Finite Group Databasebeta

← #15766688

Subgroups — #15766688

Order 3328.

398 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124633C211yesmaximal, characteristic
2#13113610C211yesmaximal, characteristic, complemented
3#13113494C211yesmaximal, characteristic, complemented
4#13113399C211yesmaximal, characteristic, complemented
5#13113157C211yesmaximal, characteristic
6#13112694C211yesmaximal, characteristic, complemented
7C13×#1804C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×#102—21no—
12C13×#382C2211yescharacteristic
13#11718876—21no—
14#11718670—22no—
15#11718669—21no—
16#11718668—21no—
17#11718625—21no—
18#11718586C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21C13×#340—21no—
22#11718117—22no—
23#11718078—21no—
24#11718073—21no—
25#11718071—22no—
26#11718044—22no—
27C22×D4×C13D411yescharacteristic
28C23×C4×C13—21no—
29C22×C8×C13—21no—
30C4×D4×C13—21no—
31C4×D4×C13—21no—
32C4×D4×C13—21no—
33C4×D4×C13—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38#88180—21no—
39#88178—21no—
40#88178—21no—
41C2×#6099—21no—
42#88124—21no—
43#88123D411yescharacteristic
44#88123D411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×#102—42no—
50C13×#95—21no—
51C13×#95—21no—
52#88072—22no—
53#88072—22no—
54C22⋊#1055—21no—
55C22⋊#1055D412yes—
56#88048—22no—
57#88047—22no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62C4×#1055—21no—
63C4×#1055—21no—
64#10469—131nomaximal, Sylow
65C24×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13—21no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13Q1612yes—
72C22×C4×C13—21no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—82no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C2×Dic26—21no—
81C2×Dic26—21no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C22⋊Dic13—41no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100#6101—41no—
101#6101—41no—
102C4×Dic13—41no—
103#6099—41no—
104#6099—41no—
105C2×#1055—22no—
106C2×#1055—22no—
107C2×#1055—41no—
108#3077—131no—
109#1804D1311yescharacteristic
110#1571—131no—
111#1542—131no—
112#1518—131no—
113#1460—131no—
114#1286—131no—
115C23×C13—22no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13#12111yescharacteristic
121D4×C13—22no—
122D4×C13—22no—
123D4×C13—41no—
124D4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—81no—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12311yescharacteristic
138C2×C4×C13#12311yescharacteristic
139C2×C4×C13#12411yescharacteristic
140C2×C4×C13C2×Q1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—41no—
145C2×Dic13—41no—
146Dic26—81no—
147Dic26—81no—
148C8×C13—81no—
149#1055—42no—
150#1055—42no—
151#1055—81no—
152#533—131no—
153C2×C4×D4C2×D1311yescharacteristic
154#478—262no—
155#476—261no—
156#474—261no—
157#431—131no—
158#431—131no—
159#428—261no—
160#423—131no—
161C2×C4⋊C8C2×D1311yescharacteristic
162#418—261no—
163C2×#102—21no—
164#382C2×D1311yescharacteristic
165#340—21no—
166#335—262no—
167#333—261no—
168#332—261no—
169#328—262no—
170#323—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—42no—
174C22×C13—82no—
175C22×C13—82no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13#39411yescharacteristic
179C22×C13#46711yescharacteristic
180C22×C13#46811yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—81no—
186C4×C13—161no—
187C4×C13#44911yescharacteristic
188C4×C13#45111yescharacteristic
189C4×C13#48411yescharacteristic
190C4×C13#48511yescharacteristic
191Dic13—81no—
192Dic13—81no—
193C22×D4C22⋊D1311yescharacteristic
194C23×C4—21no—
195C2×M16—261no—
196C22×C8—21no—
197C4⋊Q8—131no—
198C4⋊Q8—131no—
199#125—261no—
200C22⋊Q8—261no—
201C22⋊Q8—261no—
202C4×Q8—261no—
203C4×Q8—261no—
204C4×D4—21no—
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—21no—
208#117—261no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C22⋊D1311yescharacteristic
211C2×C22⋊C4—21no—
212C2×C42C22×D1311yescharacteristic
213#107—262no—
214#106—262no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—132no—
218C4⋊C8—261no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221#102—42no—
222#102—262no—
223#102—262no—
224C22⋊C8—132no—
225C22⋊C8—261no—
226C4×C8—261no—
227C4×C8—261no—
228#95—21no—
229#95—21no—
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—82no—
233C2×C13#203611yescharacteristic
234C2×C13#204811yescharacteristic
235C2×C13#205311yescharacteristic
236C24—21no—
237C2×Q8—261no—
238C2×Q8—261no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4#610712yes—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—82no—
250C22×C4D4×D1311yescharacteristic
251C22×C4#612911yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253M16—521no—
254M16—521no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—262no—
259C2×C8—262no—
260C2×C8—521no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—521no—
274C42—521no—
275C42#612711yescharacteristic
276C42#612711yescharacteristic
277C42D4×D1311yescharacteristic
278C42D4×D1311yescharacteristic
279C13#1046911yescharacteristic, complemented, Sylow
280C23—22no—
281C23—41no—
282C23—41no—
283C23—81no—
284C23—81no—
285C23#8819311yescharacteristic
286Q8—1041no—
287Q8—1041no—
288D4—22no—
289D4—22no—
290D4—41no—
291D4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4#8813711yescharacteristic
304C2×C4#8813811yescharacteristic
305C2×C4#8813811yescharacteristic
306C2×C4#8813911yescharacteristic
307C2×C4#8818311yescharacteristic
308C2×C4#8818611yescharacteristic
309C2×C4#8819111yescharacteristic
310C2×C4C2×#610711yescharacteristic
311C2×C4#8820411yescharacteristic
312C2×C4#8820511yescharacteristic
313C8—81no—
314C8—522no—
315C8—522no—
316C8—1041no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—82no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22#1171862011yescharacteristic
325C22#1171870311yescharacteristic
326C22#1171871211yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—161no—
333C4—1041no—
334C4—1041no—
335C4#1171863111yescharacteristic
336C4#1171865711yescharacteristic
337C4#1171869811yescharacteristic
338C4#1171871111yescharacteristic
339C2—21no—
340C2—21no—
341C2—82no—
342C2#1311603911yescharacteristic
343C2#1311610711yescharacteristic
344C2#1311614011yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1804C2
socleC22×C13#394
prime radicalC22×D4×C13D4
hypercenter#1804D13
hypocenterC13#10469
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13113610C2semidirect
3. #13113494C2semidirect
4. #13113399C2semidirect
6. #13112694C2semidirect
279. C13#10469semidirect

Maximal subgroups

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

subgroupindex
#131246332
#131136102
#131134942
#131133992
#131131572
#131126942
C13×#18042
#1046913