Finite Group Databasebeta

← #15764126

Subgroups — #15764126

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718744C211yesmaximal, characteristic
2#13119790C211yesmaximal, characteristic
3#13115789C211yesmaximal, characteristic, complemented
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C2×C13×#498C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88200—22no—
11C22×#6106—21no—
12C2×C4×D52C2211yescharacteristic
13C13×#498—22no—
14C13×#498—22no—
15C2×C13×#106—22no—
16C2×C4×C8×C13C2211yescharacteristic
17C2×#88075—21no—
18#11718744—22no—
19#11718744—22no—
20#11718653—22no—
21#11718649—21no—
22#11718637—21no—
23C4×C4⋊Dic13C2211yescharacteristic
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26#11718139—22no—
27#11718121—22no—
28#11718051—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D412yes—
46C2×C42×C13C2311yescharacteristic
47#88200—44no—
48#88200—44no—
49C2×#6106—24no—
50C2×#6106—42no—
51C2×#6106—42no—
52C2×#6103—24no—
53C2×#6103—21no—
54C2×C4⋊Dic13D411yescharacteristic
55C2×C4⋊Dic13D412yes—
56C2×#6101—24no—
57C2×C4×Dic13—21no—
58C22×#1055—21no—
59C22×#1055—21no—
60C4×D52—21no—
61C4×D52—21no—
62C4×D52—21no—
63C4×D52—21no—
64C13×#106—28no—
65C4×C8×C13—21no—
66C4×C8×C13D412yes—
67#88075—24no—
68#88071—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055D412yes—
73#10068—131nomaximal, Sylow
74C23×D13—21no—
75C2×Q8×C13—22no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—42no—
80C2×Q8×C13—42no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C22×C4×C13—22no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×Dic13—22no—
91C22×Dic13—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52—21no—
95C2×D52—21no—
96C2×D52—21no—
97C2×D52SD1612yes—
98C2×C4×D13—41no—
99C2×C4×D13—41no—
100C2×C4×D13—42no—
101C2×C4×D13—42no—
102C2×C8×C13—24no—
103C2×C8×C13—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13#4111yescharacteristic
116#6106—48no—
117#6103—48no—
118#6103—41no—
119#6103—41no—
120C4⋊Dic13—22no—
121C4⋊Dic13—21no—
122C4⋊Dic13—21no—
123C4⋊Dic13SD1614yescomplemented
124#6101—48no—
125C4×Dic13—41no—
126C4×Dic13—41no—
127C2×#1055—22no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—42no—
132C2×#498D1311yescharacteristic, complemented
133C2×#461—131no—
134#2542—131no—
135#1988—131no—
136C2×#332—131no—
137C2×D4⋊C8—131no—
138#1279—131no—
139C23×C13#12011yescharacteristic
140C22×D13—22no—
141C22×D13—41no—
142C22×D13—41no—
143C22×D13—42no—
144C22×D13—42no—
145Q8×C13—42no—
146Q8×C13—42no—
147Q8×C13—82no—
148Q8×C13—81no—
149Q8×C13—81no—
150Q8×C13—81no—
151Q8×C13—81no—
152C2×C4×C13—22no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13—44no—
156C2×C4×C13—81no—
157C2×C4×C13—81no—
158C2×C4×C13#12011yescharacteristic
159C2×C4×C13#12011yescharacteristic
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12711yescharacteristic
164C2×C4×C13C2×SD1611yescharacteristic
165C2×C4×C13C2×SD1612yes—
166C2×C4×C13#13511yescharacteristic
167C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C13AGL(1,ℤ/8)12yes—
169C2×C4×C13#13711yescharacteristic
170C2×Dic13—24no—
171C2×Dic13—42no—
172C2×Dic13—42no—
173C2×Dic13—41no—
174C2×Dic13—42no—
175D52—22no—
176D52—22no—
177D52—41no—
178D52—41no—
179C4×D13—82no—
180C4×D13—81no—
181C4×D13—81no—
182C8×C13—24no—
183#1055—42no—
184#1055—81no—
185C22×SD16—261no—
186C2×C4⋊Q8C2×D1311yescharacteristic
187C2×C4⋊Q8C2×D1311yescharacteristic
188C2×C22⋊Q8—262no—
189C2×C4×D4—131no—
190#498—22no—
191#498—22no—
192#461—262no—
193#461—262no—
194C2×#106—22no—
195C2×C4⋊C8—131no—
196C2×C4⋊C8—131no—
197C2×#103—261no—
198C2×C4×C8C2×D1311yescharacteristic
199#399—262no—
200#390—261no—
201#384—261no—
202C4×C4⋊C4—131no—
203#340—262no—
204#332—262no—
205D4⋊C8—262no—
206C22×C13#39211yescharacteristic
207C22×C13#44811yescharacteristic
208C22×C13#44911yescharacteristic
209C22×C13#45012yes—
210C22×C13#45612yes—
211C2×D13—44no—
212C2×D13—42no—
213C2×D13—82no—
214C2×D13—81no—
215C2×D13—81no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—82no—
219C4×C13—82no—
220C4×C13#45011yescharacteristic
221C4×C13#45211yescharacteristic
222C4×C13#46012yes—
223C4×C13#46511yescharacteristic
224C4×C13#46811yescharacteristic
225C4×C13#49211yescharacteristic
226C4×C13#49611yescharacteristic
227Dic13—44no—
228Dic13—81no—
229C22×Q8—21no—
230C22×Q8—21no—
231C22×D4—131no—
232C23×C4—261no—
233C2×SD16—264no—
234C2×SD16—522no—
235C2×SD16—522no—
236C22×C8—21no—
237C22×C8—261no—
238C22×C8—261no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8C22⋊D1312yes—
247C22⋊Q8—524no—
248C22⋊Q8—524no—
249C4×D4—261no—
250C4×D4—261no—
251C4×D4—261no—
252C4×D4—261no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—132no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4—264no—
259C2×C4⋊C4C22⋊D1312yes—
260C2×C22⋊C4—264no—
261C2×C22⋊C4—261no—
262C2×C42—261no—
263C2×C42C22×D1311yescharacteristic
264#106—28no—
265C4⋊C8—132no—
266C4⋊C8—261no—
267C4⋊C8—261no—
268C4⋊C8—261no—
269#103—264no—
270C4×C8—21no—
271C4×C8C22⋊D1312yes—
272#95—261no—
273C2×C13#165112yes—
274C2×C13#165412yes—
275C2×C13#200011yescharacteristic
276C2×C13#200511yescharacteristic
277C2×C13#201411yescharacteristic
278D13—82no—
279C24—261no—
280C2×Q8—22no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—132no—
291C2×D4—261no—
292C2×D4—261no—
293C2×D4—261no—
294C2×D4—261no—
295C2×D4—261no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—262no—
299C22×C4—261no—
300C22×C4—522no—
301C22×C4—522no—
302C22×C4—521no—
303C22×C4—521no—
304C22×C4D4×D1311yescharacteristic
305C22×C4D4×D1311yescharacteristic
306C22×C4C2×C22⋊D1311yescharacteristic
307SD16—528no—
308C2×C8—24no—
309C2×C8—22no—
310C2×C8—262no—
311C2×C8—521no—
312C2×C8—521no—
313C2×C8—522no—
314C2×C8—521no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—134no—
324C4⋊C4—262no—
325C4⋊C4—261no—
326C4⋊C4—261no—
327C4⋊C4—528no—
328C22⋊C4—528no—
329C22⋊C4—521no—
330C22⋊C4—521no—
331C42—521no—
332C42—521no—
333C42D4×D1311yescharacteristic
334C42#612911yescharacteristic
335C42C2×C22⋊D1311yescharacteristic
336C42C2×C22⋊D1311yescharacteristic
337C13#1006811yescharacteristic, complemented, Sylow
338C23—262no—
339C23—522no—
340C23—522no—
341C23—521no—
342C23—521no—
343C23#8819111yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—82no—
347Q8—81no—
348Q8—81no—
349Q8—81no—
350Q8—81no—
351D4—262no—
352D4—262no—
353D4—521no—
354D4—521no—
355C2×C4—22no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—264no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—522no—
365C2×C4—521no—
366C2×C4—1042no—
367C2×C4—1041no—
368C2×C4—1041no—
369C2×C4SD16×D1312yes—
370C2×C4SD16×D1311yescharacteristic
371C2×C4#8816812yes—
372C2×C4#8816811yescharacteristic
373C2×C4#8816911yescharacteristic
374C2×C4#8817011yescharacteristic
375C2×C4#8819111yescharacteristic
376C2×C4#8819211yescharacteristic
377C2×C4#8819311yescharacteristic
378C2×C4#8819311yescharacteristic
379C2×C4#8819411yescharacteristic
380C2×C4#8820711yescharacteristic
381C8—24no—
382C8—522no—
383C8—1041no—
384C22—522no—
385C22—524no—
386C22—1042no—
387C22—1041no—
388C22—1041no—
389C22#1171875612yes—
390C22#1171883012yes—
391C22#1171883111yescharacteristic
392C22#1171883311yescharacteristic
393C22#1171888411yescharacteristic
394C4—21no—
395C4—21no—
396C4—82no—
397C4—82no—
398C4—524no—
399C4—1041no—
400C4#1171882412yes—
401C4#1171883011yescharacteristic
402C4#1171883211yescharacteristic
403C4#1171883411yescharacteristic
404C4#1171883511yescharacteristic
405C4#1171883611yescharacteristic
406C4#1171883711yescharacteristic
407C2—1042no—
408C2#1311409612yes—
409C2#1311411712yes—
410C2#1311583611yescharacteristic
411C2#1311587211yescharacteristic
412C2#1311592211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#498C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#498D13
hypocenterC13#10068
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #13115789C2semidirect
4. C2×#11718139C2semidirect
6. #13112676C2semidirect
7. C2×C13×#498C2semidirect
123. C4⋊Dic13SD16semidirect
132. C2×#498D13semidirect
337. C13#10068semidirect

Maximal subgroups

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

subgroupindex
C2×#117187442
#131197902
#131157892
C2×#117181392
C2×#117180512
#131126762
C2×C13×#4982
#1006813