Finite Group Databasebeta

← #16019270

Subgroups — #16019270

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125422C211yesmaximal, characteristic, complemented
2#13116997C212yesmaximal, complemented
3#13116988C211yesmaximal, characteristic, complemented
4#13116983C211yesmaximal, characteristic, complemented
5#13116947C212yesmaximal
6#13116942C212yesmaximal, complemented
7#13116895C212yesmaximal, complemented
8#13116886C211yesmaximal, characteristic, complemented
9#13116881C211yesmaximal, characteristic, complemented
10#13116592C211yesmaximal, characteristic, complemented
11C13×#3168C211yesmaximal, characteristic
12C13×#529—21no—
13#11719175—21no—
14C13×#499C2211yescharacteristic
15C13×#495C2211yescharacteristic
16C13×#488—21no—
17C13×#467C2211yescharacteristic
18C13×#466C2211yescharacteristic
19C13×#465—21no—
20C4×C13×Q16C2211yescharacteristic
21C4×C13×SD16—21no—
22C4×C13×D8C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C2×#88069C2212yes—
25C2×#88067C2212yes—
26#11718777—21no—
27#11718777C2212yes—
28C2×#88052C2212yes—
29#11718360C2211yescharacteristic
30C4×Dic52—21no—
31C4×Dic52C2212yes—
32#11718343C2211yescharacteristic
33#11718342—21no—
34#11718156C2212yes—
35#11718154C2212yes—
36#11718084C2212yes—
37#11718084C2212yes—
38#11718082C2212yes—
39#11718081C2212yes—
40C4⋊#6090C2211yescharacteristic
41C4⋊#6090C2211yescharacteristic
42C4⋊#6090C2212yes—
43C2×C13×Q16C2311yescharacteristic
44C2×C13×SD16—21no—
45C2×C13×D8C2311yescharacteristic
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×#126—41no—
49C13×#125—21no—
50C13×#124—21no—
51C13×#123—41no—
52C13×C22⋊Q8—21no—
53C13×#121—21no—
54C4×Q8×C13—21no—
55C4×D4×C13—21no—
56C4×D4×C13—41no—
57C13×#117—41no—
58C2×C42×C13D411yescharacteristic
59#88180—41no—
60#88178—22no—
61#88178—41no—
62C2×Dic52—21no—
63C2×Dic52C2312yes—
64#88124—41no—
65#88123—21no—
66#88123—21no—
67C4×Dic26—22no—
68C4×Dic26—41no—
69C13×#107C2311yescharacteristic
70C13×#107C2311yescharacteristic
71C13×#106—21no—
72C13×#103—21no—
73C13×#103—21no—
74C13×#102—21no—
75C13×#102—21no—
76C4×C8×C13D411yescharacteristic
77C4×C8×C13D411yescharacteristic
78C4×C8×C13C2311yescharacteristic
79C4×C8×C13C2311yescharacteristic
80#88069—42no—
81#88067—42no—
82#88058—21no—
83#88058C2312yes—
84#88056—22no—
85#88056—22no—
86#88052—42no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33818—131nomaximal, Sylow
90C2×Q8×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—41no—
93C22×C4×C13—41no—
94C22×C4×C13D811yescharacteristic
95C22×C4×C13D811yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C2×Dic26—22no—
98C2×Dic26—41no—
99C13×Q16—21no—
100C13×Q16—21no—
101C13×SD16—42no—
102C13×D8—21no—
103C13×D8—21no—
104C2×C8×C13—21no—
105C2×C8×C13—21no—
106C2×C8×C13—41no—
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13C2×D411yescharacteristic
109C2×C8×C13C2×D411yescharacteristic
110C2×C8×C13C2411yescharacteristic
111C13×C4⋊C4—21no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4—41no—
116C13×C4⋊C4—41no—
117C13×C22⋊C4—41no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C13×C22⋊C4—41no—
121C13×C22⋊C4—41no—
122C42×C13—41no—
123C42×C13D811yescharacteristic
124C42×C13D811yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C22⋊Dic13—42no—
128C4⋊Dic13—22no—
129C4⋊Dic13—41no—
130C4⋊Dic13—41no—
131C4⋊Dic13—41no—
132#6101—42no—
133#6101—42no—
134C4×Dic13—42no—
135Dic52—22no—
136Dic52—22no—
137Dic52—42no—
138#6090—22no—
139#6090—22no—
140#3170—131no—
141#3168D1311yescharacteristic
142#2229—132no—
143#2227—131no—
144#2226—131no—
145#2220—132no—
146#2219—132no—
147#2211—132no—
148#2209—131no—
149#2208—131no—
150#2150—131no—
151C23×C13—41no—
152C23×C13C2×D811yescharacteristic
153Q8×C13—41no—
154Q8×C13—41no—
155D4×C13—41no—
156D4×C13—41no—
157D4×C13—82no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—22no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—82no—
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C2×D811yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13C22×D411yescharacteristic
172C2×Dic13—42no—
173C2×Dic13—42no—
174Dic26—42no—
175Dic26—42no—
176Dic26—82no—
177C8×C13—21no—
178C8×C13—21no—
179C8×C13—21no—
180C8×C13H(5,𝔽2)11yescharacteristic
181C8×C132−1+411yescharacteristic
182#533—261no—
183#529—21no—
184C2×Q32—132no—
185C2×SD32—132no—
186C2×M32—132no—
187#500—131no—
188#499C2×D1311yescharacteristic
189#495C2×D1311yescharacteristic
190#494—131no—
191#488—21no—
192#487—261no—
193#467—132no—
194#467—261no—
195#467C2×D1311yescharacteristic
196#466C2×D1311yescharacteristic
197#465—21no—
198C4×Q16—132no—
199C4×Q16—261no—
200C4×Q16C2×D1311yescharacteristic
201C4×SD16—21no—
202C4×D8C2×D1311yescharacteristic
203C2×C4×C8C2×D1311yescharacteristic
204#367—132no—
205#366—132no—
206C4⋊C16—131no—
207C4⋊C16—131no—
208C4⋊C16—132no—
209#358—132no—
210#358—132no—
211#358—132no—
212#357—132no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—81no—
217C22×C13—81no—
218C22×C13—81no—
219C22×C13C22×D811yescharacteristic
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13#51012yes—
228C4×C13#53711yescharacteristic
229C4×C13#57511yescharacteristic
230Dic13—82no—
231Dic13—82no—
232C2×Q16—132no—
233C2×Q16—261no—
234C2×Q16C22×D1311yescharacteristic
235C2×SD16—21no—
236C2×D8C22×D1311yescharacteristic
237C22×C8C22⋊D1311yescharacteristic
238C22×C8C22×D1311yescharacteristic
239C4⋊Q8—261no—
240C4⋊Q8—261no—
241#126—41no—
242#125—21no—
243#125—521no—
244#124—21no—
245#123—41no—
246C22⋊Q8—21no—
247C22⋊Q8—262no—
248C22⋊Q8—521no—
249#121—21no—
250C4×Q8—21no—
251C4×Q8—262no—
252C4×Q8—521no—
253C4×D4—21no—
254C4×D4—41no—
255#117—41no—
256#117—521no—
257C2×C42C22⋊D1311yescharacteristic
258Q32—522no—
259SD32—522no—
260M32—522no—
261C2×C16—132no—
262C2×C16—132no—
263#107—132no—
264#107—261no—
265#107C22×D1311yescharacteristic
266#107C22×D1311yescharacteristic
267#106—21no—
268#103—21no—
269#103—21no—
270#103—262no—
271#103—262no—
272#102—21no—
273#102—21no—
274C4×C8C22⋊D1311yescharacteristic
275C4×C8C22⋊D1311yescharacteristic
276C4×C8C22×D1311yescharacteristic
277C4×C8C22×D1311yescharacteristic
278C2×C13—41no—
279C2×C13—161no—
280C2×C13#324511yescharacteristic
281C2×C13C2×#51011yescharacteristic
282C2×C13#341411yescharacteristic
283C2×Q8—21no—
284C2×Q8—262no—
285C2×Q8—521no—
286C2×D4—21no—
287C2×D4—41no—
288C22×C4—41no—
289C22×C4#610411yescharacteristic
290C22×C4#610411yescharacteristic
291C22×C4C2×C22⋊D1311yescharacteristic
292Q16—21no—
293Q16—21no—
294Q16—262no—
295Q16—262no—
296Q16—522no—
297SD16—42no—
298D8—21no—
299D8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—41no—
303C2×C8C2×C22⋊D1311yescharacteristic
304C2×C8C2×C22⋊D1311yescharacteristic
305C2×C8C2×C22⋊D1311yescharacteristic
306C2×C8C23×D1311yescharacteristic
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—262no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C4⋊C4—522no—
317C4⋊C4—522no—
318C4⋊C4—521no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—522no—
325C42—41no—
326C42—522no—
327C42#610411yescharacteristic
328C42#610411yescharacteristic
329C42C2×C22⋊D1311yescharacteristic
330C42C2×C22⋊D1311yescharacteristic
331C16—262no—
332C16—262no—
333C13#3381811yescharacteristic, complemented, Sylow
334C23—41no—
335C23C2×#610411yescharacteristic
336Q8—41no—
337Q8—41no—
338Q8—522no—
339Q8—522no—
340Q8—1042no—
341D4—41no—
342D4—41no—
343D4—82no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—82no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4C2×#610411yescharacteristic
355C2×C4C2×#610411yescharacteristic
356C2×C4C2×#610411yescharacteristic
357C2×C4C2×#610411yescharacteristic
358C2×C4C2×#610411yescharacteristic
359C2×C4C22×C22⋊D1311yescharacteristic
360C8—21no—
361C8—21no—
362C8—21no—
363C8#8825611yescharacteristic
364C8#8825711yescharacteristic
365C22—21no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C22×#610411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—1042no—
380C4—1042no—
381C4#1171885612yes—
382C4#1171952711yescharacteristic
383C4#1171953811yescharacteristic
384C2—41no—
385C2—161no—
386C2#1312614311yescharacteristic
387C2C2×#1171885611yescharacteristic
388C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3168C2
socleC22×C13C22×D8
prime radicalC13×#466C22
hypercenter#3168D13
hypocenterC13#33818
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13125422C2semidirect
2. #13116997C2semidirect
3. #13116988C2semidirect
4. #13116983C2semidirect
6. #13116942C2semidirect
7. #13116895C2semidirect
8. #13116886C2semidirect
9. #13116881C2semidirect
10. #13116592C2semidirect
333. C13#33818semidirect

Maximal subgroups

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

subgroupindex
#131254222
#131169972
#131169882
#131169832
#131169472
#131169422
#131168952
#131168862
#131168812
#131165922
C13×#31682
#3381813