Finite Group Databasebeta

← #15751441

Subgroups — #15751441

Order 3328.

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

normal subgroups only

This group has 494 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#13123175C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic
3#13112661C212yesmaximal, complemented
4#13112660C212yesmaximal, complemented
5C13×#1728C211yesmaximal, characteristic
6C22×C13×M16—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88178C411yescharacteristic
9#11718873C411yescharacteristic
10#11718872—21no—
11#11718871—21no—
12C2×C22⋊#1055—21no—
13#11718594—21no—
14#11718594—21no—
15#11718590C411yescharacteristic
16#11718590C2211yescharacteristic
17#11718589C411yescharacteristic
18#11718589C2211yescharacteristic
19C13×#336—21no—
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—24no—
28C2×C13×M16—42no—
29C2×C13×M16—42no—
30C22×C8×C13—22no—
31C2×C42×C13—42no—
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41#88178—42no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C22×#1055—22no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—42no—
54#7695—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×Dic26—22no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C13×M16—48no—
80C2×C8×C13—24no—
81C2×C8×C13—42no—
82C2×C8×C13—42no—
83C42×C13—41no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13—41no—
87C22⋊Dic13—42no—
88C22⋊Dic13—42no—
89C4⋊Dic13—22no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92#6101—42no—
93#6101—42no—
94#6101—41no—
95#6101—41no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99#2855—131no—
100#1817—131no—
101#1728D1311yescharacteristic
102#1272—132no—
103#1271—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13#9912yes—
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—24no—
113C2×C4×C13—24no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13#10412yes—
131C2×C4×C13#13112yes—
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×C4×C13#13712yes—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147Dic26—82no—
148C8×C13—44no—
149#1055—82no—
150C22×M16—21no—
151C2×C22⋊Q8—131no—
152C22×C42C2×D1311yescharacteristic
153C2×C22⋊C8—261no—
154#391—131no—
155#391—131no—
156#389—131no—
157#389—131no—
158#387—261no—
159#387—261no—
160#385—261no—
161#381—261no—
162#380—131no—
163#336—21no—
164#336—132no—
165#336—261no—
166#336C2×D1312yes—
167C22×C13—22no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13#40811yescharacteristic
175C22×C13C2×#9911yescharacteristic
176C22×C13#41311yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13#41911yescharacteristic
179C22×C13C2×#10411yescharacteristic
180C22×C13#42111yescharacteristic
181C4×C13—22no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—41no—
187C4×C13—41no—
188Dic13—81no—
189Dic13—81no—
190Dic13—81no—
191Dic13—81no—
192C22×Q8—131no—
193C23×C4C4×D1311yescharacteristic
194C23×C4D5211yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C2×M16—24no—
197C2×M16—42no—
198C2×M16—42no—
199C22×C8—22no—
200C22×C8—262no—
201C22⋊Q8—522no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C42—42no—
211C2×C42C4×D1311yescharacteristic
212C2×C42D5211yescharacteristic
213C2×C42C22⋊D1311yescharacteristic
214C2×C42C22×D1311yescharacteristic
215C22⋊C8—522no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223C2×C13—42no—
224C2×C13#146811yescharacteristic
225C2×C13#148511yescharacteristic
226C2×C13#149511yescharacteristic
227C2×C13#150411yescharacteristic
228C2×C13#151111yescharacteristic
229C2×C13#152911yescharacteristic
230C2×C13#155911yescharacteristic
231C24#610311yescharacteristic
232C2×Q8—262no—
233C2×Q8—521no—
234C2×Q8—521no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4#610311yescharacteristic
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4C2×C4×D1311yescharacteristic
253C22×C4C2×D5211yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255M16—48no—
256C2×C8—24no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C4⋊C4—262no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—522no—
269C22⋊C4—522no—
270C22⋊C4—522no—
271C42—41no—
272C42—41no—
273C42—41no—
274C42—41no—
275C13#769511yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#8804612yes—
283C23C2×#610311yescharacteristic
284Q8—1042no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4#8804512yes—
316C2×C4#8816112yes—
317C2×C4#8816312yes—
318C2×C4#8818611yescharacteristic
319C2×C4#8819611yescharacteristic
320C8—44no—
321C8—1042no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×#8804511yescharacteristic
330C22C2×#8804611yescharacteristic
331C22#1171862711yescharacteristic
332C22#1171878111yescharacteristic
333C22#1171879011yescharacteristic
334C22#1171879311yescharacteristic
335C22#1171880011yescharacteristic
336C4—22no—
337C4—22no—
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—1041no—
344C4—1041no—
345C4—1041no—
346C4—1041no—
347C2—42no—
348C2#1311318511yescharacteristic
349C2#1311325811yescharacteristic
350C2#1311329911yescharacteristic
351C2#1311333811yescharacteristic
352C2#1311337011yescharacteristic
353C2#1311344111yescharacteristic
354C2#1311356411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1728C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1728D13
hypocenterC13#7695
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
3. #13112661C2semidirect
4. #13112660C2semidirect
275. C13#7695semidirect

Maximal subgroups

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

subgroupindex
#131231752
#131149042
#131126612
#131126602
C13×#17282
#769513