Finite Group Databasebeta

← #15755598

Subgroups — #15755598

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718594C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3C2×#11718061C212yesmaximal
4#13112678C212yesmaximal
5C13×#1797C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C22×#6101C411yescharacteristic
8C22×#6101C2211yescharacteristic
9C2×C13×C4⋊C8—21no—
10C2×C13×C22⋊C8C2212yes—
11C2×#88071C411yescharacteristic
12C2×#88071C411yescharacteristic
13C2×#88071C411yescharacteristic
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—
23#11718061—24no—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2×C411yescharacteristic
31C22×C8×C13—22no—
32C2×C42×C13—42no—
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—42no—
44C2×#6101D412yes—
45C2×#6101Q812yes—
46C22×#1055—22no—
47C13×C4⋊C8—42no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C4⋊#1055—42no—
61#8562—131nomaximal, Sylow
62C24×C13C22×C411yescharacteristic
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×Q811yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—22no—
86C22×Dic13—22no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—22no—
90C22×Dic13—22no—
91C22×Dic13—41no—
92C22×Dic13—41no—
93C22×Dic13—41no—
94C22×Dic13—41no—
95C22×Dic13—41no—
96C22×Dic13—41no—
97C22×Dic13C4⋊C412yes—
98C22×Dic13C4⋊C412yes—
99C2×C8×C13—42no—
100C2×C8×C13—42no—
101C2×C8×C13—42no—
102C42×C13—22no—
103C42×C13—22no—
104C42×C13—41no—
105C42×C13—41no—
106#6101—22no—
107#6101—22no—
108#6101—22no—
109#6101—22no—
110#6101—42no—
111#6101—42no—
112C2×#1055—42no—
113C2×#1055—42no—
114C2×#1055—42no—
115C2×#387—131no—
116#1797—131no—
117#1797D1311yescharacteristic
118C2×#324—132no—
119#1280—132no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13C2×C22⋊C411yescharacteristic
125C23×C13C2×C4⋊C411yescharacteristic
126C23×C13#11711yescharacteristic
127C23×C13#13112yes—
128C23×C13#13112yes—
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—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—44no—
148C2×C4×C13—44no—
149C2×C4×C13#9912yes—
150C2×C4×C13#10112yes—
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13C22⋊Q811yescharacteristic
154C2×C4×C13C22⋊Q811yescharacteristic
155C2×Dic13—22no—
156C2×Dic13—22no—
157C2×Dic13—24no—
158C2×Dic13—42no—
159C2×Dic13—41no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165C2×Dic13—41no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—82no—
172C2×Dic13—82no—
173C8×C13—82no—
174#1055—82no—
175C22×C4⋊C4—131no—
176C22×C4⋊C4—131no—
177C22×C42C2×D1311yescharacteristic
178C2×C4⋊C8—21no—
179C2×C4⋊C8—261no—
180C2×C22⋊C8—132no—
181C2×C22⋊C8C2×D1312yes—
182#387—261no—
183#387—261no—
184#387—261no—
185#387—261no—
186C2×#95—131no—
187C2×#95—131no—
188C2×#95—131no—
189C2×#95—131no—
190#336—21no—
191#336—261no—
192#324—264no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—22no—
198C22×C13—22no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13#38011yescharacteristic
202C22×C13#40811yescharacteristic
203C22×C13#40811yescharacteristic
204C22×C13C2×#9911yescharacteristic
205C22×C13#41011yescharacteristic
206C22×C13C2×#10111yescharacteristic
207C22×C13#41311yescharacteristic
208C22×C13#42412yes—
209C22×C13#43312yes—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—21no—
213C4×C13—21no—
214C4×C13—22no—
215C4×C13—22no—
216C4×C13—41no—
217C4×C13—41no—
218Dic13—42no—
219Dic13—42no—
220Dic13—81no—
221Dic13—81no—
222C23×C4—131no—
223C23×C4—131no—
224C23×C4—131no—
225C23×C4—131no—
226C23×C4C4×D1311yescharacteristic
227C23×C4C4×D1311yescharacteristic
228C23×C4C22×D1311yescharacteristic
229C22×C8—22no—
230C22×C8—262no—
231C2×C4⋊C4—132no—
232C2×C4⋊C4—132no—
233C2×C4⋊C4—261no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4—261no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—522no—
240C2×C42—42no—
241C2×C42D5211yescharacteristic
242C2×C42D5211yescharacteristic
243C2×C42C22⋊D1311yescharacteristic
244C2×C42C22⋊D1311yescharacteristic
245C4⋊C8—42no—
246C4⋊C8—522no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249C22⋊C8—262no—
250C22⋊C8—262no—
251#95—261no—
252#95—261no—
253#95—261no—
254#95—261no—
255#95—261no—
256#95—261no—
257#95—261no—
258#95—261no—
259C2×C13—22no—
260C2×C13—22no—
261C2×C13#146811yescharacteristic
262C2×C13#147011yescharacteristic
263C2×C13#147211yescharacteristic
264C2×C13#147311yescharacteristic
265C2×C13#179811yescharacteristic
266C2×C13#179911yescharacteristic
267C2×C13#180111yescharacteristic
268C24C2×C4×D1311yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—132no—
278C22×C4—132no—
279C22×C4—261no—
280C22×C4—261no—
281C22×C4—262no—
282C22×C4—262no—
283C22×C4—261no—
284C22×C4—261no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—262no—
288C22×C4—262no—
289C22×C4—521no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4#610311yescharacteristic
296C22×C4#610311yescharacteristic
297C22×C4#610311yescharacteristic
298C22×C4#610311yescharacteristic
299C22×C4C2×D5211yescharacteristic
300C22×C4D4×D1311yescharacteristic
301C22×C4#612911yescharacteristic
302C22×C4Q8×D1311yescharacteristic
303C22×C4#613111yescharacteristic
304C22×C4C2×C22⋊D1311yescharacteristic
305C2×C8—42no—
306C2×C8—42no—
307C2×C8—42no—
308C2×C8—522no—
309C2×C8—522no—
310C2×C8—522no—
311C4⋊C4—262no—
312C4⋊C4—262no—
313C4⋊C4—262no—
314C4⋊C4—262no—
315C4⋊C4—522no—
316C4⋊C4—522no—
317C42—22no—
318C42—22no—
319C42—41no—
320C42—41no—
321C13#856211yescharacteristic, complemented, Sylow
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C4⋊C4×D1311yescharacteristic
327C23#8814611yescharacteristic
328C23#8815512yes—
329C23#8816112yes—
330C23C2×#610311yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—264no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—522no—
355C2×C4—521no—
356C2×C4—522no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—522no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—1042no—
368C2×C4—1042no—
369C2×C4#8804612yes—
370C2×C4#8806412yes—
371C2×C4#8814911yescharacteristic
372C2×C4#8815111yescharacteristic
373C2×C4#8819211yescharacteristic
374C2×C4#8820011yescharacteristic
375C8—82no—
376C8—1042no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1171850012yes—
386C22#1171850112yes—
387C22C2×#8804611yescharacteristic
388C22#1171864811yescharacteristic
389C22#1171866711yescharacteristic
390C22#1171877111yescharacteristic
391C22#1171879011yescharacteristic
392C22#1171879311yescharacteristic
393C22C2×#8806411yescharacteristic
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—522no—
403C4—522no—
404C4—1041no—
405C4—1041no—
406C2—22no—
407C2—22no—
408C2#1311318511yescharacteristic
409C2#1311319311yescharacteristic
410C2#1311319911yescharacteristic
411C2#1311320311yescharacteristic
412C2#1311481711yescharacteristic
413C2#1311482111yescharacteristic
414C2#1311482911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1797C2
socleC23×C13C2×C22⋊C4
cosocleC23×C4×C13C23
hypercenter#1797D13
hypocenterC13#8562
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
321. C13#8562semidirect

Maximal subgroups

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

subgroupindex
C2×#117185942
#131148162
C2×#117180612
#131126782
C13×#17972
#856213