Finite Group Databasebeta

← #15781573

Subgroups — #15781573

Order 3328.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114824C211yesmaximal, characteristic
2C4×#88073C211yesmaximal, characteristic
3#13112954C212yesmaximal
4#13112954C212yesmaximal
5C13×#2579C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C13×#398—21no—
9C13×#396—21no—
10C13×#387—21no—
11C13×#386C2211yescharacteristic
12C13×#386C2211yescharacteristic
13C13×#385—21no—
14C13×#385C411yescharacteristic, complemented
15C13×#385C411yescharacteristic, complemented
16C13×#380C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19#11718873—21no—
20C4×#6099—21no—
21#11718122—21no—
22#11718118—21no—
23C22×D4×C13C2311yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4⋊Dic13—41no—
47C2×#6099—22no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53#88074—24no—
54#88073—22no—
55#88073Q814yes—
56#88071—41no—
57#88043—41no—
58C4×#1055—41no—
59#13294—131nomaximal, Sylow
60C24×C13C22×C411yescharacteristic
61C24×C13C2×D411yescharacteristic
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13C2×Q812yes—
65C2×D4×C13#4112yes—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—42no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13—81no—
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×Dic13—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—41no—
98C13×C22⋊C4—81no—
99C42×C13—21no—
100C42×C13—21no—
101C22⋊Dic13—42no—
102C22⋊Dic13—42no—
103C4⋊Dic13—82no—
104#6099—24no—
105#6099—42no—
106C2×#1055—42no—
107#2579D1311yescharacteristic
108#1799—131no—
109C4×#100—131no—
110#1390—132no—
111#1390—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13C2×C22⋊C411yescharacteristic
121C23×C13C4×Q812yes—
122C23×C13#12411yescharacteristic
123C23×C13C4⋊Q811yescharacteristic
124D4×C13—42no—
125D4×C13—42no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—82no—
154C2×C4×C13#9911yescharacteristic
155C2×C4×C13#9911yescharacteristic
156C2×C4×C13C22⋊Q812yes—
157C2×Dic13—82no—
158C2×Dic13—82no—
159C2×Dic13—82no—
160#1055—44no—
161C2×C4×D4C2×D1311yescharacteristic
162C22×C4⋊C4Dic1311yescharacteristic, complemented
163C2×#100—132no—
164C2×#99—132no—
165C4×M16—261no—
166#398—21no—
167#396—21no—
168#387—21no—
169#386C2×D1311yescharacteristic
170#386C2×D1311yescharacteristic
171#385—21no—
172#385Dic1311yescharacteristic, complemented
173#385Dic1311yescharacteristic, complemented
174#380—261no—
175#380Dic1311yescharacteristic, complemented
176#343—261no—
177#342—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—22no—
182C22×C13—21no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—42no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—81no—
192C22×C13#39111yescharacteristic
193C22×C13C2×#9911yescharacteristic
194C22×C13#41011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—22no—
198C4×C13—41no—
199C4×C13—42no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—81no—
205Dic13—162no—
206C22×D4C22×D1311yescharacteristic
207C23×C4C2×Dic1311yescharacteristic
208C23×C4C2×Dic1311yescharacteristic
209C23×C4C2×Dic1311yescharacteristic
210C23×C4C22⋊D1311yescharacteristic
211C2×M16—262no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—521no—
222C2×C4⋊C4C22⋊D1311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—262no—
226C2×C22⋊C4C2×Dic1311yescharacteristic
227C2×C22⋊C4C2×Dic1311yescharacteristic
228C2×C22⋊C4C2×Dic1311yescharacteristic
229C2×C22⋊C4C22⋊D1311yescharacteristic
230C2×C42C22⋊D1311yescharacteristic
231#100—134no—
232#100—262no—
233#99—264no—
234#97—521no—
235C4×C8—521no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—521no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—41no—
245C2×C13—42no—
246C2×C13—41no—
247C2×C13#199611yescharacteristic
248C2×C13#212011yescharacteristic
249C2×C13#212111yescharacteristic
250C24C22×Dic1311yescharacteristic
251C24C2×C22⋊D1311yescharacteristic
252C2×D4—41no—
253C2×D4—41no—
254C2×D4Q8×D1312yes—
255C2×D4#613112yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—81no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—522no—
271C22×C4C22⋊Dic1311yescharacteristic
272C22×C4C22⋊Dic1311yescharacteristic
273C22×C4C22⋊Dic1311yescharacteristic
274C22×C4C22⋊Dic1311yescharacteristic
275C22×C4C2×C22⋊D1311yescharacteristic
276M16—264no—
277M16—522no—
278C2×C8—522no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—1042no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—81no—
293C22⋊C4—522no—
294C22⋊C4—522no—
295C42—21no—
296C42—21no—
297C13#1329411yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23#8819811yescharacteristic
307C23Q8×Dic1312yes—
308C23#8820111yescharacteristic
309C23C2×C22⋊Dic1311yescharacteristic
310D4—42no—
311D4—42no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4—1042no—
341C2×C4—1042no—
342C2×C4—1042no—
343C2×C4#8807411yescharacteristic
344C2×C4#8807411yescharacteristic
345C2×C4#8820012yes—
346C8—524no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—41no—
353C22—42no—
354C22—41no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22C2×#8807411yescharacteristic
362C22#1171889111yescharacteristic
363C22#1171890111yescharacteristic
364C4—21no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—42no—
369C4—41no—
370C4—41no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—2082no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—42no—
379C2—41no—
380C2#1311582211yescharacteristic
381C2#1311647711yescharacteristic
382C2#1311648211yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2579C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2579D13
hypocenterC13#13294
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2579

Complements

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

NH ≅ G/Ntype
7. C22×C13×C4⋊C4C4semidirect
14. C13×#385C4semidirect
15. C13×#385C4semidirect
16. C13×#380C4semidirect
162. C22×C4⋊C4Dic13semidirect
172. #385Dic13semidirect
173. #385Dic13semidirect
175. #380Dic13semidirect
297. C13#13294semidirect

Maximal subgroups

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

subgroupindex
#131148242
C4×#880732
#131129542
C13×#25792
#1329413