Finite Group Databasebeta

← #15758677

Subgroups — #15758677

Order 3328.

630 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 143 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#13123175C211yesmaximal, characteristic
2C2×#11718597C211yesmaximal, characteristic
3C2×#11718059C212yesmaximal
4#13112716C212yesmaximal
5C13×#1817C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C22×C4⋊Dic13—21no—
8C2×#88178C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10#11718873C2211yescharacteristic
11#11718872—21no—
12#11718871—21no—
13C2×#88071—21no—
14C2×#88071C2212yes—
15#11718597—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—24no—
34C2×C4⋊Dic13—42no—
35C2×C4⋊Dic13—42no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C412yes—
38#88178—22no—
39#88178—22no—
40C2×#6101—22no—
41C2×#6101—21no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—22no—
44#88071—24no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49#88071—22no—
50#88071D414yes—
51#9152—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13SD1612yes—
64C22×C4×C13Q1612yes—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13#4112yes—
69C22×Dic13—22no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—24no—
73C22×Dic13—44no—
74C22×Dic13—44no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C2×Dic26—22no—
78C2×Dic26—42no—
79C2×C8×C13—44no—
80C2×C8×C13—42no—
81C42×C13—24no—
82C42×C13—24no—
83C22⋊Dic13—41no—
84C22⋊Dic13—41no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C4⋊Dic13—22no—
88C4⋊Dic13—48no—
89C4⋊Dic13—42no—
90#6101—44no—
91#6101—42no—
92#2855—131no—
93C2×#382—131no—
94#1817D1311yescharacteristic
95C2×#328—132no—
96#1294—132no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13#12011yescharacteristic
101C23×C13#12311yescharacteristic
102C23×C13C2×SD1611yescharacteristic
103C23×C13C2×Q1611yescharacteristic
104C23×C13AGL(1,ℤ/8)11yescharacteristic
105C23×C13#13711yescharacteristic
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
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—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13#10314yes—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12112yes—
124C2×Dic13—44no—
125C2×Dic13—44no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—44no—
134C2×Dic13—84no—
135C2×Dic13—84no—
136Dic26—82no—
137C8×C13—82no—
138C2×C22⋊Q8—131no—
139C22×C4⋊C4—261no—
140C22×C42C2×D1311yescharacteristic
141C2×C22⋊C8C2×D1312yes—
142#391—132no—
143#389—132no—
144#387—262no—
145#385—261no—
146#382—264no—
147#381—261no—
148#380—131no—
149C2×#95—132no—
150C2×#95—261no—
151#336—22no—
152#328—264no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13#38611yescharacteristic
162C22×C13#41012yes—
163C22×C13C2×#10311yescharacteristic
164C22×C13#41711yescharacteristic
165C22×C13#42112yes—
166C22×C13#45011yescharacteristic
167C22×C13#45111yescharacteristic
168C22×C13#48311yescharacteristic
169C22×C13#48411yescharacteristic
170C4×C13—24no—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—42no—
174Dic13—84no—
175Dic13—81no—
176Dic13—81no—
177Dic13—82no—
178C22×Q8—131no—
179C23×C4—262no—
180C23×C4D5211yescharacteristic
181C23×C4D5211yescharacteristic
182C23×C4C22×D1311yescharacteristic
183C22×C8—22no—
184C22⋊Q8—262no—
185C22⋊Q8—262no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—132no—
188C2×C4⋊C4—264no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—522no—
192C2×C4⋊C4—522no—
193C2×C22⋊C4—261no—
194C2×C22⋊C4—261no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42C4×D1312yes—
198C2×C42C22⋊D1312yes—
199C22⋊C8—22no—
200C22⋊C8—22no—
201#95—134no—
202#95—264no—
203#95—262no—
204#95—262no—
205#95—262no—
206#95—262no—
207#95—261no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#151212yes—
213C2×C13#151812yes—
214C2×C13#187211yescharacteristic
215C2×C13#189711yescharacteristic
216C2×C13#189911yescharacteristic
217C24C2×D5211yescharacteristic
218C2×Q8—262no—
219C2×Q8—522no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—264no—
229C22×C4—262no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—524no—
233C22×C4—524no—
234C22×C4—522no—
235C22×C4—522no—
236C22×C4#609512yes—
237C22×C4Dic5212yes—
238C22×C4#610312yes—
239C22×C4#610312yes—
240C22×C4C2×C4×D1311yescharacteristic
241C22×C4D4×D1312yes—
242C22×C4#612912yes—
243C22×C4C2×C22⋊D1311yescharacteristic
244C2×C8—44no—
245C2×C8—42no—
246C4⋊C4—262no—
247C4⋊C4—522no—
248C4⋊C4—528no—
249C4⋊C4—524no—
250C4⋊C4—522no—
251C22⋊C4—521no—
252C22⋊C4—521no—
253C22⋊C4—521no—
254C22⋊C4—521no—
255C42—24no—
256C42—24no—
257C13#915211yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23#8813611yescharacteristic
261C23#8814011yescharacteristic
262C23C2×#609511yescharacteristic
263C23C2×Dic5211yescharacteristic
264C23#8816211yescharacteristic
265C23#8816311yescharacteristic
266C23C2×#610311yescharacteristic
267Q8—1042no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—524no—
284C2×C4—524no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—524no—
293C2×C4—1044no—
294C2×C4—1044no—
295C2×C4#8805614yes—
296C2×C4#8813512yes—
297C2×C4#8819312yes—
298C8—82no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22#1171838211yescharacteristic
308C22#1171838311yescharacteristic
309C22#1171839211yescharacteristic
310C22#1171840011yescharacteristic
311C22#1171861911yescharacteristic
312C22#1171866712yes—
313C22C2×#8805611yescharacteristic
314C22#1171879411yescharacteristic
315C22#1171880012yes—
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—1044no—
321C4—1042no—
322C4—1041no—
323C4—1041no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2#1311337512yes—
329C2#1311340112yes—
330C2#1311514111yescharacteristic
331C2#1311528211yescharacteristic
332C2#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#9152
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
257. C13#9152semidirect

Maximal subgroups

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

subgroupindex
#131231752
C2×#117185972
C2×#117180592
#131127162
C13×#18172
#915213