Finite Group Databasebeta

← #15779997

Subgroups — #15779997

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×#88069C211yesmaximal, characteristic
2C2×#11718156C211yesmaximal, characteristic
3C2×#11718084C211yesmaximal, characteristic
4#13115697C211yesmaximal, characteristic
5#13112927C211yesmaximal, characteristic
6#13112914C211yesmaximal, characteristic
7C2×C4×C13×Q16C211yesmaximal, characteristic
8C22×C13×Q16C2211yescharacteristic
9C2×C4×Q8×C13—21no—
10C22×Dic52C2211yescharacteristic
11C4×C13×Q16—22no—
12C4×C13×Q16—22no—
13C2×C13×#107C2211yescharacteristic
14C2×C13×#103—21no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88069—22no—
17C2×#88069—22no—
18C2×#88069C414yescomplemented
19C2×#88058C2211yescharacteristic
20C2×#88056—21no—
21C22×#6090C2211yescharacteristic
22C22×#6090C2211yescharacteristic
23#11718590—21no—
24#11718156—22no—
25#11718084—22no—
26C22×Q8×C13—21no—
27C22×Dic26—21no—
28C2×C13×Q16—21no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16C2×C412yes—
32C2×C13×Q16D412yes—
33C2×C13×Q16D412yes—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13C2311yescharacteristic
36C4×Q8×C13—24no—
37C4×Q8×C13—42no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—41no—
40C2×C42×C13—41no—
41C2×C42×C13D411yescharacteristic
42C2×C4⋊Dic13—21no—
43C2×Dic52—21no—
44C2×Dic52—21no—
45C2×Dic52—21no—
46C2×Dic52—21no—
47C2×Dic52—21no—
48C2×Dic52C2×C412yes—
49C13×#107—21no—
50C13×#107D412yes—
51C13×#103—24no—
52C4×C8×C13—21no—
53C4×C8×C13—21no—
54#88071—41no—
55#88071—41no—
56#88069—28no—
57#88058—21no—
58#88058—21no—
59#88056—42no—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090—21no—
65C2×#6090C2×C412yes—
66#13015—131nomaximal, Sylow
67C2×Q8×C13—22no—
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13D811yescharacteristic
76C22×C4×C13D811yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—41no—
79C22×Dic13—41no—
80C2×Dic26—22no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C13×Q16—22no—
87C13×Q16—22no—
88C13×Q16—22no—
89C13×Q16C22⋊C414yes—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13C22×C411yescharacteristic
94C2×C8×C13C2×D411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13#4111yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C13×C4⋊C4—22no—
100C13×C4⋊C4—44no—
101C13×C4⋊C4—41no—
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—44no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107Dic52—22no—
108Dic52—22no—
109Dic52—41no—
110Dic52—41no—
111#6090—22no—
112#6090—41no—
113C22×Q32—131no—
114C2×C4×Q16D1311yescharacteristic
115C2×#358—131no—
116C2×#358—131no—
117#1969—131no—
118#1380—131no—
119#1374—131no—
120C23×C13C2×D811yescharacteristic
121Q8×C13—24no—
122Q8×C13—42no—
123Q8×C13—42no—
124Q8×C13—42no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13Q3212yescomplemented
137C2×C4×C13C4×D411yescharacteristic
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#13511yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×Dic13—42no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
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×Q16C2×D1311yescharacteristic
160C2×C4×Q8—21no—
161C2×Q32—134no—
162C2×Q32—262no—
163C2×Q32—262no—
164C22×C16—131no—
165C22×C16—131no—
166C4×Q16—22no—
167C4×Q16—22no—
168C2×#107—131no—
169C2×#107C2×D1311yescharacteristic
170C2×#103—21no—
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—44no—
185C4×C13—41no—
186C4×C13—82no—
187C4×C13#38611yescharacteristic
188C4×C13#44211yescharacteristic
189C4×C13#44911yescharacteristic
190C4×C13#46311yescharacteristic
191Dic13—82no—
192Dic13—161no—
193C22×Q8—21no—
194C22×Q8—261no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—132no—
199C2×Q16—261no—
200C2×Q16—261no—
201C2×Q16—261no—
202C2×Q16—261no—
203C2×Q16—261no—
204C2×Q16C4×D1312yes—
205C2×Q16D5212yes—
206C2×Q16C22⋊D1312yes—
207C22×C8C22⋊D1311yescharacteristic
208C22×C8C22×D1311yescharacteristic
209C4×Q8—24no—
210C4×Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—261no—
214C2×C42—41no—
215C2×C42C22⋊D1311yescharacteristic
216Q32—268no—
217C2×C16—132no—
218C2×C16—261no—
219C2×C16—261no—
220C2×C16—261no—
221C2×C16—261no—
222C2×C16—261no—
223#107—21no—
224#107—261no—
225#107—261no—
226#107C22⋊D1312yes—
227#103—24no—
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—22no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—262no—
247C2×Q8—521no—
248C2×Q8—521no—
249C2×Q8—521no—
250C2×Q8—521no—
251C2×Q8—521no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4#610411yescharacteristic
257C22×C4#610411yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259Q16—22no—
260Q16—22no—
261Q16—22no—
262Q16—262no—
263Q16—262no—
264Q16—521no—
265Q16—521no—
266Q16#610314yes—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8C2×C4×D1311yescharacteristic
271C2×C8C2×D5211yescharacteristic
272C2×C8#612711yescharacteristic
273C2×C8#612711yescharacteristic
274C2×C8C2×C22⋊D1311yescharacteristic
275C2×C8C2×C22⋊D1311yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—44no—
278C4⋊C4—41no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C42—21no—
282C42—21no—
283C42—44no—
284C16—262no—
285C16—521no—
286C13#1301511yescharacteristic, complemented, Sylow
287C23C2×#610411yescharacteristic
288Q8—24no—
289Q8—42no—
290Q8—42no—
291Q8—42no—
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—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—522no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4—1041no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4#8806912yescomplemented
314C2×C4C4×C22⋊D1311yescharacteristic
315C2×C4#8818411yescharacteristic
316C2×C4#8818611yescharacteristic
317C2×C4#8820311yescharacteristic
318C2×C4#8820411yescharacteristic
319C2×C4#8820711yescharacteristic
320C8—41no—
321C8C2×#610311yescharacteristic
322C8C4×C22⋊D1311yescharacteristic
323C8#8818311yescharacteristic
324C8#8818411yescharacteristic
325C22C4×#610411yescharacteristic
326C22#1171867611yescharacteristic
327C22#1171884011yescharacteristic
328C22C2×#8806911yescharacteristic
329C22#1171885511yescharacteristic
330C22#1171885611yescharacteristic
331C22#1171887811yescharacteristic
332C4—22no—
333C4—44no—
334C4—41no—
335C4—82no—
336C4—1042no—
337C4—2081no—
338C4#1171867511yescharacteristic
339C4#1171867711yescharacteristic
340C4#1171887411yescharacteristic
341C4#1171889911yescharacteristic
342C2#1311518411yescharacteristic
343C2C4×#8806911yescharacteristic
344C2#1311670511yescharacteristic
345C2#1311677011yescharacteristic
346C2#1311677611yescharacteristic
347C2#1311688611yescharacteristic
348C2#1311689811yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C4×C13×Q16C2
socle, prime radicalC23×C13C2×D8
cosocleC22×C8×C13C23
hypercenterC2×C4×Q16D13
hypocenterC13#13015
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
18. C2×#88069C4semidirect
136. C2×C4×C13Q32semidirect
286. C13#13015semidirect
313. C2×C4#88069semidirect

Maximal subgroups

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

subgroupindex
C22×#880692
C2×#117181562
C2×#117180842
#131156972
#131129272
#131129142
C2×C4×C13×Q162
#1301513