Finite Group Databasebeta

← #15779227

Subgroups — #15779227

Order 3328.

442 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#107C211yesmaximal, characteristic
2#13116446C211yesmaximal, characteristic
3#13114871C211yesmaximal, characteristic
4#13112946C211yesmaximal, characteristic, complemented
5#13112945C211yesmaximal, characteristic, complemented
6#13112944C211yesmaximal, characteristic, complemented
7C13×#1387C211yesmaximal, characteristic, complemented
8C22×C8×D13C2211yescharacteristic
9C2×C4⋊C4×D13—21no—
10C2×C13×M32C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13#11718787—21no—
14C2×#88059C2211yescharacteristic
15C2×#88058C2211yescharacteristic
16C2×#88052C2211yescharacteristic
17C2×#88047—21no—
18D13×#107—21no—
19D13×#107—21no—
20D13×#107C412yes—
21D13×#107C412yes—
22#11718150—21no—
23#11718099—21no—
24#11718099—21no—
25C22×C4×D13—41no—
26C22×C4×D13D411yescharacteristic
27C2×C13×M16—21no—
28C22×C8×C13C2311yescharacteristic
29C2×C13×C4⋊C4—21no—
30C2×C4⋊Dic13—21no—
31C2×#6101—41no—
32C2×#6099—21no—
33C22×#1055D411yescharacteristic
34C2×C8×D13—21no—
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—21no—
38C2×C8×D13C2×C411yescharacteristic
39C2×C8×D13C2×C411yescharacteristic
40C2×C8×D13D411yescharacteristic
41C2×C8×D13D411yescharacteristic
42C4⋊C4×D13—22no—
43C4⋊C4×D13—22no—
44C4⋊C4×D13—41no—
45C4⋊C4×D13—41no—
46C13×M32—21no—
47C13×M32—21no—
48C2×C13×C16—21no—
49C13×#108—21no—
50C13×#108—21no—
51C13×#107—21no—
52C13×#107C2×C412yes—
53#88060—41no—
54#88060—41no—
55#88059—21no—
56#88059—21no—
57#88058—21no—
58#88058C2×C412yes—
59#88052—21no—
60#88052—21no—
61C2×#6090—21no—
62#88047—22no—
63#88047—22no—
64#12871—131nomaximal, Sylow
65C23×D13SD1611yescharacteristic
66C22×C4×C13—41no—
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—41no—
69C22×Dic13SD1611yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—42no—
75C2×C4×D13—42no—
76C2×C4×D13—84no—
77C2×C4×D13C22⋊C411yescharacteristic
78C2×C4×D13C22⋊C411yescharacteristic
79C2×C4×D13D811yescharacteristic
80C2×C4×D13D811yescharacteristic
81C13×M16—41no—
82C13×M16—41no—
83C2×C8×C13—41no—
84C2×C8×C13C22×C411yescharacteristic
85C2×C8×C13C2×D411yescharacteristic
86C2×C8×C13#4111yescharacteristic
87C2×C8×C13#4111yescharacteristic
88C2×C8×C13#4111yescharacteristic
89C2×C8×C13#4111yescharacteristic
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C4⋊Dic13—22no—
93C4⋊Dic13—41no—
94#6101—42no—
95#6101—42no—
96#6099—41no—
97#6099—41no—
98C2×#1055—21no—
99C2×#1055—21no—
100C2×#1055—41no—
101C2×#1055C22⋊C411yescharacteristic
102C2×#1055C22⋊C411yescharacteristic
103C8×D13—21no—
104C8×D13—21no—
105C8×D13—21no—
106C8×D13—21no—
107C8×D13—21no—
108C8×D13—21no—
109C8×D13—21no—
110C8×D13—21no—
111C13×C16—41no—
112#6090—41no—
113C22×#107—131no—
114#2112—131no—
115#1810—131no—
116#1387—131no—
117#1387—131no—
118#1387—131no—
119#1387D1311yescharacteristic, complemented
120C23×C13C2×SD1611yescharacteristic
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—22no—
124C22×D13—22no—
125C22×D13#10211yescharacteristic
126C22×D13#10211yescharacteristic
127C2×C4×C13—42no—
128C2×C4×C13—82no—
129C2×C4×C13C2×C22⋊C411yescharacteristic
130C2×C4×C13#12311yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13C2×D811yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—42no—
138C2×Dic13—82no—
139C2×Dic13#10211yescharacteristic
140C2×Dic13#10211yescharacteristic
141C4×D13—21no—
142C4×D13—21no—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—84no—
150C4×D13—84no—
151C8×C13—81no—
152C8×C13#11711yescharacteristic
153C8×C13#11711yescharacteristic
154C8×C13#12311yescharacteristic
155C8×C13#12311yescharacteristic
156#1055—21no—
157#1055—21no—
158#1055—81no—
159C23×C8—131no—
160C22×C4⋊C4—261no—
161C2×M32—131no—
162C2×M32C2×D1311yescharacteristic
163C2×#108—131no—
164C2×#108C2×D1311yescharacteristic
165C2×#107—131no—
166C2×#107—132no—
167C2×#107—132no—
168C2×#107—261no—
169C2×#107—261no—
170C2×#107—261no—
171C2×#107C2×D1311yescharacteristic
172#407—261no—
173C22⋊C16—261no—
174C22⋊C16—261no—
175#341—261no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13C2×#10211yescharacteristic
179C22×C13#48311yescharacteristic
180C22×C13#48311yescharacteristic
181C2×D13—24no—
182C2×D13—24no—
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—21no—
187C2×D13#36112yes—
188C2×D13#36212yes—
189C4×C13—82no—
190C4×C13#38111yescharacteristic
191C4×C13#41911yescharacteristic
192C4×C13#48011yescharacteristic
193C4×C13#48011yescharacteristic
194Dic13—21no—
195Dic13—21no—
196Dic13—82no—
197C23×C4—131no—
198C23×C4—521no—
199C2×M16—21no—
200C2×M16—261no—
201C22×C8—131no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—131no—
205C22×C8—131no—
206C22×C8—261no—
207C22×C8—261no—
208C22×C8—261no—
209C22×C8—261no—
210C22×C8C22×D1311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4—262no—
213C2×C4⋊C4—262no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—521no—
216C2×C4⋊C4—521no—
217C2×C4⋊C4—521no—
218M32—21no—
219M32—21no—
220M32—261no—
221M32—261no—
222C2×C16—21no—
223C2×C16—261no—
224#108—21no—
225#108—21no—
226#108—261no—
227#108—261no—
228#107—21no—
229#107—132no—
230#107—262no—
231#107—262no—
232#107—261no—
233#107C4×D1312yes—
234C22⋊C8—521no—
235C22⋊C8—521no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#182311yescharacteristic
239C2×C13C2×#36111yescharacteristic
240C2×C13C2×#36211yescharacteristic
241D13—22no—
242D13—22no—
243C24—131no—
244C22×C4—41no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4—521no—
257C22×C4—1044no—
258C22×C4D4×D1311yescharacteristic
259M16—41no—
260M16—41no—
261M16—521no—
262M16—521no—
263C2×C8—41no—
264C2×C8—131no—
265C2×C8—131no—
266C2×C8—261no—
267C2×C8—261no—
268C2×C8—261no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—261no—
272C2×C8—261no—
273C2×C8—261no—
274C2×C8—261no—
275C2×C8—261no—
276C2×C8—521no—
277C2×C8C2×C4×D1311yescharacteristic
278C2×C8#612711yescharacteristic
279C2×C8#612711yescharacteristic
280C2×C8D4×D1311yescharacteristic
281C2×C8#612911yescharacteristic
282C2×C8#613111yescharacteristic
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—262no—
286C4⋊C4—522no—
287C4⋊C4—522no—
288C4⋊C4—521no—
289C16—41no—
290C16—521no—
291C13#1287111yescharacteristic, complemented, Sylow
292C23—131no—
293C23—131no—
294C23—262no—
295C23—262no—
296C23—261no—
297C23—261no—
298C23SD16×D1311yescharacteristic
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—522no—
314C2×C4—1044no—
315C2×C4—1044no—
316C2×C4—1042no—
317C2×C4C22⋊C4×D1311yescharacteristic
318C2×C4#8813711yescharacteristic
319C2×C4#8814811yescharacteristic
320C2×C4D8×D1311yescharacteristic
321C2×C4#8816911yescharacteristic
322C2×C4#8817211yescharacteristic
323C8—81no—
324C8—261no—
325C8—261no—
326C8—1041no—
327C8#8812611yescharacteristic
328C8#8813711yescharacteristic
329C8#8814611yescharacteristic
330C8#8814811yescharacteristic
331C22—21no—
332C22—21no—
333C22—132no—
334C22—132no—
335C22—264no—
336C22—264no—
337C22—261no—
338C22—261no—
339C22—261no—
340C22—261no—
341C22D13×#10211yescharacteristic
342C22#1171846611yescharacteristic
343C22#1171852311yescharacteristic
344C4—82no—
345C4—261no—
346C4—261no—
347C4—1042no—
348C4#1171832511yescharacteristic
349C4#1171843511yescharacteristic
350C4#1171846311yescharacteristic
351C4#1171854311yescharacteristic
352C2—21no—
353C2—21no—
354C2—262no—
355C2—262no—
356C2#1311492111yescharacteristic
357C2D13×#36111yescharacteristic
358C2D13×#36211yescharacteristic
subgroupG/H
centerC22D13×#102
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1387C2
socleC22×C13C2×#102
prime radicalC23×D13SD16
cosocleC22×C8×C13C23
hypercenter#1387D13
hypocenterC13#12871
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
4. #13112946C2semidirect
5. #13112945C2semidirect
6. #13112944C2semidirect
7. C13×#1387C2semidirect
119. #1387D13semidirect
291. C13#12871semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1072
#131164462
#131148712
#131129462
#131129452
#131129442
C13×#13872
#1287113