Finite Group Databasebeta

← #15757970

Subgroups — #15757970

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718641C211yesmaximal, characteristic
2#13117438C211yesmaximal, characteristic
3#13114922C211yesmaximal, characteristic
4C2×#11718061C211yesmaximal, characteristic
5#13112716C211yesmaximal, characteristic
6#13112714C211yesmaximal, characteristic
7C13×#1823C211yesmaximal, characteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C22×#6101—21no—
10C22×#6101C2211yescharacteristic
11C2×C13×C22⋊C8C2211yescharacteristic
12C13×#380C2211yescharacteristic
13#11718873C2211yescharacteristic
14C2×#88071—21no—
15C2×#88071C2211yescharacteristic
16C2×C22⋊#1055C2211yescharacteristic
17#11718641—22no—
18#11718641C414yescomplemented
19#11718639—22no—
20#11718604—21no—
21C22⋊C4×Dic13—21no—
22#11718316—22no—
23C13×#340—22no—
24#11718121—22no—
25#11718061—22no—
26C23×C4×C13—21no—
27C23×C4×C13C2311yescharacteristic
28C23×Dic13—21no—
29C23×Dic13D411yescharacteristic
30C23×Dic13D411yescharacteristic
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C412yes—
38C2×C13×C4⋊C4D412yes—
39C2×C13×C22⋊C4—21no—
40C2×C22⋊Dic13—21no—
41C2×C4⋊Dic13D412yes—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—24no—
47C2×#6101—42no—
48C2×#6101—42no—
49C2×#6101C2×C412yes—
50C2×#6101D412yes—
51C2×C4×Dic13—22no—
52C22×#1055—21no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×#95—21no—
56#88071—22no—
57#88071—24no—
58#88071—21no—
59#88071—21no—
60#88071—24no—
61#88071C2×C412yes—
62C22⋊#1055—21no—
63C22⋊#1055—21no—
64#9026—131nomaximal, Sylow
65C24×C13C2×D411yescharacteristic
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—24no—
82C22×Dic13—22no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—22no—
92C22×Dic13—42no—
93C22×Dic13—41no—
94C22×Dic13—41no—
95C22×Dic13—42no—
96C22×Dic13C22⋊C412yes—
97C22×Dic13C22⋊C412yes—
98C2×C8×C13—42no—
99C2×C8×C13—41no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—42no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C22⋊C4—41no—
106C13×C22⋊C4—41no—
107C22⋊Dic13—41no—
108C22⋊Dic13—41no—
109C4⋊Dic13—42no—
110#6101—22no—
111#6101—22no—
112#6101—22no—
113#6101—22no—
114#6101—48no—
115C4×Dic13—82no—
116C2×#1055—42no—
117C2×#1055—41no—
118C2×#398—131no—
119#2313—131no—
120#1823—131no—
121#1823D1311yescharacteristic
122C2×#324—131no—
123#1294—131no—
124#1294—131no—
125C23×C13—22no—
126C23×C13—22no—
127C23×C13C2×C22⋊C411yescharacteristic
128C23×C13#12011yescharacteristic
129C23×C13#12311yescharacteristic
130C23×C13#13511yescharacteristic
131C23×C13#13511yescharacteristic
132C23×C13AGL(1,ℤ/8)11yescharacteristic
133C23×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—81no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13C4×D411yescharacteristic
151C2×C4×C13C4×D411yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×Dic13—24no—
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—22no—
158C2×Dic13—22no—
159C2×Dic13—44no—
160C2×Dic13—44no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—42no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—42no—
169C2×Dic13—42no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—81no—
173C8×C13—81no—
174#1055—81no—
175C22×C4⋊C4—131no—
176C22×C4⋊C4—261no—
177C22×C4⋊C4C2×D1311yescharacteristic
178C2×C22⋊C8—131no—
179C2×C22⋊C8C2×D1311yescharacteristic
180#398—134no—
181#398—262no—
182#387—262no—
183#387—262no—
184#381—261no—
185#380—131no—
186#380C2×D1311yescharacteristic
187C4×C22⋊C4—261no—
188C2×#95—131no—
189C2×#95—261no—
190#340—22no—
191#340—262no—
192#324—262no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13#38611yescharacteristic
202C22×C13#41611yescharacteristic
203C22×C13#41811yescharacteristic
204C22×C13#44911yescharacteristic
205C22×C13#44911yescharacteristic
206C22×C13#45612yes—
207C22×C13#45812yes—
208C22×C13#48211yescharacteristic
209C22×C13#48211yescharacteristic
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—82no—
215C4×C13—82no—
216Dic13—44no—
217Dic13—42no—
218Dic13—42no—
219Dic13—82no—
220C23×C4—21no—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—261no—
224C23×C4C22×D1311yescharacteristic
225C22×C8—21no—
226C22×C8—261no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—132no—
233C2×C4⋊C4—132no—
234C2×C4⋊C4—132no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—264no—
240C2×C4⋊C4—522no—
241C2×C4⋊C4—522no—
242C2×C4⋊C4C4×D1312yes—
243C2×C4⋊C4C22⋊D1312yes—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—261no—
246C2×C42—262no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—261no—
250C22⋊C8—261no—
251#95—21no—
252#95—132no—
253#95—264no—
254#95—262no—
255#95—264no—
256#95—261no—
257#95—261no—
258C2×C13—21no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13—21no—
262C2×C13#160912yes—
263C2×C13#160912yes—
264C2×C13#187511yescharacteristic
265C2×C13#188611yescharacteristic
266C2×C13#189011yescharacteristic
267C24D4×D1311yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—132no—
278C22×C4—132no—
279C22×C4—264no—
280C22×C4—262no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—262no—
290C22×C4—522no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—522no—
294C22×C4C2×C4×D1311yescharacteristic
295C22×C4#612711yescharacteristic
296C22×C4D4×D1311yescharacteristic
297C22×C4D4×D1311yescharacteristic
298C22×C4#612911yescharacteristic
299C22×C4C2×C22⋊D1311yescharacteristic
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—522no—
303C2×C8—521no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—262no—
310C4⋊C4—262no—
311C4⋊C4—262no—
312C4⋊C4—262no—
313C4⋊C4—522no—
314C4⋊C4—528no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—521no—
318C22⋊C4—521no—
319C42—1042no—
320C13#902611yescharacteristic, complemented, Sylow
321C23—22no—
322C23—22no—
323C23C22⋊C4×D1311yescharacteristic
324C23#8813711yescharacteristic
325C23#8816511yescharacteristic
326C23#8816611yescharacteristic
327C23#8816811yescharacteristic
328C23#8817011yescharacteristic
329C23#8819111yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—264no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—522no—
352C2×C4—524no—
353C2×C4—524no—
354C2×C4—522no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—522no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—522no—
364C2×C4—1041no—
365C2×C4#8813511yescharacteristic
366C2×C4#8813811yescharacteristic
367C2×C4C4×C22⋊D1311yescharacteristic
368C2×C4#8819211yescharacteristic
369C8—81no—
370C8—1041no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22#1171843111yescharacteristic
380C22#1171843311yescharacteristic
381C22#1171844011yescharacteristic
382C22#1171844511yescharacteristic
383C22#1171861711yescharacteristic
384C22#1171871412yes—
385C22#1171881911yescharacteristic
386C22#1171883311yescharacteristic
387C22#1171886612yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—82no—
394C4—524no—
395C4—522no—
396C4—522no—
397C4—1042no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#1311383012yes—
403C2#1311383212yes—
404C2#1311515511yescharacteristic
405C2#1311522611yescharacteristic
406C2#1311524611yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1823C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1823D13
hypocenterC13#9026
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
18. #11718641C4semidirect
320. C13#9026semidirect

Maximal subgroups

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

subgroupindex
C2×#117186412
#131174382
#131149222
C2×#117180612
#131127162
#131127142
C13×#18232
#902613