2×C4—131no—
247C2×C4—134no—
248C2×C4—132no—
249C2×C4—134no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—522no—
258C2×C4C2×#611811yescharacteristic
259C2×C4D13⋊M1611yescharacteristic
260C2×C4#8823812yes—
261C2×C4D4×#26112yes—
262C8—268no—
263C8—1042no—
264C22#1171912711yescharacteristic
265C22#1171914611yescharacteristic
266C22#1171915111yescharacteristic
267C22#1171915312yes—
268C22D13⋊#10412yes—
269C4—42no—
270C4—42no—
271C4—81no—
272C4—132no—
273C4—132no—
274C4—264no—
275C4—262no—
276C4—522no—
277C4—1041no—
278C4#1171906412yes—
279C4#1171906512yes—
280C2#1313015812yes—
281C2#1313017912yes—
282C2#1313096111yescharacteristic
283C2#1313096711yescharacteristic
284C2#1313097111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#391C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#391#261
hypocenterC13#9647
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
231. C13#9647semidirect

Maximal subgroups

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

subgroupindex
#131307512
C4×#881102
C2×#117182442
C2×Q8⋊#10572
#131174052
#964713