Finite Group Databasebeta

← #15773405

Subgroups — #15773405

Order 3328.

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

normal subgroups only

This group has 586 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
1C2×#11718118C211yesmaximal, characteristic
2#13113163C211yesmaximal, characteristic
3#13112857C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2561C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C22×C13×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic13—21no—
9C13×#397C411yescharacteristic, complemented
10C13×#397C2211yescharacteristic
11C13×#393C411yescharacteristic, complemented
12C13×#393C2211yescharacteristic
13C13×#388—21no—
14C13×#388—21no—
15C13×#381—21no—
16C13×#379—21no—
17C4×C13×C22⋊C4C411yescharacteristic, complemented
18#11718868—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C22×Q8×C13C2×C411yescharacteristic, complemented
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×Dic13—41no—
28C13×C22⋊Q8—41no—
29C13×C22⋊Q8—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—41no—
39C2×C13×C22⋊C4—41no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13—21no—
45C2×C22⋊Dic13—24no—
46C2×C22⋊Dic13—22no—
47C2×C22⋊Dic13—41no—
48C2×C22⋊Dic13—42no—
49C2×#6099—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic, complemented
55C13×#95C2×C411yescharacteristic, complemented
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11759—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13—21no—
61C24×C13—22no—
62C24×C13—21no—
63C24×C13—21no—
64C24×C13—42no—
65C24×C13—81no—
66C24×C13C22⋊C411yescharacteristic
67C24×C13C22⋊C411yescharacteristic
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—41no—
70C2×Q8×C13—81no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—42no—
80C22×C4×C13—81no—
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—44no—
86C22×Dic13—42no—
87C22×Dic13—82no—
88C22×Dic13—82no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C13×C22⋊C4—81no—
102C13×C22⋊C4—81no—
103C42×C13—81no—
104C22⋊Dic13—24no—
105C22⋊Dic13—44no—
106C22⋊Dic13—42no—
107#6099—82no—
108C2×#1055—42no—
109#2561D1311yescharacteristic
110C2×#342—131no—
111#1462—131no—
112#1351—132no—
113#1344—132no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13—41no—
126C23×C13—42no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—42no—
132C23×C13—81no—
133C23×C13—81no—
134C23×C13—84no—
135C23×C13—82no—
136C23×C13—82no—
137C23×C13#9911yescharacteristic
138C23×C13#9911yescharacteristic
139C23×C13#10412yes—
140C23×C13C2×C22⋊C411yescharacteristic
141C23×C13AGL(1,ℤ/8)11yescharacteristic
142C23×C13#13711yescharacteristic
143Q8×C13—82no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
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—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—81no—
166C2×C4×C13—81no—
167C2×C4×C13—81no—
168C2×Dic13—44no—
169C2×Dic13—88no—
170C2×Dic13—82no—
171C2×Dic13—82no—
172#1055—82no—
173C2×C22⋊Q8Dic1311yescharacteristic, complemented
174C22×C22⋊C4—261no—
175C22×C22⋊C4C2×D1311yescharacteristic
176#407—261no—
177#397Dic1311yescharacteristic, complemented
178#397C2×D1311yescharacteristic
179#393Dic1311yescharacteristic, complemented
180#393C2×D1311yescharacteristic
181#388—21no—
182#388—21no—
183#381—21no—
184#379—21no—
185C4×C22⋊C4Dic1311yescharacteristic, complemented
186#342—132no—
187#342—261no—
188#323—132no—
189#323—261no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—22no—
199C22×C13—21no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—44no—
206C22×C13—44no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13—82no—
214C22×C13—82no—
215C22×C13#35412yes—
216C22×C13C2×#9911yescharacteristic
217C22×C13#41711yescharacteristic
218C22×C13C2×#10411yescharacteristic
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—81no—
224C4×C13—81no—
225C4×C13—81no—
226C4×C13—81no—
227Dic13—84no—
228C25C22⋊D1311yescharacteristic
229C22×Q8C2×Dic1311yescharacteristic, complemented
230C23×C4—521no—
231C23×C4C2×Dic1311yescharacteristic
232C23×C4C22⋊D1311yescharacteristic
233C2×M16—521no—
234C22⋊Q8—41no—
235C22⋊Q8—41no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—264no—
247C2×C22⋊C4—262no—
248C2×C22⋊C4—521no—
249C2×C22⋊C4—522no—
250C2×C22⋊C4C2×Dic1311yescharacteristic
251C2×C22⋊C4C22⋊D1311yescharacteristic
252C2×C22⋊C4C22⋊D1311yescharacteristic
253C2×C22⋊C4C22×D1311yescharacteristic
254C2×C42—21no—
255C22⋊C8—262no—
256C22⋊C8—521no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95C2×Dic1311yescharacteristic, complemented
262#95C2×Dic1311yescharacteristic, complemented
263C2×C13—21no—
264C2×C13—21no—
265C2×C13—22no—
266C2×C13—41no—
267C2×C13—41no—
268C2×C13—42no—
269C2×C13—41no—
270C2×C13#150411yescharacteristic
271C2×C13#212111yescharacteristic
272C2×C13C2×#35411yescharacteristic
273C24—21no—
274C24—21no—
275C24—22no—
276C24—21no—
277C24—21no—
278C24—42no—
279C24—81no—
280C24C22⋊Dic1311yescharacteristic
281C24C22⋊Dic1311yescharacteristic
282C24C2×C22⋊D1311yescharacteristic
283C2×Q8—41no—
284C2×Q8—81no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—42no—
294C22×C4—81no—
295C22×C4—524no—
296C22×C4—522no—
297C22×C4—1042no—
298C22×C4—1042no—
299C22×C4C22⋊Dic1311yescharacteristic
300C22×C4C22⋊Dic1311yescharacteristic
301C22×C4C22×Dic1311yescharacteristic
302C22×C4C2×C22⋊D1311yescharacteristic
303M16—1042no—
304C2×C8—522no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—81no—
319C22⋊C4—264no—
320C22⋊C4—524no—
321C22⋊C4—522no—
322C42—81no—
323C13#1175911yescharacteristic, complemented, Sylow
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—22no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—42no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—42no—
342C23—81no—
343C23—81no—
344C23—84no—
345C23—82no—
346C23—82no—
347C23#8807411yescharacteristic
348C23#8807411yescharacteristic
349C23#8807712yes—
350C23#8820311yescharacteristic
351C23#8820511yescharacteristic
352C23C2×C22⋊Dic1311yescharacteristic
353Q8—82no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—524no—
379C2×C4—1048no—
380C2×C4—1042no—
381C2×C4—1042no—
382C8—1042no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—21no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—44no—
399C22—44no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22—81no—
406C22—82no—
407C22—82no—
408C22#1171813312yes—
409C22C2×#8807411yescharacteristic
410C22#1171889311yescharacteristic
411C22C2×#8807711yescharacteristic
412C4—41no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—81no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—1044no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—41no—
425C2—41no—
426C2—42no—
427C2—41no—
428C2#1311334011yescharacteristic
429C2#1311648211yescharacteristic
430C2C2×#1171813311yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2561C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2561D13
hypocenterC13#11759
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2561

Complements

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

NH ≅ G/Ntype
3. #13112857C2semidirect
4. #13112836C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
9. C13×#397C4semidirect
11. C13×#393C4semidirect
17. C4×C13×C22⋊C4C4semidirect
24. C22×Q8×C13C2×C4semidirect
31. C2×C13×C4⋊C4C2×C4semidirect
54. C13×#95C2×C4semidirect
55. C13×#95C2×C4semidirect
173. C2×C22⋊Q8Dic13semidirect
177. #397Dic13semidirect
179. #393Dic13semidirect
185. C4×C22⋊C4Dic13semidirect
229. C22×Q8C2×Dic13semidirect
237. C2×C4⋊C4C2×Dic13semidirect
261. #95C2×Dic13semidirect
262. #95C2×Dic13semidirect
323. C13#11759semidirect

Maximal subgroups

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

subgroupindex
C2×#117181182
#131131632
#131128572
#131128362
C13×#25612
#1175913