Finite Group Databasebeta

← #15766527

Subgroups — #15766527

Order 3328.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11718692C211yesmaximal, characteristic
2#13113612C211yesmaximal, characteristic
3#13113509C211yesmaximal, characteristic
4#13113509C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic
6#13112731C211yesmaximal, characteristic
7C13×#1801C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C22×#6107—21no—
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C13×#423C2211yescharacteristic
13C2×C13×#101—21no—
14#11718692—22no—
15#11718692—22no—
16C2×#88050—21no—
17#11718586C2211yescharacteristic
18#11718586C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C13×#343—21no—
21Q8⋊#1055—22no—
22#11718074—22no—
23#11718074—22no—
24#11718071—22no—
25C22×Q8×C13D411yescharacteristic
26C22×Dic26—21no—
27C2×C13×M16—21no—
28C2×C13×M16—21no—
29C4×Q8×C13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6107—24no—
38C2×#6107—42no—
39C2×#6107—42no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C22×#1055—21no—
43#88123—21no—
44#88123—21no—
45#88123—21no—
46#88123D412yes—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×#101—42no—
52C22⋊#1055—21no—
53C22⋊#1055—21no—
54#88050—24no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055D412yes—
58C4⋊#1055D412yes—
59C4×#1055—21no—
60C4×#1055—21no—
61#10446—131nomaximal, Sylow
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13D812yes—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C22×Dic13—41no—
74C2×Dic26—22no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C13×M16—41no—
81C13×M16—41no—
82C13×M16—41no—
83C13×M16—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13#4111yescharacteristic
96#6107—48no—
97C4⋊Dic13—22no—
98C4⋊Dic13—22no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#462—131no—
107#1801D1311yescharacteristic
108#1571—131no—
109#1546—131no—
110#1546—131no—
111#1479—131no—
112#1301—131no—
113C23×C13#12311yescharacteristic
114Q8×C13—22no—
115Q8×C13—22no—
116Q8×C13—41no—
117Q8×C13—41no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—81no—
125C2×C4×C13#12011yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12311yescharacteristic
130C2×C4×C13#12411yescharacteristic
131C2×C4×C13C2×D811yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—42no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138Dic26—42no—
139Dic26—42no—
140Dic26—81no—
141Dic26—81no—
142C8×C13—81no—
143C8×C13—81no—
144#1055—42no—
145#1055—42no—
146#1055—81no—
147C22×Q16—261no—
148C2×C4⋊Q8—131no—
149C2×C4×Q8C2×D1311yescharacteristic
150#462—262no—
151#462—262no—
152#431—131no—
153#431—131no—
154#423C2×D1311yescharacteristic
155#423C2×D1311yescharacteristic
156C2×C4⋊C8—131no—
157C2×#103—261no—
158C2×#101—21no—
159#343—21no—
160#335—262no—
161#332—262no—
162#332—262no—
163Q8⋊C8—262no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13#39411yescharacteristic
167C22×C13#48011yescharacteristic
168C22×C13#48211yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—42no—
173C4×C13—81no—
174C4×C13#44711yescharacteristic
175C4×C13#45211yescharacteristic
176C4×C13#46611yescharacteristic
177C4×C13#46811yescharacteristic
178C4×C13#47312yes—
179Dic13—82no—
180C22×Q8—261no—
181C22×Q8C22⋊D1311yescharacteristic
182C2×Q16—264no—
183C2×Q16—522no—
184C2×Q16—522no—
185C2×M16—21no—
186C2×M16—21no—
187C22×C8—261no—
188C4⋊Q8—132no—
189C4⋊Q8—261no—
190C4⋊Q8—261no—
191C4⋊Q8—261no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C42—21no—
201C2×C42C22×D1311yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—132no—
207C4⋊C8—132no—
208C4⋊C8—261no—
209C4⋊C8—261no—
210#103—264no—
211#101—42no—
212C22⋊C8—261no—
213C22⋊C8—261no—
214C4×C8—261no—
215C4×C8—261no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13#203311yescharacteristic
219C2×C13#204711yescharacteristic
220C2×C13#204911yescharacteristic
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8—262no—
227C2×Q8—521no—
228C2×Q8—521no—
229C2×Q8—521no—
230C2×Q8—521no—
231C2×Q8—521no—
232C2×Q8#610412yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—521no—
236C22×C4#612711yescharacteristic
237C22×C4#612711yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239Q16—528no—
240M16—41no—
241M16—41no—
242M16—41no—
243M16—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—262no—
247C2×C8—262no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—262no—
256C4⋊C4—262no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C42—41no—
260C42—41no—
261C42D4×D1311yescharacteristic
262C42D4×D1311yescharacteristic
263C42D4×D1311yescharacteristic
264C42#612911yescharacteristic
265C13#1044611yescharacteristic, complemented, Sylow
266C23#8818311yescharacteristic
267Q8—22no—
268Q8—22no—
269Q8—41no—
270Q8—41no—
271Q8—522no—
272Q8—522no—
273Q8—1041no—
274Q8—1041no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4—522no—
283C2×C4—1041no—
284C2×C4—1041no—
285C2×C4#8813711yescharacteristic
286C2×C4#8813811yescharacteristic
287C2×C4#8813811yescharacteristic
288C2×C4#8813911yescharacteristic
289C2×C4C2×#610411yescharacteristic
290C2×C4#8819111yescharacteristic
291C2×C4#8819311yescharacteristic
292C2×C4#8819611yescharacteristic
293C2×C4#8820311yescharacteristic
294C2×C4#8820411yescharacteristic
295C8—81no—
296C8—81no—
297C8—522no—
298C8—522no—
299C8—1041no—
300C22—21no—
301C22—21no—
302C22#1171862011yescharacteristic
303C22#1171862811yescharacteristic
304C22#1171866411yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—1042no—
311C4#1171841612yes—
312C4#1171869711yescharacteristic
313C4#1171869911yescharacteristic
314C4#1171870811yescharacteristic
315C4#1171871011yescharacteristic
316C2—21no—
317C2—21no—
318C2#1311601811yescharacteristic
319C2#1311610211yescharacteristic
320C2#1311611611yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1801D13
hypocenterC13#10446
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
265. C13#10446semidirect

Maximal subgroups

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

subgroupindex
C2×#117186922
#131136122
#131135092
#131132312
#131127312
C13×#18012
#1044613