Finite Group Databasebeta

← #16778689

Subgroups — #16778689

Order 3328.

562 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C4×C22⋊#1057C211yesmaximal, characteristic
2#13130499C211yesmaximal, characteristic
3#13129655C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5#13123186C211yesmaximal, characteristic
6C22×#6122—21no—
7C22×C4×Dic13C2211yescharacteristic
8C2×#88142C411yescharacteristic
9C2×#88132—21no—
10C2×C22⋊#1057—21no—
11C2×C4×#1057—21no—
12C13×#380C411yescharacteristic
13#11718873C411yescharacteristic
14#11718646C2211yescharacteristic
15#11718637C411yescharacteristic
16#11718634C2211yescharacteristic
17#11718603—21no—
18#11718308—21no—
19#11718307—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×Dic26—21no—
27C2×#6122—24no—
28C2×#6122—42no—
29C2×#6122—42no—
30C22×#1057—22no—
31C22×#1057—22no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C22⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
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
48#88142—42no—
49#88132—44no—
50C22⋊#1057—24no—
51C4×#1057—42no—
52C13×#95—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#7688—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—41no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13SD1612yes—
75C22×Dic13Q1612yes—
76C22×Dic13C2×D411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C2×Dic26—42no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81#6122—48no—
82C2×#1057—24no—
83C2×#1057—24no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C22⋊C4—42no—
91C22⋊Dic13—42no—
92C4⋊Dic13—22no—
93C4⋊Dic13—42no—
94C4⋊Dic13—41no—
95#6101—42no—
96#6101—42no—
97#6101—42no—
98#6101—42no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103#2857—131no—
104C4×C22⋊C8—131no—
105#1728—131no—
106#1271—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—44no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13#10112yes—
128C2×C4×C13#13112yes—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—24no—
136C2×Dic13—24no—
137C2×Dic13—44no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13#9912yes—
145C2×Dic13#10312yes—
146C2×Dic13#10412yes—
147C2×Dic13#10412yes—
148C2×Dic13C2×SD1611yescharacteristic
149C2×Dic13C2×Q1611yescharacteristic
150C2×Dic13AGL(1,ℤ/8)12yes—
151Dic26—84no—
152#1057—44no—
153#1057—44no—
154C22×M16—261no—
155C2×C4⋊Q8—131no—
156C2×C22⋊Q8—261no—
157C22×C42—131no—
158C2×C22⋊C8—261no—
159C2×C4×C8—261no—
160#391—261no—
161#389—131no—
162#389—131no—
163#389—261no—
164#384—131no—
165#380—131no—
166#380—261no—
167#380#26111yescharacteristic
168#336—132no—
169#336—132no—
170#336—261no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13#40811yescharacteristic
179C22×C13C2×#9911yescharacteristic
180C22×C13C2×#10111yescharacteristic
181C22×C13C2×#10311yescharacteristic
182C22×C13#41811yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C22×C13C2×#10411yescharacteristic
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—81no—
188C4×C13—81no—
189Dic13—21no—
190Dic13—21no—
191Dic13—22no—
192Dic13—22no—
193Dic13—81no—
194Dic13—81no—
195Dic13#32814yes—
196C22×Q8—261no—
197C23×C4—131no—
198C23×C4—131no—
199C23×C4C2×#26111yescharacteristic
200C2×M16—264no—
201C2×M16—522no—
202C2×M16—522no—
203C22×C8—262no—
204C22×C8—262no—
205C4⋊Q8—522no—
206C22⋊Q8—524no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4C2×#26111yescharacteristic
215C2×C4⋊C4C2×#26111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—261no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—522no—
223C22⋊C8—264no—
224C4×C8—522no—
225#95—21no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13—42no—
230C2×C13#147211yescharacteristic
231C2×C13#148411yescharacteristic
232C2×C13#149311yescharacteristic
233C2×C13C2×#32811yescharacteristic
234C2×C13#150711yescharacteristic
235C2×C13#152611yescharacteristic
236C2×C13#154911yescharacteristic
237C24C22⋊#26111yescharacteristic
238C2×Q8—522no—
239C2×Q8—522no—
240C2×Q8—522no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—131no—
247C22×C4—132no—
248C22×C4—132no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—262no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—521no—
259C22×C4C22⋊#26111yescharacteristic
260C22×C4C22×#26111yescharacteristic
261M16—528no—
262C2×C8—264no—
263C2×C8—264no—
264C2×C8—522no—
265C2×C8—522no—
266C2×C8—522no—
267C2×C8—522no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—262no—
271C4⋊C4—521no—
272C4⋊C4—522no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C4⋊C4—522no—
276C4⋊C4—522no—
277C22⋊C4—42no—
278C22⋊C4—522no—
279C42—262no—
280C42—262no—
281C42—521no—
282C42—521no—
283C13#768811yescharacteristic, complemented, Sylow
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23#8811712yes—
291C23C2×C22⋊#26111yescharacteristic
292Q8—1044no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—132no—
307C2×C4—132no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—132no—
311C2×C4—264no—
312C2×C4—264no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—524no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4#8811312yes—
327C2×C4#8823812yes—
328C8—524no—
329C8—524no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C2×#8811311yescharacteristic
338C22#1171913811yescharacteristic
339C22D13⋊#9911yescharacteristic
340C22#1171914611yescharacteristic
341C22C2×#8811711yescharacteristic
342C22D13⋊#10411yescharacteristic
343C22D13⋊#10411yescharacteristic
344C4—22no—
345C4—22no—
346C4—81no—
347C4—81no—
348C4—134no—
349C4—261no—
350C4—261no—
351C4—262no—
352C4—262no—
353C4—1041no—
354C4—1041no—
355C2—42no—
356C2#1313011511yescharacteristic
357C2#1313015511yescharacteristic
358C2#1313018411yescharacteristic
359C2D13⋊#32811yescharacteristic
360C2#1313023111yescharacteristic
361C2#1313029311yescharacteristic
362C2#1313035111yescharacteristic
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#7688
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. #13129655C2semidirect
4. #13129654C2semidirect
283. C13#7688semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#10572
#131304992
#131296552
#131296542
#131231862
#768813