Finite Group Databasebeta

← #16019150

Subgroups — #16019150

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#13125486C211yesmaximal, characteristic
2#13117119C211yesmaximal, characteristic, complemented
3#13117112C211yesmaximal, characteristic, complemented
4#13117079C211yesmaximal, characteristic, complemented
5#13117061C211yesmaximal, characteristic, complemented
6#13117027C211yesmaximal, characteristic, complemented
7#13117027C211yesmaximal, characteristic, complemented
8#13117021C211yesmaximal, characteristic, complemented
9#13117016C211yesmaximal, characteristic, complemented
10#13116990C211yesmaximal, characteristic, complemented
11#13116990C211yesmaximal, characteristic, complemented
12#13116980C211yesmaximal, characteristic, complemented
13#13116970C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#3164C211yesmaximal, characteristic, complemented
16C13×#544—21no—
17#11719240—21no—
18C13×#501—21no—
19C13×#501—21no—
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#428—21no—
25C13×#427C2211yescharacteristic
26C2×C13×#107C2211yescharacteristic
27C13×#405C2211yescharacteristic
28#11718796—21no—
29#11718776C2211yescharacteristic
30#11718776C2211yescharacteristic
31#11718374—21no—
32#11718372—21no—
33#11718356C2211yescharacteristic
34C4×D104C2211yescharacteristic
35C4×D104C2211yescharacteristic
36#11718344C2211yescharacteristic
37C22⋊#6090C2211yescharacteristic
38C22⋊#6090C2211yescharacteristic
39#11718083C2211yescharacteristic
40#11718083C2211yescharacteristic
41#11718083C2211yescharacteristic
42#11718083C2211yescharacteristic
43#11718083C2211yescharacteristic
44#11718083C2211yescharacteristic
45#11718083C2211yescharacteristic
46#11718083C2211yescharacteristic
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×M16D411yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—41no—
64C13×#125—21no—
65C13×#125—21no—
66C13×#125—41no—
67C13×C22⋊Q8—41no—
68C13×C22⋊Q8—41no—
69C13×#117—21no—
70C13×#117D411yescharacteristic
71C2×C13×C4⋊C4—21no—
72#88184—21no—
73#88184—21no—
74C2×D104—21no—
75C2×D104C2311yescharacteristic
76C2×D104C2311yescharacteristic
77#88148—41no—
78#88148—41no—
79#88138—41no—
80#88138—41no—
81#88128—21no—
82C4×D52—21no—
83C4×D52—21no—
84#88124—21no—
85C13×#107—21no—
86C13×#107—21no—
87C13×#107—21no—
88C13×#107C2311yescharacteristic
89C13×#107C2311yescharacteristic
90C13×#107C2311yescharacteristic
91C13×#107C2311yescharacteristic
92C13×#106—21no—
93C13×#106—21no—
94C13×#106—21no—
95C13×#97D411yescharacteristic
96C13×#97D411yescharacteristic
97C4×C8×C13C2311yescharacteristic
98C4×C8×C13C2311yescharacteristic
99#88061—21no—
100#88061—21no—
101#88061—21no—
102#88061—21no—
103#88058C2311yescharacteristic
104#88058C2311yescharacteristic
105#88057—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108C2×#6090C2311yescharacteristic
109C2×#6090C2311yescharacteristic
110#33807—131nomaximal, Sylow
111C2×Q8×C13—41no—
112C2×Q8×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13C2×D411yescharacteristic
115C2×C22⋊D13—41no—
116C2×C22⋊D13—41no—
117C2×D52—21no—
118C2×D52—21no—
119C2×D52—41no—
120C2×D52—41no—
121C2×C4×D13—41no—
122C2×C4×D13—41no—
123C13×M16—22no—
124C2×C8×C13—21no—
125C2×C8×C13—21no—
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2×D411yescharacteristic
129C2×C8×C13C2411yescharacteristic
130C13×C4⋊C4—21no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—21no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4—41no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4—41no—
139C13×C4⋊C4—41no—
140C13×C4⋊C4—41no—
141C13×C4⋊C4D811yescharacteristic
142C13×C4⋊C4D811yescharacteristic
143C13×C22⋊C4—41no—
144C13×C22⋊C4D811yescharacteristic
145C13×C22⋊C4D811yescharacteristic
146C42×C13—41no—
147C42×C13C2×D411yescharacteristic
148C42×C13C2×D411yescharacteristic
149#6103—41no—
150#6103—41no—
151#6103—41no—
152#6103—41no—
153C4⋊Dic13—21no—
154C4⋊Dic13—21no—
155#6101—41no—
156#6101—41no—
157D104—21no—
158D104—21no—
159D104—21no—
160D104—21no—
161D104—42no—
162#6090—21no—
163#6090—21no—
164#6090—21no—
165#6090—21no—
166#3176—131no—
167#3164D1311yescharacteristic, complemented
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×C13C2×D811yescharacteristic
182C22×D13—41no—
183C22×D13—41no—
184Q8×C13—161no—
185Q8×C13—161no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—161no—
193C2×C4×C13C2×D811yescharacteristic
194C2×C4×C13C2×D811yescharacteristic
195C2×C4×C13C2×D811yescharacteristic
196C2×C4×C13C2×D811yescharacteristic
197C2×C4×C13C2×D811yescharacteristic
198C2×C4×C13C22×D411yescharacteristic
199C22⋊D13—161no—
200C22⋊D13—161no—
201C2×Dic13—41no—
202C2×Dic13—41no—
203D52—41no—
204D52—41no—
205D52—41no—
206D52—41no—
207D52—161no—
208D52—161no—
209C4×D13—161no—
210C4×D13—161no—
211C8×C13—21no—
212C8×C13—21no—
213C8×C13#13712yes—
214C8×C132−1+411yescharacteristic
215C8×C132−1+411yescharacteristic
216#544—21no—
217#540—261no—
218#501—21no—
219#501—21no—
220#500C2×D1311yescharacteristic
221#500C2×D1311yescharacteristic
222#499—131no—
223#499C2×D1311yescharacteristic
224#499C2×D1311yescharacteristic
225#493—131no—
226#490—261no—
227#469—261no—
228#466—131no—
229#466—131no—
230#442—261no—
231C4×D8—131no—
232C4×D8—131no—
233#428—21no—
234#427C2×D1311yescharacteristic
235C2×#107C2×D1311yescharacteristic
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×C13C22×D811yescharacteristic
263C2×D13—81no—
264C2×D13—81no—
265C2×D13—81no—
266C2×D13—81no—
267C2×D13—81no—
268C2×D13—81no—
269C4×C13—21no—
270C4×C13—21no—
271C4×C13—21no—
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—81no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13—81no—
278C4×C13#53611yescharacteristic
279C4×C13C2×#13711yescharacteristic
280Dic13—81no—
281Dic13—81no—
282C2×D8—131no—
283C2×D8—131no—
284C2×D8—261no—
285C2×M16C22⋊D1311yescharacteristic
286C22×C8C22×D1311yescharacteristic
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—41no—
290#127—261no—
291#125—21no—
292#125—21no—
293#125—41no—
294#125—261no—
295#123—521no—
296#123—521no—
297C22⋊Q8—41no—
298C22⋊Q8—41no—
299#121—261no—
300#121—261no—
301#121—521no—
302#121—521no—
303C4×D4—261no—
304C4×D4—261no—
305#117—21no—
306#117C22⋊D1311yescharacteristic
307C2×C4⋊C4—21no—
308C2×C16—131no—
309C2×C16—131no—
310C2×C16—131no—
311C2×C16—131no—
312#107—21no—
313#107—21no—
314#107—21no—
315#107—131no—
316#107—131no—
317#107C22×D1311yescharacteristic
318#107C22×D1311yescharacteristic
319#107C22×D1311yescharacteristic
320#107C22×D1311yescharacteristic
321#106—21no—
322#106—21no—
323#106—21no—
324#106—261no—
325#102—261no—
326#102—261no—
327#102—261no—
328#102—261no—
329#97C22⋊D1311yescharacteristic
330#97C22⋊D1311yescharacteristic
331C4×C8C22×D1311yescharacteristic
332C4×C8C22×D1311yescharacteristic
333C2×C13—41no—
334C2×C13#322611yescharacteristic
335C2×C13#341511yescharacteristic
336C2×C13#341611yescharacteristic
337D13—161no—
338D13—161no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×D4—261no—
342C2×D4—261no—
343C2×D4—521no—
344C2×D4—521no—
345C2×D4—521no—
346C2×D4—521no—
347C22×C4—41no—
348C22×C4—521no—
349C22×C4—521no—
350C22×C4C2×C22⋊D1311yescharacteristic
351D8—261no—
352D8—261no—
353D8—261no—
354D8—261no—
355D8—522no—
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—21no—
366C4⋊C4—21no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—261no—
375C4⋊C4—261no—
376C4⋊C4—521no—
377C4⋊C4—521no—
378C4⋊C4#610411yescharacteristic
379C4⋊C4#610411yescharacteristic
380C22⋊C4—41no—
381C22⋊C4—521no—
382C22⋊C4—521no—
383C22⋊C4—521no—
384C22⋊C4—521no—
385C22⋊C4#610411yescharacteristic
386C22⋊C4#610411yescharacteristic
387C42—41no—
388C42C2×C22⋊D1311yescharacteristic
389C42C2×C22⋊D1311yescharacteristic
390C16—261no—
391C16—261no—
392C16—261no—
393C16—261no—
394C13#3380711yescharacteristic, complemented, Sylow
395C23—521no—
396C23—521no—
397C23C2×#610411yescharacteristic
398Q8—161no—
399Q8—161no—
400D4—521no—
401D4—521no—
402D4—521no—
403D4—521no—
404D4—2081no—
405D4—2081no—
406D4—2081no—
407D4—2081no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—161no—
415C2×C4—521no—
416C2×C4—521no—
417C2×C4—2081no—
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#8819612yes—
428C8#8825411yescharacteristic
429C8#8825411yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—1041no—
434C22—1041no—
435C22—1041no—
436C22—1041no—
437C22—1041no—
438C22—1041no—
439C22C22×#610411yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—1041no—
450C4—1041no—
451C4C2×#8819611yescharacteristic
452C4#1171952111yescharacteristic
453C2—41no—
454C2—2081no—
455C2—2081no—
456C2#1312595711yescharacteristic
457C2#1312797511yescharacteristic
458C2#1312798011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3164C2
socleC22×C13C22×D8
prime radical#13125486C2
hypercenter#3164D13
hypocenterC13#33807
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13117119C2semidirect
3. #13117112C2semidirect
4. #13117079C2semidirect
5. #13117061C2semidirect
6. #13117027C2semidirect
7. #13117027C2semidirect
8. #13117021C2semidirect
9. #13117016C2semidirect
10. #13116990C2semidirect
11. #13116990C2semidirect
12. #13116980C2semidirect
13. #13116970C2semidirect
14. #13116643C2semidirect
15. C13×#3164C2semidirect
167. #3164D13semidirect
394. C13#33807semidirect

Maximal subgroups

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

subgroupindex
#131254862
#131171192
#131171122
#131170792
#131170612
#131170272
#131170212
#131170162
#131169902
#131169802
#131169702
#131166432
C13×#31642
#3380713