Finite Group Databasebeta

← #15759949

Subgroups — #15759949

Order 3328.

478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 103 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#13118002C211yesmaximal, characteristic
2#13115822C211yesmaximal, characteristic
3#13113369C211yesmaximal, characteristic
4#13113356C211yesmaximal, characteristic
5#13112743C211yesmaximal, characteristic
6#13112690C211yesmaximal, characteristic
7C13×#3195C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C2×C13×C22⋊Q8C2211yescharacteristic
10C13×#483—21no—
11C13×#483C412yescomplemented
12C13×#470—22no—
13C13×#451—21no—
14C13×#451C412yescomplemented
15C13×#407C2211yescharacteristic
16#11718891—21no—
17#11718873C2211yescharacteristic
18#11718872C2211yescharacteristic
19C4×C22⋊Dic13C2211yescharacteristic
20#11718868C2211yescharacteristic
21#11718646—21no—
22#11718642—21no—
23#11718642—21no—
24#11718612—21no—
25#11718612—21no—
26#11718130—22no—
27#11718130—21no—
28#11718130—21no—
29#11718118—21no—
30#11718118—21no—
31C22×Q8×C13C2×C411yescharacteristic
32C22×Q8×C13D411yescharacteristic
33C23×C4×C13C2311yescharacteristic
34C2×C13×Q16—22no—
35C2×C13×M16—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C13×C22⋊Q8—21no—
42C13×C22⋊Q8C2×C412yes—
43C13×C22⋊Q8D412yes—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C22⋊Dic13—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13D411yescharacteristic
53C2×C22⋊Dic13D411yescharacteristic
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×C4×Dic13—21no—
58C2×C4×Dic13—21no—
59C2×C4×Dic13—21no—
60C2×#6099—21no—
61C13×#106—22no—
62C13×#103—22no—
63C13×#103—22no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8C2×C412yes—
66#88071—21no—
67#88071—21no—
68#88071—21no—
69#88071—21no—
70#88071—21no—
71#88071—21no—
72#88071—21no—
73#88071D411yescharacteristic
74#88071D411yescharacteristic
75C22⋊#1055—21no—
76C22⋊#1055—21no—
77#9342—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—81no—
83C2×Q8×C13—81no—
84C2×Q8×C13C22⋊C412yes—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—81no—
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×C4×C13#4111yescharacteristic
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—41no—
101C13×Q16—82no—
102C13×M16—81no—
103C2×C8×C13—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4C22⋊C412yes—
112C13×C22⋊C4—22no—
113C13×C22⋊C4—22no—
114C13×C22⋊C4—41no—
115C13×C22⋊C4—41no—
116C22⋊Dic13—22no—
117C22⋊Dic13—41no—
118C22⋊Dic13—41no—
119C22⋊Dic13—41no—
120C22⋊Dic13—81no—
121C4⋊Dic13—81no—
122C4⋊Dic13—81no—
123C4⋊Dic13—81no—
124C4×Dic13—81no—
125C4×Dic13—81no—
126C4×Dic13—81no—
127#6099—81no—
128C2×#1055—41no—
129#3195D1311yescharacteristic
130#2378—131no—
131#1996—131no—
132#1511—131no—
133#1508—131no—
134#1305—131no—
135#1284—131no—
136C23×C13—21no—
137C23×C13—21no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13C4×D411yescharacteristic
141C23×C13#12011yescharacteristic
142C23×C13#12111yescharacteristic
143Q8×C13—42no—
144Q8×C13—42no—
145Q8×C13—81no—
146Q8×C13—81no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—81no—
162C2×C4×C13—81no—
163C2×C4×C13C2×C22⋊C411yescharacteristic
164C2×C4×C13C4×D411yescharacteristic
165C2×C4×C13#12111yescharacteristic
166C2×C4×C13#12311yescharacteristic
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—42no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C8×C13—42no—
183#1055—81no—
184C2×C22⋊Q8C2×D1311yescharacteristic
185C2×C22⋊Q8C2×D1311yescharacteristic
186#483—21no—
187#483Dic1312yescomplemented
188#470—22no—
189#451—21no—
190#451Dic1312yescomplemented
191#407—131no—
192#407C2×D1311yescharacteristic
193#391—261no—
194#389—261no—
195#388—261no—
196#388—261no—
197#387—261no—
198#387—261no—
199#381—131no—
200#380—131no—
201C4×C22⋊C4—131no—
202#342—261no—
203#342—261no—
204#328—261no—
205#328—261no—
206#328—262no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13#38611yescharacteristic
218C22×C13#45511yescharacteristic
219C22×C13#45611yescharacteristic
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—42no—
225C4×C13—42no—
226C4×C13—81no—
227C4×C13—81no—
228Dic13—81no—
229Dic13—81no—
230Dic13—81no—
231Dic13—81no—
232Dic13—82no—
233C22×Q8C2×Dic1311yescharacteristic
234C22×Q8C22⋊D1311yescharacteristic
235C23×C4C22×D1311yescharacteristic
236C2×Q16—22no—
237C2×M16—21no—
238C2×M16—261no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8C2×Dic1312yes—
246C22⋊Q8C22⋊D1312yes—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—261no—
250C2×C4⋊C4—261no—
251C2×C4⋊C4—261no—
252C2×C4⋊C4C2×Dic1311yescharacteristic
253C2×C4⋊C4C22⋊D1311yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—131no—
257C2×C22⋊C4—131no—
258C2×C22⋊C4—261no—
259C2×C22⋊C4—261no—
260C2×C42—261no—
261C2×C42—261no—
262C2×C42—261no—
263#106—22no—
264#103—22no—
265#103—22no—
266C22⋊C8—21no—
267C22⋊C8—261no—
268C22⋊C8—261no—
269C22⋊C8C2×Dic1312yes—
270#95—131no—
271#95—131no—
272#95—261no—
273#95—261no—
274#95—261no—
275#95—261no—
276#95—261no—
277#95—261no—
278#95—261no—
279C2×C13—21no—
280C2×C13—21no—
281C2×C13—41no—
282C2×C13—41no—
283C2×C13#188211yescharacteristic
284C2×C13#190511yescharacteristic
285C2×C13#191311yescharacteristic
286C24D4×D1311yescharacteristic
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—81no—
291C2×Q8—81no—
292C2×Q8C22⋊Dic1312yes—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—81no—
298C22×C4—261no—
299C22×C4—261no—
300C22×C4—261no—
301C22×C4—261no—
302C22×C4—521no—
303C22×C4D4×D1311yescharacteristic
304C22×C4#612911yescharacteristic
305C22×C4#612911yescharacteristic
306C22×C4C22×Dic1311yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308C22×C4C2×C22⋊D1311yescharacteristic
309Q16—82no—
310M16—81no—
311M16—1041no—
312C2×C8—22no—
313C2×C8—521no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—1041no—
322C4⋊C4—1041no—
323C4⋊C4—1041no—
324C4⋊C4C22⋊Dic1312yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—262no—
330C22⋊C4—521no—
331C22⋊C4—521no—
332C22⋊C4—521no—
333C22⋊C4—1041no—
334C42—1041no—
335C42—1041no—
336C42—1041no—
337C13#934211yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23D4×Dic1311yescharacteristic
343C23#8819111yescharacteristic
344C23#8819311yescharacteristic
345Q8—42no—
346Q8—42no—
347Q8—81no—
348Q8—81no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—522no—
368C2×C4—521no—
369C2×C4—521no—
370C2×C4—521no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—521no—
374C2×C4—521no—
375C2×C4—521no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—1041no—
379C2×C4—1041no—
380C2×C4D4×Dic1311yescharacteristic
381C2×C4#8818911yescharacteristic
382C2×C4#8819311yescharacteristic
383C2×C4C2×C22⋊Dic1311yescharacteristic
384C8—42no—
385C8—1041no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—81no—
395C22—81no—
396C22#1171886311yescharacteristic
397C22#1171886611yescharacteristic
398C22#1171888111yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—81no—
407C4—1041no—
408C4—1041no—
409C4—1041no—
410C4—1041no—
411C4—1042no—
412C2—21no—
413C2—21no—
414C2—41no—
415C2—41no—
416C2#1311520711yescharacteristic
417C2#1311533211yescharacteristic
418C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#3195C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#3195D13
hypocenterC13#9342
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
11. C13×#483C4semidirect
14. C13×#451C4semidirect
187. #483Dic13semidirect
190. #451Dic13semidirect
337. C13#9342semidirect

Maximal subgroups

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

subgroupindex
#131180022
#131158222
#131133692
#131133562
#131127432
#131126902
C13×#31952
#934213