Finite Group Databasebeta

← #15759000

Subgroups — #15759000

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124624C211yesmaximal, characteristic
2#41×#1055C211yesmaximal, characteristic
3#13113334C211yesmaximal, characteristic, complemented
4#13113290C211yesmaximal, characteristic, complemented
5#13112731C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1806C211yesmaximal, characteristic
8C4×C13×#41C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×#104—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13#11718894—21no—
14Q8×#1055—21no—
15#11718683—21no—
16#11718682C411yescharacteristic, complemented
17#11718681C411yescharacteristic, complemented
18D4×#1055—21no—
19D4×#1055—22no—
20#11718670—21no—
21#11718669C411yescharacteristic, complemented
22#11718668C411yescharacteristic, complemented
23#11718659—21no—
24#11718586—21no—
25#11718586C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27C2×C4×#1055—21no—
28C2×C4×#1055C2211yescharacteristic
29C13×#339—21no—
30#11718076—21no—
31#11718076—21no—
32#11718044—22no—
33C2×C13×#41D411yescharacteristic
34C2×C13×M16—21no—
35C4×Q8×C13C2×C411yescharacteristic
36C4×Q8×C13D411yescharacteristic
37C4×D4×C13—21no—
38C4×D4×C13—21no—
39C4×D4×C13C2×C411yescharacteristic
40C4×D4×C13D411yescharacteristic
41C13×#117—21no—
42C13×#117D411yescharacteristic
43C2×C13×C4⋊C4—21no—
44C2×C42×C13—21no—
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47#88180—21no—
48#88178—21no—
49#88178—21no—
50C22×#1055—22no—
51C22×#1055—21no—
52C22×#1055—21no—
53#88124—21no—
54#88123C2×C411yescharacteristic
55#88123C2×C411yescharacteristic
56C4×Dic26—21no—
57C4×Dic26—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×#104—42no—
61C13×#95—21no—
62#88075—21no—
63#88075—21no—
64#88072—21no—
65#88072—21no—
66C22⋊#1055—22no—
67C22⋊#1055D412yes—
68#88048—21no—
69#88048—21no—
70#88047—21no—
71#88047—21no—
72C4⋊#1055—22no—
73C4⋊#1055—21no—
74C4⋊#1055—21no—
75C4⋊#1055C2×C411yescharacteristic
76C4⋊#1055C2×C411yescharacteristic
77C4×#1055—22no—
78C4×#1055—21no—
79C4×#1055—21no—
80C4×#1055D411yescharacteristic
81C4×#1055D411yescharacteristic
82#9207—131nomaximal, Sylow
83C13×#41—21no—
84C13×#41—21no—
85C13×#41SD1612yes—
86C13×#41Q1612yes—
87C2×Q8×C13C22⋊C411yescharacteristic
88C2×D4×C13—21no—
89C2×D4×C13C22⋊C411yescharacteristic
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—41no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13#4111yescharacteristic
97C2×Dic26—21no—
98C2×Dic26—21no—
99C13×M16—41no—
100C13×M16—41no—
101C2×C8×C13—41no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4C22⋊C411yescharacteristic
107C13×C4⋊C4C22⋊C411yescharacteristic
108C13×C22⋊C4—21no—
109C13×C22⋊C4—21no—
110C13×C22⋊C4—21no—
111C42×C13—21no—
112C42×C13—21no—
113C42×C13—21no—
114C42×C13—41no—
115C42×C13—41no—
116C42×C13C22×C411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13#4111yescharacteristic
120C22⋊Dic13—41no—
121C4⋊Dic13—21no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C4⋊Dic13—21no—
125#6101—41no—
126#6101—41no—
127C4×Dic13—41no—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—21no—
131C2×#1055—21no—
132C2×#1055—22no—
133C2×#1055—42no—
134C2×#1055—44no—
135C2×#1055—41no—
136C2×#1055—41no—
137#3076—131no—
138C8×#41—131no—
139#1806D1311yescharacteristic
140#1503—131no—
141#1493—131no—
142#1301—131no—
143#1279—131no—
144C23×C13—21no—
145C23×C13#12111yescharacteristic
146Q8×C13—21no—
147Q8×C13#10312yes—
148D4×C13—22no—
149D4×C13—22no—
150D4×C13—21no—
151D4×C13#10312yes—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—42no—
164C2×C4×C13—81no—
165C2×C4×C13—81no—
166C2×C4×C13C2×C22⋊C411yescharacteristic
167C2×C4×C13C4×D411yescharacteristic
168C2×C4×C13C4×D411yescharacteristic
169C2×C4×C13#12011yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×C4×C13#12311yescharacteristic
172C2×C4×C13C2×SD1611yescharacteristic
173C2×C4×C13C2×Q1611yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13#13511yescharacteristic
176C2×Dic13—41no—
177C2×Dic13—41no—
178Dic26—41no—
179Dic26—41no—
180Dic26—81no—
181C8×C13—81no—
182#1055—22no—
183#1055—41no—
184#1055—42no—
185#1055—41no—
186#1055—41no—
187#533—131no—
188C4×#41C2×D1311yescharacteristic
189#479—261no—
190#478—261no—
191#477—131no—
192#476—131no—
193#475—131no—
194#474—131no—
195C8×Q8—261no—
196C8×D4—262no—
197C8×D4—261no—
198#431—131no—
199#431—261no—
200#427—261no—
201#423C2×D1311yescharacteristic
202C2×C4⋊C8—131no—
203C2×#104—21no—
204#416—261no—
205C2×C4×C8—131no—
206C2×C4×C8—261no—
207C4×C4⋊C4C2×D1311yescharacteristic
208#339—21no—
209#328—262no—
210Q8⋊C8—261no—
211Q8⋊C8—261no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—22no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13#38611yescharacteristic
218C22×C13#46511yescharacteristic
219C22×C13#46711yescharacteristic
220C4×C13—21no—
221C4×C13—22no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—41no—
225C4×C13—41no—
226C4×C13—82no—
227C4×C13C2×#10311yescharacteristic
228C4×C13#41611yescharacteristic
229C4×C13#44311yescharacteristic
230C4×C13#44411yescharacteristic
231C4×C13#46511yescharacteristic
232C4×C13#46711yescharacteristic
233Dic13—81no—
234Dic13—81no—
235C2×#41C22⋊D1311yescharacteristic
236C2×M16—21no—
237C22×C8—262no—
238C22×C8—261no—
239C22×C8—261no—
240C4⋊Q8—131no—
241C4⋊Q8—131no—
242#125—261no—
243C22⋊Q8—261no—
244C22⋊Q8—261no—
245C4×Q8—261no—
246C4×Q8—261no—
247C4×Q8C4×D1311yescharacteristic
248C4×Q8D5211yescharacteristic
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C4×D1311yescharacteristic
252C4×D4D5211yescharacteristic
253#117—21no—
254#117—261no—
255#117C22⋊D1311yescharacteristic
256C2×C4⋊C4—21no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42C22×D1311yescharacteristic
260#107—261no—
261#107—261no—
262#106—261no—
263#106—261no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—131no—
267C4⋊C8—131no—
268C4⋊C8—262no—
269C4⋊C8—261no—
270C4⋊C8—261no—
271#104—42no—
272#103—261no—
273#103—261no—
274#102—261no—
275#102—261no—
276C22⋊C8—132no—
277C22⋊C8—262no—
278C4×C8—131no—
279C4×C8—131no—
280C4×C8—262no—
281C4×C8—261no—
282C4×C8—261no—
283#95—21no—
284C2×C13—21no—
285C2×C13—21no—
286C2×C13—42no—
287C2×C13#187611yescharacteristic
288C2×C13#189211yescharacteristic
289C2×C13#190611yescharacteristic
290#41—21no—
291#41—21no—
292#41#610512yes—
293#41#610712yes—
294C2×Q8—261no—
295C2×Q8—261no—
296C2×Q8#610311yescharacteristic
297C2×D4—21no—
298C2×D4#610311yescharacteristic
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4D4×D1311yescharacteristic
304C22×C4#612911yescharacteristic
305C22×C4C2×C22⋊D1311yescharacteristic
306M16—41no—
307M16—41no—
308C2×C8—41no—
309C2×C8—261no—
310C2×C8—261no—
311C2×C8—262no—
312C2×C8—261no—
313C2×C8—261no—
314C2×C8—522no—
315C2×C8—524no—
316C2×C8—521no—
317C2×C8—521no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—261no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4—261no—
326C4⋊C4—521no—
327C4⋊C4—521no—
328C4⋊C4#610311yescharacteristic
329C4⋊C4#610311yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—521no—
334C42—21no—
335C42—21no—
336C42—21no—
337C42—41no—
338C42—41no—
339C42—521no—
340C42C2×C4×D1311yescharacteristic
341C42C2×D5211yescharacteristic
342C42D4×D1311yescharacteristic
343C42#612911yescharacteristic
344C13#920711yescharacteristic, complemented, Sylow
345C23—21no—
346C23#8819311yescharacteristic
347Q8—21no—
348Q8—521no—
349Q8—521no—
350Q8—1041no—
351Q8#8805012yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#8805012yes—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4#8813511yescharacteristic
373C2×C4#8813511yescharacteristic
374C2×C4#8813611yescharacteristic
375C2×C4#8814011yescharacteristic
376C2×C4C2×#610311yescharacteristic
377C2×C4C2×#610511yescharacteristic
378C2×C4#8819311yescharacteristic
379C2×C4C2×#610711yescharacteristic
380C2×C4#8820411yescharacteristic
381C2×C4#8820411yescharacteristic
382C8—81no—
383C8—262no—
384C8—521no—
385C8—522no—
386C8—521no—
387C8—521no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#1171861911yescharacteristic
394C22#1171870211yescharacteristic
395C22#1171871211yescharacteristic
396C4—21no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—1041no—
404C4—1041no—
405C4#1171848411yescharacteristic
406C4#1171848511yescharacteristic
407C4C2×#8805011yescharacteristic
408C4#1171866311yescharacteristic
409C4#1171870211yescharacteristic
410C4#1171871211yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#1311516111yescharacteristic
415C2#1311525711yescharacteristic
416C2#1311533511yescharacteristic
subgroupG/H
centerC2×C4#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1806C2
socleC22×C13#386
prime radicalC2×C13×#41D4
cosocleC2×C42×C13C23
hypercenter#1806D13
hypocenterC13#9207
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. #13113334C2semidirect
4. #13113290C2semidirect
5. #13112731C2semidirect
6. #13112677C2semidirect
16. #11718682C4semidirect
17. #11718681C4semidirect
21. #11718669C4semidirect
22. #11718668C4semidirect
344. C13#9207semidirect

Maximal subgroups

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

subgroupindex
#131246242
#41×#10552
#131133342
#131132902
#131127312
#131126772
C13×#18062
#920713