Finite Group Databasebeta

← #16016383

Subgroups — #16016383

Order 3328.

632 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718856C211yesmaximal, characteristic
2#13123753C211yesmaximal, characteristic
3#13123703C211yesmaximal, characteristic, complemented
4#13116724C218yesmaximal, complemented
5#13116608C211yesmaximal, characteristic, complemented
6C2×#11718109C211yesmaximal, characteristic, complemented
7#13116440C211yesmaximal, characteristic, complemented
8C13×#2145C211yesmaximal, characteristic
9C2×C13×#135C2211yescharacteristic
10#11719524—21no—
11C22×Dic52C2211yescharacteristic
12#11719221—21no—
13C2×C13×M32C2211yescharacteristic
14C13×#427C2211yescharacteristic
15#11718897—21no—
16#11718858C2214yes—
17#11718857—22no—
18#11718856C414yescomplemented
19#11718856C2214yes—
20C2×#88069C412yescomplemented
21C2×#88067C412yescomplemented
22C2×#88059C2211yescharacteristic
23#11718762C2211yescharacteristic
24C2×#88052C2211yescharacteristic
25#11718665—21no—
26#11718534—22no—
27#11718514C2214yescomplemented
28C13×#360C2214yes—
29#11718109C2214yescomplemented
30#11718104C2214yescomplemented
31#11718079C2214yescomplemented
32C2×C13×#41—21no—
33C22×Dic26—21no—
34C13×#135—21no—
35C13×#135—21no—
36C13×#135C2×C412yes—
37C13×#135C2312yes—
38C2×C13×Q16C2×C411yescharacteristic
39C2×C13×SD16—21no—
40C2×C13×D8C2×C411yescharacteristic
41C22×C8×C13C2311yescharacteristic
42C13×#117—21no—
43#88202—24no—
44#88202—42no—
45#88180D411yescharacteristic
46C2×#6099—21no—
47C2×#6099—42no—
48C2×#6099D411yescharacteristic
49C2×Dic52—21no—
50C2×Dic52—21no—
51C2×Dic52—21no—
52C2×Dic52C2×C412yes—
53C2×Dic52C2×C412yes—
54C2×Dic52C2312yes—
55#88141—24no—
56#88131—42no—
57C4×Dic26—42no—
58C13×M32—21no—
59C13×M32C2312yes—
60C2×C13×C16—21no—
61C13×#107—21no—
62C13×#106C2312yes—
63#88077—24no—
64#88069C2×C418yes—
65#88067C2×C418yes—
66#88059—21no—
67#88059C2312yes—
68#88055C2312yes—
69C8×Dic13D412yes—
70#88052C2×C412yes—
71#88052C2312yes—
72C2×#6090C2×C412yes—
73#88050—24no—
74#33470—131nomaximal, Sylow
75C13×#41—22no—
76C13×#41—22no—
77C13×#41—41no—
78C13×#41—41no—
79C2×Q8×C13—21no—
80C2×D4×C13—21no—
81C2×D4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—41no—
85C2×Dic26—22no—
86C2×Dic26—22no—
87C2×Dic26—22no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C2×Dic26—41no—
91C13×Q16—21no—
92C13×Q16C22×C412yes—
93C13×SD16—22no—
94C13×SD16—22no—
95C13×D8—21no—
96C13×D8C22×C412yes—
97C2×C8×C13C22×C411yescharacteristic
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13#4111yescharacteristic
101C2×C8×C13#4111yescharacteristic
102C2×C8×C13C2411yescharacteristic
103C13×C4⋊C4—22no—
104C13×C22⋊C4—41no—
105C42×C13—41no—
106C22⋊Dic13—21no—
107C4⋊Dic13—21no—
108#6101—44no—
109C4×Dic13—44no—
110C4×Dic13C2×D412yes—
111#6099—21no—
112#6099—21no—
113#6099—22no—
114#6099—44no—
115#6099—41no—
116C2×#1055—44no—
117C2×#1055—41no—
118C2×#1055C2×D412yes—
119Dic52—22no—
120Dic52—22no—
121Dic52—22no—
122Dic52C22×C414yes—
123C13×C16—22no—
124#6090C22×C414yes—
125C2×#510—131no—
126#2957—131no—
127#2950—131no—
128#2180—138no—
129#2155—131no—
130C2×#362—131no—
131#2145D1311yescharacteristic
132#2110—131no—
133C23×C13—41no—
134C23×C13AGL(1,ℤ/8)11yescharacteristic
135Q8×C13—22no—
136Q8×C13—41no—
137D4×C13—22no—
138D4×C13—42no—
139D4×C13—42no—
140D4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13C22×D411yescharacteristic
151C2×Dic13—22no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155Dic26—24no—
156Dic26—42no—
157Dic26—42no—
158Dic26—42no—
159C8×C13C4×D411yescharacteristic
160C8×C13C4×D411yescharacteristic
161C8×C13C23×C411yescharacteristic
162C8×C13C2×#4111yescharacteristic
163#1055—22no—
164#1055—42no—
165C2×#135C2×D1311yescharacteristic
166C22×Q16—131no—
167#568—261no—
168#519—261no—
169#510—134no—
170#510—134no—
171C2×Q32—132no—
172C2×SD32—132no—
173C2×M32—131no—
174C2×M32C2×D1311yescharacteristic
175#444—134no—
176#443—262no—
177#441—134no—
178C4×Q16—262no—
179C2×#108—131no—
180#427C2×D1311yescharacteristic
181#421—261no—
182#419—261no—
183#405—131no—
184#365—134no—
185#362—134no—
186#360C2×D1314yes—
187#347—134no—
188C22×C13—41no—
189C22×C13—42no—
190C22×C13—161no—
191C22×C13#44211yescharacteristic
192C22×C13#44211yescharacteristic
193C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
194C4×C13—42no—
195C4×C13—82no—
196C4×C13#44211yescharacteristic
197C4×C13#44211yescharacteristic
198C4×C13C2×C4×D411yescharacteristic
199C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
200Dic13—42no—
201Dic13—44no—
202C2×#41—21no—
203C22×Q8—261no—
204#135—21no—
205#135—21no—
206#135C4×D1312yes—
207#135C22×D1312yes—
208C2×Q16—132no—
209C2×Q16—132no—
210C2×Q16—132no—
211C2×Q16—261no—
212C2×Q16—261no—
213C2×Q16—261no—
214C2×Q16C4×D1311yescharacteristic
215C2×SD16—21no—
216C2×D8C4×D1311yescharacteristic
217#131—264no—
218#131—522no—
219C2×M16—131no—
220C2×M16—261no—
221C2×M16—522no—
222C22×C8C22×D1311yescharacteristic
223C4×Q8—264no—
224C4×Q8—522no—
225#117—21no—
226#117—131no—
227#117—522no—
228Q32—138no—
229SD32—138no—
230M32—21no—
231M32—132no—
232M32—132no—
233M32C22×D1312yes—
234C2×C16—21no—
235C2×C16—132no—
236#108—132no—
237#108—261no—
238#107—21no—
239#106C22×D1312yes—
240#104—264no—
241#103—264no—
242#97—132no—
243C4×C8—132no—
244C2×C13—21no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—82no—
248C2×C13C2×#44211yescharacteristic
249#41—22no—
250#41—22no—
251#41—41no—
252#41—41no—
253C2×Q8—21no—
254C2×Q8—262no—
255C2×Q8—262no—
256C2×Q8—262no—
257C2×Q8—521no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—41no—
263C22×C4—521no—
264C22×C4D4×D1311yescharacteristic
265Q16—21no—
266Q16—134no—
267Q16—262no—
268Q16—262no—
269Q16—262no—
270Q16C2×C4×D1312yes—
271SD16—22no—
272SD16—22no—
273D8—21no—
274D8C2×C4×D1312yes—
275M16—261no—
276M16—261no—
277M16—262no—
278M16—524no—
279M16—521no—
280C2×C8—132no—
281C2×C8—524no—
282C2×C8—521no—
283C2×C8C2×C4×D1311yescharacteristic
284C2×C8C2×C4×D1311yescharacteristic
285C2×C8D4×D1311yescharacteristic
286C2×C8#612911yescharacteristic
287C2×C8#612911yescharacteristic
288C2×C8C23×D1311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—261no—
291C4⋊C4—524no—
292C22⋊C4—41no—
293C22⋊C4—261no—
294C42—41no—
295C42—132no—
296C42—524no—
297C16—22no—
298C16—134no—
299C13#3347011yescharacteristic, complemented, Sylow
300C23—41no—
301C23#8816511yescharacteristic
302Q8—22no—
303Q8—41no—
304Q8—264no—
305Q8—522no—
306Q8—522no—
307Q8—522no—
308D4—22no—
309D4—42no—
310D4—42no—
311D4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—262no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4#8813511yescharacteristic
321C2×C4#8813511yescharacteristic
322C2×C4#8816511yescharacteristic
323C2×C4#8816811yescharacteristic
324C2×C4#8816811yescharacteristic
325C2×C4C2×D4×D1311yescharacteristic
326C8—262no—
327C8—522no—
328C8#8813511yescharacteristic
329C8#8813511yescharacteristic
330C8C22×C4×D1311yescharacteristic
331C8C2×#612911yescharacteristic
332C22—41no—
333C22—42no—
334C22—161no—
335C22#1171844611yescharacteristic
336C22#1171844611yescharacteristic
337C22C2×#8816511yescharacteristic
338C4—42no—
339C4—82no—
340C4—522no—
341C4—524no—
342C4#1171844611yescharacteristic
343C4#1171844611yescharacteristic
344C4C2×#8813511yescharacteristic
345C4C2×#8816811yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—82no—
350C2C2×#1171844611yescharacteristic
subgroupG/H
centerC2C2×#11718446
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2145C2
socleC2×C13C2×#442
prime radicalC2×C13×#135C22
cosocleC2×C8×C13C24
hypercenter#2145D13
hypocenterC13#33470
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2145

Complements

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

NH ≅ G/Ntype
3. #13123703C2semidirect
4. #13116724C2semidirect
5. #13116608C2semidirect
6. C2×#11718109C2semidirect
7. #13116440C2semidirect
18. #11718856C4semidirect
20. C2×#88069C4semidirect
21. C2×#88067C4semidirect
27. #11718514C22semidirect
29. #11718109C22semidirect
30. #11718104C22semidirect
31. #11718079C22semidirect
299. C13#33470semidirect

Maximal subgroups

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

subgroupindex
C2×#117188562
#131237532
#131237032
#131167242
#131166082
C2×#117181092
#131164402
C13×#21452
#3347013