Finite Group Databasebeta

← #15762972

Subgroups — #15762972

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718594C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3#13112678C212yesmaximal
4#13112678C212yesmaximal
5C13×#1749C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C22×#6101C411yescharacteristic
8C22×#6101C411yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10C2×C13×#97—21no—
11C2×#88071C411yescharacteristic
12C2×#88071C411yescharacteristic
13C2×#88071C2211yescharacteristic
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718594—21no—
17#11718594—21no—
18#11718594—21no—
19#11718594—21no—
20C2×C4⋊#1055—21no—
21C13×#336—21no—
22#11718116—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C22×C8×C13—22no—
31C2×C42×C13—42no—
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—22no—
39C2×#6101—22no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—42no—
43C22×#1055—22no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8Q814yes—
46C13×#97—42no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—24no—
56C4⋊#1055—42no—
57#9881—131nomaximal, Sylow
58C24×C13C22×C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×Q812yes—
75C22×C4×C13#4112yes—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—22no—
83C22×Dic13—22no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13—41no—
89C22×Dic13—41no—
90C22×Dic13—41no—
91C22×Dic13—41no—
92C22×Dic13M1612yes—
93C22×Dic13M1612yes—
94C2×C8×C13—24no—
95C2×C8×C13—42no—
96C2×C8×C13—42no—
97C42×C13—22no—
98C42×C13—22no—
99C42×C13—41no—
100C42×C13—41no—
101#6101—24no—
102#6101—24no—
103#6101—42no—
104#6101—42no—
105C2×#1055—42no—
106C2×#1055—42no—
107C2×#1055—42no—
108C2×#387—131no—
109#1797—131no—
110#1749D1311yescharacteristic
111#1280—132no—
112#1280—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×C22⋊C411yescharacteristic
118C23×C13C4×Q812yes—
119C23×C13C2×M1611yescharacteristic
120C23×C13C2×M1611yescharacteristic
121C23×C13#13112yes—
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—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—44no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13#9912yes—
143C2×C4×C13C22⋊Q812yes—
144C2×C4×C13#12411yescharacteristic
145C2×C4×C13C4⋊Q811yescharacteristic
146C2×Dic13—22no—
147C2×Dic13—22no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—82no—
163C2×Dic13—82no—
164C8×C13—44no—
165#1055—82no—
166C22×C4⋊C4—131no—
167C22×C4⋊C4—131no—
168C22×C42C2×D1311yescharacteristic
169C2×C4⋊C8—261no—
170C2×C22⋊C8—132no—
171C2×C22⋊C8C2×D1312yes—
172C2×#97—21no—
173#387—261no—
174#387—261no—
175#387—261no—
176#387—261no—
177C2×#95—131no—
178C2×#95—131no—
179C2×#95—131no—
180C2×#95—131no—
181#336—21no—
182#336—261no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13#39111yescharacteristic
192C22×C13#40711yescharacteristic
193C22×C13#40811yescharacteristic
194C22×C13C2×#9911yescharacteristic
195C22×C13#41011yescharacteristic
196C22×C13#41311yescharacteristic
197C22×C13#41311yescharacteristic
198C22×C13#44612yes—
199C22×C13#44612yes—
200C4×C13—22no—
201C4×C13—21no—
202C4×C13—22no—
203C4×C13—21no—
204C4×C13—41no—
205C4×C13—41no—
206C4×C13—41no—
207Dic13—42no—
208Dic13—42no—
209Dic13—81no—
210Dic13—81no—
211C23×C4—131no—
212C23×C4—131no—
213C23×C4—131no—
214C23×C4—131no—
215C23×C4C4×D1311yescharacteristic
216C23×C4C4×D1311yescharacteristic
217C23×C4C22×D1311yescharacteristic
218C22×C8—22no—
219C22×C8—262no—
220C2×C4⋊C4—262no—
221C2×C4⋊C4—262no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—522no—
227C2×C42—42no—
228C2×C42D5211yescharacteristic
229C2×C42D5211yescharacteristic
230C2×C42C22⋊D1311yescharacteristic
231C2×C42C22⋊D1311yescharacteristic
232C4⋊C8—522no—
233C22⋊C8—22no—
234C22⋊C8—264no—
235C22⋊C8Dic2614yes—
236#97—42no—
237#95—261no—
238#95—261no—
239#95—261no—
240#95—261no—
241#95—261no—
242#95—261no—
243#95—261no—
244#95—261no—
245C2×C13—22no—
246C2×C13—22no—
247C2×C13#146411yescharacteristic
248C2×C13#146511yescharacteristic
249C2×C13#146811yescharacteristic
250C2×C13#147311yescharacteristic
251C2×C13#198511yescharacteristic
252C2×C13#199611yescharacteristic
253C2×C13#199811yescharacteristic
254C24C2×C4×D1311yescharacteristic
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—132no—
265C22×C4—132no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—262no—
273C22×C4—262no—
274C22×C4—521no—
275C22×C4—521no—
276C22×C4—521no—
277C22×C4—521no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4#610311yescharacteristic
283C22×C4#610311yescharacteristic
284C22×C4#610311yescharacteristic
285C22×C4#610311yescharacteristic
286C22×C4C2×Dic2612yes—
287C22×C4C2×D5211yescharacteristic
288C22×C4#612712yes—
289C22×C4C2×C22⋊D1311yescharacteristic
290C2×C8—24no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—522no—
294C2×C8—522no—
295C2×C8—522no—
296C4⋊C4—264no—
297C4⋊C4—264no—
298C4⋊C4—522no—
299C4⋊C4—522no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C13#988111yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C4×Dic2612yes—
310C23M16×D1311yescharacteristic
311C23M16×D1311yescharacteristic
312C23#8816112yes—
313C23C2×#610311yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—262no—
335C2×C4—262no—
336C2×C4—522no—
337C2×C4—522no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4—1042no—
351C2×C4—1042no—
352C2×C4#8804612yes—
353C2×C4#8812311yescharacteristic
354C2×C4#8812911yescharacteristic
355C2×C4#8817812yes—
356C8—44no—
357C8—1042no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22#1171836212yes—
367C22#1171836212yes—
368C22#1171859011yescharacteristic
369C22C2×#8804611yescharacteristic
370C22#1171866711yescharacteristic
371C22#1171878711yescharacteristic
372C22#1171879011yescharacteristic
373C22#1171879311yescharacteristic
374C22#1171879311yescharacteristic
375C4—22no—
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—522no—
383C4—522no—
384C4—1041no—
385C4—1041no—
386C2—22no—
387C2—22no—
388C2#1311316811yescharacteristic
389C2#1311317211yescharacteristic
390C2#1311318511yescharacteristic
391C2#1311320611yescharacteristic
392C2#1311577611yescharacteristic
393C2#1311582111yescharacteristic
394C2#1311582911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1749C2
socleC23×C13C2×C22⋊C4
cosocleC23×C4×C13C23
hypercenter#1749D13
hypocenterC13#9881
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
304. C13#9881semidirect

Maximal subgroups

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

subgroupindex
C2×#117185942
#131148162
#131126782
C13×#17492
#988113