Finite Group Databasebeta

← #15766268

Subgroups — #15766268

Order 3328.

620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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#13120950C211yesmaximal, characteristic
2#13115141C212yesmaximal
3C2×#11718059C212yesmaximal
4#13113100C211yesmaximal, characteristic
5C13×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic13C2211yescharacteristic
7C2×#88178C2212yes—
8C22×#6101—21no—
9C2×C13×C22⋊C8C2212yes—
10C2×C13×#95C2211yescharacteristic
11#11718873—21no—
12#11718873—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×#88056—22no—
16#11718322—22no—
17#11718317—22no—
18#11718143—22no—
19#11718059—24no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C22×Dic26D412yes—
26C22×C8×C13—22no—
27C2×C22⋊Dic13—22no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—42no—
34C2×C4⋊Dic13D412yes—
35#88178—22no—
36#88178—22no—
37#88178—22no—
38#88178—22no—
39C2×#6101—22no—
40C2×#6101—42no—
41C2×#6101—42no—
42C2×#6101—42no—
43C13×C22⋊C8—22no—
44C13×C22⋊C8—22no—
45C13×#95—22no—
46#88071—22no—
47#88071—22no—
48#88071—21no—
49#88071—42no—
50#88071D412yes—
51#88056—44no—
52#10406—131nomaximal, Sylow
53C24×C13C2×D411yescharacteristic
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×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13SD1612yes—
65C22×C4×C13Q1612yes—
66C22×C4×C13C2×D412yes—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13#4112yes—
69C22×C4×C13#4111yescharacteristic
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—22no—
75C22×Dic13—22no—
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×Dic26—22no—
87C2×Dic26—22no—
88C2×Dic26—42no—
89C2×Dic26—42no—
90C2×C8×C13—42no—
91C2×C8×C13—42no—
92C2×C8×C13—42no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C4⋊Dic13—24no—
96C4⋊Dic13—22no—
97C4⋊Dic13—22no—
98C4⋊Dic13—42no—
99C4⋊Dic13—81no—
100C4⋊Dic13—81no—
101C4⋊Dic13—81no—
102C4⋊Dic13—81no—
103#6101—48no—
104#6101—42no—
105#6101—42no—
106#2659—131no—
107#1872—132no—
108C2×#328—132no—
109#1444—131no—
110#1280D1311yescharacteristic
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13#12011yescharacteristic
116C23×C13#12111yescharacteristic
117C23×C13#12411yescharacteristic
118C23×C13C2×SD1611yescharacteristic
119C23×C13C2×Q1611yescharacteristic
120C23×C13#13711yescharacteristic
121C23×C13#13711yescharacteristic
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13#12112yes—
138C2×C4×C13#12312yes—
139C2×Dic13—24no—
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—42no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—81no—
156C2×Dic13—81no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159Dic26—44no—
160Dic26—82no—
161C8×C13—82no—
162C2×C22⋊Q8—132no—
163C22×C4⋊C4—131no—
164C22×C4⋊C4—261no—
165C2×#103—262no—
166C2×C22⋊C8C2×D1312yes—
167#398—262no—
168#395—262no—
169#380—261no—
170#380—261no—
171C2×#95—131no—
172C2×#95—261no—
173C2×#95C2×D1311yescharacteristic
174#340—262no—
175#328—264no—
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—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13#39411yescharacteristic
189C22×C13#44811yescharacteristic
190C22×C13#45111yescharacteristic
191C22×C13#45311yescharacteristic
192C22×C13#45611yescharacteristic
193C22×C13B(4,𝔽2)11yescharacteristic
194C22×C13#45811yescharacteristic
195C22×C13#46111yescharacteristic
196C22×C13#46211yescharacteristic
197C22×C13#48711yescharacteristic
198C22×C13#49111yescharacteristic
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—42no—
202C4×C13—42no—
203Dic13—44no—
204Dic13—82no—
205Dic13—82no—
206Dic13—82no—
207C22×Q8—132no—
208C23×C4—261no—
209C23×C4—261no—
210C23×C4D5211yescharacteristic
211C23×C4D5211yescharacteristic
212C23×C4C22×D1311yescharacteristic
213C22×C8—22no—
214C22⋊Q8—262no—
215C22⋊Q8—262no—
216C22⋊Q8—262no—
217C22⋊Q8—262no—
218C2×C4⋊C4—132no—
219C2×C4⋊C4—262no—
220C2×C4⋊C4—262no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—522no—
226C2×C4⋊C4—522no—
227C2×C4⋊C4—522no—
228C2×C4⋊C4—522no—
229C2×C22⋊C4—262no—
230#103—524no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233#95—22no—
234#95—132no—
235#95—262no—
236#95—262no—
237#95—261no—
238#95—522no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—21no—
243C2×C13#159611yescharacteristic
244C2×C13#160511yescharacteristic
245C2×C13#161111yescharacteristic
246C2×C13#161411yescharacteristic
247C2×C13#203911yescharacteristic
248C2×C13#204311yescharacteristic
249C2×C13#204411yescharacteristic
250C24C2×D5211yescharacteristic
251C2×Q8—262no—
252C2×Q8—262no—
253C2×Q8—522no—
254C2×Q8—522no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—262no—
266C22×C4—262no—
267C22×C4—262no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4—262no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4—521no—
274C22×C4—521no—
275C22×C4—521no—
276C22×C4—521no—
277C22×C4—521no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4#609512yes—
282C22×C4Dic5212yes—
283C22×C4#612712yes—
284C22×C4D4×D1312yes—
285C22×C4D4×D1311yescharacteristic
286C22×C4#613111yescharacteristic
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—42no—
290C4⋊C4—264no—
291C4⋊C4—262no—
292C4⋊C4—262no—
293C4⋊C4—522no—
294C4⋊C4—528no—
295C4⋊C4—522no—
296C4⋊C4—522no—
297C4⋊C4—1041no—
298C4⋊C4—1041no—
299C4⋊C4—1041no—
300C4⋊C4—1041no—
301C22⋊C4—522no—
302C22⋊C4—522no—
303C13#1040611yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#8812911yescharacteristic
309C23#8813611yescharacteristic
310C23#8814911yescharacteristic
311C23C2×#609511yescharacteristic
312C23C2×Dic5211yescharacteristic
313C23#8816311yescharacteristic
314C23#8816311yescharacteristic
315Q8—524no—
316Q8—1042no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—264no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—522no—
338C2×C4—522no—
339C2×C4—522no—
340C2×C4—522no—
341C2×C4—522no—
342C2×C4—522no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—1041no—
349C2×C4—1041no—
350C2×C4—1041no—
351C2×C4—1041no—
352C2×C4#8813812yes—
353C2×C4#8814812yes—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1171833311yescharacteristic
368C22#1171834211yescharacteristic
369C22#1171836411yescharacteristic
370C22#1171839911yescharacteristic
371C22#1171840011yescharacteristic
372C22#1171840211yescharacteristic
373C22#1171840311yescharacteristic
374C22#1171840811yescharacteristic
375C22#1171841311yescharacteristic
376C22#1171850211yescharacteristic
377C22#1171851011yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—524no—
383C4—1042no—
384C4—1042no—
385C4—1042no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#1311376111yescharacteristic
391C2#1311381211yescharacteristic
392C2#1311384611yescharacteristic
393C2#1311386311yescharacteristic
394C2#1311606111yescharacteristic
395C2#1311608311yescharacteristic
396C2#1311608811yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#1280C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#1280D13
hypocenterC13#10406
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
303. C13#10406semidirect

Maximal subgroups

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

subgroupindex
#131209502
#131151412
C2×#117180592
#131131002
C13×#12802
#1040613