Finite Group Databasebeta

← #15758500

Subgroups — #15758500

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718587C211yesmaximal, characteristic
2C2×#11718130C212yesmaximal
3#13113063C211yesmaximal, characteristic
4#13112714C212yesmaximal
5C13×#2855C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C13×#391C411yescharacteristic, complemented
9C13×#391C411yescharacteristic, complemented
10C13×#389C411yescharacteristic, complemented
11C13×#389C411yescharacteristic, complemented
12C13×#387—21no—
13C13×#387—21no—
14C13×#385—21no—
15C13×#381—21no—
16C13×#380C2211yescharacteristic
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88071C2212yes—
20C2×C22⋊#1055C2212yes—
21#11718587—24no—
22C2×C4⋊#1055—21no—
23C2×#88043—21no—
24#11718130—24no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C23×Dic13—22no—
30C13×C22⋊Q8—22no—
31C13×C22⋊Q8—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—22no—
41C2×C42×C13—22no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C22×#1055—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#88071—24no—
55#88071—22no—
56#88071—22no—
57#88071—42no—
58C22⋊#1055—22no—
59C22⋊#1055D414yes—
60C4⋊#1055—24no—
61#88043—24no—
62#9116—131nomaximal, Sylow
63C24×C13C2×D411yescharacteristic
64C2×Q8×C13—22no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22×C411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13#4112yes—
88C22×Dic13—24no—
89C22×Dic13—42no—
90C22×Dic13—42no—
91C22×Dic13—42no—
92C22×Dic13—42no—
93C22×Dic13—42no—
94C22×Dic13—42no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—42no—
99C13×C4⋊C4—42no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13—21no—
108C42×C13—21no—
109C42×C13—21no—
110C42×C13—21no—
111C2×#1055—24no—
112C2×#1055—42no—
113C2×#1055—42no—
114C2×#432—131no—
115#2855D1311yescharacteristic
116C2×#328—132no—
117#1434—131no—
118#1294—132no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13C2×C22⋊C411yescharacteristic
124C23×C13#12112yes—
125C23×C13AGL(1,ℤ/8)11yescharacteristic
126C23×C13#13711yescharacteristic
127C23×C13#13712yes—
128Q8×C13—82no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13—44no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13#10412yes—
162C2×C4×C13C4×D412yes—
163C2×C4×C13#12011yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C2×Dic13—44no—
166C2×Dic13—44no—
167C2×Dic13—44no—
168C2×Dic13—82no—
169C2×Dic13—82no—
170C2×Dic13—82no—
171C2×Dic13—82no—
172#1055—44no—
173C2×C22⋊Q8C2×D1311yescharacteristic
174C22×C42C2×D1311yescharacteristic
175#432—264no—
176C2×C4⋊C8—261no—
177C2×C22⋊C8—132no—
178C2×#97—261no—
179#391Dic1311yescharacteristic, complemented
180#391Dic1311yescharacteristic, complemented
181#389Dic1311yescharacteristic, complemented
182#389Dic1311yescharacteristic, complemented
183#387—21no—
184#387—21no—
185#385—21no—
186#381—21no—
187#380C2×D1311yescharacteristic
188C2×#95—132no—
189C2×#95—261no—
190C2×#95—261no—
191#328—264no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—22no—
200C22×C13#38611yescharacteristic
201C22×C13#41011yescharacteristic
202C22×C13#41011yescharacteristic
203C22×C13#41711yescharacteristic
204C22×C13#41911yescharacteristic
205C22×C13C2×#10411yescharacteristic
206C22×C13#42111yescharacteristic
207C22×C13#46812yes—
208C22×C13#47012yes—
209C4×C13—22no—
210C4×C13—21no—
211C4×C13—22no—
212C4×C13—21no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—41no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13—81no—
219C4×C13—81no—
220Dic13—84no—
221C22×Q8C2×Dic1311yescharacteristic
222C23×C4—262no—
223C23×C4C22⋊D1311yescharacteristic
224C23×C4C22⋊D1311yescharacteristic
225C23×C4C22×D1311yescharacteristic
226C22×C8—262no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4C2×Dic1311yescharacteristic
233C2×C4⋊C4C2×Dic1311yescharacteristic
234C2×C4⋊C4C2×Dic1311yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42C2×Dic1311yescharacteristic
240C2×C42C2×Dic1311yescharacteristic
241C2×C42C22⋊D1311yescharacteristic
242C2×C42C22⋊D1311yescharacteristic
243C4⋊C8—264no—
244C22⋊C8—134no—
245C22⋊C8—262no—
246#97—264no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—264no—
255#95—262no—
256#95—262no—
257#95—522no—
258C2×C13—22no—
259C2×C13—22no—
260C2×C13#150611yescharacteristic
261C2×C13#150911yescharacteristic
262C2×C13#151211yescharacteristic
263C2×C13#151511yescharacteristic
264C2×C13#187111yescharacteristic
265C2×C13#189411yescharacteristic
266C2×C13#189911yescharacteristic
267C24C2×C22⋊D1311yescharacteristic
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—264no—
285C22×C4—522no—
286C22×C4—522no—
287C22×C4—522no—
288C22×C4—522no—
289C22×C4—522no—
290C22×C4—522no—
291C22×C4C22⋊Dic1311yescharacteristic
292C22×C4C22⋊Dic1311yescharacteristic
293C22×C4C22⋊Dic1311yescharacteristic
294C22×C4C22⋊Dic1311yescharacteristic
295C22×C4D4×D1312yes—
296C22×C4#612912yes—
297C22×C4C22×Dic1311yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299C2×C8—264no—
300C2×C8—522no—
301C2×C8—522no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—42no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C42—22no—
313C42—22no—
314C42—21no—
315C42—21no—
316C42—21no—
317C42—21no—
318C13#911611yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23#8819312yes—
324C23#8819612yes—
325C23#8820311yescharacteristic
326C23#8820511yescharacteristic
327C23C2×C22⋊Dic1311yescharacteristic
328Q8—82no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—524no—
362C2×C4—524no—
363C2×C4—524no—
364C2×C4—1042no—
365C2×C4—1042no—
366C2×C4—1042no—
367C2×C4—1042no—
368C2×C4#8807712yes—
369C2×C4D4×Dic1312yes—
370C2×C4#8818911yescharacteristic
371C2×C4#8819111yescharacteristic
372C8—524no—
373C22—22no—
374C22—22no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—22no—
381C22#1171871012yes—
382C22#1171871312yes—
383C22#1171888111yescharacteristic
384C22#1171888611yescharacteristic
385C22#1171889311yescharacteristic
386C22C2×#8807711yescharacteristic
387C22#1171889711yescharacteristic
388C22#1171890111yescharacteristic
389C22#1171890111yescharacteristic
390C4—22no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—81no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—1044no—
402C2—22no—
403C2—22no—
404C2#1311334811yescharacteristic
405C2#1311336111yescharacteristic
406C2#1311337411yescharacteristic
407C2#1311338711yescharacteristic
408C2#1311513911yescharacteristic
409C2#1311527011yescharacteristic
410C2#1311529511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2855C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2855D13
hypocenterC13#9116
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
8. C13×#391C4semidirect
9. C13×#391C4semidirect
10. C13×#389C4semidirect
11. C13×#389C4semidirect
179. #391Dic13semidirect
180. #391Dic13semidirect
181. #389Dic13semidirect
182. #389Dic13semidirect
318. C13#9116semidirect

Maximal subgroups

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

subgroupindex
C2×#117185872
C2×#117181302
#131130632
#131127142
C13×#28552
#911613