Finite Group Databasebeta

← #16778739

Subgroups — #16778739

Order 3328.

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

normal subgroups only

This group has 470 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#13130690C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129657C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5#13123176C211yesmaximal, characteristic
6C2×#88178C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—21no—
9C2×C22⋊#1057—21no—
10C2×#88110—21no—
11C2×C4⋊#1057—21no—
12C13×#380C411yescharacteristic
13#11718646C411yescharacteristic
14#11718646C2211yescharacteristic
15#11718635C411yescharacteristic
16#11718635C2211yescharacteristic
17#11718611—21no—
18#11718604—21no—
19#11718314—21no—
20#11718314—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
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⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36#88178—42no—
37C2×#6101—21no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43C22⋊#1057—24no—
44C22⋊#1057—42no—
45#88110—42no—
46C4⋊#1057—42no—
47C13×#95—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7701—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—21no—
65C22×Dic13—21no—
66C22×Dic13—22no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C22×Dic13C2×D411yescharacteristic
76C2×Dic26—22no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×#1057—24no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—42no—
88C22⋊Dic13—42no—
89C4⋊Dic13—42no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—42no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98#2855—131no—
99#1797—131no—
100#1749—131no—
101#1272—132no—
102#1271—132no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13#10412yes—
110C23×C13C2×C22⋊C411yescharacteristic
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—44no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#9912yes—
123C2×C4×C13#13112yes—
124C2×Dic13—21no—
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—21no—
134C2×Dic13—44no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13AGL(1,ℤ/8)11yescharacteristic
144C2×Dic13#13711yescharacteristic
145C2×Dic13#13712yes—
146Dic26—82no—
147#1057—44no—
148#1057—82no—
149C2×C22⋊Q8—131no—
150C22×C42—131no—
151C2×C4⋊C8—261no—
152C2×C22⋊C8—261no—
153C2×C22⋊C8—261no—
154C2×#97—261no—
155#391—131no—
156#391—131no—
157#389—131no—
158#389—131no—
159#387—261no—
160#387—261no—
161#385—261no—
162#381—261no—
163#380#26111yescharacteristic
164#336—132no—
165#336—132no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13#40811yescharacteristic
174C22×C13C2×#9911yescharacteristic
175C22×C13#41311yescharacteristic
176C22×C13#41711yescharacteristic
177C22×C13#41911yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13#42111yescharacteristic
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—81no—
183C4×C13—81no—
184Dic13—22no—
185Dic13—21no—
186Dic13—21no—
187Dic13—41no—
188Dic13—41no—
189Dic13—81no—
190Dic13—81no—
191C22×Q8—131no—
192C23×C4—131no—
193C23×C4—131no—
194C23×C4C2×#26111yescharacteristic
195C22×C8—262no—
196C22×C8—262no—
197C22⋊Q8—522no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4C2×#26111yescharacteristic
203C2×C4⋊C4C2×#26111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—261no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—522no—
211C4⋊C8—522no—
212C22⋊C8—264no—
213C22⋊C8—522no—
214#97—522no—
215#95—21no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222C2×C13—42no—
223C2×C13#146811yescharacteristic
224C2×C13#148311yescharacteristic
225C2×C13#149711yescharacteristic
226C2×C13#150811yescharacteristic
227C2×C13#151311yescharacteristic
228C2×C13#153211yescharacteristic
229C2×C13#155911yescharacteristic
230C24C22⋊#26111yescharacteristic
231C2×Q8—262no—
232C2×Q8—521no—
233C2×Q8—521no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—261no—
244C22×C4—262no—
245C22×C4—261no—
246C22×C4—262no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—521no—
250C22×C4—521no—
251C22×C4—521no—
252C22×C4C22⋊#26111yescharacteristic
253C22×C4C22×#26111yescharacteristic
254C2×C8—264no—
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—522no—
267C22⋊C4—42no—
268C22⋊C4—522no—
269C42—262no—
270C42—262no—
271C42—521no—
272C42—521no—
273C13#770111yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23#8811612yes—
281C23C2×C22⋊#26111yescharacteristic
282Q8—1042no—
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—131no—
296C2×C4—131no—
297C2×C4—261no—
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—261no—
307C2×C4—524no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4#8810712yes—
317C2×C4#8823812yes—
318C8—524no—
319C8—1042no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22C2×#8810711yescharacteristic
328C22C2×#8811611yescharacteristic
329C22#1171914611yescharacteristic
330C22#1171914811yescharacteristic
331C22#1171915311yescharacteristic
332C22#1171916411yescharacteristic
333C22#1171916611yescharacteristic
334C4—22no—
335C4—22no—
336C4—81no—
337C4—81no—
338C4—261no—
339C4—261no—
340C4—262no—
341C4—521no—
342C4—521no—
343C4—1041no—
344C4—1041no—
345C2—42no—
346C2#1313010311yescharacteristic
347C2#1313015111yescharacteristic
348C2#1313019811yescharacteristic
349C2#1313023511yescharacteristic
350C2#1313025311yescharacteristic
351C2#1313031211yescharacteristic
352C2#1313037211yescharacteristic
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#7701
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. #13129657C2semidirect
4. #13129654C2semidirect
273. C13#7701semidirect

Maximal subgroups

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

subgroupindex
#131306902
#131305622
#131296572
#131296542
#131231762
#770113