Finite Group Databasebeta

← #16784555

Subgroups — #16784555

Order 3328.

656 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#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3C2×#11718286C214yesmaximal
4C2×#11718634C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×#6101C2212yes—
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057C2212yes—
10C2×C22⋊#1057C2212yes—
11C2×C4⋊#1057—21no—
12C2×C4×#1057—21no—
13C2×#88071C412yes—
14#11718634—21no—
15#11718634—21no—
16#11718634—21no—
17#11718634—21no—
18#11718290—21no—
19#11718290—21no—
20#11718286—28no—
21C23×C4×C13C2×C412yes—
22C23×C4×C13C2×C411yescharacteristic
23C23×Dic13C2×C412yes—
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2311yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13C814yescomplemented
35C2×#6101—24no—
36C2×#6101—22no—
37C2×#6101—22no—
38C2×#6101—24no—
39C2×C4×Dic13—42no—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C22⋊#1057—22no—
45C22⋊#1057—24no—
46C22⋊#1057D414yes—
47C4⋊#1057—42no—
48C4×#1057—42no—
49#88071—22no—
50#88071—22no—
51#9650—131nomaximal, Sylow
52C24×C13C22×C411yescharacteristic
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—24no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C2×C812yes—
62C22×C4×C13M1612yes—
63C22×Dic13—22no—
64C22×Dic13—24no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—24no—
68C22×Dic13—22no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C2×C814yes—
75C22×Dic13C2×D411yescharacteristic
76C22×Dic13C2×D411yescharacteristic
77C22×Dic13C2×D412yes—
78C22×Dic13#4112yes—
79C2×#1057—24no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C4⋊Dic13—24no—
88C4⋊Dic13—24no—
89#6101—44no—
90#6101—42no—
91#6101—42no—
92C4×Dic13—22no—
93C4×Dic13—22no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C2×#389—131no—
97#1797—131no—
98C4×C22⋊C8—131no—
99C2×#324—134no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13C4×D412yes—
106C23×C13C22×C811yescharacteristic
107C23×C13C2×M1611yescharacteristic
108C23×C13#13112yes—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—24no—
112C2×C4×C13—24no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—84no—
117C2×C4×C13C22⋊C812yes—
118C2×C4×C13C22⋊C812yes—
119C2×C4×C13#9912yes—
120C2×C4×C13#10112yes—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—24no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—28no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—44no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—44no—
138C2×Dic13#10112yes—
139C2×Dic13#12112yes—
140C2×Dic13#12411yescharacteristic
141C2×Dic13#12711yescharacteristic
142#1057—44no—
143#1057—82no—
144C22×C4⋊C4—131no—
145C22×C4⋊C4—132no—
146C22×C4⋊C4#26111yescharacteristic
147C22×C42—131no—
148C2×C4⋊C8—261no—
149C2×C22⋊C8—132no—
150C2×C22⋊C8—132no—
151C2×C4×C8—261no—
152#389—261no—
153#389—261no—
154#389—261no—
155#389—261no—
156C2×#95—132no—
157#336—261no—
158#336—261no—
159#324—268no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13#39011yescharacteristic
169C22×C13C2×C22⋊C811yescharacteristic
170C22×C13#40811yescharacteristic
171C22×C13C2×#9911yescharacteristic
172C22×C13#41011yescharacteristic
173C22×C13C2×#10111yescharacteristic
174C22×C13C2×#10111yescharacteristic
175C22×C13C8×D412yes—
176C22×C13#43612yes—
177C4×C13—22no—
178C4×C13—82no—
179C4×C13#32414yescomplemented
180Dic13—22no—
181Dic13—21no—
182Dic13—21no—
183Dic13—22no—
184Dic13—44no—
185Dic13—41no—
186C23×C4—131no—
187C23×C4—132no—
188C23×C4—131no—
189C23×C4C2×#26112yes—
190C23×C4C2×#26111yescharacteristic
191C22×C8—262no—
192C22×C8—262no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—134no—
197C2×C4⋊C4—262no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—264no—
201C2×C4⋊C4—264no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—262no—
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—522no—
209C4⋊C8—522no—
210C22⋊C8—134no—
211C22⋊C8—262no—
212C22⋊C8—264no—
213C4×C8—522no—
214#95—262no—
215#95—262no—
216C2×C13—22no—
217C2×C13—22no—
218C2×C13C2×#32411yescharacteristic
219C2×C13#146111yescharacteristic
220C2×C13#147011yescharacteristic
221C2×C13#147211yescharacteristic
222C2×C13#195411yescharacteristic
223C2×C13#196411yescharacteristic
224C2×C13#196611yescharacteristic
225C24C22×#26111yescharacteristic
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—132no—
236C22×C4—132no—
237C22×C4—134no—
238C22×C4—131no—
239C22×C4—262no—
240C22×C4—262no—
241C22×C4—264no—
242C22×C4—262no—
243C22×C4—264no—
244C22×C4—262no—
245C22×C4—521no—
246C22×C4—521no—
247C22×C4—521no—
248C22×C4D13⋊C812yes—
249C22×C4#611812yes—
250C22×C4C22⋊#26111yescharacteristic
251C22×C4C22⋊#26111yescharacteristic
252C2×C8—264no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—522no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—264no—
261C4⋊C4—264no—
262C4⋊C4—524no—
263C4⋊C4—522no—
264C4⋊C4—522no—
265C42—262no—
266C42—262no—
267C42—521no—
268C42—521no—
269C13#965011yescharacteristic, complemented, Sylow
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23C2×D13⋊C811yescharacteristic
275C23C2×#611811yescharacteristic
276C23D4×#26112yes—
277C23#8824012yes—
278C23C2×C22⋊#26111yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—84no—
287C2×C4—132no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—132no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—268no—
298C2×C4—264no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4—524no—
305C2×C4—524no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4#8811112yes—
309C2×C4#8811112yes—
310C2×C4#8811312yes—
311C2×C4#8811912yes—
312C8—524no—
313C8—1042no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22#1171907312yes—
323C22#1171907612yes—
324C22C2×#8811111yescharacteristic
325C22C2×#8811311yescharacteristic
326C22#1171914211yescharacteristic
327C22#1171915111yescharacteristic
328C22#1171915911yescharacteristic
329C22D13⋊#10111yescharacteristic
330C22C2×#8811911yescharacteristic
331C4—22no—
332C4—82no—
333C4—262no—
334C4—262no—
335C4—261no—
336C4—261no—
337C4—521no—
338C4—524no—
339C4#1171828614yescomplemented
340C2—22no—
341C2—22no—
342C2C2×#1171828611yescharacteristic
343C2#1313008011yescharacteristic
344C2#1313011011yescharacteristic
345C2#1313011611yescharacteristic
346C2#1313095811yescharacteristic
347C2#1313097511yescharacteristic
348C2#1313097911yescharacteristic
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#9650
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
34. C2×C4⋊Dic13C8semidirect
179. C4×C13#324semidirect
269. C13#9650semidirect
339. C4#11718286semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
C2×#117182862
C2×#117186342
#965013