Finite Group Databasebeta

← #15780083

Subgroups — #15780083

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#135×Dic13C211yesmaximal, characteristic, complemented
2#13116572C211yesmaximal, characteristic, complemented
3#13116564C211yesmaximal, characteristic, complemented
4#13115725C211yesmaximal, characteristic, complemented
5#13112951C211yesmaximal, characteristic, complemented
6#13112917C211yesmaximal, characteristic, complemented
7C13×#3414C211yesmaximal, characteristic
8C2×C13×#135C2211yescharacteristic
9C2×C13×#135C2211yescharacteristic
10#41×Dic13—21no—
11C13×#510—21no—
12C13×#510C412yescomplemented
13C13×#509—21no—
14C13×#509C412yescomplemented
15C13×#508—22no—
16C2×C13×M32C2211yescharacteristic
17C2×#88077—21no—
18#11718895—21no—
19#11718894—21no—
20Q16×Dic13—21no—
21SD16×Dic13—22no—
22D8×Dic13—21no—
23C2×#88059C2211yescharacteristic
24#11718767C2211yescharacteristic
25C2×C8×Dic13C2211yescharacteristic
26C2×#88052C2211yescharacteristic
27#11718159—22no—
28#11718158—22no—
29C2×C13×#41—21no—
30C2×C13×#41—21no—
31C13×#135—21no—
32C13×#135—21no—
33C13×#135—21no—
34C13×#135—21no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135C2×C412yes—
38C13×#135D412yes—
39C2×C13×Q16C2×C411yescharacteristic, complemented
40C2×C13×Q16D411yescharacteristic
41C2×C13×SD16—21no—
42C2×C13×SD16—21no—
43C2×C13×D8C2×C411yescharacteristic, complemented
44C2×C13×D8D411yescharacteristic
45C22×C8×C13C2311yescharacteristic
46Q8×Dic13—22no—
47D4×Dic13—22no—
48D4×Dic13—42no—
49#88180—21no—
50#88180—41no—
51C2×C4×Dic13—41no—
52C2×C4×Dic13D411yescharacteristic
53C2×#6099—21no—
54C22×#1055D411yescharacteristic
55C13×Q32—22no—
56C13×SD32—22no—
57C13×SD32—22no—
58C13×D16—22no—
59C13×M32—21no—
60C13×M32C2×C412yescomplemented
61C2×C13×C16—21no—
62#88077—41no—
63#88077—41no—
64#88075—22no—
65#88072—22no—
66C22⋊#1055—42no—
67#88059—21no—
68#88059—21no—
69#88058—21no—
70#88057D412yes—
71C8×Dic13—21no—
72C8×Dic13—21no—
73#88052—21no—
74#88052—21no—
75C2×#6090—21no—
76#13027—131nomaximal, Sylow
77C13×#41—22no—
78C13×#41—22no—
79C13×#41—41no—
80C13×#41—41no—
81C13×#41—41no—
82C13×#41—41no—
83C13×#41—41no—
84C13×#41—41no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13—41no—
93C22×C4×C13C2×D411yescharacteristic
94C22×Dic13—21no—
95C22×Dic13—42no—
96C13×Q16—21no—
97C13×Q16—21no—
98C13×Q16—21no—
99C13×Q16C22⋊C412yes—
100C13×SD16—22no—
101C13×SD16—22no—
102C13×SD16—41no—
103C13×SD16—41no—
104C13×D8—21no—
105C13×D8—21no—
106C13×D8—21no—
107C13×D8C22⋊C412yes—
108C2×C8×C13C22×C411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13#4111yescharacteristic
113C2×C8×C13#4111yescharacteristic
114C22⋊Dic13—42no—
115C22⋊Dic13—41no—
116C4⋊Dic13—22no—
117C4⋊Dic13—42no—
118C4×Dic13—21no—
119C4×Dic13—42no—
120C4×Dic13—41no—
121C4×Dic13D811yescharacteristic
122C4×Dic13D811yescharacteristic
123#6099—41no—
124#6099—41no—
125C2×#1055—21no—
126C2×#1055—21no—
127C2×#1055—21no—
128C2×#1055—41no—
129C13×C16—22no—
130#6090—41no—
131#3414D1311yescharacteristic
132C4×#135—131no—
133#2145—131no—
134#2143—131no—
135#1974—131no—
136#1389—131no—
137#1376—131no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13AGL(1,ℤ/8)11yescharacteristic
141Q8×C13—22no—
142Q8×C13—41no—
143Q8×C13—41no—
144Q8×C13—41no—
145D4×C13—22no—
146D4×C13—42no—
147D4×C13—42no—
148D4×C13—41no—
149D4×C13—41no—
150D4×C13—41no—
151D4×C13—81no—
152D4×C13—81no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13C4×D411yescharacteristic
160C2×C4×C13#12011yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13C2×D811yescharacteristic
163C2×C4×C13#13511yescharacteristic
164C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—42no—
168C2×Dic13—42no—
169C2×Dic13—84no—
170C8×C13C2×C22⋊C411yescharacteristic
171C8×C13C4×D411yescharacteristic
172C8×C13#12111yescharacteristic
173C8×C13#12311yescharacteristic
174#1055—41no—
175#1055—81no—
176C2×#135C2×D1311yescharacteristic
177C2×#135C2×D1311yescharacteristic
178C4×#41—261no—
179#510—21no—
180#510Dic1312yescomplemented
181#509—21no—
182#509Dic1312yescomplemented
183#508—22no—
184C2×M32—131no—
185C2×M32C2×D1311yescharacteristic
186C4×Q16—261no—
187C4×SD16—262no—
188C4×D8—261no—
189C2×#108—131no—
190#427—131no—
191C2×#104—261no—
192#416—261no—
193#408—261no—
194C2×C4×C8—131no—
195#360—262no—
196#359—262no—
197C22×C13—41no—
198C22×C13—42no—
199C22×C13—82no—
200C22×C13—82no—
201C22×C13—81no—
202C22×C13#44211yescharacteristic
203C22×C13#44711yescharacteristic
204C22×C13#46311yescharacteristic
205C4×C13—42no—
206C4×C13—81no—
207C4×C13#38611yescharacteristic
208C4×C13C4×D811yescharacteristic
209C4×C13#44911yescharacteristic
210C4×C13#45911yescharacteristic
211Dic13—22no—
212Dic13—41no—
213Dic13—82no—
214C2×#41—21no—
215C2×#41—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135—21no—
220#135—21no—
221#135—21no—
222#135C2×Dic1312yes—
223#135C22⋊D1312yes—
224C2×Q16C2×Dic1311yescharacteristic, complemented
225C2×Q16C22⋊D1311yescharacteristic
226C2×SD16—21no—
227C2×SD16—21no—
228C2×D8C2×Dic1311yescharacteristic, complemented
229C2×D8C22⋊D1311yescharacteristic
230C2×M16—261no—
231C22×C8—131no—
232C22×C8C22×D1311yescharacteristic
233C4×Q8—262no—
234C4×D4—262no—
235C4×D4—522no—
236#117—261no—
237#117—521no—
238C2×C42—131no—
239C2×C42—521no—
240Q32—22no—
241SD32—22no—
242SD32—22no—
243D16—22no—
244M32—21no—
245M32—261no—
246M32—261no—
247M32C2×Dic1312yescomplemented
248C2×C16—21no—
249C2×C16—261no—
250#108—261no—
251#108—261no—
252#107—261no—
253#106—132no—
254#104—521no—
255#104—521no—
256#103—262no—
257#102—262no—
258C22⋊C8—522no—
259C4×C8—261no—
260C4×C8—261no—
261C2×C13—21no—
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—82no—
265C2×C13—161no—
266C2×C13#187911yescharacteristic
267#41—22no—
268#41—22no—
269#41—41no—
270#41—41no—
271#41—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—261no—
284C22×C4—522no—
285C22×C4D4×D1311yescharacteristic
286Q16—21no—
287Q16—21no—
288Q16—21no—
289Q16C22⋊Dic1312yes—
290SD16—22no—
291SD16—22no—
292SD16—41no—
293SD16—41no—
294D8—21no—
295D8—21no—
296D8—21no—
297D8C22⋊Dic1312yes—
298M16—521no—
299M16—521no—
300C2×C8—261no—
301C2×C8—261no—
302C2×C8—261no—
303C2×C8—521no—
304C2×C8D4×D1311yescharacteristic
305C2×C8#612911yescharacteristic
306C2×C8#612911yescharacteristic
307C2×C8C22×Dic1311yescharacteristic
308C2×C8C2×C22⋊D1311yescharacteristic
309C2×C8C2×C22⋊D1311yescharacteristic
310C4⋊C4—262no—
311C4⋊C4—522no—
312C22⋊C4—522no—
313C22⋊C4—521no—
314C42—131no—
315C42—131no—
316C42—261no—
317C42—522no—
318C42—521no—
319C16—22no—
320C16—521no—
321C13#1302711yescharacteristic, complemented, Sylow
322C23—41no—
323C23—41no—
324C23#8816511yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—81no—
336D4—81no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—1044no—
348C2×C4D8×D1311yescharacteristic
349C2×C4#8816511yescharacteristic
350C2×C4#8816611yescharacteristic
351C2×C4D4×Dic1311yescharacteristic
352C2×C4#8819111yescharacteristic
353C2×C4#8819311yescharacteristic
354C8—521no—
355C8—1041no—
356C8D4×Dic1311yescharacteristic
357C8#8818911yescharacteristic
358C8#8819311yescharacteristic
359C8C2×C22⋊Dic1311yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—81no—
365C22#1171881311yescharacteristic
366C22#1171881411yescharacteristic
367C22#1171881711yescharacteristic
368C4—42no—
369C4—81no—
370C4—262no—
371C4—521no—
372C4—1042no—
373C4D8×Dic1311yescharacteristic
374C4#1171881111yescharacteristic
375C4#1171881911yescharacteristic
376C4#1171888111yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—161no—
382C2#1311518611yescharacteristic
subgroupG/H
centerC4#11718811
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3414C2
socleC2×C13#1879
cosocleC22×C8×C13C23
hypercenter#3414D13
hypocenterC13#13027
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #135×Dic13C2semidirect
2. #13116572C2semidirect
3. #13116564C2semidirect
4. #13115725C2semidirect
5. #13112951C2semidirect
6. #13112917C2semidirect
12. C13×#510C4semidirect
14. C13×#509C4semidirect
39. C2×C13×Q16C2×C4semidirect
43. C2×C13×D8C2×C4semidirect
60. C13×M32C2×C4semidirect
180. #510Dic13semidirect
182. #509Dic13semidirect
224. C2×Q16C2×Dic13semidirect
228. C2×D8C2×Dic13semidirect
247. M32C2×Dic13semidirect
321. C13#13027semidirect

Maximal subgroups

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

subgroupindex
#135×Dic132
#131165722
#131165642
#131157252
#131129512
#131129172
C13×#34142
#1302713