Finite Group Databasebeta

← #15779996

Subgroups — #15779996

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic104C211yesmaximal, characteristic
2C2×C4×Dic52C211yesmaximal, characteristic
3C2×#11718095C211yesmaximal, characteristic
4C2×#11718095C211yesmaximal, characteristic
5#13115697C211yesmaximal, characteristic
6#13112928C211yesmaximal, characteristic
7C13×#1374C211yesmaximal, characteristic
8C22×Dic52C2211yescharacteristic
9C22×Dic52C2211yescharacteristic
10C2×C4×Dic26—21no—
11C22×C13×C16C2211yescharacteristic
12C22×C13×C16C2211yescharacteristic
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88058C2211yescharacteristic
15C2×#88058C2211yescharacteristic
16C2×#88056—21no—
17C2×#88056—21no—
18#11718590—21no—
19C2×Dic104—22no—
20C2×Dic104—22no—
21C2×Dic104C414yescomplemented
22C4×Dic52—22no—
23C4×Dic52—22no—
24#11718095—22no—
25#11718095—22no—
26C22×Dic26—21no—
27C22×Dic26—21no—
28C22×C8×C13D411yescharacteristic
29C22×C8×C13C2311yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×#6101—41no—
34C2×C4×Dic13—41no—
35C2×Dic52—21no—
36C2×Dic52—21no—
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52—21no—
41C2×Dic52—21no—
42C2×Dic52—21no—
43C2×Dic52C2×C412yes—
44C2×Dic52C2×C412yes—
45C2×Dic52D412yes—
46C2×Dic52D412yes—
47C4×Dic26—24no—
48C4×Dic26—42no—
49C2×C13×C16—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C2×C13×C16—21no—
53C2×C13×C16—21no—
54C2×C13×C16C2×C412yes—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57#88071—41no—
58#88071—41no—
59#88058—21no—
60#88058—21no—
61#88058—21no—
62#88058D412yes—
63#88056—24no—
64#88056—42no—
65Dic104—28no—
66#13015—131nomaximal, Sylow
67C22×C4×C13D811yescharacteristic
68C22×C4×C13D811yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—22no—
77C2×Dic26—22no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×C8×C13—21no—
87C2×C8×C13—21no—
88C2×C8×C13—21no—
89C2×C8×C13C22×C411yescharacteristic
90C2×C8×C13C2×D411yescharacteristic
91C2×C8×C13C2×D411yescharacteristic
92C2×C8×C13C2×D411yescharacteristic
93C2×C8×C13#4111yescharacteristic
94C2×C8×C13#4111yescharacteristic
95C42×C13—21no—
96C42×C13—21no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101#6101—44no—
102C4×Dic13—44no—
103Dic52—22no—
104Dic52—22no—
105Dic52—22no—
106Dic52—22no—
107Dic52—22no—
108Dic52—41no—
109Dic52—41no—
110Dic52C22⋊C414yes—
111C13×C16—22no—
112C13×C16—41no—
113C22×Q32—131no—
114C2×C4×Q16—131no—
115C2×#358—131no—
116C2×#358—131no—
117#1969—131no—
118#1380—131no—
119#1374D1311yescharacteristic
120C23×C13C2×D811yescharacteristic
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13Q3212yescomplemented
127C2×C4×C13C4×D411yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#13511yescharacteristic
131C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145Dic26—24no—
146Dic26—42no—
147Dic26—42no—
148Dic26—42no—
149Dic26—42no—
150Dic26—42no—
151Dic26—81no—
152Dic26—81no—
153C8×C13—41no—
154C8×C13C2×C22⋊C411yescharacteristic
155C8×C13C4×D411yescharacteristic
156C8×C13#12111yescharacteristic
157C8×C13#12311yescharacteristic
158C22×Q16—131no—
159C22×Q16—131no—
160C2×C4×Q8—261no—
161C2×Q32—134no—
162C2×Q32—262no—
163C2×Q32—262no—
164C22×C16C2×D1311yescharacteristic
165C22×C16C2×D1311yescharacteristic
166C4×Q16—262no—
167C4×Q16—262no—
168C2×#107—131no—
169C2×#107—131no—
170C2×#103—261no—
171C2×#103—261no—
172C2×C4×C8C2×D1311yescharacteristic
173#391—261no—
174#358—262no—
175#358—262no—
176C22×C13C4×D811yescharacteristic
177C22×C13#44711yescharacteristic
178C22×C13#45911yescharacteristic
179C22×C13C2×Q3211yescharacteristic
180C22×C13#50811yescharacteristic
181C22×C13#51011yescharacteristic
182C22×C13#51011yescharacteristic
183C4×C13—22no—
184C4×C13—41no—
185C4×C13#38611yescharacteristic
186C4×C13#44211yescharacteristic
187C4×C13#44911yescharacteristic
188C4×C13#46311yescharacteristic
189Dic13—44no—
190Dic13—82no—
191Dic13—82no—
192Dic13—161no—
193C22×Q8—261no—
194C22×Q8—261no—
195C2×Q16—132no—
196C2×Q16—132no—
197C2×Q16—132no—
198C2×Q16—132no—
199C2×Q16—261no—
200C2×Q16—261no—
201C2×Q16—261no—
202C2×Q16—261no—
203C2×Q16—261no—
204C2×Q16—261no—
205C2×Q16—261no—
206C2×Q16—261no—
207C22×C8D5211yescharacteristic
208C22×C8C22×D1311yescharacteristic
209C4×Q8—264no—
210C4×Q8—522no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—521no—
214C2×C42—521no—
215C2×C42D5211yescharacteristic
216Q32—268no—
217C2×C16—21no—
218C2×C16—21no—
219C2×C16—21no—
220C2×C16—21no—
221C2×C16—21no—
222C2×C16C4×D1312yes—
223#107—132no—
224#107—261no—
225#107—261no—
226#107—261no—
227#103—264no—
228#103—522no—
229C4×C8—21no—
230C4×C8—21no—
231#95—521no—
232#95—521no—
233C2×C13#187911yescharacteristic
234C2×C13C4×Q3211yescharacteristic
235C2×C13#217611yescharacteristic
236C2×C13#218811yescharacteristic
237C2×C13#218911yescharacteristic
238C2×C13#220911yescharacteristic
239C2×C13#221111yescharacteristic
240C2×Q8—262no—
241C2×Q8—262no—
242C2×Q8—262no—
243C2×Q8—262no—
244C2×Q8—521no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×Q8—521no—
248C2×Q8—521no—
249C2×Q8—521no—
250C2×Q8—521no—
251C2×Q8—521no—
252C22×C4—521no—
253C22×C4—521no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4D10411yescharacteristic
257C22×C4D10411yescharacteristic
258C22×C4C2×D5211yescharacteristic
259Q16—134no—
260Q16—262no—
261Q16—262no—
262Q16—262no—
263Q16—262no—
264Q16—262no—
265Q16—521no—
266Q16—521no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8C2×C4×D1311yescharacteristic
271C2×C8#612711yescharacteristic
272C2×C8D4×D1311yescharacteristic
273C2×C8D4×D1311yescharacteristic
274C2×C8D4×D1311yescharacteristic
275C2×C8#613111yescharacteristic
276C4⋊C4—262no—
277C4⋊C4—524no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C42—21no—
282C42—21no—
283C42—524no—
284C16—22no—
285C16—41no—
286C13#1301511yescharacteristic, complemented, Sylow
287C23C2×D10411yescharacteristic
288Q8—264no—
289Q8—522no—
290Q8—522no—
291Q8—522no—
292Q8—522no—
293Q8—522no—
294Q8—1041no—
295Q8—1041no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—522no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4—1041no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4Dic10412yescomplemented
314C2×C4C4×D5211yescharacteristic
315C2×C4#8813611yescharacteristic
316C2×C4#8814911yescharacteristic
317C2×C4#8815811yescharacteristic
318C2×C4#8816211yescharacteristic
319C2×C4#8816211yescharacteristic
320C8—41no—
321C8C22⋊C4×D1311yescharacteristic
322C8#8813811yescharacteristic
323C8#8814711yescharacteristic
324C8#8814811yescharacteristic
325C22C4×D10411yescharacteristic
326C22#1171839311yescharacteristic
327C22#1171850411yescharacteristic
328C22#1171856511yescharacteristic
329C22C2×Dic10411yescharacteristic
330C22#1171857011yescharacteristic
331C22#1171857011yescharacteristic
332C4—22no—
333C4—41no—
334C4—524no—
335C4—1042no—
336C4—1042no—
337C4—2081no—
338C4#1171832611yescharacteristic
339C4#1171837211yescharacteristic
340C4#1171839511yescharacteristic
341C4#1171850511yescharacteristic
342C2#1311518311yescharacteristic
343C2C4×Dic10411yescharacteristic
344C2#1311670811yescharacteristic
345C2#1311677211yescharacteristic
346C2#1311677811yescharacteristic
347C2#1311688711yescharacteristic
348C2#1311689911yescharacteristic
subgroupG/H
centerC23C2×D104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1374C2
socle, prime radicalC23×C13C2×D8
cosocleC22×C8×C13C23
hypercenter#1374D13
hypocenterC13#13015
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
21. C2×Dic104C4semidirect
126. C2×C4×C13Q32semidirect
286. C13#13015semidirect
313. C2×C4Dic104semidirect

Maximal subgroups

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

subgroupindex
C22×Dic1042
C2×C4×Dic522
C2×#117180952
#131156972
#131129282
C13×#13742
#1301513