Finite Group Databasebeta

← #15756919

Subgroups — #15756919

Order 3328.

612 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117454C211yesmaximal, characteristic
2#13115031C212yesmaximal
3#13113089C211yesmaximal, characteristic
4#13112716C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88180—21no—
8C22×C4⋊Dic13C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10#11718873—21no—
11#11718873C2212yes—
12C2×#88071—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×#88057—22no—
16#11718646—22no—
17#11718646—22no—
18C13×#324C414yescomplemented
19#11718143—22no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×C8×C13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4Q812yes—
30C2×C22⋊Dic13—22no—
31#88180—42no—
32#88180—42no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—42no—
39C2×C4⋊Dic13D412yes—
40C2×C4⋊Dic13D412yes—
41C2×C4×Dic13—22no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8C2×C414yes—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#88071—42no—
48#88071—42no—
49#88057—44no—
50#8857—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13C4⋊C412yes—
63C22×C4×C13C4⋊C412yes—
64C22×C4×C13SD1612yes—
65C22×C4×C13SD1612yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×Q811yescharacteristic
69C22×C4×C13#4112yes—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—41no—
82C22×Dic13—41no—
83C22×Dic13—41no—
84C22×Dic13—41no—
85C22×Dic13—41no—
86C2×C8×C13—24no—
87C2×C8×C13—42no—
88C2×C8×C13—42no—
89C13×C4⋊C4—24no—
90C13×C4⋊C4—24no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C4⋊Dic13—24no—
94C4⋊Dic13—42no—
95C4⋊Dic13—42no—
96C4⋊Dic13—42no—
97C4⋊Dic13—42no—
98C4⋊Dic13—42no—
99C4⋊Dic13—81no—
100C4⋊Dic13—81no—
101C4×Dic13—44no—
102#2316—131no—
103#1853—132no—
104C2×#324D1311yescharacteristic
105#1441—131no—
106#1294—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C2×C4⋊C411yescharacteristic
112C23×C13#12011yescharacteristic
113C23×C13#12311yescharacteristic
114C23×C13C2×SD1611yescharacteristic
115C23×C13C2×SD1611yescharacteristic
116C23×C13AGL(1,ℤ/8)11yescharacteristic
117C23×C13#13711yescharacteristic
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13#10614yescomplemented
135C2×C4×C13C4×D412yes—
136C2×C4×C13C22⋊Q812yes—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13—81no—
152C2×Dic13—81no—
153C2×Dic13—81no—
154C2×Dic13—81no—
155C2×Dic13—81no—
156C2×Dic13—81no—
157C8×C13—44no—
158C2×#117—261no—
159C22×C4⋊C4—131no—
160C22×C4⋊C4C2×D1311yescharacteristic
161C2×#106—262no—
162C2×C22⋊C8C2×D1312yes—
163#389—262no—
164#389—262no—
165#380—132no—
166#380—261no—
167C2×#95—131no—
168C2×#95—261no—
169C2×#95—261no—
170#340—262no—
171#324Dic1314yescomplemented
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13#38511yescharacteristic
185C22×C13C2×#10611yescharacteristic
186C22×C13#42811yescharacteristic
187C22×C13#44811yescharacteristic
188C22×C13#45011yescharacteristic
189C22×C13#45411yescharacteristic
190C22×C13#45611yescharacteristic
191C22×C13B(4,𝔽2)11yescharacteristic
192C22×C13#45811yescharacteristic
193C22×C13#48111yescharacteristic
194C22×C13#48311yescharacteristic
195C4×C13—24no—
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—42no—
199Dic13—82no—
200Dic13—82no—
201Dic13—82no—
202Dic13—82no—
203C23×C4—261no—
204C23×C4—261no—
205C23×C4D5211yescharacteristic
206C23×C4D5211yescharacteristic
207C23×C4C22×D1311yescharacteristic
208C22×C8—22no—
209#117—522no—
210#117—522no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—132no—
214C2×C4⋊C4—132no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—522no—
221C2×C4⋊C4Dic2612yes—
222C2×C4⋊C4C2×Dic1312yes—
223C2×C22⋊C4—262no—
224C2×C42—262no—
225#106—524no—
226C22⋊C8—22no—
227C22⋊C8C2×Dic1314yes—
228#95—262no—
229#95—262no—
230#95—262no—
231#95—522no—
232#95—522no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13#159911yescharacteristic
238C2×C13#160411yescharacteristic
239C2×C13#161111yescharacteristic
240C2×C13#161611yescharacteristic
241C2×C13#185311yescharacteristic
242C2×C13#185711yescharacteristic
243C2×C13#186711yescharacteristic
244C24C2×D5211yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—262no—
256C22×C4—262no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—521no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—521no—
271C22×C4#609512yes—
272C22×C4#609512yes—
273C22×C4C4⋊Dic1312yes—
274C22×C4C4⋊Dic1312yes—
275C22×C4C2×Dic2611yescharacteristic
276C22×C4D4×D1312yes—
277C22×C4#612912yes—
278C22×C4C22×Dic1311yescharacteristic
279C2×C8—24no—
280C2×C8—42no—
281C2×C8—42no—
282C4⋊C4—24no—
283C4⋊C4—24no—
284C4⋊C4—264no—
285C4⋊C4—522no—
286C4⋊C4—522no—
287C4⋊C4—522no—
288C4⋊C4—522no—
289C4⋊C4—522no—
290C4⋊C4—1041no—
291C4⋊C4—1041no—
292C22⋊C4—522no—
293C22⋊C4—522no—
294C42—524no—
295C13#885711yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23#8813611yescharacteristic
301C23#8814011yescharacteristic
302C23C2×#609511yescharacteristic
303C23C2×#609511yescharacteristic
304C23#8816211yescharacteristic
305C23#8816311yescharacteristic
306C23C2×C4⋊Dic1311yescharacteristic
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—1041no—
336C2×C4—1041no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4—1041no—
340C2×C4—1041no—
341C2×C4—1041no—
342C2×C4—1041no—
343C2×C4#8805714yescomplemented
344C2×C4#8813212yes—
345C2×C4D4×Dic1312yes—
346C8—44no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22#1171838211yescharacteristic
360C22#1171839211yescharacteristic
361C22#1171839611yescharacteristic
362C22#1171839911yescharacteristic
363C22#1171840211yescharacteristic
364C22#1171840311yescharacteristic
365C22#1171841311yescharacteristic
366C22#1171841411yescharacteristic
367C22#1171861111yescharacteristic
368C22C2×#8805711yescharacteristic
369C22#1171878211yescharacteristic
370C4—24no—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—1042no—
375C4—1042no—
376C4—1042no—
377C4—1042no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—21no—
382C2#1311377811yescharacteristic
383C2#1311380711yescharacteristic
384C2#1311384611yescharacteristic
385C2#1311387511yescharacteristic
386C2#1311503111yescharacteristic
387C2#1311505311yescharacteristic
388C2#1311511911yescharacteristic
subgroupG/H
centerC23#88136
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#8857
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
18. C13×#324C4semidirect
134. C2×C4×C13#106semidirect
171. #324Dic13semidirect
295. C13#8857semidirect
343. C2×C4#88057semidirect

Maximal subgroups

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

subgroupindex
#131174542
#131150312
#131130892
#131127162
C2×C13×#3242
#885713