Finite Group Databasebeta

← #16018057

Subgroups — #16018057

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125495C211yesmaximal, characteristic, complemented
2#13117038C211yesmaximal, characteristic, complemented
3#13117033C211yesmaximal, characteristic, complemented
4#13117000C211yesmaximal, characteristic, complemented
5#13116993C211yesmaximal, characteristic, complemented
6#13116886C211yesmaximal, characteristic, complemented
7#13116881C211yesmaximal, characteristic, complemented
8#13116776C211yesmaximal, characteristic
9#13116776C211yesmaximal, characteristic
10#13116705C211yesmaximal, characteristic, complemented
11#13116700C211yesmaximal, characteristic, complemented
12C4×#88069C211yesmaximal, characteristic, complemented
13C4×#88067C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#2951C211yesmaximal, characteristic
16C2×C13×#135C2211yescharacteristic
17C13×#520—21no—
18#11719223—21no—
19C13×#440—21no—
20C13×#440—21no—
21C4×C13×Q16C2211yescharacteristic
22C4×C13×Q16C2211yescharacteristic
23C4×C13×D8C2211yescharacteristic
24C4×C13×D8C2211yescharacteristic
25C2×C13×#107C2211yescharacteristic
26C13×#417—21no—
27C13×#405C2211yescharacteristic
28C2×#88069C2211yescharacteristic
29C2×#88069C2211yescharacteristic
30C2×#88067C2211yescharacteristic
31C2×#88067C2211yescharacteristic
32#11718798—21no—
33#11718777C2211yescharacteristic
34#11718777C2211yescharacteristic
35#11718377—21no—
36#11718364—21no—
37#11718360C2211yescharacteristic
38C4×Dic52C2211yescharacteristic
39C4×Dic52C2211yescharacteristic
40#11718344C2211yescharacteristic
41#11718156C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718154C2211yescharacteristic
44#11718154C2211yescharacteristic
45C22⋊#6090C2211yescharacteristic
46C22⋊#6090C2211yescharacteristic
47#11718084C2211yescharacteristic
48#11718084C2211yescharacteristic
49#11718084C2211yescharacteristic
50#11718084C2211yescharacteristic
51#11718082C2211yescharacteristic
52#11718082C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56C4⋊#6090C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×#41—21no—
60C13×#135—22no—
61C13×#135—22no—
62C2×C13×Q16C2311yescharacteristic
63C2×C13×SD16—21no—
64C2×C13×D8C2311yescharacteristic
65C2×C13×M16D411yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×Q8×C13—21no—
68C4×Q8×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13—41no—
72C4×D4×C13—41no—
73C13×#117—41no—
74C13×#117D411yescharacteristic
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—41no—
77#88178—21no—
78#88178—21no—
79C2×Dic52—21no—
80C2×Dic52C2311yescharacteristic
81C2×Dic52C2311yescharacteristic
82#88143—41no—
83#88143—41no—
84#88133—41no—
85#88133—41no—
86#88124—21no—
87#88123—21no—
88C4×Dic26—21no—
89C4×Dic26—21no—
90C13×#107—21no—
91C13×#107C2311yescharacteristic
92C13×#107C2311yescharacteristic
93C13×#103—21no—
94C13×#103—21no—
95C13×#102—21no—
96C13×#102—21no—
97C13×#97D411yescharacteristic
98C13×#97D411yescharacteristic
99C4×C8×C13C2311yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88069—22no—
102#88069—22no—
103#88067—22no—
104#88067—22no—
105#88058C2311yescharacteristic
106#88058C2311yescharacteristic
107#88057—21no—
108#88056—21no—
109#88056—21no—
110#88056—21no—
111#88056—21no—
112C2×#6090C2311yescharacteristic
113C2×#6090C2311yescharacteristic
114C2×#6090C2311yescharacteristic
115C2×#6090C2311yescharacteristic
116#33680—131nomaximal, Sylow
117C13×#41—24no—
118C13×#41—42no—
119C2×Q8×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13C2×D411yescharacteristic
127C2×Dic26—21no—
128C2×Dic26—21no—
129C13×Q16—21no—
130C13×Q16#4112yes—
131C13×SD16—24no—
132C13×D8—21no—
133C13×D8#4112yes—
134C13×M16—41no—
135C2×C8×C13—21no—
136C2×C8×C13—21no—
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2×D411yescharacteristic
140C2×C8×C13C2411yescharacteristic
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—41no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C4⋊C4D811yescharacteristic
147C13×C4⋊C4D811yescharacteristic
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4D811yescharacteristic
151C13×C22⋊C4D811yescharacteristic
152C42×C13—41no—
153C42×C13—41no—
154C42×C13C2×D411yescharacteristic
155C42×C13C2×D411yescharacteristic
156C22⋊Dic13—41no—
157C22⋊Dic13—41no—
158C4⋊Dic13—21no—
159C4⋊Dic13—21no—
160C4⋊Dic13—41no—
161C4⋊Dic13—41no—
162#6101—41no—
163#6101—41no—
164#6101—41no—
165#6101—41no—
166#6101—41no—
167#6101—41no—
168C4×Dic13—41no—
169C4×Dic13—41no—
170Dic52—21no—
171Dic52—21no—
172Dic52—21no—
173Dic52—21no—
174Dic52—42no—
175#6090—21no—
176#6090—21no—
177#6090—21no—
178#6090—21no—
179#3177—131no—
180#2951D1311yescharacteristic
181#2236—131no—
182#2235—131no—
183#2229—131no—
184#2228—131no—
185#2209—131no—
186#2208—131no—
187#2189—131no—
188#2189—131no—
189#2176—131no—
190#2175—131no—
191C4×Q32—131no—
192C4×SD32—131no—
193#2164—131no—
194C23×C13—41no—
195C23×C13C2×D811yescharacteristic
196Q8×C13—22no—
197Q8×C13—41no—
198D4×C13—22no—
199D4×C13—44no—
200D4×C13—41no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—44no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—161no—
208C2×C4×C13—161no—
209C2×C4×C13—161no—
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C2×D811yescharacteristic
215C2×C4×C13C22×D411yescharacteristic
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220Dic26—41no—
221Dic26—41no—
222Dic26—41no—
223Dic26—41no—
224C8×C13—21no—
225C8×C13—21no—
226C8×C13—21no—
227C8×C13C2×#4111yescharacteristic
228C8×C13C2×#4111yescharacteristic
229C2×#135C2×D1311yescharacteristic
230#541—261no—
231#520—21no—
232C2×Q32—131no—
233C2×Q32—131no—
234C2×SD32—131no—
235C2×SD32—131no—
236#499—131no—
237#494—131no—
238#491—261no—
239#470—261no—
240#467—131no—
241#467—131no—
242#441—261no—
243#440—21no—
244#440—21no—
245C4×Q16—131no—
246C4×Q16—131no—
247C4×Q16C2×D1311yescharacteristic
248C4×Q16C2×D1311yescharacteristic
249C4×D8C2×D1311yescharacteristic
250C4×D8C2×D1311yescharacteristic
251C2×#107C2×D1311yescharacteristic
252#417—21no—
253#405C2×D1311yescharacteristic
254#367—131no—
255#367—131no—
256#366—131no—
257#366—131no—
258C4⋊C16—131no—
259C4⋊C16—131no—
260#358—131no—
261#358—131no—
262#358—131no—
263#358—131no—
264#358—131no—
265#358—131no—
266#357—131no—
267#357—131no—
268C22⋊C16—131no—
269C22⋊C16—131no—
270#346—131no—
271C4×C16—131no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—21no—
275C22×C13—42no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13C22×D811yescharacteristic
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—42no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13#52511yescharacteristic
288C4×C13#57511yescharacteristic
289Dic13—81no—
290Dic13—81no—
291Dic13—81no—
292Dic13—81no—
293C2×#41—21no—
294#135—22no—
295#135—22no—
296C2×Q16—131no—
297C2×Q16—131no—
298C2×Q16—261no—
299C2×Q16C22×D1311yescharacteristic
300C2×SD16—21no—
301C2×D8C22×D1311yescharacteristic
302C2×M16C22⋊D1311yescharacteristic
303C22×C8C22×D1311yescharacteristic
304C4⋊Q8—261no—
305#126—521no—
306#126—521no—
307#125—261no—
308#125—521no—
309#125—521no—
310C22⋊Q8—261no—
311C22⋊Q8—261no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—261no—
315C4×Q8—261no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—41no—
319C4×D4—41no—
320#117—41no—
321#117C22⋊D1311yescharacteristic
322C2×C4⋊C4—21no—
323C2×C4⋊C4—41no—
324Q32—262no—
325Q32—262no—
326SD32—262no—
327SD32—262no—
328C2×C16—131no—
329C2×C16—131no—
330C2×C16—131no—
331C2×C16—131no—
332#107—21no—
333#107—131no—
334#107—131no—
335#107C22×D1311yescharacteristic
336#107C22×D1311yescharacteristic
337#106—261no—
338#103—21no—
339#103—21no—
340#103—261no—
341#103—261no—
342#103—261no—
343#103—261no—
344#102—21no—
345#102—21no—
346#97C22⋊D1311yescharacteristic
347#97C22⋊D1311yescharacteristic
348C4×C8C22×D1311yescharacteristic
349C4×C8C22×D1311yescharacteristic
350C2×C13—41no—
351C2×C13—82no—
352C2×C13#310011yescharacteristic
353C2×C13#341611yescharacteristic
354C2×C13#341711yescharacteristic
355#41—24no—
356#41—42no—
357C2×Q8—21no—
358C2×Q8—261no—
359C2×Q8—261no—
360C2×D4—21no—
361C2×D4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4C2×C22⋊D1311yescharacteristic
367Q16—21no—
368Q16—261no—
369Q16—261no—
370Q16—261no—
371Q16—261no—
372Q16—522no—
373Q16#612712yes—
374SD16—24no—
375D8—21no—
376D8#612712yes—
377M16—41no—
378C2×C8—21no—
379C2×C8—21no—
380C2×C8C2×C22⋊D1311yescharacteristic
381C2×C8C2×C22⋊D1311yescharacteristic
382C2×C8C2×C22⋊D1311yescharacteristic
383C2×C8C23×D1311yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—261no—
390C4⋊C4—261no—
391C4⋊C4—521no—
392C4⋊C4—521no—
393C4⋊C4—521no—
394C4⋊C4—521no—
395C4⋊C4—521no—
396C4⋊C4—521no—
397C4⋊C4—521no—
398C4⋊C4—521no—
399C4⋊C4#610411yescharacteristic
400C4⋊C4#610411yescharacteristic
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—521no—
404C22⋊C4—521no—
405C22⋊C4#610411yescharacteristic
406C22⋊C4#610411yescharacteristic
407C42—41no—
408C42—41no—
409C42—521no—
410C42—521no—
411C42C2×C22⋊D1311yescharacteristic
412C42C2×C22⋊D1311yescharacteristic
413C16—261no—
414C16—261no—
415C16—261no—
416C16—261no—
417C13#3368011yescharacteristic, complemented, Sylow
418C23—41no—
419C23C2×#610411yescharacteristic
420Q8—22no—
421Q8—41no—
422Q8—521no—
423Q8—521no—
424Q8—521no—
425Q8—521no—
426D4—22no—
427D4—44no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—161no—
436C2×C4—161no—
437C2×C4—161no—
438C2×C4—521no—
439C2×C4—521no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4C2×#610411yescharacteristic
443C2×C4C2×#610411yescharacteristic
444C2×C4C2×#610411yescharacteristic
445C2×C4C2×#610411yescharacteristic
446C2×C4C2×#610411yescharacteristic
447C2×C4C22×C22⋊D1311yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#612711yescharacteristic
452C8C2×#612711yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22C22×#610411yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—1041no—
469C4—1041no—
470C4—1041no—
471C4—1041no—
472C4#1171949611yescharacteristic
473C4#1171952711yescharacteristic
474C2—41no—
475C2—82no—
476C2#1312483611yescharacteristic
477C2#1312798311yescharacteristic
478C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2951C2
socleC22×C13C22×D8
prime radicalC2×C13×#135C22
hypercenter#2951D13
hypocenterC13#33680
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #13125495C2semidirect
2. #13117038C2semidirect
3. #13117033C2semidirect
4. #13117000C2semidirect
5. #13116993C2semidirect
6. #13116886C2semidirect
7. #13116881C2semidirect
10. #13116705C2semidirect
11. #13116700C2semidirect
12. C4×#88069C2semidirect
13. C4×#88067C2semidirect
14. #13116643C2semidirect
417. C13#33680semidirect

Maximal subgroups

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

subgroupindex
#131254952
#131170382
#131170332
#131170002
#131169932
#131168862
#131168812
#131167762
#131167052
#131167002
C4×#880692
C4×#880672
#131166432
C13×#29512
#3368013