Finite Group Databasebeta

← #16798250

Subgroups — #16798250

Order 3328.

608 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130767C212yesmaximal, complemented
2#13130755C212yesmaximal, complemented
3#13130745C212yesmaximal
4#13130721C211yesmaximal, characteristic
5#13130719C211yesmaximal, characteristic
6#13130642C212yesmaximal, complemented
7#13130592C212yesmaximal
8#13130557C212yesmaximal, complemented
9#13123265C211yesmaximal, characteristic
10C2×#88161C2211yescharacteristic
11C2×#88161C2211yescharacteristic
12C4×#6127C2211yescharacteristic
13#11719132C2212yes—
14#11719116C2212yes—
15D13⋊#108C2212yes—
16#11719092C2212yes—
17#11719089C2214yes—
18C4×C13×M16C411yescharacteristic, complemented
19#11718783C411yescharacteristic, complemented
20#11718783C411yescharacteristic, complemented
21C2×#88043C411yescharacteristic, complemented
22#11718368C411yescharacteristic, complemented
23#11718368C2211yescharacteristic
24D13×#97C411yescharacteristic, complemented
25D13×#97C2211yescharacteristic
26#11718350C411yescharacteristic, complemented
27#11718350C411yescharacteristic, complemented
28#11718350C2211yescharacteristic
29#11718350C2211yescharacteristic
30#11718269C2212yes—
31#11718267C2212yes—
32#11718266C2214yes—
33#11718235C2214yes—
34#11718234C2214yes—
35C2×#6127C2311yescharacteristic
36#88237C2314yes—
37D13⋊M16C2314yes—
38C2×C13×M16C2×C411yescharacteristic
39C2×C13×M16C2×C411yescharacteristic
40C2×C42×C13C2×C411yescharacteristic
41C4×C22⋊D13—21no—
42C4×C22⋊D13—21no—
43#88180C2×C411yescharacteristic
44C22×#1055C2×C411yescharacteristic
45C22×#1055C2×C411yescharacteristic
46#88161—24no—
47#88161—22no—
48#88161—22no—
49C2×#6094C2×C411yescharacteristic
50C2×#6094C2×C411yescharacteristic
51C2×#6094C2311yescharacteristic
52C2×#6094C2311yescharacteristic
53C2×C8×D13C2×C411yescharacteristic
54C2×C8×D13C2×C411yescharacteristic
55C2×C8×D13C2311yescharacteristic
56C2×C8×D13C2311yescharacteristic
57C4×D52—21no—
58#88126C2×C411yescharacteristic
59#88126C2311yescharacteristic
60C42×D13C2×C411yescharacteristic
61C42×D13C2311yescharacteristic
62C4×Dic26—21no—
63#88121—22no—
64#88119—22no—
65#88113—22no—
66#88107—22no—
67#88104—22no—
68#88103—22no—
69#88102—22no—
70#88101—22no—
71#88100—24no—
72C8×#261—24no—
73C13×#97C2×C411yescharacteristic
74C13×#97C2×C411yescharacteristic
75C4×C8×C13C2×C411yescharacteristic
76C4×C8×C13C2×C411yescharacteristic
77#88055C2×C411yescharacteristic
78#88055C2×C411yescharacteristic
79#88055C2×C411yescharacteristic
80#88055C2×C411yescharacteristic
81C8×Dic13C2×C411yescharacteristic
82C8×Dic13C2×C411yescharacteristic
83C8×Dic13C2×C411yescharacteristic
84C8×Dic13C2×C411yescharacteristic
85#88043C2×C411yescharacteristic
86#88043C2×C411yescharacteristic
87#88043C2×C411yescharacteristic
88#88043C2×C411yescharacteristic
89#20788—131nomaximal, Sylow
90C22×C4×C13—21no—
91C22×C4×C13C22×C411yescharacteristic
92C2×C22⋊D13#4111yescharacteristic
93C2×C22⋊D13#4111yescharacteristic
94#6127—22no—
95#6127—22no—
96C2×D52#4111yescharacteristic
97C2×C4×D13—21no—
98C2×C4×D13—21no—
99C2×C4×D13C22×C411yescharacteristic
100C2×C4×D13C2411yescharacteristic
101C2×Dic26#4111yescharacteristic
102C22⋊#261—24no—
103#6122—24no—
104C4⋊#261—24no—
105C4×#261—24no—
106#6118—24no—
107D13⋊C8—24no—
108C13×M16—22no—
109C13×M16—22no—
110C2×C8×C13C22×C411yescharacteristic
111C2×C8×C13C22×C411yescharacteristic
112C2×C8×C13C22×C411yescharacteristic
113C2×C8×C13C22×C411yescharacteristic
114C42×C13—21no—
115C42×C13C22×C411yescharacteristic
116C42×C13C22×C411yescharacteristic
117C22⋊Dic13—21no—
118#6103—21no—
119#6103—21no—
120C4⋊Dic13—21no—
121#6101—21no—
122#6101—21no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13C22×C411yescharacteristic
126C4×Dic13C22×C411yescharacteristic
127C2×#1055—21no—
128C2×#1055—21no—
129C2×#1055—22no—
130C2×#1055C22×C411yescharacteristic
131C2×#1055C22×C411yescharacteristic
132C2×#1055C22×C411yescharacteristic
133C2×#1055C22×C411yescharacteristic
134#6094—22no—
135#6094—22no—
136#6094—22no—
137#6094—22no—
138C8×D13—21no—
139C8×D13—21no—
140C8×D13—22no—
141C8×D13#4114yes—
142C8×D13#4112yes—
143C8×D13#4112yes—
144#2875—131no—
145#1841—132no—
146#1833—132no—
147#1827—132no—
148#1813—131no—
149#1812—131no—
150#1773—132no—
151#1757—132no—
152#1747—132no—
153C23×C13#11711yescharacteristic
154C22×D13#11711yescharacteristic
155C22×D13C2×#4111yescharacteristic
156C2×#261—44no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—81no—
162C2×C4×C13#11711yescharacteristic
163C2×C4×C13C23×C411yescharacteristic
164C22⋊D13—22no—
165C22⋊D13—22no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13#11711yescharacteristic
169C2×Dic13C2×#4111yescharacteristic
170D52—22no—
171C4×D13—21no—
172C4×D13—21no—
173C4×D13—81no—
174C4×D13—81no—
175C4×D13C2×#4112yes—
176C4×D13C2×#4112yes—
177Dic26—22no—
178#1057—44no—
179C8×C13—21no—
180C8×C13—21no—
181C8×C13#11712yes—
182C8×C13#11712yes—
183#1055—21no—
184#1055—21no—
185#1055#11711yescharacteristic
186#1055#11711yescharacteristic
187#1055#11712yes—
188C2×#131—131no—
189C2×#131—131no—
190C4×#41—131no—
191C2×#108—132no—
192#427—132no—
193#413—132no—
194#410—132no—
195#405—131no—
196#405—131no—
197#405—131no—
198#405—131no—
199#405—131no—
200#405—131no—
201#405—134no—
202C4×M16—131no—
203C4×M16—131no—
204C4×M16#26111yescharacteristic, complemented
205C2×#97—131no—
206C2×#97—131no—
207C2×#97—131no—
208#344—134no—
209#339—134no—
210#338—132no—
211H(3,ℤ/4)—132no—
212H(3,ℤ/4)—134no—
213C22×C13—21no—
214C22×C13—41no—
215C22×C13C2×#11711yescharacteristic
216C2×D13—21no—
217C2×D13—41no—
218C2×D13—41no—
219C2×D13#52912yes—
220#261—84no—
221C4×C13—21no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13C2×#11711yescharacteristic
225C4×C13C2×#11711yescharacteristic
226Dic13—21no—
227Dic13—41no—
228Dic13—41no—
229Dic13#52912yes—
230C2×#41—131no—
231#131—264no—
232#131—262no—
233#131—262no—
234C2×M16—131no—
235C2×M16—131no—
236C2×M16—131no—
237C2×M16—131no—
238C2×M16—134no—
239C2×M16C2×#26111yescharacteristic
240C2×M16C2×#26111yescharacteristic
241C22×C8—131no—
242C22×C8—131no—
243C22×C8—131no—
244C22×C8—131no—
245C22×C8—131no—
246C22×C8—131no—
247C4×Q8—261no—
248C4×D4—261no—
249C4×D4—261no—
250C4×D4—261no—
251#117—131no—
252#117—131no—
253#117—131no—
254#117—134no—
255C2×C42—131no—
256C2×C42—131no—
257C2×C42C2×#26111yescharacteristic
258#108—262no—
259#108—262no—
260#107—262no—
261#106—262no—
262#101—262no—
263#100—262no—
264#99—262no—
265#99—262no—
266#97—131no—
267#97—131no—
268#97—131no—
269#97—131no—
270#97—131no—
271#97—131no—
272#97—131no—
273#97—131no—
274#97—264no—
275#97C2×#26111yescharacteristic
276#97C2×#26111yescharacteristic
277C4×C8—131no—
278C4×C8—131no—
279C4×C8—131no—
280C4×C8—131no—
281C4×C8—264no—
282C4×C8C2×#26111yescharacteristic
283C4×C8C2×#26111yescharacteristic
284C2×C13—21no—
285C2×C13—41no—
286C2×C13#228311yescharacteristic
287D13—22no—
288D13—41no—
289#41—262no—
290#41—262no—
291C2×Q8—131no—
292C2×D4—131no—
293C2×D4—131no—
294C2×D4—131no—
295C22×C4—21no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—261no—
299C22×C4—261no—
300C22×C4C22×#26111yescharacteristic
301M16—22no—
302M16—22no—
303M16—262no—
304M16—262no—
305M16—262no—
306M16—262no—
307M16—264no—
308M16—264no—
309C2×C8—131no—
310C2×C8—131no—
311C2×C8—134no—
312C2×C8—132no—
313C2×C8—132no—
314C2×C8—131no—
315C2×C8—131no—
316C2×C8—261no—
317C2×C8—261no—
318C2×C8—262no—
319C2×C8—261no—
320C2×C8—261no—
321C2×C8—262no—
322C2×C8—264no—
323C2×C8C22×#26111yescharacteristic
324C2×C8C22×#26111yescharacteristic
325C2×C8C22×#26111yescharacteristic
326C2×C8C22×#26111yescharacteristic
327C4⋊C4—261no—
328C4⋊C4—261no—
329C4⋊C4—264no—
330C4⋊C4—261no—
331C22⋊C4—261no—
332C22⋊C4—261no—
333C22⋊C4—261no—
334C22⋊C4—264no—
335C42—21no—
336C42—131no—
337C42—131no—
338C42—261no—
339C42—261no—
340C42—264no—
341C42C22×#26111yescharacteristic
342C42C22×#26111yescharacteristic
343C13#2078811yescharacteristic, complemented, Sylow
344C23—131no—
345C23—131no—
346C23#8823711yescharacteristic
347Q8—262no—
348D4—262no—
349D4—262no—
350D4—262no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—81no—
356C2×C4—131no—
357C2×C4—132no—
358C2×C4—132no—
359C2×C4—131no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—524no—
365C2×C4—1041no—
366C2×C4—1041no—
367C2×C4#8823711yescharacteristic
368C2×C4C23×#26111yescharacteristic
369C8—21no—
370C8—21no—
371C8—131no—
372C8—131no—
373C8—132no—
374C8—261no—
375C8—261no—
376C8—524no—
377C8#8823712yes—
378C8#8823712yes—
379C22—21no—
380C22—41no—
381C22—132no—
382C22—261no—
383C22—521no—
384C22—521no—
385C22C2×#8823711yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—132no—
390C4—261no—
391C4—521no—
392C4—521no—
393C4—1044no—
394C4C2×#8823711yescharacteristic
395C4C2×#8823711yescharacteristic
396C2—21no—
397C2—41no—
398C2—262no—
399C2—521no—
400C2#1313128311yescharacteristic
subgroupG/H
centerC4C2×#88237
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC4×C13×M16C4
socleC2×C13#2283
prime radicalC2×#6127C23
cosocleC2×C4×D13C24
hypercenterC4×M16#261
hypocenterC13#20788
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C4×C8 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. #13130767C2semidirect
2. #13130755C2semidirect
6. #13130642C2semidirect
8. #13130557C2semidirect
18. C4×C13×M16C4semidirect
19. #11718783C4semidirect
20. #11718783C4semidirect
21. C2×#88043C4semidirect
22. #11718368C4semidirect
24. D13×#97C4semidirect
26. #11718350C4semidirect
27. #11718350C4semidirect
204. C4×M16#261semidirect
343. C13#20788semidirect

Maximal subgroups

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

subgroupindex
#131307672
#131307552
#131307452
#131307212
#131307192
#131306422
#131305922
#131305572
#131232652
#2078813