Finite Group Databasebeta

← #16785089

Subgroups — #16785089

Order 3328.

600 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 122 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#13130690C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129674C212yesmaximal
4#13129674C212yesmaximal
5C2×#11718633C211yesmaximal, characteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C22×#6101C411yescharacteristic
8C22×#6101C411yescharacteristic
9C22×#6101C411yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C22⋊#1057C2212yes—
12C2×C22⋊#1057C2212yes—
13C2×#88110—21no—
14C2×C4⋊#1057—21no—
15C2×#88071C2211yescharacteristic
16C2×#88071C2211yescharacteristic
17#11718633—21no—
18#11718633—21no—
19#11718633—21no—
20#11718633—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2311yescharacteristic
30C22×#1057—22no—
31C22×#1057—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—42no—
35C2×#6101—22no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—22no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—42no—
44C2×#6101—42no—
45C2×C4×Dic13—42no—
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C22⋊#1057—22no—
51C22⋊#1057—24no—
52C22⋊#1057Q814yes—
53#88110—42no—
54C4⋊#1057—42no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#9883—131nomaximal, Sylow
60C24×C13C22×C411yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13M1612yes—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—22no—
78C22×Dic13—22no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—22no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13—41no—
89C22×Dic13C22⋊C411yescharacteristic
90C22×Dic13C22⋊C411yescharacteristic
91C22×Dic13M1612yes—
92C22×Dic13C2×D411yescharacteristic
93C22×Dic13C2×D411yescharacteristic
94C22×Dic13C2×Q812yes—
95C22×Dic13#4112yes—
96C2×#1057—24no—
97C2×#1057—42no—
98C2×#1057—42no—
99C2×#1057—42no—
100C2×#1057—42no—
101C2×#1057—42no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—42no—
104#6101—24no—
105#6101—24no—
106#6101—42no—
107#6101—42no—
108#6101—42no—
109#6101—42no—
110C4×Dic13—22no—
111C4×Dic13—22no—
112C4×Dic13—41no—
113C4×Dic13—41no—
114C2×#389—131no—
115#1797—131no—
116#1749—131no—
117#1280—132no—
118#1280—132no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13C2×C22⋊C411yescharacteristic
124C23×C13C4×Q812yes—
125C23×C13C2×M1611yescharacteristic
126C23×C13C2×M1611yescharacteristic
127C23×C13#13112yes—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—22no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—44no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—82no—
143C2×C4×C13#10012yes—
144C2×Dic13—24no—
145C2×Dic13—24no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—22no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—82no—
165C2×Dic13#9912yes—
166C2×Dic13#10112yes—
167C2×Dic13C22⋊Q812yes—
168C2×Dic13#12411yescharacteristic
169C2×Dic13C4⋊Q811yescharacteristic
170#1057—44no—
171#1057—82no—
172C22×C4⋊C4—131no—
173C22×C4⋊C4—131no—
174C22×C4⋊C4—131no—
175C22×C4⋊C4#26111yescharacteristic
176C22×C42—131no—
177C2×C4⋊C8—261no—
178C2×C22⋊C8—132no—
179C2×C22⋊C8—132no—
180C2×#97—261no—
181#389—261no—
182#389—261no—
183#389—261no—
184#389—261no—
185C2×#95—131no—
186C2×#95—131no—
187#336—261no—
188#336—261no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13#39111yescharacteristic
198C22×C13#40711yescharacteristic
199C22×C13#40811yescharacteristic
200C22×C13C2×#9911yescharacteristic
201C22×C13#41011yescharacteristic
202C22×C13C2×#10011yescharacteristic
203C22×C13C2×#10111yescharacteristic
204C22×C13#44612yes—
205C22×C13#44612yes—
206C4×C13—22no—
207C4×C13—42no—
208C4×C13—41no—
209C4×C13—81no—
210Dic13—22no—
211Dic13—22no—
212Dic13—22no—
213Dic13—21no—
214Dic13—21no—
215Dic13—42no—
216Dic13—81no—
217C23×C4—131no—
218C23×C4—131no—
219C23×C4—131no—
220C23×C4—131no—
221C23×C4C2×#26111yescharacteristic
222C23×C4C2×#26111yescharacteristic
223C23×C4C2×#26111yescharacteristic
224C22×C8—262no—
225C22×C8—262no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4—262no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—522no—
238C2×C4⋊C4—522no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—522no—
244C4⋊C8—522no—
245C22⋊C8—134no—
246C22⋊C8—262no—
247C22⋊C8—264no—
248#97—522no—
249#95—261no—
250#95—261no—
251#95—261no—
252#95—261no—
253C2×C13—22no—
254C2×C13—22no—
255C2×C13#146311yescharacteristic
256C2×C13#146611yescharacteristic
257C2×C13#147011yescharacteristic
258C2×C13#147111yescharacteristic
259C2×C13#198511yescharacteristic
260C2×C13#199611yescharacteristic
261C2×C13#199711yescharacteristic
262C24C22×#26111yescharacteristic
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—132no—
279C22×C4—132no—
280C22×C4—132no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—262no—
289C22×C4—521no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4#611812yes—
296C22×C4C22⋊#26111yescharacteristic
297C22×C4C22⋊#26111yescharacteristic
298C2×C8—264no—
299C2×C8—522no—
300C2×C8—522no—
301C2×C8—522no—
302C2×C8—522no—
303C2×C8—522no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—264no—
307C4⋊C4—264no—
308C4⋊C4—522no—
309C4⋊C4—522no—
310C4⋊C4—522no—
311C4⋊C4—522no—
312C42—262no—
313C42—262no—
314C42—521no—
315C42—521no—
316C13#988311yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×#611811yescharacteristic
322C23D13⋊M1611yescharacteristic
323C23#8823812yes—
324C23Q8×#26112yes—
325C23C2×C22⋊#26111yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—132no—
342C2×C4—132no—
343C2×C4—132no—
344C2×C4—131no—
345C2×C4—131no—
346C2×C4—264no—
347C2×C4—264no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—262no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—522no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—1042no—
367C2×C4#8812112yes—
368C8—524no—
369C8—1042no—
370C22—22no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22#1171907812yes—
379C22#1171908012yes—
380C22#1171911611yescharacteristic
381C22#1171912711yescharacteristic
382C22D13⋊#9911yescharacteristic
383C22#1171914611yescharacteristic
384C22D13⋊#10111yescharacteristic
385C22(C2×#261)⋊Q811yescharacteristic
386C22C2×#8812111yescharacteristic
387C4—22no—
388C4—42no—
389C4—41no—
390C4—81no—
391C4—262no—
392C4—261no—
393C4—261no—
394C4—262no—
395C4—262no—
396C4—522no—
397C4—1041no—
398C2—22no—
399C2—22no—
400C2#1313008511yescharacteristic
401C2#1313009511yescharacteristic
402C2#1313010811yescharacteristic
403C2#1313011211yescharacteristic
404C2#1313100911yescharacteristic
405C2#1313102711yescharacteristic
406C2#1313102811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#9883
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
316. C13#9883semidirect

Maximal subgroups

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

subgroupindex
#131306902
#131305622
#131296742
C2×#117186332
#988313