Finite Group Databasebeta

← #16785141

Subgroups — #16785141

Order 3328.

438 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 118 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#13130769C211yesmaximal, characteristic
2#13130621C211yesmaximal, characteristic
3#13129714C212yesmaximal
4#13129714C212yesmaximal
5#13123195C211yesmaximal, characteristic
6C2×#88143—21no—
7C2×#88112—21no—
8C2×#88112C2212yes—
9C2×#88112C2212yes—
10C2×#88110—21no—
11C2×C4⋊#1057—21no—
12C13×#389C411yescharacteristic
13#11718646C411yescharacteristic
14#11718637C2211yescharacteristic
15#11718637C2211yescharacteristic
16#11718634C411yescharacteristic
17#11718633—21no—
18C42×Dic13C2211yescharacteristic
19#11718589C411yescharacteristic
20#11718311—21no—
21#11718308—21no—
22#11718290—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88143—44no—
45#88112—22no—
46#88112—24no—
47#88112—42no—
48#88112Q814yes—
49#88110—42no—
50C4⋊#1057—42no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#9902—131nomaximal, Sylow
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×#1057—24no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—42no—
76C42×C13—41no—
77C4⋊Dic13—42no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80#6101—42no—
81#6101—42no—
82#6101—42no—
83#6101—42no—
84#6101—41no—
85#6101—41no—
86#6101—41no—
87#6101—41no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—22no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—41no—
94C4×Dic13SD1612yes—
95C4×Dic13Q1612yes—
96C4×Dic13C2×Q812yes—
97C4×Dic13#4112yes—
98#2859—131no—
99#1842—131no—
100#1767—131no—
101#1296—132no—
102#1296—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#10312yes—
118C2×C4×C13C4×Q812yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13#10312yes—
131C2×Dic13C22⋊Q812yes—
132C2×Dic13#12411yescharacteristic
133C2×Dic13C4⋊Q811yescharacteristic
134C2×Dic13C2×SD1611yescharacteristic
135C2×Dic13C2×Q1611yescharacteristic
136C2×Dic13AGL(1,ℤ/8)12yes—
137C2×Dic13AGL(1,ℤ/8)11yescharacteristic
138C2×Dic13AGL(1,ℤ/8)11yescharacteristic
139C2×Dic13#13711yescharacteristic
140C2×Dic13#13711yescharacteristic
141#1057—44no—
142#1057—82no—
143C2×#125—261no—
144C2×C4⋊C8—132no—
145C2×C4⋊C8—132no—
146C2×C4⋊C8—261no—
147C2×C4⋊C8—261no—
148C2×#97—261no—
149#389—131no—
150#389—131no—
151#389—131no—
152#389—261no—
153#389—261no—
154#389#26111yescharacteristic
155#384—131no—
156#384—131no—
157#382—261no—
158C43—131no—
159#336—261no—
160C22×C13#39111yescharacteristic
161C22×C13#41311yescharacteristic
162C22×C13#41311yescharacteristic
163C22×C13C2×#10311yescharacteristic
164C22×C13#41711yescharacteristic
165C22×C13#41711yescharacteristic
166C22×C13#41811yescharacteristic
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—41no—
170C4×C13—81no—
171C4×C13—81no—
172Dic13—22no—
173Dic13—41no—
174Dic13—81no—
175Dic13—81no—
176Dic13#47612yes—
177Dic13#47712yes—
178Dic13#49011yescharacteristic
179Dic13#49111yescharacteristic
180Dic13#50111yescharacteristic
181Dic13#50111yescharacteristic
182C22×C8—262no—
183C22×C8—262no—
184#125—524no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4C2×#26111yescharacteristic
196C2×C4⋊C4C2×#26111yescharacteristic
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42C2×#26111yescharacteristic
204C4⋊C8—134no—
205C4⋊C8—262no—
206C4⋊C8—264no—
207C4⋊C8—522no—
208C4⋊C8—522no—
209#97—522no—
210#95—21no—
211#95—261no—
212#95—261no—
213#95—261no—
214C2×C13#155011yescharacteristic
215C2×C13#155011yescharacteristic
216C2×C13#155711yescharacteristic
217C2×C13#155711yescharacteristic
218C2×C13#198711yescharacteristic
219C2×C13#199211yescharacteristic
220C2×C13#199811yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—522no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C4⋊C4—521no—
250C4⋊C4—522no—
251C4⋊C4—522no—
252C42—41no—
253C42—132no—
254C42—132no—
255C42—132no—
256C42—132no—
257C42—261no—
258C42—261no—
259C42—262no—
260C42—261no—
261C42—261no—
262C42—521no—
263C13#990211yescharacteristic, complemented, Sylow
264C23C2×C22⋊#26111yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—132no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—132no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—132no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4#8811712yes—
301C2×C4Q8×#26112yes—
302C8—524no—
303C8—1042no—
304C22#1171913211yescharacteristic
305C22#1171913811yescharacteristic
306C22#1171914811yescharacteristic
307C22C2×#8811711yescharacteristic
308C22(C2×#261)⋊Q811yescharacteristic
309C22#1171916411yescharacteristic
310C22#1171916411yescharacteristic
311C4—22no—
312C4—22no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—132no—
317C4—132no—
318C4—131no—
319C4—131no—
320C4—131no—
321C4—131no—
322C4—262no—
323C4—521no—
324C4—1041no—
325C4—1041no—
326C2#1313035311yescharacteristic
327C2#1313035411yescharacteristic
328C2#1313036711yescharacteristic
329C2#1313036811yescharacteristic
330C2#1313101411yescharacteristic
331C2#1313101911yescharacteristic
332C2#1313103011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9902
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
263. C13#9902semidirect

Maximal subgroups

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

subgroupindex
#131307692
#131306212
#131297142
#131231952
#990213