Finite Group Databasebeta

← #15758530

Subgroups — #15758530

Order 3328.

614 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6099C211yesmaximal, characteristic
2#13114598C211yesmaximal, characteristic
3C2×#11718135C212yesmaximal, complemented
4#13112717C212yesmaximal, complemented
5C13×#2851C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C22×#6099—21no—
9C13×#389C411yescharacteristic
10C13×#389C411yescharacteristic
11C13×#387—21no—
12C13×#387—21no—
13C13×#385—21no—
14C13×#385—21no—
15C13×#382C2211yescharacteristic
16C13×#380C411yescharacteristic
17C13×#380C411yescharacteristic
18C2×C22⋊#1055—21no—
19C4×#6099—24no—
20C2×#88043C2212yes—
21C2×#88043C2212yes—
22C2×C4×#1055—21no—
23#11718135—24no—
24#11718116—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#125—22no—
29C13×#125—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—22no—
41C2×C42×C13—22no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C2×#6099—24no—
47C2×#6099—24no—
48C2×#6099—24no—
49C22×#1055—22no—
50C22×#1055—22no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C22⋊#1055—24no—
58#88043—22no—
59#88043—22no—
60#88043—22no—
61#88043D414yes—
62C4×#1055—24no—
63#9122—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C42×C13—22no—
97C42×C13—21no—
98C42×C13—22no—
99C42×C13—21no—
100C42×C13C2×D412yes—
101C42×C13#4112yes—
102#6099—216no—
103C2×#1055—24no—
104C2×#1055—24no—
105C2×#1055—24no—
106C2×#1055—24no—
107C2×#1055—42no—
108C2×#1055—42no—
109C2×C4×M16—131no—
110#2851D1311yescharacteristic
111#1749—131no—
112C2×#330—132no—
113#1295—132no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13#10412yes—
121C23×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13—24no—
123C2×C4×C13—24no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—44no—
137C2×C4×C13—44no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13#10112yes—
151C2×C4×C13#10412yes—
152C2×C4×C13#10412yes—
153C2×C4×C13C4×D412yes—
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12112yes—
156C2×C4×C13#12311yescharacteristic
157#1055—28no—
158#1055—44no—
159C22×M16—261no—
160C2×#125C2×D1311yescharacteristic
161C22×C42C2×D1311yescharacteristic
162C2×C22⋊C8—261no—
163C4×M16—264no—
164C2×#97—132no—
165C2×#97—132no—
166C2×C4×C8—261no—
167#389Dic1311yescharacteristic
168#389Dic1311yescharacteristic
169#387—21no—
170#387—21no—
171#385—21no—
172#385—21no—
173#382C2×D1311yescharacteristic
174#380Dic1311yescharacteristic
175#380Dic1311yescharacteristic
176#336—261no—
177#330—264no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13#38611yescharacteristic
186C22×C13C2×#10111yescharacteristic
187C22×C13#41311yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13C2×#10411yescharacteristic
190C22×C13C2×#10411yescharacteristic
191C22×C13#42111yescharacteristic
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—22no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—81no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203C23×C4C2×Dic1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C23×C4C22⋊D1311yescharacteristic
206C2×M16—264no—
207C2×M16—264no—
208C2×M16—264no—
209C22×C8—262no—
210C22×C8—262no—
211#125—22no—
212#125—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C2×Dic1311yescharacteristic
218C2×C4⋊C4C2×Dic1311yescharacteristic
219C2×C4⋊C4C2×Dic1311yescharacteristic
220C2×C4⋊C4C2×Dic1311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42C2×Dic1311yescharacteristic
226C2×C42C22⋊D1311yescharacteristic
227C2×C42C22⋊D1311yescharacteristic
228C2×C42C22×D1311yescharacteristic
229C22⋊C8—264no—
230#97—134no—
231#97—262no—
232#97—262no—
233#97—262no—
234C4×C8—264no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×C13—42no—
242C2×C13#152411yescharacteristic
243C2×C13#152611yescharacteristic
244C2×C13#152811yescharacteristic
245C2×C13#152911yescharacteristic
246C2×C13#187111yescharacteristic
247C2×C13#189611yescharacteristic
248C2×C13#190111yescharacteristic
249C24C22⋊Dic1311yescharacteristic
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4C22⋊Dic1311yescharacteristic
266C22×C4C22⋊Dic1311yescharacteristic
267C22×C4C22×Dic1311yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270M16—2616no—
271C2×C8—264no—
272C2×C8—264no—
273C2×C8—264no—
274C2×C8—264no—
275C2×C8—522no—
276C2×C8—522no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—22no—
289C42—21no—
290C42—21no—
291C42—22no—
292C42D4×D1312yes—
293C42#612912yes—
294C13#912211yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23#8807712yes—
302C23C2×C22⋊Dic1311yescharacteristic
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4#8807612yes—
332C2×C4#8807712yes—
333C2×C4#8807712yes—
334C2×C4D4×Dic1312yes—
335C2×C4#8818911yescharacteristic
336C2×C4#8819111yescharacteristic
337C2×C4#8819312yes—
338C8—268no—
339C8—524no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22#1171888111yescharacteristic
348C22C2×#8807611yescharacteristic
349C22C2×#8807711yescharacteristic
350C22C2×#8807711yescharacteristic
351C22C2×#8807711yescharacteristic
352C22#1171889711yescharacteristic
353C22#1171889811yescharacteristic
354C4—22no—
355C4—22no—
356C4—21no—
357C4—22no—
358C4—21no—
359C4—22no—
360C4—22no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C2—42no—
366C2#1311342411yescharacteristic
367C2#1311343111yescharacteristic
368C2#1311343811yescharacteristic
369C2#1311344311yescharacteristic
370C2#1311513911yescharacteristic
371C2#1311528011yescharacteristic
372C2#1311530511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2851C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2851D13
hypocenterC13#9122
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#11718135C2semidirect
4. #13112717C2semidirect
294. C13#9122semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#60992
#131145982
C2×#117181352
#131127172
C13×#28512
#912213