Finite Group Databasebeta

← #15882742

Subgroups — #15882742

Order 3328.

850 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic13C211yesmaximal, characteristic
2#13117808C212yesmaximal, complemented
3#13115713C211yesmaximal, characteristic
4#13115459C212yesmaximal, complemented
5#13115453C212yesmaximal, complemented
6#13114997C211yesmaximal, characteristic, complemented
7#13114844C212yesmaximal, complemented
8#13114736C211yesmaximal, characteristic, complemented
9#13114733C211yesmaximal, characteristic, complemented
10#13114704C211yesmaximal, characteristic, complemented
11C13×#1972C211yesmaximal, characteristic
12C22×C13×D8C2211yescharacteristic
13C2×D4×Dic13C2212yes—
14C2×C13×#106C2211yescharacteristic
15C2×C13×#102C2212yes—
16C2×C13×#97C2211yescharacteristic
17C13×#390C2212yes—
18#11718882C2212yes—
19C2×#88072C2212yes—
20C2×#88072C2212yes—
21D8×Dic13C418yescomplemented
22C2×#88058C2211yescharacteristic
23C2×#88057C2211yescharacteristic
24C2×#88055C2211yescharacteristic
25C2×#88054C2211yescharacteristic
26C2×C8×Dic13C2211yescharacteristic
27#11718638C2212yes—
28C4⋊C4×Dic13C2212yes—
29C2×#88047C2212yes—
30#11718606—22no—
31#11718605—22no—
32#11718604—22no—
33C22⋊C4×Dic13—22no—
34C4×C4⋊Dic13C2212yes—
35C4×#6101C2211yescharacteristic
36#11718143C2212yes—
37#11718142C2211yescharacteristic
38#11718121C2212yes—
39#11718116C2211yescharacteristic
40C22×D4×C13C2312yes—
41C23×Dic13—22no—
42C2×C13×D8—22no—
43C2×C13×D8—22no—
44C2×C13×D8C2×C414yes—
45C22×C8×C13C2311yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C2×C13×C4⋊C4C2312yes—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—22no—
50C2×C42×C13C2311yescharacteristic
51C2×C22⋊Dic13—22no—
52C2×C22⋊Dic13—22no—
53C2×C22⋊Dic13—22no—
54D4×Dic13—24no—
55D4×Dic13C2×C418yes—
56C2×C4⋊Dic13C2312yes—
57C2×C4⋊Dic13C2312yes—
58C2×#6101D412yes—
59C2×C4×Dic13—22no—
60C2×C4×Dic13—22no—
61C2×C4×Dic13C2311yescharacteristic
62C2×C4×Dic13C2311yescharacteristic
63C22×#1055C2311yescharacteristic
64C22×#1055C2311yescharacteristic
65C13×#106—22no—
66C13×#102—42no—
67C13×#97—22no—
68#88072—42no—
69#88072C2×C418yes—
70#88071—22no—
71#88071—22no—
72#88071—22no—
73#88071—22no—
74#88071D412yes—
75#88058C2×C414yes—
76#88057—22no—
77#88055—22no—
78#88054—22no—
79C8×Dic13C2×C414yes—
80#88047—42no—
81#22816—131nomaximal, Sylow
82C24×C13—22no—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13C22×C414yes—
89C22×C4×C13—22no—
90C22×C4×C13C2×D412yes—
91C22×C4×C13C2411yescharacteristic
92C22×Dic13—22no—
93C22×Dic13—28no—
94C22×Dic13—22no—
95C22×Dic13—82no—
96C22×Dic13—82no—
97C22×Dic13C2×D412yes—
98C22×Dic13C2×D411yescharacteristic
99C22×Dic13C2×D411yescharacteristic
100C13×D8—28no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13C22×C412yes—
105C2×C8×C13#4112yes—
106C2×C8×C13#4112yes—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C22⋊C4—44no—
110C13×C22⋊C4—82no—
111C42×C13—21no—
112C42×C13—21no—
113C22⋊Dic13—28no—
114C22⋊Dic13—44no—
115C22⋊Dic13—82no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118C4⋊Dic13—22no—
119C4⋊Dic13C22×C414yes—
120#6101—42no—
121C4×Dic13—21no—
122C4×Dic13—21no—
123C4×Dic13—82no—
124C4×Dic13—82no—
125C4×Dic13C22×C412yes—
126C4×Dic13#4112yes—
127C2×#1055—21no—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—21no—
131C2×#1055—21no—
132C2×#1055C22×C412yes—
133C2×C4×D8—131no—
134#2357—132no—
135#1972—131no—
136#1972D1311yescharacteristic
137#1925—132no—
138#1925—132no—
139#1846—131no—
140#1804—132no—
141#1776—131no—
142#1776—131no—
143#1770—131no—
144C23×C13—24no—
145C23×C13—42no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—42no—
151C23×C13C22×D411yescharacteristic
152D4×C13—24no—
153D4×C13—24no—
154D4×C13—42no—
155D4×C13—42no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13C23×C411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C2×C4×C13C2×#4111yescharacteristic
165C2×C4×C13C2×#4111yescharacteristic
166C2×C4×C13H(5,𝔽2)11yescharacteristic
167C2×C4×C132−1+411yescharacteristic
168C2×Dic13—22no—
169C2×Dic13—22no—
170C2×Dic13—24no—
171C2×Dic13—22no—
172C2×Dic13—22no—
173C2×Dic13—22no—
174C2×Dic13—42no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—88no—
180C2×Dic13C4×D412yes—
181C2×Dic13C4×D412yes—
182C8×C13—41no—
183C8×C13#11714yes—
184#1055—22no—
185#1055—41no—
186C22×D8C2×D1311yescharacteristic
187C2×C4×D4—132no—
188C4×D8—138no—
189C2×#107—131no—
190C2×#107—132no—
191C2×#106—131no—
192C2×#106C2×D1311yescharacteristic
193C2×C4⋊C8—131no—
194C2×#102—132no—
195C2×#102—132no—
196C2×#102C2×D1312yes—
197C2×#97—131no—
198C2×#97C2×D1311yescharacteristic
199C2×C4×C8—131no—
200#390—132no—
201#390C2×D1312yes—
202#388—262no—
203#388—262no—
204#382—132no—
205#381—262no—
206C4×C4⋊C4—131no—
207C4×C4⋊C4—132no—
208C4×C4⋊C4—132no—
209C4×C22⋊C4—262no—
210#340—132no—
211#340—132no—
212#336—131no—
213#336—131no—
214C22×C13—44no—
215C22×C13—44no—
216C22×C13—44no—
217C22×C13—82no—
218C22×C13—82no—
219C22×C13—82no—
220C22×C13—82no—
221C22×C13C2×C4×D411yescharacteristic
222C22×C13#54711yescharacteristic
223C22×C13#55011yescharacteristic
224C22×C13#57512yes—
225C22×C13#57612yes—
226C4×C13—42no—
227C4×C13—82no—
228C4×C13C2×#11711yescharacteristic
229C4×C13#52011yescharacteristic
230C4×C13#55511yescharacteristic
231C4×C13#55611yescharacteristic
232Dic13—22no—
233Dic13—22no—
234Dic13—42no—
235Dic13—44no—
236Dic13—82no—
237C22×D4C22×D1312yes—
238C23×C4—262no—
239C2×D8—22no—
240C2×D8—22no—
241C2×D8C4×D1314yes—
242C22×C8—131no—
243C22×C8—131no—
244C22×C8C22×D1311yescharacteristic
245C22×C8C22×D1311yescharacteristic
246C4×D4—138no—
247C4×D4—264no—
248C2×C4⋊C4—132no—
249C2×C4⋊C4—132no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4C22×D1312yes—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—262no—
255C2×C22⋊C4—262no—
256C2×C22⋊C4—262no—
257C2×C42—131no—
258C2×C42—131no—
259C2×C42—262no—
260C2×C42—262no—
261C2×C42C22×D1311yescharacteristic
262#107—134no—
263#107—522no—
264#106—22no—
265#106—262no—
266C4⋊C8—262no—
267#102—42no—
268#102—138no—
269#102—522no—
270#97—22no—
271#97—262no—
272C4×C8—134no—
273#95—132no—
274#95—262no—
275#95—262no—
276#95—262no—
277#95—262no—
278C2×C13—84no—
279C2×C13#235411yescharacteristic
280C2×C13#294311yescharacteristic
281C2×C13#294811yescharacteristic
282C2×C13#335512yes—
283C2×C13#340312yes—
284C24—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4C2×C4×D1314yes—
291C22×C4—22no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—132no—
295C22×C4—268no—
296C22×C4—262no—
297C22×C4—262no—
298C22×C4—1042no—
299C22×C4—1042no—
300C22×C4D4×D1312yes—
301C22×C4C23×D1311yescharacteristic
302D8—28no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—132no—
307C2×C8—261no—
308C2×C8—261no—
309C2×C8—261no—
310C2×C8—261no—
311C2×C8—261no—
312C2×C8C2×C4×D1312yes—
313C2×C8#612912yes—
314C2×C8#612912yes—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—134no—
318C4⋊C4—262no—
319C4⋊C4—262no—
320C4⋊C4—262no—
321C4⋊C4—522no—
322C22⋊C4—44no—
323C22⋊C4—82no—
324C22⋊C4—268no—
325C22⋊C4—524no—
326C22⋊C4—1042no—
327C42—21no—
328C42—21no—
329C42—132no—
330C42—132no—
331C42—261no—
332C42—261no—
333C42—1042no—
334C42—1042no—
335C13#2281611yescharacteristic, complemented, Sylow
336C23—24no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23C2×D4×D1311yescharacteristic
344D4—24no—
345D4—24no—
346D4—42no—
347D4—42no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—264no—
361C2×C4—262no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4—1048no—
368C2×C4C22×C4×D1311yescharacteristic
369C2×C4C2×#612911yescharacteristic
370C2×C4C2×#612911yescharacteristic
371C2×C4#8825111yescharacteristic
372C2×C4#41×D1311yescharacteristic
373C2×C4#8825711yescharacteristic
374C8—41no—
375C8—262no—
376C8—521no—
377C8#8813114yes—
378C22—44no—
379C22—44no—
380C22—44no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—82no—
385C22C4×D4×D1311yescharacteristic
386C22#1171931611yescharacteristic
387C22#1171942311yescharacteristic
388C22#1171947812yes—
389C22#1171947912yes—
390C4—42no—
391C4—82no—
392C4—262no—
393C4—262no—
394C4—522no—
395C4—524no—
396C4—1042no—
397C4C2×#8813111yescharacteristic
398C4#1171925111yescharacteristic
399C4#1171932111yescharacteristic
400C4#1171937611yescharacteristic
401C2—84no—
402C2#1311778411yescharacteristic
403C2#1312363311yescharacteristic
404C2#1312368511yescharacteristic
405C2#1312743712yes—
406C2#1312792112yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1972C2
socleC23×C13C22×D4
prime radicalC22×C13×D8C22
cosocleC22×C4×C13C24
hypercenter#1972D13
hypocenterC13#22816
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. #13117808C2semidirect
4. #13115459C2semidirect
5. #13115453C2semidirect
6. #13114997C2semidirect
7. #13114844C2semidirect
8. #13114736C2semidirect
9. #13114733C2semidirect
10. #13114704C2semidirect
21. D8×Dic13C4semidirect
335. C13#22816semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic132
#131178082
#131157132
#131154592
#131154532
#131149972
#131148442
#131147362
#131147332
#131147042
C13×#19722
#2281613