Finite Group Databasebeta

← #15751465

Subgroups — #15751465

Order 3328.

470 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123177C211yesmaximal, characteristic
2#13114815C211yesmaximal, characteristic
3#13114597C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic, complemented
5#13112660C211yesmaximal, characteristic, complemented
6#13112658C211yesmaximal, characteristic, complemented
7C13×#1272C211yesmaximal, characteristic, complemented
8C2×#88200C411yescharacteristic
9C2×C42×D13C2211yescharacteristic
10C13×#391C2211yescharacteristic
11#11718891C411yescharacteristic
12C2×#88060—21no—
13C2×#88060—21no—
14C2×#88055—21no—
15C2×#88054—21no—
16#11718648C411yescharacteristic
17#11718646C411yescharacteristic
18#11718589C2211yescharacteristic
19#11718329—21no—
20#11718325—21no—
21#11718315—21no—
22#11718313—21no—
23C13×#336C2211yescharacteristic
24C13×#336C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic
28C22×C4×D13C2×C411yescharacteristic
29C22×C4×D13D411yescharacteristic
30C22×C4×D13D411yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35#88200—42no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055—21no—
48C42×D13—42no—
49C13×#95—21no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88060—24no—
57#88060—42no—
58#88055—42no—
59#88054—42no—
60#7701—131nomaximal, Sylow
61C23×D13C22⋊C411yescharacteristic
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C2×C4×D13—22no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13—21no—
80C2×C4×D13—21no—
81C2×C4×D13—21no—
82C2×C4×D13—21no—
83C2×C4×D13—22no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C8×C13—22no—
89C2×C8×C13—41no—
90C2×C8×C13—41no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C13×C4⋊C4—41no—
95C42×C13—41no—
96#6103—42no—
97#6103—42no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—42no—
101C4⋊Dic13—41no—
102#6101—41no—
103#6101—41no—
104#6101—42no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C4×Dic13—41no—
108C2×#1055—22no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—41no—
114#2855—131no—
115#1797—131no—
116#1749—131no—
117#1272—131no—
118#1272D1311yescharacteristic, complemented
119#1271—131no—
120#1271—131no—
121C23×C13C2×C22⋊C411yescharacteristic
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13#10412yes—
129Q8×C13—81no—
130Q8×C13—81no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13#13111yescharacteristic
144C2×C4×C13#13111yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C2×C4×C13#13711yescharacteristic
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13#9912yes—
164C4×D13—42no—
165C4×D13—42no—
166C4×D13—42no—
167C4×D13—42no—
168C4×D13—42no—
169C4×D13—42no—
170C8×C13—42no—
171C8×C13—81no—
172#1055—42no—
173#1055—81no—
174C2×C22⋊Q8—131no—
175C22×C42—131no—
176C2×C4⋊C8—261no—
177C2×C22⋊C8—261no—
178C2×C22⋊C8—261no—
179C2×#97—261no—
180#391—131no—
181#391C2×D1311yescharacteristic
182#389—131no—
183#389—131no—
184#387—261no—
185#387—261no—
186#385—261no—
187#381—261no—
188#380—131no—
189#336—131no—
190#336—131no—
191#336C2×D1311yescharacteristic
192#336C2×D1311yescharacteristic
193C22×C13#40811yescharacteristic
194C22×C13C2×#9911yescharacteristic
195C22×C13#41311yescharacteristic
196C22×C13#41711yescharacteristic
197C22×C13#41911yescharacteristic
198C22×C13C2×#10411yescharacteristic
199C22×C13#42111yescharacteristic
200C2×D13—22no—
201C2×D13—22no—
202C2×D13—22no—
203C2×D13—41no—
204C2×D13—41no—
205C2×D13—41no—
206C2×D13—41no—
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—81no—
214C4×C13—81no—
215Dic13—22no—
216Dic13—41no—
217Dic13—41no—
218Dic13—81no—
219Dic13—81no—
220C22×Q8C4×D1311yescharacteristic
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—131no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—261no—
227C22×C8—261no—
228C22⋊Q8—522no—
229C2×C4⋊C4—131no—
230C2×C4⋊C4—131no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—261no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4C4×D1311yescharacteristic
235C2×C22⋊C4—261no—
236C2×C22⋊C4—261no—
237C2×C42—131no—
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—522no—
241C2×C42C22×D1311yescharacteristic
242C4⋊C8—522no—
243C22⋊C8—264no—
244C22⋊C8—522no—
245#97—522no—
246#95—21no—
247#95—21no—
248#95—261no—
249#95—261no—
250#95—261no—
251#95—261no—
252#95—261no—
253C2×C13#146811yescharacteristic
254C2×C13#148311yescharacteristic
255C2×C13#149711yescharacteristic
256C2×C13#150811yescharacteristic
257C2×C13#151311yescharacteristic
258C2×C13#153211yescharacteristic
259C2×C13#155911yescharacteristic
260D13—42no—
261C24—131no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8—41no—
265C2×Q8—41no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—262no—
272C22×C4—262no—
273C22×C4—261no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4C2×C4×D1311yescharacteristic
286C22×C4D4×D1311yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—262no—
295C2×C8—521no—
296C2×C8—521no—
297C2×C8—521no—
298C2×C8—521no—
299C2×C8—521no—
300C4⋊C4—41no—
301C4⋊C4—261no—
302C4⋊C4—261no—
303C4⋊C4—521no—
304C4⋊C4—522no—
305C4⋊C4—522no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C22⋊C4—522no—
309C22⋊C4—522no—
310C42—41no—
311C42—262no—
312C42—262no—
313C42—521no—
314C13#770111yescharacteristic, complemented, Sylow
315C23—132no—
316C23—261no—
317C23—261no—
318C23—261no—
319C23—261no—
320C23—261no—
321C23—261no—
322C23C22⋊C4×D1311yescharacteristic
323Q8—81no—
324Q8—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—132no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—522no—
349C2×C4—522no—
350C2×C4—522no—
351C2×C4—522no—
352C2×C4—521no—
353C2×C4—521no—
354C2×C4—521no—
355C2×C4—521no—
356C2×C4—521no—
357C2×C4—521no—
358C2×C4#8815511yescharacteristic
359C2×C4#8816111yescharacteristic
360C2×C4#8816811yescharacteristic
361C2×C4#8816911yescharacteristic
362C2×C4#8817211yescharacteristic
363C2×C4#8817211yescharacteristic
364C8—42no—
365C8—81no—
366C8—522no—
367C8—1041no—
368C22—262no—
369C22—262no—
370C22—262no—
371C22—521no—
372C22—521no—
373C22—521no—
374C22—521no—
375C22#1171838811yescharacteristic
376C22D13×#9911yescharacteristic
377C22#1171840611yescharacteristic
378C22#1171846311yescharacteristic
379C22#1171846411yescharacteristic
380C22D13×#10411yescharacteristic
381C22#1171848211yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—262no—
391C4—521no—
392C4—521no—
393C4—1041no—
394C4—1041no—
395C2—522no—
396C2#1311318111yescharacteristic
397C2#1311324811yescharacteristic
398C2#1311330711yescharacteristic
399C2#1311335411yescharacteristic
400C2#1311337811yescharacteristic
401C2#1311345311yescharacteristic
402C2#1311356311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7701
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #13112662C2semidirect
5. #13112660C2semidirect
6. #13112658C2semidirect
7. C13×#1272C2semidirect
118. #1272D13semidirect
314. C13#7701semidirect

Maximal subgroups

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

subgroupindex
#131231772
#131148152
#131145972
#131126622
#131126602
#131126582
C13×#12722
#770113