Finite Group Databasebeta

← #13128923

Subgroups — #13128923

Order 1664.

992 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Q8×C13C211yesmaximal, characteristic, complemented
2Q8×C22⋊D13C211yesmaximal, characteristic, complemented
3Q8×C22⋊D13C211yesmaximal, characteristic, complemented
4#11719517C211yesmaximal, characteristic, complemented
5C2×Q8×Dic13C211yesmaximal, characteristic, complemented
6#11719436C213yesmaximal, complemented
7#11719426C213yesmaximal, complemented
8#11719347C213yesmaximal, complemented
9#11719346C213yesmaximal, complemented
10#11719330C213yesmaximal, complemented
11#11719327C213yesmaximal, complemented
12#11719277C211yesmaximal, characteristic, complemented
13#11719274C211yesmaximal, characteristic, complemented
14#11719246C213yesmaximal, complemented
15#11719243C213yesmaximal
16C22×Q8×C13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×Q8×D13C2211yescharacteristic
19C13×C4⋊Q8C2213yes—
20C13×C22⋊Q8C2213yes—
21C13×C22⋊Q8C2213yes—
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13C2213yes—
24#88200C2213yes—
25#88200C2213yes—
26Q8×Dic13C2213yes—
27Q8×Dic13C2213yes—
28Q8×Dic13C2213yes—
29Q8×Dic13C2213yes—
30Q8×Dic13C2211yescharacteristic
31Q8×Dic13C2211yescharacteristic
32Q8×Dic13C2211yescharacteristic
33#88198C2213yes—
34#88198C2213yes—
35#88193C2211yescharacteristic
36#88189C2213yes—
37C4×C22⋊D13C2213yes—
38C4×C22⋊D13C2213yes—
39#88180C2213yes—
40#88180C2213yes—
41C2×C4⋊Dic13C2213yes—
42#88178C2213yes—
43#88178C2213yes—
44C2×C4×Dic13C2213yes—
45#88152C2213yes—
46#88152C2216yes—
47#88146C2213yes—
48#88144C2216yes—
49#88144C2213yes—
50#88143C2213yes—
51#88143C2216yes—
52#88143C2216yes—
53#88142C2213yes—
54#88141C2216yes—
55#88141C2213yes—
56#88140C2213yes—
57#88139C2213yes—
58#88133C2213yes—
59#88133C2216yes—
60#88132C2213yes—
61#88131C2216yes—
62#88126C2213yes—
63#88124C2213yes—
64C4×Dic26C2213yes—
65C4×Dic26C2213yes—
66C2×Q8×C13—24no—
67C2×Q8×C13—24no—
68C2×Q8×C13C2313yes—
69C2×Q8×C13C2313yes—
70C2×Q8×C13C2311yescharacteristic
71C2×D4×C13C2311yescharacteristic
72C22×C4×C13C2313yes—
73C22×C4×C13C2313yes—
74C2×C22⋊D13C2311yescharacteristic
75C2×C22⋊D13C2311yescharacteristic
76C22×Dic13C2313yes—
77C22×Dic13C2311yescharacteristic
78Q8×D13—24no—
79C2×C4×D13C2313yes—
80C2×Dic26C2313yes—
81C2×Dic26C2313yes—
82C13×C4⋊C4C2313yes—
83C13×C4⋊C4C2316yes—
84C13×C4⋊C4C2313yes—
85C13×C22⋊C4C2313yes—
86C13×C22⋊C4C2313yes—
87C42×C13C2313yes—
88C22⋊Dic13C2313yes—
89C22⋊Dic13C2313yes—
90C22⋊Dic13C2311yescharacteristic
91C22⋊Dic13C2313yes—
92#6103C2311yescharacteristic
93#6103C2313yes—
94#6103C2313yes—
95#6103C2313yes—
96C4⋊Dic13C2313yes—
97C4⋊Dic13C2313yes—
98C4⋊Dic13C2313yes—
99C4⋊Dic13C2313yes—
100C4⋊Dic13C2313yes—
101C4⋊Dic13C2316yes—
102C4⋊Dic13C2313yes—
103#6101C2311yescharacteristic
104#6101C2313yes—
105#6101C2313yes—
106#6101C2316yes—
107#6101C2313yes—
108#6101C2316yes—
109#6101C2313yes—
110#6101C2316yes—
111#6101C2313yes—
112C4×Dic13C2316yes—
113C4×Dic13C2313yes—
114C4×Dic13C2313yes—
115C4×Dic13C2313yes—
116C4×Dic13C2316yes—
117C4×Dic13C2313yes—
118C4×Dic13C2313yes—
119#3523—131nomaximal, Sylow
120C23×C13C2411yescharacteristic
121C23×C13C2411yescharacteristic
122C22×D13C2411yescharacteristic
123Q8×C13—26no—
124Q8×C13—26no—
125Q8×C13#4114yes—
126D4×C13—22no—
127C2×C4×C13—26no—
128C2×C4×C13—26no—
129C2×C4×C13C2413yes—
130C2×C4×C13C2413yes—
131C2×C4×C13C2413yes—
132C2×C4×C13C2411yescharacteristic
133C2×C4×C13C2413yes—
134C22⋊D13—22no—
135C22⋊D13—22no—
136C2×Dic13—26no—
137C2×Dic13—22no—
138C2×Dic13C2411yescharacteristic
139C2×Dic13C2413yes—
140C2×Dic13C2413yes—
141C2×Dic13C2411yescharacteristic
142C2×Dic13C2413yes—
143C2×Dic13C2413yes—
144C2×Dic13C2411yescharacteristic
145C4×D13—26no—
146Dic26—26no—
147Dic26—26no—
148#557—133no—
149#557—131no—
150#556—133no—
151#552—133no—
152#552—133no—
153D4×Q8—131no—
154D4×Q8—131no—
155D4×Q8D1311yescharacteristic, complemented
156#541—133no—
157#541—133no—
158#533—133no—
159#529—133no—
160#519—131no—
161#519—131no—
162C2×C4×Q8—131no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C132−1+412yes—
169C22×C13C2511yescharacteristic
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—21no—
173C4×C13—23no—
174C4×C13—23no—
175C4×C13—23no—
176C4×C13—21no—
177C4×C13C2×#4116yes—
178Dic13—23no—
179Dic13—23no—
180Dic13—23no—
181Dic13—23no—
182Dic13—21no—
183Dic13—21no—
184Dic132−1+412yes—
185C22×Q8—131no—
186C22×Q8C2×D1311yescharacteristic
187C22×Q8C2×D1311yescharacteristic
188C4⋊Q8—133no—
189C4⋊Q8—133no—
190C4⋊Q8—133no—
191C4⋊Q8C2×D1313yes—
192#126—133no—
193#126—136no—
194#126—133no—
195#126—136no—
196#125—133no—
197#125—136no—
198#125—136no—
199#125—136no—
200#125—133no—
201#125—133no—
202#124—133no—
203#123—133no—
204#123—133no—
205C22⋊Q8—133no—
206C22⋊Q8—133no—
207C22⋊Q8—133no—
208C22⋊Q8—133no—
209C22⋊Q8—133no—
210C22⋊Q8C2×D1313yes—
211C22⋊Q8C2×D1313yes—
212#121—131no—
213C4×Q8—131no—
214C4×Q8—133no—
215C4×Q8—131no—
216C4×Q8—133no—
217C4×Q8—133no—
218C4×Q8—131no—
219C4×Q8—133no—
220C4×Q8—133no—
221C4×Q8—136no—
222C4×Q8—133no—
223C4×Q8—133no—
224C4×Q8C2×D1311yescharacteristic
225C4×D4—133no—
226C4×D4—133no—
227C4×D4C2×D1313yes—
228#117—133no—
229#117—133no—
230#117—133no—
231#117—136no—
232#117—133no—
233C2×C4⋊C4—133no—
234C2×C42—133no—
235C2×C13—22no—
236C2×C13—41no—
237C2×C13C22×#4111yescharacteristic
238C2×C13C2×2−1+411yescharacteristic
239C2×C13C2×2−1+411yescharacteristic
240D13—41no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—133no—
244C2×Q8—133no—
245C2×Q8—264no—
246C2×Q8C22×D1313yes—
247C2×Q8C22×D1313yes—
248C2×Q8C22×D1311yescharacteristic
249C2×D4—131no—
250C2×D4—131no—
251C2×D4C22×D1311yescharacteristic
252C22×C4—131no—
253C22×C4—133no—
254C22×C4—133no—
255C22×C4C22×D1313yes—
256C22×C4C22×D1313yes—
257C4⋊C4—133no—
258C4⋊C4—133no—
259C4⋊C4—136no—
260C4⋊C4—133no—
261C4⋊C4—133no—
262C4⋊C4—133no—
263C4⋊C4—133no—
264C4⋊C4—133no—
265C4⋊C4—136no—
266C4⋊C4—136no—
267C4⋊C4—133no—
268C4⋊C4—133no—
269C4⋊C4—131no—
270C4⋊C4—136no—
271C4⋊C4—133no—
272C4⋊C4—133no—
273C4⋊C4C22×D1313yes—
274C4⋊C4C22×D1313yes—
275C4⋊C4C22×D1316yes—
276C22⋊C4—131no—
277C22⋊C4—133no—
278C22⋊C4—133no—
279C22⋊C4—133no—
280C22⋊C4—131no—
281C22⋊C4—133no—
282C22⋊C4—133no—
283C22⋊C4—133no—
284C22⋊C4C22×D1313yes—
285C22⋊C4C22×D1313yes—
286C42—133no—
287C42—133no—
288C42—133no—
289C42—133no—
290C42—136no—
291C42—136no—
292C42—133no—
293C42C22×D1313yes—
294C13#352311yescharacteristic, complemented, Sylow
295C23—131no—
296C23C23×D1311yescharacteristic
297C23C23×D1311yescharacteristic
298Q8—26no—
299Q8—26no—
300Q8—266no—
301Q8—266no—
302Q8#612914yes—
303D4—22no—
304D4—262no—
305D4—262no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—131no—
309C2×C4—133no—
310C2×C4—131no—
311C2×C4—133no—
312C2×C4—131no—
313C2×C4—133no—
314C2×C4—133no—
315C2×C4—262no—
316C2×C4—266no—
317C2×C4—266no—
318C2×C4C23×D1313yes—
319C2×C4C23×D1313yes—
320C2×C4C23×D1313yes—
321C2×C4C23×D1311yescharacteristic
322C2×C4C23×D1313yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—261no—
329C22—261no—
330C22—261no—
331C22#8825412yes—
332C22C24×D1311yescharacteristic
333C4—23no—
334C4—23no—
335C4—21no—
336C4—23no—
337C4—132no—
338C4—263no—
339C4—263no—
340C4—263no—
341C4—261no—
342C4—261no—
343C4—263no—
344C4C2×#612916yes—
345C2—22no—
346C2—41no—
347C2—521no—
348C2C22×#612911yescharacteristic
349C2C2×#8825411yescharacteristic
350C2D13×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingD4×Q8×C13C2
prime radical#88193C22
hypercenterD4×Q8D13
hypocenterC13#3523
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. D4×Q8×C13C2semidirect
2. Q8×C22⋊D13C2semidirect
3. Q8×C22⋊D13C2semidirect
4. #11719517C2semidirect
5. C2×Q8×Dic13C2semidirect
6. #11719436C2semidirect
7. #11719426C2semidirect
8. #11719347C2semidirect
9. #11719346C2semidirect
10. #11719330C2semidirect
11. #11719327C2semidirect
12. #11719277C2semidirect
13. #11719274C2semidirect
14. #11719246C2semidirect
155. D4×Q8D13semidirect
294. C13#3523semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C132
Q8×C22⋊D132
#117195172
C2×Q8×Dic132
#117194362
#117194262
#117193472
#117193462
#117193302
#117193272
#117192772
#117192742
#117192462
#117192432
#352313