Finite Group Databasebeta

← #15835406

Subgroups — #15835406

Order 3328.

1210 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124772C212yesmaximal, complemented
2#13119123C211yesmaximal, characteristic, complemented
3#13113873C214yesmaximal, complemented
4#13113839C214yesmaximal, complemented
5#13113365C212yesmaximal, complemented
6#13113166C211yesmaximal, characteristic, complemented
7C2×C13×#537C211yesmaximal, characteristic
8C22×C13×#41—21no—
9C13×#537—24no—
10C13×#537—22no—
11C13×#537C2214yes—
12C2×C13×C22⋊Q8—22no—
13C2×C13×#121—22no—
14C2×C13×#121—21no—
15C2×C13×#121C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18#11718876—22no—
19#11718872—21no—
20#11718872C2211yescharacteristic
21#11718871—21no—
22#11718868C2212yes—
23#11718696—24no—
24#11718695C2214yescomplemented
25#11718694C2214yescomplemented
26#11718647C2212yescomplemented
27#11718644C2212yescomplemented
28#11718639—22no—
29#11718625—22no—
30#11718129C2218yescomplemented
31#11718120C2214yescomplemented
32C2×C13×#41—24no—
33C2×C13×#41—24no—
34C2×C13×#41—48no—
35C22×Q8×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—22no—
38C22×D4×C13—21no—
39C22×D4×C13D412yes—
40C23×C4×C13—22no—
41C23×C4×C13D411yescharacteristic
42C23×C4×C13D411yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C13×C22⋊Q8—28no—
45C13×C22⋊Q8—28no—
46C13×#121—24no—
47C13×#121—28no—
48C13×#121—28no—
49C13×#121—24no—
50C13×#121—22no—
51C13×#121—22no—
52C13×#121D414yes—
53C13×#121C2314yes—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4D412yes—
58C2×C13×C4⋊C4D412yes—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—21no—
64#88180—22no—
65#88180—22no—
66C2×C4⋊Dic13C2311yescharacteristic
67C2×C4⋊Dic13C2311yescharacteristic
68C2×#6101—22no—
69C2×C4×Dic13—21no—
70C2×#6099—22no—
71#88072—24no—
72#88072—24no—
73#88071—22no—
74#88071—22no—
75#88071—22no—
76#88071—21no—
77#88071C2312yes—
78C22⋊#1055—22no—
79C22⋊#1055C2314yes—
80#88048—24no—
81#88047—24no—
82#18147—131nomaximal, Sylow
83C24×C13—22no—
84C24×C13C2×D411yescharacteristic
85C13×#41—416no—
86C13×#41—48no—
87C13×#41—48no—
88C2×Q8×C13—24no—
89C2×Q8×C13—44no—
90C2×D4×C13—24no—
91C2×D4×C13—24no—
92C2×D4×C13—24no—
93C2×D4×C13—24no—
94C2×D4×C13—22no—
95C2×D4×C13—44no—
96C2×D4×C13—44no—
97C2×D4×C13—48no—
98C2×D4×C13—82no—
99C2×D4×C13C2×D414yes—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—24no—
103C22×C4×C13—28no—
104C22×C4×C13—21no—
105C22×C4×C13—22no—
106C22×C4×C13—21no—
107C22×C4×C13—42no—
108C22×C4×C13—48no—
109C22×C4×C13—42no—
110C22×C4×C13C2×D412yes—
111C22×C4×C13C2×D412yes—
112C22×C4×C13C2×D412yes—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2411yescharacteristic
116C22×Dic13—22no—
117C22×Dic13—21no—
118C22×Dic13—21no—
119C13×C4⋊C4—24no—
120C13×C4⋊C4—24no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—24no—
123C13×C4⋊C4C2×D414yes—
124C13×C22⋊C4—28no—
125C13×C22⋊C4—24no—
126C13×C22⋊C4—24no—
127C22⋊Dic13—42no—
128C22⋊Dic13—41no—
129C22⋊Dic13—41no—
130C4⋊Dic13—22no—
131C4⋊Dic13—22no—
132#6101—44no—
133C4×Dic13—42no—
134#6099—44no—
135C2×#1055—24no—
136C2×#537D1311yescharacteristic
137#3094—132no—
138#2484—131no—
139#1616—134no—
140#1610—134no—
141#1510—132no—
142#1463—131no—
143C23×C13—22no—
144C23×C13—22no—
145C23×C13—24no—
146C23×C13—41no—
147C23×C13—44no—
148C23×C13—44no—
149C23×C13—44no—
150C23×C13#12011yescharacteristic
151C23×C13#12011yescharacteristic
152C23×C13C22×D411yescharacteristic
153Q8×C13—48no—
154D4×C13—48no—
155D4×C13—44no—
156D4×C13—48no—
157D4×C13—48no—
158D4×C13—82no—
159D4×C13—84no—
160C2×C4×C13—24no—
161C2×C4×C13—24no—
162C2×C4×C13—22no—
163C2×C4×C13—22no—
164C2×C4×C13—24no—
165C2×C4×C13—22no—
166C2×C4×C13—24no—
167C2×C4×C13—42no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—416no—
171C2×C4×C13—44no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—81no—
175C2×C4×C13#12012yes—
176C2×C4×C13AGL(1,ℤ/8)14yes—
177C2×C4×C13C22×D412yes—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—42no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185#1055—44no—
186C22×#41—21no—
187#537—24no—
188#537—22no—
189#537C2×D1314yes—
190C2×C22⋊Q8—22no—
191C2×#121—22no—
192C2×#121—21no—
193C2×#121C2×D1312yes—
194C2×#117—131no—
195C22×C4⋊C4C2×D1311yescharacteristic
196#482—264no—
197#481—134no—
198#480—134no—
199#428—262no—
200#418—262no—
201#407—132no—
202#400—132no—
203#398—132no—
204#387—262no—
205#385—261no—
206#381—131no—
207#381—261no—
208#327—138no—
209#324—134no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—44no—
218C22×C13—44no—
219C22×C13—44no—
220C22×C13—44no—
221C22×C13—88no—
222C22×C13#45812yes—
223C22×C13C2×#12011yescharacteristic
224C22×C13C2×AGL(1,ℤ/8)12yes—
225C4×C13—24no—
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—44no—
229C4×C13—42no—
230Dic13—82no—
231Dic13—81no—
232Dic13—81no—
233C2×#41—24no—
234C2×#41—24no—
235C2×#41—48no—
236C22×Q8—21no—
237C22×D4—21no—
238C22×D4—22no—
239C22×D4—21no—
240C22×D4C22⋊D1312yes—
241C23×C4—22no—
242C23×C4C22⋊D1311yescharacteristic
243C23×C4C22⋊D1311yescharacteristic
244C23×C4C22×D1311yescharacteristic
245C2×M16—262no—
246C22⋊Q8—28no—
247C22⋊Q8—28no—
248#121—24no—
249#121—28no—
250#121—28no—
251#121—24no—
252#121—22no—
253#121—22no—
254#121C22⋊D1314yes—
255#121C22×D1314yes—
256#117—262no—
257#117—262no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—131no—
262C2×C4⋊C4—131no—
263C2×C4⋊C4—262no—
264C2×C4⋊C4C22⋊D1312yes—
265C2×C4⋊C4C22⋊D1312yes—
266C2×C4⋊C4C22×D1312yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—261no—
270C2×C22⋊C4—261no—
271C2×C42—261no—
272#107—264no—
273#106—264no—
274#102—264no—
275#102—264no—
276C22⋊C8—134no—
277C22⋊C8—262no—
278#95—132no—
279#95—261no—
280#95—262no—
281#95—262no—
282#95—262no—
283C2×C13—22no—
284C2×C13—22no—
285C2×C13—41no—
286C2×C13—84no—
287C2×C13#300311yescharacteristic
288C2×C13#302011yescharacteristic
289C2×C13C2×#45811yescharacteristic
290C24—22no—
291C24C2×C22⋊D1311yescharacteristic
292#41—416no—
293#41—48no—
294#41—48no—
295C2×Q8—24no—
296C2×Q8—44no—
297C2×D4—24no—
298C2×D4—24no—
299C2×D4—24no—
300C2×D4—24no—
301C2×D4—22no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—48no—
305C2×D4—82no—
306C2×D4C2×C22⋊D1314yes—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—28no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—48no—
316C22×C4—42no—
317C22×C4—262no—
318C22×C4—261no—
319C22×C4—261no—
320C22×C4C2×C22⋊D1312yes—
321C22×C4C2×C22⋊D1312yes—
322C22×C4C2×C22⋊D1312yes—
323C22×C4C2×C22⋊D1311yescharacteristic
324C22×C4C2×C22⋊D1312yes—
325C22×C4C23×D1311yescharacteristic
326M16—524no—
327C2×C8—264no—
328C4⋊C4—24no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4—24no—
332C4⋊C4—262no—
333C4⋊C4—262no—
334C4⋊C4—524no—
335C4⋊C4C2×C22⋊D1314yes—
336C22⋊C4—28no—
337C22⋊C4—24no—
338C22⋊C4—24no—
339C22⋊C4—522no—
340C22⋊C4—521no—
341C22⋊C4—521no—
342C42—522no—
343C13#1814711yescharacteristic, complemented, Sylow
344C23—22no—
345C23—22no—
346C23—24no—
347C23—41no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23#8820711yescharacteristic
352C23#8820711yescharacteristic
353C23C22×C22⋊D1311yescharacteristic
354Q8—48no—
355D4—44no—
356D4—48no—
357D4—48no—
358D4—48no—
359D4—82no—
360D4—84no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—416no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—81no—
376C2×C4—522no—
377C2×C4—522no—
378C2×C4—522no—
379C2×C4—522no—
380C2×C4—522no—
381C2×C4—521no—
382C2×C4—521no—
383C2×C4#8818614yes—
384C2×C4#8820712yes—
385C2×C4C22×C22⋊D1312yes—
386C8—524no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—44no—
395C22—44no—
396C22—44no—
397C22—44no—
398C22—88no—
399C22#1171890412yes—
400C22C2×#8818612yes—
401C22C2×#8820711yescharacteristic
402C4—22no—
403C4—22no—
404C4—24no—
405C4—42no—
406C4—44no—
407C4—1042no—
408C4—1041no—
409C4—1041no—
410C2—22no—
411C2—22no—
412C2—41no—
413C2—84no—
414C2#1312406311yescharacteristic
415C2#1312420011yescharacteristic
416C2C2×#1171890411yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#537C2
socleC22×C13C2×#120
hypercenterC2×#537D13
hypocenterC13#18147
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13124772C2semidirect
2. #13119123C2semidirect
3. #13113873C2semidirect
4. #13113839C2semidirect
5. #13113365C2semidirect
6. #13113166C2semidirect
24. #11718695C22semidirect
25. #11718694C22semidirect
26. #11718647C22semidirect
27. #11718644C22semidirect
30. #11718129C22semidirect
31. #11718120C22semidirect
343. C13#18147semidirect

Maximal subgroups

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

subgroupindex
#131247722
#131191232
#131138732
#131138392
#131133652
#131131662
C2×C13×#5372
#1814713