Finite Group Databasebeta

← #16785074

Subgroups — #16785074

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129674C214yesmaximal
4C2×#11718646C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13C412yes—
7C22×C4⋊Dic13C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057C2212yes—
10C2×C22⋊#1057C2212yes—
11C2×C4⋊#1057—21no—
12C2×C4×#1057—21no—
13C2×#88071C2212yes—
14#11718646—21no—
15#11718646—21no—
16#11718646—21no—
17#11718646—21no—
18#11718290—21no—
19#11718290—21no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C412yes—
24C23×Dic13C2311yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C814yescomplemented
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—44no—
36C2×C4⋊Dic13—42no—
37C2×C4×Dic13—42no—
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C22⋊#1057—22no—
43C22⋊#1057—24no—
44C22⋊#1057Q814yes—
45C4⋊#1057—42no—
46C4×#1057—42no—
47#88071—22no—
48#88071—22no—
49#9879—131nomaximal, Sylow
50C24×C13C22×C411yescharacteristic
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C2×C812yes—
60C22×C4×C13C2×C814yes—
61C22×C4×C13M1612yes—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—24no—
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13—41no—
69C22×Dic13—42no—
70C22×Dic13—42no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C22×Dic13C2×Q812yes—
76C22×Dic13#4112yes—
77C2×#1057—24no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C13×C4⋊C4—24no—
84C13×C4⋊C4—24no—
85C4⋊Dic13—44no—
86C4⋊Dic13—42no—
87C4⋊Dic13—42no—
88C4⋊Dic13—44no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C2×#389—131no—
94#1797—131no—
95C4×C22⋊C8—131no—
96#1280—134no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13C2×C22⋊C411yescharacteristic
102C23×C13C4×Q812yes—
103C23×C13C22×C811yescharacteristic
104C23×C13C2×M1611yescharacteristic
105C23×C13#13112yes—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—24no—
109C2×C4×C13—24no—
110C2×C4×C13—24no—
111C2×C4×C13—44no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—44no—
115C2×C4×C13C22⋊C812yes—
116C2×C4×C13C22⋊C812yes—
117C2×C4×C13#9912yes—
118C2×C4×C13#10112yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—44no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—84no—
135C2×Dic13#10012yes—
136C2×Dic13C22⋊Q812yes—
137C2×Dic13#12411yescharacteristic
138C2×Dic13C4⋊Q811yescharacteristic
139#1057—44no—
140#1057—82no—
141C22×C4⋊C4—132no—
142C22×C4⋊C4—131no—
143C22×C4⋊C4#26111yescharacteristic
144C22×C42—131no—
145C2×C4⋊C8—261no—
146C2×C22⋊C8—132no—
147C2×C22⋊C8—132no—
148C2×C4×C8—261no—
149#389—261no—
150#389—261no—
151#389—261no—
152#389—261no—
153C2×#95—132no—
154#336—261no—
155#336—261no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13#39111yescharacteristic
165C22×C13C2×C22⋊C811yescharacteristic
166C22×C13#40811yescharacteristic
167C22×C13C2×#9911yescharacteristic
168C22×C13#41011yescharacteristic
169C22×C13C2×#10011yescharacteristic
170C22×C13C2×#10111yescharacteristic
171C22×C13C8×Q812yes—
172C22×C13#44612yes—
173C4×C13—22no—
174C4×C13—44no—
175C4×C13#32414yes—
176Dic13—22no—
177Dic13—22no—
178Dic13—21no—
179Dic13—21no—
180Dic13—41no—
181Dic13—82no—
182C23×C4—131no—
183C23×C4—131no—
184C23×C4—132no—
185C23×C4C2×#26112yes—
186C23×C4C2×#26111yescharacteristic
187C22×C8—262no—
188C22×C8—262no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—262no—
193C2×C4⋊C4—262no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—522no—
197C2×C4⋊C4—524no—
198C2×C4⋊C4#105714yescomplemented
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42—522no—
204C4⋊C8—522no—
205C22⋊C8—134no—
206C22⋊C8—262no—
207C22⋊C8—264no—
208C4×C8—522no—
209#95—262no—
210#95—262no—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13C2×#32411yescharacteristic
214C2×C13#146011yescharacteristic
215C2×C13#147011yescharacteristic
216C2×C13#147111yescharacteristic
217C2×C13#198411yescharacteristic
218C2×C13#199611yescharacteristic
219C2×C13#199711yescharacteristic
220C24C22×#26111yescharacteristic
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—132no—
231C22×C4—132no—
232C22×C4—131no—
233C22×C4—262no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4—264no—
237C22×C4—521no—
238C22×C4—521no—
239C22×C4—521no—
240C22×C4—522no—
241C22×C4—522no—
242C22×C4C2×#105712yes—
243C22×C4C2×#105714yes—
244C22×C4#612212yes—
245C22×C4C22⋊#26111yescharacteristic
246C22×C4C22⋊#26111yescharacteristic
247C2×C8—264no—
248C2×C8—522no—
249C2×C8—522no—
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C4⋊C4—522no—
256C4⋊C4—524no—
257C4⋊C4—524no—
258C4⋊C4—522no—
259C42—262no—
260C42—262no—
261C42—521no—
262C42—521no—
263C13#987911yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#8824012yes—
269C23Q8×#26112yes—
270C23C22×#105711yescharacteristic
271C23C2×#612211yescharacteristic
272C23C2×C22⋊#26111yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—44no—
282C2×C4—132no—
283C2×C4—132no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—524no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—1044no—
302C2×C4#8810712yes—
303C2×C4#8811312yes—
304C2×C4C22⋊#105712yes—
305C2×C4C22⋊#105712yes—
306C8—524no—
307C8—1042no—
308C22—22no—
309C22—22no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22C2×#8810711yescharacteristic
317C22C2×#8811311yescharacteristic
318C22#1171914211yescharacteristic
319C22D13⋊#10011yescharacteristic
320C22Q8×#105712yes—
321C22#1171915812yes—
322C22#1171915911yescharacteristic
323C22(C2×#261)⋊Q811yescharacteristic
324C22C2×C22⋊#105711yescharacteristic
325C4—22no—
326C4—44no—
327C4—262no—
328C4—261no—
329C4—261no—
330C4—262no—
331C4—521no—
332C4—1042no—
333C4#1171828514yes—
334C2—22no—
335C2—22no—
336C2C2×#1171828511yescharacteristic
337C2#1313007611yescharacteristic
338C2#1313011011yescharacteristic
339C2#1313011311yescharacteristic
340C2#1313100511yescharacteristic
341C2#1313102611yescharacteristic
342C2#1313102911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#9879
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
30. C2×C13×C4⋊C4C8semidirect
198. C2×C4⋊C4#1057semidirect
263. C13#9879semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
#131296742
C2×#117186462
#987913