Finite Group Databasebeta

← #15767374

Subgroups — #15767374

Order 3328.

406 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120075C211yesmaximal, characteristic
2#13115600C211yesmaximal, characteristic
3#13115599C211yesmaximal, characteristic
4#13114996C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic
7C13×#1279C211yesmaximal, characteristic
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C4×C8×C13C2211yescharacteristic
10C4×C13×C4⋊C4C2211yescharacteristic
11C2×#88058—22no—
12C2×#88057—21no—
13#11718638—21no—
14#11718634—21no—
15C2×#88048—21no—
16#11718597—21no—
17#11718596C2211yescharacteristic
18#11718596C2211yescharacteristic
19C4×C4⋊Dic13C2211yescharacteristic
20#11718589—21no—
21C2×C4⋊#1055C2211yescharacteristic
22#11718321—22no—
23#11718143—21no—
24#11718121—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C42×C13—21no—
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D412yes—
39C2×#6101—22no—
40C2×C4×Dic13—21no—
41C22×#1055—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8Q812yes—
44C4×C8×C13—21no—
45C4×C8×C13Q812yes—
46C13×#95—21no—
47#88071—22no—
48#88071—22no—
49#88071—22no—
50#88071—21no—
51#88058—44no—
52#88057—42no—
53#88048—42no—
54C4⋊#1055—21no—
55C4⋊#1055Q812yes—
56#10576—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—22no—
65C22×Dic13—41no—
66C2×C8×C13—22no—
67C2×C8×C13—22no—
68C2×C8×C13—22no—
69C2×C8×C13—22no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C42×C13—41no—
77C42×C13—41no—
78C42×C13C2×Q811yescharacteristic
79C42×C13C2×Q811yescharacteristic
80C42×C13C2×Q811yescharacteristic
81C42×C13#4111yescharacteristic
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—42no—
91C4⋊Dic13—42no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96#6101—82no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C2×#1055—22no—
100C2×#1055—41no—
101C2×#1055—41no—
102#2571—131no—
103#1948—131no—
104#1948—131no—
105#1845—131no—
106#1296—131no—
107#1279—131no—
108#1279D1311yescharacteristic
109C23×C13#12011yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13C22⋊Q811yescharacteristic
119C2×C4×C13C22⋊Q811yescharacteristic
120C2×C4×C13C22⋊Q811yescharacteristic
121C2×C4×C13C4⋊Q811yescharacteristic
122C2×C4×C13C4⋊Q811yescharacteristic
123C2×C4×C13C4⋊Q811yescharacteristic
124C2×C4×C13#13511yescharacteristic
125C2×C4×C13#13511yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—42no—
140C2×Dic13—41no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C8×C13—24no—
145C8×C13—42no—
146#1055—42no—
147C2×#107—262no—
148C2×#106—261no—
149C2×#106—261no—
150C2×C4⋊C8—131no—
151C2×C4⋊C8C2×D1311yescharacteristic
152C2×C4×C8C2×D1311yescharacteristic
153#400—262no—
154#389—261no—
155#389—261no—
156#384—131no—
157#384—131no—
158#382—261no—
159#382—261no—
160C4×C4⋊C4—131no—
161C4×C4⋊C4C2×D1311yescharacteristic
162#340—261no—
163#340—261no—
164C22×C13#39511yescharacteristic
165C22×C13#44911yescharacteristic
166C22×C13#44911yescharacteristic
167C22×C13#45211yescharacteristic
168C22×C13#45211yescharacteristic
169C22×C13#45311yescharacteristic
170C22×C13#45611yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—81no—
174C4×C13—81no—
175C4×C13#47811yescharacteristic
176C4×C13#47811yescharacteristic
177C4×C13#47911yescharacteristic
178C4×C13#47911yescharacteristic
179C4×C13#49911yescharacteristic
180C4×C13#49911yescharacteristic
181C4×C13#50111yescharacteristic
182C4×C13#50111yescharacteristic
183Dic13—82no—
184Dic13—81no—
185Dic13—81no—
186Dic13—161no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—261no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—132no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—262no—
199C2×C4⋊C4D5211yescharacteristic
200C2×C4⋊C4D5211yescharacteristic
201C2×C42—21no—
202C2×C42—261no—
203C2×C42C22×D1311yescharacteristic
204#107—524no—
205#106—522no—
206#106—522no—
207C4⋊C8—21no—
208C4⋊C8—132no—
209C4⋊C8—261no—
210C4⋊C8Dic2612yes—
211C4×C8—21no—
212C4×C8Dic2612yes—
213#95—21no—
214#95—262no—
215#95—262no—
216#95—262no—
217#95—261no—
218C2×C13#162011yescharacteristic
219C2×C13#163411yescharacteristic
220C2×C13#165011yescharacteristic
221C2×C13#165011yescharacteristic
222C2×C13#205911yescharacteristic
223C2×C13#205911yescharacteristic
224C2×C13#206011yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—262no—
230C22×C4—521no—
231C22×C4C2×D5211yescharacteristic
232C22×C4D4×D1311yescharacteristic
233C22×C4D4×D1311yescharacteristic
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—262no—
241C2×C8—521no—
242C2×C8—521no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—522no—
252C4⋊C4—522no—
253C4⋊C4—521no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—1042no—
262C42—41no—
263C42—41no—
264C42—521no—
265C42—521no—
266C42C2×Dic2611yescharacteristic
267C42C2×Dic2611yescharacteristic
268C42#612911yescharacteristic
269C42Q8×D1311yescharacteristic
270C13#1057611yescharacteristic, complemented, Sylow
271C23#8813611yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—522no—
283C2×C4—522no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—522no—
289C2×C4—1041no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4#8812311yescharacteristic
293C2×C4#8813211yescharacteristic
294C2×C4#8813211yescharacteristic
295C2×C4#8814211yescharacteristic
296C2×C4#8814211yescharacteristic
297C2×C4#8815111yescharacteristic
298C2×C4#8815811yescharacteristic
299C2×C4#8815811yescharacteristic
300C2×C4#8816211yescharacteristic
301C2×C4#8816311yescharacteristic
302C2×C4#8816611yescharacteristic
303C2×C4#8816811yescharacteristic
304C2×C4#8816911yescharacteristic
305C2×C4#8817311yescharacteristic
306C8—24no—
307C8—42no—
308C8—522no—
309C22#1171831711yescharacteristic
310C22#1171839411yescharacteristic
311C22#1171839511yescharacteristic
312C22#1171844411yescharacteristic
313C22#1171847211yescharacteristic
314C22#1171848311yescharacteristic
315C22#1171848711yescharacteristic
316C4—21no—
317C4—21no—
318C4—81no—
319C4—81no—
320C4—1042no—
321C4—1041no—
322C4—1041no—
323C4—2081no—
324C4#1171834411yescharacteristic
325C4#1171836311yescharacteristic
326C4#1171842711yescharacteristic
327C4#1171845711yescharacteristic
328C4#1171849011yescharacteristic
329C4#1171850811yescharacteristic
330C4#1171851711yescharacteristic
331C4#1171853911yescharacteristic
332C2#1311389711yescharacteristic
333C2#1311398311yescharacteristic
334C2#1311409411yescharacteristic
335C2#1311409511yescharacteristic
336C2#1311617511yescharacteristic
337C2#1311617711yescharacteristic
338C2#1311618011yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socle, prime radicalC23×C13#120
hypercenter#1279D13
hypocenterC13#10576
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
270. C13#10576semidirect

Maximal subgroups

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

subgroupindex
#131200752
#131156002
#131155992
#131149962
#131127202
#131126762
C13×#12792
#1057613