Finite Group Databasebeta

← #15846355

Subgroups — #15846355

Order 3328.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126011C212yesmaximal
2#13125422C211yesmaximal, characteristic, complemented
3#13114364C211yesmaximal, characteristic, complemented
4#13114359C211yesmaximal, characteristic, complemented
5#13114330C211yesmaximal, characteristic, complemented
6#13114325C211yesmaximal, characteristic, complemented
7#13114294C212yesmaximal, complemented
8#13114287C212yesmaximal, complemented
9#13113584C211yesmaximal, characteristic, complemented
10#13113547C212yesmaximal, complemented
11C13×#2966C211yesmaximal, characteristic
12C13×#529C2211yescharacteristic
13#11719175C2212yes—
14C13×#446C2211yescharacteristic
15C8×Q8×C13C2211yescharacteristic
16C13×#436C2211yescharacteristic
17C13×#435—21no—
18C8×D4×C13—21no—
19C8×D4×C13C2211yescharacteristic
20C13×#433—21no—
21C13×#432C2211yescharacteristic
22C13×#405—21no—
23C2×C4×C8×C13C2211yescharacteristic
24#11718777—21no—
25#11718777—21no—
26#11718725—22no—
27#11718717—22no—
28#11718706—22no—
29#11718696—22no—
30#11718682C2212yes—
31#11718681C2212yes—
32#11718669C2212yes—
33#11718668C2212yes—
34#11718586C2212yes—
35#11718360C2211yescharacteristic
36C4×Dic52—21no—
37C4×Dic52—21no—
38#11718343C2211yescharacteristic
39#11718342C2212yes—
40#11718074C2212yes—
41#11718074C2212yes—
42#11718073C2212yes—
43#11718073C2212yes—
44#11718050C2212yes—
45#11718049C2211yescharacteristic
46#11718049C2211yescharacteristic
47C2×C13×M16—21no—
48C22×C8×C13—21no—
49C22×C8×C13D411yescharacteristic
50C22×C8×C13D411yescharacteristic
51C13×#126—21no—
52C13×#125D411yescharacteristic
53C13×#124D411yescharacteristic
54C13×#123—21no—
55C13×C22⋊Q8D411yescharacteristic
56C13×#121D411yescharacteristic
57C4×Q8×C13C2311yescharacteristic
58C4×D4×C13—21no—
59C4×D4×C13C2311yescharacteristic
60C13×#117—21no—
61C2×C42×C13C2311yescharacteristic
62#88180—22no—
63#88178—22no—
64#88178—22no—
65C2×Dic52—21no—
66C2×Dic52—21no—
67#88124—22no—
68#88123C2312yes—
69#88123C2312yes—
70C4×Dic26—22no—
71C4×Dic26—22no—
72C13×C4⋊C8—21no—
73C13×C4⋊C8—21no—
74C13×C4⋊C8C2311yescharacteristic
75C13×C4⋊C8C2311yescharacteristic
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×#97—21no—
80C13×#97—21no—
81C4×C8×C13—21no—
82C4×C8×C13D411yescharacteristic
83C4×C8×C13D411yescharacteristic
84C4×C8×C13C2311yescharacteristic
85C4×C8×C13C2311yescharacteristic
86#88075—22no—
87#88075—22no—
88#88072—22no—
89#88072—22no—
90C22⋊#1055—22no—
91#88058—21no—
92#88058—21no—
93#88056—22no—
94#88056—22no—
95#88048—22no—
96#88048—22no—
97#88047—22no—
98#88047—22no—
99C4⋊#1055C2312yes—
100C4⋊#1055C2312yes—
101C4×#1055—22no—
102#19226—131nomaximal, Sylow
103C2×Q8×C13C2×D411yescharacteristic
104C2×D4×C13—21no—
105C2×D4×C13C2×D411yescharacteristic
106C22×C4×C13—21no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C2×Dic26—22no—
111C2×Dic26—22no—
112C13×M16—42no—
113C2×C8×C13—22no—
114C2×C8×C13—21no—
115C2×C8×C13—21no—
116C2×C8×C13—41no—
117C2×C8×C13—42no—
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2×D411yescharacteristic
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4C2×D411yescharacteristic
127C13×C4⋊C4C2×D411yescharacteristic
128C13×C22⋊C4—21no—
129C13×C22⋊C4—21no—
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C42×C13—21no—
134C42×C13C2×D411yescharacteristic
135C42×C13C2×D411yescharacteristic
136C42×C13#4111yescharacteristic
137C42×C13C2411yescharacteristic
138C22⋊Dic13—42no—
139C4⋊Dic13—22no—
140C4⋊Dic13—22no—
141C4⋊Dic13—22no—
142C4⋊Dic13—22no—
143#6101—42no—
144#6101—42no—
145C4×Dic13—42no—
146C2×#1055—22no—
147C2×#1055—22no—
148Dic52—42no—
149Dic52—42no—
150#3233—132no—
151#3170—131no—
152#2966D1311yescharacteristic
153#1696—131no—
154#1695—131no—
155#1690—131no—
156#1689—131no—
157#1684—132no—
158#1683—132no—
159#1564—131no—
160#1554—132no—
161C23×C13—21no—
162C23×C13#12111yescharacteristic
163Q8×C13—22no—
164D4×C13—22no—
165D4×C13—42no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—22no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#12111yescharacteristic
177C2×C4×C13#12111yescharacteristic
178C2×C4×C13C22×D411yescharacteristic
179C2×C4×C13C22×D411yescharacteristic
180C2×C4×C13C2×#4111yescharacteristic
181C2×Dic13—42no—
182C2×Dic13—42no—
183Dic26—42no—
184Dic26—42no—
185Dic26—82no—
186C8×C13—21no—
187C8×C13—21no—
188C8×C13—21no—
189C8×C13—41no—
190C8×C13—41no—
191C8×C13#13512yes—
192#1055—42no—
193#1055—42no—
194#533—132no—
195#529C2×D1311yescharacteristic
196#500—131no—
197#499—262no—
198#494—131no—
199#488—262no—
200#487—132no—
201#485—262no—
202#482—262no—
203#477—132no—
204#476—132no—
205#475—132no—
206#474—132no—
207#467—261no—
208#467—261no—
209#446C2×D1311yescharacteristic
210C8×Q8C2×D1311yescharacteristic
211C4×Q16—261no—
212C4×Q16—261no—
213#436C2×D1311yescharacteristic
214#435—21no—
215C8×D4—21no—
216C8×D4C2×D1311yescharacteristic
217#433—21no—
218#432C2×D1311yescharacteristic
219#431—132no—
220#405—21no—
221C2×C4×C8C2×D1311yescharacteristic
222#335—132no—
223#334—131no—
224#334—131no—
225#333—132no—
226#333—132no—
227#332—132no—
228#332—132no—
229C22×C13—21no—
230C22×C13—21no—
231C22×C13—21no—
232C22×C13—41no—
233C22×C13—41no—
234C22×C13—41no—
235C22×C13C2×#12111yescharacteristic
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—41no—
241C4×C13—41no—
242C4×C13—41no—
243C4×C13C2×#13511yescharacteristic
244C4×C13#57511yescharacteristic
245C4×C13#57812yes—
246Dic13—82no—
247Dic13—82no—
248C2×Q16—261no—
249C2×Q16—261no—
250C2×M16—21no—
251C22×C8—21no—
252C22×C8C22⋊D1311yescharacteristic
253C22×C8C22⋊D1311yescharacteristic
254C4⋊Q8—132no—
255C4⋊Q8—132no—
256#126—21no—
257#125—262no—
258#125D5211yescharacteristic
259#124D5211yescharacteristic
260#123—21no—
261C22⋊Q8—262no—
262C22⋊Q8—262no—
263C22⋊Q8D5211yescharacteristic
264#121D5211yescharacteristic
265C4×Q8—262no—
266C4×Q8—262no—
267C4×Q8C22×D1311yescharacteristic
268C4×D4—21no—
269C4×D4C22×D1311yescharacteristic
270#117—21no—
271#117—262no—
272C2×C42C22×D1311yescharacteristic
273#107—261no—
274#107—261no—
275#107—262no—
276#107—262no—
277#106—262no—
278#106—262no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—132no—
282C4⋊C8—132no—
283C4⋊C8C22×D1311yescharacteristic
284C4⋊C8C22×D1311yescharacteristic
285#103—262no—
286#103—262no—
287#103—262no—
288#103—262no—
289#102—262no—
290#102—262no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—262no—
295#97—21no—
296#97—21no—
297C4×C8—21no—
298C4×C8—262no—
299C4×C8C22⋊D1311yescharacteristic
300C4×C8C22⋊D1311yescharacteristic
301C4×C8C22×D1311yescharacteristic
302C4×C8C22×D1311yescharacteristic
303C2×C13—41no—
304C2×C13—81no—
305C2×C13#303511yescharacteristic
306C2×C13#305911yescharacteristic
307C2×C13#306711yescharacteristic
308C2×Q8—262no—
309C2×Q8—262no—
310C2×Q8C2×D5211yescharacteristic
311C2×D4—21no—
312C2×D4C2×D5211yescharacteristic
313C22×C4—21no—
314C22×C4C2×D5211yescharacteristic
315C22×C4#612711yescharacteristic
316C22×C4C2×C22⋊D1311yescharacteristic
317Q16—522no—
318Q16—522no—
319M16—42no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—41no—
324C2×C8—42no—
325C2×C8—262no—
326C2×C8—262no—
327C2×C8C2×C22⋊D1311yescharacteristic
328C2×C8C2×C22⋊D1311yescharacteristic
329C2×C8C2×C22⋊D1311yescharacteristic
330C2×C8C2×C22⋊D1311yescharacteristic
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—262no—
336C4⋊C4—262no—
337C4⋊C4—262no—
338C4⋊C4—262no—
339C4⋊C4—522no—
340C4⋊C4—522no—
341C4⋊C4C2×D5211yescharacteristic
342C4⋊C4C2×D5211yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—522no—
349C42—21no—
350C42—522no—
351C42C2×D5211yescharacteristic
352C42#612711yescharacteristic
353C42C2×C22⋊D1311yescharacteristic
354C42C23×D1311yescharacteristic
355C13#1922611yescharacteristic, complemented, Sylow
356C23—21no—
357C23#8818411yescharacteristic
358Q8—22no—
359Q8—522no—
360Q8—522no—
361Q8—1042no—
362D4—22no—
363D4—42no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—522no—
374C2×C4—522no—
375C2×C4#8818411yescharacteristic
376C2×C4#8818411yescharacteristic
377C2×C4#8818411yescharacteristic
378C2×C4C22×D5211yescharacteristic
379C2×C4C2×#612711yescharacteristic
380C2×C4C22×C22⋊D1311yescharacteristic
381C8—21no—
382C8—21no—
383C8—21no—
384C8—41no—
385C8—41no—
386C8—522no—
387C8—522no—
388C8#8820412yes—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22C2×#8818411yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—1042no—
404C4—1042no—
405C4#1171945812yes—
406C4C2×#8820411yescharacteristic
407C4#1171952711yescharacteristic
408C2—41no—
409C2—81no—
410C2#1312429111yescharacteristic
411C2#1312449111yescharacteristic
412C2#1312455611yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2966C2
socleC22×C13C2×#121
prime radicalC13×#121D4
hypercenter#2966D13
hypocenterC13#19226
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13125422C2semidirect
3. #13114364C2semidirect
4. #13114359C2semidirect
5. #13114330C2semidirect
6. #13114325C2semidirect
7. #13114294C2semidirect
8. #13114287C2semidirect
9. #13113584C2semidirect
10. #13113547C2semidirect
355. C13#19226semidirect

Maximal subgroups

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

subgroupindex
#131260112
#131254222
#131143642
#131143592
#131143302
#131143252
#131142942
#131142872
#131135842
#131135472
C13×#29662
#1922613