Finite Group Databasebeta

← #16018072

Subgroups — #16018072

Order 3328.

532 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#13125475C211yesmaximal, characteristic
2#13117044C211yesmaximal, characteristic, complemented
3#13117027C211yesmaximal, characteristic
4#13116988C211yesmaximal, characteristic, complemented
5#13116978C211yesmaximal, characteristic, complemented
6#13116898C211yesmaximal, characteristic, complemented
7#13116898C211yesmaximal, characteristic, complemented
8#13116770C211yesmaximal, characteristic, complemented
9#13116753C211yesmaximal, characteristic
10#13116705C211yesmaximal, characteristic, complemented
11#13116698C211yesmaximal, characteristic, complemented
12C4×#88069C211yesmaximal, characteristic, complemented
13C4×#88068C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#2950C211yesmaximal, characteristic, complemented
16C22×C13×Q16C2211yescharacteristic
17C13×#519—21no—
18#11719239—21no—
19C13×#441—21no—
20C13×#441—21no—
21C4×C13×Q16C2211yescharacteristic
22C4×C13×Q16C2211yescharacteristic
23C4×C13×Q16C2211yescharacteristic
24C4×C13×Q16C2211yescharacteristic
25C13×#427C2211yescharacteristic
26C13×#419—21no—
27C13×#405C2211yescharacteristic
28C2×#88069C2211yescharacteristic
29C2×#88069C2211yescharacteristic
30C2×#88068C2211yescharacteristic
31C2×#88068C2211yescharacteristic
32#11718795—21no—
33#11718777C2211yescharacteristic
34#11718776C2211yescharacteristic
35#11718375—21no—
36#11718371—21no—
37C4×Dic52C2211yescharacteristic
38#11718357C2211yescharacteristic
39C4×D104C2211yescharacteristic
40#11718343C2211yescharacteristic
41#11718156C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718156C2211yescharacteristic
44#11718156C2211yescharacteristic
45C22⋊#6090C2211yescharacteristic
46C22⋊#6090C2211yescharacteristic
47#11718084C2211yescharacteristic
48#11718084C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718083C2211yescharacteristic
51#11718082C2211yescharacteristic
52#11718082C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56C4⋊#6090C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C22×Q8×C13—21no—
60C2×C13×Q16—22no—
61C2×C13×Q16—22no—
62C2×C13×Q16—21no—
63C2×C13×Q16C2311yescharacteristic
64C2×C13×Q16C2311yescharacteristic
65C2×C13×M16D411yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×Q8×C13—21no—
68C4×Q8×C13—21no—
69C4×Q8×C13—21no—
70C4×Q8×C13—21no—
71C4×Q8×C13—41no—
72C4×Q8×C13—41no—
73C13×#117—21no—
74C13×#117—41no—
75C13×#117—41no—
76C13×#117D411yescharacteristic
77#88184—21no—
78#88178—21no—
79C2×Dic52C2311yescharacteristic
80C2×D104C2311yescharacteristic
81C2×#6095—21no—
82#88152—41no—
83#88150—41no—
84#88139—41no—
85#88137—41no—
86#88129—21no—
87C4×D52—21no—
88#88123—21no—
89C4×Dic26—21no—
90C13×#107C2311yescharacteristic
91C13×#107C2311yescharacteristic
92C13×#106—21no—
93C13×#103—21no—
94C13×#103—21no—
95C13×#103—21no—
96C13×#103—21no—
97C13×#97D411yescharacteristic
98C13×#97D411yescharacteristic
99C4×C8×C13C2311yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88069—22no—
102#88069—22no—
103#88068—22no—
104#88068—22no—
105#88061—21no—
106#88061—21no—
107#88058—21no—
108#88058C2311yescharacteristic
109#88058C2311yescharacteristic
110#88056—21no—
111#88056—21no—
112C2×#6090C2311yescharacteristic
113C2×#6090C2311yescharacteristic
114C2×#6090C2311yescharacteristic
115C2×#6090C2311yescharacteristic
116#33681—131nomaximal, Sylow
117C2×Q8×C13—24no—
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×Q8×C13—42no—
121C2×Q8×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13C2×D411yescharacteristic
124C2×C22⋊D13—41no—
125C2×D52—21no—
126C2×C4×D13—41no—
127C2×Dic26—21no—
128C2×Dic26—41no—
129C13×Q16—24no—
130C13×Q16—21no—
131C13×Q16—21no—
132C13×Q16#4112yes—
133C13×Q16#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⋊C4—41no—
147C13×C4⋊C4D811yescharacteristic
148C13×C4⋊C4D811yescharacteristic
149C13×C22⋊C4—41no—
150C13×C22⋊C4D811yescharacteristic
151C13×C22⋊C4D811yescharacteristic
152C42×C13—41no—
153C42×C13—41no—
154C42×C13—41no—
155C42×C13—41no—
156C42×C13—41no—
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C22⋊Dic13—41no—
160#6103—41no—
161#6103—41no—
162#6103—41no—
163#6103—41no—
164C4⋊Dic13—21no—
165C4⋊Dic13—21no—
166C4⋊Dic13—41no—
167#6101—41no—
168#6101—41no—
169C4×Dic13—41no—
170Dic52—21no—
171Dic52—21no—
172D104—21no—
173D104—21no—
174#6095—42no—
175#6090—21no—
176#6090—21no—
177#6090—21no—
178#6090—21no—
179#3175—131no—
180#2950D1311yescharacteristic, complemented
181#2237—131no—
182#2234—131no—
183#2227—131no—
184#2225—131no—
185#2211—131no—
186#2211—131no—
187#2188—131no—
188#2185—131no—
189#2176—131no—
190#2175—131no—
191C4×Q32—131no—
192C4×SD32—131no—
193#2164—131no—
194C23×C13C2×D811yescharacteristic
195C22×D13—41no—
196Q8×C13—22no—
197Q8×C13—22no—
198Q8×C13—44no—
199Q8×C13—41no—
200Q8×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—41no—
208C2×C4×C13C2×D811yescharacteristic
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C22×D411yescharacteristic
214C22⋊D13—161no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218D52—41no—
219D52—41no—
220C4×D13—161no—
221Dic26—41no—
222Dic26—41no—
223Dic26—161no—
224C8×C13—21no—
225C8×C13—21no—
226C8×C13—21no—
227C8×C13C2×#4111yescharacteristic
228C8×C13C2×#4111yescharacteristic
229C22×Q16C2×D1311yescharacteristic
230#542—261no—
231#519—21no—
232C2×Q32—131no—
233C2×Q32—131no—
234C2×SD32—131no—
235C2×SD32—131no—
236#500—131no—
237#495—131no—
238#489—261no—
239#468—261no—
240#467—131no—
241#466—131no—
242#441—21no—
243#441—21no—
244#440—261no—
245C4×Q16—131no—
246C4×Q16C2×D1311yescharacteristic
247C4×Q16C2×D1311yescharacteristic
248C4×Q16C2×D1311yescharacteristic
249C4×Q16C2×D1311yescharacteristic
250C4×D8—131no—
251#427C2×D1311yescharacteristic
252#419—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×C13C22×D811yescharacteristic
276C2×D13—81no—
277C2×D13—81no—
278C2×D13—81no—
279C4×C13—21no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—42no—
285C4×C13—42no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13#52511yescharacteristic
289C4×C13#57511yescharacteristic
290Dic13—81no—
291Dic13—81no—
292Dic13—81no—
293C22×Q8—21no—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×Q16—21no—
297C2×Q16—131no—
298C2×Q16C22×D1311yescharacteristic
299C2×Q16C22×D1311yescharacteristic
300C2×SD16—261no—
301C2×D8—131no—
302C2×M16C22⋊D1311yescharacteristic
303C22×C8C22×D1311yescharacteristic
304C4⋊Q8—261no—
305#126—521no—
306#124—261no—
307#124—521no—
308#123—521no—
309C22⋊Q8—261no—
310C22⋊Q8—521no—
311#121—261no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—41no—
317C4×Q8—41no—
318C4×Q8—261no—
319C4×D4—261no—
320#117—21no—
321#117—41no—
322#117—41no—
323#117C22⋊D1311yescharacteristic
324Q32—262no—
325Q32—262no—
326SD32—262no—
327SD32—262no—
328C2×C16—131no—
329C2×C16—131no—
330C2×C16—131no—
331C2×C16—131no—
332#107—131no—
333#107—131no—
334#107—261no—
335#107C22×D1311yescharacteristic
336#107C22×D1311yescharacteristic
337#106—21no—
338#103—21no—
339#103—21no—
340#103—21no—
341#103—21no—
342#103—261no—
343#103—261no—
344#102—261no—
345#102—261no—
346#97C22⋊D1311yescharacteristic
347#97C22⋊D1311yescharacteristic
348C4×C8C22×D1311yescharacteristic
349C4×C8C22×D1311yescharacteristic
350C2×C13—41no—
351C2×C13#310011yescharacteristic
352C2×C13#341611yescharacteristic
353C2×C13#341711yescharacteristic
354D13—161no—
355C2×Q8—24no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—42no—
359C2×Q8—41no—
360C2×Q8—261no—
361C2×Q8—521no—
362C2×D4—261no—
363C2×D4—521no—
364C22×C4—41no—
365C22×C4—521no—
366C22×C4C2×C22⋊D1311yescharacteristic
367Q16—24no—
368Q16—21no—
369Q16—21no—
370Q16—261no—
371Q16—261no—
372Q16#612712yes—
373Q16#612712yes—
374SD16—522no—
375D8—261no—
376D8—261no—
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—41no—
390C4⋊C4—261no—
391C4⋊C4—261no—
392C4⋊C4—521no—
393C4⋊C4—521no—
394C4⋊C4—521no—
395C4⋊C4#610411yescharacteristic
396C4⋊C4#610411yescharacteristic
397C22⋊C4—41no—
398C22⋊C4—521no—
399C22⋊C4—521no—
400C22⋊C4—521no—
401C22⋊C4—521no—
402C22⋊C4—521no—
403C22⋊C4#610411yescharacteristic
404C22⋊C4#610411yescharacteristic
405C42—41no—
406C42—41no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—521no—
411C42C2×C22⋊D1311yescharacteristic
412C42C2×C22⋊D1311yescharacteristic
413C16—261no—
414C16—261no—
415C16—261no—
416C16—261no—
417C13#3368111yescharacteristic, complemented, Sylow
418C23—521no—
419C23C2×#610411yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—521no—
426Q8—521no—
427Q8—2081no—
428D4—521no—
429D4—521no—
430D4—2081no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—521no—
439C2×C4—521no—
440C2×C4—521no—
441C2×C4—2081no—
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—1041no—
457C22—1041no—
458C22—1041no—
459C22C22×#610411yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—1041no—
470C4—1041no—
471C4—1041no—
472C4#1171949611yescharacteristic
473C4#1171952711yescharacteristic
474C2—41no—
475C2—2081no—
476C2#1312483611yescharacteristic
477C2#1312798011yescharacteristic
478C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2950C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenter#2950D13
hypocenterC13#33681
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2950

Complements

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

NH ≅ G/Ntype
2. #13117044C2semidirect
4. #13116988C2semidirect
5. #13116978C2semidirect
6. #13116898C2semidirect
7. #13116898C2semidirect
8. #13116770C2semidirect
10. #13116705C2semidirect
11. #13116698C2semidirect
12. C4×#88069C2semidirect
13. C4×#88068C2semidirect
14. #13116643C2semidirect
15. C13×#2950C2semidirect
180. #2950D13semidirect
417. C13#33681semidirect

Maximal subgroups

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

subgroupindex
#131254752
#131170442
#131170272
#131169882
#131169782
#131168982
#131167702
#131167532
#131167052
#131166982
C4×#880692
C4×#880682
#131166432
C13×#29502
#3368113