Finite Group Databasebeta

← #15761728

Subgroups — #15761728

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88201C211yesmaximal, characteristic
2#13114987C211yesmaximal, characteristic, complemented
3C4×#88055C211yesmaximal, characteristic, complemented
4C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6C2×#11718075C211yesmaximal, characteristic
7C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C13C2211yescharacteristic
9C2×#88201C411yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13#11718891C411yescharacteristic
14C2×#88055—22no—
15C2×#88054—22no—
16#11718651—22no—
17#11718649C411yescharacteristic
18#11718638C411yescharacteristic
19C4×#6103—22no—
20C42×Dic13C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23C13×Q8⋊C8—22no—
24Q8⋊#1055—22no—
25#11718075—22no—
26#11718051—22no—
27C22×Q8×C13C2×C411yescharacteristic
28C22×D52C2×C411yescharacteristic
29C22×C4×D13—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40#88201—22no—
41#88201—22no—
42C2×#6103—22no—
43C2×#6103—21no—
44C2×#6103—22no—
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13D412yes—
49C2×C4×Dic13D412yes—
50C22×#1055—21no—
51C22×#1055—21no—
52C4×D52—21no—
53C4×D52—21no—
54C4×D52—21no—
55C4×D52—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C4×C8×C13—21no—
59C4×C8×C13D412yes—
60#88071—22no—
61#88071—22no—
62#88055—28no—
63#88054—44no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4×#1055—21no—
67C4×#1055D412yes—
68#9646—131nomaximal, Sylow
69C23×D13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13M1612yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13C22⋊C412yes—
83C22×Dic13C22⋊C412yes—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52M1612yes—
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C4×D13—42no—
93C2×C4×D13—42no—
94C2×C8×C13—24no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C2×C8×C13—42no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C42×C13—41no—
103C42×C13—41no—
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108#6103—28no—
109#6103—41no—
110#6103—41no—
111#6103—44no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C4×Dic13—21no—
115C4×Dic13—21no—
116C4×Dic13—21no—
117C4×Dic13—21no—
118C4×Dic13—22no—
119C4×Dic13—22no—
120C4×Dic13—24no—
121C2×#1055—24no—
122C2×#1055—22no—
123C2×#1055—41no—
124C2×#1055—42no—
125C4×#124—131no—
126#1842—131no—
127C4×#97—131no—
128C2×Q8⋊C8—131no—
129C2×Q8⋊C8D1311yescharacteristic, complemented
130C2×D4⋊C8—131no—
131C2×D4⋊C8—131no—
132C23×C13C2×C22⋊C411yescharacteristic
133C22×D13—22no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13—42no—
137C22×D13—42no—
138Q8×C13—22no—
139Q8×C13—22no—
140Q8×C13—41no—
141Q8×C13—41no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—42no—
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13C4×D411yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12411yescharacteristic
153C2×C4×C13#12711yescharacteristic
154C2×C4×C13C2×M1611yescharacteristic
155C2×C4×C13C2×M1611yescharacteristic
156C2×C4×C13#13111yescharacteristic
157C2×C4×C13#13111yescharacteristic
158C2×C4×C13AGL(1,ℤ/8)12yes—
159C2×C4×C13#13712yes—
160C2×Dic13—22no—
161C2×Dic13—22no—
162C2×Dic13—22no—
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—41no—
166C2×Dic13—42no—
167C2×Dic13#10414yes—
168D52—22no—
169D52—22no—
170D52—41no—
171D52—41no—
172C4×D13—82no—
173C4×D13—81no—
174C4×D13—81no—
175C8×C13—24no—
176C8×C13—81no—
177#1055—24no—
178#1055—81no—
179C2×#124—131no—
180C2×C4×Q8C2×D1311yescharacteristic
181C2×C4×D4—131no—
182C2×C4⋊C8—131no—
183C2×C4⋊C8—262no—
184C2×C4⋊C8C2×D1311yescharacteristic
185C2×#97—262no—
186C2×C4×C8—131no—
187C2×C4×C8C2×D1311yescharacteristic
188#391—131no—
189#390—131no—
190#388—262no—
191#382—131no—
192C4×C22⋊C4—262no—
193C43—131no—
194Q8⋊C8—22no—
195Q8⋊C8—262no—
196D4⋊C8—262no—
197D4⋊C8—262no—
198C22×C13#39011yescharacteristic
199C22×C13#40711yescharacteristic
200C22×C13#40811yescharacteristic
201C22×C13#41712yes—
202C22×C13C2×#10412yes—
203C2×D13—42no—
204C2×D13—44no—
205C2×D13—81no—
206C2×D13—81no—
207C2×D13—82no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—42no—
211C4×C13—81no—
212C4×C13#43511yescharacteristic
213C4×C13#43511yescharacteristic
214C4×C13#43511yescharacteristic
215C4×C13#43511yescharacteristic
216C4×C13#48912yes—
217C4×C13#49611yescharacteristic
218C4×C13#49711yescharacteristic
219Dic13—24no—
220Dic13—42no—
221Dic13—81no—
222C22×Q8C4×D1311yescharacteristic
223C22×D4—131no—
224C23×C4—261no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—261no—
228C22×C8—261no—
229#124—262no—
230#124—262no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×D4—261no—
236C4×D4—261no—
237C4×D4—261no—
238C4×D4—261no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—131no—
241C2×C4⋊C4C4×D1311yescharacteristic
242C2×C22⋊C4—262no—
243C2×C22⋊C4—262no—
244C2×C22⋊C4—261no—
245C2×C42—21no—
246C2×C42—131no—
247C2×C42—131no—
248C2×C42—132no—
249C2×C42—132no—
250C2×C42C22×D1311yescharacteristic
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—261no—
254C4⋊C8—261no—
255C4⋊C8—524no—
256#97—268no—
257C4×C8—21no—
258C4×C8—132no—
259C4×C8—261no—
260C4×C8C22⋊D1312yes—
261#95—262no—
262#95—262no—
263C2×C13#148312yes—
264C2×C13#148912yes—
265C2×C13#195511yescharacteristic
266C2×C13#195911yescharacteristic
267C2×C13#196211yescharacteristic
268D13—82no—
269C24—261no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8#609412yes—
276C2×D4—132no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—261no—
281C2×D4—261no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—132no—
285C22×C4—132no—
286C22×C4—261no—
287C22×C4—521no—
288C22×C4—522no—
289C22×C4—522no—
290C22×C4—521no—
291C22×C4C2×C4×D1311yescharacteristic
292C22×C4D4×D1311yescharacteristic
293C22×C4D4×D1311yescharacteristic
294C2×C8—24no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—41no—
298C2×C8—264no—
299C2×C8—262no—
300C2×C8—522no—
301C2×C8—521no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—261no—
307C4⋊C4—261no—
308C22⋊C4—268no—
309C22⋊C4—524no—
310C22⋊C4—521no—
311C22⋊C4—521no—
312C42—41no—
313C42—41no—
314C42—264no—
315C42—261no—
316C42—261no—
317C42—261no—
318C42—261no—
319C42—262no—
320C42—262no—
321C42#612711yescharacteristic
322C42D4×D1311yescharacteristic
323C42#612911yescharacteristic
324C42C2×C22⋊D1311yescharacteristic
325C13#964611yescharacteristic, complemented, Sylow
326C23—262no—
327C23—522no—
328C23—522no—
329C23—521no—
330C23—521no—
331C23C22⋊C4×D1311yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336D4—262no—
337D4—262no—
338D4—521no—
339D4—521no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—134no—
347C2×C4—262no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—522no—
353C2×C4—521no—
354C2×C4—1042no—
355C2×C4—1041no—
356C2×C4—1041no—
357C2×C4#8813511yescharacteristic
358C2×C4#8813811yescharacteristic
359C2×C4#8813911yescharacteristic
360C2×C4C2×#609411yescharacteristic
361C2×C4#8815511yescharacteristic
362C2×C4M16×D1311yescharacteristic
363C2×C4#8816111yescharacteristic
364C2×C4#8816812yes—
365C2×C4#8817212yes—
366C2×C4C4×C22⋊D1311yescharacteristic
367C2×C4#8819311yescharacteristic
368C2×C4#8819411yescharacteristic
369C8—24no—
370C8—81no—
371C8—264no—
372C8—1041no—
373C22—524no—
374C22—522no—
375C22—1041no—
376C22—1041no—
377C22—1042no—
378C22#1171838711yescharacteristic
379C22#1171838811yescharacteristic
380C22#1171846412yes—
381C22D13×#10412yes—
382C22#1171861811yescharacteristic
383C4—21no—
384C4—21no—
385C4—42no—
386C4—81no—
387C4—264no—
388C4—522no—
389C4—1041no—
390C4#1171838911yescharacteristic
391C4#1171839111yescharacteristic
392C4#1171845612yes—
393C4#1171877211yescharacteristic
394C4#1171878811yescharacteristic
395C4#1171883711yescharacteristic
396C4#1171885111yescharacteristic
397C2—1042no—
398C2#1311324812yes—
399C2#1311327412yes—
400C2#1311563211yescharacteristic
401C2#1311564911yescharacteristic
402C2#1311566211yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×Q8⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenterC2×Q8⋊C8D13
hypocenterC13#9646
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #13114987C2semidirect
3. C4×#88055C2semidirect
4. C2×Q8⋊#1055C2semidirect
7. C2×C13×Q8⋊C8C2semidirect
129. C2×Q8⋊C8D13semidirect
325. C13#9646semidirect

Maximal subgroups

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

subgroupindex
C4×#882012
#131149872
C4×#880552
C2×Q8⋊#10552
C2×#117180512
C2×#117180752
C2×C13×Q8⋊C82
#964613