Finite Group Databasebeta

← #15759420

Subgroups — #15759420

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125758C211yesmaximal, characteristic
2#13123580C211yesmaximal, characteristic
3#13115824C211yesmaximal, characteristic, complemented
4C2×#11718073C211yesmaximal, characteristic, complemented
5#13112731C211yesmaximal, characteristic, complemented
6#13112686C211yesmaximal, characteristic, complemented
7C13×#1547C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×#88202—21no—
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13#11718895—21no—
14#11718754—21no—
15#11718737—21no—
16#11718701C414yes—
17#11718680—22no—
18#11718673—21no—
19#11718672—22no—
20D4×#1055—21no—
21#11718586C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C4×#6099C2211yescharacteristic
24C13×#332—21no—
25C13×#331—21no—
26#11718146—21no—
27#11718146—21no—
28#11718073—21no—
29#11718073—21no—
30C2×C13×#41—21no—
31C22×Dic26C2×C412yes—
32C2×C13×M16—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8D411yescharacteristic
35C13×#127D411yescharacteristic
36C13×#124—21no—
37C13×#121—21no—
38C13×#121C2×C412yes—
39C4×D4×C13—21no—
40C4×D4×C13D412yes—
41C2×C42×C13C2311yescharacteristic
42#88202—42no—
43#88202—42no—
44C2×#6105—24no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×#6099—22no—
48C2×#6099D411yescharacteristic
49C2×#6099D411yescharacteristic
50C22×#1055—22no—
51C22×#1055—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62C22⋊#1055C2×C412yes—
63#88050—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D411yescharacteristic
67C4⋊#1055D411yescharacteristic
68#88043—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71#9267—131nomaximal, Sylow
72C13×#41—41no—
73C13×#41—41no—
74C13×#41—41no—
75C13×#41—41no—
76C2×Q8×C13—21no—
77C2×D4×C13—22no—
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13C22⋊C412yes—
81C22×C4×C13—22no—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4111yescharacteristic
85C22×Dic13—22no—
86C2×Dic26—22no—
87C2×Dic26—22no—
88C2×Dic26—82no—
89C13×M16—41no—
90C13×M16—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—81no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4C22⋊C412yes—
96C13×C22⋊C4—22no—
97C13×C22⋊C4—22no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102#6105—84no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107#6099—21no—
108#6099—21no—
109#6099—21no—
110#6099—44no—
111#6099SD1612yescomplemented
112C2×#1055—21no—
113C2×#1055—22no—
114C2×#1055—21no—
115C2×#1055—21no—
116C2×#1055—21no—
117C2×#1055—44no—
118C2×#1055—41no—
119C2×#1055—41no—
120#3206—131no—
121#2935—131no—
122#1997—131no—
123#1547D1311yescharacteristic
124C2×#333—131no—
125#1301—131no—
126#1283—131no—
127C23×C13—22no—
128C23×C13C4×D411yescharacteristic
129Q8×C13—41no—
130Q8×C13—41no—
131D4×C13—42no—
132D4×C13—42no—
133D4×C13—42no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—41no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×Dic13—42no—
155C2×Dic13—82no—
156Dic26—44no—
157Dic26—82no—
158C8×C13—81no—
159C8×C13—81no—
160#1055—22no—
161#1055—42no—
162#1055—41no—
163#1055—41no—
164#1055—41no—
165C2×#131—261no—
166#532C2×D1311yescharacteristic
167C2×C4⋊Q8—131no—
168#492—261no—
169#487—261no—
170#461—262no—
171#448—134no—
172#436—261no—
173#435—262no—
174C8×D4—261no—
175#431—131no—
176#423C2×D1311yescharacteristic
177C2×C4⋊C8—131no—
178C2×C4⋊C8C2×D1311yescharacteristic
179#408—261no—
180C4×M16—131no—
181#343—261no—
182#343—261no—
183#333—261no—
184#333—261no—
185#332—21no—
186#331—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13#38611yescharacteristic
193C22×C13C4×SD1611yescharacteristic
194C22×C13#44011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13#45011yescharacteristic
200C4×C13#45211yescharacteristic
201C4×C13#46111yescharacteristic
202C4×C13#46311yescharacteristic
203C4×C13#47111yescharacteristic
204C4×C13#47311yescharacteristic
205Dic13—82no—
206C2×#41—21no—
207C22×Q8—132no—
208C2×SD16—264no—
209#131—522no—
210#131—522no—
211C2×M16—21no—
212C2×M16—131no—
213C2×M16—131no—
214C2×M16—262no—
215C22×C8—21no—
216C22×C8—262no—
217C22×C8—261no—
218C4⋊Q8—261no—
219C4⋊Q8—261no—
220C4⋊Q8—261no—
221C4⋊Q8—261no—
222C4⋊Q8C22⋊D1311yescharacteristic
223#127C22⋊D1311yescharacteristic
224#124—21no—
225#121—21no—
226#121C4×D1312yes—
227C4×D4—21no—
228C4×D4D5212yes—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C42C22×D1311yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—131no—
237C4⋊C8—131no—
238C4⋊C8—261no—
239C4⋊C8—261no—
240#103—264no—
241C22⋊C8—132no—
242C22⋊C8—262no—
243C22⋊C8—262no—
244#97—261no—
245C4×C8—261no—
246C4×C8—261no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—82no—
250C2×C13#187711yescharacteristic
251C2×C13#190811yescharacteristic
252C2×C13#191411yescharacteristic
253#41—41no—
254#41—41no—
255#41—41no—
256#41—41no—
257C2×Q8—21no—
258C2×Q8—262no—
259C2×Q8—262no—
260C2×Q8—1042no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4#610312yes—
265C22×C4—22no—
266C22×C4—262no—
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4D4×D1311yescharacteristic
269C22×C4#612911yescharacteristic
270SD16—1044no—
271M16—41no—
272M16—41no—
273M16—132no—
274M16—261no—
275M16—261no—
276M16—261no—
277M16—524no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—81no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—262no—
286C2×C8—524no—
287C2×C8—521no—
288C2×C8—521no—
289C4⋊C4—21no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C4⋊C4#610312yes—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C42C2×D5211yescharacteristic
298C42D4×D1311yescharacteristic
299C42#612911yescharacteristic
300C42C2×C22⋊D1311yescharacteristic
301C13#926711yescharacteristic, complemented, Sylow
302C23—22no—
303C23#8813511yescharacteristic
304Q8—41no—
305Q8—41no—
306Q8—524no—
307Q8—1042no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—41no—
312D4—41no—
313D4—41no—
314D4—41no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—522no—
322C2×C4—1042no—
323C2×C4#8813511yescharacteristic
324C2×C4#8813611yescharacteristic
325C2×C4#8814011yescharacteristic
326C2×C4#8816511yescharacteristic
327C2×C4#8816611yescharacteristic
328C2×C4SD16×D1311yescharacteristic
329C2×C4#8816911yescharacteristic
330C2×C4C2×#610311yescharacteristic
331C2×C4#8819311yescharacteristic
332C2×C4#8819311yescharacteristic
333C8—81no—
334C8—81no—
335C8—262no—
336C8—522no—
337C8—521no—
338C8—521no—
339C8—521no—
340C22—21no—
341C22—21no—
342C22—42no—
343C22—42no—
344C22—42no—
345C22#1171841811yescharacteristic
346C22#1171841911yescharacteristic
347C22#1171861911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—42no—
352C4—1042no—
353C4#1171843711yescharacteristic
354C4#1171844411yescharacteristic
355C4#1171881411yescharacteristic
356C4#1171882311yescharacteristic
357C4#1171886111yescharacteristic
358C4#1171886511yescharacteristic
359C2—21no—
360C2—21no—
361C2—82no—
362C2#1311516811yescharacteristic
363C2#1311534911yescharacteristic
364C2#1311538111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1547C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1547D13
hypocenterC13#9267
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
3. #13115824C2semidirect
4. C2×#11718073C2semidirect
5. #13112731C2semidirect
6. #13112686C2semidirect
111. #6099SD16semidirect
301. C13#9267semidirect

Maximal subgroups

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

subgroupindex
#131257582
#131235802
#131158242
C2×#117180732
#131127312
#131126862
C13×#15472
#926713