Finite Group Databasebeta

← #16782713

Subgroups — #16782713

Order 3328.

684 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#1057C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3C2×#11718244C212yesmaximal, complemented
4#13129672C212yesmaximal, complemented
5#13117364C211yesmaximal, characteristic
6C23×#1057—21no—
7C2×#88178C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×#88141C2211yescharacteristic
10C2×C22⋊#1057—21no—
11C2×C4⋊#1057—21no—
12C2×C4⋊#1057—24no—
13C2×C4⋊#1057C2212yes—
14C2×C4×#1057C2212yes—
15C13×#380C411yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17#11718635C411yescharacteristic
18#11718634C411yescharacteristic
19#11718607—21no—
20C22⋊C4×Dic13—21no—
21#11718313—21no—
22#11718310—21no—
23#11718290—21no—
24#11718244—24no—
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13D411yescharacteristic
27C23×Dic13D411yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C22×#1057—24no—
30C22×#1057—22no—
31C22×#1057—22no—
32C22×#1057—42no—
33C22×#1057—42no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39#88178—22no—
40#88178C814yescomplemented
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13—22no—
45C2×C4×Dic13—22no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13—21no—
48C2×C4×Dic13C2×C411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C2×C4×Dic13C2311yescharacteristic
52#88141—22no—
53#88141—22no—
54C22⋊#1057—24no—
55C4⋊#1057—24no—
56C4⋊#1057—22no—
57C4⋊#1057D414yes—
58C4×#1057—22no—
59C4×#1057—22no—
60C13×#95—21no—
61#88071—21no—
62#88071—21no—
63#88071—21no—
64#88071—21no—
65#8937—131nomaximal, Sylow
66C24×C13C22⋊C411yescharacteristic
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C2×C812yes—
73C22×C4×C13M1612yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—22no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—22no—
83C22×Dic13—41no—
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13SD1612yes—
87C22×Dic13Q1612yes—
88C22×Dic13C2×D411yescharacteristic
89C22×Dic13C2×D411yescharacteristic
90C2×Dic26—22no—
91C2×Dic26—22no—
92C2×Dic26—21no—
93C2×Dic26C2×C812yescomplemented
94C2×#1057—24no—
95C2×#1057—24no—
96C2×#1057—42no—
97C2×#1057—48no—
98C2×#1057—42no—
99C2×#1057—42no—
100C2×#1057—42no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C22⋊C4—42no—
104C22⋊Dic13—24no—
105C4⋊Dic13—21no—
106C4⋊Dic13C2×C812yescomplemented
107#6101—24no—
108#6101—42no—
109#6101—42no—
110C4×Dic13—22no—
111C4×Dic13—21no—
112C4×Dic13—22no—
113C4×Dic13—21no—
114C4×Dic13—41no—
115C4×Dic13—41no—
116C4×Dic13—41no—
117C4×Dic13—41no—
118C4×Dic13C2×D412yes—
119C4×Dic13#4112yes—
120C22×C4⋊C8—131no—
121C4×C22⋊Q8—131no—
122C4×C22⋊C8—131no—
123C2×Q8⋊C8—132no—
124#1279—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13C22⋊C812yes—
130C23×C13#10312yes—
131C23×C13#10412yes—
132C23×C13C2×C22⋊C411yescharacteristic
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13C22⋊C812yes—
144C2×C4×C13C4×D412yes—
145C2×C4×C13C22×C811yescharacteristic
146C2×C4×C13C2×M1611yescharacteristic
147C2×C4×C13#13112yes—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—22no—
155C2×Dic13—22no—
156C2×Dic13—21no—
157C2×Dic13—22no—
158C2×Dic13—22no—
159C2×Dic13—21no—
160C2×Dic13—21no—
161C2×Dic13—44no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13#10312yes—
167C2×Dic13#12011yescharacteristic
168C2×Dic13#12112yes—
169C2×Dic13#12311yescharacteristic
170C2×Dic13C2×SD1611yescharacteristic
171C2×Dic13C2×Q1611yescharacteristic
172C2×Dic13AGL(1,ℤ/8)11yescharacteristic
173C2×Dic13#13711yescharacteristic
174Dic26—24no—
175Dic26—42no—
176#1057—44no—
177#1057—44no—
178C23×C8—261no—
179C2×C22⋊Q8—131no—
180C2×C4×Q8—131no—
181C22×C42—131no—
182C2×C4⋊C8—132no—
183C2×C4⋊C8—264no—
184C2×C4⋊C8—261no—
185C2×C22⋊C8—261no—
186C2×C4×C8—132no—
187#391—131no—
188#389—131no—
189#387—261no—
190#385—261no—
191#380#26111yescharacteristic
192C4×C4⋊C4—131no—
193C4×C4⋊C4—261no—
194C4×C22⋊C4—261no—
195#336—261no—
196Q8⋊C8—264no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13—22no—
202C22×C13—22no—
203C22×C13Q8⋊C814yescomplemented
204C22×C13#38611yescharacteristic
205C22×C13C2×C22⋊C811yescharacteristic
206C22×C13#40811yescharacteristic
207C22×C13C2×#10311yescharacteristic
208C22×C13#41711yescharacteristic
209C22×C13C2×#10411yescharacteristic
210C22×C13#42111yescharacteristic
211C4×C13—22no—
212C4×C13—81no—
213C4×C13—81no—
214C4×C13C8×D412yes—
215C4×C13#43512yes—
216Dic13—22no—
217Dic13—22no—
218Dic13—42no—
219Dic13—41no—
220Dic13—42no—
221Dic13#45011yescharacteristic
222Dic13#45111yescharacteristic
223Dic13#48311yescharacteristic
224Dic13#48411yescharacteristic
225C22×Q8—131no—
226C23×C4—131no—
227C23×C4—131no—
228C23×C4C2×#26111yescharacteristic
229C22×C8—262no—
230C22×C8—262no—
231C22×C8—264no—
232C22×C8—522no—
233C22×C8—522no—
234C22⋊Q8—134no—
235C22⋊Q8—262no—
236C4×Q8—262no—
237C4×Q8—262no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—261no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4C2×#26111yescharacteristic
243C2×C4⋊C4C2×#26111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—261no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—131no—
249C2×C42—131no—
250C2×C42—262no—
251C2×C42—262no—
252C2×C42—261no—
253C2×C42—261no—
254C4⋊C8—134no—
255C4⋊C8—262no—
256C4⋊C8—264no—
257C22⋊C8—264no—
258C4×C8—262no—
259C4×C8—262no—
260#95—21no—
261#95—261no—
262#95—261no—
263#95—261no—
264#95—261no—
265C2×C13—24no—
266C2×C13C2×Q8⋊C811yescharacteristic
267C2×C13#147711yescharacteristic
268C2×C13#148111yescharacteristic
269C2×C13#148311yescharacteristic
270C2×C13#186911yescharacteristic
271C2×C13#187111yescharacteristic
272C2×C13#187211yescharacteristic
273C24C22⋊#26111yescharacteristic
274C2×Q8—132no—
275C2×Q8—261no—
276C2×Q8—262no—
277C2×Q8—262no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—131no—
283C22×C4—132no—
284C22×C4—132no—
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—261no—
292C22×C4—262no—
293C22×C4—262no—
294C22×C4—261no—
295C22×C4—261no—
296C22×C4—521no—
297C22×C4D13⋊C812yes—
298C22×C4#611812yes—
299C22×C4C22⋊#26111yescharacteristic
300C22×C4C22×#26111yescharacteristic
301C2×C8—264no—
302C2×C8—264no—
303C2×C8—522no—
304C2×C8—522no—
305C2×C8—522no—
306C2×C8—528no—
307C2×C8—522no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—132no—
311C4⋊C4—264no—
312C4⋊C4—261no—
313C4⋊C4—522no—
314C4⋊C4—522no—
315C22⋊C4—42no—
316C22⋊C4—264no—
317C42—132no—
318C42—132no—
319C42—261no—
320C42—261no—
321C42—262no—
322C42—262no—
323C42—521no—
324C42—521no—
325C42—521no—
326C42—521no—
327C13#893711yescharacteristic, complemented, Sylow
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23#8811112yes—
333C23#8811612yes—
334C23#8811712yes—
335C23C2×C22⋊#26111yescharacteristic
336Q8—264no—
337Q8—522no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—131no—
349C2×C4—131no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—131no—
353C2×C4—131no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—262no—
365C2×C4—262no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—524no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4#8811112yes—
375C2×C4C2×D13⋊C811yescharacteristic
376C2×C4C2×#611811yescharacteristic
377C2×C4#8823812yes—
378C2×C4D4×#26112yes—
379C8—524no—
380C8—524no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22#1171824414yescomplemented
388C22C2×#8811111yescharacteristic
389C22C2×#8811611yescharacteristic
390C22#1171914611yescharacteristic
391C22#1171915011yescharacteristic
392C22C2×#8811711yescharacteristic
393C22#1171916411yescharacteristic
394C22#1171916611yescharacteristic
395C4—22no—
396C4—81no—
397C4—81no—
398C4—131no—
399C4—131no—
400C4—131no—
401C4—131no—
402C4—262no—
403C4—262no—
404C4—522no—
405C4—521no—
406C4—522no—
407C4#1171906312yes—
408C4#1171906412yes—
409C2—24no—
410C2C2×#1171824411yescharacteristic
411C2#1313013311yescharacteristic
412C2#1313014411yescharacteristic
413C2#1313015111yescharacteristic
414C2#1313081111yescharacteristic
415C2#1313081911yescharacteristic
416C2#1313082111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#8937
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#11718244C2semidirect
4. #13129672C2semidirect
40. #88178C8semidirect
93. C2×Dic26C2×C8semidirect
106. C4⋊Dic13C2×C8semidirect
203. C22×C13Q8⋊C8semidirect
327. C13#8937semidirect
387. C22#11718244semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#10572
C4×C22⋊#10572
C2×#117182442
#131296722
#131173642
#893713