Finite Group Databasebeta

← #16781858

Subgroups — #16781858

Order 3328.

546 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
1#13130691C212yesmaximal
2C2×#11718254C211yesmaximal, characteristic, complemented
3C2×#11718253C211yesmaximal, characteristic, complemented
4#13129666C212yesmaximal, complemented
5C2×#11718368C211yesmaximal, characteristic
6C22×#6094C411yescharacteristic
7C22×#6094C411yescharacteristic
8C2×C42×D13C2211yescharacteristic
9C2×#88111—22no—
10C2×C4⋊#1057C2212yes—
11C2×C4⋊#1057C2212yes—
12C2×C13×#97C411yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15C2×#88043C411yescharacteristic
16#11718368—22no—
17#11718368—22no—
18#11718290—22no—
19#11718254—22no—
20#11718253—22no—
21C22×C4×D13C2×C411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×C4×D13Q811yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4×Dic13D411yescharacteristic
30C2×C4×Dic13Q811yescharacteristic
31C2×C4×Dic13C2311yescharacteristic
32C22×#1055C2×C411yescharacteristic
33C22×#1055C2×C411yescharacteristic
34C2×#6094—22no—
35C2×#6094—22no—
36C2×#6094—22no—
37C2×#6094—22no—
38C2×#6094—22no—
39C2×#6094C814yescomplemented
40C42×D13—21no—
41C42×D13—21no—
42C42×D13—21no—
43C42×D13—21no—
44#88111—44no—
45C4⋊#1057—22no—
46C4⋊#1057—22no—
47C4⋊#1057—22no—
48C4⋊#1057—22no—
49C13×#97—22no—
50C8×Dic13—21no—
51C8×Dic13—21no—
52C8×Dic13D412yes—
53C8×Dic13D412yes—
54#88043—22no—
55#8597—131nomaximal, Sylow
56C23×D13C4⋊C411yescharacteristic
57C22×C4×C13C4⋊C411yescharacteristic
58C22×C4×C13C4⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×Dic13C4⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×Q811yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—22no—
72C2×C4×D13—22no—
73C2×C4×D13—42no—
74C2×C4×D13C2×C812yes—
75C2×C4×D13M1612yes—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13C22⋊C412yes—
85C2×C8×C13C2×C812yes—
86C2×C8×C13M1612yes—
87C2×C8×C13M1612yes—
88C42×C13—21no—
89C42×C13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13C2×D411yescharacteristic
95C4×Dic13C2×D411yescharacteristic
96C4×Dic13#4111yescharacteristic
97C4×Dic13#4111yescharacteristic
98C2×#1055—21no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055C22⋊C412yes—
103C2×#1055C2×C812yes—
104#6094—28no—
105#6094—28no—
106C2×C4×M16—131no—
107#1797—132no—
108C2×#335—131no—
109C2×#334—131no—
110#1277—132no—
111C23×C13C2×C4⋊C411yescharacteristic
112C22×D13—21no—
113C22×D13—21no—
114C22×D13—22no—
115C22×D13—22no—
116C22×D13C4⋊C812yes—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13#11711yescharacteristic
123C2×C4×C13C22×C811yescharacteristic
124C2×C4×C13C2×M1611yescharacteristic
125C2×C4×C13C2×M1611yescharacteristic
126C2×C4×C13C2×M1611yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—22no—
130C2×Dic13C4⋊C812yes—
131C2×Dic13#12111yescharacteristic
132C2×Dic13#12111yescharacteristic
133C2×Dic13C22⋊Q811yescharacteristic
134C2×Dic13C22⋊Q811yescharacteristic
135C2×Dic13AGL(1,ℤ/8)12yes—
136C2×Dic13#13712yes—
137C4×D13—22no—
138C4×D13—22no—
139C4×D13—22no—
140C4×D13—22no—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—42no—
144C4×D13—41no—
145C4×D13—41no—
146#1057—82no—
147#1057—82no—
148C8×C13—22no—
149C8×C13C22⋊C814yescomplemented
150#1055—22no—
151#1055—22no—
152C22×M16—131no—
153C22×M16—131no—
154C22×C42—131no—
155C2×C4⋊C8—132no—
156C2×C4⋊C8—132no—
157C2×C22⋊C8—262no—
158C4×M16—262no—
159C4×M16—262no—
160C2×#97—131no—
161C2×#97#26111yescharacteristic
162C2×C4×C8—131no—
163C2×C4×C8—131no—
164#336—262no—
165#335—262no—
166#334—262no—
167C22×C13#38011yescharacteristic
168C22×C13C2×C4⋊C811yescharacteristic
169C22×C13#42311yescharacteristic
170C22×C13#42812yes—
171C22×C13#43012yes—
172C2×D13—22no—
173C2×D13—24no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—42no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×C22⋊C811yescharacteristic
180C4×C13#40711yescharacteristic
181C4×C13#43111yescharacteristic
182C4×C13#43211yescharacteristic
183Dic13—22no—
184Dic13—21no—
185Dic13—21no—
186Dic13#46812yes—
187Dic13#46911yescharacteristic
188Dic13#47011yescharacteristic
189C23×C4—131no—
190C23×C4—131no—
191C23×C4—131no—
192C2×M16—134no—
193C2×M16—262no—
194C2×M16—262no—
195C2×M16—262no—
196C2×M16—262no—
197C2×M16—262no—
198C22×C8—131no—
199C22×C8—131no—
200C22×C8—262no—
201C22×C8—262no—
202C22×C8C2×#26111yescharacteristic
203C22×C8C2×#26111yescharacteristic
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—261no—
208C2×C42—261no—
209C2×C42—261no—
210C2×C42—261no—
211C2×C42C2×#26111yescharacteristic
212C4⋊C8—262no—
213C4⋊C8—262no—
214C4⋊C8—262no—
215C4⋊C8—262no—
216C22⋊C8—524no—
217#97—22no—
218#97—262no—
219C4×C8—132no—
220C4×C8—132no—
221C4×C8—261no—
222C4×C8—261no—
223C2×C13#156512yes—
224C2×C13#156912yes—
225C2×C13#179711yescharacteristic
226C2×C13#180911yescharacteristic
227C2×C13#181111yescharacteristic
228D13—42no—
229C24—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—132no—
234C22×C4—132no—
235C22×C4—262no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—262no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—522no—
246C22×C4C4⋊#26111yescharacteristic
247C22×C4C4⋊#26111yescharacteristic
248C22×C4C22×#26111yescharacteristic
249M16—268no—
250M16—268no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—132no—
254C2×C8—132no—
255C2×C8—261no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C2×C8—522no—
263C2×C8—522no—
264C2×C8—522no—
265C2×C8D13⋊C812yes—
266C2×C8#611812yes—
267C2×C8#611812yes—
268C2×C8C22⋊#26112yes—
269C42—21no—
270C42—21no—
271C42—131no—
272C42—131no—
273C42—131no—
274C42—131no—
275C42—261no—
276C42—261no—
277C42—261no—
278C42—261no—
279C13#859711yescharacteristic, complemented, Sylow
280C23—132no—
281C23—261no—
282C23—262no—
283C23—262no—
284C23—261no—
285C23C2×C4⋊#26111yescharacteristic
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—132no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—261no—
298C2×C4—262no—
299C2×C4—261no—
300C2×C4—262no—
301C2×C4—262no—
302C2×C4—262no—
303C2×C4—262no—
304C2×C4—522no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4C2×D13⋊C811yescharacteristic
310C2×C4C2×#611811yescharacteristic
311C2×C4C2×#611811yescharacteristic
312C2×C4D13⋊M1611yescharacteristic
313C2×C4#8823711yescharacteristic
314C2×C4C2×C22⋊#26111yescharacteristic
315C8—22no—
316C8—262no—
317C8—262no—
318C8—1042no—
319C8—1042no—
320C8#8811114yescomplemented
321C22—264no—
322C22—262no—
323C22—522no—
324C22—521no—
325C22—521no—
326C22D13⋊(C4⋊C8)11yescharacteristic
327C22#1171905211yescharacteristic
328C22#1171909812yes—
329C22#1171910012yes—
330C22#1171913611yescharacteristic
331C4—41no—
332C4—41no—
333C4—132no—
334C4—131no—
335C4—131no—
336C4—262no—
337C4—261no—
338C4—261no—
339C4#1171905111yescharacteristic
340C4#1171905411yescharacteristic
341C4C2×#8811111yescharacteristic
342C4#1171912711yescharacteristic
343C2—522no—
344C2#1313038812yes—
345C2#1313040112yes—
346C2#1313069111yescharacteristic
347C2#1313071411yescharacteristic
348C2#1313071711yescharacteristic
subgroupG/H
centerC23C2×C4⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#97C4
socleC23×C13C2×C4⋊C4
prime radicalC23×D13C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#97#261
hypocenterC13#8597
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×#11718254C2semidirect
3. C2×#11718253C2semidirect
4. #13129666C2semidirect
39. C2×#6094C8semidirect
149. C8×C13C22⋊C8semidirect
279. C13#8597semidirect
320. C8#88111semidirect

Maximal subgroups

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

subgroupindex
#131306912
C2×#117182542
C2×#117182532
#131296662
C2×#117183682
#859713