Finite Group Databasebeta

← #16019144

Subgroups — #16019144

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125375C211yesmaximal, characteristic, complemented
2#13117123C211yesmaximal, characteristic, complemented
3#13117112C211yesmaximal, characteristic, complemented
4#13117077C211yesmaximal, characteristic, complemented
5#13117059C211yesmaximal, characteristic, complemented
6#13117024C211yesmaximal, characteristic, complemented
7#13117024C211yesmaximal, characteristic, complemented
8#13117019C211yesmaximal, characteristic, complemented
9#13117014C211yesmaximal, characteristic, complemented
10#13116993C211yesmaximal, characteristic, complemented
11#13116993C211yesmaximal, characteristic, complemented
12#13116983C211yesmaximal, characteristic, complemented
13#13116973C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#3176C211yesmaximal, characteristic
16C13×#540—21no—
17#11719224—21no—
18C13×#499C2211yescharacteristic
19C13×#493C2211yescharacteristic
20C13×#490—21no—
21C13×#469—21no—
22C13×#466C2211yescharacteristic
23C13×#466C2211yescharacteristic
24C13×#442—21no—
25C4×C13×D8C2211yescharacteristic
26C4×C13×D8C2211yescharacteristic
27C13×#405C2211yescharacteristic
28#11718782—21no—
29#11718767C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31#11718363—21no—
32#11718363—21no—
33#11718344C2211yescharacteristic
34#11718344C2211yescharacteristic
35#11718343C2211yescharacteristic
36#11718343C2211yescharacteristic
37#11718154C2211yescharacteristic
38#11718154C2211yescharacteristic
39#11718154C2211yescharacteristic
40#11718154C2211yescharacteristic
41#11718154C2211yescharacteristic
42#11718154C2211yescharacteristic
43#11718154C2211yescharacteristic
44#11718154C2211yescharacteristic
45C22⋊#6090C2211yescharacteristic
46C22⋊#6090C2211yescharacteristic
47#11718082C2211yescharacteristic
48#11718082C2211yescharacteristic
49#11718082C2211yescharacteristic
50#11718082C2211yescharacteristic
51#11718081C2211yescharacteristic
52#11718081C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56C4⋊#6090C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×D8—21no—
60C2×C13×D8C2311yescharacteristic
61C2×C13×D8C2311yescharacteristic
62C2×C13×M16D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×#127—21no—
65C13×#125—21no—
66C13×#123—41no—
67C13×#123—41no—
68C13×#121—21no—
69C13×#121—21no—
70C13×#121—41no—
71C13×#121—41no—
72C4×D4×C13—21no—
73C4×D4×C13—21no—
74C13×#117D411yescharacteristic
75#88180—21no—
76C2×C4⋊Dic13—21no—
77#88144—41no—
78#88142—41no—
79#88132—41no—
80#88132—41no—
81#88124—21no—
82#88124—21no—
83#88123—21no—
84#88123—21no—
85C13×#107C2311yescharacteristic
86C13×#107C2311yescharacteristic
87C13×#106—21no—
88C13×#102—21no—
89C13×#102—21no—
90C13×#102—21no—
91C13×#102—21no—
92C13×#97D411yescharacteristic
93C13×#97D411yescharacteristic
94C4×C8×C13C2311yescharacteristic
95C4×C8×C13C2311yescharacteristic
96#88058—21no—
97#88058—21no—
98#88058—21no—
99#88058C2311yescharacteristic
100#88058C2311yescharacteristic
101#88058C2311yescharacteristic
102#88058C2311yescharacteristic
103#88057—21no—
104#88057—21no—
105#88057—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108C2×#6090C2311yescharacteristic
109C2×#6090C2311yescharacteristic
110#33807—131nomaximal, Sylow
111C2×D4×C13—21no—
112C2×D4×C13—21no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C22×C4×C13—41no—
118C22×C4×C13—41no—
119C22×C4×C13C2×D411yescharacteristic
120C22×Dic13—41no—
121C2×Dic26—41no—
122C2×Dic26—41no—
123C13×D8—21no—
124C13×D8—21no—
125C13×D8—21no—
126C13×D8—21no—
127C13×D8—42no—
128C13×M16—22no—
129C2×C8×C13—21no—
130C2×C8×C13—21no—
131C2×C8×C13C2×D411yescharacteristic
132C2×C8×C13C2×D411yescharacteristic
133C2×C8×C13C2×D411yescharacteristic
134C2×C8×C13C2411yescharacteristic
135C13×C4⋊C4—21no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4D811yescharacteristic
140C13×C4⋊C4D811yescharacteristic
141C13×C22⋊C4—41no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4D811yescharacteristic
146C13×C22⋊C4D811yescharacteristic
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149C22⋊Dic13—41no—
150C4⋊Dic13—21no—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153C4⋊Dic13—21no—
154C4⋊Dic13—41no—
155C4⋊Dic13—41no—
156C4⋊Dic13—41no—
157#6101—41no—
158#6101—41no—
159#6101—41no—
160#6101—41no—
161C4×Dic13—41no—
162#6090—21no—
163#6090—21no—
164#6090—21no—
165#6090—21no—
166#3176D1311yescharacteristic
167#3164—131no—
168#2255—131no—
169#2253—131no—
170#2244—131no—
171#2240—131no—
172#2234—131no—
173#2234—131no—
174#2233—131no—
175#2232—131no—
176#2228—131no—
177#2228—131no—
178#2226—131no—
179#2224—131no—
180#2164—131no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13C2×D811yescharacteristic
184D4×C13—41no—
185D4×C13—41no—
186D4×C13—41no—
187D4×C13—41no—
188D4×C13—161no—
189D4×C13—161no—
190D4×C13—161no—
191D4×C13—161no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—161no—
197C2×C4×C13—161no—
198C2×C4×C13C2×D811yescharacteristic
199C2×C4×C13C2×D811yescharacteristic
200C2×C4×C13C2×D811yescharacteristic
201C2×C4×C13C2×D811yescharacteristic
202C2×C4×C13C2×D811yescharacteristic
203C2×C4×C13C22×D411yescharacteristic
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—161no—
209Dic26—161no—
210Dic26—161no—
211C8×C13—21no—
212C8×C13—21no—
213C8×C13#13712yes—
214C8×C132−1+411yescharacteristic
215C8×C132−1+411yescharacteristic
216#544—261no—
217#540—21no—
218#501—261no—
219#501—261no—
220#500—131no—
221#500—131no—
222#499—131no—
223#499—131no—
224#499C2×D1311yescharacteristic
225#493C2×D1311yescharacteristic
226#490—21no—
227#469—21no—
228#466C2×D1311yescharacteristic
229#466C2×D1311yescharacteristic
230#442—21no—
231C4×D8C2×D1311yescharacteristic
232C4×D8C2×D1311yescharacteristic
233#428—261no—
234#427—131no—
235C2×#107—131no—
236#405C2×D1311yescharacteristic
237#367—131no—
238#367—131no—
239#367—131no—
240#367—131no—
241#366—131no—
242#366—131no—
243#366—131no—
244#366—131no—
245C4⋊C16—131no—
246C4⋊C16—131no—
247#357—131no—
248#357—131no—
249#357—131no—
250#357—131no—
251#357—131no—
252#357—131no—
253#357—131no—
254#357—131no—
255C22⋊C16—131no—
256C22⋊C16—131no—
257#346—131no—
258C4×C16—131no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13C22×D811yescharacteristic
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13#53611yescharacteristic
277C4×C13C2×#13711yescharacteristic
278Dic13—81no—
279Dic13—81no—
280Dic13—81no—
281Dic13—81no—
282C2×D8—21no—
283C2×D8C22×D1311yescharacteristic
284C2×D8C22×D1311yescharacteristic
285C2×M16C22⋊D1311yescharacteristic
286C22×C8C22×D1311yescharacteristic
287C4⋊Q8—261no—
288C4⋊Q8—261no—
289C4⋊Q8—521no—
290#127—21no—
291#125—21no—
292#125—261no—
293#125—261no—
294#125—521no—
295#123—41no—
296#123—41no—
297C22⋊Q8—521no—
298C22⋊Q8—521no—
299#121—21no—
300#121—21no—
301#121—41no—
302#121—41no—
303C4×D4—21no—
304C4×D4—21no—
305#117—261no—
306#117C22⋊D1311yescharacteristic
307C2×C4⋊C4—261no—
308C2×C16—131no—
309C2×C16—131no—
310C2×C16—131no—
311C2×C16—131no—
312#107—131no—
313#107—131no—
314#107—131no—
315#107—131no—
316#107—261no—
317#107—261no—
318#107—261no—
319#107C22×D1311yescharacteristic
320#107C22×D1311yescharacteristic
321#106—21no—
322#106—261no—
323#106—261no—
324#106—261no—
325#102—21no—
326#102—21no—
327#102—21no—
328#102—21no—
329#97C22⋊D1311yescharacteristic
330#97C22⋊D1311yescharacteristic
331C4×C8C22×D1311yescharacteristic
332C4×C8C22×D1311yescharacteristic
333C2×C13—41no—
334C2×C13—161no—
335C2×C13—161no—
336C2×C13#322611yescharacteristic
337C2×C13#341511yescharacteristic
338C2×C13#341611yescharacteristic
339C2×Q8—521no—
340C2×Q8—521no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—521no—
350C22×C4C2×C22⋊D1311yescharacteristic
351D8—21no—
352D8—21no—
353D8—21no—
354D8—21no—
355D8—42no—
356M16—22no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8C2×C22⋊D1311yescharacteristic
360C2×C8C2×C22⋊D1311yescharacteristic
361C2×C8C2×C22⋊D1311yescharacteristic
362C2×C8C23×D1311yescharacteristic
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—261no—
368C4⋊C4—261no—
369C4⋊C4—261no—
370C4⋊C4—261no—
371C4⋊C4—521no—
372C4⋊C4—521no—
373C4⋊C4—521no—
374C4⋊C4—521no—
375C4⋊C4—521no—
376C4⋊C4—521no—
377C4⋊C4—521no—
378C4⋊C4#610411yescharacteristic
379C4⋊C4#610411yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—521no—
385C22⋊C4#610411yescharacteristic
386C22⋊C4#610411yescharacteristic
387C42—521no—
388C42C2×C22⋊D1311yescharacteristic
389C42C2×C22⋊D1311yescharacteristic
390C16—261no—
391C16—261no—
392C16—261no—
393C16—261no—
394C13#3380711yescharacteristic, complemented, Sylow
395C23—41no—
396C23—41no—
397C23C2×#610411yescharacteristic
398Q8—2081no—
399Q8—2081no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—161no—
405D4—161no—
406D4—161no—
407D4—161no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—161no—
413C2×C4—161no—
414C2×C4—521no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—521no—
418C2×C4—2081no—
419C2×C4C2×#610411yescharacteristic
420C2×C4C2×#610411yescharacteristic
421C2×C4C2×#610411yescharacteristic
422C2×C4C2×#610411yescharacteristic
423C2×C4C2×#610411yescharacteristic
424C2×C4C22×C22⋊D1311yescharacteristic
425C8—21no—
426C8—21no—
427C8#8820512yes—
428C8#8825711yescharacteristic
429C8#8825711yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22C22×#610411yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—1041no—
448C4—1041no—
449C4—1041no—
450C4—1041no—
451C4C2×#8820511yescharacteristic
452C4#1171953011yescharacteristic
453C2—41no—
454C2—161no—
455C2—161no—
456C2#1312595411yescharacteristic
457C2#1312797511yescharacteristic
458C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3176C2
socleC22×C13C22×D8
hypercenter#3176D13
hypocenterC13#33807
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #13125375C2semidirect
2. #13117123C2semidirect
3. #13117112C2semidirect
4. #13117077C2semidirect
5. #13117059C2semidirect
6. #13117024C2semidirect
7. #13117024C2semidirect
8. #13117019C2semidirect
9. #13117014C2semidirect
10. #13116993C2semidirect
11. #13116993C2semidirect
12. #13116983C2semidirect
13. #13116973C2semidirect
14. #13116643C2semidirect
394. C13#33807semidirect

Maximal subgroups

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

subgroupindex
#131253752
#131171232
#131171122
#131170772
#131170592
#131170242
#131170192
#131170142
#131169932
#131169832
#131169732
#131166432
C13×#31762
#3380713