Finite Group Databasebeta

← #16018466

Subgroups — #16018466

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125406C211yesmaximal, characteristic, complemented
2#13117112C211yesmaximal, characteristic, complemented
3#13117095C211yesmaximal, characteristic, complemented
4#13117070C211yesmaximal, characteristic, complemented
5#13117067C211yesmaximal, characteristic, complemented
6#13116934C211yesmaximal, characteristic, complemented
7#13116930C211yesmaximal, characteristic, complemented
8#13116925C211yesmaximal, characteristic, complemented
9#13116920C211yesmaximal, characteristic
10C4×#88069C211yesmaximal, characteristic, complemented
11C4×#88068C211yesmaximal, characteristic, complemented
12C4×#88067C211yesmaximal, characteristic, complemented
13C4×#88066C211yesmaximal, characteristic, complemented
14C2×C4×#6090C211yesmaximal, characteristic, complemented
15C13×#3168C211yesmaximal, characteristic, complemented
16C13×#529—21no—
17#11719184—21no—
18C13×#499C2211yescharacteristic
19C13×#495C2211yescharacteristic
20C13×#488—21no—
21C13×#467C2211yescharacteristic
22C13×#466C2211yescharacteristic
23C13×#465—21no—
24C4×C13×Q16C2211yescharacteristic
25C4×C13×SD16—21no—
26C4×C13×D8C2211yescharacteristic
27C2×C4×C8×C13C2211yescharacteristic
28C2×#88069C2211yescharacteristic
29C2×#88068C2211yescharacteristic
30C2×#88067C2211yescharacteristic
31C2×#88066C2211yescharacteristic
32#11718777C2211yescharacteristic
33#11718776C2211yescharacteristic
34#11718775—21no—
35C22×#6090C2211yescharacteristic
36C22×#6090C2211yescharacteristic
37C4×Dic52C2211yescharacteristic
38#11718358—21no—
39#11718357C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095—21no—
42#11718344C2211yescharacteristic
43#11718156C2211yescharacteristic
44#11718156C2211yescharacteristic
45#11718154C2211yescharacteristic
46#11718154C2211yescharacteristic
47#11718084C2211yescharacteristic
48#11718084C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718083C2211yescharacteristic
51#11718082C2211yescharacteristic
52#11718082C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55C4×#6090C2211yescharacteristic
56C4×#6090C2211yescharacteristic
57C4×#6090C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×Q16C2311yescharacteristic
60C2×C13×SD16—21no—
61C2×C13×D8C2311yescharacteristic
62C22×C8×C13D411yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C13×#126—41no—
65C13×#125—21no—
66C13×#124—21no—
67C13×#123—41no—
68C13×C22⋊Q8—21no—
69C13×#121—21no—
70C4×Q8×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13—41no—
73C13×#117—41no—
74C2×C42×C13D411yescharacteristic
75#88184—21no—
76#88183—41no—
77C4×C22⋊D13—41no—
78#88178—21no—
79C2×Dic52C2311yescharacteristic
80C2×D104C2311yescharacteristic
81C2×#6095—21no—
82#88130—41no—
83#88129—21no—
84C4×D52—21no—
85#88126—41no—
86#88124—21no—
87C4×Dic26—21no—
88C13×#107C2311yescharacteristic
89C13×#107C2311yescharacteristic
90C13×#106—21no—
91C13×#103—21no—
92C13×#103—21no—
93C13×#102—21no—
94C13×#102—21no—
95C4×C8×C13D411yescharacteristic
96C4×C8×C13D411yescharacteristic
97C4×C8×C13C2311yescharacteristic
98C4×C8×C13C2311yescharacteristic
99#88069—22no—
100#88068—22no—
101#88067—22no—
102#88066—22no—
103#88061—21no—
104#88061—21no—
105#88058C2311yescharacteristic
106#88058C2311yescharacteristic
107#88057—21no—
108#88056—21no—
109#88056—21no—
110C2×#6090—22no—
111C2×#6090—22no—
112C2×#6090C2311yescharacteristic
113C2×#6090C2311yescharacteristic
114C2×#6090C2311yescharacteristic
115C2×#6090C2311yescharacteristic
116#33735—131nomaximal, Sylow
117C2×Q8×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13D811yescharacteristic
122C22×C4×C13D811yescharacteristic
123C22×C4×C13C2×D411yescharacteristic
124C2×C22⋊D13—41no—
125C2×D52—21no—
126C2×C4×D13—41no—
127C2×Dic26—21no—
128C13×Q16—21no—
129C13×Q16—21no—
130C13×SD16—42no—
131C13×D8—21no—
132C13×D8—21no—
133C2×C8×C13—22no—
134C2×C8×C13—21no—
135C2×C8×C13—21no—
136C2×C8×C13C2×D411yescharacteristic
137C2×C8×C13C2×D411yescharacteristic
138C2×C8×C13C2×D411yescharacteristic
139C2×C8×C13C2411yescharacteristic
140C13×C4⋊C4—21no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—41no—
143C13×C4⋊C4—41no—
144C13×C4⋊C4—41no—
145C13×C4⋊C4—41no—
146C13×C22⋊C4—41no—
147C13×C22⋊C4—41no—
148C13×C22⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C42×C13—41no—
152C42×C13D811yescharacteristic
153C42×C13D811yescharacteristic
154C42×C13C2×D411yescharacteristic
155C42×C13C2×D411yescharacteristic
156C22⋊Dic13—41no—
157#6103—41no—
158#6103—41no—
159#6103—41no—
160#6103—41no—
161C4⋊Dic13—21no—
162C4⋊Dic13—21no—
163#6101—41no—
164#6101—41no—
165#6101—41no—
166#6101—41no—
167C4×Dic13—41no—
168Dic52—21no—
169Dic52—21no—
170D104—21no—
171D104—21no—
172#6095—42no—
173#6090—21no—
174#6090—21no—
175#6090#4112yes—
176#6090#4112yes—
177#3168—131no—
178#3168D1311yescharacteristic, complemented
179#2253—131no—
180#2249—131no—
181#2242—131no—
182#2242—131no—
183#2217—131no—
184#2217—131no—
185#2216—131no—
186#2215—131no—
187C4×Q32—131no—
188C4×SD32—131no—
189C4×SD32—131no—
190C4×D16—131no—
191C2×C4×C16—131no—
192C23×C13—41no—
193C23×C13C2×D811yescharacteristic
194C22×D13—41no—
195Q8×C13—41no—
196Q8×C13—41no—
197D4×C13—41no—
198D4×C13—41no—
199D4×C13—82no—
200C2×C4×C13—22no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—22no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—82no—
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—82no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218D52—41no—
219D52—41no—
220C4×D13—82no—
221Dic26—41no—
222Dic26—41no—
223C8×C13—21no—
224C8×C13—21no—
225C8×C13#13512yes—
226C8×C13C2×#4111yescharacteristic
227C8×C13C2×#4111yescharacteristic
228#529—21no—
229#529—261no—
230C2×Q32—131no—
231C2×SD32—131no—
232C2×SD32—131no—
233C2×D16—131no—
234C22×C16—131no—
235C22×C16—131no—
236#499—131no—
237#499C2×D1311yescharacteristic
238#495—131no—
239#495C2×D1311yescharacteristic
240#488—21no—
241#488—261no—
242#467—131no—
243#467C2×D1311yescharacteristic
244#466—131no—
245#466C2×D1311yescharacteristic
246#465—21no—
247#465—261no—
248C4×Q16—131no—
249C4×Q16C2×D1311yescharacteristic
250C4×SD16—21no—
251C4×SD16—261no—
252C4×D8—131no—
253C4×D8C2×D1311yescharacteristic
254C2×C4×C8C2×D1311yescharacteristic
255#367—131no—
256#367—131no—
257#366—131no—
258#366—131no—
259#358—131no—
260#358—131no—
261#358—131no—
262#358—131no—
263#357—131no—
264#357—131no—
265#357—131no—
266#357—131no—
267C4×C16—131no—
268C4×C16—131no—
269C4×C16—131no—
270C4×C16—131no—
271C22×C13—21no—
272C22×C13—21no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13#50812yes—
277C22×C13C22×D811yescharacteristic
278C2×D13—81no—
279C2×D13—81no—
280C2×D13—81no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—21no—
284C4×C13—21no—
285C4×C13—81no—
286C4×C13—81no—
287C4×C13—81no—
288C4×C13#50812yes—
289C4×C13#53211yescharacteristic
290C4×C13C2×#13511yescharacteristic
291Dic13—81no—
292Dic13—81no—
293Dic13—81no—
294C2×Q16—131no—
295C2×Q16C22×D1311yescharacteristic
296C2×SD16—21no—
297C2×SD16—261no—
298C2×D8—131no—
299C2×D8C22×D1311yescharacteristic
300C22×C8C22⋊D1311yescharacteristic
301C22×C8C22×D1311yescharacteristic
302#126—41no—
303#126—521no—
304#125—21no—
305#125—261no—
306#124—21no—
307#124—261no—
308#123—41no—
309#123—521no—
310C22⋊Q8—21no—
311C22⋊Q8—261no—
312#121—21no—
313#121—261no—
314C4×Q8—21no—
315C4×Q8—261no—
316C4×D4—21no—
317C4×D4—41no—
318C4×D4—261no—
319C4×D4—521no—
320#117—41no—
321#117—521no—
322C2×C42C22⋊D1311yescharacteristic
323Q32—262no—
324SD32—262no—
325SD32—262no—
326D16—262no—
327C2×C16—131no—
328C2×C16—131no—
329C2×C16—131no—
330C2×C16—131no—
331C2×C16—262no—
332C2×C16—262no—
333#107—131no—
334#107—131no—
335#107C22×D1311yescharacteristic
336#107C22×D1311yescharacteristic
337#106—21no—
338#106—261no—
339#103—21no—
340#103—21no—
341#103—261no—
342#103—261no—
343#102—21no—
344#102—21no—
345#102—261no—
346#102—261no—
347C4×C8C22⋊D1311yescharacteristic
348C4×C8C22⋊D1311yescharacteristic
349C4×C8C22×D1311yescharacteristic
350C4×C8C22×D1311yescharacteristic
351C2×C13—22no—
352C2×C13—161no—
353C2×C13#316911yescharacteristic
354C2×C13C2×#50811yescharacteristic
355C2×C13C2×#50811yescharacteristic
356D13—161no—
357C2×Q8—21no—
358C2×Q8—261no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—261no—
362C2×D4—521no—
363C22×C4—41no—
364C22×C4—521no—
365C22×C4#610411yescharacteristic
366C22×C4#610411yescharacteristic
367C22×C4C2×C22⋊D1311yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—261no—
371Q16—261no—
372SD16—42no—
373SD16—522no—
374D8—21no—
375D8—21no—
376D8—261no—
377D8—261no—
378C2×C8—22no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D1311yescharacteristic
382C2×C8C2×C22⋊D1311yescharacteristic
383C2×C8C2×C22⋊D1311yescharacteristic
384C2×C8C23×D1311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—261no—
392C4⋊C4—261no—
393C4⋊C4—521no—
394C4⋊C4—521no—
395C4⋊C4—521no—
396C4⋊C4—521no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—521no—
403C22⋊C4—521no—
404C22⋊C4—521no—
405C22⋊C4—521no—
406C22⋊C4—521no—
407C42—41no—
408C42—521no—
409C42#610411yescharacteristic
410C42#610411yescharacteristic
411C42C2×C22⋊D1311yescharacteristic
412C42C2×C22⋊D1311yescharacteristic
413C16—132no—
414C16—132no—
415C16—261no—
416C16—261no—
417C13#3373511yescharacteristic, complemented, Sylow
418C23—41no—
419C23—521no—
420C23C2×#610411yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—521no—
424Q8—521no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—521no—
429D4—521no—
430D4—1042no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—521no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4—1042no—
443C2×C4C2×#610411yescharacteristic
444C2×C4C2×#610411yescharacteristic
445C2×C4C2×#610411yescharacteristic
446C2×C4C2×#610411yescharacteristic
447C2×C4C2×#610411yescharacteristic
448C2×C4C22×C22⋊D1311yescharacteristic
449C8—21no—
450C8—21no—
451C8#8820412yes—
452C8#41×D1311yescharacteristic
453C8#41×D1311yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—1041no—
460C22—1041no—
461C22—1041no—
462C22#1171885512yes—
463C22C22×#610411yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—1041no—
472C4—1041no—
473C4—1041no—
474C4#1171885512yes—
475C4C2×#8820411yescharacteristic
476C4#1171953711yescharacteristic
477C2—22no—
478C2—161no—
479C2—2081no—
480C2#1312541111yescharacteristic
481C2C2×#1171885511yescharacteristic
482C2C2×#1171885511yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
prime radical#13116920C2
hypercenter#3168D13
hypocenterC13#33735
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13125406C2semidirect
2. #13117112C2semidirect
3. #13117095C2semidirect
4. #13117070C2semidirect
5. #13117067C2semidirect
6. #13116934C2semidirect
7. #13116930C2semidirect
8. #13116925C2semidirect
10. C4×#88069C2semidirect
11. C4×#88068C2semidirect
12. C4×#88067C2semidirect
13. C4×#88066C2semidirect
14. C2×C4×#6090C2semidirect
15. C13×#3168C2semidirect
178. #3168D13semidirect
417. C13#33735semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131171122
#131170952
#131170702
#131170672
#131169342
#131169302
#131169252
#131169202
C4×#880692
C4×#880682
C4×#880672
C4×#880662
C2×C4×#60902
C13×#31682
#3373513