Finite Group Databasebeta

← #16782196

Subgroups — #16782196

Order 3328.

514 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 114 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#13130692C211yesmaximal, characteristic
2#13130692C211yesmaximal, characteristic
3#13129714C212yesmaximal, complemented
4#13129714C212yesmaximal, complemented
5#13117238C211yesmaximal, characteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×#88131—21no—
8C2×C22⋊#1057—21no—
9C2×C22⋊#1057—21no—
10C2×#88112C2212yes—
11C2×#88112C2212yes—
12C13×#380C411yescharacteristic
13#11718873C411yescharacteristic
14#11718637C2211yescharacteristic
15#11718637C2211yescharacteristic
16C4⋊C4×Dic13C411yescharacteristic
17C4⋊C4×Dic13C411yescharacteristic
18#11718603—21no—
19#11718311—21no—
20#11718310—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C22⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—24no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88131—44no—
46C22⋊#1057—42no—
47C22⋊#1057—42no—
48#88112—24no—
49#88112—24no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#8727—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
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—21no—
70C22×Dic13—21no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13SD1612yes—
74C22×Dic13Q1612yes—
75C22×Dic13C2×D411yescharacteristic
76C22×Dic13C2×D411yescharacteristic
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89#6101—42no—
90#6101—42no—
91#6101—42no—
92#6101—41no—
93#6101—41no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—42no—
98C4×Dic13—42no—
99C4×Dic13#4114yes—
100#2285—131no—
101#1797—131no—
102#1797—131no—
103#1296—132no—
104#1296—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13#10312yes—
112C23×C13C2×C22⋊C411yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—44no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13#11712yes—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—24no—
129C2×Dic13—24no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13#10312yes—
142C2×Dic13#12312yes—
143C2×Dic13#12312yes—
144C2×Dic13C2×SD1611yescharacteristic
145C2×Dic13C2×Q1611yescharacteristic
146C2×Dic13#13512yes—
147C2×Dic13AGL(1,ℤ/8)12yes—
148C2×Dic13AGL(1,ℤ/8)11yescharacteristic
149C2×Dic13#13711yescharacteristic
150#1057—82no—
151#1057—82no—
152C2×#117—261no—
153C22×C42—131no—
154C2×C4⋊C8—132no—
155C2×C4⋊C8—132no—
156C2×C22⋊C8—261no—
157C2×C22⋊C8—261no—
158#384—131no—
159#384—131no—
160#382—261no—
161#380—131no—
162#380—261no—
163#380#26111yescharacteristic
164C4×C4⋊C4—131no—
165C4×C4⋊C4—131no—
166C4×C4⋊C4—261no—
167#336—261no—
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#38111yescharacteristic
177C22×C13#41311yescharacteristic
178C22×C13#41311yescharacteristic
179C22×C13C2×#10311yescharacteristic
180C22×C13#41611yescharacteristic
181C22×C13#41711yescharacteristic
182C22×C13#41811yescharacteristic
183C4×C13—22no—
184C4×C13—41no—
185C4×C13—81no—
186C4×C13—81no—
187Dic13—22no—
188Dic13—41no—
189Dic13—81no—
190Dic13—81no—
191Dic13#48112yes—
192Dic13#48212yes—
193Dic13#48412yes—
194Dic13#48512yes—
195C23×C4—131no—
196C23×C4—131no—
197C23×C4C2×#26111yescharacteristic
198C22×C8—262no—
199C22×C8—262no—
200#117—524no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C2×#26111yescharacteristic
208C2×C4⋊C4C2×#26111yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—261no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—264no—
216C2×C42—261no—
217C2×C42—261no—
218C4⋊C8—264no—
219C4⋊C8—264no—
220C22⋊C8—522no—
221C22⋊C8—522no—
222#95—21no—
223#95—261no—
224#95—261no—
225#95—261no—
226C2×C13—42no—
227C2×C13#154211yescharacteristic
228C2×C13#155011yescharacteristic
229C2×C13#155311yescharacteristic
230C2×C13#155711yescharacteristic
231C2×C13#182211yescharacteristic
232C2×C13#182411yescharacteristic
233C2×C13#182511yescharacteristic
234C24C22⋊#26111yescharacteristic
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—261no—
249C22×C4—262no—
250C22×C4—261no—
251C22×C4—262no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4C22⋊#26111yescharacteristic
255C22×C4C22×#26111yescharacteristic
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—522no—
267C4⋊C4—522no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—522no—
271C22⋊C4—42no—
272C22⋊C4—522no—
273C42—134no—
274C42—262no—
275C42—262no—
276C42—262no—
277C42—522no—
278C42—522no—
279C13#872711yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23#8811712yes—
287C23C2×C22⋊#26111yescharacteristic
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—132no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—131no—
307C2×C4—132no—
308C2×C4—132no—
309C2×C4—264no—
310C2×C4—264no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4#8823712yes—
325C8—1042no—
326C8—1042no—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22#1171913511yescharacteristic
335C22#1171913811yescharacteristic
336C22#1171914811yescharacteristic
337C22#1171914811yescharacteristic
338C22C2×#8811711yescharacteristic
339C22#1171916411yescharacteristic
340C22#1171916511yescharacteristic
341C4—22no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—132no—
346C4—132no—
347C4—132no—
348C4—132no—
349C4—262no—
350C4—521no—
351C4—1041no—
352C4—1041no—
353C2—42no—
354C2#1313033811yescharacteristic
355C2#1313035411yescharacteristic
356C2#1313036011yescharacteristic
357C2#1313036811yescharacteristic
358C2#1313073811yescharacteristic
359C2#1313074011yescharacteristic
360C2#1313074111yescharacteristic
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#8727
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. #13129714C2semidirect
4. #13129714C2semidirect
279. C13#8727semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131297142
#131172382
#872713