Finite Group Databasebeta

← #16778761

Subgroups — #16778761

Order 3328.

500 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 92 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
1#13130726C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129655C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5#13123186C211yesmaximal, characteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×#88142C411yescharacteristic
8C2×#88132—21no—
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11C2×#88110—21no—
12C13×#380C411yescharacteristic
13#11718873C411yescharacteristic
14#11718646C2211yescharacteristic
15#11718637C411yescharacteristic
16#11718634C2211yescharacteristic
17#11718603—21no—
18#11718308—21no—
19#11718307—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×Dic26—21no—
27C22×#1057—22no—
28C22×#1057—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—21no—
32C2×C22⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13—42no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88142—42no—
46#88132—44no—
47C22⋊#1057—24no—
48C22⋊#1057—42no—
49#88110—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7708—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—41no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C2×Dic26—42no—
76C2×Dic26—42no—
77C2×Dic26—42no—
78C2×#1057—24no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—22no—
89C4⋊Dic13—42no—
90C4⋊Dic13—41no—
91#6101—42no—
92#6101—42no—
93#6101—42no—
94#6101—42no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99#2857—131no—
100#1817—131no—
101#1749—131no—
102#1271—132no—
103#1271—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13#10112yes—
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—44no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13#13112yes—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—44no—
134C2×Dic13—44no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13#9912yes—
142C2×Dic13#10412yes—
143C2×Dic13AGL(1,ℤ/8)12yes—
144C2×Dic13#13712yes—
145Dic26—84no—
146#1057—44no—
147#1057—82no—
148C2×C4⋊Q8—131no—
149C2×C22⋊Q8—261no—
150C22×C42—131no—
151C2×C22⋊C8—261no—
152C2×C22⋊C8—261no—
153C2×#97—261no—
154#391—261no—
155#389—131no—
156#389—131no—
157#389—261no—
158#384—131no—
159#380—131no—
160#380—261no—
161#380#26111yescharacteristic
162#336—132no—
163#336—132no—
164#336—261no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13#40811yescharacteristic
173C22×C13C2×#9911yescharacteristic
174C22×C13C2×#10111yescharacteristic
175C22×C13#41811yescharacteristic
176C22×C13#41911yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C22×C13#42111yescharacteristic
179C4×C13—22no—
180C4×C13—41no—
181C4×C13—81no—
182C4×C13—81no—
183Dic13—22no—
184Dic13—22no—
185Dic13—22no—
186Dic13—22no—
187Dic13—81no—
188Dic13—81no—
189C22×Q8—261no—
190C23×C4—131no—
191C23×C4—131no—
192C23×C4C2×#26111yescharacteristic
193C22×C8—262no—
194C22×C8—262no—
195C4⋊Q8—522no—
196C22⋊Q8—524no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4C2×#26111yescharacteristic
205C2×C4⋊C4C2×#26111yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—261no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—522no—
213C22⋊C8—264no—
214C22⋊C8—522no—
215#97—522no—
216#95—21no—
217#95—261no—
218#95—261no—
219#95—261no—
220C2×C13—42no—
221C2×C13#147211yescharacteristic
222C2×C13#148411yescharacteristic
223C2×C13#149711yescharacteristic
224C2×C13#150811yescharacteristic
225C2×C13#151011yescharacteristic
226C2×C13#153111yescharacteristic
227C2×C13#155611yescharacteristic
228C24C22⋊#26111yescharacteristic
229C2×Q8—522no—
230C2×Q8—522no—
231C2×Q8—522no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4—262no—
244C22×C4—262no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4C22⋊#26111yescharacteristic
250C22×C4C22×#26111yescharacteristic
251C2×C8—264no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8—522no—
256C2×C8—522no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—262no—
260C4⋊C4—521no—
261C4⋊C4—522no—
262C4⋊C4—522no—
263C4⋊C4—522no—
264C4⋊C4—522no—
265C4⋊C4—522no—
266C22⋊C4—42no—
267C22⋊C4—522no—
268C42—262no—
269C42—262no—
270C42—521no—
271C42—521no—
272C13#770811yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#8811312yes—
280C23C2×C22⋊#26111yescharacteristic
281Q8—1044no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—44no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—132no—
295C2×C4—132no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—524no—
307C2×C4—524no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4#8823812yes—
315C8—524no—
316C8—1042no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22C2×#8811311yescharacteristic
325C22#1171913811yescharacteristic
326C22D13⋊#9911yescharacteristic
327C22#1171914611yescharacteristic
328C22#1171915311yescharacteristic
329C22D13⋊#10411yescharacteristic
330C22#1171916611yescharacteristic
331C4—22no—
332C4—41no—
333C4—81no—
334C4—81no—
335C4—262no—
336C4—262no—
337C4—262no—
338C4—262no—
339C4—1041no—
340C4—1041no—
341C2—42no—
342C2#1313011511yescharacteristic
343C2#1313015511yescharacteristic
344C2#1313019811yescharacteristic
345C2#1313023411yescharacteristic
346C2#1313024211yescharacteristic
347C2#1313030811yescharacteristic
348C2#1313036511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#7708
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129655C2semidirect
4. #13129654C2semidirect
272. C13#7708semidirect

Maximal subgroups

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

subgroupindex
#131307262
#131305622
#131296552
#131296542
#131231862
#770813