Finite Group Databasebeta

← #15758637

Subgroups — #15758637

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123175C211yesmaximal, characteristic
2C2×C4×C4⋊Dic13C211yesmaximal, characteristic
3C2×#11718059C212yesmaximal
4#13112716C212yesmaximal
5C13×#1817C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C22×C4⋊Dic13—21no—
8C2×#88178C2211yescharacteristic
9C22×C4×Dic13—21no—
10C2×C13×C22⋊C8C2212yes—
11#11718873C2211yescharacteristic
12#11718872—21no—
13#11718871—21no—
14C2×#88071C2212yes—
15C4×C4⋊Dic13—24no—
16#11718594—22no—
17#11718590C412yescomplemented
18#11718589C412yescomplemented
19C13×#336—22no—
20#11718059—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C23×Dic13—22no—
25C22×Dic26C2×C411yescharacteristic
26C22×C8×C13—22no—
27C2×C42×C13—22no—
28C2×C42×C13—22no—
29C2×C42×C13C2×C412yes—
30C2×C42×C13D412yes—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C4⋊Dic13—28no—
34C2×C4⋊Dic13—24no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C412yes—
37#88178—22no—
38#88178—22no—
39C2×#6101—22no—
40C2×#6101—21no—
41C2×C4×Dic13—24no—
42C2×C4×Dic13—42no—
43C2×C4×Dic13—42no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46#88071—22no—
47#88071—22no—
48#88071—22no—
49#88071—21no—
50#88071—22no—
51#88071D414yes—
52#9144—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—24no—
61C22×C4×C13—42no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13SD1612yes—
65C22×C4×C13Q1612yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4112yes—
70C22×Dic13—28no—
71C22×Dic13—24no—
72C22×Dic13—22no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—44no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C2×Dic26—22no—
79C2×Dic26—42no—
80C2×C8×C13—44no—
81C2×C8×C13—42no—
82C42×C13—24no—
83C42×C13—24no—
84C22⋊Dic13—41no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C22⋊Dic13—41no—
88C4⋊Dic13—216no—
89C4⋊Dic13—22no—
90C4⋊Dic13—42no—
91#6101—44no—
92#6101—42no—
93C4×Dic13—48no—
94#2855—131no—
95C2×C4×C4⋊C4—131no—
96#1817D1311yescharacteristic
97C2×#328—132no—
98#1294—132no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13C2×C22⋊C411yescharacteristic
102C23×C13#12011yescharacteristic
103C23×C13#12311yescharacteristic
104C23×C13C2×SD1611yescharacteristic
105C23×C13C2×Q1611yescharacteristic
106C23×C13AGL(1,ℤ/8)11yescharacteristic
107C23×C13#13711yescharacteristic
108C2×C4×C13—24no—
109C2×C4×C13—24no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13#10314yes—
123C2×C4×C13#10414yes—
124C2×C4×C13C4×D412yes—
125C2×C4×C13#12112yes—
126C2×Dic13—28no—
127C2×Dic13—44no—
128C2×Dic13—48no—
129C2×Dic13—48no—
130C2×Dic13—44no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138Dic26—82no—
139C8×C13—82no—
140C2×C22⋊Q8—131no—
141C22×C4⋊C4—261no—
142C22×C42—261no—
143C22×C42C2×D1311yescharacteristic
144C2×C22⋊C8C2×D1312yes—
145#391—132no—
146#389—132no—
147#387—262no—
148#385—261no—
149#381—261no—
150#380—131no—
151C4×C4⋊C4—264no—
152C2×#95—132no—
153#336—22no—
154#328—264no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13#38611yescharacteristic
164C22×C13#41012yes—
165C22×C13C2×#10311yescharacteristic
166C22×C13#41711yescharacteristic
167C22×C13C2×#10412yes—
168C22×C13#45011yescharacteristic
169C22×C13#45111yescharacteristic
170C22×C13#48311yescharacteristic
171C22×C13#48411yescharacteristic
172C4×C13—24no—
173C4×C13—24no—
174C4×C13—22no—
175C4×C13—22no—
176Dic13—48no—
177Dic13—81no—
178Dic13—81no—
179Dic13—82no—
180C22×Q8—131no—
181C23×C4—262no—
182C23×C4D5211yescharacteristic
183C23×C4D5211yescharacteristic
184C23×C4C22×D1311yescharacteristic
185C22×C8—22no—
186C22⋊Q8—262no—
187C22⋊Q8—262no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—132no—
190C2×C4⋊C4—268no—
191C2×C4⋊C4—264no—
192C2×C4⋊C4—262no—
193C2×C4⋊C4—261no—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—261no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—264no—
199C2×C42—522no—
200C2×C42—522no—
201C2×C42C4×D1312yes—
202C2×C42C22⋊D1312yes—
203C22⋊C8—22no—
204C22⋊C8—22no—
205#95—134no—
206#95—262no—
207#95—262no—
208#95—262no—
209#95—262no—
210#95—261no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13#150312yes—
216C2×C13#150912yes—
217C2×C13#187211yescharacteristic
218C2×C13#189611yescharacteristic
219C2×C13#189911yescharacteristic
220C24C2×D5211yescharacteristic
221C2×Q8—262no—
222C2×Q8—522no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—42no—
231C22×C4—268no—
232C22×C4—264no—
233C22×C4—262no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—524no—
237C22×C4—522no—
238C22×C4—522no—
239C22×C4#609512yes—
240C22×C4Dic5212yes—
241C22×C4#610312yes—
242C22×C4#610312yes—
243C22×C4C2×C4×D1311yescharacteristic
244C22×C4D4×D1312yes—
245C22×C4#612912yes—
246C22×C4C2×C22⋊D1311yescharacteristic
247C2×C8—44no—
248C2×C8—42no—
249C4⋊C4—2616no—
250C4⋊C4—262no—
251C4⋊C4—522no—
252C4⋊C4—524no—
253C4⋊C4—522no—
254C22⋊C4—521no—
255C22⋊C4—521no—
256C22⋊C4—521no—
257C22⋊C4—521no—
258C42—24no—
259C42—24no—
260C42—528no—
261C13#914411yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23#8813611yescharacteristic
265C23#8814011yescharacteristic
266C23C2×#609511yescharacteristic
267C23C2×Dic5211yescharacteristic
268C23#8816211yescharacteristic
269C23#8816311yescharacteristic
270C23C2×#610311yescharacteristic
271Q8—1042no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—268no—
287C2×C4—528no—
288C2×C4—524no—
289C2×C4—528no—
290C2×C4—524no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4#8805614yes—
299C2×C4#8806514yes—
300C2×C4#8813512yes—
301C2×C4#8819312yes—
302C8—82no—
303C22—22no—
304C22—22no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—22no—
311C22#1171838211yescharacteristic
312C22#1171838311yescharacteristic
313C22#1171839211yescharacteristic
314C22#1171840011yescharacteristic
315C22#1171861911yescharacteristic
316C22#1171866712yes—
317C22C2×#8805611yescharacteristic
318C22#1171879411yescharacteristic
319C22C2×#8806512yes—
320C4—24no—
321C4—24no—
322C4—22no—
323C4—22no—
324C4—528no—
325C4—1042no—
326C4—1041no—
327C4—1041no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1311333612yes—
333C2#1311336212yes—
334C2#1311514111yescharacteristic
335C2#1311527711yescharacteristic
336C2#1311529211yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1817C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1817D13
hypocenterC13#9144
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
17. #11718590C4semidirect
18. #11718589C4semidirect
261. C13#9144semidirect

Maximal subgroups

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

subgroupindex
#131231752
C2×C4×C4⋊Dic132
C2×#117180592
#131127162
C13×#18172
#914413