Finite Group Databasebeta

← #15779838

Subgroups — #15779838

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718562C211yesmaximal, characteristic, complemented
2#13123737C211yesmaximal, characteristic
3#13116465C211yesmaximal, characteristic, complemented
4#13116457C211yesmaximal, characteristic, complemented
5#13112924C211yesmaximal, characteristic, complemented
6#13112921C211yesmaximal, characteristic, complemented
7C2×C13×#350C211yesmaximal, characteristic, complemented
8C2×C13×#131C2211yescharacteristic
9#11719527C411yescharacteristic
10C2×#88155C2211yescharacteristic
11C2×C13×M32C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13#11718897C411yescharacteristic
14#11718806—22no—
15#11718805—22no—
16#11718800C411yescharacteristic
17#11718785C411yescharacteristic
18#11718762C2211yescharacteristic
19C2×#88052C2211yescharacteristic
20C2×#88052C2211yescharacteristic
21#11718562—22no—
22#11718562—22no—
23C2×#88038—21no—
24C2×C16×D13—21no—
25C13×#350—21no—
26C13×#350—21no—
27#11718145—22no—
28#11718107—22no—
29C2×C13×#41C2×C411yescharacteristic
30C2×#6127C2×C411yescharacteristic
31C13×#131—21no—
32C13×#131—21no—
33C13×#131—21no—
34C13×#131—21no—
35C2×C13×M16—21no—
36C2×C13×M16C2×C411yescharacteristic
37C22×C8×C13—21no—
38C22×C8×C13C2311yescharacteristic
39#88205—21no—
40#88204—22no—
41#88203—21no—
42#88196C812yes—
43#88186C812yes—
44#88180C2×C411yescharacteristic
45C2×#6099C2×C411yescharacteristic
46C2×#6099C2×C411yescharacteristic
47#88155—21no—
48#88155—21no—
49#88155D412yes—
50#88155D412yes—
51C2×#6094—21no—
52C2×C8×D13—21no—
53C13×M32—21no—
54C13×M32—21no—
55C2×C13×C16—21no—
56C2×C13×C16—21no—
57C2×C13×C16—21no—
58C2×C13×C16D411yescharacteristic
59C2×C13×C16D411yescharacteristic
60#88077—22no—
61#88065—22no—
62#88062—22no—
63#88055—21no—
64C8×Dic13—21no—
65#88052—21no—
66#88052—21no—
67#88052—21no—
68#88052D412yes—
69C2×#6090—21no—
70C2×#6090—21no—
71#88038—24no—
72C16×D13—24no—
73#12987—131nomaximal, Sylow
74C13×#41—21no—
75C13×#41—21no—
76C13×#41—21no—
77C13×#41—21no—
78C2×Q8×C13C2×C811yescharacteristic
79C2×D4×C13—21no—
80C2×D4×C13C2×C811yescharacteristic
81C22×C4×C13—21no—
82C22×C4×C13C22×C411yescharacteristic
83C2×C22⋊D13—21no—
84#6127—21no—
85#6127—21no—
86#6127C22⋊C412yes—
87#6127C2×C812yes—
88C2×D52M1611yescharacteristic
89C2×C4×D13—21no—
90C2×Dic26M1611yescharacteristic
91C13×M16—21no—
92C13×M16—21no—
93C13×M16—41no—
94C13×M16—41no—
95C2×C8×C13—21no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C22⋊Dic13—21no—
105#6107—22no—
106#6106—22no—
107#6105—22no—
108#6104—22no—
109C4⋊Dic13—21no—
110C4×Dic13—21no—
111#6099—21no—
112#6099—21no—
113#6099C22⋊C412yes—
114#6099C2×C812yes—
115C2×#1055—21no—
116C2×#1055—21no—
117#6094—22no—
118#6094—22no—
119C8×D13—22no—
120C8×D13—22no—
121C13×C16—21no—
122C13×C16—21no—
123C13×C16—41no—
124#6090—22no—
125#6090—41no—
126C2×#504—131no—
127#2955—131no—
128#2117—131no—
129C2×#350D1311yescharacteristic, complemented
130#2115—131no—
131#1379—131no—
132#1378—131no—
133C23×C13—21no—
134C23×C13#13111yescharacteristic
135C22×D13—21no—
136Q8×C13—21no—
137Q8×C13—21no—
138D4×C13—21no—
139D4×C13—21no—
140D4×C13—41no—
141D4×C13—41no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13C2×C22⋊C411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13C22×C811yescharacteristic
149C2×C4×C13C2×M1611yescharacteristic
150C2×C4×C13#13111yescharacteristic
151C22⋊D13—22no—
152C22⋊D13—22no—
153C2×Dic13—21no—
154C2×Dic13—41no—
155D52—21no—
156D52C22⋊C812yes—
157C4×D13—22no—
158C4×D13—22no—
159Dic26—21no—
160Dic26C22⋊C812yes—
161C8×C13—41no—
162C8×C13#12011yescharacteristic
163C8×C13#12111yescharacteristic
164C8×C13#12111yescharacteristic
165C8×C13#12311yescharacteristic
166#1055—22no—
167#1055—22no—
168#575—131no—
169C2×#131—131no—
170C2×#131C2×D1311yescharacteristic
171#504—262no—
172#504—262no—
173C2×M32—131no—
174C2×M32—131no—
175C2×M32—261no—
176C2×M32C2×D1311yescharacteristic
177C22×C16—261no—
178C22×C16C2×D1311yescharacteristic
179#444—262no—
180#443—262no—
181#430—131no—
182#421—131no—
183#421—131no—
184#405—131no—
185#350—21no—
186#350—21no—
187#350—262no—
188#349—262no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—81no—
192C22×C13#40811yescharacteristic
193C22×C13C8×D411yescharacteristic
194C22×C13#43511yescharacteristic
195C2×D13—22no—
196C2×D13—42no—
197C4×C13—41no—
198C4×C13#38611yescharacteristic
199C4×C13C2×C22⋊C811yescharacteristic
200C4×C13C8×D411yescharacteristic
201C4×C13#43511yescharacteristic
202Dic13—22no—
203Dic13—81no—
204C2×#41—131no—
205C2×#41C4×D1311yescharacteristic
206#137—132no—
207#137—261no—
208AGL(1,ℤ/8)—132no—
209AGL(1,ℤ/8)—261no—
210#135—262no—
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—132no—
216#131—132no—
217#131—261no—
218#131—261no—
219C2×M16—21no—
220C2×M16—131no—
221C2×M16—131no—
222C2×M16—261no—
223C2×M16C4×D1311yescharacteristic
224C22×C8—21no—
225C22×C8—261no—
226C22×C8C22×D1311yescharacteristic
227#117—131no—
228M32—21no—
229M32—21no—
230M32—132no—
231M32—264no—
232M32—261no—
233M32—261no—
234M32—261no—
235C2×C16—21no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—264no—
239C2×C16—261no—
240C2×C16—261no—
241C2×C16C22⋊D1311yescharacteristic
242C2×C16C22⋊D1311yescharacteristic
243#108—262no—
244#104—262no—
245#104—262no—
246#97—261no—
247C4×C8—261no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13—81no—
252C2×C13#186911yescharacteristic
253D13—42no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—132no—
259#41—132no—
260#41—261no—
261#41—261no—
262C2×Q8—131no—
263C2×Q8C8×D1311yescharacteristic
264C2×D4—21no—
265C2×D4—131no—
266C2×D4—261no—
267C2×D4C8×D1311yescharacteristic
268C22×C4—21no—
269C22×C4—261no—
270C22×C4C2×C4×D1311yescharacteristic
271Q16—262no—
272SD16—262no—
273SD16—262no—
274D8—262no—
275M16—21no—
276M16—21no—
277M16—41no—
278M16—41no—
279M16—132no—
280M16—132no—
281M16—261no—
282M16—261no—
283M16—262no—
284M16—262no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8—262no—
291C2×C8—262no—
292C2×C8#612711yescharacteristic
293C2×C8D4×D1311yescharacteristic
294C2×C8D4×D1311yescharacteristic
295C2×C8D4×D1311yescharacteristic
296C2×C8#612911yescharacteristic
297C2×C8C2×C22⋊D1311yescharacteristic
298C4⋊C4—261no—
299C22⋊C4—261no—
300C42—261no—
301C16—21no—
302C16—21no—
303C16—41no—
304C16—262no—
305C16—521no—
306C13#1298711yescharacteristic, complemented, Sylow
307C23—21no—
308C23—261no—
309C23#8816111yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—132no—
313Q8—261no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—132no—
319D4—262no—
320D4—262no—
321D4—261no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—261no—
326C2×C4—262no—
327C2×C4—262no—
328C2×C4—521no—
329C2×C4C22⋊C4×D1311yescharacteristic
330C2×C4#8813511yescharacteristic
331C2×C4C2×C8×D1311yescharacteristic
332C2×C4#8815511yescharacteristic
333C2×C4M16×D1311yescharacteristic
334C2×C4C4×C22⋊D1311yescharacteristic
335C8—41no—
336C8—262no—
337C8—262no—
338C8#8813711yescharacteristic
339C8#8813811yescharacteristic
340C8#8819111yescharacteristic
341C8#8819211yescharacteristic
342C22—41no—
343C22—41no—
344C22—81no—
345C22—262no—
346C22—522no—
347C22#1171838611yescharacteristic
348C22#1171838811yescharacteristic
349C22#1171878811yescharacteristic
350C4—41no—
351C4—262no—
352C4—1041no—
353C4D13×C22⋊C811yescharacteristic
354C4#1171838911yescharacteristic
355C4#1171861711yescharacteristic
356C4C8×C22⋊D1311yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—522no—
362C2#1311512511yescharacteristic
subgroupG/H
centerC8#88192
commutatorC2×C4×C13C22×C8
FrattiniC22×C8C22×D13
FittingC2×C13×#350C2
socleC2×C13#1869
prime radical#11719527C4
cosocleC22×C8×C13C23
hypercenterC2×#350D13
hypocenterC13#12987
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
1. C2×#11718562C2semidirect
3. #13116465C2semidirect
4. #13116457C2semidirect
5. #13112924C2semidirect
6. #13112921C2semidirect
7. C2×C13×#350C2semidirect
129. C2×#350D13semidirect
306. C13#12987semidirect

Maximal subgroups

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

subgroupindex
C2×#117185622
#131237372
#131164652
#131164572
#131129242
#131129212
C2×C13×#3502
#1298713