Finite Group Databasebeta

← #16020691

Subgroups — #16020691

Order 3328.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127728C211yesmaximal, characteristic, complemented
2#13117077C211yesmaximal, characteristic
3#13117072C211yesmaximal, characteristic, complemented
4#13117067C211yesmaximal, characteristic, complemented
5#13117000C211yesmaximal, characteristic, complemented
6#13116993C211yesmaximal, characteristic, complemented
7#13116983C211yesmaximal, characteristic, complemented
8#13116895C211yesmaximal, characteristic, complemented
9#13116895C211yesmaximal, characteristic, complemented
10#13116873C211yesmaximal, characteristic
11#13116745C211yesmaximal, characteristic, complemented
12#13116705C211yesmaximal, characteristic, complemented
13#13116700C211yesmaximal, characteristic, complemented
14C4×#88067C211yesmaximal, characteristic, complemented
15C13×#3396C211yesmaximal, characteristic
16C13×#559—21no—
17#11719272—21no—
18C13×#495C2211yescharacteristic
19C13×#495C2211yescharacteristic
20C13×#493C2211yescharacteristic
21C13×#463—21no—
22C13×#463—21no—
23C13×#460—21no—
24C8×Q8×C13C2211yescharacteristic
25C4×C13×Q16C2211yescharacteristic
26C4×C13×D8C2211yescharacteristic
27C4×C13×D8C2211yescharacteristic
28C2×#88069C2211yescharacteristic
29C2×#88067C2211yescharacteristic
30C2×#88067C2211yescharacteristic
31#11718512—21no—
32#11718490—21no—
33#11718490—21no—
34C4×Dic52C2211yescharacteristic
35C4×Dic52C2211yescharacteristic
36C4×Dic52C2211yescharacteristic
37#11718344C2211yescharacteristic
38#11718344C2211yescharacteristic
39#11718343C2211yescharacteristic
40#11718156C2211yescharacteristic
41#11718156C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718154C2211yescharacteristic
44#11718154C2211yescharacteristic
45#11718154C2211yescharacteristic
46#11718154C2211yescharacteristic
47#11718154C2211yescharacteristic
48#11718154C2211yescharacteristic
49#11718084C2211yescharacteristic
50#11718082C2211yescharacteristic
51#11718082C2211yescharacteristic
52#11718081C2211yescharacteristic
53C4⋊#6090C2211yescharacteristic
54C4⋊#6090C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56#11718053C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×SD16—21no—
61C2×C13×SD16—21no—
62C2×C13×D8—21no—
63C2×C13×D8C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C13×#127—21no—
66C13×#124—21no—
67C13×#124—21no—
68C13×#124—41no—
69C13×#123—41no—
70C13×#123—41no—
71C4×Q8×C13—21no—
72C4×Q8×C13D411yescharacteristic
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13—41no—
76#88198—41no—
77C2×Dic52C2311yescharacteristic
78#88143—41no—
79#88143—41no—
80#88141—41no—
81#88124—21no—
82#88124—21no—
83#88123—21no—
84C4×Dic26—21no—
85C4×Dic26—21no—
86C4×Dic26—21no—
87C13×#107C2311yescharacteristic
88C13×C4⋊C8D411yescharacteristic
89C13×C4⋊C8D411yescharacteristic
90C13×C4⋊C8D411yescharacteristic
91C13×#103—21no—
92C13×#102—21no—
93C13×#102—21no—
94C4×C8×C13C2311yescharacteristic
95C4×C8×C13C2311yescharacteristic
96C4×C8×C13C2311yescharacteristic
97#88069—22no—
98#88067—22no—
99#88067—22no—
100#88058—21no—
101#88058C2311yescharacteristic
102#88058C2311yescharacteristic
103#88058C2311yescharacteristic
104#88057—21no—
105#88057—21no—
106#88056—21no—
107#88056—21no—
108#88056—21no—
109C2×#6090C2311yescharacteristic
110C2×#6090C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112C2×#6090C2311yescharacteristic
113#33938—131nomaximal, Sylow
114C2×Q8×C13—21no—
115C2×Q8×C13D811yescharacteristic
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—41no—
119C2×D4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C2×Dic26—21no—
123C2×Dic26—41no—
124C13×Q16—21no—
125C13×Q16—21no—
126C13×SD16—81no—
127C13×SD16—81no—
128C13×D8—21no—
129C13×D8—21no—
130C13×D8—21no—
131C13×D8—21no—
132C13×D8—81no—
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2×D411yescharacteristic
135C2×C8×C13C2×D411yescharacteristic
136C2×C8×C13C2411yescharacteristic
137C13×C4⋊C4—21no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4D811yescharacteristic
140C13×C4⋊C4D811yescharacteristic
141C13×C4⋊C4D811yescharacteristic
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C42×C13—41no—
149C42×C13C2×D411yescharacteristic
150C42×C13C2×D411yescharacteristic
151C42×C13C2×D411yescharacteristic
152C4⋊Dic13—21no—
153C4⋊Dic13—21no—
154C4⋊Dic13—21no—
155C4⋊Dic13—41no—
156#6101—41no—
157#6101—41no—
158#6101—41no—
159#6101—41no—
160#6101—41no—
161#6101—41no—
162#6101—41no—
163C4×Dic13—41no—
164C4×Dic13—41no—
165C4×Dic13—41no—
166Dic52—21no—
167Dic52#4112yes—
168#6090—21no—
169#6090—21no—
170#6090—21no—
171#6090—21no—
172#3396D1311yescharacteristic
173#3383—131no—
174#2244—131no—
175#2243—131no—
176#2242—131no—
177#2229—131no—
178#2228—131no—
179#2226—131no—
180#2211—131no—
181#2211—131no—
182#2207—131no—
183#2183—131no—
184#2176—131no—
185#2175—131no—
186C4×SD32—131no—
187C23×C13—41no—
188C23×C13—41no—
189Q8×C13—41no—
190Q8×C13—41no—
191Q8×C13—41no—
192D4×C13—41no—
193D4×C13—41no—
194D4×C13—41no—
195D4×C13—41no—
196D4×C13—82no—
197D4×C13—161no—
198C2×C4×C13—41no—
199C2×C4×C13—41no—
200C2×C4×C13—161no—
201C2×C4×C13—161no—
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13C2×D811yescharacteristic
204C2×C4×C13C2×D811yescharacteristic
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×D811yescharacteristic
208C2×C4×C13C22×D411yescharacteristic
209C2×Dic13—41no—
210C2×Dic13—41no—
211C2×Dic13—41no—
212C2×Dic13—41no—
213Dic26—22no—
214Dic26—41no—
215Dic26—82no—
216C8×C13—21no—
217C8×C13—21no—
218C8×C13—21no—
219C8×C13C2×#4111yescharacteristic
220C8×C132−1+411yescharacteristic
221#559—21no—
222#557—261no—
223C2×Q32—131no—
224C2×SD32—131no—
225C2×SD32—131no—
226#500—131no—
227#499—131no—
228#499—131no—
229#495C2×D1311yescharacteristic
230#495C2×D1311yescharacteristic
231#493C2×D1311yescharacteristic
232#479—261no—
233#479—261no—
234#475—261no—
235#463—21no—
236#463—21no—
237#460—21no—
238C8×Q8C2×D1311yescharacteristic
239C4×Q16—131no—
240C4×Q16—131no—
241C4×Q16—131no—
242C4×Q16C2×D1311yescharacteristic
243C4×D8C2×D1311yescharacteristic
244C4×D8C2×D1311yescharacteristic
245#367—131no—
246#367—131no—
247#366—131no—
248C4⋊C16—131no—
249C4⋊C16—131no—
250C4⋊C16—131no—
251#358—131no—
252#358—131no—
253#358—131no—
254#358—131no—
255#357—131no—
256#357—131no—
257#357—131no—
258#357—131no—
259#357—131no—
260#357—131no—
261#346—131no—
262#346—131no—
263C4×C16—131no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13—81no—
270C22×C13C22×D811yescharacteristic
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—81no—
278C4×C13—81no—
279C4×C13#54811yescharacteristic
280C4×C13#57711yescharacteristic
281Dic13—42no—
282Dic13—81no—
283Dic13—81no—
284Dic13—81no—
285C2×Q16—131no—
286C2×Q16C22×D1311yescharacteristic
287C2×SD16—21no—
288C2×SD16—21no—
289C2×D8—21no—
290C2×D8C22×D1311yescharacteristic
291C2×D8C22×D1311yescharacteristic
292C4⋊Q8—261no—
293C4⋊Q8—521no—
294#127—21no—
295#125—261no—
296#125—261no—
297#125—521no—
298#125—521no—
299#124—21no—
300#124—21no—
301#124—41no—
302#123—41no—
303#123—41no—
304C4×Q8—21no—
305C4×Q8—261no—
306C4×Q8—261no—
307C4×Q8—261no—
308C4×Q8—521no—
309C4×Q8C22⋊D1311yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—41no—
313Q32—262no—
314SD32—262no—
315SD32—262no—
316C2×C16—131no—
317C2×C16—131no—
318C2×C16—131no—
319C2×C16—131no—
320#107—131no—
321#107—131no—
322#107—131no—
323#107—261no—
324#107C22×D1311yescharacteristic
325#106—261no—
326#106—261no—
327C4⋊C8C22⋊D1311yescharacteristic
328C4⋊C8C22⋊D1311yescharacteristic
329C4⋊C8C22⋊D1311yescharacteristic
330#103—21no—
331#103—261no—
332#103—261no—
333#103—261no—
334#102—21no—
335#102—21no—
336C4×C8C22×D1311yescharacteristic
337C4×C8C22×D1311yescharacteristic
338C4×C8C22×D1311yescharacteristic
339C2×C13—161no—
340C2×C13—161no—
341C2×C13#335811yescharacteristic
342C2×C13#341411yescharacteristic
343C2×C13#341611yescharacteristic
344C2×Q8—21no—
345C2×Q8—261no—
346C2×Q8—521no—
347C2×Q8#610411yescharacteristic
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C22×C4—41no—
353C22×C4—41no—
354Q16—21no—
355Q16—21no—
356Q16—132no—
357Q16—261no—
358SD16—81no—
359SD16—81no—
360D8—21no—
361D8—21no—
362D8—21no—
363D8—21no—
364D8—81no—
365C2×C8C2×C22⋊D1311yescharacteristic
366C2×C8C2×C22⋊D1311yescharacteristic
367C2×C8C2×C22⋊D1311yescharacteristic
368C2×C8C23×D1311yescharacteristic
369C4⋊C4—21no—
370C4⋊C4—41no—
371C4⋊C4—261no—
372C4⋊C4—261no—
373C4⋊C4—261no—
374C4⋊C4—521no—
375C4⋊C4—521no—
376C4⋊C4—521no—
377C4⋊C4—521no—
378C4⋊C4—521no—
379C4⋊C4—521no—
380C4⋊C4—521no—
381C4⋊C4—521no—
382C4⋊C4#610411yescharacteristic
383C4⋊C4#610411yescharacteristic
384C4⋊C4#610411yescharacteristic
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C42—41no—
392C42—521no—
393C42—521no—
394C42—521no—
395C42C2×C22⋊D1311yescharacteristic
396C42C2×C22⋊D1311yescharacteristic
397C42C2×C22⋊D1311yescharacteristic
398C16—261no—
399C16—261no—
400C16—261no—
401C16—261no—
402C13#3393811yescharacteristic, complemented, Sylow
403C23—41no—
404C23—41no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—262no—
409Q8—521no—
410Q8—1042no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—82no—
416D4—161no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—161no—
420C2×C4—161no—
421C2×C4—521no—
422C2×C4—521no—
423C2×C4—521no—
424C2×C4—521no—
425C2×C4C2×#610411yescharacteristic
426C2×C4C2×#610411yescharacteristic
427C2×C4C2×#610411yescharacteristic
428C2×C4C2×#610411yescharacteristic
429C2×C4C2×#610411yescharacteristic
430C2×C4C2×#610411yescharacteristic
431C2×C4C22×C22⋊D1311yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8#41×D1311yescharacteristic
436C8#8825711yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C22×#610411yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—81no—
451C4—81no—
452C4—522no—
453C4—1041no—
454C4—1041no—
455C4—1041no—
456C4#1171953611yescharacteristic
457C4#1171954111yescharacteristic
458C2—161no—
459C2—161no—
460C2#1312746711yescharacteristic
461C2#1312797011yescharacteristic
462C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3396C2
socleC22×C13C22×D8
prime radicalC13×#493C22
hypercenter#3396D13
hypocenterC13#33938
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #13127728C2semidirect
3. #13117072C2semidirect
4. #13117067C2semidirect
5. #13117000C2semidirect
6. #13116993C2semidirect
7. #13116983C2semidirect
8. #13116895C2semidirect
9. #13116895C2semidirect
11. #13116745C2semidirect
12. #13116705C2semidirect
13. #13116700C2semidirect
14. C4×#88067C2semidirect
402. C13#33938semidirect

Maximal subgroups

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

subgroupindex
#131277282
#131170772
#131170722
#131170672
#131170002
#131169932
#131169832
#131168952
#131168732
#131167452
#131167052
#131167002
C4×#880672
C13×#33962
#3393813