Finite Group Databasebeta

← #16797629

Subgroups — #16797629

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⋊#424C211yesmaximal, characteristic
2#13131298C211yesmaximal, characteristic
3#13130634C212yesmaximal, complemented
4#13130630C212yesmaximal, complemented
5#13130625C212yesmaximal, complemented
6#13130623C212yesmaximal, complemented
7#13130579C212yesmaximal
8#13130575C212yesmaximal
9D13×#433C211yesmaximal, characteristic
10C2×D13⋊M16C2211yescharacteristic
11C22×D13⋊C8C2211yescharacteristic
12D13×#117C2211yescharacteristic
13C4×C22⋊#261C2212yes—
14C2×#88100C2212yes—
15C2×#88100C2212yes—
16C2×#88100C2212yes—
17C2×C8×#261C2212yes—
18#11719082C414yes—
19#11719079C414yescomplemented
20#11719071C414yes—
21#11719067C414yescomplemented
22C4×C4⋊#261C2212yes—
23#11719057C2211yescharacteristic
24C42×#261C2211yescharacteristic
25D13⋊(C4⋊C8)C2212yes—
26D13⋊(C4⋊C8)C2212yes—
27C13×#433C411yescharacteristic, complemented
28#11718661C411yescharacteristic, complemented
29#11718501C412yescomplemented
30D13×C4⋊C8C2212yes—
31D13×C22⋊C8C2212yes—
32#11718381C412yescomplemented
33#11718370C411yescharacteristic, complemented
34D13×#97C2211yescharacteristic
35#11718351C411yescharacteristic, complemented
36C4×C8×D13C2211yescharacteristic
37(C2×#261)⋊C8C2212yes—
38(C2×#261)⋊C8C2212yes—
39(C2×#261)⋊C8C2212yes—
40(C2×#261)⋊C8C2212yes—
41C22×C4×D13C2311yescharacteristic
42C2×C22⋊#261C2×C414yes—
43C2×#6122C2×C412yes—
44C22×#1057C2×C412yes—
45C2×C4⋊#261C2×C414yes—
46C2×C4×#261C2×C414yes—
47C2×C4×#261C2312yes—
48C2×C4×#261C2312yes—
49D13⋊M16—42no—
50C2×#6118C2×C412yes—
51C2×D13⋊C8—42no—
52C2×D13⋊C8C2×C412yes—
53C2×D13⋊C8C2312yes—
54C2×D13⋊C8C2312yes—
55C13×#117C2×C411yescharacteristic
56#88180C2×C411yescharacteristic
57C2×C8×D13C2312yes—
58C2×C8×D13C2312yes—
59#88146C2×C412yes—
60C4⋊C4×D13C2×C412yes—
61C22⋊C4×D13C2×C412yes—
62#88131C2×C412yes—
63#88126C2×C411yescharacteristic
64#88126C2×C411yescharacteristic
65C42×D13C2311yescharacteristic
66C42×D13C2311yescharacteristic
67(C2×#261)⋊C4C2×C414yes—
68(C2×#261)⋊C4C2×C414yes—
69(C2×#261)⋊C4C2×C414yes—
70#88112C2×C414yes—
71#88112C2×C414yes—
72C4⋊#1057C2×C414yes—
73C4⋊#1057C2×C414yes—
74#88100—42no—
75#88100—42no—
76#88100—42no—
77C8×#261—42no—
78C13×C4⋊C8C2×C412yes—
79C13×C22⋊C8C2×C412yes—
80C13×#97C2×C411yescharacteristic
81C4×C8×C13C2×C411yescharacteristic
82C22⋊#1055C2×C412yes—
83#88060C2×C412yes—
84#88060C2×C412yes—
85#88055C2×C412yes—
86#88054C2×C412yes—
87#88054C2×C412yes—
88C8×Dic13C2×C412yes—
89C4⋊#1055C2×C412yes—
90#88043C2×C411yescharacteristic
91C4×#1055C2×C411yescharacteristic
92#20554—131nomaximal, Sylow
93C23×D13C22×C411yescharacteristic
94C22×#261C22×C414yes—
95C22×#261C22×C414yes—
96C22×C4×C13C22×C411yescharacteristic
97C22×Dic13C22×C411yescharacteristic
98C2×C4×D13—22no—
99C2×C4×D13—22no—
100C2×C4×D13C22×C411yescharacteristic
101C2×C4×D13C22×C412yes—
102C2×C4×D13C22×C412yes—
103C2×C4×D13C22×C411yescharacteristic
104C2×C4×D13C22×C411yescharacteristic
105C2×C4×D13C2411yescharacteristic
106C22⋊#261—44no—
107#6122—42no—
108C2×#1057—42no—
109C2×#1057C22×C414yes—
110C2×#1057C22×C414yes—
111C4⋊#261—44no—
112C4×#261—22no—
113C4×#261—22no—
114C4×#261—22no—
115C4×#261—22no—
116C4×#261—44no—
117#6118—42no—
118D13⋊C8—22no—
119D13⋊C8—22no—
120D13⋊C8—22no—
121D13⋊C8—22no—
122D13⋊C8—42no—
123C2×C8×C13C22×C412yes—
124C2×C8×C13C22×C412yes—
125C13×C4⋊C4C4212yes—
126C13×C22⋊C4C4212yes—
127C42×C13C22×C411yescharacteristic
128C42×C13C22×C411yescharacteristic
129C22⋊Dic13C4212yes—
130#6103C4212yes—
131#6103C4212yes—
132C4⋊Dic13C4212yes—
133#6101C4212yes—
134#6101C4212yes—
135C4×Dic13C22×C411yescharacteristic
136C4×Dic13C22×C411yescharacteristic
137C4×Dic13C22×C412yes—
138C4×Dic13C22×C412yes—
139C2×#1055C22×C412yes—
140C2×#1055C22×C412yes—
141C8×D13—22no—
142C8×D13—22no—
143C8×D13—22no—
144C8×D13—22no—
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—22no—
166C2×C4×C13C2×C4212yes—
167C2×C4×C13C2×C4212yes—
168C2×C4×C13C2×C4211yescharacteristic
169C2×C4×C13C23×C411yescharacteristic
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13C2×C4212yes—
173C2×Dic13C2×C4212yes—
174C2×Dic13C2×C4211yescharacteristic
175C2×Dic13C23×C411yescharacteristic
176C4×D13—22no—
177C4×D13—24no—
178C4×D13—24no—
179C4×D13—22no—
180C4×D13—21no—
181C4×D13—21no—
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—131no—
194#433—132no—
195#433—132no—
196#433—131no—
197#433—131no—
198#433#26111yescharacteristic, complemented
199#424—134no—
200#424—134no—
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#52012yes—
235Dic13—22no—
236Dic13—22no—
237Dic13—21no—
238Dic13#51811yescharacteristic
239Dic13#51911yescharacteristic
240C23×C4—131no—
241C2×M16—132no—
242C2×M16—132no—
243C2×M16—522no—
244C22×C8—132no—
245C22×C8—132no—
246C22×C8—132no—
247C22×C8—132no—
248C22×C8—132no—
249C22×C8—132no—
250C22×C8—522no—
251#117—131no—
252#117—132no—
253#117—132no—
254#117—131no—
255#117—131no—
256#117C2×#26111yescharacteristic
257C2×C4⋊C4—132no—
258C2×C4⋊C4—134no—
259C2×C22⋊C4—132no—
260C2×C22⋊C4—134no—
261C2×C42—131no—
262C2×C42—131no—
263C2×C42—132no—
264C2×C42—132no—
265C2×C42—134no—
266C4⋊C8—134no—
267C4⋊C8—134no—
268C4⋊C8—134no—
269C4⋊C8—134no—
270C4⋊C8—132no—
271C4⋊C8—132no—
272C4⋊C8—132no—
273C4⋊C8C2×#26112yes—
274C22⋊C8—132no—
275C22⋊C8—132no—
276C22⋊C8—132no—
277C22⋊C8C2×#26112yes—
278#97—132no—
279#97—131no—
280#97—522no—
281#97—522no—
282#97—522no—
283#97C2×#26111yescharacteristic
284C4×C8—132no—
285C4×C8—131no—
286C4×C8—522no—
287C4×C8C2×#26111yescharacteristic
288#95—134no—
289#95—134no—
290#95—134no—
291C2×C13—41no—
292C2×C13#227411yescharacteristic
293C2×C13#287512yes—
294D13—41no—
295D13#299514yes—
296C24—131no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—131no—
300C22×C4—132no—
301C22×C4—132no—
302C22×C4—131no—
303C22×C4—131no—
304C22×C4—134no—
305C22×C4—134no—
306C22×C4—262no—
307C22×C4—262no—
308C22×C4C22×#26111yescharacteristic
309M16—522no—
310M16—522no—
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—522no—
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—22no—
355C2×C4—131no—
356C2×C4—132no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—132no—
360C2×C4—131no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—264no—
364C2×C4—264no—
365C2×C4—262no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—262no—
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—131no—
397C4—131no—
398C4—261no—
399C4—262no—
400C4—262no—
401C4—524no—
402C4—524no—
403C4#1171963112yes—
404C2—41no—
405C2—134no—
406C2—521no—
407C2#1313127311yescharacteristic
408C2#1313140612yes—
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC13×#433C4
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenter#433#261
hypocenterC13#20554
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
3. #13130634C2semidirect
4. #13130630C2semidirect
5. #13130625C2semidirect
6. #13130623C2semidirect
19. #11719079C4semidirect
21. #11719067C4semidirect
27. C13×#433C4semidirect
28. #11718661C4semidirect
29. #11718501C4semidirect
32. #11718381C4semidirect
33. #11718370C4semidirect
35. #11718351C4semidirect
198. #433#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⋊#4242
#131312982
#131306342
#131306302
#131306252
#131306232
#131305792
#131305752
D13×#4332
#2055413