Finite Group Databasebeta

← #15751173

Subgroups — #15751173

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88178C211yesmaximal, characteristic
2#13114530C211yesmaximal, characteristic
3#13112661C212yesmaximal, complemented
4#13112658C212yesmaximal, complemented
5C13×#1749C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C22×#6099—21no—
9C2×C4×Dic26C411yescharacteristic
10C2×C13×C22⋊C8—21no—
11C2×C13×#97—21no—
12#11718873C411yescharacteristic
13#11718871—21no—
14C4×C22⋊Dic13—21no—
15C4×C4⋊Dic13C411yescharacteristic
16#11718594—21no—
17C4×#6101—21no—
18#11718590C2211yescharacteristic
19#11718589C2211yescharacteristic
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—22no—
28C2×C42×C13—42no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C411yescharacteristic
38#88178—22no—
39#88178—22no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×#6099—24no—
46C2×#6099—42no—
47C2×#6099—42no—
48C22×#1055—22no—
49C4×Dic26—42no—
50C13×C22⋊C8—24no—
51C13×#97—42no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#7634—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C2×Dic26—21no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26M1612yescomplemented
84C2×C8×C13—24no—
85C2×C8×C13—42no—
86C2×C8×C13—42no—
87C42×C13—22no—
88C42×C13—22no—
89C42×C13—41no—
90C42×C13—41no—
91C22⋊Dic13—24no—
92C22⋊Dic13—42no—
93C4⋊Dic13—21no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13M1612yescomplemented
97#6101—24no—
98#6101—42no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—42no—
102C4×Dic13—42no—
103#6099—48no—
104C2×#1055—24no—
105C2×#1055—42no—
106C2×#1055—42no—
107C4×C22⋊Q8—131no—
108#1749D1311yescharacteristic
109#1728—131no—
110#1272—132no—
111#1271—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13#10412yes—
119C23×C13C2×C22⋊C411yescharacteristic
120C2×C4×C13—24no—
121C2×C4×C13—24no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—44no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13#9912yes—
139C2×C4×C13#10412yes—
140C2×C4×C13C2×M1611yescharacteristic
141C2×C4×C13C2×M1611yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×C4×C13#13712yes—
145C2×Dic13—22no—
146C2×Dic13—22no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157Dic26—42no—
158Dic26—42no—
159C8×C13—44no—
160#1055—44no—
161C22×M16—261no—
162C2×C22⋊Q8—131no—
163C2×C4×Q8—131no—
164C22×C42C2×D1311yescharacteristic
165C2×C22⋊C8—21no—
166C2×#97—21no—
167#391—131no—
168#389—131no—
169#387—261no—
170#385—261no—
171#380—131no—
172C4×C4⋊C4—131no—
173C4×C4⋊C4—261no—
174C4×C22⋊C4—261no—
175#336—132no—
176#336—261no—
177#336C2×D1312yes—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13#40711yescharacteristic
186C22×C13C2×#9911yescharacteristic
187C22×C13#41311yescharacteristic
188C22×C13#41711yescharacteristic
189C22×C13#41911yescharacteristic
190C22×C13C2×#10411yescharacteristic
191C22×C13C2×#10411yescharacteristic
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—22no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—41no—
200Dic13—42no—
201Dic13—42no—
202Dic13—81no—
203Dic13—81no—
204C22×Q8—131no—
205C23×C4C4×D1311yescharacteristic
206C23×C4D5211yescharacteristic
207C23×C4C22⋊D1311yescharacteristic
208C2×M16—264no—
209C2×M16—522no—
210C2×M16—522no—
211C22×C8—22no—
212C22×C8—262no—
213C22⋊Q8—262no—
214C22⋊Q8—262no—
215C4×Q8—522no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C22⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C42—42no—
225C2×C42—261no—
226C2×C42—261no—
227C2×C42C4×D1311yescharacteristic
228C2×C42D5211yescharacteristic
229C2×C42C22⋊D1311yescharacteristic
230C2×C42C22×D1311yescharacteristic
231C22⋊C8—24no—
232#97—42no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238C2×C13—42no—
239C2×C13#146511yescharacteristic
240C2×C13#148911yescharacteristic
241C2×C13#149111yescharacteristic
242C2×C13#150411yescharacteristic
243C2×C13#150811yescharacteristic
244C2×C13#152411yescharacteristic
245C2×C13#155911yescharacteristic
246C24#610311yescharacteristic
247C2×Q8—132no—
248C2×Q8—261no—
249C2×Q8—521no—
250C2×Q8—521no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4#610311yescharacteristic
267C22×C4#610311yescharacteristic
268C22×C4#610311yescharacteristic
269C22×C4C2×C4×D1311yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272M16—528no—
273C2×C8—24no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—264no—
277C2×C8—522no—
278C2×C8—522no—
279C4⋊C4—132no—
280C4⋊C4—264no—
281C4⋊C4—261no—
282C4⋊C4—521no—
283C4⋊C4—521no—
284C4⋊C4—521no—
285C4⋊C4—521no—
286C4⋊C4—522no—
287C22⋊C4—264no—
288C22⋊C4—522no—
289C42—22no—
290C42—22no—
291C42—41no—
292C42—41no—
293C42—522no—
294C42—522no—
295C13#763411yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23#8806512yes—
303C23C2×#610311yescharacteristic
304Q8—522no—
305Q8—522no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—262no—
325C2×C4—262no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4#8804512yes—
337C2×C4#8804612yes—
338C2×C4M16×D1311yescharacteristic
339C2×C4M16×D1311yescharacteristic
340C2×C4#8816211yescharacteristic
341C2×C4#8816311yescharacteristic
342C2×C4#8820512yes—
343C8—44no—
344C8—524no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22C2×#8804511yescharacteristic
353C22C2×#8804611yescharacteristic
354C22#1171866511yescharacteristic
355C22#1171878711yescharacteristic
356C22#1171879311yescharacteristic
357C22#1171879411yescharacteristic
358C22C2×#8806511yescharacteristic
359C4—22no—
360C4—22no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—22no—
366C4—41no—
367C4—522no—
368C4—522no—
369C4—1041no—
370C4—1041no—
371C2—42no—
372C2#1311317211yescharacteristic
373C2#1311327611yescharacteristic
374C2#1311328211yescharacteristic
375C2#1311334111yescharacteristic
376C2#1311335511yescharacteristic
377C2#1311342211yescharacteristic
378C2#1311356711yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1749C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1749D13
hypocenterC13#7634
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #13112661C2semidirect
4. #13112658C2semidirect
83. C2×Dic26M16semidirect
96. C4⋊Dic13M16semidirect
295. C13#7634semidirect

Maximal subgroups

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

subgroupindex
C4×#881782
#131145302
#131126612
#131126582
C13×#17492
#763413