Finite Group Databasebeta

← #15780295

Subgroups — #15780295

Order 3328.

506 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88038C211yesmaximal, characteristic
2C2×#11718548C211yesmaximal, characteristic
3C2×#11718095C211yesmaximal, characteristic, complemented
4C2×#11718084C211yesmaximal, characteristic, complemented
5#13114862C211yesmaximal, characteristic
6#13112927C211yesmaximal, characteristic, complemented
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×Dic52C2211yescharacteristic
9C22×C8×D13C2211yescharacteristic
10C2×#88151—21no—
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×C13×#107C2211yescharacteristic
14C2×#88058C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16#11718648—21no—
17C2×#88050—21no—
18C2×#88038—22no—
19C2×#88038—22no—
20C2×#88038—22no—
21#11718548—22no—
22#11718548C414yescomplemented
23#11718121—21no—
24#11718095—22no—
25#11718084—22no—
26C22×C4×D13D411yescharacteristic
27C22×Dic26—21no—
28C22×C8×C13C2311yescharacteristic
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×#6103—41no—
32C2×#6103—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—41no—
35C22×#1055D411yescharacteristic
36C2×Dic52—21no—
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52—21no—
41C2×Dic52C2×C412yes—
42C2×C8×D13—21no—
43C2×C8×D13—21no—
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C2×C8×D13C2×C412yes—
47C2×C8×D13D412yes—
48#88151—24no—
49#88151—42no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C2×C13×C16D412yes—
53C13×#107—21no—
54C13×#107—21no—
55C13×#107—21no—
56C13×#107C2×C412yes—
57#88071—41no—
58#88058—21no—
59#88058—21no—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090D412yes—
63#88050—24no—
64#88038—28no—
65#13062—131nomaximal, Sylow
66C23×D13D811yescharacteristic
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13D811yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13C22⋊C412yes—
78C2×C4×D13SD1612yes—
79C2×Dic26—22no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×C8×C13C22×C411yescharacteristic
86C2×C8×C13C2×D411yescharacteristic
87C2×C8×C13C2×D411yescharacteristic
88C2×C8×C13C2×D411yescharacteristic
89C2×C8×C13#4111yescharacteristic
90C2×C8×C13#4111yescharacteristic
91C13×C4⋊C4—22no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95#6103—44no—
96#6103—82no—
97C4⋊Dic13—44no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055C22⋊C412yes—
103Dic52—22no—
104Dic52—22no—
105Dic52—41no—
106Dic52—41no—
107C8×D13—22no—
108C8×D13—22no—
109C8×D13—22no—
110C8×D13—22no—
111C13×C16—22no—
112#6090—22no—
113C22×M32—131no—
114C2×#467—131no—
115C2×#358—131no—
116C2×#358—131no—
117#1808—131no—
118#1380—131no—
119#1380D1311yescharacteristic, complemented
120C23×C13C2×D811yescharacteristic
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13#10212yes—
128C2×C4×C13—42no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13C2×C22⋊C411yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—42no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13#10212yes—
149C4×D13—22no—
150C4×D13—22no—
151C4×D13—22no—
152C4×D13—22no—
153Dic26—42no—
154Dic26—42no—
155Dic26—81no—
156Dic26—81no—
157C8×C13C4×D411yescharacteristic
158C8×C13C4×D411yescharacteristic
159C8×C13#12011yescharacteristic
160C8×C13#12311yescharacteristic
161#1055—22no—
162C22×Q16—131no—
163C23×C8—131no—
164C2×C22⋊Q8—261no—
165C2×M32—262no—
166C2×M32—262no—
167C2×M32—262no—
168C22×C16—131no—
169C22×C16C2×D1311yescharacteristic
170#467—134no—
171#467—262no—
172C2×#107—131no—
173C2×#107C2×D1311yescharacteristic
174C2×#107C2×D1311yescharacteristic
175C2×#103—261no—
176#380—261no—
177#358—262no—
178#358—262no—
179#340—261no—
180C22×C13C2×#10211yescharacteristic
181C22×C13#46611yescharacteristic
182C22×C13#46611yescharacteristic
183C22×C13#50911yescharacteristic
184C22×C13#51011yescharacteristic
185C22×C13#51011yescharacteristic
186C22×C13#51011yescharacteristic
187C2×D13—22no—
188C2×D13—22no—
189C2×D13—22no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—41no—
193C2×D13—41no—
194C4×C13—82no—
195C4×C13—161no—
196C4×C13#38611yescharacteristic
197C4×C13#41611yescharacteristic
198C4×C13#46511yescharacteristic
199C4×C13#46511yescharacteristic
200Dic13—22no—
201Dic13—82no—
202Dic13—161no—
203C22×Q8—261no—
204C23×C4—131no—
205C2×Q16—132no—
206C2×Q16—261no—
207C2×Q16—261no—
208C2×Q16—261no—
209C2×Q16—261no—
210C2×Q16—261no—
211C22×C8—131no—
212C22×C8—132no—
213C22×C8—132no—
214C22×C8—261no—
215C22×C8—261no—
216C22×C8—261no—
217C22×C8—261no—
218C22×C8C22×D1311yescharacteristic
219C22⋊Q8—264no—
220C22⋊Q8—522no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—521no—
225C2×C22⋊C4—521no—
226C2×C22⋊C4—521no—
227M32—268no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—132no—
231C2×C16—261no—
232C2×C16—261no—
233C2×C16D5212yes—
234#107—21no—
235#107—21no—
236#107—21no—
237#107—261no—
238#107—261no—
239#107C4×D1312yes—
240#103—264no—
241#95—521no—
242C2×C13#189311yescharacteristic
243C2×C13#213911yescharacteristic
244C2×C13#214111yescharacteristic
245C2×C13#221911yescharacteristic
246C2×C13#221911yescharacteristic
247C2×C13#222011yescharacteristic
248C2×C13#222011yescharacteristic
249D13—42no—
250C24—131no—
251C2×Q8—262no—
252C2×Q8—521no—
253C2×Q8—521no—
254C2×Q8—521no—
255C2×Q8—521no—
256C2×Q8—521no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—131no—
260C22×C4—132no—
261C22×C4—132no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4D4×D1311yescharacteristic
269Q16—262no—
270Q16—262no—
271Q16—521no—
272Q16—521no—
273C2×C8—132no—
274C2×C8—261no—
275C2×C8—261no—
276C2×C8—262no—
277C2×C8—262no—
278C2×C8—262no—
279C2×C8—262no—
280C2×C8C2×C4×D1311yescharacteristic
281C2×C8C2×D5211yescharacteristic
282C2×C8#612711yescharacteristic
283C2×C8D4×D1311yescharacteristic
284C2×C8D4×D1311yescharacteristic
285C2×C8#613111yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—524no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C22⋊C4—524no—
294C22⋊C4—1042no—
295C16—22no—
296C16—262no—
297C13#1306211yescharacteristic, complemented, Sylow
298C23—132no—
299C23—261no—
300C23—261no—
301C23—261no—
302C23—261no—
303C23—261no—
304C23—261no—
305C23D8×D1311yescharacteristic
306Q8—522no—
307Q8—522no—
308Q8—1041no—
309Q8—1041no—
310C2×C4—42no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—132no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—522no—
324C2×C4—1041no—
325C2×C4—1041no—
326C2×C4—1041no—
327C2×C4—1041no—
328C2×C4—1041no—
329C2×C4C22⋊C4×D1311yescharacteristic
330C2×C4#8813811yescharacteristic
331C2×C4#8814911yescharacteristic
332C2×C4SD16×D1311yescharacteristic
333C2×C4#8817011yescharacteristic
334C2×C4#8817311yescharacteristic
335C8—262no—
336C8C4×D5211yescharacteristic
337C8#8813611yescharacteristic
338C8#8814711yescharacteristic
339C8#8814811yescharacteristic
340C22—262no—
341C22—262no—
342C22—262no—
343C22—521no—
344C22—521no—
345C22—521no—
346C22—521no—
347C22D13×#10211yescharacteristic
348C22#1171843611yescharacteristic
349C22#1171854411yescharacteristic
350C22#1171857211yescharacteristic
351C22#1171857611yescharacteristic
352C22#1171857611yescharacteristic
353C22#1171857911yescharacteristic
354C4—82no—
355C4—161no—
356C4—262no—
357C4—1042no—
358C4—2081no—
359C4#1171832611yescharacteristic
360C4#1171846511yescharacteristic
361C4#1171846811yescharacteristic
362C4#1171852511yescharacteristic
363C2—522no—
364C2#1311526311yescharacteristic
365C2#1311654511yescharacteristic
366C2#1311655411yescharacteristic
367C2#1311694311yescharacteristic
368C2#1311694511yescharacteristic
369C2#1311694811yescharacteristic
370C2#1311695011yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC23×D13D8
cosocleC22×C8×C13C23
hypercenter#1380D13
hypocenterC13#13062
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#11718095C2semidirect
4. C2×#11718084C2semidirect
6. #13112927C2semidirect
7. C13×#1380C2semidirect
22. #11718548C4semidirect
119. #1380D13semidirect
297. C13#13062semidirect

Maximal subgroups

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

subgroupindex
C22×#880382
C2×#117185482
C2×#117180952
C2×#117180842
#131148622
#131129272
C13×#13802
#1306213