Finite Group Databasebeta

← #15779947

Subgroups — #15779947

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718803C211yesmaximal, characteristic
2C2×#11718087C211yesmaximal, characteristic, complemented
3C2×#11718087C211yesmaximal, characteristic, complemented
4#13116464C211yesmaximal, characteristic, complemented
5#13112949C211yesmaximal, characteristic, complemented
6#13112939C211yesmaximal, characteristic, complemented
7C13×#2916C211yesmaximal, characteristic, complemented
8C13×#568—21no—
9C2×C13×#131C2211yescharacteristic
10C2×#88203—21no—
11C22×D104C2211yescharacteristic
12C13×#430—21no—
13C13×#430—22no—
14C2×C13×#108—22no—
15C2×C13×#108C2211yescharacteristic
16C2×C13×#108C2211yescharacteristic
17#11718803—22no—
18#11718803C414yes—
19C2×#88063—21no—
20C2×#88059C2211yescharacteristic
21C2×#88052C2211yescharacteristic
22C2×#88052C2211yescharacteristic
23#11718153—22no—
24#11718087—22no—
25#11718087—22no—
26C2×C13×#41D411yescharacteristic
27C22×D52—21no—
28C13×#131—21no—
29C13×#131—21no—
30C13×#131—42no—
31C13×#131—42no—
32C13×#131C2×C412yes—
33C13×#131D412yes—
34C2×C13×M16—21no—
35C2×C13×M16—24no—
36C2×C13×M16—21no—
37C2×C13×M16—21no—
38C2×C13×M16D411yescharacteristic
39C22×C8×C13—21no—
40C22×C8×C13C2311yescharacteristic
41#88203—24no—
42#88203—42no—
43C2×#6106—41no—
44C2×#6104—41no—
45C2×#6099—21no—
46C2×D104—21no—
47C2×D104—21no—
48C2×D104—21no—
49C2×D104—21no—
50C2×D104—21no—
51C2×D104C2×C412yes—
52C13×#108—24no—
53C13×#108—21no—
54C13×#108—21no—
55C13×#108D412yes—
56C13×#108D412yes—
57#88063—24no—
58#88059—21no—
59#88059C2×C412yes—
60#88052—21no—
61#88052—21no—
62#88052—21no—
63#88052—21no—
64C2×#6090—21no—
65C2×#6090—21no—
66#13007—131nomaximal, Sylow
67C23×D13—41no—
68C13×#41—21no—
69C13×#41—21no—
70C13×#41C22⋊C412yes—
71C13×#41D812yes—
72C2×Q8×C13SD1611yescharacteristic
73C2×D4×C13—21no—
74C2×D4×C13SD1611yescharacteristic
75C22×C4×C13—21no—
76C22×C4×C13C2×D411yescharacteristic
77C2×D52—22no—
78C2×D52—41no—
79C2×D52—41no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C13×M16—21no—
84C13×M16—22no—
85C13×M16—22no—
86C13×M16—22no—
87C13×M16—22no—
88C13×M16—44no—
89C13×M16—41no—
90C13×M16—41no—
91C13×M16C22⋊C412yes—
92C2×C8×C13—21no—
93C2×C8×C13—22no—
94C2×C8×C13—22no—
95C2×C8×C13—44no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C2×C8×C13#4111yescharacteristic
104#6106—44no—
105#6104—44no—
106#6099—22no—
107#6099—41no—
108C2×#1055—41no—
109D104—22no—
110D104—22no—
111D104—41no—
112D104—41no—
113#6090—41no—
114#6090—41no—
115C2×#472—131no—
116#2916D1311yescharacteristic, complemented
117C2×#361—131no—
118C2×#361—131no—
119#2117—131no—
120#1388—131no—
121#1385—131no—
122C23×C13—21no—
123C23×C13#13711yescharacteristic
124C22×D13—42no—
125C22×D13—81no—
126C22×D13—81no—
127C22×D13—162no—
128Q8×C13—21no—
129Q8×C13#10212yes—
130D4×C13—22no—
131D4×C13—22no—
132D4×C13—21no—
133D4×C13#10212yes—
134C2×C4×C13—21no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×D811yescharacteristic
141C2×C4×C13C2×SD1611yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143D52—42no—
144D52—42no—
145D52—81no—
146D52—81no—
147C8×C13—22no—
148C8×C13—42no—
149C8×C13—42no—
150C8×C13C4×D411yescharacteristic
151C8×C13C4×D411yescharacteristic
152C8×C13#12111yescharacteristic
153C8×C13#12111yescharacteristic
154#1055—42no—
155C2×AGL(1,ℤ/8)—261no—
156C22×D8—131no—
157#568—21no—
158C2×#131C2×D1311yescharacteristic
159C2×M32—131no—
160C2×M32—131no—
161#472—134no—
162#472—262no—
163#430—21no—
164#430—22no—
165C2×#108—22no—
166C2×#108—131no—
167C2×#108C2×D1311yescharacteristic
168C2×#108C2×D1311yescharacteristic
169C2×#100—261no—
170#361—262no—
171#361—262no—
172#350—262no—
173C22×C13—22no—
174C22×C13—41no—
175C22×C13—81no—
176C22×C13#41711yescharacteristic
177C22×C13#44811yescharacteristic
178C22×C13#48011yescharacteristic
179C2×D13—82no—
180C2×D13—162no—
181C2×D13—162no—
182C2×D13—162no—
183C4×C13—22no—
184C4×C13#38611yescharacteristic
185C4×C13C2×#10211yescharacteristic
186C4×C13#44711yescharacteristic
187C4×C13#48111yescharacteristic
188C2×#41C22⋊D1311yescharacteristic
189C22×D4—261no—
190AGL(1,ℤ/8)—264no—
191AGL(1,ℤ/8)—522no—
192C2×SD16—521no—
193C2×D8—132no—
194C2×D8—261no—
195C2×D8—261no—
196C2×D8—261no—
197C2×D8—261no—
198C2×D8—261no—
199C2×D8—521no—
200#131—21no—
201#131—21no—
202#131—42no—
203#131—42no—
204#131C4×D1312yes—
205#131D5212yes—
206C2×M16—21no—
207C2×M16—24no—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—261no—
211C2×M16C22⋊D1311yescharacteristic
212C22×C8—21no—
213C22×C8C22×D1311yescharacteristic
214M32—261no—
215M32—261no—
216M32—261no—
217M32—261no—
218C2×C16—261no—
219C2×C16—261no—
220#108—24no—
221#108—21no—
222#108—21no—
223#108—132no—
224#108—261no—
225#108C22⋊D1312yes—
226#108C22⋊D1312yes—
227#100—264no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—42no—
232C2×C13#187411yescharacteristic
233D13—162no—
234C24—521no—
235#41—21no—
236#41—21no—
237#41#610312yes—
238#41#610412yes—
239C2×Q8#610611yescharacteristic
240C2×D4—21no—
241C2×D4—262no—
242C2×D4—521no—
243C2×D4—521no—
244C2×D4—521no—
245C2×D4—521no—
246C2×D4—521no—
247C2×D4#610611yescharacteristic
248C22×C4—21no—
249C22×C4C2×C22⋊D1311yescharacteristic
250SD16—524no—
251D8—262no—
252D8—262no—
253D8—524no—
254D8—521no—
255D8—521no—
256M16—21no—
257M16—22no—
258M16—22no—
259M16—22no—
260M16—22no—
261M16—44no—
262M16—41no—
263M16—41no—
264M16—262no—
265M16—521no—
266M16#610312yes—
267C2×C8—21no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—44no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—521no—
274C2×C8C2×C4×D1311yescharacteristic
275C2×C8C2×D5211yescharacteristic
276C2×C8#612711yescharacteristic
277C2×C8#612711yescharacteristic
278C2×C8C2×C22⋊D1311yescharacteristic
279C2×C8C2×C22⋊D1311yescharacteristic
280C16—521no—
281C16—521no—
282C13#1300711yescharacteristic, complemented, Sylow
283C23—21no—
284C23—522no—
285C23—1041no—
286C23—1041no—
287C23—2082no—
288C23#8819611yescharacteristic
289Q8—21no—
290Q8#8804912yes—
291D4—22no—
292D4—22no—
293D4—21no—
294D4—522no—
295D4—522no—
296D4—1041no—
297D4—1041no—
298D4#8804912yes—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4C2×#610311yescharacteristic
303C2×C4#8818311yescharacteristic
304C2×C4C2×#610411yescharacteristic
305C2×C4#8818611yescharacteristic
306C2×C4C2×#610611yescharacteristic
307C2×C4#8820711yescharacteristic
308C8—22no—
309C8—42no—
310C8—42no—
311C8—522no—
312C8C4×C22⋊D1311yescharacteristic
313C8C4×C22⋊D1311yescharacteristic
314C8#8818411yescharacteristic
315C8#8818411yescharacteristic
316C22—22no—
317C22—41no—
318C22—81no—
319C22—1042no—
320C22—2082no—
321C22—2082no—
322C22—2082no—
323C22#1171862711yescharacteristic
324C22#1171862811yescharacteristic
325C22#1171888811yescharacteristic
326C4—22no—
327C4C2×#8804911yescharacteristic
328C4#1171862911yescharacteristic
329C4#1171887411yescharacteristic
330C4#1171887811yescharacteristic
331C2—21no—
332C2—21no—
333C2—21no—
334C2—42no—
335C2—2082no—
336C2#1311515311yescharacteristic
subgroupG/H
centerC2#13115153
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#2916C2
socleC2×C13#1874
prime radicalC2×#11718803C2
cosocleC22×C8×C13C23
hypercenter#2916D13
hypocenterC13#13007
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #2916

Complements

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

NH ≅ G/Ntype
2. C2×#11718087C2semidirect
3. C2×#11718087C2semidirect
4. #13116464C2semidirect
5. #13112949C2semidirect
6. #13112939C2semidirect
7. C13×#2916C2semidirect
116. #2916D13semidirect
282. C13#13007semidirect

Maximal subgroups

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

subgroupindex
C2×#117188032
C2×#117180872
#131164642
#131129492
#131129392
C13×#29162
#1300713