Finite Group Databasebeta

← #15780088

Subgroups — #15780088

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718856C211yesmaximal, characteristic
2C2×#11718088C211yesmaximal, characteristic, complemented
3#13116548C211yesmaximal, characteristic
4#13115697C211yesmaximal, characteristic, complemented
5#13112946C211yesmaximal, characteristic, complemented
6#13112918C211yesmaximal, characteristic, complemented
7C2×C13×#443C211yesmaximal, characteristic
8C2×C13×#135C2211yescharacteristic
9C2×C13×#131—21no—
10C22×Dic52C2211yescharacteristic
11C13×#443—22no—
12C13×#443—22no—
13C2×C13×#108C2211yescharacteristic
14C2×C13×#104—21no—
15C2×C4×C8×C13C2211yescharacteristic
16#11718856—22no—
17#11718856C414yescomplemented
18C2×#88069—21no—
19C2×#88067—21no—
20C2×#88058C2211yescharacteristic
21C2×#88056—21no—
22C2×#88052C2211yescharacteristic
23C2×#88052C2211yescharacteristic
24#11718590—21no—
25#11718156—21no—
26#11718154—21no—
27#11718088—22no—
28C2×C13×#41—21no—
29C22×Dic26—21no—
30C13×#135—21no—
31C13×#135—21no—
32C13×#135C2×C412yes—
33C13×#135D412yes—
34C2×C13×Q16D411yescharacteristic
35C2×C13×SD16—21no—
36C2×C13×D8D411yescharacteristic
37C13×#131—24no—
38C13×#131—42no—
39C2×C13×M16—21no—
40C2×C13×M16—41no—
41C22×C8×C13—41no—
42C22×C8×C13D411yescharacteristic
43C22×C8×C13C2311yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C4⋊Dic13—21no—
46C2×Dic52—21no—
47C2×Dic52—21no—
48C2×Dic52—21no—
49C2×Dic52—21no—
50C2×Dic52—21no—
51C2×Dic52C2×C412yes—
52C13×#108—21no—
53C13×#108D412yes—
54C13×#104—24no—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57#88071—42no—
58#88069—24no—
59#88067—24no—
60#88058—21no—
61#88058—21no—
62#88056—41no—
63#88056—41no—
64#88052—21no—
65#88052—21no—
66#88052—21no—
67#88052C2×C412yes—
68C2×#6090—21no—
69C2×#6090—21no—
70#13028—131nomaximal, Sylow
71C13×#41—22no—
72C13×#41—22no—
73C13×#41—41no—
74C13×#41—41no—
75C2×Q8×C13—21no—
76C2×D4×C13—21no—
77C2×D4×C13—41no—
78C22×C4×C13—21no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—41no—
82C22×Dic13—41no—
83C2×Dic26—22no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C13×Q16—21no—
90C13×Q16C22⋊C412yes—
91C13×SD16—22no—
92C13×SD16—22no—
93C13×D8—21no—
94C13×D8C22⋊C412yes—
95C13×M16—22no—
96C13×M16—44no—
97C13×M16—41no—
98C2×C8×C13—21no—
99C2×C8×C13—21no—
100C2×C8×C13—44no—
101C2×C8×C13—41no—
102C2×C8×C13D811yescharacteristic
103C2×C8×C13D811yescharacteristic
104C2×C8×C13C22×C411yescharacteristic
105C2×C8×C13C2×D411yescharacteristic
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13C2×D411yescharacteristic
108C2×C8×C13#4111yescharacteristic
109C2×C8×C13#4111yescharacteristic
110C42×C13—21no—
111C42×C13—21no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114Dic52—22no—
115Dic52—22no—
116Dic52—41no—
117Dic52—41no—
118#6090—22no—
119#6090—41no—
120C2×#510—131no—
121C2×#443D1311yescharacteristic
122C2×#362—131no—
123#2139—131no—
124#1969—131no—
125#1387—131no—
126#1376—131no—
127C23×C13—41no—
128C23×C13AGL(1,ℤ/8)11yescharacteristic
129Q8×C13—22no—
130Q8×C13—41no—
131D4×C13—22no—
132D4×C13—42no—
133D4×C13—42no—
134D4×C13—41no—
135C2×C4×C13—22no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13C2×D811yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×Dic13—42no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—82no—
151C2×Dic13—81no—
152Dic26—42no—
153Dic26—42no—
154Dic26—81no—
155Dic26—81no—
156C8×C13—21no—
157C8×C13—21no—
158C8×C13—42no—
159C8×C13C2×C22⋊C411yescharacteristic
160C8×C13C4×D411yescharacteristic
161C8×C13#12111yescharacteristic
162C8×C13#12311yescharacteristic
163C2×#135C2×D1311yescharacteristic
164C22×Q16—131no—
165C2×#131—21no—
166#510—134no—
167#510—262no—
168C2×Q32—261no—
169C2×SD32—261no—
170C2×M32—131no—
171C2×M32—131no—
172#443—22no—
173#443—22no—
174C2×#108C2×D1311yescharacteristic
175C2×#107—131no—
176C2×#104—21no—
177C2×#103—261no—
178C2×C4×C8C2×D1311yescharacteristic
179#391—261no—
180#362—262no—
181#358—261no—
182#357—261no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—42no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#44211yescharacteristic
189C22×C13#44911yescharacteristic
190C22×C13#45911yescharacteristic
191C4×C13—42no—
192C4×C13—42no—
193C4×C13#38611yescharacteristic
194C4×C13C4×D811yescharacteristic
195C4×C13#44711yescharacteristic
196C4×C13#46311yescharacteristic
197Dic13—82no—
198Dic13—161no—
199C2×#41—21no—
200C22×Q8—261no—
201#135—21no—
202#135—21no—
203#135C4×D1312yes—
204#135C22⋊D1312yes—
205C2×Q16—132no—
206C2×Q16—261no—
207C2×Q16—261no—
208C2×Q16—261no—
209C2×Q16—261no—
210C2×Q16—261no—
211C2×Q16D5211yescharacteristic
212C2×SD16—21no—
213C2×D8D5211yescharacteristic
214#131—24no—
215#131—42no—
216C2×M16—21no—
217C2×M16—41no—
218C22×C8—41no—
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22×D1311yescharacteristic
221C2×C4⋊C4—261no—
222C2×C42C22⋊D1311yescharacteristic
223Q32—264no—
224SD32—264no—
225M32—132no—
226M32—261no—
227M32—261no—
228M32—261no—
229C2×C16—261no—
230C2×C16—261no—
231#108—21no—
232#108C22⋊D1312yes—
233#107—261no—
234#107—261no—
235#104—24no—
236#103—521no—
237#103—521no—
238C4×C8—21no—
239C4×C8—21no—
240#95—522no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13—82no—
244C2×C13#187911yescharacteristic
245C2×C13#221211yescharacteristic
246C2×C13#221411yescharacteristic
247#41—22no—
248#41—22no—
249#41—41no—
250#41—41no—
251C2×Q8—21no—
252C2×Q8—262no—
253C2×Q8—521no—
254C2×Q8—521no—
255C2×Q8—521no—
256C2×Q8—521no—
257C2×Q8—521no—
258C2×D4—21no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4C2×C22⋊D1311yescharacteristic
265Q16—21no—
266Q16—262no—
267Q16—262no—
268Q16—521no—
269Q16—521no—
270Q16#610312yes—
271SD16—22no—
272SD16—22no—
273D8—21no—
274D8#610312yes—
275M16—22no—
276M16—44no—
277M16—41no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—44no—
281C2×C8—41no—
282C2×C8#610411yescharacteristic
283C2×C8#610411yescharacteristic
284C2×C8C2×C4×D1311yescharacteristic
285C2×C8C2×D5211yescharacteristic
286C2×C8#612711yescharacteristic
287C2×C8#612711yescharacteristic
288C2×C8C2×C22⋊D1311yescharacteristic
289C2×C8C2×C22⋊D1311yescharacteristic
290C4⋊C4—521no—
291C4⋊C4—521no—
292C42—21no—
293C42—21no—
294C16—262no—
295C16—521no—
296C13#1302811yescharacteristic, complemented, Sylow
297C23—41no—
298C23#8820311yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—522no—
302Q8—522no—
303Q8—1041no—
304Q8—1041no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—522no—
316C2×C4—1041no—
317C2×C4—1041no—
318C2×C4—1042no—
319C2×C4—1041no—
320C2×C4C4×C22⋊D1311yescharacteristic
321C2×C4#8818411yescharacteristic
322C2×C4C2×#610411yescharacteristic
323C2×C4#8818611yescharacteristic
324C2×C4#8820411yescharacteristic
325C2×C4#8820711yescharacteristic
326C8—21no—
327C8—21no—
328C8—42no—
329C8C2×#610311yescharacteristic
330C8C4×C22⋊D1311yescharacteristic
331C8#8818311yescharacteristic
332C8#8818411yescharacteristic
333C22—21no—
334C22—21no—
335C22—42no—
336C22—81no—
337C22—81no—
338C22#1171867511yescharacteristic
339C22#1171867611yescharacteristic
340C22#1171889911yescharacteristic
341C4—42no—
342C4—42no—
343C4—1042no—
344C4—2081no—
345C4C4×#610411yescharacteristic
346C4#1171867711yescharacteristic
347C4#1171887411yescharacteristic
348C4#1171887811yescharacteristic
349C2—21no—
350C2—21no—
351C2—82no—
352C2#1311518411yescharacteristic
353C2#1311690511yescharacteristic
354C2#1311691711yescharacteristic
subgroupG/H
centerC22#11718676
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#443C2
socleC22×C13#459
prime radicalC2×C13×#135C22
cosocleC22×C8×C13C23
hypercenterC2×#443D13
hypocenterC13#13028
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#11718088C2semidirect
4. #13115697C2semidirect
5. #13112946C2semidirect
6. #13112918C2semidirect
17. #11718856C4semidirect
296. C13#13028semidirect

Maximal subgroups

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

subgroupindex
C2×#117188562
C2×#117180882
#131165482
#131156972
#131129462
#131129182
C2×C13×#4432
#1302813