Finite Group Databasebeta

← #16780491

Subgroups — #16780491

Order 3328.

498 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#1057C211yesmaximal, characteristic
2#13130551C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal
4#13129672C212yesmaximal
5#13117307C211yesmaximal, characteristic
6C2×#88141C2211yescharacteristic
7C2×C4⋊#1057C2212yes—
8C2×C4×#1057—21no—
9C2×C4×#1057C2212yes—
10C13×#389C411yescharacteristic
11#11718646C411yescharacteristic
12#11718639—21no—
13C4⋊C4×Dic13—21no—
14C4⋊C4×Dic13C2211yescharacteristic
15#11718635C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718590C411yescharacteristic
18#11718316—21no—
19#11718309—21no—
20#11718290—21no—
21#11718290—21no—
22#11718290—21no—
23#11718244C418yescomplemented
24C22×Dic26C2×C411yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42#88141—22no—
43#88141C2×C414yes—
44C4⋊#1057—22no—
45C4⋊#1057C2×C414yes—
46C4×#1057—22no—
47C4×#1057—42no—
48C4×#1057C2×C414yes—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#8182—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C2×Dic26—22no—
69C2×Dic26—22no—
70C2×Dic26—21no—
71C2×Dic26C4212yes—
72C2×#1057—24no—
73C2×#1057—24no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4C4212yes—
82C42×C13—22no—
83C4⋊Dic13—22no—
84C4⋊Dic13—42no—
85#6101—24no—
86C4×Dic13—22no—
87C4×Dic13—24no—
88C4×Dic13—22no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13—42no—
92C4×Dic13SD1612yes—
93C4×Dic13Q1612yes—
94C4×Dic13C22×C412yes—
95C4×Dic13#4112yes—
96#2295—131no—
97C4×C4⋊C8—131no—
98#1744—131no—
99C2×Q8⋊C8—132no—
100#1279—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13#10312yes—
114C2×C4×C13C2×C4211yescharacteristic
115C2×C4×C13#11711yescharacteristic
116C2×C4×C13#13112yes—
117C2×C4×C13#13112yes—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13#10312yes—
132C2×Dic13C4×D412yes—
133C2×Dic13C4×D412yes—
134C2×Dic13C2×SD1611yescharacteristic
135C2×Dic13C2×Q1611yescharacteristic
136C2×Dic13#13512yes—
137Dic26—24no—
138Dic26—42no—
139#1057—44no—
140#1057—44no—
141C2×C4×Q8—131no—
142C2×C4⋊C8—132no—
143C2×C4×C8—132no—
144C2×C4×C8—261no—
145#391—131no—
146#391—131no—
147#389—131no—
148#389#26111yescharacteristic
149#387—261no—
150#387—261no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—261no—
153#376—261no—
154C43—131no—
155#336—261no—
156#336—261no—
157#336—261no—
158Q8⋊C8—138no—
159C22×C13C4×C22⋊C411yescharacteristic
160C22×C13#40811yescharacteristic
161C22×C13#40811yescharacteristic
162C22×C13C2×#10311yescharacteristic
163C22×C13#41611yescharacteristic
164C22×C13#42111yescharacteristic
165C22×C13#42111yescharacteristic
166C4×C13—22no—
167C4×C13—41no—
168C4×C13—42no—
169C4×C13—81no—
170C4×C13#40512yes—
171C4×C13#43312yes—
172Dic13—22no—
173Dic13—22no—
174Dic13—41no—
175Dic13—42no—
176Dic13—81no—
177Dic13C4×SD1612yes—
178Dic13C4×Q1612yes—
179C22×Q8—131no—
180C22×C8—262no—
181C22×C8—262no—
182C4×Q8—134no—
183C4×Q8—262no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C2×#26111yescharacteristic
189C2×C4⋊C4C2×#26111yescharacteristic
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42—261no—
198C2×C42C2×#26111yescharacteristic
199C4⋊C8—134no—
200C4⋊C8—262no—
201C4×C8—134no—
202C4×C8—262no—
203C4×C8—522no—
204#95—21no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211C2×C13#148111yescharacteristic
212C2×C13#148111yescharacteristic
213C2×C13#148211yescharacteristic
214C2×C13#148211yescharacteristic
215C2×C13#175011yescharacteristic
216C2×C13#175911yescharacteristic
217C2×C13C4×#10311yescharacteristic
218C2×Q8—132no—
219C2×Q8—261no—
220C2×Q8—262no—
221C2×Q8—262no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22⋊#26111yescharacteristic
232C22×C4C22×#26111yescharacteristic
233C2×C8—264no—
234C2×C8—264no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C2×C8—522no—
239C4⋊C4—21no—
240C4⋊C4—22no—
241C4⋊C4—42no—
242C4⋊C4—264no—
243C4⋊C4—262no—
244C4⋊C4—522no—
245C4⋊C4C4×#26112yes—
246C42—22no—
247C42—132no—
248C42—132no—
249C42—132no—
250C42—132no—
251C42—262no—
252C42—264no—
253C42—262no—
254C42—521no—
255C42—521no—
256C42—522no—
257C13#818211yescharacteristic, complemented, Sylow
258C23C2×C22⋊#26111yescharacteristic
259Q8—264no—
260Q8—522no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—132no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—132no—
276C2×C4—132no—
277C2×C4—132no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—262no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4#8811712yes—
292C2×C4C2×C4×#26111yescharacteristic
293C2×C4#8823711yescharacteristic
294C2×C4#8823812yes—
295C2×C4#8824012yes—
296C8—524no—
297C8—524no—
298C22C4×C22⋊#26111yescharacteristic
299C22#1171914011yescharacteristic
300C22#1171914611yescharacteristic
301C22C2×#8811711yescharacteristic
302C22#1171915911yescharacteristic
303C22#1171916511yescharacteristic
304C22#1171916611yescharacteristic
305C4—22no—
306C4—42no—
307C4—41no—
308C4—81no—
309C4—132no—
310C4—132no—
311C4—262no—
312C4—262no—
313C4—522no—
314C4—521no—
315C4—1041no—
316C4#1171907212yes—
317C4#1171907712yes—
318C2#1313014411yescharacteristic
319C2#1313014611yescharacteristic
320C2#1313014711yescharacteristic
321C2#1313015011yescharacteristic
322C2#1313056511yescharacteristic
323C2#1313059911yescharacteristic
324C2C4×#8811711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#8182
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
23. #11718244C4semidirect
257. C13#8182semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#10572
#131305512
C2×#117182442
#131296722
#131173072
#818213