Finite Group Databasebeta

← #16797630

Subgroups — #16797630

Order 3328.

850 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
1D13⋊#433C211yesmaximal, characteristic
2#13131298C211yesmaximal, characteristic
3#13130637C212yesmaximal, complemented
4#13130633C212yesmaximal, complemented
5#13130625C212yesmaximal, complemented
6#13130623C212yesmaximal, complemented
7#13130576C212yesmaximal
8#13130572C212yesmaximal
9D13×#424C211yesmaximal, characteristic
10C2×M16×D13C2211yescharacteristic
11C22×C8×D13C2211yescharacteristic
12D13×#117C2211yescharacteristic
13C4×C22⋊#261C2212yes—
14D13⋊(C22⋊C8)C2212yes—
15C2×#88100C2212yes—
16C2×#88100C2212yes—
17C2×#88100C2212yes—
18C2×C8×#261C2212yes—
19#11719082C414yes—
20#11719077C414yescomplemented
21#11719071C414yes—
22#11719068C414yescomplemented
23C4×C4⋊#261C2212yes—
24#11719057C2211yescharacteristic
25C42×#261C2211yescharacteristic
26D13⋊(C4⋊C8)C2212yes—
27#11719047C2211yescharacteristic
28C4×D13⋊C8C2211yescharacteristic
29C13×#424C411yescharacteristic, complemented
30#11718780C411yescharacteristic, complemented
31#11718763C411yescharacteristic, complemented
32#11718660C411yescharacteristic, complemented
33#11718500C412yescomplemented
34#11718500C412yescomplemented
35D13×C4⋊C8C2212yes—
36D13×C4⋊C8C2212yes—
37(C2×#261)⋊C8C2212yes—
38(C2×#261)⋊C8C2212yes—
39(C2×#261)⋊C8C2212yes—
40(C2×#261)⋊C8C2212yes—
41C22×C4×D13C2311yescharacteristic
42C2×C22⋊#261C2×C414yes—
43C2×C4⋊#261C2×C414yes—
44C2×C4×#261C2×C414yes—
45C2×C4×#261C2312yes—
46C2×C4×#261C2312yes—
47C2×D13⋊C8C2312yes—
48C2×D13⋊C8C2312yes—
49C2×C13×M16C2×C411yescharacteristic
50C22×C8×C13C2×C411yescharacteristic
51C13×#117C2×C411yescharacteristic
52#88180C2×C411yescharacteristic
53C2×#6099C2×C411yescharacteristic
54C22×#1055C2×C411yescharacteristic
55M16×D13—42no—
56C2×#6094C2×C412yes—
57C2×C8×D13—42no—
58C2×C8×D13C2×C412yes—
59C2×C8×D13C2312yes—
60C2×C8×D13C2312yes—
61#88146C2×C412yes—
62C4⋊C4×D13C2×C412yes—
63C22⋊C4×D13C2×C412yes—
64#88131C2×C412yes—
65#88126C2×C411yescharacteristic
66#88126C2×C411yescharacteristic
67C42×D13C2311yescharacteristic
68C42×D13C2311yescharacteristic
69C22⋊#1057C2×C414yes—
70(C2×#261)⋊C4C2×C414yes—
71(C2×#261)⋊C4C2×C414yes—
72(C2×#261)⋊C4C2×C414yes—
73#88112C2×C414yes—
74#88111C2×C414yes—
75#88110C2×C414yes—
76C4⋊#1057C2×C414yes—
77C4×#1057C2×C414yes—
78#88100—42no—
79#88100—42no—
80#88100—42no—
81C8×#261—42no—
82C13×C4⋊C8C2×C412yes—
83C13×C4⋊C8C2×C412yes—
84#88054C2×C412yes—
85#88054C2×C412yes—
86#88054C2×C412yes—
87#88054C2×C412yes—
88C4⋊#1055C2×C412yes—
89C4⋊#1055C2×C412yes—
90#20554—131nomaximal, Sylow
91C23×D13C22×C411yescharacteristic
92C22×#261C22×C414yes—
93C22×#261C22×C414yes—
94C22×C4×C13C22×C411yescharacteristic
95C22×Dic13C22×C411yescharacteristic
96C2×C4×D13—22no—
97C2×C4×D13—22no—
98C2×C4×D13C22×C411yescharacteristic
99C2×C4×D13C22×C412yes—
100C2×C4×D13C22×C412yes—
101C2×C4×D13C22×C411yescharacteristic
102C2×C4×D13C22×C411yescharacteristic
103C2×C4×D13C2411yescharacteristic
104C22⋊#261—44no—
105C2×#1057C22×C414yes—
106C2×#1057C22×C414yes—
107C4⋊#261—44no—
108C4×#261—22no—
109C4×#261—22no—
110C4×#261—22no—
111C4×#261—22no—
112C4×#261—44no—
113D13⋊C8—22no—
114D13⋊C8—22no—
115D13⋊C8—22no—
116D13⋊C8—22no—
117C13×M16—41no—
118C2×C8×C13—41no—
119C2×C8×C13C22×C412yes—
120C2×C8×C13C22×C412yes—
121C13×C4⋊C4C4212yes—
122C13×C22⋊C4C4212yes—
123C42×C13C22×C411yescharacteristic
124C42×C13C22×C411yescharacteristic
125C22⋊Dic13C4212yes—
126#6103C4212yes—
127#6103C4212yes—
128C4⋊Dic13C4212yes—
129#6101C4212yes—
130#6101C4212yes—
131C4×Dic13C22×C411yescharacteristic
132C4×Dic13C22×C411yescharacteristic
133C4×Dic13C22×C412yes—
134C4×Dic13C22×C412yes—
135#6099—41no—
136C2×#1055—41no—
137C2×#1055C22×C412yes—
138C2×#1055C22×C412yes—
139#6094—42no—
140C8×D13—22no—
141C8×D13—22no—
142C8×D13—22no—
143C8×D13—22no—
144C8×D13—42no—
145C2×#433—131no—
146C2×#424—131no—
147#2298—131no—
148#1771—132no—
149#1770—132no—
150#1768—132no—
151#1767—132no—
152#1753—132no—
153#1752—132no—
154C23×C13C2×C4211yescharacteristic
155C22×D13—22no—
156C22×D13—24no—
157C22×D13C2×C4211yescharacteristic
158C22×D13C23×C411yescharacteristic
159C2×#261—24no—
160C2×#261—24no—
161C2×#261—24no—
162C2×#261—24no—
163C2×#261—24no—
164C2×#261—24no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13C2×C4212yes—
168C2×C4×C13C2×C4212yes—
169C2×C4×C13C2×C4211yescharacteristic
170C2×C4×C13C23×C411yescharacteristic
171C2×Dic13—22no—
172C2×Dic13C2×C4212yes—
173C2×Dic13C2×C4212yes—
174C2×Dic13C2×C4211yescharacteristic
175C2×Dic13C23×C411yescharacteristic
176C4×D13—22no—
177C4×D13—24no—
178C4×D13—24no—
179C4×D13—21no—
180C4×D13—21no—
181C4×D13—22no—
182C4×D13H(5,𝔽2)12yes—
183C4×D132−1+412yes—
184#1057—24no—
185#1057—24no—
186C8×C13—22no—
187C8×C13—22no—
188#1055—22no—
189#1055—22no—
190C22×M16—131no—
191C23×C8—131no—
192C2×#117—131no—
193#433—134no—
194#433—134no—
195#424—131no—
196#424—131no—
197#424—131no—
198#424—132no—
199#424—132no—
200#424#26111yescharacteristic, complemented
201C2×C4⋊C8—132no—
202C2×C4⋊C8—132no—
203C2×C4⋊C8—132no—
204C2×C22⋊C8—132no—
205C2×#97—131no—
206C2×#97—132no—
207C2×#97—132no—
208C2×#97—132no—
209C2×C4×C8—131no—
210C2×C4×C8—132no—
211#388—134no—
212#387—134no—
213C4×C4⋊C4—132no—
214C4×C22⋊C4—132no—
215#376—131no—
216C43—131no—
217#336—132no—
218#336—132no—
219#336—132no—
220#336—132no—
221C22×C13—22no—
222C22×C13—21no—
223C22×C13C22×C4211yescharacteristic
224C2×D13—22no—
225C2×D13—21no—
226C2×D13—44no—
227C2×D13#52012yes—
228C2×D13#56814yes—
229#261—44no—
230#261—44no—
231C4×C13—22no—
232C4×C13—22no—
233C4×C13—21no—
234C4×C13#51811yescharacteristic
235C4×C13#51911yescharacteristic
236Dic13—22no—
237Dic13—22no—
238Dic13—21no—
239Dic13#52012yes—
240C23×C4—131no—
241C2×M16—131no—
242C2×M16—132no—
243C2×M16—522no—
244C2×M16C2×#26111yescharacteristic
245C22×C8—132no—
246C22×C8—132no—
247C22×C8—131no—
248C22×C8—132no—
249C22×C8—132no—
250C22×C8—132no—
251C22×C8—522no—
252C22×C8C2×#26111yescharacteristic
253#117—131no—
254#117—132no—
255#117—132no—
256#117—131no—
257#117—131no—
258#117C2×#26111yescharacteristic
259C2×C4⋊C4—132no—
260C2×C4⋊C4—134no—
261C2×C22⋊C4—132no—
262C2×C22⋊C4—134no—
263C2×C42—131no—
264C2×C42—131no—
265C2×C42—132no—
266C2×C42—132no—
267C2×C42—134no—
268C4⋊C8—134no—
269C4⋊C8—134no—
270C4⋊C8—132no—
271C4⋊C8—132no—
272C4⋊C8—132no—
273C4⋊C8—132no—
274C4⋊C8—132no—
275C4⋊C8—132no—
276C4⋊C8C2×#26112yes—
277C4⋊C8C2×#26112yes—
278C22⋊C8—134no—
279C22⋊C8—134no—
280#97—134no—
281#97—522no—
282#97—522no—
283#97—522no—
284C4×C8—134no—
285C4×C8—522no—
286#95—134no—
287#95—134no—
288#95—134no—
289C2×C13—41no—
290C2×C13#227411yescharacteristic
291C2×C13#287512yes—
292D13—41no—
293D13#299514yes—
294C24—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—132no—
299C22×C4—132no—
300C22×C4—131no—
301C22×C4—131no—
302C22×C4—134no—
303C22×C4—134no—
304C22×C4—262no—
305C22×C4—262no—
306C22×C4C22×#26111yescharacteristic
307M16—41no—
308M16—522no—
309M16—521no—
310C2×C8—41no—
311C2×C8—134no—
312C2×C8—134no—
313C2×C8—132no—
314C2×C8—132no—
315C2×C8—262no—
316C2×C8—262no—
317C2×C8—262no—
318C2×C8—262no—
319C2×C8—262no—
320C2×C8—262no—
321C2×C8—262no—
322C2×C8—262no—
323C2×C8—522no—
324C2×C8—521no—
325C2×C8C22×#26112yes—
326C2×C8C22×#26112yes—
327C4⋊C4—132no—
328C4⋊C4—132no—
329C4⋊C4—132no—
330C4⋊C4—524no—
331C4⋊C4C4×#26112yes—
332C22⋊C4—132no—
333C22⋊C4—132no—
334C22⋊C4—132no—
335C22⋊C4—524no—
336C22⋊C4C4×#26112yes—
337C42—132no—
338C42—132no—
339C42—131no—
340C42—131no—
341C42—262no—
342C42—262no—
343C42—262no—
344C42—262no—
345C42—524no—
346C42C22×#26111yescharacteristic
347C42C22×#26111yescharacteristic
348C13#2055411yescharacteristic, complemented, Sylow
349C23—131no—
350C23—131no—
351C23—264no—
352C23—262no—
353C23C2×C4×#26111yescharacteristic
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—131no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—132no—
360C2×C4—132no—
361C2×C4—131no—
362C2×C4—262no—
363C2×C4—264no—
364C2×C4—264no—
365C2×C4—262no—
366C2×C4—262no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—264no—
370C2×C4—264no—
371C2×C4—264no—
372C2×C4—264no—
373C2×C4—264no—
374C2×C4—264no—
375C2×C4C2×C4×#26112yes—
376C2×C4C2×C4×#26112yes—
377C2×C4C2×C4×#26111yescharacteristic
378C2×C4C23×#26111yescharacteristic
379C8—22no—
380C8—22no—
381C8—264no—
382C8—264no—
383C8—262no—
384C8—262no—
385C22—21no—
386C22—22no—
387C22—132no—
388C22—134no—
389C22—261no—
390C22—262no—
391C22—524no—
392C22C22×C4×#26111yescharacteristic
393C4—21no—
394C4—22no—
395C4—22no—
396C4—132no—
397C4—261no—
398C4—262no—
399C4—262no—
400C4—524no—
401C4—524no—
402C4#1171962311yescharacteristic
403C4#1171962711yescharacteristic
404C2—41no—
405C2—134no—
406C2—521no—
407C2#1313127411yescharacteristic
408C2#1313140612yes—
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC13×#424C4
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenter#424#261
hypocenterC13#20554
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #13130637C2semidirect
4. #13130633C2semidirect
5. #13130625C2semidirect
6. #13130623C2semidirect
20. #11719077C4semidirect
22. #11719068C4semidirect
29. C13×#424C4semidirect
30. #11718780C4semidirect
31. #11718763C4semidirect
32. #11718660C4semidirect
33. #11718500C4semidirect
34. #11718500C4semidirect
200. #424#261semidirect
348. C13#20554semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4332
#131312982
#131306372
#131306332
#131306252
#131306232
#131305762
#131305722
D13×#4242
#2055413