Finite Group Databasebeta

← #16017628

Subgroups — #16017628

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125375C211yesmaximal, characteristic, complemented
2#13117000C212yesmaximal, complemented
3#13116993C212yesmaximal, complemented
4#13116988C212yesmaximal, complemented
5#13116973C212yesmaximal, complemented
6#13116622C211yesmaximal, characteristic, complemented
7C2×#11718081C211yesmaximal, characteristic, complemented
8#13116595C211yesmaximal, characteristic, complemented
9#13116548C211yesmaximal, characteristic
10#13116543C211yesmaximal, characteristic
11C13×#2951C211yesmaximal, characteristic
12C2×C13×#135C2211yescharacteristic
13C13×#520—21no—
14#11719224—21no—
15C13×#440—22no—
16C4×C13×Q16C2212yes—
17C4×C13×D8C2212yes—
18C2×C13×#107C2211yescharacteristic
19C13×#417—21no—
20C13×#405C2211yescharacteristic
21#11718782—21no—
22#11718767C2211yescharacteristic
23C2×#88058C2211yescharacteristic
24C2×#88052C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26#11718363—22no—
27#11718344C2212yes—
28#11718343C2212yes—
29#11718156C2211yescharacteristic
30#11718156C2212yes—
31#11718156C2211yescharacteristic
32#11718154C2211yescharacteristic
33#11718154C2212yes—
34#11718154C2211yescharacteristic
35#11718082C2212yes—
36#11718081C2212yes—
37#11718081C2212yes—
38#11718081C2212yes—
39C4⋊#6090C2212yes—
40C4⋊#6090C2212yes—
41C2×C13×#41—21no—
42C13×#135—22no—
43C13×#135Q814yescomplemented
44C2×C13×Q16C2311yescharacteristic
45C2×C13×SD16—21no—
46C2×C13×D8C2311yescharacteristic
47C2×C13×M16D411yescharacteristic
48C22×C8×C13C2311yescharacteristic
49C4×Q8×C13—22no—
50C4×D4×C13—22no—
51C4×D4×C13—42no—
52C13×#117—41no—
53C13×#117D411yescharacteristic
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—41no—
56#88180—21no—
57C2×C4⋊Dic13—21no—
58#88144—41no—
59#88142—41no—
60#88132—42no—
61#88124—22no—
62#88123—22no—
63C13×#107—21no—
64C13×#107C2312yes—
65C13×#103—22no—
66C13×#102—22no—
67C13×#97D412yes—
68C4×C8×C13C2312yes—
69#88058—21no—
70#88058—22no—
71#88058C2312yes—
72#88058C2311yescharacteristic
73#88058C2311yescharacteristic
74#88057—21no—
75#88057—22no—
76#88052—22no—
77C2×#6090—22no—
78C2×#6090C2311yescharacteristic
79C2×#6090C2311yescharacteristic
80C2×#6090C2312yes—
81#33633—131nomaximal, Sylow
82C13×#41—24no—
83C13×#41—42no—
84C2×Q8×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13—42no—
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—41no—
92C2×Dic26—42no—
93C13×Q16—21no—
94C13×Q16C2×Q812yes—
95C13×SD16—24no—
96C13×D8—21no—
97C13×D8C2×Q812yes—
98C13×M16—22no—
99C2×C8×C13C2×D412yes—
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×Q812yes—
102C2×C8×C13#4112yes—
103C2×C8×C13C2411yescharacteristic
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—42no—
107C13×C4⋊C4D811yescharacteristic
108C13×C4⋊C4D811yescharacteristic
109C13×C22⋊C4—42no—
110C13×C22⋊C4D812yes—
111C42×C13—42no—
112C42×C13C2×D412yes—
113C22⋊Dic13—41no—
114C4⋊Dic13—21no—
115C4⋊Dic13—22no—
116C4⋊Dic13—21no—
117C4⋊Dic13—42no—
118C4⋊Dic13—41no—
119#6101—42no—
120#6101—42no—
121C4×Dic13—41no—
122#6090—21no—
123#6090—21no—
124#6090—22no—
125#3164—131no—
126#2951D1311yescharacteristic
127#2229—132no—
128#2228—132no—
129#2227—132no—
130#2224—132no—
131#2159—131no—
132C2×#366—131no—
133#2151—131no—
134#2139—131no—
135#2138—131no—
136C23×C13—41no—
137C23×C13C2×D811yescharacteristic
138Q8×C13—22no—
139Q8×C13—41no—
140D4×C13—22no—
141D4×C13—44no—
142D4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—44no—
145C2×C4×C13—42no—
146C2×C4×C13—162no—
147C2×C4×C13—161no—
148C2×C4×C13C22⋊Q812yes—
149C2×C4×C13C2×D812yes—
150C2×C4×C13C2×D812yes—
151C2×C4×C13C2×D811yescharacteristic
152C2×C4×C13#13712yes—
153C2×C4×C13C22×D411yescharacteristic
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—42no—
157C2×Dic13—161no—
158Dic26—162no—
159C8×C13—22no—
160C8×C13C22⋊Q812yes—
161C8×C13C22×Q811yescharacteristic
162C8×C13C2×#4111yescharacteristic
163C2×#135C2×D1311yescharacteristic
164#544—261no—
165#520—21no—
166C2×M32—131no—
167C22×C16—131no—
168#501—262no—
169#500—132no—
170#499—132no—
171#440—22no—
172C4×Q16C2×D1312yes—
173C4×D8C2×D1312yes—
174#428—261no—
175#427—131no—
176C2×#107—131no—
177C2×#107C2×D1311yescharacteristic
178#417—21no—
179#405C2×D1311yescharacteristic
180#367—132no—
181#366—132no—
182#366—132no—
183#366—132no—
184C4⋊C16—132no—
185C4⋊C16—132no—
186#358—131no—
187#358—131no—
188#358—132no—
189#357—131no—
190#357—131no—
191#357—132no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—42no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13#47412yes—
198C22×C13C22×D811yescharacteristic
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—42no—
202C4×C13—82no—
203C4×C13#47412yes—
204C4×C13C2×C22⋊Q811yescharacteristic
205C4×C13C2×#13711yescharacteristic
206Dic13—81no—
207Dic13—82no—
208Dic13—81no—
209C2×#41—21no—
210#135—22no—
211#135Dic2614yescomplemented
212C2×Q16C22×D1311yescharacteristic
213C2×SD16—21no—
214C2×D8C22×D1311yescharacteristic
215C2×M16C22⋊D1311yescharacteristic
216C22×C8C22×D1311yescharacteristic
217C4⋊Q8—262no—
218C4⋊Q8—521no—
219#125—262no—
220#125—521no—
221C22⋊Q8—522no—
222C4×Q8—22no—
223C4×D4—22no—
224C4×D4—42no—
225#117—41no—
226#117—261no—
227#117C22⋊D1311yescharacteristic
228C2×C4⋊C4—21no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—261no—
231M32—262no—
232C2×C16—131no—
233C2×C16—131no—
234C2×C16—132no—
235C2×C16—262no—
236#107—21no—
237#107—132no—
238#107—131no—
239#107—131no—
240#107—261no—
241#107—262no—
242#107C22×D1312yes—
243#106—261no—
244#106—262no—
245#103—22no—
246#102—22no—
247#97C22⋊D1312yes—
248C4×C8C22×D1312yes—
249C2×C13—22no—
250C2×C13—82no—
251C2×C13C2×#47411yescharacteristic
252C2×C13#341511yescharacteristic
253C2×C13#341711yescharacteristic
254#41—24no—
255#41—42no—
256C2×Q8—21no—
257C2×Q8—522no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—521no—
264C22×C4C2×C22⋊D1311yescharacteristic
265Q16—21no—
266Q16C2×Dic2612yes—
267SD16—24no—
268D8—21no—
269D8C2×Dic2612yes—
270M16—22no—
271C2×C8C2×Dic2612yes—
272C2×C8#612712yes—
273C2×C8C2×C22⋊D1312yes—
274C2×C8C2×C22⋊D1311yescharacteristic
275C2×C8C23×D1311yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—261no—
280C4⋊C4—262no—
281C4⋊C4—261no—
282C4⋊C4—521no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C4⋊C4—522no—
286C4⋊C4#610411yescharacteristic
287C4⋊C4#610411yescharacteristic
288C22⋊C4—42no—
289C22⋊C4—521no—
290C22⋊C4#610412yes—
291C42—42no—
292C42—521no—
293C42C2×C22⋊D1312yes—
294C16—261no—
295C16—261no—
296C16—262no—
297C13#3363311yescharacteristic, complemented, Sylow
298C23—41no—
299C23C2×#610411yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—2082no—
303D4—22no—
304D4—44no—
305D4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—162no—
310C2×C4—161no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—522no—
314C2×C4—2081no—
315C2×C4#8817812yes—
316C2×C4C2×#610412yes—
317C2×C4C2×#610412yes—
318C2×C4C2×#610411yescharacteristic
319C2×C4#8820512yes—
320C2×C4C22×C22⋊D1311yescharacteristic
321C8—22no—
322C8#8817812yes—
323C8C22×Dic2611yescharacteristic
324C8C2×#612711yescharacteristic
325C22—21no—
326C22—21no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22#1171866812yes—
331C22C22×#610411yescharacteristic
332C4—22no—
333C4—22no—
334C4—42no—
335C4—82no—
336C4—1042no—
337C4—1041no—
338C4—1041no—
339C4#1171866812yes—
340C4C2×#8817811yescharacteristic
341C4C2×#8820511yescharacteristic
342C2—22no—
343C2—82no—
344C2C2×#1171866811yescharacteristic
345C2#1312797511yescharacteristic
346C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2951C2
socleC22×C13C22×D8
prime radicalC2×C13×#135C22
hypercenter#2951D13
hypocenterC13#33633
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #13125375C2semidirect
2. #13117000C2semidirect
3. #13116993C2semidirect
4. #13116988C2semidirect
5. #13116973C2semidirect
6. #13116622C2semidirect
7. C2×#11718081C2semidirect
8. #13116595C2semidirect
43. C13×#135Q8semidirect
211. #135Dic26semidirect
297. C13#33633semidirect

Maximal subgroups

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

subgroupindex
#131253752
#131170002
#131169932
#131169882
#131169732
#131166222
C2×#117180812
#131165952
#131165482
#131165432
C13×#29512
#3363313