Finite Group Databasebeta

← #16778758

Subgroups — #16778758

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#13129657C212yesmaximal, complemented
4#13129656C212yesmaximal, complemented
5#13123184C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×#88198C411yescharacteristic
8C2×#88178C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057—21no—
11C2×C22⋊#1057—21no—
12C2×#88110—21no—
13#11718891C2211yescharacteristic
14#11718637C411yescharacteristic
15#11718635C2211yescharacteristic
16#11718633—21no—
17#11718633—21no—
18#11718603—21no—
19#11718603—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×Dic13D411yescharacteristic
26C23×Dic13D411yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C22×#1057—22no—
29C22×#1057—22no—
30C13×C22⋊Q8—42no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C22⋊Dic13—21no—
35#88198—42no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37#88178—42no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—42no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13C2311yescharacteristic
48C22⋊#1057—24no—
49C22⋊#1057—42no—
50#88110—42no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7707—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C2×Q8×C13—22no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—41no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C22×Dic13C2×D411yescharacteristic
79C2×Dic26—22no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×#1057—24no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—42no—
90C13×C22⋊C4—42no—
91C22⋊Dic13—42no—
92C4⋊Dic13—41no—
93#6101—42no—
94#6101—42no—
95#6101—42no—
96#6101—42no—
97#6101—42no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—41no—
101C4×Dic13—41no—
102#2857—131no—
103#1817—131no—
104#1749—131no—
105#1272—132no—
106#1272—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13#10012yes—
114C23×C13C2×C22⋊C411yescharacteristic
115Q8×C13—82no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—44no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#13112yes—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—44no—
138C2×Dic13—44no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13#9912yes—
146C2×Dic13#10412yes—
147C2×Dic13#13712yes—
148C2×Dic13#13712yes—
149Dic26—82no—
150#1057—44no—
151#1057—82no—
152C2×C4⋊Q8—131no—
153C2×C22⋊Q8—131no—
154C2×C22⋊Q8#26111yescharacteristic
155C22×C42—131no—
156C2×C22⋊C8—261no—
157C2×C22⋊C8—261no—
158C2×#97—261no—
159#391—131no—
160#391—131no—
161#389—261no—
162#389—261no—
163#384—131no—
164#380—261no—
165#380—261no—
166#336—132no—
167#336—132no—
168#336—261no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13#40811yescharacteristic
177C22×C13C2×#9911yescharacteristic
178C22×C13C2×#10011yescharacteristic
179C22×C13#41911yescharacteristic
180C22×C13#41911yescharacteristic
181C22×C13C2×#10411yescharacteristic
182C22×C13#42111yescharacteristic
183C4×C13—22no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187Dic13—22no—
188Dic13—22no—
189Dic13—22no—
190Dic13—22no—
191Dic13—81no—
192Dic13—81no—
193C22×Q8—131no—
194C22×Q8C2×#26111yescharacteristic
195C23×C4—131no—
196C23×C4—131no—
197C23×C4C2×#26111yescharacteristic
198C22×C8—262no—
199C22×C8—262no—
200C4⋊Q8—522no—
201C22⋊Q8—42no—
202C22⋊Q8—522no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4C2×#26111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—261no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—522no—
218C22⋊C8—264no—
219C22⋊C8—522no—
220#97—522no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225C2×C13—42no—
226C2×C13#147111yescharacteristic
227C2×C13#148511yescharacteristic
228C2×C13#149711yescharacteristic
229C2×C13#150811yescharacteristic
230C2×C13#151111yescharacteristic
231C2×C13#153011yescharacteristic
232C2×C13#155811yescharacteristic
233C24C22⋊#26111yescharacteristic
234C2×Q8—22no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—262no—
238C2×Q8—521no—
239C2×Q8—521no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—262no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4—262no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—521no—
256C22×C4—521no—
257C22×C4C22⋊#26111yescharacteristic
258C22×C4C22×#26111yescharacteristic
259C2×C8—264no—
260C2×C8—522no—
261C2×C8—522no—
262C2×C8—522no—
263C2×C8—522no—
264C2×C8—522no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—521no—
268C4⋊C4—522no—
269C4⋊C4—522no—
270C4⋊C4—522no—
271C4⋊C4—522no—
272C4⋊C4—522no—
273C22⋊C4—42no—
274C22⋊C4—522no—
275C42—262no—
276C42—262no—
277C42—521no—
278C42—521no—
279C13#770711yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23#8812112yes—
287C23C2×C22⋊#26111yescharacteristic
288Q8—82no—
289Q8—1042no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—132no—
303C2×C4—132no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—524no—
315C2×C4—524no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4#8823812yes—
323C8—524no—
324C8—1042no—
325C22—22no—
326C22—22no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22D13⋊#9911yescharacteristic
333C22#1171914611yescharacteristic
334C22#1171915311yescharacteristic
335C22#1171915311yescharacteristic
336C22D13⋊#10411yescharacteristic
337C22#1171916611yescharacteristic
338C22C2×#8812111yescharacteristic
339C4—22no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—262no—
344C4—262no—
345C4—262no—
346C4—262no—
347C4—1041no—
348C4—1041no—
349C2—42no—
350C2#1313011211yescharacteristic
351C2#1313015811yescharacteristic
352C2#1313019811yescharacteristic
353C2#1313023411yescharacteristic
354C2#1313024511yescharacteristic
355C2#1313030511yescharacteristic
356C2#1313036911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C22⋊Q8#261
hypocenterC13#7707
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129657C2semidirect
4. #13129656C2semidirect
279. C13#7707semidirect

Maximal subgroups

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

subgroupindex
#131307262
#131305622
#131296572
#131296562
#131231842
#770713