Finite Group Databasebeta

← #15778916

Subgroups — #15778916

Order 3328.

500 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 103 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#124×Dic13C211yesmaximal, characteristic
2C2×#11718134C211yesmaximal, characteristic
3#13114830C212yesmaximal, complemented
4#13112962C212yesmaximal, complemented
5C2×C13×#355C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×D4×Dic13C411yescharacteristic
9C2×C13×#101C2212yes—
10#11718891C2211yescharacteristic
11C2×#88076C2212yes—
12#11718882C411yescharacteristic
13#11718779—22no—
14#11718612—22no—
15C22⋊C4×Dic13—22no—
16#11718597C411yescharacteristic
17C42×Dic13C411yescharacteristic
18C13×#355—22no—
19#11718146—22no—
20#11718134—22no—
21C22×Q8×C13C2311yescharacteristic
22C22×D4×C13C2×C411yescharacteristic
23C23×Dic13—21no—
24C2×C13×M16—22no—
25C13×#124—22no—
26C13×#124D412yes—
27C13×#124Q812yes—
28C2×C13×C22⋊C4—22no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—22no—
32Q8×Dic13—41no—
33Q8×Dic13—41no—
34D4×Dic13—41no—
35D4×Dic13—41no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13D412yes—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D412yes—
44C2×#6099—22no—
45C13×#101—22no—
46C13×#101—22no—
47#88076—22no—
48#88076—22no—
49#88071—22no—
50#88071—22no—
51#88054—42no—
52#88054—42no—
53#12801—131nomaximal, Sylow
54C24×C13—21no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13C2×D411yescharacteristic
58C2×Q8×C13C2×Q811yescharacteristic
59C2×Q8×C13#4112yes—
60C2×D4×C13—21no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13C4⋊C412yes—
64C22×C4×C13—21no—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—44no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C412yes—
74C22×Dic13C22⋊C411yescharacteristic
75C13×M16—42no—
76C13×M16—42no—
77C2×C8×C13—42no—
78C13×C22⋊C4—24no—
79C13×C22⋊C4—24no—
80C42×C13—21no—
81C42×C13C4⋊C412yes—
82C22⋊Dic13—42no—
83C22⋊Dic13—44no—
84C4⋊Dic13—41no—
85C4⋊Dic13—42no—
86C4⋊Dic13—41no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—42no—
92C4×Dic13—42no—
93C4×Dic13—41no—
94#6099—42no—
95#6099—42no—
96C2×#1055—42no—
97C4×#124—131no—
98C2×#355—131no—
99C2×#355D1311yescharacteristic
100#1801—132no—
101#1394—132no—
102C23×C13—22no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13C2×C22⋊C411yescharacteristic
108Q8×C13—41no—
109Q8×C13—41no—
110Q8×C13—42no—
111D4×C13—42no—
112D4×C13—42no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13C2×C4⋊C411yescharacteristic
121C2×C4×C13#11711yescharacteristic
122C2×C4×C13#12112yes—
123C2×C4×C13C22⋊Q812yes—
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—21no—
127C2×Dic13—22no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—41no—
134C2×Dic13—82no—
135C2×Dic13—82no—
136C2×Dic13#9911yescharacteristic
137C2×Dic13#9911yescharacteristic
138C8×C13—82no—
139#1055—82no—
140C2×#124C2×D1311yescharacteristic
141C2×C4×Q8—131no—
142C2×C4×D4—131no—
143#423—262no—
144C2×#101—132no—
145C2×#101C2×D1312yes—
146#391—131no—
147#390—131no—
148#388—262no—
149#382—131no—
150C4×C22⋊C4—262no—
151C43—131no—
152#355—22no—
153#355—262no—
154#343—262no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—82no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13#38011yescharacteristic
163C22×C13C2×#9911yescharacteristic
164C22×C13#41011yescharacteristic
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—22no—
169C4×C13—42no—
170Dic13—21no—
171Dic13—42no—
172Dic13—41no—
173Dic13—42no—
174Dic13—81no—
175Dic13#35512yescomplemented
176C22×Q8C22×D1311yescharacteristic
177C22×D4C4×D1311yescharacteristic
178C23×C4—261no—
179C2×M16—22no—
180C2×M16—262no—
181#124—22no—
182#124Dic2612yes—
183#124C22⋊D1312yes—
184C4×Q8—521no—
185C4×Q8—521no—
186C4×D4—521no—
187C4×D4—521no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—132no—
190C2×C4⋊C4—131no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—261no—
193C2×C22⋊C4—262no—
194C2×C42—131no—
195C2×C42—132no—
196C2×C42—131no—
197C2×C42—261no—
198C2×C42—261no—
199C2×C42C4×D1311yescharacteristic
200C4⋊C8—522no—
201C4⋊C8—522no—
202#101—22no—
203#101—22no—
204#101—262no—
205#101—262no—
206#95—262no—
207#95—262no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—82no—
211C2×C13#179911yescharacteristic
212C2×C13C2×#35511yescharacteristic
213C2×C13#213211yescharacteristic
214C24—21no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8C2×Dic2611yescharacteristic
218C2×Q8#612912yes—
219C2×Q8C2×C22⋊D1311yescharacteristic
220C2×D4—21no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4#610112yes—
224C22×C4—21no—
225C22×C4—131no—
226C22×C4—132no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—521no—
231C22×C4—521no—
232C22×C4—524no—
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4D4×D1312yes—
235M16—42no—
236M16—42no—
237M16—522no—
238M16—522no—
239C2×C8—42no—
240C2×C8—522no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—521no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—522no—
247C22⋊C4—524no—
248C42—21no—
249C42—262no—
250C42—262no—
251C42—261no—
252C42—261no—
253C42—521no—
254C42—522no—
255C42—522no—
256C42#610112yes—
257C13#1280111yescharacteristic, complemented, Sylow
258C23—22no—
259C23—42no—
260C23—42no—
261C23—41no—
262C23—41no—
263C23C22⋊C4×D1311yescharacteristic
264Q8—41no—
265Q8—42no—
266Q8—41no—
267D4—42no—
268D4—42no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—261no—
281C2×C4—262no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—521no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4#8813111yescharacteristic
291C2×C4#8813212yes—
292C2×C4C2×#610111yescharacteristic
293C2×C4#8819312yes—
294C8—82no—
295C8—1042no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—42no—
300C22—82no—
301C22—81no—
302C22—81no—
303C22#1171840111yescharacteristic
304C22D13×#9911yescharacteristic
305C22#1171860311yescharacteristic
306C4—22no—
307C4—21no—
308C4—22no—
309C4—21no—
310C4—42no—
311C4—132no—
312C4—261no—
313C4—522no—
314C4—521no—
315C4—522no—
316C4—1041no—
317C2—21no—
318C2—21no—
319C2—82no—
320C2#1311482211yescharacteristic
321C2D13×#35511yescharacteristic
322C2#1311651811yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC2×C13×#355C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Q8×C13C23
hypercenterC2×#355D13
hypocenterC13#12801
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #13114830C2semidirect
4. #13112962C2semidirect
175. Dic13#355semidirect
257. C13#12801semidirect

Maximal subgroups

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

subgroupindex
#124×Dic132
C2×#117181342
#131148302
#131129622
C2×C13×#3552
#1280113