Finite Group Databasebeta

← #15758944

Subgroups — #15758944

Order 3328.

478 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 105 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#13123473C211yesmaximal, characteristic
2#13120603C211yesmaximal, characteristic
3#13113508C211yesmaximal, characteristic, complemented
4#13113148C211yesmaximal, characteristic
5#13112696C211yesmaximal, characteristic, complemented
6#13112695C211yesmaximal, characteristic, complemented
7C13×#1546C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88200—21no—
10C2×#88126C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13#11718891—21no—
14#11718787—21no—
15M16×Dic13—21no—
16#11718654—21no—
17#11718654C412yes—
18#11718641—21no—
19#11718641C412yes—
20#11718597C2211yescharacteristic
21#11718586C2211yescharacteristic
22#11718585C2211yescharacteristic
23#11718501—22no—
24#11718501—22no—
25C13×#332—22no—
26#11718139—22no—
27#11718061—21no—
28#11718060—21no—
29C22×Q8×C13—21no—
30C22×C4×D13D411yescharacteristic
31C2×C13×M16—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C412yes—
38C2×C42×C13C2311yescharacteristic
39#88200—42no—
40#88200—42no—
41C2×#6103—22no—
42C2×#6103C2×C411yescharacteristic
43C2×#6103D411yescharacteristic
44C2×C4⋊Dic13—21no—
45C2×#6101—22no—
46C2×#6101C2×C411yescharacteristic
47C2×#6101D411yescharacteristic
48C2×C4×Dic13D411yescharacteristic
49C2×#6099—21no—
50#88126—21no—
51#88126—21no—
52#88126—21no—
53#88126—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8D412yes—
57C13×C22⋊C8—21no—
58C4×C8×C13—21no—
59#88071—21no—
60#88071—22no—
61#88071—22no—
62#88071C2×C412yes—
63C22⋊#1055—21no—
64#88060—24no—
65#88055—22no—
66C8×Dic13—22no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70C4×#1055—21no—
71#9196—131nomaximal, Sylow
72C23×D13C22⋊C411yescharacteristic
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C22×C4×C13—22no—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—22no—
84C22×Dic13C22⋊C411yescharacteristic
85C22×Dic13C22⋊C411yescharacteristic
86C22×Dic13C22⋊C411yescharacteristic
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×C4×D13—21no—
92C2×C4×D13—21no—
93C13×M16—41no—
94C13×M16—41no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13#4111yescharacteristic
104C42×C13#4111yescharacteristic
105#6103—21no—
106#6103—21no—
107#6103—21no—
108#6103—21no—
109#6103—44no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112#6101—21no—
113#6101—21no—
114#6101—21no—
115#6101—21no—
116#6101—44no—
117C4×Dic13—21no—
118C4×Dic13—21no—
119#6099—41no—
120#6099—41no—
121C2×#1055—22no—
122C2×#1055—41no—
123#2921—131no—
124#2621—131no—
125#1546—131no—
126#1546D1311yescharacteristic, complemented
127#1458—131no—
128#1286—131no—
129#1286—131no—
130C23×C13C2×C22⋊C411yescharacteristic
131C22×D13—21no—
132C22×D13—21no—
133C22×D13—21no—
134C22×D13—41no—
135C22×D13—41no—
136Q8×C13—81no—
137Q8×C13—81no—
138Q8×C13—81no—
139Q8×C13—81no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12311yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13#13511yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C4×D13—41no—
166C4×D13—41no—
167C4×D13—41no—
168C4×D13—41no—
169C8×C13—42no—
170C8×C13—81no—
171#1055—42no—
172#1055—81no—
173C2×C4⋊Q8C2×D1311yescharacteristic
174C2×C22⋊Q8—261no—
175C2×#117—131no—
176#433—262no—
177#433—262no—
178#431—131no—
179#431C2×D1311yescharacteristic
180#423—131no—
181#423C2×D1311yescharacteristic
182#407—261no—
183C4×M16—261no—
184#398—132no—
185#398—261no—
186#397—132no—
187#397—261no—
188#391—261no—
189#382—131no—
190#332—22no—
191#332—262no—
192#324—261no—
193#323—261no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13#38611yescharacteristic
197C22×C13#41611yescharacteristic
198C22×C13#41811yescharacteristic
199C2×D13—42no—
200C2×D13—41no—
201C2×D13—41no—
202C2×D13—41no—
203C2×D13—81no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—82no—
209C4×C13#44911yescharacteristic
210C4×C13#44911yescharacteristic
211C4×C13#48211yescharacteristic
212C4×C13#48211yescharacteristic
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216Dic13—82no—
217C22×Q8—21no—
218C23×C4—131no—
219C2×M16—21no—
220C2×M16—261no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C22⋊Q8—522no—
226C22⋊Q8—522no—
227#117—261no—
228#117—261no—
229#117—261no—
230#117—261no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—262no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4C4×D1312yes—
237C2×C22⋊C4—131no—
238C2×C22⋊C4—131no—
239C2×C22⋊C4—262no—
240C2×C42—131no—
241C2×C42C22×D1311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—132no—
245C4⋊C8—261no—
246C4⋊C8—261no—
247C4⋊C8C22⋊D1312yes—
248C22⋊C8—21no—
249C22⋊C8—264no—
250C22⋊C8—261no—
251#97—262no—
252C4×C8—21no—
253C4×C8—262no—
254C4×C8—261no—
255#95—132no—
256#95—262no—
257#95—262no—
258#95—261no—
259C2×C13—21no—
260C2×C13—21no—
261C2×C13#187511yescharacteristic
262C2×C13#190911yescharacteristic
263C2×C13#191511yescharacteristic
264D13—81no—
265C24—131no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C22×C4—22no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—261no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—261no—
282C22×C4—262no—
283C22×C4C2×C4×D1311yescharacteristic
284C22×C4D4×D1311yescharacteristic
285C22×C4D4×D1311yescharacteristic
286M16—41no—
287M16—41no—
288M16—521no—
289M16—521no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—262no—
293C2×C8—521no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4—524no—
303C4⋊C4—521no—
304C4⋊C4—521no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C22⋊C4—524no—
310C42—261no—
311C42—261no—
312C42#612711yescharacteristic
313C42D4×D1311yescharacteristic
314C42#612911yescharacteristic
315C42C2×C22⋊D1311yescharacteristic
316C13#919611yescharacteristic, complemented, Sylow
317C23—261no—
318C23—261no—
319C23—261no—
320C23—521no—
321C23—521no—
322C23C22⋊C4×D1311yescharacteristic
323Q8—81no—
324Q8—81no—
325Q8—81no—
326Q8—81no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—521no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4#8813511yescharacteristic
347C2×C4#8813711yescharacteristic
348C2×C4#8813811yescharacteristic
349C2×C4#8816511yescharacteristic
350C2×C4#8816611yescharacteristic
351C2×C4#8816811yescharacteristic
352C2×C4#8817011yescharacteristic
353C2×C4C4×C22⋊D1311yescharacteristic
354C2×C4#8819111yescharacteristic
355C2×C4#8819211yescharacteristic
356C8—42no—
357C8—81no—
358C8—522no—
359C8—1041no—
360C22—21no—
361C22—21no—
362C22—522no—
363C22—521no—
364C22—521no—
365C22—521no—
366C22—1041no—
367C22#1171843111yescharacteristic
368C22#1171843311yescharacteristic
369C22#1171861711yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—82no—
375C4—521no—
376C4—521no—
377C4—521no—
378C4—1042no—
379C4#1171844011yescharacteristic
380C4#1171844511yescharacteristic
381C4#1171881911yescharacteristic
382C4#1171883311yescharacteristic
383C2—21no—
384C2—21no—
385C2—1041no—
386C2#1311515511yescharacteristic
387C2#1311535511yescharacteristic
388C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1546C2
socleC22×C13#386
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1546D13
hypocenterC13#9196
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. #13113508C2semidirect
5. #13112696C2semidirect
6. #13112695C2semidirect
7. C13×#1546C2semidirect
126. #1546D13semidirect
316. C13#9196semidirect

Maximal subgroups

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

subgroupindex
#131234732
#131206032
#131135082
#131131482
#131126962
#131126952
C13×#15462
#919613