Finite Group Databasebeta

← #16789373

Subgroups — #16789373

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#504C211yesmaximal, characteristic
2#13131048C211yesmaximal, characteristic, complemented
3C2×C16×#261C211yesmaximal, characteristic, complemented
4#13130610C211yesmaximal, characteristic
5#13129889C211yesmaximal, characteristic, complemented
6#13129879C211yesmaximal, characteristic, complemented
7D13×#350C211yesmaximal, characteristic
8D13×#131C2211yescharacteristic
9#11719165C411yescharacteristic
10D13⋊#104C411yescharacteristic
11#11719162C412yescomplemented
12#11719096—22no—
13#11719096C412yescomplemented
14#11719089C2211yescharacteristic
15C2×C8×#261C2211yescharacteristic
16D13⋊M32—21no—
17D13⋊M32C2211yescharacteristic
18C2×D13⋊C16—21no—
19C2×D13⋊C16C2211yescharacteristic
20D13×M32C2211yescharacteristic
21C2×C16×D13C2211yescharacteristic
22#11718273C411yescharacteristic
23#11718272C411yescharacteristic
24#11718216—21no—
25C16×#261—22no—
26C16×#261—21no—
27C13×#350C411yescharacteristic, complemented
28#11718153C411yescharacteristic, complemented
29#11718107C411yescharacteristic, complemented
30#11718100C411yescharacteristic, complemented
31#41×D13C2×C411yescharacteristic
32#88237C2×C411yescharacteristic
33C2×C4×#261C2×C411yescharacteristic
34D13⋊M16C2×C411yescharacteristic
35C2×D13⋊C8C2×C411yescharacteristic
36C13×#131C2×C411yescharacteristic
37#88202C2×C411yescharacteristic
38#88161—21no—
39#88161C2×C411yescharacteristic
40M16×D13—21no—
41M16×D13C2×C411yescharacteristic
42#88155—21no—
43#88155C2×C411yescharacteristic
44C2×C8×D13—21no—
45C2×C8×D13C2311yescharacteristic
46#88118C812yes—
47#88117C812yes—
48#88116C812yes—
49#88115C812yes—
50#88106—22no—
51#88106C2×C412yes—
52C2×#6092—22no—
53C2×#6092C2×C412yes—
54#88100—21no—
55C8×#261—21no—
56C8×#261—21no—
57C8×#261—21no—
58#88098—21no—
59#88098—22no—
60D13⋊C16—21no—
61D13⋊C16—22no—
62D13⋊C16D411yescharacteristic
63D13⋊C16D412yes—
64D13⋊C16D411yescharacteristic
65C13×M32C2×C411yescharacteristic
66C2×C13×C16C2×C411yescharacteristic
67#88052C2×C411yescharacteristic
68C2×#6090C2×C411yescharacteristic
69#88038—21no—
70C16×D13—21no—
71C16×D13—21no—
72C16×D13—21no—
73#12614—131nomaximal, Sylow
74C22×#261—21no—
75C13×#41C4211yescharacteristic
76#6131C2×C811yescharacteristic
77Q8×D13C2×C811yescharacteristic
78#6129—21no—
79#6129C2×C811yescharacteristic
80D4×D13—21no—
81D4×D13C2×C811yescharacteristic
82#6127—21no—
83#6127C4211yescharacteristic
84C2×C4×D13—21no—
85C2×C4×D13C22×C411yescharacteristic
86C22⋊#261—21no—
87#6122—21no—
88C2×#1057—21no—
89C4⋊#261C2×C812yes—
90C4×#261—21no—
91C4×#261—21no—
92C4×#261C2×C812yes—
93#6118C2×C812yes—
94D13⋊C8—21no—
95D13⋊C8—21no—
96D13⋊C8C2×C812yes—
97C13×M16—21no—
98C13×M16C4211yescharacteristic
99C2×C8×C13—21no—
100C2×C8×C13C22×C411yescharacteristic
101#6099—21no—
102#6099C4211yescharacteristic
103C2×#1055—21no—
104C2×#1055C22×C411yescharacteristic
105#6094—21no—
106#6094—21no—
107#6094—21no—
108C8×D13—21no—
109C8×D13—21no—
110C8×D13—21no—
111C8×D13C2×D411yescharacteristic
112C8×D13C2×D411yescharacteristic
113C8×D13#4111yescharacteristic
114C8×D13#4111yescharacteristic
115#6092—22no—
116#6092C22⋊C412yes—
117#6092C22⋊C412yes—
118C13×C16—21no—
119C13×C16—21no—
120#6090—21no—
121#6090—21no—
122C2×#504—131no—
123C2×#350—131no—
124#2108—131no—
125C2×C4×C16—131no—
126#1764—131no—
127#1379—131no—
128#1376—131no—
129C22×D13—21no—
130C22×D13#13111yescharacteristic
131C2×#261—24no—
132C2×#261—22no—
133C2×#261—22no—
134Q8×C13C4×C811yescharacteristic
135D4×C13—21no—
136D4×C13C4×C811yescharacteristic
137C2×C4×C13—21no—
138C2×C4×C13C2×C4211yescharacteristic
139C22⋊D13—21no—
140C22⋊D13—21no—
141C22⋊D13—21no—
142C2×Dic13—21no—
143C2×Dic13#13111yescharacteristic
144D52—21no—
145D52C4×C811yescharacteristic
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13C4×D411yescharacteristic
150C4×D13C4×D411yescharacteristic
151C4×D13C22×C811yescharacteristic
152C4×D13C22×C811yescharacteristic
153Dic26—21no—
154Dic26C4×C811yescharacteristic
155#1057—22no—
156#1057—22no—
157C8×C13—21no—
158C8×C13C4×D411yescharacteristic
159C8×C13C4×D411yescharacteristic
160#1055—21no—
161#1055C2×C22⋊C411yescharacteristic
162#1055#11711yescharacteristic
163C2×#131—131no—
164#504—132no—
165#504—132no—
166#504—262no—
167C2×M32—131no—
168C2×M32—131no—
169C2×M32—261no—
170C22×C16—131no—
171C22×C16—131no—
172C22×C16—261no—
173C2×#104—131no—
174#416—131no—
175#405—131no—
176C2×C4×C8—131no—
177#350—131no—
178#350—131no—
179#350—131no—
180#350#26111yescharacteristic, complemented
181#346—261no—
182C4×C16—262no—
183C4×C16—261no—
184#341—131no—
185#339—131no—
186C22×C13—21no—
187C22×C13#40511yescharacteristic
188C2×D13—22no—
189C2×D13—21no—
190C2×D13—42no—
191C2×D13C8×D411yescharacteristic
192C2×D13C8×D411yescharacteristic
193#261—24no—
194#261—42no—
195C4×C13—21no—
196C4×C13C4×C22⋊C411yescharacteristic
197C4×C13C2×C4×C811yescharacteristic
198Dic13—21no—
199Dic13C8×D411yescharacteristic
200Dic13C8×D411yescharacteristic
201C2×#41—131no—
202#131—131no—
203#131—131no—
204#131—131no—
205#131—261no—
206#131—261no—
207#131C2×#26111yescharacteristic
208C2×M16—131no—
209C2×M16—131no—
210C2×M16—261no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—261no—
214#117—131no—
215C2×C42—131no—
216M32—132no—
217M32—131no—
218M32—261no—
219M32—262no—
220M32—262no—
221M32—261no—
222M32C2×#26111yescharacteristic
223C2×C16—131no—
224C2×C16—132no—
225C2×C16—131no—
226C2×C16—132no—
227C2×C16—131no—
228C2×C16—261no—
229C2×C16—261no—
230C2×C16—261no—
231C2×C16—262no—
232C2×C16—262no—
233C2×C16—261no—
234C2×C16C2×#26111yescharacteristic
235#104—132no—
236#104—132no—
237#103—132no—
238#102—132no—
239#97—261no—
240C4×C8—261no—
241C4×C8—261no—
242C4×C8—261no—
243C2×C13—21no—
244C2×C13—41no—
245C2×C13C8×C22⋊C411yescharacteristic
246D13—21no—
247D13—41no—
248D13#217012yes—
249#41—131no—
250#41—131no—
251#41—131no—
252#41—261no—
253#41—261no—
254#41C4×#26111yescharacteristic
255C2×Q8—131no—
256C2×D4—131no—
257C2×D4—261no—
258C22×C4—131no—
259C22×C4—261no—
260C22×C4—261no—
261M16—21no—
262M16—132no—
263M16—131no—
264M16—261no—
265M16—261no—
266M16—261no—
267M16—261no—
268M16—261no—
269M16C4×#26111yescharacteristic
270C2×C8—21no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8—131no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8—132no—
277C2×C8—261no—
278C2×C8—261no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8C22×#26111yescharacteristic
285C4⋊C4—132no—
286C22⋊C4—261no—
287C42—132no—
288C42—261no—
289C42—261no—
290C16—21no—
291C16—21no—
292C16—132no—
293C16—132no—
294C16—262no—
295C16—261no—
296C16—261no—
297C13#1261411yescharacteristic, complemented, Sylow
298C23—131no—
299C23—261no—
300Q8—131no—
301Q8—261no—
302Q8C8×#26111yescharacteristic
303D4—21no—
304D4—131no—
305D4—261no—
306D4—261no—
307D4—261no—
308D4—261no—
309D4C8×#26111yescharacteristic
310C2×C4—21no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—262no—
320C2×C4—264no—
321C2×C4—261no—
322C2×C4—262no—
323C2×C4C2×C4×#26111yescharacteristic
324C8—21no—
325C8—131no—
326C8—131no—
327C8—262no—
328C8—262no—
329C8—261no—
330C8D4×#26111yescharacteristic
331C8D4×#26111yescharacteristic
332C22—21no—
333C22—131no—
334C22—131no—
335C22—262no—
336C22—261no—
337C22—522no—
338C22#1171909911yescharacteristic
339C4—21no—
340C4—131no—
341C4—131no—
342C4—264no—
343C4—261no—
344C4—522no—
345C4C22⋊C4×#26111yescharacteristic
346C4C2×C8×#26111yescharacteristic
347C2—21no—
348C2—41no—
349C2—132no—
350C2—261no—
351C2—521no—
352C2#1313057111yescharacteristic
subgroupG/H
centerC8D4×#261
commutatorC4×C13C2×C4×C8
FrattiniC2×C8C22×#261
FittingC13×#350C4
socleC2×C13C8×C22⋊C4
prime radical#41×D13C2×C4
cosocleC2×C8×D13C23
hypercenter#350#261
hypocenterC13#12614
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. #13131048C2semidirect
3. C2×C16×#261C2semidirect
5. #13129889C2semidirect
6. #13129879C2semidirect
11. #11719162C4semidirect
13. #11719096C4semidirect
27. C13×#350C4semidirect
28. #11718153C4semidirect
29. #11718107C4semidirect
30. #11718100C4semidirect
180. #350#261semidirect
297. C13#12614semidirect

Maximal subgroups

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

subgroupindex
D13⋊#5042
#131310482
C2×C16×#2612
#131306102
#131298892
#131298792
D13×#3502
#1261413