Finite Group Databasebeta

← #16778550

Subgroups — #16778550

Order 3328.

500 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130727C211yesmaximal, characteristic
2#13130692C211yesmaximal, characteristic
3#13129657C212yesmaximal, complemented
4#13129655C212yesmaximal, complemented
5#13117364C211yesmaximal, characteristic
6C2×#88178C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×#88141C411yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11C2×#88112—21no—
12C13×#380C411yescharacteristic
13C4⋊C4×Dic13C411yescharacteristic
14#11718635C2211yescharacteristic
15#11718634C2211yescharacteristic
16#11718607—21no—
17C22⋊C4×Dic13—21no—
18#11718313—21no—
19#11718310—21no—
20#11718290—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⋊Dic13C2×C411yescharacteristic
34#88178—22no—
35#88178—22no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—42no—
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13C2311yescharacteristic
46#88141—42no—
47C22⋊#1057—42no—
48C22⋊#1057—42no—
49#88112—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7648—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13SD1612yes—
75C22×Dic13Q1612yes—
76C22×Dic13C2×D411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26M1612yes—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C22⋊C4—42no—
91C22⋊Dic13—24no—
92C4⋊Dic13—21no—
93C4⋊Dic13M1612yes—
94#6101—24no—
95#6101—42no—
96#6101—42no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C4×Dic13—42no—
102C4×Dic13—42no—
103C4×C22⋊Q8—131no—
104#1817—131no—
105#1797—131no—
106#1272—132no—
107#1271—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13#10312yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13C2×M1611yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—22no—
140C2×Dic13—22no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—44no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13#9912yes—
149C2×Dic13#10312yes—
150C2×Dic13C2×SD1611yescharacteristic
151C2×Dic13C2×Q1611yescharacteristic
152C2×Dic13#13512yes—
153Dic26—42no—
154Dic26—42no—
155#1057—82no—
156#1057—82no—
157C2×C22⋊Q8—131no—
158C2×C4×Q8—131no—
159C22×C42—131no—
160C2×C4⋊C8—261no—
161C2×C22⋊C8—261no—
162C2×C22⋊C8—261no—
163#391—131no—
164#389—131no—
165#387—261no—
166#385—261no—
167#380#26111yescharacteristic
168C4×C4⋊C4—131no—
169C4×C4⋊C4—261no—
170C4×C22⋊C4—261no—
171#336—132no—
172#336—132no—
173#336—261no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13#40711yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13#41311yescharacteristic
184C22×C13C2×#10311yescharacteristic
185C22×C13#41611yescharacteristic
186C22×C13#42111yescharacteristic
187C22×C13#42111yescharacteristic
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—41no—
191C4×C13—81no—
192C4×C13—81no—
193Dic13—22no—
194Dic13—22no—
195Dic13—21no—
196Dic13—22no—
197Dic13—21no—
198Dic13—42no—
199Dic13—42no—
200C22×Q8—131no—
201C23×C4—131no—
202C23×C4—131no—
203C23×C4C2×#26111yescharacteristic
204C22×C8—262no—
205C22×C8—262no—
206C22⋊Q8—262no—
207C22⋊Q8—262no—
208C4×Q8—522no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4C2×#26111yescharacteristic
214C2×C4⋊C4C2×#26111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—261no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—261no—
222C2×C42—261no—
223C2×C42—522no—
224C4⋊C8—522no—
225C22⋊C8—522no—
226C22⋊C8—522no—
227#95—21no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—42no—
233C2×C13#146511yescharacteristic
234C2×C13#148711yescharacteristic
235C2×C13#148811yescharacteristic
236C2×C13#151611yescharacteristic
237C2×C13#152011yescharacteristic
238C2×C13#153511yescharacteristic
239C2×C13#154211yescharacteristic
240C24C22⋊#26111yescharacteristic
241C2×Q8—132no—
242C2×Q8—261no—
243C2×Q8—521no—
244C2×Q8—521no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4C22⋊#26111yescharacteristic
265C22×C4C22×#26111yescharacteristic
266C2×C8—522no—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—132no—
275C4⋊C4—264no—
276C4⋊C4—261no—
277C4⋊C4—522no—
278C4⋊C4—522no—
279C22⋊C4—42no—
280C22⋊C4—264no—
281C42—262no—
282C42—262no—
283C42—521no—
284C42—521no—
285C42—522no—
286C42—522no—
287C13#764811yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#8811712yes—
295C23C2×C22⋊#26111yescharacteristic
296Q8—522no—
297Q8—522no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—132no—
312C2×C4—131no—
313C2×C4—132no—
314C2×C4—131no—
315C2×C4—132no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—262no—
325C2×C4—262no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—524no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4D13⋊M1611yescharacteristic
334C2×C4D13⋊M1611yescharacteristic
335C8—1042no—
336C8—1042no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22#1171912611yescharacteristic
345C22#1171914011yescharacteristic
346C22D13⋊#9911yescharacteristic
347C22#1171914811yescharacteristic
348C22C2×#8811711yescharacteristic
349C22#1171916511yescharacteristic
350C22#1171916611yescharacteristic
351C4—21no—
352C4—21no—
353C4—41no—
354C4—81no—
355C4—81no—
356C4—262no—
357C4—262no—
358C4—261no—
359C4—262no—
360C4—261no—
361C4—522no—
362C4—522no—
363C2—42no—
364C2#1313009411yescharacteristic
365C2#1313016611yescharacteristic
366C2#1313016911yescharacteristic
367C2#1313026111yescharacteristic
368C2#1313027411yescharacteristic
369C2#1313032111yescharacteristic
370C2#1313033811yescharacteristic
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#7648
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. #13129655C2semidirect
287. C13#7648semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131306922
#131296572
#131296552
#131173642
#764813