Finite Group Databasebeta

← #16797219

Subgroups — #16797219

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#430C211yesmaximal, characteristic
2#13131399C212yesmaximal
3C2×#11719099C211yesmaximal, characteristic
4#13130657C214yesmaximal, complemented
5#108×#261C214yesmaximal, complemented
6C2×#11718273C212yesmaximal
7D13×#430C211yesmaximal, characteristic
8C2×#88237C2211yescharacteristic
9C2×D13⋊M16C2212yes—
10C22×D13⋊C8C2211yescharacteristic
11C2×M16×D13C2212yes—
12C2×M16×D13C2211yescharacteristic
13#11719100C418yescomplemented
14#11719099—24no—
15#11719099C418yes—
16M16×#261C2218yes—
17D13⋊#108C2214yes—
18#11719089—24no—
19C2×#88100C2212yes—
20C2×C8×#261C2212yes—
21C13×#430C411yescharacteristic, complemented
22#11718786C411yescharacteristic, complemented
23#11718785C412yescomplemented
24#11718554C414yescomplemented
25D13×#108C2214yes—
26#11718273C2214yes—
27#11718273C2214yes—
28C22×C4×D13C2311yescharacteristic
29C2×C22⋊#261Q812yes—
30C2×#6122—22no—
31C22×#1057—21no—
32#88237C2×C414yes—
33#88237D414yes—
34C2×C4⋊#261Q812yes—
35C2×C4×#261C2312yes—
36D13⋊M16—22no—
37D13⋊M16—22no—
38D13⋊M16C2×C414yes—
39D13⋊M16C2314yes—
40C2×#6118C2×C414yes—
41C2×D13⋊C8—22no—
42C2×D13⋊C8—21no—
43C2×D13⋊C8—22no—
44C2×D13⋊C8C2×C414yes—
45C2×D13⋊C8C2311yescharacteristic
46C2×D13⋊C8C2311yescharacteristic
47C2×C13×M16C2×C412yes—
48C2×C13×M16C2×C411yescharacteristic
49C2×#6099C2×C412yes—
50C2×#6099C2×C411yescharacteristic
51M16×D13—22no—
52M16×D13—22no—
53M16×D13C2×C414yes—
54M16×D13C2×C414yes—
55M16×D13C2×C414yes—
56M16×D13C2314yes—
57C2×#6094—22no—
58C2×#6094C2×C412yes—
59C2×C8×D13—22no—
60C2×C8×D13C2312yes—
61#88104C2×C418yes—
62#88103C2×C418yes—
63#88100—28no—
64#88100C2×C418yes—
65C8×#261—28no—
66C8×#261C2×C418yes—
67C13×#108C2×C414yes—
68#88062C2×C418yes—
69#88059C2×C414yes—
70#20459—131nomaximal, Sylow
71C23×D13C2×Q811yescharacteristic
72C22×#261C2×Q814yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×Dic13#4111yescharacteristic
75C2×C4×D13C22×C411yescharacteristic
76C2×C4×D13C22×C412yes—
77C2×C4×D13C22×C412yes—
78C2×C4×D13C2×D412yes—
79C2×C4×D13C2×Q811yescharacteristic
80C2×C4×D13#4111yescharacteristic
81C2×C4×D13#4112yes—
82C2×C4×D13C2411yescharacteristic
83C22⋊#261C4⋊C418yes—
84#6122—24no—
85#6122—24no—
86C2×#1057—24no—
87C2×#1057—24no—
88C2×#1057—21no—
89C2×#1057—21no—
90C4⋊#261C4⋊C418yes—
91C4×#261C22×C414yes—
92C4×#261C2×D414yes—
93#6118—24no—
94#6118C22×C418yes—
95D13⋊C8—24no—
96D13⋊C8—24no—
97D13⋊C8—24no—
98D13⋊C8—21no—
99D13⋊C8—21no—
100D13⋊C8C22×C412yes—
101D13⋊C8C22×C412yes—
102C13×M16—22no—
103C13×M16C4214yes—
104C13×M16C22×C414yes—
105C2×C8×C13—22no—
106C2×C8×C13C22×C412yes—
107#6099—22no—
108#6099C4214yes—
109#6099C22×C414yes—
110C2×#1055—22no—
111C2×#1055C22×C412yes—
112#6094—24no—
113#6094—24no—
114#6094C4218yes—
115C8×D13—24no—
116C8×D13—24no—
117C8×D13C22×C414yes—
118C8×D13C22×C414yes—
119C2×#430—131no—
120C2×#430—131no—
121#2873—132no—
122C2×#405—131no—
123#1778—134no—
124C4×#108—134no—
125C2×#341—132no—
126C23×C13C4×Q811yescharacteristic
127C22×D13—42no—
128C22×D13C2×C4⋊C412yes—
129C22×D13C4×Q812yes—
130C22×D13C4×Q811yescharacteristic
131C22×D13C22×Q811yescharacteristic
132C2×#261—44no—
133C2×#261C2×C4⋊C418yes—
134C2×C4×C13C2×C4212yes—
135C2×C4×C13C4×D412yes—
136C2×C4×C13C4×Q811yescharacteristic
137C2×C4×C13C23×C411yescharacteristic
138C2×Dic13#11712yes—
139C2×Dic13C4×D412yes—
140C2×Dic13C4×Q811yescharacteristic
141C2×Dic13C2×#4111yescharacteristic
142C4×D13C2×C4212yes—
143C4×D13C2×C4⋊C412yes—
144C4×D13#11712yes—
145C4×D13C4×D412yes—
146C4×D13C4×D412yes—
147C4×D13C4×Q812yes—
148C4×D13C23×C411yescharacteristic
149C4×D13C23×C411yescharacteristic
150C4×D13C22×D411yescharacteristic
151C4×D13C2×#4111yescharacteristic
152#1057—22no—
153#1057—22no—
154#1057—28no—
155C8×C13—24no—
156C8×C13C2×C4214yes—
157#1055—24no—
158#1055C2×C4214yes—
159C22×M16—131no—
160C22×M16—132no—
161C22×M16—132no—
162C23×C8—131no—
163C2×#117—131no—
164#430—138no—
165#430—132no—
166#430—131no—
167#430—134no—
168#430#26111yescharacteristic, complemented
169C2×#108—134no—
170C2×#108—134no—
171#405—138no—
172#405—264no—
173#405—264no—
174C4×M16—138no—
175C2×#97—132no—
176C2×C4×C8—132no—
177#341—134no—
178#341—134no—
179C22×C13—41no—
180C22×C13C4×C4⋊C412yes—
181C22×C13C2×C4×Q811yescharacteristic
182C2×D13—22no—
183C2×D13—24no—
184C2×D13—42no—
185C2×D13—41no—
186C2×D13C4×C4⋊C412yes—
187C2×D13C22×C4⋊C411yescharacteristic
188C2×D13C2×C4×Q811yescharacteristic
189#261—28no—
190C4×C13C4×C4⋊C412yes—
191C4×C13C22×C4211yescharacteristic
192C4×C13C2×C4×D411yescharacteristic
193Dic13C4×C4⋊C412yes—
194Dic13C2×#11711yescharacteristic
195Dic13C2×C4×D411yescharacteristic
196C23×C4—131no—
197C2×M16—131no—
198C2×M16—134no—
199C2×M16—134no—
200C2×M16—132no—
201C2×M16—134no—
202C2×M16—134no—
203C2×M16—134no—
204C2×M16—132no—
205C2×M16—134no—
206C2×M16—134no—
207C2×M16—262no—
208C2×M16—262no—
209C2×M16—262no—
210C2×M16—262no—
211C2×M16—262no—
212C2×M16—262no—
213C2×M16C2×#26112yes—
214C2×M16C2×#26111yescharacteristic
215C22×C8—132no—
216C22×C8—131no—
217C22×C8—131no—
218C22×C8—134no—
219C22×C8—262no—
220C22×C8—262no—
221C22×C8—261no—
222C22×C8—261no—
223C22×C8—262no—
224#117—134no—
225#117—134no—
226C2×C4⋊C4—132no—
227C2×C22⋊C4—132no—
228C2×C42—132no—
229#108—138no—
230#108—138no—
231#108—138no—
232#108—134no—
233#108C2×#26114yes—
234#97—138no—
235#97—268no—
236C4×C8—138no—
237C4×C8—268no—
238C2×C13—21no—
239C2×C13—22no—
240C2×C13C2×C4×C4⋊C411yescharacteristic
241D13—21no—
242D13—22no—
243D13#291612yes—
244C24—131no—
245C22×C4—131no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—132no—
249C22×C4—132no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—134no—
255C22×C4C22×#26111yescharacteristic
256M16—22no—
257M16—134no—
258M16—138no—
259M16—138no—
260M16—134no—
261M16—264no—
262M16—264no—
263M16—264no—
264M16—264no—
265M16—264no—
266M16—262no—
267M16C4×#26114yes—
268M16C22×#26114yes—
269C2×C8—22no—
270C2×C8—132no—
271C2×C8—134no—
272C2×C8—134no—
273C2×C8—132no—
274C2×C8—132no—
275C2×C8—264no—
276C2×C8—264no—
277C2×C8—264no—
278C2×C8—264no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—264no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—264no—
285C2×C8—264no—
286C2×C8—262no—
287C2×C8C22×#26112yes—
288C4⋊C4—138no—
289C22⋊C4—138no—
290C42—134no—
291C42—134no—
292C13#2045911yescharacteristic, complemented, Sylow
293C23—132no—
294C23—131no—
295C23—132no—
296C23—131no—
297C23—522no—
298C23Q8×#26111yescharacteristic
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—132no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—132no—
307C2×C4—131no—
308C2×C4—131no—
309C2×C4—132no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—132no—
313C2×C4—138no—
314C2×C4—524no—
315C2×C4C2×C4×#26112yes—
316C2×C4D4×#26112yes—
317C2×C4Q8×#26111yescharacteristic
318C2×C4C23×#26111yescharacteristic
319C8—24no—
320C8—134no—
321C8—262no—
322C8—262no—
323C8—268no—
324C8—264no—
325C8C2×C4×#26114yes—
326C22—41no—
327C22—131no—
328C22—131no—
329C22—132no—
330C22—262no—
331C22—264no—
332C22—522no—
333C22—521no—
334C22C4⋊C4×#26112yes—
335C22C2×Q8×#26111yescharacteristic
336C4—131no—
337C4—131no—
338C4—132no—
339C4—268no—
340C4C4⋊C4×#26112yes—
341C4C22×C4×#26111yescharacteristic
342C4C2×D4×#26111yescharacteristic
343C2—22no—
344C2—21no—
345C2—132no—
346C2—261no—
347C2—262no—
348C2C2×C4⋊C4×#26111yescharacteristic
subgroupG/H
centerC4C2×D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC13×#430C4
socleC2×C13C2×C4×C4⋊C4
prime radicalC23×D13C2×Q8
cosocleC2×C4×D13C24
hypercenter#430#261
hypocenterC13#20459
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
4. #13130657C2semidirect
5. #108×#261C2semidirect
13. #11719100C4semidirect
21. C13×#430C4semidirect
22. #11718786C4semidirect
23. #11718785C4semidirect
24. #11718554C4semidirect
168. #430#261semidirect
292. C13#20459semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4302
#131313992
C2×#117190992
#131306572
#108×#2612
C2×#117182732
D13×#4302
#2045913