Finite Group Databasebeta

← #15779436

Subgroups — #15779436

Order 3328.

404 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#108C211yesmaximal, characteristic
2C2×#11718098C211yesmaximal, characteristic, complemented
3C2×#11718085C211yesmaximal, characteristic, complemented
4C2×#11718099C211yesmaximal, characteristic
5#13114871C211yesmaximal, characteristic
6#13112929C211yesmaximal, characteristic, complemented
7C13×#1381C211yesmaximal, characteristic, complemented
8C2×M16×D13—21no—
9C22×C8×D13C2211yescharacteristic
10C22×C13×C16C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C2×C13×#108C2211yescharacteristic
13#11718787—21no—
14C2×#88062—21no—
15C2×#88059C2211yescharacteristic
16C2×#88059C2211yescharacteristic
17C22×#6090C2211yescharacteristic
18D13×#108—22no—
19D13×#108—22no—
20#11718150—21no—
21#11718099C412yes—
22#11718099C412yes—
23#11718098—22no—
24#11718085—22no—
25C22×C4×D13D411yescharacteristic
26C2×C13×M16—21no—
27C2×C13×M16—21no—
28C22×C8×C13C2311yescharacteristic
29C2×#6099—21no—
30C2×#6099—21no—
31C22×#1055D411yescharacteristic
32M16×D13—24no—
33M16×D13—42no—
34C2×#6094—41no—
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—21no—
38C2×C8×D13—21no—
39C2×C8×D13—41no—
40C2×C8×D13C2×C411yescharacteristic
41C2×C8×D13C2×C411yescharacteristic
42C2×C8×D13Q811yescharacteristic
43C2×C8×D13Q811yescharacteristic
44C2×C13×C16—21no—
45C2×C13×C16—21no—
46C2×C13×C16C2×C412yes—
47C13×#108—21no—
48C13×#108—21no—
49C13×#108—21no—
50C13×#108D412yes—
51#88062—24no—
52#88060—41no—
53#88060—41no—
54#88059—21no—
55#88059—21no—
56#88059—21no—
57#88059D412yes—
58C2×#6090—21no—
59C2×#6090—21no—
60C2×#6090C2×C412yes—
61#12922—131nomaximal, Sylow
62C23×D13Q1611yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13Q1611yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C4⋊C411yescharacteristic
70C2×C4×D13C4⋊C411yescharacteristic
71C2×C4×D13D811yescharacteristic
72C2×C4×D13D811yescharacteristic
73C13×M16—22no—
74C13×M16—41no—
75C13×M16—41no—
76C13×M16—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13C22×C411yescharacteristic
80C2×C8×C13C2×D411yescharacteristic
81C2×C8×C13C2×D411yescharacteristic
82C2×C8×C13C2×Q811yescharacteristic
83C2×C8×C13#4111yescharacteristic
84C2×C8×C13#4111yescharacteristic
85#6099—22no—
86#6099—41no—
87#6099—41no—
88#6099—41no—
89C2×#1055—21no—
90C2×#1055—21no—
91C2×#1055—41no—
92C2×#1055—41no—
93C2×#1055C4⋊C411yescharacteristic
94C2×#1055C4⋊C411yescharacteristic
95#6094—44no—
96C8×D13—21no—
97C8×D13—21no—
98C8×D13—21no—
99C8×D13—21no—
100C8×D13—21no—
101C8×D13—21no—
102C8×D13—21no—
103C8×D13—21no—
104C8×D13—44no—
105C13×C16—22no—
106#6090—22no—
107C22×#108—131no—
108C2×#368—131no—
109C2×#368—131no—
110C2×C22⋊C16—131no—
111#1810—131no—
112#1381—131no—
113#1381D1311yescharacteristic, complemented
114C23×C13C2×Q1611yescharacteristic
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—22no—
118C22×D13—41no—
119C22×D13#10711yescharacteristic
120C22×D13#10711yescharacteristic
121C2×C4×C13C2×C4⋊C411yescharacteristic
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13C2×D811yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13#10711yescharacteristic
130C2×Dic13#10711yescharacteristic
131C4×D13—21no—
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—21no—
139C8×C13—42no—
140C8×C13—81no—
141C8×C13C4×D411yescharacteristic
142C8×C13C4×D411yescharacteristic
143C8×C13C22⋊Q811yescharacteristic
144C8×C13C22⋊Q811yescharacteristic
145#1055—21no—
146#1055—21no—
147#1055—42no—
148#1055—81no—
149C22×M16—261no—
150C23×C8—131no—
151C22×C16—131no—
152C22×C16C2×D1311yescharacteristic
153C2×#108—131no—
154C2×#108—131no—
155C2×#108—262no—
156C2×#108—261no—
157C2×#108—262no—
158C2×#108C2×D1311yescharacteristic
159C2×#108C2×D1311yescharacteristic
160#407—261no—
161#368—262no—
162#368—262no—
163C22⋊C16—132no—
164C22⋊C16—132no—
165#341—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13C2×#10711yescharacteristic
169C22×C13#45111yescharacteristic
170C22×C13#48411yescharacteristic
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—21no—
175C2×D13—21no—
176C2×D13—42no—
177C2×D13—42no—
178C2×D13#36812yescomplemented
179C4×C13#38511yescharacteristic
180C4×C13#42811yescharacteristic
181C4×C13#44711yescharacteristic
182C4×C13#48011yescharacteristic
183Dic13—21no—
184Dic13—21no—
185C23×C4—131no—
186C2×M16—21no—
187C2×M16—21no—
188C2×M16—264no—
189C2×M16—261no—
190C2×M16—261no—
191C2×M16—521no—
192C2×M16—522no—
193C22×C8—131no—
194C22×C8—131no—
195C22×C8—131no—
196C22×C8—131no—
197C22×C8—131no—
198C22×C8—261no—
199C22×C8—261no—
200C22×C8—261no—
201C22×C8—261no—
202C22×C8—521no—
203C22×C8C22×D1311yescharacteristic
204C2×C16—21no—
205C2×C16—21no—
206C2×C16—132no—
207C2×C16—261no—
208C2×C16—261no—
209C2×C16C4×D1312yes—
210#108—21no—
211#108—21no—
212#108—21no—
213#108—132no—
214#108—264no—
215#108—261no—
216#108—261no—
217#108—261no—
218#108D5212yes—
219C22⋊C8—521no—
220C22⋊C8—521no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13#185211yescharacteristic
224C2×C13C2×#36811yescharacteristic
225C2×C13#216111yescharacteristic
226D13—22no—
227D13—41no—
228C24—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4D4×D1311yescharacteristic
239M16—22no—
240M16—41no—
241M16—41no—
242M16—41no—
243M16—262no—
244M16—524no—
245M16—521no—
246M16—521no—
247M16—521no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—131no—
251C2×C8—131no—
252C2×C8—261no—
253C2×C8—261no—
254C2×C8—261no—
255C2×C8—261no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—261no—
260C2×C8—261no—
261C2×C8—261no—
262C2×C8—524no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8C2×C4×D1311yescharacteristic
266C2×C8C2×D5211yescharacteristic
267C2×C8#612711yescharacteristic
268C2×C8D4×D1311yescharacteristic
269C2×C8#612911yescharacteristic
270C2×C8Q8×D1311yescharacteristic
271C16—22no—
272C16—262no—
273C13#1292211yescharacteristic, complemented, Sylow
274C23—131no—
275C23—131no—
276C23—262no—
277C23—261no—
278C23—261no—
279C23—521no—
280C23Q16×D1311yescharacteristic
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4#8813611yescharacteristic
294C2×C4#8813711yescharacteristic
295C2×C4C4⋊C4×D1311yescharacteristic
296C2×C4D8×D1311yescharacteristic
297C2×C4#8816811yescharacteristic
298C2×C4#8816911yescharacteristic
299C8—42no—
300C8—81no—
301C8—261no—
302C8—261no—
303C8—522no—
304C8—1041no—
305C8C4×D5211yescharacteristic
306C8#8813511yescharacteristic
307C8#8815011yescharacteristic
308C8#8815111yescharacteristic
309C22—21no—
310C22—21no—
311C22—132no—
312C22—261no—
313C22—261no—
314C22—261no—
315C22—261no—
316C22—261no—
317C22—522no—
318C22—522no—
319C22#1171846911yescharacteristic
320C22#1171847011yescharacteristic
321C22D13×#10711yescharacteristic
322C4—261no—
323C4—261no—
324C4#1171832911yescharacteristic
325C4#1171843411yescharacteristic
326C4#1171843511yescharacteristic
327C4#1171852211yescharacteristic
328C2—21no—
329C2—21no—
330C2—262no—
331C2—521no—
332C2#1311502511yescharacteristic
333C2D13×#36811yescharacteristic
334C2#1311662911yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1381C2
socleC22×C13C2×#107
prime radicalC23×D13Q16
cosocleC22×C8×C13C23
hypercenter#1381D13
hypocenterC13#12922
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

Complements

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

NH ≅ G/Ntype
2. C2×#11718098C2semidirect
3. C2×#11718085C2semidirect
6. #13112929C2semidirect
7. C13×#1381C2semidirect
113. #1381D13semidirect
178. C2×D13#368semidirect
273. C13#12922semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1082
C2×#117180982
C2×#117180852
C2×#117180992
#131148712
#131129292
C13×#13812
#1292213