Finite Group Databasebeta

← #15751027

Subgroups — #15751027

Order 3328.

504 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88178C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3#13112661C212yesmaximal, complemented
4#13112658C212yesmaximal, complemented
5C13×#1817C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10#11718873C411yescharacteristic
11#11718871—21no—
12C4×C22⋊Dic13—21no—
13C2×C22⋊#1055—21no—
14C4×C4⋊Dic13C411yescharacteristic
15#11718594—21no—
16C4×#6101—21no—
17#11718590C2211yescharacteristic
18#11718589C2211yescharacteristic
19C2×C4⋊#1055—21no—
20C13×#336—21no—
21C13×#336C2212yes—
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#88178C814yescomplemented
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C22×#1055—22no—
46C4×Dic26—42no—
47C13×C22⋊C8—42no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—42no—
54C4⋊#1055—42no—
55#7600—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C2×C812yes—
70C22×C4×C13M1612yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26C2×C812yes—
82C2×C8×C13—42no—
83C2×C8×C13—42no—
84C2×C8×C13—42no—
85C42×C13—22no—
86C42×C13—22no—
87C42×C13—41no—
88C42×C13—41no—
89C22⋊Dic13—24no—
90C22⋊Dic13—42no—
91C4⋊Dic13—21no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13C2×C812yes—
95#6101—24no—
96#6101—42no—
97#6101—41no—
98#6101—41no—
99C4×Dic13—42no—
100C4×Dic13—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103C2×#1055—42no—
104C4×C22⋊Q8—131no—
105#1817D1311yescharacteristic
106#1797—131no—
107#1272—132no—
108#1271—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C22⋊C812yes—
116C23×C13C2×C22⋊C411yescharacteristic
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
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—42no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13C22⋊C812yes—
136C2×C4×C13#9912yes—
137C2×C4×C13C22×C811yescharacteristic
138C2×C4×C13C2×M1611yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×C4×C13#13712yes—
142C2×Dic13—22no—
143C2×Dic13—22no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154Dic26—42no—
155Dic26—42no—
156C8×C13—82no—
157#1055—82no—
158C2×C22⋊Q8—131no—
159C2×C4×Q8—131no—
160C22×C42C2×D1311yescharacteristic
161C2×C4⋊C8—261no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8—261no—
164#391—131no—
165#389—131no—
166#387—261no—
167#385—261no—
168#380—131no—
169C4×C4⋊C4—131no—
170C4×C4⋊C4—261no—
171C4×C22⋊C4—261no—
172#336—21no—
173#336—132no—
174#336C2×D1312yes—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C2×C22⋊C811yescharacteristic
183C22×C13C2×#9911yescharacteristic
184C22×C13#41311yescharacteristic
185C22×C13#41711yescharacteristic
186C22×C13#41911yescharacteristic
187C22×C13#42111yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—22no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—41no—
197Dic13—42no—
198Dic13—42no—
199Dic13—81no—
200Dic13—81no—
201C22×Q8—131no—
202C23×C4C4×D1311yescharacteristic
203C23×C4D5211yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C22×C8—22no—
206C22×C8—262no—
207C22⋊Q8—134no—
208C22⋊Q8—262no—
209C4×Q8—522no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C42—42no—
219C2×C42—261no—
220C2×C42—261no—
221C2×C42C4×D1311yescharacteristic
222C2×C42D5211yescharacteristic
223C2×C42C22⋊D1311yescharacteristic
224C2×C42C22×D1311yescharacteristic
225C4⋊C8—522no—
226C22⋊C8—42no—
227C22⋊C8—522no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13—42no—
234C2×C13#145911yescharacteristic
235C2×C13#147711yescharacteristic
236C2×C13#147911yescharacteristic
237C2×C13#151111yescharacteristic
238C2×C13#151311yescharacteristic
239C2×C13#153511yescharacteristic
240C2×C13#155911yescharacteristic
241C24#610311yescharacteristic
242C2×Q8—132no—
243C2×Q8—261no—
244C2×Q8—521no—
245C2×Q8—521no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4C8×D1312yes—
260C22×C4#609412yes—
261C22×C4#610311yescharacteristic
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4C2×C4×D1311yescharacteristic
265C22×C4C2×D5211yescharacteristic
266C22×C4C2×C22⋊D1311yescharacteristic
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—522no—
271C2×C8—522no—
272C2×C8—522no—
273C4⋊C4—132no—
274C4⋊C4—261no—
275C4⋊C4—264no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C4⋊C4—522no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C22⋊C4—264no—
282C22⋊C4—522no—
283C42—22no—
284C42—22no—
285C42—41no—
286C42—41no—
287C42—522no—
288C42—522no—
289C13#760011yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#8806012yes—
297C23C2×#610311yescharacteristic
298Q8—522no—
299Q8—522no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4#8804612yes—
331C2×C4#8806012yes—
332C2×C4C2×C8×D1311yescharacteristic
333C2×C4C2×#609411yescharacteristic
334C2×C4#8816211yescharacteristic
335C2×C4#8816311yescharacteristic
336C2×C4#8820512yes—
337C8—82no—
338C8—1042no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×#8804611yescharacteristic
347C22#1171866511yescharacteristic
348C22#1171866611yescharacteristic
349C22C2×#8806011yescharacteristic
350C22#1171879311yescharacteristic
351C22#1171879411yescharacteristic
352C22#1171880011yescharacteristic
353C4—22no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—22no—
360C4—41no—
361C4—522no—
362C4—522no—
363C4—1041no—
364C4—1041no—
365C2—42no—
366C2#1311315211yescharacteristic
367C2#1311322411yescharacteristic
368C2#1311323011yescharacteristic
369C2#1311336811yescharacteristic
370C2#1311338011yescharacteristic
371C2#1311346511yescharacteristic
372C2#1311356711yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1817C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1817D13
hypocenterC13#7600
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #13112661C2semidirect
4. #13112658C2semidirect
39. #88178C8semidirect
289. C13#7600semidirect

Maximal subgroups

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

subgroupindex
C4×#881782
#131148162
#131126612
#131126582
C13×#18172
#760013