Finite Group Databasebeta

← #16778342

Subgroups — #16778342

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130690C211yesmaximal, characteristic
2C2×#11718290C211yesmaximal, characteristic
3#13129656C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5C22⋊Q8×Dic13C211yesmaximal, characteristic
6C23×#1057—21no—
7C2×C13×C22⋊Q8C411yescharacteristic
8C2×Q8×Dic13C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057—21no—
11C2×C4⋊#1057—21no—
12#11718891C2211yescharacteristic
13#11718873C411yescharacteristic
14#11718646C2211yescharacteristic
15#11718642—21no—
16C4⋊C4×Dic13—21no—
17C4⋊C4×Dic13C411yescharacteristic
18#11718611—21no—
19C22⋊C4×Dic13—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×Dic13D411yescharacteristic
26C23×Dic13D411yescharacteristic
27C22×#1057—24no—
28C22×#1057—22no—
29C22×#1057—22no—
30C22×#1057—42no—
31C22×#1057—42no—
32C13×C22⋊Q8—22no—
33C13×C22⋊Q8C814yescomplemented
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C22⋊Dic13—21no—
38Q8×Dic13—42no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13—42no—
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×C4×Dic13C2311yescharacteristic
50C22⋊#1057—42no—
51C4⋊#1057—42no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#7589—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2×C812yescomplemented
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C2×C812yes—
69C22×C4×C13M1612yes—
70C22×C4×C13C22×C411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C22⋊C411yescharacteristic
81C22×Dic13SD1612yes—
82C22×Dic13Q1612yes—
83C22×Dic13C2×D411yescharacteristic
84C22×Dic13C2×D411yescharacteristic
85C2×#1057—24no—
86C2×#1057—48no—
87C2×#1057—42no—
88C2×#1057—42no—
89C2×#1057—42no—
90C2×#1057—42no—
91C2×#1057—42no—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4C2×C812yescomplemented
95C13×C22⋊C4—24no—
96C22⋊Dic13—42no—
97C4⋊Dic13—42no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4×Dic13—22no—
103C4×Dic13—22no—
104C4×Dic13—41no—
105C4×Dic13—41no—
106C4×Dic13—42no—
107C4×Dic13—42no—
108C4×C22⋊Q8—131no—
109#1797—131no—
110C2×#336—131no—
111#1272—132no—
112#1271—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C22⋊C812yes—
118C23×C13#10312yes—
119C23×C13#10412yes—
120C23×C13C2×C22⋊C411yescharacteristic
121Q8×C13—42no—
122Q8×C13—42no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13C22⋊C812yes—
136C2×C4×C13C22×C811yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×Dic13—24no—
139C2×Dic13—24no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13#9912yes—
157C2×Dic13#10312yes—
158C2×Dic13C2×SD1611yescharacteristic
159C2×Dic13C2×Q1611yescharacteristic
160C2×Dic13AGL(1,ℤ/8)11yescharacteristic
161C2×Dic13#13711yescharacteristic
162#1057—44no—
163#1057—82no—
164C23×C8—261no—
165C2×C22⋊Q8#26111yescharacteristic
166C2×C4×Q8—131no—
167C22×C42—131no—
168C2×C4⋊C8—261no—
169C2×C22⋊C8—261no—
170#391—131no—
171#389—131no—
172#387—261no—
173#385—261no—
174#380—131no—
175C4×C4⋊C4—131no—
176C4×C4⋊C4—261no—
177C4×C22⋊C4—261no—
178#336—132no—
179#336—132no—
180#336—261no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13Q8⋊C814yes—
188C22×C13C2×C22⋊C811yescharacteristic
189C22×C13C2×#9911yescharacteristic
190C22×C13#41311yescharacteristic
191C22×C13C2×#10311yescharacteristic
192C22×C13#41711yescharacteristic
193C22×C13C2×#10411yescharacteristic
194C22×C13#42111yescharacteristic
195C4×C13—22no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—42no—
199C4×C13—42no—
200Dic13—21no—
201Dic13—22no—
202Dic13—21no—
203Dic13—21no—
204Dic13—22no—
205Dic13—21no—
206Dic13—81no—
207Dic13—81no—
208C22×Q8C2×#26111yescharacteristic
209C23×C4—131no—
210C23×C4—131no—
211C23×C4C2×#26111yescharacteristic
212C22×C8—262no—
213C22×C8—264no—
214C22×C8—262no—
215C22×C8—522no—
216C22×C8—522no—
217C22⋊Q8—22no—
218C22⋊Q8#105714yescomplemented
219C4×Q8—522no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4C2×#26111yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—261no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—131no—
232C2×C42—261no—
233C2×C42—261no—
234C2×C42—522no—
235C4⋊C8—522no—
236C22⋊C8—522no—
237#95—261no—
238#95—261no—
239#95—261no—
240#95—261no—
241#95—261no—
242C2×C13—24no—
243C2×C13#145911yescharacteristic
244C2×C13C2×Q8⋊C811yescharacteristic
245C2×C13#147711yescharacteristic
246C2×C13#150411yescharacteristic
247C2×C13#152011yescharacteristic
248C2×C13#153211yescharacteristic
249C2×C13#155011yescharacteristic
250C24C22⋊#26111yescharacteristic
251C2×Q8—21no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8C2×#105712yescomplemented
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—132no—
264C22×C4—132no—
265C22×C4—262no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4—262no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4C2×#105712yes—
274C22×C4#612212yes—
275C22×C4C22⋊#26111yescharacteristic
276C22×C4C22×#26111yescharacteristic
277C2×C8—264no—
278C2×C8—522no—
279C2×C8—528no—
280C2×C8—522no—
281C2×C8—522no—
282C2×C8—522no—
283C2×C8—522no—
284C4⋊C4—24no—
285C4⋊C4—21no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C4⋊C4—522no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4C2×#105712yescomplemented
292C22⋊C4—24no—
293C22⋊C4—522no—
294C42—262no—
295C42—262no—
296C42—521no—
297C42—521no—
298C42—522no—
299C42—522no—
300C13#758911yescharacteristic, complemented, Sylow
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23#8811712yes—
306C23#8811812yes—
307C23C22⋊#105712yes—
308C23C2×C22⋊#26111yescharacteristic
309Q8—42no—
310Q8—42no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—132no—
324C2×C4—131no—
325C2×C4—132no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—264no—
330C2×C4—264no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4C22⋊#105712yes—
348C2×C4C22×#105711yescharacteristic
349C2×C4C2×#612211yescharacteristic
350C8—524no—
351C8—1042no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22Q8⋊#105714yes—
359C22D13⋊#9911yescharacteristic
360C22#1171914811yescharacteristic
361C22C2×#8811711yescharacteristic
362C22C2×#8811811yescharacteristic
363C22#1171916411yescharacteristic
364C22#1171916611yescharacteristic
365C22C2×C22⋊#105711yescharacteristic
366C4—22no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—42no—
371C4—261no—
372C4—262no—
373C4—261no—
374C4—261no—
375C4—262no—
376C4—261no—
377C4—1041no—
378C4—1041no—
379C2—24no—
380C2#1313007211yescharacteristic
381C2C2×Q8⋊#105711yescharacteristic
382C2#1313013111yescharacteristic
383C2#1313022311yescharacteristic
384C2#1313027411yescharacteristic
385C2#1313031411yescharacteristic
386C2#1313035411yescharacteristic
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#7589
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13129656C2semidirect
4. #13129654C2semidirect
33. C13×C22⋊Q8C8semidirect
62. C2×Q8×C13C2×C8semidirect
94. C13×C4⋊C4C2×C8semidirect
218. C22⋊Q8#1057semidirect
254. C2×Q8C2×#1057semidirect
291. C4⋊C4C2×#1057semidirect
300. C13#7589semidirect

Maximal subgroups

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

subgroupindex
#131306902
C2×#117182902
#131296562
#131296542
C22⋊Q8×Dic132
#758913