Finite Group Databasebeta

← #16782194

Subgroups — #16782194

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—42no—
46#88131—42no—
47C22⋊#1057—42no—
48C22⋊#1057—42no—
49#88112—24no—
50#88112—24no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#8726—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13D812yes—
75C22×Dic13SD1612yes—
76C22×Dic13C2×D411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90#6101—41no—
91#6101—41no—
92#6101—41no—
93#6101—41no—
94#6101—42no—
95#6101—41no—
96#6101—41no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—42no—
101C4×Dic13—42no—
102C4×Dic13#4114yes—
103#2285—131no—
104#1797—131no—
105#1797—131no—
106#1296—132no—
107#1296—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13#10212yes—
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—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#11712yes—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—24no—
132C2×Dic13—24no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13#10212yes—
145C2×Dic13#12312yes—
146C2×Dic13#12312yes—
147C2×Dic13C2×D811yescharacteristic
148C2×Dic13C2×SD1611yescharacteristic
149C2×Dic13#13512yes—
150C2×Dic13AGL(1,ℤ/8)11yescharacteristic
151C2×Dic13#13712yes—
152C2×Dic13#13711yescharacteristic
153#1057—82no—
154#1057—82no—
155C2×#117—261no—
156C22×C42—131no—
157C2×C4⋊C8—132no—
158C2×C4⋊C8—132no—
159C2×C22⋊C8—261no—
160C2×C22⋊C8—261no—
161#384—131no—
162#384—131no—
163#382—261no—
164#380—131no—
165#380—261no—
166#380#26111yescharacteristic
167C4×C4⋊C4—131no—
168C4×C4⋊C4—131no—
169C4×C4⋊C4—261no—
170#336—261no—
171#336—261no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13#38111yescharacteristic
180C22×C13#41311yescharacteristic
181C22×C13#41311yescharacteristic
182C22×C13C2×#10211yescharacteristic
183C22×C13#41611yescharacteristic
184C22×C13#41711yescharacteristic
185C22×C13#41911yescharacteristic
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—81no—
189C4×C13—81no—
190Dic13—22no—
191Dic13—41no—
192Dic13—81no—
193Dic13—81no—
194Dic13#48012yes—
195Dic13#48212yes—
196Dic13#48312yes—
197Dic13#48512yes—
198C23×C4—131no—
199C23×C4—131no—
200C23×C4C2×#26111yescharacteristic
201C22×C8—262no—
202C22×C8—262no—
203#117—522no—
204#117—522no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4C2×#26111yescharacteristic
212C2×C4⋊C4C2×#26111yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—261no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—264no—
220C2×C42—261no—
221C2×C42—261no—
222C4⋊C8—264no—
223C4⋊C8—264no—
224C22⋊C8—522no—
225C22⋊C8—522no—
226#95—21no—
227#95—261no—
228#95—261no—
229#95—261no—
230C2×C13—42no—
231C2×C13#154011yescharacteristic
232C2×C13#154711yescharacteristic
233C2×C13#155411yescharacteristic
234C2×C13#155911yescharacteristic
235C2×C13#182211yescharacteristic
236C2×C13#182311yescharacteristic
237C2×C13#182511yescharacteristic
238C24C22⋊#26111yescharacteristic
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—262no—
251C22×C4—262no—
252C22×C4—261no—
253C22×C4—262no—
254C22×C4—261no—
255C22×C4—262no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4C22⋊#26111yescharacteristic
259C22×C4C22×#26111yescharacteristic
260C2×C8—522no—
261C2×C8—522no—
262C2×C8—522no—
263C2×C8—522no—
264C2×C8—522no—
265C2×C8—522no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—522no—
277C22⋊C4—42no—
278C22⋊C4—522no—
279C42—134no—
280C42—262no—
281C42—262no—
282C42—262no—
283C42—522no—
284C42—522no—
285C13#872611yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23#8811512yes—
293C23C2×C22⋊#26111yescharacteristic
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—132no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—264no—
316C2×C4—264no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4#8823712yes—
331C8—1042no—
332C8—1042no—
333C22—22no—
334C22—22no—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1171913511yescharacteristic
341C22C2×#8811511yescharacteristic
342C22#1171914811yescharacteristic
343C22#1171914811yescharacteristic
344C22#1171915311yescharacteristic
345C22#1171916411yescharacteristic
346C22#1171916511yescharacteristic
347C4—22no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—132no—
352C4—132no—
353C4—132no—
354C4—132no—
355C4—262no—
356C4—521no—
357C4—1041no—
358C4—1041no—
359C2—42no—
360C2#1313033411yescharacteristic
361C2#1313034811yescharacteristic
362C2#1313036211yescharacteristic
363C2#1313037211yescharacteristic
364C2#1313073811yescharacteristic
365C2#1313073911yescharacteristic
366C2#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#8726
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
285. C13#8726semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131297142
#131172382
#872613