Finite Group Databasebeta

← #16018723

Subgroups — #16018723

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718777C211yesmaximal, characteristic, complemented
2#13117044C212yesmaximal, complemented
3#13117036C211yesmaximal, characteristic, complemented
4#13117019C211yesmaximal, characteristic, complemented
5#13116947C212yesmaximal, complemented
6#13116942C212yesmaximal, complemented
7#13116776C212yesmaximal, complemented
8#13116769C211yesmaximal, characteristic, complemented
9#13116752C211yesmaximal, characteristic, complemented
10#13116447C211yesmaximal, characteristic, complemented
11C13×#3050C211yesmaximal, characteristic
12C2×C13×#135C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C13×#525—21no—
15C2×#88178—21no—
16C22×Dic52C2211yescharacteristic
17C13×#467C2211yescharacteristic
18C13×#467C2211yescharacteristic
19C13×#466C2211yescharacteristic
20C13×#466C2211yescharacteristic
21C13×#465—21no—
22C13×#465—21no—
23C13×#427C2211yescharacteristic
24C13×#416—21no—
25C2×#88069C2212yescomplemented
26C2×#88067C2212yescomplemented
27#11718777—21no—
28#11718777—21no—
29#11718777C2212yes—
30#11718777C2212yes—
31C2×#88058C2211yescharacteristic
32C2×#88056—21no—
33C2×#88052C2212yes—
34#11718156C2212yescomplemented
35#11718154C2212yescomplemented
36C22⋊#6090C2211yescharacteristic
37C22⋊#6090C2211yescharacteristic
38C22⋊#6090C2212yes—
39#11718084C2212yescomplemented
40#11718084C2212yescomplemented
41#11718082C2212yescomplemented
42#11718081C2212yescomplemented
43C2×C13×#41—21no—
44C23×C4×C13D411yescharacteristic
45C22×Dic26—21no—
46C13×#135—42no—
47C2×C13×Q16C2311yescharacteristic
48C2×C13×SD16—21no—
49C2×C13×D8C2311yescharacteristic
50C22×C8×C13—42no—
51C22×C8×C13D411yescharacteristic
52C22×C8×C13D411yescharacteristic
53C22×C8×C13D411yescharacteristic
54C22×C8×C13C2311yescharacteristic
55C22×C8×C13C2311yescharacteristic
56C22×C8×C13C2311yescharacteristic
57C13×#123—41no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8—21no—
60C13×#121—21no—
61C13×#121—21no—
62C13×#120—41no—
63C4×D4×C13—41no—
64C4×D4×C13—41no—
65C13×#117—21no—
66C2×C22⋊Dic13—41no—
67C2×C4⋊Dic13—21no—
68#88178—22no—
69#88178—22no—
70#88178—41no—
71#88178—41no—
72C2×#6101—41no—
73C2×Dic52—21no—
74C2×Dic52—42no—
75C2×Dic52C2312yes—
76C13×#107C2311yescharacteristic
77C13×#107C2311yescharacteristic
78C13×#106—21no—
79C13×#103—21no—
80C13×#103—21no—
81C13×#102—21no—
82C13×#102—21no—
83#88069—42no—
84#88067—42no—
85#88058—21no—
86#88058C2312yes—
87#88056—22no—
88#88056—22no—
89#88052—42no—
90C2×#6090C2312yes—
91C2×#6090C2312yes—
92#33762—131nomaximal, Sylow
93C24×C13D811yescharacteristic
94C13×#41—42no—
95C13×#41—42no—
96C2×Q8×C13—21no—
97C2×D4×C13—21no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13D811yescharacteristic
105C22×C4×C13D811yescharacteristic
106C22×C4×C13D811yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×Dic13—41no—
111C22×Dic13—41no—
112C2×Dic26—22no—
113C2×Dic26—42no—
114C2×Dic26—42no—
115C2×Dic26—41no—
116C13×Q16—22no—
117C13×SD16—42no—
118C13×D8—22no—
119C2×C8×C13—22no—
120C2×C8×C13—22no—
121C2×C8×C13—22no—
122C2×C8×C13—41no—
123C2×C8×C13—41no—
124C2×C8×C13—41no—
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2×D411yescharacteristic
127C2×C8×C13C2×D411yescharacteristic
128C2×C8×C13C2411yescharacteristic
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C42×C13—41no—
139C22⋊Dic13—42no—
140C22⋊Dic13—42no—
141C4⋊Dic13—22no—
142C4⋊Dic13—41no—
143#6101—42no—
144#6101—42no—
145Dic52—22no—
146Dic52—22no—
147Dic52—42no—
148#6090—22no—
149#6090—22no—
150#3050D1311yescharacteristic
151C2×#467—131no—
152#2237—132no—
153#2236—131no—
154#2233—131no—
155#2220—132no—
156#2219—132no—
157#2189—132no—
158#2188—131no—
159#2185—131no—
160#2112—131no—
161C23×C13—22no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13C2×D811yescharacteristic
166C23×C13C2×D811yescharacteristic
167C23×C13C2×D811yescharacteristic
168Q8×C13—41no—
169Q8×C13—41no—
170D4×C13—41no—
171D4×C13—41no—
172D4×C13—82no—
173D4×C13—82no—
174D4×C13—82no—
175C2×C4×C13—21no—
176C2×C4×C13—21no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—82no—
188C2×C4×C13C2×D811yescharacteristic
189C2×C4×C13C2×D811yescharacteristic
190C2×C4×C13C2×D811yescharacteristic
191C2×C4×C13C22×D411yescharacteristic
192C2×Dic13—42no—
193C2×Dic13—42no—
194C2×Dic13—82no—
195C2×Dic13—82no—
196Dic26—42no—
197Dic26—42no—
198Dic26—82no—
199C8×C13—21no—
200C8×C13—21no—
201C8×C13—21no—
202C8×C13H(5,𝔽2)12yes—
203C2×#135C2×D1311yescharacteristic
204C22×Q16—131no—
205C23×C8C2×D1311yescharacteristic
206#525—21no—
207C2×C22⋊Q8—261no—
208C2×Q32—132no—
209C2×SD32—132no—
210C2×M32—132no—
211#467—132no—
212#467—132no—
213#467—261no—
214#467—261no—
215#467C2×D1311yescharacteristic
216#467C2×D1311yescharacteristic
217#466C2×D1311yescharacteristic
218#466C2×D1311yescharacteristic
219#465—21no—
220#465—21no—
221#427C2×D1311yescharacteristic
222C2×#107—131no—
223#416—21no—
224C2×#103—261no—
225#367—132no—
226#366—132no—
227#358—132no—
228#358—132no—
229#358—132no—
230#357—132no—
231C22⋊C16—131no—
232C22⋊C16—131no—
233C22⋊C16—132no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—21no—
237C22×C13—21no—
238C22×C13—21no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—44no—
243C22×C13—81no—
244C22×C13—81no—
245C22×C13—81no—
246C22×C13#51012yes—
247C22×C13C22×D811yescharacteristic
248C4×C13—21no—
249C4×C13—21no—
250C4×C13—21no—
251C4×C13—81no—
252C4×C13—81no—
253C4×C13—81no—
254C4×C13#53411yescharacteristic
255C4×C13#57511yescharacteristic
256Dic13—82no—
257Dic13—82no—
258C2×#41—21no—
259C22×Q8—261no—
260C23×C4C22⋊D1311yescharacteristic
261#135—42no—
262C2×Q16—132no—
263C2×Q16—261no—
264C2×Q16—522no—
265C2×Q16C22×D1311yescharacteristic
266C2×SD16—21no—
267C2×D8C22×D1311yescharacteristic
268C22×C8—42no—
269C22×C8C22⋊D1311yescharacteristic
270C22×C8C22⋊D1311yescharacteristic
271C22×C8C22⋊D1311yescharacteristic
272C22×C8C22×D1311yescharacteristic
273C22×C8C22×D1311yescharacteristic
274C22×C8C22×D1311yescharacteristic
275#123—41no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—262no—
279C22⋊Q8—262no—
280C22⋊Q8—521no—
281C22⋊Q8—521no—
282#121—21no—
283#121—21no—
284#120—41no—
285C4×D4—41no—
286C4×D4—41no—
287#117—21no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4—521no—
290C2×C22⋊C4—521no—
291Q32—522no—
292SD32—522no—
293M32—522no—
294C2×C16—132no—
295C2×C16—132no—
296#107—132no—
297#107—261no—
298#107C22×D1311yescharacteristic
299#107C22×D1311yescharacteristic
300#106—21no—
301#103—21no—
302#103—21no—
303#103—262no—
304#103—262no—
305#102—21no—
306#102—21no—
307C2×C13—22no—
308C2×C13—41no—
309C2×C13—41no—
310C2×C13—161no—
311C2×C13#318611yescharacteristic
312C2×C13C2×#51011yescharacteristic
313C2×C13#341411yescharacteristic
314C24#610411yescharacteristic
315#41—42no—
316#41—42no—
317C2×Q8—21no—
318C2×Q8—262no—
319C2×Q8—522no—
320C2×Q8—522no—
321C2×Q8—521no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—521no—
330C22×C4—521no—
331C22×C4#610411yescharacteristic
332C22×C4#610411yescharacteristic
333C22×C4#610411yescharacteristic
334C22×C4C2×C22⋊D1311yescharacteristic
335C22×C4C2×C22⋊D1311yescharacteristic
336C22×C4C2×C22⋊D1311yescharacteristic
337Q16—22no—
338Q16—262no—
339Q16—262no—
340Q16—522no—
341SD16—42no—
342D8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8C2×C22⋊D1311yescharacteristic
350C2×C8C2×C22⋊D1311yescharacteristic
351C2×C8C2×C22⋊D1311yescharacteristic
352C2×C8C23×D1311yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—262no—
358C4⋊C4—521no—
359C4⋊C4—522no—
360C4⋊C4—522no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—522no—
367C22⋊C4—522no—
368C42—41no—
369C16—262no—
370C16—262no—
371C13#3376211yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23C2×#610411yescharacteristic
377C23C2×#610411yescharacteristic
378C23C2×#610411yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—522no—
382Q8—522no—
383Q8—1042no—
384D4—41no—
385D4—41no—
386D4—82no—
387D4—82no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—82no—
402C2×C4—522no—
403C2×C4—522no—
404C2×C4—1042no—
405C2×C4—1042no—
406C2×C4C2×#610411yescharacteristic
407C2×C4C2×#610411yescharacteristic
408C2×C4C2×#610411yescharacteristic
409C2×C4C22×C22⋊D1311yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8#8825112yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—44no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1171885612yes—
427C22C22×#610411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—1042no—
435C4—1042no—
436C4#1171950911yescharacteristic
437C4#1171952711yescharacteristic
438C2—22no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2#1312558411yescharacteristic
443C2C2×#1171885611yescharacteristic
444C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3050C2
socleC22×C13C22×D8
hypercenter#3050D13
hypocenterC13#33762
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#11718777C2semidirect
2. #13117044C2semidirect
3. #13117036C2semidirect
4. #13117019C2semidirect
5. #13116947C2semidirect
6. #13116942C2semidirect
7. #13116776C2semidirect
8. #13116769C2semidirect
9. #13116752C2semidirect
10. #13116447C2semidirect
25. C2×#88069C22semidirect
26. C2×#88067C22semidirect
34. #11718156C22semidirect
35. #11718154C22semidirect
39. #11718084C22semidirect
40. #11718084C22semidirect
41. #11718082C22semidirect
42. #11718081C22semidirect
371. C13#33762semidirect

Maximal subgroups

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

subgroupindex
C2×#117187772
#131170442
#131170362
#131170192
#131169472
#131169422
#131167762
#131167692
#131167522
#131164472
C13×#30502
#3376213