Finite Group Databasebeta

← #16783063

Subgroups — #16783063

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
1C2×#11719119C211yesmaximal, characteristic
2#13130690C211yesmaximal, characteristic
3C2×Q8⋊#1057C212yesmaximal, complemented
4#13129672C212yesmaximal, complemented
5C22⋊Q8×Dic13C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11#11719119—24no—
12C2×C4⋊#1057—21no—
13C2×C4⋊#1057C2212yes—
14C2×C4×#1057C2212yes—
15#11718891C411yescharacteristic
16#11718873C411yescharacteristic
17#11718646C411yescharacteristic
18#11718642—21no—
19C4⋊C4×Dic13—21no—
20C4⋊C4×Dic13C2211yescharacteristic
21#11718611—21no—
22C22⋊C4×Dic13—21no—
23Q8⋊#1057—24no—
24#11718290—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×Dic13D411yescharacteristic
28C23×Dic13D411yescharacteristic
29C22×#1057—22no—
30C22×#1057—22no—
31C13×C22⋊Q8—22no—
32C13×C22⋊Q8C814yescomplemented
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C22⋊Dic13—21no—
37Q8×Dic13—22no—
38Q8×Dic13—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4×Dic13—22no—
44C2×C4×Dic13—22no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13C2×C411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13C2311yescharacteristic
51C22⋊#1057—24no—
52C22⋊#1057—42no—
53C4⋊#1057—24no—
54C4⋊#1057—22no—
55C4⋊#1057—22no—
56C4×#1057—22no—
57C4×#1057D414yes—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63#9073—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C2×Q8×C13—21no—
66C2×Q8×C13—22no—
67C2×Q8×C13—22no—
68C2×Q8×C13C2×C812yes—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C2×C812yes—
75C22×C4×C13M1612yes—
76C22×C4×C13C22×C411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—22no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—22no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13C22⋊C411yescharacteristic
88C22×Dic13C22⋊C411yescharacteristic
89C22×Dic13C2×D411yescharacteristic
90C22×Dic13C2×D411yescharacteristic
91C2×#1057—24no—
92C2×#1057—42no—
93C2×#1057—42no—
94C2×#1057—42no—
95C2×#1057—42no—
96C2×#1057—42no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4C2×C812yes—
100C13×C22⋊C4—24no—
101C22⋊Dic13—42no—
102C4⋊Dic13—22no—
103C4⋊Dic13—22no—
104C4⋊Dic13—42no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4×Dic13—22no—
108C4×Dic13—21no—
109C4×Dic13—22no—
110C4×Dic13—21no—
111C4×Dic13—42no—
112C4×Dic13—41no—
113C4×Dic13—41no—
114C4×Dic13C2×D412yes—
115C4×Dic13#4112yes—
116C2×#431—131no—
117C4×C22⋊Q8—131no—
118#1797—131no—
119C2×Q8⋊C8—132no—
120#1279—132no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13C22⋊C812yes—
128C23×C13C2×C22⋊C411yescharacteristic
129Q8×C13—24no—
130Q8×C13—42no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—24no—
134C2×C4×C13—24no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13C22⋊C812yes—
142C2×C4×C13C4×D412yes—
143C2×C4×C13C22×C811yescharacteristic
144C2×C4×C13C2×M1611yescharacteristic
145C2×C4×C13#13112yes—
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—42no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13#12011yescharacteristic
165C2×Dic13#12112yes—
166C2×Dic13#12311yescharacteristic
167C2×Dic13AGL(1,ℤ/8)11yescharacteristic
168C2×Dic13#13712yes—
169C2×Dic13#13711yescharacteristic
170#1057—44no—
171#1057—82no—
172C2×C22⋊Q8#26111yescharacteristic
173C2×C4×Q8—131no—
174C22×C42—131no—
175#431—264no—
176C2×C4⋊C8—132no—
177C2×C4⋊C8—261no—
178C2×C22⋊C8—261no—
179C2×C22⋊C8—261no—
180C2×C4×C8—132no—
181#391—131no—
182#389—131no—
183#387—261no—
184#385—261no—
185#380—131no—
186C4×C4⋊C4—131no—
187C4×C4⋊C4—261no—
188C4×C22⋊C4—261no—
189#336—261no—
190Q8⋊C8—264no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13#38611yescharacteristic
199C22×C13C2×C22⋊C811yescharacteristic
200C22×C13#40811yescharacteristic
201C22×C13#41711yescharacteristic
202C22×C13#41911yescharacteristic
203C22×C13#42111yescharacteristic
204C22×C13#42111yescharacteristic
205C4×C13—22no—
206C4×C13—42no—
207C4×C13—42no—
208C4×C13C8×D412yes—
209C4×C13#43512yes—
210Dic13—21no—
211Dic13—21no—
212Dic13—41no—
213Dic13—41no—
214Dic13—81no—
215Dic13—81no—
216Dic13#46812yes—
217Dic13#47012yes—
218C22×Q8C2×#26111yescharacteristic
219C23×C4—131no—
220C23×C4—131no—
221C23×C4C2×#26111yescharacteristic
222C22×C8—262no—
223C22×C8—262no—
224C22⋊Q8—22no—
225C22⋊Q8#105714yescomplemented
226C4×Q8—262no—
227C4×Q8—262no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4C2×#26111yescharacteristic
234C2×C22⋊C4—21no—
235C2×C22⋊C4—261no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—262no—
241C2×C42—262no—
242C2×C42—261no—
243C2×C42—261no—
244C4⋊C8—262no—
245C4⋊C8—262no—
246C4⋊C8—264no—
247C22⋊C8—264no—
248C22⋊C8—522no—
249C4×C8—134no—
250C4×C8—262no—
251#95—261no—
252#95—261no—
253#95—261no—
254#95—261no—
255#95—261no—
256C2×C13—42no—
257C2×C13#147711yescharacteristic
258C2×C13#147911yescharacteristic
259C2×C13#149511yescharacteristic
260C2×C13#149711yescharacteristic
261C2×C13#186911yescharacteristic
262C2×C13#189411yescharacteristic
263C2×C13#189711yescharacteristic
264C24C22⋊#26111yescharacteristic
265C2×Q8—21no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8C2×#105712yes—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—262no—
280C22×C4—261no—
281C22×C4—262no—
282C22×C4—261no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—521no—
286C22×C4—521no—
287C22×C4C2×#105712yes—
288C22×C4#612212yes—
289C22×C4C22⋊#26111yescharacteristic
290C22×C4C22×#26111yescharacteristic
291C2×C8—264no—
292C2×C8—522no—
293C2×C8—522no—
294C2×C8—522no—
295C2×C8—522no—
296C2×C8—522no—
297C4⋊C4—24no—
298C4⋊C4—21no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C4⋊C4—522no—
304C4⋊C4C2×#105712yes—
305C22⋊C4—24no—
306C22⋊C4—522no—
307C42—132no—
308C42—132no—
309C42—261no—
310C42—262no—
311C42—261no—
312C42—262no—
313C42—522no—
314C42—521no—
315C42—521no—
316C13#907311yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C22⋊#105712yes—
324C23C2×C22⋊#26111yescharacteristic
325Q8—24no—
326Q8—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—132no—
338C2×C4—132no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—522no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4C22⋊#105712yes—
362C2×C4#8823812yes—
363C2×C4D4×#26112yes—
364C2×C4C22×#105711yescharacteristic
365C2×C4C2×#612211yescharacteristic
366C8—524no—
367C8—1042no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22#1171914611yescharacteristic
376C22#1171915011yescharacteristic
377C22#1171915311yescharacteristic
378C22#1171915511yescharacteristic
379C22#1171916411yescharacteristic
380C22#1171916611yescharacteristic
381C22C2×C22⋊#105711yescharacteristic
382C4—22no—
383C4—42no—
384C4—42no—
385C4—132no—
386C4—132no—
387C4—261no—
388C4—261no—
389C4—521no—
390C4—521no—
391C4—1041no—
392C4—1041no—
393C4D4×#105712yes—
394C4#1171914412yes—
395C2—42no—
396C2#1313013111yescharacteristic
397C2#1313013811yescharacteristic
398C2#1313019311yescharacteristic
399C2#1313019811yescharacteristic
400C2#1313080911yescharacteristic
401C2#1313085111yescharacteristic
402C2#1313085511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊Q8C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C22⋊Q8#261
hypocenterC13#9073
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#1057C2semidirect
4. #13129672C2semidirect
32. C13×C22⋊Q8C8semidirect
225. C22⋊Q8#1057semidirect
316. C13#9073semidirect

Maximal subgroups

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

subgroupindex
C2×#117191192
#131306902
C2×Q8⋊#10572
#131296722
C22⋊Q8×Dic132
#907313