Finite Group Databasebeta

← #15773248

Subgroups — #15773248

Order 3328.

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

normal subgroups only

This group has 606 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
1C4×#88074C211yesmaximal, characteristic, complemented
2#13113154C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2397C211yesmaximal, characteristic
6C2×C4×D4×C13—21no—
7C2×C4×D4×C13—21no—
8C2×C4×D4×C13C411yescharacteristic, complemented
9C2×C4×D4×C13C2211yescharacteristic
10C13×#399—21no—
11C13×#399C411yescharacteristic, complemented
12C13×#399C2211yescharacteristic
13C13×#392—21no—
14C13×#392C411yescharacteristic, complemented
15C13×#392C2211yescharacteristic
16C13×#376C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19C2×C22⋊#1055—21no—
20#11718120—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C4×D4×C13—44no—
33C4×D4×C13—44no—
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4C2311yescharacteristic
47C2×C42×C13—21no—
48C2×C42×C13C2×C411yescharacteristic
49C2×C22⋊Dic13—22no—
50C2×C4×Dic13—41no—
51C22×#1055—41no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55#88074—24no—
56#88071—41no—
57C22⋊#1055—22no—
58C22⋊#1055—41no—
59#11726—131nomaximal, Sylow
60C24×C13—21no—
61C24×C13C22⋊C411yescharacteristic
62C24×C13C2×D411yescharacteristic
63C2×D4×C13—22no—
64C2×D4×C13—22no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—42no—
82C22×C4×C13—42no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—41no—
86C22×C4×C13—41no—
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22⋊C411yescharacteristic
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×Dic13—42no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—42no—
96C13×C4⋊C4—42no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—42no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—42no—
102C13×C22⋊C4—42no—
103C13×C22⋊C4—42no—
104C42×C13—24no—
105C42×C13—21no—
106C42×C13—21no—
107C22⋊Dic13—24no—
108C22⋊Dic13—42no—
109C4×Dic13—82no—
110C2×#1055—42no—
111C2×#1055—82no—
112#2397D1311yescharacteristic
113C4×#99—131no—
114#1459—131no—
115#1352—132no—
116#1343—132no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—21no—
121C23×C13—22no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13#10412yes—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#13512yes—
135D4×C13—44no—
136D4×C13—48no—
137D4×C13—48no—
138D4×C13—42no—
139D4×C13—42no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
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×C13—82no—
164C2×C4×C13—82no—
165C2×C4×C13#9911yescharacteristic
166C2×C4×C13#9911yescharacteristic
167C2×Dic13—44no—
168C2×Dic13—82no—
169C2×Dic13—82no—
170#1055—82no—
171C2×C4×D4—21no—
172C2×C4×D4—21no—
173C2×C4×D4Dic1311yescharacteristic, complemented
174C2×C4×D4C2×D1311yescharacteristic
175C2×#99—261no—
176C2×C22⋊C8—261no—
177#399—21no—
178#399Dic1311yescharacteristic, complemented
179#399C2×D1311yescharacteristic
180#392—21no—
181#392Dic1311yescharacteristic, complemented
182#392C2×D1311yescharacteristic
183C4×C22⋊C4—261no—
184#376Dic1311yescharacteristic, complemented
185#342—132no—
186#324—261no—
187#323—132no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—41no—
200C22×C13—42no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13—81no—
207C22×C13C2×#9911yescharacteristic
208C22×C13#41611yescharacteristic
209C22×C13C2×#10411yescharacteristic
210C4×C13—21no—
211C4×C13—42no—
212C4×C13—42no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—41no—
216C4×C13—41no—
217C4×C13—81no—
218C4×C13#35312yes—
219Dic13—84no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4C2×Dic1311yescharacteristic
223C22×D4C22⋊D1311yescharacteristic
224C23×C4—21no—
225C23×C4C22⋊D1311yescharacteristic
226C23×C4C22⋊D1311yescharacteristic
227C22×C8—521no—
228C4×D4—41no—
229C4×D4—41no—
230C4×D4—44no—
231C4×D4—44no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×Dic1311yescharacteristic
237C2×C4⋊C4C22⋊D1311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—262no—
244C2×C22⋊C4C2×Dic1311yescharacteristic
245C2×C22⋊C4C22×D1311yescharacteristic
246C2×C42—21no—
247C2×C42—521no—
248C2×C42C2×Dic1311yescharacteristic
249#99—264no—
250C22⋊C8—262no—
251C22⋊C8—521no—
252#95—21no—
253#95—521no—
254#95C2×Dic1311yescharacteristic
255#95C2×Dic1311yescharacteristic
256C2×C13—21no—
257C2×C13—21no—
258C2×C13—42no—
259C2×C13—42no—
260C2×C13—82no—
261C2×C13#150111yescharacteristic
262C2×C13#212011yescharacteristic
263C2×C13C2×#35311yescharacteristic
264C24—21no—
265C24C22⋊Dic1311yescharacteristic
266C24C2×C22⋊D1311yescharacteristic
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—522no—
292C22×C4C22⋊Dic1311yescharacteristic
293C22×C4C22⋊Dic1311yescharacteristic
294C22×C4C22⋊Dic1311yescharacteristic
295C22×C4C22×Dic1311yescharacteristic
296C22×C4C2×C22⋊D1311yescharacteristic
297C2×C8—522no—
298C2×C8—1042no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—42no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—264no—
311C22⋊C4—522no—
312C42—24no—
313C42—21no—
314C42—21no—
315C42—1042no—
316C13#1172611yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23#8807712yes—
333C23#8820412yes—
334C23C2×C22⋊Dic1311yescharacteristic
335D4—44no—
336D4—42no—
337D4—48no—
338D4—48no—
339D4—42no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—524no—
366C2×C4—1042no—
367C2×C4—1042no—
368C2×C4#8807411yescharacteristic
369C2×C4#8807411yescharacteristic
370C8—1042no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22C2×#8807411yescharacteristic
391C22#1171889411yescharacteristic
392C22C2×#8807711yescharacteristic
393C4—21no—
394C4—42no—
395C4—42no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—81no—
401C4—1044no—
402C4#1171813712yes—
403C2—21no—
404C2—21no—
405C2—42no—
406C2—42no—
407C2—82no—
408C2#1311332711yescharacteristic
409C2#1311647711yescharacteristic
410C2C2×#1171813711yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2397C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2397D13
hypocenterC13#11726
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. C4×#88074C2semidirect
2. #13113154C2semidirect
3. #13112860C2semidirect
4. #13112833C2semidirect
8. C2×C4×D4×C13C4semidirect
11. C13×#399C4semidirect
14. C13×#392C4semidirect
16. C13×#376C4semidirect
173. C2×C4×D4Dic13semidirect
178. #399Dic13semidirect
181. #392Dic13semidirect
184. #376Dic13semidirect
316. C13#11726semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131542
#131128602
#131128332
C13×#23972
#1172613