Finite Group Databasebeta

← #15780081

Subgroups — #15780081

Order 3328.

484 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#13127970C211yesmaximal, characteristic
2#13116571C211yesmaximal, characteristic, complemented
3#13116564C211yesmaximal, characteristic, complemented
4#13115724C211yesmaximal, characteristic, complemented
5#13112952C211yesmaximal, characteristic, complemented
6#13112918C211yesmaximal, characteristic, complemented
7C4×C13×#135C211yesmaximal, characteristic, complemented
8C2×C13×#135C2211yescharacteristic
9C4×C13×#41—21no—
10C2×#88158C2211yescharacteristic
11C4×C13×Q16—21no—
12C4×C13×SD16—22no—
13C4×C13×D8—21no—
14C13×#427C2211yescharacteristic
15C13×#416—21no—
16C2×C4×C8×C13C2211yescharacteristic
17#11718856C412yescomplemented
18#11718855—22no—
19#11718854C412yescomplemented
20#11718840—21no—
21#11718808—21no—
22#11718771—21no—
23C2×#88059C2211yescharacteristic
24C2×#88052C2211yescharacteristic
25C2×#88052C2211yescharacteristic
26C2×#88045—21no—
27#11718159—22no—
28#11718080—22no—
29C2×C13×#41—21no—
30C2×#6127—21no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135C2×C412yes—
34C13×#135D412yes—
35C2×C13×Q16D411yescharacteristic
36C2×C13×SD16—21no—
37C2×C13×D8D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C22×C8×C13C2311yescharacteristic
40C4×Q8×C13—22no—
41C4×D4×C13—22no—
42C4×D4×C13—42no—
43C13×#117—21no—
44C13×#117—41no—
45C2×C42×C13—41no—
46C2×C42×C13D411yescharacteristic
47C2×#6099—21no—
48C2×Dic52C2×C411yescharacteristic, complemented
49#88158—21no—
50#88158—21no—
51#88158—21no—
52#88158—21no—
53C2×D104C2×C411yescharacteristic, complemented
54C2×#6095—21no—
55C13×#107—21no—
56C13×#106D412yes—
57C13×#103—22no—
58C13×#102—22no—
59C4×C8×C13—21no—
60C4×C8×C13—21no—
61#88069—22no—
62#88068—22no—
63#88067—22no—
64#88066—22no—
65#88060—42no—
66#88059—21no—
67#88059—21no—
68#88052—21no—
69#88052—21no—
70#88052—21no—
71#88052C2×C412yescomplemented
72C2×#6090—21no—
73C2×#6090—21no—
74#88045—41no—
75#88045—41no—
76#13027—131nomaximal, Sylow
77C13×#41—22no—
78C13×#41—22no—
79C13×#41—41no—
80C13×#41—41no—
81C2×Q8×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—42no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C2×C22⋊D13—41no—
89#6127—41no—
90#6127—41no—
91#6127—41no—
92#6127—41no—
93C2×D52—21no—
94C2×C4×D13—41no—
95C2×Dic26—21no—
96C13×Q16—21no—
97C13×Q16C22⋊C412yes—
98C13×SD16—22no—
99C13×SD16—22no—
100C13×D8—21no—
101C13×D8C22⋊C412yes—
102C2×C8×C13—21no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13C22×C411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13#4111yescharacteristic
110C2×C8×C13#4111yescharacteristic
111C13×C4⋊C4—22no—
112C13×C4⋊C4—42no—
113C13×C22⋊C4—42no—
114C13×C22⋊C4—41no—
115C42×C13—21no—
116C42×C13—42no—
117C42×C13—41no—
118C42×C13D811yescharacteristic
119C42×C13D811yescharacteristic
120#6099—41no—
121#6099—41no—
122C2×#1055—41no—
123Dic52—21no—
124Dic52—21no—
125D104—21no—
126D104—21no—
127#6095—41no—
128#6095—41no—
129#6090—22no—
130#6090—41no—
131#3414—131no—
132C4×#135D1311yescharacteristic, complemented
133#2145—131no—
134#2143—131no—
135#1974—131no—
136#1389—131no—
137#1376—131no—
138C23×C13—41no—
139C23×C13AGL(1,ℤ/8)11yescharacteristic
140C22×D13—41no—
141Q8×C13—22no—
142Q8×C13—41no—
143D4×C13—22no—
144D4×C13—42no—
145D4×C13—42no—
146D4×C13—41no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—42no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—84no—
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13C2×D811yescharacteristic
159C2×C4×C13#13511yescharacteristic
160C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
161C22⋊D13—81no—
162C22⋊D13—81no—
163C2×Dic13—41no—
164D52—41no—
165D52—41no—
166C4×D13—81no—
167C4×D13—81no—
168Dic26—41no—
169Dic26—41no—
170C8×C13—41no—
171C8×C13C2×C22⋊C411yescharacteristic
172C8×C13C4×D411yescharacteristic
173C8×C13#12111yescharacteristic
174C8×C13#12311yescharacteristic
175#1055—81no—
176C2×#135—131no—
177C2×#135C2×D1311yescharacteristic
178C4×#41—21no—
179#510—132no—
180#510—261no—
181#509—132no—
182#509—261no—
183#508—262no—
184C2×M32—131no—
185C2×M32—131no—
186C4×Q16—21no—
187C4×SD16—22no—
188C4×D8—21no—
189C2×#108—131no—
190#427C2×D1311yescharacteristic
191C2×#104—261no—
192#416—21no—
193#408—261no—
194C2×C4×C8C2×D1311yescharacteristic
195#360—262no—
196#359—262no—
197C22×C13—41no—
198C22×C13—42no—
199C22×C13—82no—
200C22×C13#44211yescharacteristic
201C22×C13#44711yescharacteristic
202C22×C13#46311yescharacteristic
203C2×D13—82no—
204C2×D13—81no—
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—42no—
208C4×C13—82no—
209C4×C13#38611yescharacteristic
210C4×C13C4×D811yescharacteristic
211C4×C13#44911yescharacteristic
212C4×C13#45911yescharacteristic
213Dic13—81no—
214C2×#41—21no—
215C2×#41—261no—
216#135—21no—
217#135—21no—
218#135—261no—
219#135—261no—
220#135—261no—
221#135—261no—
222#135C4×D1312yes—
223#135D5212yes—
224C2×Q16—131no—
225C2×Q16C22⋊D1311yescharacteristic
226C2×SD16—21no—
227C2×SD16—261no—
228C2×D8—131no—
229C2×D8C22⋊D1311yescharacteristic
230C2×M16—261no—
231C22×C8C22⋊D1311yescharacteristic
232C22×C8C22×D1311yescharacteristic
233C4×Q8—22no—
234C4×D4—22no—
235C4×D4—42no—
236#117—21no—
237#117—41no—
238C2×C42—41no—
239C2×C42C22⋊D1311yescharacteristic
240Q32—262no—
241SD32—262no—
242SD32—262no—
243D16—262no—
244M32—132no—
245M32—261no—
246M32—261no—
247M32—261no—
248C2×C16—261no—
249C2×C16—261no—
250#108—261no—
251#108—261no—
252#107—21no—
253#106C22⋊D1312yes—
254#104—521no—
255#104—521no—
256#103—22no—
257#102—22no—
258C22⋊C8—522no—
259C4×C8—21no—
260C4×C8—21no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—82no—
265C2×C13#187911yescharacteristic
266D13—161no—
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271#41—521no—
272#41—521no—
273#41—521no—
274#41—521no—
275C2×Q8—21no—
276C2×Q8—261no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—261no—
280C2×D4—521no—
281C22×C4—21no—
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—521no—
285C22×C4C2×C22⋊D1311yescharacteristic
286Q16—21no—
287Q16—261no—
288Q16—261no—
289Q16#610312yes—
290SD16—22no—
291SD16—22no—
292SD16—521no—
293SD16—521no—
294D8—21no—
295D8—261no—
296D8—261no—
297D8#610312yes—
298M16—521no—
299M16—521no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—521no—
304C2×C8C2×C4×D1311yescharacteristic
305C2×C8C2×D5211yescharacteristic
306C2×C8#612711yescharacteristic
307C2×C8#612711yescharacteristic
308C2×C8C2×C22⋊D1311yescharacteristic
309C2×C8C2×C22⋊D1311yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C42—21no—
315C42—42no—
316C42—41no—
317C42#610411yescharacteristic
318C42#610411yescharacteristic
319C16—262no—
320C16—521no—
321C13#1302711yescharacteristic, complemented, Sylow
322C23—41no—
323C23—521no—
324C23#8818611yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—521no—
328Q8—521no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—521no—
334D4—521no—
335D4—1041no—
336D4—1041no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—84no—
345C2×C4—521no—
346C2×C4—1041no—
347C2×C4—1041no—
348C2×C4C4×C22⋊D1311yescharacteristic
349C2×C4#8818411yescharacteristic
350C2×C4C2×#610411yescharacteristic
351C2×C4#8820311yescharacteristic
352C2×C4#8820411yescharacteristic
353C2×C4#8820711yescharacteristic
354C8—41no—
355C8—1041no—
356C8C2×#610311yescharacteristic
357C8C4×C22⋊D1311yescharacteristic
358C8#8818311yescharacteristic
359C8#8818411yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—1042no—
364C22—1041no—
365C22#1171867511yescharacteristic
366C22#1171867711yescharacteristic
367C22#1171887811yescharacteristic
368C4—22no—
369C4—41no—
370C4—42no—
371C4—82no—
372C4—1041no—
373C4C4×#610411yescharacteristic
374C4#1171867611yescharacteristic
375C4#1171887411yescharacteristic
376C4#1171889911yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—2081no—
382C2#1311518411yescharacteristic
subgroupG/H
centerC4#11718676
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC4×C13×#135C2
socleC2×C13#1879
prime radical#13127970C2
cosocleC22×C8×C13C23
hypercenterC4×#135D13
hypocenterC13#13027
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. #13116571C2semidirect
3. #13116564C2semidirect
4. #13115724C2semidirect
5. #13112952C2semidirect
6. #13112918C2semidirect
7. C4×C13×#135C2semidirect
17. #11718856C4semidirect
19. #11718854C4semidirect
48. C2×Dic52C2×C4semidirect
53. C2×D104C2×C4semidirect
71. #88052C2×C4semidirect
132. C4×#135D13semidirect
321. C13#13027semidirect

Maximal subgroups

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

subgroupindex
#131279702
#131165712
#131165642
#131157242
#131129522
#131129182
C4×C13×#1352
#1302713