Finite Group Databasebeta

← #15757858

Subgroups — #15757858

Order 3328.

578 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11718721C211yesmaximal, characteristic
2#13115808C212yesmaximal, complemented
3C2×#11718132C211yesmaximal, characteristic
4#13112717C212yesmaximal, complemented
5C13×#2379C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7C22×#6107—21no—
8C22×#6105—21no—
9C2×#88123C2211yescharacteristic
10C13×#391—21no—
11C13×#388—22no—
12C13×#386—21no—
13C13×#385—22no—
14C13×#382C2212yes—
15#11718721—22no—
16#11718721C414yescomplemented
17C2×#88043C2212yes—
18C2×#88043C2211yescharacteristic
19#11718132—22no—
20#11718121—22no—
21#11718121—22no—
22C22×Q8×C13D411yescharacteristic
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C22×Dic26—21no—
26C13×#124—22no—
27C13×#124C2×C412yes—
28C13×#124D412yes—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4D412yes—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—21no—
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6107—24no—
38C2×#6107—42no—
39C2×#6107—42no—
40C2×#6105—24no—
41C2×#6105—42no—
42C2×#6105—42no—
43C2×C4⋊Dic13—22no—
44C22×#1055—21no—
45C22×#1055—22no—
46#88123—22no—
47#88123—21no—
48#88123C2×C412yescomplemented
49C13×#95—22no—
50C13×#95—22no—
51C13×#95—22no—
52#88043—21no—
53#88043—22no—
54#88043—22no—
55#88043C2×C412yescomplemented
56#9003—131nomaximal, Sylow
57C24×C13—21no—
58C2×Q8×C13—21no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13C22⋊C412yes—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13C22⋊C412yes—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—81no—
70C22×C4×C13—82no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×Dic13—41no—
74C2×Dic26—22no—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—81no—
83C13×C22⋊C4—24no—
84C13×C22⋊C4—24no—
85C13×C22⋊C4—81no—
86C13×C22⋊C4—82no—
87C42×C13—81no—
88C42×C13C22×C411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13#4112yes—
91#6107—48no—
92#6105—48no—
93C4⋊Dic13—24no—
94C4⋊Dic13—42no—
95C2×#1055—22no—
96C2×#1055—22no—
97C2×#1055—22no—
98C2×#1055—24no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#497—131no—
102#2379D1311yescharacteristic
103#1993—132no—
104C2×#329—131no—
105#1295—132no—
106C23×C13—22no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13#12011yescharacteristic
112Q8×C13—42no—
113Q8×C13—81no—
114D4×C13—42no—
115D4×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—84no—
130C2×C4×C13C2×C22⋊C411yescharacteristic
131C2×C4×C13C4×D412yes—
132C2×C4×C13#12112yes—
133C2×C4×C13#12311yescharacteristic
134C2×Dic13—42no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137Dic26—42no—
138Dic26—42no—
139Dic26—81no—
140Dic26—81no—
141#1055—24no—
142#1055—44no—
143C22×Q16—261no—
144C22×SD16—261no—
145C2×C4⋊Q8—131no—
146C2×#124C2×D1311yescharacteristic
147#497—134no—
148#497—262no—
149C2×#97—131no—
150C2×#97—132no—
151#391—21no—
152#388—22no—
153#386—21no—
154#385—22no—
155#382C2×D1312yes—
156#340—262no—
157#340—262no—
158#329—262no—
159C22×C13—44no—
160C22×C13—42no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—82no—
164C22×C13#38611yescharacteristic
165C22×C13#45311yescharacteristic
166C22×C13#45311yescharacteristic
167C22×C13#45512yes—
168C22×C13#45612yes—
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—42no—
174C4×C13—82no—
175C4×C13—82no—
176Dic13—82no—
177C22×Q8—261no—
178C22×Q8C22⋊D1311yescharacteristic
179C22×D4C22⋊D1311yescharacteristic
180C23×C4—21no—
181C2×Q16—264no—
182C2×Q16—522no—
183C2×Q16—522no—
184C2×SD16—264no—
185C2×SD16—522no—
186C2×SD16—522no—
187C22×C8—261no—
188C22×C8—262no—
189C4⋊Q8—132no—
190C4⋊Q8—261no—
191C4⋊Q8—262no—
192#124—22no—
193#124C4×D1312yes—
194#124D5212yes—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—262no—
197C2×C4⋊C4C22⋊D1312yes—
198C2×C4⋊C4C22⋊D1312yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—21no—
202C2×C42—21no—
203C2×C42C22×D1311yescharacteristic
204#97—132no—
205#97—261no—
206#97—262no—
207#97—262no—
208#95—22no—
209#95—22no—
210#95—22no—
211C2×C13—82no—
212C2×C13#165911yescharacteristic
213C2×C13#166011yescharacteristic
214C2×C13#166112yes—
215C2×C13#188212yes—
216C2×C13#188711yescharacteristic
217C24—21no—
218C2×Q8—21no—
219C2×Q8—41no—
220C2×Q8—41no—
221C2×Q8—262no—
222C2×Q8—521no—
223C2×Q8—521no—
224C2×Q8—521no—
225C2×Q8—521no—
226C2×Q8—521no—
227C2×Q8#610312yes—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4#610312yes—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—81no—
236C22×C4—82no—
237C22×C4—521no—
238C22×C4C2×C22⋊D1311yescharacteristic
239C22×C4C2×C22⋊D1312yes—
240Q16—528no—
241SD16—528no—
242C2×C8—262no—
243C2×C8—262no—
244C2×C8—262no—
245C2×C8—264no—
246C2×C8—522no—
247C2×C8—522no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—81no—
251C4⋊C4—264no—
252C4⋊C4—522no—
253C22⋊C4—24no—
254C22⋊C4—24no—
255C22⋊C4—81no—
256C22⋊C4—82no—
257C42—81no—
258C42C2×C4×D1311yescharacteristic
259C42C2×D5211yescharacteristic
260C42#612712yes—
261C13#900311yescharacteristic, complemented, Sylow
262C23—22no—
263C23—41no—
264C23—41no—
265C23—42no—
266C23—42no—
267C23#8820711yescharacteristic
268Q8—42no—
269Q8—81no—
270Q8—522no—
271Q8—522no—
272Q8—1041no—
273Q8—1041no—
274D4—42no—
275D4—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4—522no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4C2×#610311yescharacteristic
294C2×C4C4×C22⋊D1312yes—
295C2×C4#8818311yescharacteristic
296C2×C4#8818412yes—
297C8—264no—
298C8—524no—
299C22—44no—
300C22—42no—
301C22—81no—
302C22—81no—
303C22—82no—
304C22#1171887411yescharacteristic
305C22#1171890211yescharacteristic
306C22#1171890211yescharacteristic
307C22#1171890312yes—
308C22#1171890712yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—82no—
315C4—82no—
316C4—1042no—
317C2—82no—
318C2#1311414211yescharacteristic
319C2#1311414711yescharacteristic
320C2#1311415312yes—
321C2#1311520512yes—
322C2#1311523411yescharacteristic
subgroupG/H
centerC23#88207
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2379C2
socleC23×C13#120
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2379D13
hypocenterC13#9003
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2379

Complements

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

NH ≅ G/Ntype
2. #13115808C2semidirect
4. #13112717C2semidirect
16. #11718721C4semidirect
48. #88123C2×C4semidirect
55. #88043C2×C4semidirect
261. C13#9003semidirect

Maximal subgroups

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

subgroupindex
C2×#117187212
#131158082
C2×#117181322
#131127172
C13×#23792
#900313