Finite Group Databasebeta

← #15750957

Subgroups — #15750957

Order 3328.

522 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88178C211yesmaximal, characteristic
2C4×C22⋊#1055C211yesmaximal, characteristic
3#13112661C212yesmaximal, complemented
4#13112660C212yesmaximal, 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—24no—
54C4×#1055—42no—
55#7583—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C2×C812yes—
69C22×C4×C13M1612yes—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×Dic26—21no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26C2×C812yes—
81C2×C8×C13—42no—
82C2×C8×C13—42no—
83C2×C8×C13—42no—
84C42×C13—22no—
85C42×C13—22no—
86C42×C13—41no—
87C42×C13—41no—
88C22⋊Dic13—24no—
89C22⋊Dic13—42no—
90C4⋊Dic13—21no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13C2×C812yes—
94#6101—24no—
95#6101—42no—
96#6101—42no—
97C4×Dic13—42no—
98C4×Dic13—42no—
99C2×#1055—24no—
100C2×#1055—42no—
101C2×#1055—42no—
102C4×C22⋊Q8—131no—
103#1817D1311yescharacteristic
104C4×C22⋊C8—131no—
105#1272—132no—
106#1271—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13C22⋊C812yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13—21no—
116C2×C4×C13—21no—
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—42no—
128C2×C4×C13—42no—
129C2×C4×C13—44no—
130C2×C4×C13—44no—
131C2×C4×C13C22⋊C812yes—
132C2×C4×C13#9912yes—
133C2×C4×C13#10412yes—
134C2×C4×C13C22×C811yescharacteristic
135C2×C4×C13C2×M1611yescharacteristic
136C2×C4×C13#13512yes—
137C2×C4×C13#13712yes—
138C2×Dic13—22no—
139C2×Dic13—22no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150Dic26—42no—
151Dic26—42no—
152C8×C13—82no—
153#1055—44no—
154C2×C22⋊Q8—131no—
155C2×C4×Q8—131no—
156C22×C42C2×D1311yescharacteristic
157C2×C22⋊C8—21no—
158C2×C22⋊C8—261no—
159C2×C4×C8—261no—
160#391—131no—
161#389—131no—
162#387—261no—
163#385—261no—
164#380—131no—
165C4×C4⋊C4—131no—
166C4×C4⋊C4—261no—
167C4×C22⋊C4—261no—
168#336—21no—
169#336—132no—
170#336C2×D1312yes—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13C2×C22⋊C811yescharacteristic
179C22×C13C2×#9911yescharacteristic
180C22×C13#41311yescharacteristic
181C22×C13#41611yescharacteristic
182C22×C13#41911yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C22×C13#42111yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—22no—
192Dic13—42no—
193Dic13—42no—
194Dic13—81no—
195Dic13—81no—
196C22×Q8—131no—
197C23×C4C4×D1311yescharacteristic
198C23×C4D5211yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C22×C8—22no—
201C22×C8—262no—
202C22⋊Q8—134no—
203C22⋊Q8—262no—
204C4×Q8—522no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C42—42no—
214C2×C42—261no—
215C2×C42—261no—
216C2×C42C4×D1311yescharacteristic
217C2×C42D5211yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C2×C42C22×D1311yescharacteristic
220C22⋊C8—42no—
221C22⋊C8—264no—
222C4×C8—522no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13—42no—
229C2×C13#145911yescharacteristic
230C2×C13#147611yescharacteristic
231C2×C13#147911yescharacteristic
232C2×C13#150811yescharacteristic
233C2×C13#151611yescharacteristic
234C2×C13#152911yescharacteristic
235C2×C13#155411yescharacteristic
236C24#610311yescharacteristic
237C2×Q8—132no—
238C2×Q8—261no—
239C2×Q8—521no—
240C2×Q8—521no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C8×D1312yes—
254C22×C4#609412yes—
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4#610311yescharacteristic
258C22×C4C2×C4×D1311yescharacteristic
259C22×C4C2×D5211yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C2×C8—264no—
265C2×C8—522no—
266C2×C8—522no—
267C4⋊C4—132no—
268C4⋊C4—261no—
269C4⋊C4—264no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—522no—
273C4⋊C4—522no—
274C22⋊C4—264no—
275C22⋊C4—522no—
276C42—22no—
277C42—22no—
278C42—41no—
279C42—41no—
280C42—522no—
281C42—522no—
282C13#758311yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#8806012yes—
290C23C2×#610311yescharacteristic
291Q8—522no—
292Q8—522no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—262no—
310C2×C4—262no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4#8804612yes—
322C2×C4#8806012yes—
323C2×C4#8806512yes—
324C2×C4C2×C8×D1311yescharacteristic
325C2×C4C2×#609411yescharacteristic
326C2×C4#8816312yes—
327C2×C4#8820412yes—
328C8—82no—
329C8—524no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×#8804611yescharacteristic
338C22#1171866311yescharacteristic
339C22#1171866611yescharacteristic
340C22C2×#8806011yescharacteristic
341C22#1171878111yescharacteristic
342C22#1171879311yescharacteristic
343C22C2×#8806511yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—22no—
348C4—21no—
349C4—21no—
350C4—22no—
351C4—522no—
352C4—522no—
353C4—1041no—
354C4—1041no—
355C2—42no—
356C2#1311315211yescharacteristic
357C2#1311321611yescharacteristic
358C2#1311323211yescharacteristic
359C2#1311335711yescharacteristic
360C2#1311339011yescharacteristic
361C2#1311344411yescharacteristic
362C2#1311354711yescharacteristic
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#7583
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. #13112660C2semidirect
39. #88178C8semidirect
282. C13#7583semidirect

Maximal subgroups

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

subgroupindex
C4×#881782
C4×C22⋊#10552
#131126612
#131126602
C13×#18172
#758313