Finite Group Databasebeta

← #16783055

Subgroups — #16783055

Order 3328.

726 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
1C22×C4×#1057C211yesmaximal, characteristic
2#13130690C211yesmaximal, characteristic
3C2×Q8⋊#1057C212yesmaximal, complemented
4#13129672C212yesmaximal, complemented
5C22⋊Q8×Dic13C211yesmaximal, characteristic
6C23×#1057—21no—
7C2×C13×C22⋊Q8C411yescharacteristic
8C2×Q8×Dic13C2211yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057—21no—
11C2×C4⋊#1057C2212yes—
12C2×C4×#1057—21no—
13C2×C4×#1057—24no—
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—24no—
30C22×#1057—24no—
31C22×#1057—24no—
32C22×#1057—22no—
33C22×#1057—22no—
34C13×C22⋊Q8—22no—
35C13×C22⋊Q8C814yescomplemented
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C22⋊Dic13—21no—
40Q8×Dic13—22no—
41Q8×Dic13—22no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×C4×Dic13—22no—
47C2×C4×Dic13—22no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—21no—
50C2×C4×Dic13C2×C411yescharacteristic
51C2×C4×Dic13D411yescharacteristic
52C2×C4×Dic13D411yescharacteristic
53C2×C4×Dic13C2311yescharacteristic
54C22⋊#1057—42no—
55C4⋊#1057—22no—
56C4⋊#1057—22no—
57C4×#1057—24no—
58C4×#1057—22no—
59C4×#1057D414yes—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63#88071—21no—
64#88071—21no—
65#9071—131nomaximal, Sylow
66C24×C13C22⋊C411yescharacteristic
67C2×Q8×C13—21no—
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13C2×C812yescomplemented
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C2×C812yes—
77C22×C4×C13M1612yes—
78C22×C4×C13C22×C411yescharacteristic
79C22×Dic13—22no—
80C22×Dic13—22no—
81C22×Dic13—21no—
82C22×Dic13—22no—
83C22×Dic13—21no—
84C22×Dic13—22no—
85C22×Dic13—21no—
86C22×Dic13—21no—
87C22×Dic13C22⋊C411yescharacteristic
88C22×Dic13C22⋊C411yescharacteristic
89C22×Dic13SD1612yes—
90C22×Dic13Q1612yes—
91C22×Dic13C2×D411yescharacteristic
92C22×Dic13C2×D411yescharacteristic
93C2×#1057—216no—
94C2×#1057—24no—
95C2×#1057—24no—
96C2×#1057—24no—
97C2×#1057—42no—
98C2×#1057—42no—
99C2×#1057—42no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4C2×C812yescomplemented
103C13×C22⋊C4—24no—
104C22⋊Dic13—42no—
105C4⋊Dic13—22no—
106C4⋊Dic13—22no—
107C4⋊Dic13—42no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4×Dic13—22no—
111C4×Dic13—21no—
112C4×Dic13—22no—
113C4×Dic13—21no—
114C4×Dic13—42no—
115C4×Dic13—42no—
116C4×Dic13C2×D412yes—
117C4×Dic13#4112yes—
118C22×C4×C8—131no—
119C4×C22⋊Q8—131no—
120#1797—131no—
121C2×Q8⋊C8—132no—
122#1279—132no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13C22⋊C812yes—
128C23×C13#10312yes—
129C23×C13#10412yes—
130C23×C13C2×C22⋊C411yescharacteristic
131Q8×C13—24no—
132Q8×C13—42no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
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—24no—
149C2×Dic13—24no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—24no—
157C2×Dic13—24no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13#10312yes—
165C2×Dic13#10412yes—
166C2×Dic13#12011yescharacteristic
167C2×Dic13#12112yes—
168C2×Dic13#12311yescharacteristic
169C2×Dic13C2×SD1611yescharacteristic
170C2×Dic13C2×Q1611yescharacteristic
171C2×Dic13#13512yes—
172#1057—28no—
173#1057—82no—
174C23×C8—261no—
175C2×C22⋊Q8#26111yescharacteristic
176C2×C4×Q8—131no—
177C22×C42—131no—
178C2×C4⋊C8—132no—
179C2×C22⋊C8—261no—
180C2×C4×C8—132no—
181C2×C4×C8—264no—
182C2×C4×C8—261no—
183#391—131no—
184#389—131no—
185#387—261no—
186#385—261no—
187#380—131no—
188C4×C4⋊C4—131no—
189C4×C4⋊C4—261no—
190C4×C22⋊C4—261no—
191#336—261no—
192Q8⋊C8—264no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13Q8⋊C814yescomplemented
200C22×C13#38611yescharacteristic
201C22×C13C2×C22⋊C811yescharacteristic
202C22×C13#40811yescharacteristic
203C22×C13C2×#10311yescharacteristic
204C22×C13#41611yescharacteristic
205C22×C13C2×#10411yescharacteristic
206C22×C13C2×#10411yescharacteristic
207C4×C13—22no—
208C4×C13—42no—
209C4×C13—42no—
210C4×C13C8×D412yes—
211C4×C13#43512yes—
212Dic13—22no—
213Dic13—21no—
214Dic13—22no—
215Dic13—21no—
216Dic13—81no—
217Dic13—81no—
218Dic13#46512yes—
219Dic13#46712yes—
220C22×Q8C2×#26111yescharacteristic
221C23×C4—131no—
222C23×C4—131no—
223C23×C4C2×#26111yescharacteristic
224C22×C8—262no—
225C22×C8—264no—
226C22×C8—264no—
227C22×C8—264no—
228C22×C8—262no—
229C22⋊Q8—22no—
230C22⋊Q8#105714yescomplemented
231C4×Q8—262no—
232C4×Q8—262no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4C2×#26111yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—261no—
241C2×C42—131no—
242C2×C42—131no—
243C2×C42—131no—
244C2×C42—131no—
245C2×C42—262no—
246C2×C42—262no—
247C2×C42—261no—
248C2×C42—261no—
249C4⋊C8—262no—
250C4⋊C8—262no—
251C22⋊C8—522no—
252C4×C8—134no—
253C4×C8—262no—
254C4×C8—264no—
255#95—261no—
256#95—261no—
257#95—261no—
258#95—261no—
259#95—261no—
260C2×C13—24no—
261C2×C13C2×Q8⋊C811yescharacteristic
262C2×C13#147611yescharacteristic
263C2×C13#149311yescharacteristic
264C2×C13#149411yescharacteristic
265C2×C13#186911yescharacteristic
266C2×C13#189211yescharacteristic
267C2×C13#189611yescharacteristic
268C24C22⋊#26111yescharacteristic
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8C2×#105712yescomplemented
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—131no—
278C22×C4—132no—
279C22×C4—132no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—131no—
283C22×C4—261no—
284C22×C4—262no—
285C22×C4—261no—
286C22×C4—262no—
287C22×C4—262no—
288C22×C4—262no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4C2×#105712yes—
292C22×C4#612212yes—
293C22×C4C22⋊#26111yescharacteristic
294C22×C4C22×#26111yescharacteristic
295C2×C8—264no—
296C2×C8—2616no—
297C2×C8—264no—
298C2×C8—264no—
299C2×C8—522no—
300C2×C8—522no—
301C2×C8—522no—
302C4⋊C4—24no—
303C4⋊C4—21no—
304C4⋊C4—262no—
305C4⋊C4—262no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C4⋊C4—522no—
309C4⋊C4C2×#105712yescomplemented
310C22⋊C4—24no—
311C22⋊C4—522no—
312C42—132no—
313C42—132no—
314C42—261no—
315C42—262no—
316C42—261no—
317C42—262no—
318C42—522no—
319C42—522no—
320C13#907111yescharacteristic, complemented, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23#8811712yes—
326C23#8811812yes—
327C23C22⋊#105712yes—
328C23C2×C22⋊#26111yescharacteristic
329Q8—24no—
330Q8—42no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—132no—
342C2×C4—131no—
343C2×C4—131no—
344C2×C4—132no—
345C2×C4—131no—
346C2×C4—131no—
347C2×C4—132no—
348C2×C4—132no—
349C2×C4—264no—
350C2×C4—264no—
351C2×C4—264no—
352C2×C4—264no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4C22⋊#105712yes—
366C2×C4#8823812yes—
367C2×C4D4×#26112yes—
368C2×C4C22×#105711yescharacteristic
369C2×C4C2×#612211yescharacteristic
370C8—268no—
371C8—1042no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22Q8⋊#105714yescomplemented
379C22#1171914611yescharacteristic
380C22#1171915011yescharacteristic
381C22C2×#8811711yescharacteristic
382C22C2×#8811811yescharacteristic
383C22D13⋊#10411yescharacteristic
384C22#1171916511yescharacteristic
385C22C2×C22⋊#105711yescharacteristic
386C4—22no—
387C4—42no—
388C4—42no—
389C4—132no—
390C4—132no—
391C4—262no—
392C4—261no—
393C4—262no—
394C4—261no—
395C4—1041no—
396C4—1041no—
397C4D4×#105712yes—
398C4#1171914412yes—
399C2—24no—
400C2C2×Q8⋊#105711yescharacteristic
401C2#1313012711yescharacteristic
402C2#1313018411yescharacteristic
403C2#1313018911yescharacteristic
404C2#1313080911yescharacteristic
405C2#1313084911yescharacteristic
406C2#1313085311yescharacteristic
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#9071
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
35. C13×C22⋊Q8C8semidirect
70. C2×Q8×C13C2×C8semidirect
102. C13×C4⋊C4C2×C8semidirect
199. C22×C13Q8⋊C8semidirect
230. C22⋊Q8#1057semidirect
272. C2×Q8C2×#1057semidirect
309. C4⋊C4C2×#1057semidirect
320. C13#9071semidirect
378. C22Q8⋊#1057semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#10572
#131306902
C2×Q8⋊#10572
#131296722
C22⋊Q8×Dic132
#907113