Finite Group Databasebeta

← #15763018

Subgroups — #15763018

Order 3328.

432 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123221C211yesmaximal, characteristic
2#13114690C211yesmaximal, characteristic
3#97×Dic13C211yesmaximal, characteristic
4#13112718C211yesmaximal, characteristic
5#13112718C211yesmaximal, characteristic
6#13112717C211yesmaximal, characteristic
7C13×#1295C211yesmaximal, characteristic
8C2×C13×#97C2211yescharacteristic
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11C2×#88055—21no—
12C2×#88054—21no—
13C2×C8×Dic13—21no—
14#11718646C411yescharacteristic
15#11718646C411yescharacteristic
16#11718634C411yescharacteristic
17#11718634C411yescharacteristic
18#11718597C2211yescharacteristic
19C42×Dic13C2211yescharacteristic
20C2×#88043C2211yescharacteristic
21C2×#88043C2211yescharacteristic
22#11718316—21no—
23#11718316—21no—
24#11718315—21no—
25#11718315—21no—
26#11718142—21no—
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C22×#1055—21no—
45C22×#1055—21no—
46C13×#97—21no—
47C13×#97—21no—
48C13×#97—21no—
49C13×#97Q812yes—
50C13×#95—21no—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88055—24no—
59#88054—24no—
60C8×Dic13—24no—
61#88043—21no—
62#88043—21no—
63#88043—21no—
64#88043Q812yes—
65#9892—131nomaximal, Sylow
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C2×C8×C13—22no—
78C2×C8×C13—22no—
79C2×C8×C13—22no—
80C2×C8×C13—22no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C42×C13C2×Q811yescharacteristic
86C42×C13C2×Q811yescharacteristic
87C42×C13#4111yescharacteristic
88C42×C13#4111yescharacteristic
89C4⋊Dic13—42no—
90C4⋊Dic13—42no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—42no—
94#6101—42no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—22no—
104C2×#1055—22no—
105C2×#1055—41no—
106C2×#1055—41no—
107#2864—131no—
108#1767—131no—
109C4×#97—131no—
110#1295—131no—
111#1295—131no—
112#1295—131no—
113#1295D1311yescharacteristic
114C23×C13C2×C22⋊C411yescharacteristic
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—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13C4×Q811yescharacteristic
128C2×C4×C13C4×Q811yescharacteristic
129C2×C4×C13C22⋊Q811yescharacteristic
130C2×C4×C13C22⋊Q811yescharacteristic
131C2×C4×C13#12411yescharacteristic
132C2×C4×C13C4⋊Q811yescharacteristic
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13#10412yes—
149C2×Dic13#10412yes—
150C2×Dic13#10412yes—
151C8×C13—24no—
152C8×C13—42no—
153#1055—24no—
154#1055—42no—
155C2×C4⋊C8—261no—
156C2×#97—131no—
157C2×#97—131no—
158C2×#97—261no—
159C2×#97C2×D1311yescharacteristic
160C2×#97C2×D1311yescharacteristic
161C2×C4×C8—261no—
162#389—131no—
163#389—131no—
164#389—131no—
165#389—131no—
166#387—261no—
167#387—261no—
168#387—261no—
169#387—261no—
170#382—131no—
171#382C2×D1311yescharacteristic
172C43—131no—
173#336—261no—
174C22×C13#39111yescharacteristic
175C22×C13#41311yescharacteristic
176C22×C13#41311yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13C2×#10411yescharacteristic
180C22×C13#42111yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—81no—
188C4×C13—81no—
189Dic13—22no—
190Dic13—22no—
191Dic13—22no—
192Dic13—41no—
193Dic13—81no—
194Dic13—81no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—261no—
198C22×C8—261no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C4×D1311yescharacteristic
206C2×C4⋊C4C4×D1311yescharacteristic
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42C22×D1311yescharacteristic
214C4⋊C8—264no—
215#97—21no—
216#97—21no—
217#97—21no—
218#97—132no—
219#97—264no—
220#97—261no—
221#97—261no—
222#97—261no—
223#97Dic2612yes—
224C4×C8—264no—
225#95—21no—
226#95—21no—
227#95—261no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13#152411yescharacteristic
234C2×C13#152411yescharacteristic
235C2×C13#152911yescharacteristic
236C2×C13#153211yescharacteristic
237C2×C13#198611yescharacteristic
238C2×C13#199411yescharacteristic
239C2×C13#199811yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4D4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—262no—
260C2×C8—262no—
261C2×C8—521no—
262C2×C8—521no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—522no—
268C4⋊C4—522no—
269C4⋊C4—522no—
270C4⋊C4—522no—
271C42—262no—
272C42—262no—
273C42—262no—
274C42—521no—
275C42—521no—
276C42—521no—
277C42C2×Dic2611yescharacteristic
278C42#612711yescharacteristic
279C42#612911yescharacteristic
280C42Q8×D1311yescharacteristic
281C13#989211yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1311yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—132no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4C4×Dic2611yescharacteristic
314C2×C4#8813211yescharacteristic
315C2×C4#8813911yescharacteristic
316C2×C4#8814111yescharacteristic
317C2×C4#8814211yescharacteristic
318C2×C4#8815011yescharacteristic
319C8—24no—
320C8—42no—
321C8—264no—
322C8—522no—
323C22#1171830711yescharacteristic
324C22#1171840611yescharacteristic
325C22#1171841211yescharacteristic
326C22D13×#10411yescharacteristic
327C22D13×#10411yescharacteristic
328C22D13×#10411yescharacteristic
329C22#1171848211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—81no—
338C4—262no—
339C4—262no—
340C4—262no—
341C4—521no—
342C4—1041no—
343C4—1041no—
344C2#1311342111yescharacteristic
345C2#1311342311yescharacteristic
346C2#1311344011yescharacteristic
347C2#1311345511yescharacteristic
348C2#1311577811yescharacteristic
349C2#1311581111yescharacteristic
350C2#1311582711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13#9892
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
281. C13#9892semidirect

Maximal subgroups

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

subgroupindex
#131232212
#131146902
#97×Dic132
#131127182
#131127172
C13×#12952
#989213