Finite Group Databasebeta

← #15758985

Subgroups — #15758985

Order 3328.

622 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 127 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#13120578C211yesmaximal, characteristic
2#13117454C211yesmaximal, characteristic, complemented
3#13113405C212yesmaximal
4#13112704C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×#88183—21no—
9C2×#88180—21no—
10C2×C13×C22⋊C8C2212yes—
11#11718874—21no—
12#11718873—21no—
13#11718873C2211yescharacteristic
14#11718873C2212yes—
15#11718655—22no—
16#11718652C412yescomplemented
17#11718646—24no—
18#11718644C412yescomplemented
19C13×#324—22no—
20#11718062—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×C22⋊D13—21no—
25C22×D52C2×C411yescharacteristic
26C22×C8×C13—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—21no—
33#88184—22no—
34#88184—22no—
35#88183—42no—
36#88183—42no—
37C2×#6103—22no—
38C2×#6103—21no—
39C2×#6103—22no—
40#88180—42no—
41#88180—42no—
42C2×C4⋊Dic13—22no—
43C2×C4⋊Dic13—22no—
44C2×C4⋊Dic13—22no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13C2×C411yescharacteristic
47C2×#6101—22no—
48C2×C4×Dic13—22no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51#88071—22no—
52#88071—22no—
53#88071C2×C412yes—
54#88071D414yes—
55#9204—131nomaximal, Sylow
56C24×C13C2×D411yescharacteristic
57C23×D13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—81no—
65C22×C4×C13—81no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13D812yes—
69C22×C4×C13SD1612yes—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4112yes—
74C2×C22⋊D13—41no—
75C2×C22⋊D13—41no—
76C2×C22⋊D13—41no—
77C2×C22⋊D13—41no—
78C2×C22⋊D13—41no—
79C2×C22⋊D13—41no—
80C22×Dic13—21no—
81C22×Dic13—22no—
82C22×Dic13—24no—
83C2×D52—22no—
84C2×D52—81no—
85C2×C8×C13—42no—
86C2×C8×C13—82no—
87C13×C4⋊C4—24no—
88C13×C4⋊C4—24no—
89C22⋊Dic13—42no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92C22⋊Dic13—42no—
93#6103—44no—
94#6103—42no—
95#6103—82no—
96C4⋊Dic13—22no—
97C4⋊Dic13—44no—
98C4⋊Dic13—82no—
99C4⋊Dic13—82no—
100C4⋊Dic13—81no—
101#6101—44no—
102C4×Dic13—44no—
103#2618—131no—
104#2316—131no—
105#1519—132no—
106C2×#324D1311yescharacteristic, complemented
107#1289—132no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13#12011yescharacteristic
112C23×C13#12311yescharacteristic
113C23×C13C2×D811yescharacteristic
114C23×C13C2×SD1611yescharacteristic
115C23×C13AGL(1,ℤ/8)11yescharacteristic
116C23×C13#13711yescharacteristic
117C22×D13—42no—
118C22×D13—42no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—41no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—81no—
136C2×C4×C13#10214yes—
137C2×C4×C13C4×D412yes—
138C2×C4×C13#12112yes—
139C22⋊D13—81no—
140C22⋊D13—81no—
141C22⋊D13—81no—
142C22⋊D13—81no—
143C2×Dic13—44no—
144C2×Dic13—42no—
145C2×Dic13—44no—
146C2×Dic13—42no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—44no—
152D52—82no—
153C8×C13—82no—
154C2×#123—261no—
155C2×#121—131no—
156C2×#117—261no—
157C22×C4⋊C4C2×D1311yescharacteristic
158C2×C22⋊C8C2×D1312yes—
159#398—132no—
160#396—262no—
161#394—132no—
162#389—264no—
163#386—261no—
164#380—131no—
165#380—132no—
166#380—261no—
167#327—264no—
168#324—22no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13#38611yescharacteristic
180C22×C13C2×#10211yescharacteristic
181C22×C13#41711yescharacteristic
182C22×C13#44711yescharacteristic
183C22×C13#44811yescharacteristic
184C22×C13#48011yescharacteristic
185C22×C13#48111yescharacteristic
186C2×D13—82no—
187C2×D13—82no—
188C2×D13—81no—
189C2×D13—81no—
190C2×D13—81no—
191C4×C13—24no—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—42no—
195Dic13—84no—
196Dic13—82no—
197Dic13—81no—
198C22×D4—131no—
199C22×D4—261no—
200C23×C4D5211yescharacteristic
201C23×C4D5211yescharacteristic
202C23×C4C22×D1311yescharacteristic
203C22×C8—22no—
204#123—522no—
205#123—522no—
206#121—262no—
207#121—262no—
208#117—522no—
209#117—522no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—262no—
214C2×C4⋊C4—262no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—262no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4C4×D1312yes—
219C2×C4⋊C4C22⋊D1312yes—
220C2×C22⋊C4—262no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4—262no—
223C2×C22⋊C4—261no—
224C2×C22⋊C4—262no—
225C2×C42—262no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228#95—132no—
229#95—134no—
230#95—262no—
231#95—262no—
232C2×C13—21no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#187411yescharacteristic
239C2×C13#191211yescharacteristic
240C2×C13#191311yescharacteristic
241D13—161no—
242C24—261no—
243C24C2×D5211yescharacteristic
244C2×D4—262no—
245C2×D4—521no—
246C2×D4—521no—
247C2×D4—521no—
248C2×D4—521no—
249C2×D4—521no—
250C2×D4—521no—
251C2×D4—1041no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—264no—
261C22×C4—262no—
262C22×C4—261no—
263C22×C4#609512yes—
264C22×C4D10412yes—
265C22×C4#610312yes—
266C22×C4#610312yes—
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4D4×D1312yes—
269C22×C4#612912yes—
270C22×C4C2×C22⋊D1311yescharacteristic
271C2×C8—42no—
272C2×C8—82no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—262no—
276C4⋊C4—524no—
277C4⋊C4—524no—
278C4⋊C4—1042no—
279C4⋊C4—1041no—
280C4⋊C4—1042no—
281C22⋊C4—521no—
282C22⋊C4—522no—
283C22⋊C4—521no—
284C22⋊C4—522no—
285C22⋊C4—522no—
286C22⋊C4—524no—
287C22⋊C4—1042no—
288C42—524no—
289C13#920411yescharacteristic, complemented, Sylow
290C23—41no—
291C23—41no—
292C23—522no—
293C23—522no—
294C23—521no—
295C23—521no—
296C23—521no—
297C23#8813611yescharacteristic
298C23#8814011yescharacteristic
299C23C2×#609511yescharacteristic
300C23C2×D10411yescharacteristic
301C23#8816211yescharacteristic
302C23#8816311yescharacteristic
303C23C2×#610311yescharacteristic
304D4—1042no—
305D4—1041no—
306D4—1041no—
307D4—1041no—
308D4—1041no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—522no—
324C2×C4—524no—
325C2×C4—524no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—524no—
332C2×C4#8806114yes—
333C2×C4#8813512yes—
334C2×C4#8819312yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—1042no—
347C22—1042no—
348C22—1041no—
349C22—1041no—
350C22—1041no—
351C22#1171839311yescharacteristic
352C22#1171839611yescharacteristic
353C22#1171839711yescharacteristic
354C22#1171839911yescharacteristic
355C22#1171861911yescharacteristic
356C22C2×#8806111yescharacteristic
357C22#1171879411yescharacteristic
358C4—24no—
359C4—22no—
360C4—22no—
361C4—42no—
362C4—1044no—
363C4—1042no—
364C4—1041no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—2081no—
372C2#1311515111yescharacteristic
373C2#1311537111yescharacteristic
374C2#1311537611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9204
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13117454C2semidirect
4. #13112704C2semidirect
5. C2×C13×#324C2semidirect
16. #11718652C4semidirect
18. #11718644C4semidirect
106. C2×#324D13semidirect
289. C13#9204semidirect

Maximal subgroups

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

subgroupindex
#131205782
#131174542
#131134052
#131127042
C2×C13×#3242
#920413