Finite Group Databasebeta

← #15752777

Subgroups — #15752777

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123467C211yesmaximal, characteristic
2#13123466C211yesmaximal, characteristic
3#13117233C211yesmaximal, characteristic
4#13112702C211yesmaximal, characteristic, complemented
5#13112701C211yesmaximal, characteristic, complemented
6#13112700C211yesmaximal, characteristic, complemented
7C13×#1288C211yesmaximal, characteristic, complemented
8C2×C42×D13C2211yescharacteristic
9C13×#432C2211yescharacteristic
10C4×C13×M16C2211yescharacteristic
11C13×#383C2211yescharacteristic
12#11718787—21no—
13#11718779—21no—
14#11718598C2211yescharacteristic
15#11718587C2211yescharacteristic
16C4×#6099C2211yescharacteristic
17#11718498—21no—
18#11718494—21no—
19#11718387—21no—
20#11718379—21no—
21#11718368C412yescomplemented
22#11718366—21no—
23#11718366—21no—
24#11718366C412yescomplemented
25#11718346C412yescomplemented
26#11718346C412yescomplemented
27#11718328C412yes—
28#11718327—21no—
29#11718325—21no—
30#11718311—21no—
31#11718310—21no—
32#11718309C412yes—
33C22×C4×D13C2×C411yescharacteristic
34C22×C4×D13D411yescharacteristic
35C22×C4×D13D411yescharacteristic
36C2×C13×M16—21no—
37C2×C42×C13C2311yescharacteristic
38C2×#6103—22no—
39C2×#6101—22no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×#6099—21no—
45C2×#6094—22no—
46C42×D13C2×C411yescharacteristic
47C42×D13C2×C411yescharacteristic
48C42×D13C2×C411yescharacteristic
49C42×D13C2×C411yescharacteristic
50C42×D13D411yescharacteristic
51C42×D13D411yescharacteristic
52C42×D13Q811yescharacteristic
53C42×D13Q811yescharacteristic
54C13×C4⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×#97—21no—
57C13×#97C2×C412yes—
58C4×C8×C13C2×C412yes—
59C13×#95—21no—
60C13×#95—21no—
61C13×#95C2×C412yes—
62#88071—21no—
63#88071—21no—
64#88071—22no—
65#88071C2×C412yes—
66C22⋊#1055—21no—
67#88060—22no—
68#88060—22no—
69#88060—22no—
70#88054—22no—
71#88054—22no—
72#88054—22no—
73C8×Dic13—22no—
74C4⋊#1055—21no—
75#88043—21no—
76#88043C2×C412yes—
77C4×#1055C2×C412yes—
78#7976—131nomaximal, Sylow
79C23×D13C22⋊C411yescharacteristic
80C22×C4×C13—22no—
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—22no—
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C22×Dic13C22⋊C411yescharacteristic
88C2×C4×D13—42no—
89C2×C4×D13—42no—
90C2×C4×D13—42no—
91C2×C4×D13C4211yescharacteristic
92C2×C4×D13C4211yescharacteristic
93C2×C4×D13C22⋊C411yescharacteristic
94C2×C4×D13C22⋊C411yescharacteristic
95C2×C4×D13C22⋊C411yescharacteristic
96C2×C4×D13C22⋊C411yescharacteristic
97C2×C4×D13C4⋊C411yescharacteristic
98C2×C4×D13C4⋊C411yescharacteristic
99C2×C4×D13C4⋊C411yescharacteristic
100C2×C4×D13C4⋊C411yescharacteristic
101C2×C4×D13C4⋊C411yescharacteristic
102C2×C4×D13C4⋊C411yescharacteristic
103C13×M16—42no—
104C2×C8×C13—22no—
105C2×C8×C13—22no—
106C42×C13C22×C411yescharacteristic
107C42×C13C22×C411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13C2×Q811yescharacteristic
110#6103—44no—
111#6101—44no—
112C4×Dic13—44no—
113C4×Dic13C4211yescharacteristic
114C4×Dic13C4211yescharacteristic
115C4×Dic13C22⋊C411yescharacteristic
116C4×Dic13C22⋊C411yescharacteristic
117C4×Dic13C22⋊C411yescharacteristic
118C4×Dic13C22⋊C411yescharacteristic
119C4×Dic13C4⋊C411yescharacteristic
120C4×Dic13C4⋊C411yescharacteristic
121C4×Dic13C4⋊C411yescharacteristic
122C4×Dic13C4⋊C411yescharacteristic
123C4×Dic13C4⋊C411yescharacteristic
124C4×Dic13C4⋊C411yescharacteristic
125#6099—42no—
126C2×#1055—22no—
127C2×#1055—22no—
128#6094—44no—
129#2920—131no—
130#2920—131no—
131#2283—131no—
132#1288—131no—
133#1288—131no—
134#1288—131no—
135#1288D1311yescharacteristic, complemented
136C23×C13C2×C22⋊C411yescharacteristic
137C22×D13—22no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13#9511yescharacteristic
141C22×D13#9511yescharacteristic
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13C2×C4211yescharacteristic
149C2×C4×C13C2×C22⋊C411yescharacteristic
150C2×C4×C13C2×C22⋊C411yescharacteristic
151C2×C4×C13C2×C4⋊C411yescharacteristic
152C2×C4×C13C2×C4⋊C411yescharacteristic
153C2×C4×C13C2×C4⋊C411yescharacteristic
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—42no—
160C2×Dic13#9511yescharacteristic
161C2×Dic13#9511yescharacteristic
162C2×Dic13#9511yescharacteristic
163C2×Dic13#9511yescharacteristic
164C2×Dic13#9511yescharacteristic
165C2×Dic13#9511yescharacteristic
166C4×D13—22no—
167C4×D13—22no—
168C4×D13—22no—
169C4×D13—22no—
170C4×D13—41no—
171C4×D13—41no—
172C4×D13—41no—
173C4×D13—41no—
174C4×D13—41no—
175C4×D13—41no—
176C4×D13—41no—
177C4×D13—41no—
178C8×C13—42no—
179C8×C13—42no—
180#1055—42no—
181#1055—42no—
182C22×C42—131no—
183#432—131no—
184#432—132no—
185#432—261no—
186#432—261no—
187#432C2×D1311yescharacteristic
188#431—132no—
189#431—132no—
190#431—261no—
191#431—261no—
192#423—261no—
193#423—261no—
194#407—261no—
195#407—261no—
196C4×M16—131no—
197C4×M16—132no—
198C4×M16C2×D1311yescharacteristic
199#383—131no—
200#383C2×D1311yescharacteristic
201#382—261no—
202#381—261no—
203#380—132no—
204C4×C4⋊C4—261no—
205C4×C22⋊C4—261no—
206#376—132no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13C2×#9511yescharacteristic
210C22×C13#42112yes—
211C2×D13—21no—
212C2×D13—21no—
213C2×D13—21no—
214C2×D13—21no—
215C2×D13—21no—
216C2×D13—21no—
217C2×D13—44no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—82no—
225Dic13—21no—
226Dic13—21no—
227Dic13—21no—
228Dic13—21no—
229Dic13—82no—
230Dic13H(3,ℤ/4)12yes—
231Dic13#34412yes—
232C23×C4—131no—
233C23×C4—131no—
234C23×C4—131no—
235C2×M16—21no—
236C2×M16—262no—
237C2×M16—261no—
238C2×C4⋊C4—262no—
239C2×C22⋊C4—262no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—131no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42—131no—
251C2×C42—262no—
252C2×C42C22×D1311yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—262no—
255C4⋊C8—262no—
256C4⋊C8—262no—
257C4⋊C8—261no—
258C22⋊C8—21no—
259C22⋊C8—262no—
260C22⋊C8—262no—
261C22⋊C8—262no—
262C22⋊C8—261no—
263#97—21no—
264#97—132no—
265#97—261no—
266#97C4×D1312yes—
267C4×C8—132no—
268C4×C8—262no—
269C4×C8C4×D1312yes—
270#95—21no—
271#95—21no—
272#95—132no—
273#95—262no—
274#95—261no—
275#95—261no—
276#95C4×D1312yes—
277C2×C13—22no—
278C2×C13C2×H(3,ℤ/4)11yescharacteristic
279C2×C13#173311yescharacteristic
280C2×C13C2×#34411yescharacteristic
281D13—41no—
282D13—41no—
283C24—131no—
284C22×C4—22no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—131no—
300C22×C4—262no—
301C22×C4—522no—
302C22×C4—522no—
303C22×C4—522no—
304C22×C4C2×C4×D1311yescharacteristic
305C22×C4D4×D1311yescharacteristic
306C22×C4D4×D1311yescharacteristic
307M16—42no—
308M16—524no—
309M16—522no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—262no—
313C2×C8—262no—
314C4⋊C4—524no—
315C22⋊C4—524no—
316C42—131no—
317C42—131no—
318C42—131no—
319C42—131no—
320C42—131no—
321C42—131no—
322C42—131no—
323C42—131no—
324C42—131no—
325C42—131no—
326C42—131no—
327C42—131no—
328C42—524no—
329C42C2×C4×D1311yescharacteristic
330C42C2×C4×D1311yescharacteristic
331C42D4×D1311yescharacteristic
332C42Q8×D1311yescharacteristic
333C13#797611yescharacteristic, complemented, Sylow
334C23—131no—
335C23—131no—
336C23—262no—
337C23—521no—
338C23—521no—
339C23C22⋊C4×D1311yescharacteristic
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—131no—
347C2×C4—131no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4C42×D1311yescharacteristic
371C2×C4C22⋊C4×D1311yescharacteristic
372C2×C4C22⋊C4×D1311yescharacteristic
373C2×C4C4⋊C4×D1311yescharacteristic
374C2×C4C4⋊C4×D1311yescharacteristic
375C2×C4C4⋊C4×D1311yescharacteristic
376C8—42no—
377C8—42no—
378C8—522no—
379C8—522no—
380C22—21no—
381C22—21no—
382C22—261no—
383C22—261no—
384C22—261no—
385C22—261no—
386C22—261no—
387C22—261no—
388C22—524no—
389C22D13×#9511yescharacteristic
390C22#1171848212yes—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—82no—
398C4—132no—
399C4—132no—
400C4—261no—
401C4—261no—
402C4—261no—
403C4—261no—
404C4—1042no—
405C2—22no—
406C2—521no—
407C2—521no—
408C2D13×H(3,ℤ/4)11yescharacteristic
409C2#1311454411yescharacteristic
410C2D13×#34411yescharacteristic
subgroupG/H
centerC22D13×#95
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1288C2
socleC22×C13C2×#95
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1288D13
hypocenterC13#7976
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
4. #13112702C2semidirect
5. #13112701C2semidirect
6. #13112700C2semidirect
7. C13×#1288C2semidirect
21. #11718368C4semidirect
24. #11718366C4semidirect
25. #11718346C4semidirect
26. #11718346C4semidirect
135. #1288D13semidirect
333. C13#7976semidirect

Maximal subgroups

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

subgroupindex
#131234672
#131234662
#131172332
#131127022
#131127012
#131127002
C13×#12882
#797613