Finite Group Databasebeta

← #15867214

Subgroups — #15867214

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic13C211yesmaximal, characteristic
2#13117473C212yesmaximal, complemented
3#13115713C211yesmaximal, characteristic
4#13115574C211yesmaximal, characteristic, complemented
5#13115572C211yesmaximal, characteristic, complemented
6#13115522C212yesmaximal, complemented
7#13115516C212yesmaximal, complemented
8#106×Dic13C211yesmaximal, characteristic, complemented
9#13114663C212yesmaximal, complemented
10#13114524C211yesmaximal, 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×#88055C2211yescharacteristic
26C2×C8×Dic13C2211yescharacteristic
27C2×C8×Dic13C2211yescharacteristic
28C4⋊C4×Dic13C2212yes—
29#11718634C2212yes—
30#11718606—22no—
31#11718605—22no—
32#11718604—22no—
33#11718603—22no—
34#11718593C2211yescharacteristic
35#11718589C2212yes—
36C2×C4×#1055C2211yescharacteristic
37#11718143C2212yes—
38#11718121C2212yes—
39#11718121C2212yes—
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×#6101—22no—
59C2×#6101—22no—
60C2×C4×Dic13—22no—
61C2×C4×Dic13C2311yescharacteristic
62C2×C4×Dic13C2311yescharacteristic
63C22×#1055C2311yescharacteristic
64C22×#1055C2311yescharacteristic
65C13×#106—22no—
66C13×#102—24no—
67C13×#97—22no—
68#88072—24no—
69#88072C2×C418yes—
70#88071—22no—
71#88071—22no—
72#88071—22no—
73#88071D412yes—
74#88071D412yes—
75#88058C2×C414yes—
76#88057—22no—
77#88055—22no—
78#88055—22no—
79C8×Dic13—22no—
80C8×Dic13C2×C414yes—
81C4×#1055—22no—
82#21284—131nomaximal, Sylow
83C24×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13—22no—
89C2×D4×C13C22×C414yes—
90C22×C4×C13—22no—
91C22×C4×C13C2×D412yes—
92C22×C4×C13C2411yescharacteristic
93C22×Dic13—22no—
94C22×Dic13—28no—
95C22×Dic13—22no—
96C22×Dic13—82no—
97C22×Dic13—82no—
98C22×Dic13C2×D412yes—
99C22×Dic13C2×D411yescharacteristic
100C22×Dic13C2×D411yescharacteristic
101C13×D8—28no—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13C22×C412yes—
105C2×C8×C13#4112yes—
106C2×C8×C13#4112yes—
107C2×C8×C13#4112yes—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C22⋊C4—82no—
111C13×C22⋊C4—82no—
112C42×C13—21no—
113C42×C13—21no—
114C22⋊Dic13—28no—
115C22⋊Dic13—82no—
116C22⋊Dic13—82no—
117C4⋊Dic13—22no—
118C4⋊Dic13—22no—
119C4⋊Dic13—22no—
120C4⋊Dic13C22×C414yes—
121#6101—82no—
122#6101—82no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—82no—
126C4×Dic13C22×C412yes—
127C4×Dic13#4112yes—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—21no—
131C2×#1055—21no—
132C2×#1055C22×C412yes—
133C2×#1055#4112yes—
134C2×C4×D8—131no—
135#2319—132no—
136#1972—131no—
137#1972D1311yescharacteristic
138#1943—131no—
139#1943—131no—
140#1934—132no—
141#1934—132no—
142C4×#106—131no—
143#1762—132no—
144#1726—131no—
145C23×C13—24no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—42no—
151C23×C13—42no—
152C23×C13C22×D411yescharacteristic
153D4×C13—24no—
154D4×C13—24no—
155D4×C13—42no—
156D4×C13—42no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—22no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13C23×C411yescharacteristic
164C2×C4×C13C2×#4111yescharacteristic
165C2×C4×C13C2×#4111yescharacteristic
166C2×C4×C13C2×#4111yescharacteristic
167C2×C4×C13C2×#4111yescharacteristic
168C2×C4×C13C2×#4111yescharacteristic
169C2×Dic13—22no—
170C2×Dic13—22no—
171C2×Dic13—24no—
172C2×Dic13—22no—
173C2×Dic13—22no—
174C2×Dic13—22no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—88no—
181C2×Dic13C4×D412yes—
182C2×Dic13C4×D412yes—
183C8×C13—22no—
184C8×C13#11714yes—
185#1055—22no—
186#1055—22no—
187C22×D8C2×D1311yescharacteristic
188C2×C4×D4—132no—
189C4×D8—138no—
190C2×#107—131no—
191C2×#106—131no—
192C2×#106C2×D1311yescharacteristic
193C2×#102—132no—
194C2×#102—132no—
195C2×#102C2×D1312yes—
196C2×#97—131no—
197C2×#97—131no—
198C2×#97C2×D1311yescharacteristic
199C2×C4×C8—131no—
200C2×C4×C8—131no—
201C2×C4×C8—131no—
202#390—132no—
203#390C2×D1312yes—
204#389—132no—
205#389—132no—
206#388—262no—
207#388—262no—
208#381—262no—
209#380—262no—
210C4×C4⋊C4—132no—
211#376—131no—
212#340—132no—
213#340—132no—
214#340—132no—
215C22×C13—44no—
216C22×C13—44no—
217C22×C13—44no—
218C22×C13—82no—
219C22×C13—82no—
220C22×C13—82no—
221C22×C13—82no—
222C22×C13C2×C4×D411yescharacteristic
223C22×C13#53211yescharacteristic
224C22×C13#53211yescharacteristic
225C22×C13#57612yes—
226C22×C13#57712yes—
227C4×C13—42no—
228C4×C13—82no—
229C4×C13C2×#11711yescharacteristic
230C4×C13C4×#4111yescharacteristic
231C4×C13#52911yescharacteristic
232C4×C13#52911yescharacteristic
233Dic13—22no—
234Dic13—22no—
235Dic13—42no—
236Dic13—44no—
237Dic13—82no—
238C22×D4C22×D1312yes—
239C23×C4—262no—
240C2×D8—22no—
241C2×D8—22no—
242C2×D8C4×D1314yes—
243C22×C8—131no—
244C22×C8—131no—
245C22×C8C22×D1311yescharacteristic
246C22×C8C22×D1311yescharacteristic
247C4×D4—138no—
248C4×D4—264no—
249C2×C4⋊C4—132no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—262no—
252C2×C4⋊C4—262no—
253C2×C4⋊C4C22×D1312yes—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—262no—
257C2×C22⋊C4—262no—
258C2×C22⋊C4—262no—
259C2×C42—131no—
260C2×C42—131no—
261C2×C42—262no—
262C2×C42C22×D1311yescharacteristic
263#107—134no—
264#106—22no—
265#106—262no—
266#102—24no—
267#102—138no—
268#102—264no—
269#97—22no—
270#97—262no—
271#97—262no—
272C4×C8—134no—
273C4×C8—262no—
274C4×C8—262no—
275#95—132no—
276#95—132no—
277#95—262no—
278#95—262no—
279#95—262no—
280C2×C13—84no—
281C2×C13#229311yescharacteristic
282C2×C13#294811yescharacteristic
283C2×C13#295211yescharacteristic
284C2×C13#317912yes—
285C2×C13#317912yes—
286C24—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4C2×C4×D1314yes—
293C22×C4—22no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—132no—
297C22×C4—268no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—1042no—
301C22×C4—1042no—
302C22×C4D4×D1312yes—
303C22×C4C23×D1311yescharacteristic
304D8—28no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—132no—
308C2×C8—132no—
309C2×C8—261no—
310C2×C8—261no—
311C2×C8—261no—
312C2×C8—261no—
313C2×C8C2×C4×D1312yes—
314C2×C8#612912yes—
315C2×C8#612912yes—
316C2×C8#612912yes—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—134no—
320C4⋊C4—262no—
321C4⋊C4—262no—
322C4⋊C4—262no—
323C4⋊C4—1042no—
324C4⋊C4—1042no—
325C22⋊C4—82no—
326C22⋊C4—82no—
327C22⋊C4—268no—
328C22⋊C4—1042no—
329C22⋊C4—1042no—
330C42—21no—
331C42—21no—
332C42—132no—
333C42—132no—
334C42—261no—
335C42—261no—
336C42—1042no—
337C13#2128411yescharacteristic, complemented, Sylow
338C23—24no—
339C23—42no—
340C23—42no—
341C23—42no—
342C23—42no—
343C23—42no—
344C23—42no—
345C23C2×D4×D1311yescharacteristic
346D4—24no—
347D4—24no—
348D4—42no—
349D4—42no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—132no—
357C2×C4—132no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—262no—
361C2×C4—262no—
362C2×C4—264no—
363C2×C4—262no—
364C2×C4—522no—
365C2×C4—522no—
366C2×C4—522no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4—1048no—
370C2×C4C22×C4×D1311yescharacteristic
371C2×C4C2×#612911yescharacteristic
372C2×C4C2×#612911yescharacteristic
373C2×C4C2×#612911yescharacteristic
374C2×C4#41×D1311yescharacteristic
375C2×C4#41×D1311yescharacteristic
376C8—22no—
377C8—262no—
378C8—262no—
379C8#8813114yes—
380C22—44no—
381C22—44no—
382C22—44no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—82no—
387C22C4×D4×D1311yescharacteristic
388C22#1171930111yescharacteristic
389C22#1171942111yescharacteristic
390C22#1171947912yes—
391C22#1171948012yes—
392C4—42no—
393C4—82no—
394C4—262no—
395C4—262no—
396C4—524no—
397C4—522no—
398C4—1042no—
399C4C2×#8813111yescharacteristic
400C4C4×#612911yescharacteristic
401C4#1171930511yescharacteristic
402C4#1171938511yescharacteristic
403C2—84no—
404C2#1311729811yescharacteristic
405C2#1312368511yescharacteristic
406C2#1312371811yescharacteristic
407C2#1312551612yes—
408C2#1312552012yes—
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#21284
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. #13117473C2semidirect
4. #13115574C2semidirect
5. #13115572C2semidirect
6. #13115522C2semidirect
7. #13115516C2semidirect
8. #106×Dic13C2semidirect
9. #13114663C2semidirect
10. #13114524C2semidirect
21. D8×Dic13C4semidirect
337. C13#21284semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic132
#131174732
#131157132
#131155742
#131155722
#131155222
#131155162
#106×Dic132
#131146632
#131145242
C13×#19722
#2128413