Finite Group Databasebeta

← #16778296

Subgroups — #16778296

Order 3328.

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

normal subgroups only

This group has 444 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#13130752C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3#13129656C212yesmaximal
4#13129655C212yesmaximal
5#13117311C211yesmaximal, characteristic
6C2×Q8×Dic13C411yescharacteristic
7C2×#88112—21no—
8C2×#88112—21no—
9C2×C4×#1057—21no—
10C13×#391C411yescharacteristic
11#11718891C2211yescharacteristic
12C4⋊C4×Dic13C411yescharacteristic
13#11718634C2211yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718589C411yescharacteristic
16#11718315—21no—
17#11718314—21no—
18#11718310—21no—
19#11718309—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28Q8×Dic13—22no—
29Q8×Dic13C814yescomplemented
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43#88112—24no—
44#88112—42no—
45C4×#1057—42no—
46C13×#95—21no—
47C13×#95—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7577—131nomaximal, Sylow
54C2×Q8×C13—21no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13C2×C812yes—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×#1057—24no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—41no—
76C42×C13—41no—
77C4⋊Dic13—21no—
78C4⋊Dic13—24no—
79C4⋊Dic13—41no—
80C4⋊Dic13C2×C812yes—
81#6101—42no—
82#6101—41no—
83#6101—41no—
84C4×Dic13—24no—
85C4×Dic13—22no—
86C4×Dic13—21no—
87C4×Dic13—21no—
88C4×Dic13—41no—
89C4×Dic13—41no—
90C4×Dic13—42no—
91C4×Dic13C2×C812yes—
92C4×Dic13M1612yes—
93C4×Dic13SD1612yes—
94C4×Dic13Q1612yes—
95#2295—131no—
96#1831—131no—
97C4×C4⋊C8—131no—
98#1272—132no—
99#1271—132no—
100C23×C13C2×C22⋊C411yescharacteristic
101Q8×C13—42no—
102Q8×C13—42no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
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#10312yes—
117C2×C4×C13C22×C811yescharacteristic
118C2×C4×C13C2×M1611yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13C22⋊C812yes—
132C2×Dic13C22⋊C812yes—
133C2×Dic13#10312yes—
134C2×Dic13#10412yes—
135C2×Dic13C2×SD1611yescharacteristic
136C2×Dic13C2×Q1611yescharacteristic
137C2×Dic13AGL(1,ℤ/8)11yescharacteristic
138C2×Dic13#13711yescharacteristic
139#1057—44no—
140#1057—82no—
141C2×C4×Q8—131no—
142C2×C4⋊C8—261no—
143C2×C4⋊C8—261no—
144C2×C4×C8—261no—
145#391—131no—
146#391#26111yescharacteristic
147#389—131no—
148#389—131no—
149#387—261no—
150#387—261no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—261no—
153#376—261no—
154C43—131no—
155#336—132no—
156#336—132no—
157#336—261no—
158C22×C13C2×C22⋊C811yescharacteristic
159C22×C13#41011yescharacteristic
160C22×C13#41311yescharacteristic
161C22×C13C2×#10311yescharacteristic
162C22×C13#41711yescharacteristic
163C22×C13C2×#10411yescharacteristic
164C22×C13#42111yescharacteristic
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—42no—
169C4×C13—41no—
170C4×C13—81no—
171Dic13—22no—
172Dic13—21no—
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—42no—
177Dic13—81no—
178Dic13Q8⋊C814yes—
179C22×Q8C2×#26111yescharacteristic
180C22×C8—262no—
181C22×C8—262no—
182C4×Q8—134no—
183C4×Q8—262no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4C2×#26111yescharacteristic
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42—261no—
198C2×C42C2×#26111yescharacteristic
199C4⋊C8—264no—
200C4⋊C8—522no—
201C4×C8—522no—
202#95—21no—
203#95—21no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209C2×C13#145811yescharacteristic
210C2×C13C2×Q8⋊C811yescharacteristic
211C2×C13#147711yescharacteristic
212C2×C13#150911yescharacteristic
213C2×C13#151811yescharacteristic
214C2×C13#152911yescharacteristic
215C2×C13#155011yescharacteristic
216C2×Q8—21no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×Q8D13⋊C812yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4C22⋊#26111yescharacteristic
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22×#26111yescharacteristic
231C2×C8—264no—
232C2×C8—522no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—522no—
237C4⋊C4—41no—
238C4⋊C4—132no—
239C4⋊C4—264no—
240C4⋊C4—261no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C42—41no—
246C42—132no—
247C42—132no—
248C42—132no—
249C42—132no—
250C42—261no—
251C42—262no—
252C42—261no—
253C42—264no—
254C42—521no—
255C42—521no—
256C42—522no—
257C13#757711yescharacteristic, complemented, Sylow
258C23C2×C22⋊#26111yescharacteristic
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—132no—
275C2×C4—132no—
276C2×C4—132no—
277C2×C4—132no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—262no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4#8811712yes—
295C2×C4C2×D13⋊C811yescharacteristic
296C2×C4D13⋊M1611yescharacteristic
297C8—524no—
298C8—1042no—
299C22D13⋊(C22⋊C8)11yescharacteristic
300C22#1171914211yescharacteristic
301C22#1171914811yescharacteristic
302C22C2×#8811711yescharacteristic
303C22#1171915511yescharacteristic
304C22D13⋊#10411yescharacteristic
305C22#1171916411yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—41no—
310C4—42no—
311C4—81no—
312C4—134no—
313C4—261no—
314C4—261no—
315C4—262no—
316C4—261no—
317C4—261no—
318C4—522no—
319C4—1041no—
320C2#1313006811yescharacteristic
321C2D13⋊(Q8⋊C8)11yescharacteristic
322C2#1313013411yescharacteristic
323C2#1313023711yescharacteristic
324C2#1313027011yescharacteristic
325C2#1313030411yescharacteristic
326C2#1313035411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#391C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#391#261
hypocenterC13#7577
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
29. Q8×Dic13C8semidirect
257. C13#7577semidirect

Maximal subgroups

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

subgroupindex
#131307522
C4×#881122
#131296562
#131296552
#131173112
#757713