Finite Group Databasebeta

← #15773385

Subgroups — #15773385

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#13112860C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2482C211yesmaximal, characteristic
6C2×C13×#117C411yescharacteristic, complemented
7C22×C13×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic13—21no—
9C13×#399C411yescharacteristic, complemented
10C13×#399C2211yescharacteristic
11C13×#397C411yescharacteristic, complemented
12C13×#397C2211yescharacteristic
13C13×#388—21no—
14C13×#388—21no—
15C13×#385—21no—
16C13×#381C411yescharacteristic, complemented
17C13×#379—21no—
18#11718868—21no—
19#11718118—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C25×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13—41no—
27C13×#117—41no—
28C13×#117—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
32C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
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—21no—
39C2×C13×C22⋊C4—41no—
40C2×C13×C22⋊C4—41no—
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C13×C22⋊C4C2311yescharacteristic
45C2×C42×C13—21no—
46C2×C22⋊Dic13—24no—
47C2×C22⋊Dic13—22no—
48C2×C22⋊Dic13—41no—
49C2×C22⋊Dic13—42no—
50C2×#6099—41no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic, complemented
55C13×#95C2×C411yescharacteristic, complemented
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11755—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
69C22×C4×C13—21no—
70C22×C4×C13—21no—
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—42no—
78C22×C4×C13—81no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—44no—
84C22×Dic13—42no—
85C22×Dic13—82no—
86C22×Dic13—82no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C4⋊C4—81no—
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—42no—
104C22⋊Dic13—24no—
105C22⋊Dic13—44no—
106C22⋊Dic13—42no—
107#6099—82no—
108C2×#1055—42no—
109#2482D1311yescharacteristic
110C2×#342—131no—
111#1462—131no—
112#1352—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
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—42no—
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—41no—
166C2×C4×C13—81no—
167C2×Dic13—44no—
168C2×Dic13—88no—
169C2×Dic13—82no—
170C2×Dic13—82no—
171#1055—82no—
172C2×#117Dic1311yescharacteristic, complemented
173C22×C22⋊C4—261no—
174C22×C22⋊C4C2×D1311yescharacteristic
175#407—261no—
176#399Dic1311yescharacteristic, complemented
177#399C2×D1311yescharacteristic
178#397Dic1311yescharacteristic, complemented
179#397C2×D1311yescharacteristic
180#388—21no—
181#388—21no—
182#385—21no—
183#381Dic1311yescharacteristic, complemented
184#379—21no—
185#342—132no—
186#342—261no—
187#323—132no—
188#323—261no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—21no—
199C22×C13—42no—
200C22×C13—42no—
201C22×C13—42no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—44no—
205C22×C13—44no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—82no—
213C22×C13—82no—
214C22×C13#35212yes—
215C22×C13C2×#9911yescharacteristic
216C22×C13#41711yescharacteristic
217C22×C13C2×#10411yescharacteristic
218C4×C13—41no—
219C4×C13—41no—
220C4×C13—41no—
221C4×C13—41no—
222C4×C13—81no—
223C4×C13—81no—
224C4×C13—81no—
225C4×C13—81no—
226Dic13—84no—
227C25C22⋊D1311yescharacteristic
228C23×C4—521no—
229C23×C4C2×Dic1311yescharacteristic
230C23×C4C22⋊D1311yescharacteristic
231C2×M16—521no—
232#117—41no—
233#117—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×Dic1311yescharacteristic, complemented
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#95C2×Dic1311yescharacteristic, complemented
261#95C2×Dic1311yescharacteristic, complemented
262C2×C13—21no—
263C2×C13—21no—
264C2×C13—22no—
265C2×C13—41no—
266C2×C13—41no—
267C2×C13—42no—
268C2×C13—41no—
269C2×C13#150411yescharacteristic
270C2×C13C2×#35211yescharacteristic
271C2×C13#212711yescharacteristic
272C24—21no—
273C24—21no—
274C24—22no—
275C24—21no—
276C24—21no—
277C24—42no—
278C24—81no—
279C24C22⋊Dic1311yescharacteristic
280C24C22⋊Dic1311yescharacteristic
281C24C2×C22⋊D1311yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—81no—
292C22×C4—524no—
293C22×C4—522no—
294C22×C4—1042no—
295C22×C4—1042no—
296C22×C4C22⋊Dic1311yescharacteristic
297C22×C4C22⋊Dic1311yescharacteristic
298C22×C4C22×Dic1311yescharacteristic
299C22×C4C2×C22⋊D1311yescharacteristic
300M16—1042no—
301C2×C8—522no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—81no—
305C4⋊C4—81no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—81no—
317C22⋊C4—81no—
318C22⋊C4—264no—
319C22⋊C4—524no—
320C22⋊C4—522no—
321C42—42no—
322C13#1175511yescharacteristic, complemented, Sylow
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—22no—
332C23—21no—
333C23—21no—
334C23—41no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—84no—
344C23—82no—
345C23—82no—
346C23#8807411yescharacteristic
347C23#8807411yescharacteristic
348C23#8807712yes—
349C23#8820311yescharacteristic
350C23#8820511yescharacteristic
351C23C2×C22⋊Dic1311yescharacteristic
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
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—524no—
377C2×C4—1048no—
378C2×C4—1042no—
379C2×C4—1042no—
380C8—1042no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—22no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—41no—
395C22—41no—
396C22—44no—
397C22—44no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22—81no—
404C22—82no—
405C22—82no—
406C22#1171813112yes—
407C22C2×#8807411yescharacteristic
408C22#1171889311yescharacteristic
409C22C2×#8807711yescharacteristic
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4—81no—
418C4—1044no—
419C2—21no—
420C2—21no—
421C2—22no—
422C2—41no—
423C2—41no—
424C2—42no—
425C2—41no—
426C2#1311334011yescharacteristic
427C2C2×#1171813111yescharacteristic
428C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2482C2
socleC22×C13C2×#99
prime radicalC25×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2482D13
hypocenterC13#11755
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2482

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112836C2semidirect
6. C2×C13×#117C4semidirect
9. C13×#399C4semidirect
11. C13×#397C4semidirect
16. C13×#381C4semidirect
31. C2×C13×C4⋊C4C2×C4semidirect
32. C2×C13×C4⋊C4C2×C4semidirect
54. C13×#95C2×C4semidirect
55. C13×#95C2×C4semidirect
172. C2×#117Dic13semidirect
176. #399Dic13semidirect
178. #397Dic13semidirect
183. #381Dic13semidirect
236. C2×C4⋊C4C2×Dic13semidirect
237. C2×C4⋊C4C2×Dic13semidirect
260. #95C2×Dic13semidirect
261. #95C2×Dic13semidirect
322. C13#11755semidirect

Maximal subgroups

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

subgroupindex
C2×#117181182
#131131632
#131128602
#131128362
C13×#24822
#1175513