Finite Group Databasebeta

← #15758787

Subgroups — #15758787

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124645C211yesmaximal, characteristic
2#13123401C211yesmaximal, characteristic
3#13113521C211yesmaximal, characteristic, complemented
4#13113221C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic, complemented
6#13112711C211yesmaximal, characteristic, complemented
7C2×C13×#333C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88155—21no—
10C4×#6127C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13#11718763—21no—
14#11718755C412yes—
15#11718752—21no—
16#11718748C412yes—
17#11718745—21no—
18#11718627—21no—
19#11718625—21no—
20#11718586C2211yescharacteristic
21#11718585C2211yescharacteristic
22#11718585C2211yescharacteristic
23#11718500—22no—
24#11718498—21no—
25D13×C4⋊C8—21no—
26C13×#333—21no—
27C13×#333—21no—
28#11718139—22no—
29#11718076—21no—
30#11718075—21no—
31C22×Q8×C13—21no—
32C2×#6127D411yescharacteristic
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8C2×C412yes—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C4×C22⋊D13—21no—
43C4×C22⋊D13—21no—
44#88180D411yescharacteristic
45C2×#6099—21no—
46C2×#6099—21no—
47#88155—42no—
48#88155—42no—
49C2×#6094—22no—
50C2×C8×D13—22no—
51C4×D52C2×C411yescharacteristic
52C4×D52D411yescharacteristic
53#88126—21no—
54C42×D13—21no—
55C4×Dic26C2×C411yescharacteristic
56C4×Dic26D411yescharacteristic
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8D411yescharacteristic
61C13×C4⋊C8D411yescharacteristic
62C22⋊#1055—21no—
63#88054—22no—
64#88054—22no—
65#88050—22no—
66#88049—22no—
67#88048—22no—
68#88047—22no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055—21no—
72C4⋊#1055C2×C412yes—
73C4⋊#1055D412yes—
74C4×#1055—21no—
75#9169—131nomaximal, Sylow
76C2×Q8×C13—22no—
77C2×Q8×C13—41no—
78C2×Q8×C13—82no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C2×C22⋊D13—21no—
84#6127—21no—
85#6127—21no—
86#6127SD1612yes—
87#6127Q1612yes—
88C2×D52C22⋊C411yescharacteristic
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×C4×D13—21no—
92C2×Dic26C22⋊C411yescharacteristic
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—81no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C42×C13C22×C411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107C22⋊Dic13—21no—
108#6103—21no—
109#6103—21no—
110C4⋊Dic13C22⋊C411yescharacteristic
111C4⋊Dic13C22⋊C411yescharacteristic
112#6101—21no—
113#6101—21no—
114C4×Dic13—21no—
115C4×Dic13—21no—
116C4×Dic13—21no—
117#6099—41no—
118#6099—41no—
119#6099—41no—
120#6099—41no—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—41no—
124#6094—44no—
125C8×D13—44no—
126#3079—131no—
127#2906—131no—
128#1549—131no—
129C2×#333D1311yescharacteristic, complemented
130#1477—131no—
131#1301—131no—
132#1292—131no—
133C23×C13#12311yescharacteristic
134C22×D13—21no—
135Q8×C13—82no—
136Q8×C13—82no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—82no—
142C2×C4×C13C2×C22⋊C411yescharacteristic
143C2×C4×C13C4×D411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13C2×SD1611yescharacteristic
149C2×C4×C13C2×Q1611yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C22⋊D13—22no—
153C22⋊D13—22no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157D52—21no—
158D52#10312yes—
159C4×D13—22no—
160C4×D13—22no—
161C4×D13—41no—
162C4×D13—41no—
163C4×D13—81no—
164Dic26—21no—
165Dic26#10312yes—
166C8×C13—41no—
167C8×C13—41no—
168C8×C13—81no—
169#1055—42no—
170#1055—42no—
171#1055—81no—
172C2×#131—261no—
173C2×C4⋊Q8C2×D1311yescharacteristic
174C4×#41—131no—
175#477—261no—
176#476—261no—
177#475—132no—
178#474—132no—
179#431—131no—
180#428—261no—
181#424—262no—
182#424—261no—
183#423—131no—
184#423—131no—
185#423—261no—
186C2×C4⋊C8—261no—
187C2×C4⋊C8C2×D1311yescharacteristic
188C2×C4⋊C8C2×D1311yescharacteristic
189#417—261no—
190#333—21no—
191#333—21no—
192#332—262no—
193Q8⋊C8—261no—
194D4⋊C8—261no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13#38611yescharacteristic
198C22×C13#48311yescharacteristic
199C22×C13#48411yescharacteristic
200C2×D13—22no—
201C2×D13—41no—
202C2×D13—41no—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—82no—
207C4×C13C2×#10311yescharacteristic
208C4×C13#41711yescharacteristic
209C4×C13#45011yescharacteristic
210C4×C13#45111yescharacteristic
211C4×C13#47111yescharacteristic
212C4×C13#47311yescharacteristic
213Dic13—22no—
214Dic13—41no—
215Dic13—41no—
216C2×#41—131no—
217C22×Q8—21no—
218#131—522no—
219#131—522no—
220C2×M16—262no—
221C2×M16—261no—
222C2×M16—261no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—262no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8C4×D1312yes—
230C4×Q8—131no—
231C4×Q8—131no—
232C4×D4—131no—
233C4×D4—131no—
234C4×D4—261no—
235C4×D4—261no—
236#117—131no—
237#117—261no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C42—261no—
241C2×C42C22×D1311yescharacteristic
242#107—262no—
243#106—262no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—132no—
248C4⋊C8—132no—
249C4⋊C8—262no—
250C4⋊C8—262no—
251C4⋊C8—261no—
252C4⋊C8—261no—
253C4⋊C8—261no—
254C4⋊C8C22⋊D1311yescharacteristic
255C4⋊C8C22⋊D1311yescharacteristic
256#103—262no—
257#102—262no—
258C22⋊C8—261no—
259C4×C8—261no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13#187211yescharacteristic
263C2×C13#190311yescharacteristic
264C2×C13#190811yescharacteristic
265D13—42no—
266#41—132no—
267#41—132no—
268#41—261no—
269#41—261no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—82no—
273C2×Q8—131no—
274C2×D4—131no—
275C2×D4—261no—
276C22×C4—41no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4#612711yescharacteristic
281C22×C4D4×D1311yescharacteristic
282C22×C4#612911yescharacteristic
283M16—524no—
284M16—521no—
285M16—521no—
286M16—521no—
287M16—521no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—81no—
294C2×C8—262no—
295C2×C8—262no—
296C2×C8—524no—
297C2×C8—521no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—131no—
303C4⋊C4—131no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C42—261no—
310C42—261no—
311C42—261no—
312C42C2×C4×D1311yescharacteristic
313C42D4×D1311yescharacteristic
314C42D4×D1311yescharacteristic
315C42C2×C22⋊D1311yescharacteristic
316C13#916911yescharacteristic, complemented, Sylow
317C23—261no—
318C23#8813711yescharacteristic
319Q8—82no—
320Q8—82no—
321Q8—132no—
322Q8—261no—
323D4—132no—
324D4—262no—
325D4—262no—
326D4—261no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—261no—
333C2×C4—262no—
334C2×C4—262no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—1041no—
340C2×C4C22⋊C4×D1311yescharacteristic
341C2×C4#8813511yescharacteristic
342C2×C4#8813811yescharacteristic
343C2×C4SD16×D1311yescharacteristic
344C2×C4#8816811yescharacteristic
345C2×C4Q16×D1311yescharacteristic
346C2×C4#8817211yescharacteristic
347C2×C4C4×C22⋊D1311yescharacteristic
348C2×C4#8819111yescharacteristic
349C2×C4#8819211yescharacteristic
350C8—41no—
351C8—41no—
352C8—81no—
353C8—522no—
354C8—522no—
355C8—1041no—
356C22—21no—
357C22—21no—
358C22—262no—
359C22—521no—
360C22—521no—
361C22#1171846611yescharacteristic
362C22#1171847011yescharacteristic
363C22#1171861711yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—262no—
369C4—521no—
370C4—521no—
371C4D13×#10311yescharacteristic
372C4#1171846411yescharacteristic
373C4#1171883011yescharacteristic
374C4#1171883811yescharacteristic
375C4#1171884711yescharacteristic
376C4#1171885311yescharacteristic
377C2—21no—
378C2—21no—
379C2—522no—
380C2#1311514011yescharacteristic
381C2#1311531911yescharacteristic
382C2#1311535411yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socleC22×C13#386
prime radicalC2×#6127D4
cosocleC2×C42×C13C23
hypercenterC2×#333D13
hypocenterC13#9169
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
3. #13113521C2semidirect
5. #13112733C2semidirect
6. #13112711C2semidirect
7. C2×C13×#333C2semidirect
129. C2×#333D13semidirect
316. C13#9169semidirect

Maximal subgroups

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

subgroupindex
#131246452
#131234012
#131135212
#131132212
#131127332
#131127112
C2×C13×#3332
#916913