Finite Group Databasebeta

← #15758687

Subgroups — #15758687

Order 3328.

902 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 135 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#13123123C211yesmaximal, characteristic
2C2×#11718872C211yesmaximal, characteristic
3C2×#11718059C212yesmaximal, complemented
4#13112716C212yesmaximal, complemented
5C13×#1779C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C22×C22⋊Dic13—21no—
8C2×#88178C412yescomplemented
9C2×#88178C2211yescharacteristic
10C2×C13×C22⋊C8—22no—
11C2×C13×C22⋊C8C2212yes—
12#11718908—21no—
13#11718873C412yescomplemented
14#11718873C2211yescharacteristic
15#11718872—24no—
16#11718871—21no—
17#11718871—22no—
18C2×#88071—21no—
19C2×#88071C2212yes—
20#11718059—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13—22no—
23C23×C4×C13—22no—
24C23×C4×C13—44no—
25C23×C4×C13C2×C412yes—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D412yes—
28C23×C4×C13C2311yescharacteristic
29C23×Dic13—22no—
30C22×Dic26C2×C411yescharacteristic
31C22×C8×C13—22no—
32C2×C22⋊Dic13—24no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—44no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C412yes—
40#88178—22no—
41#88178—22no—
42#88178—44no—
43C2×#6101—22no—
44C2×#6101—21no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—44no—
48#88071—24no—
49#88071—22no—
50#88071—22no—
51#88071—21no—
52#88071D414yes—
53#9154—131nomaximal, Sylow
54C24×C13—24no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—22no—
58C24×C13—22no—
59C24×C13—42no—
60C24×C13C22⋊C412yes—
61C24×C13C2×D411yescharacteristic
62C22×C4×C13—24no—
63C22×C4×C13—24no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—24no—
67C22×C4×C13—24no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—48no—
73C22×C4×C13—48no—
74C22×C4×C13C22⋊C412yes—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D412yes—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4112yes—
79C22×Dic13—21no—
80C22×Dic13—22no—
81C22×Dic13—21no—
82C22×Dic13—24no—
83C22×Dic13—44no—
84C22×Dic13—44no—
85C22×Dic13—42no—
86C22×Dic13—42no—
87C2×Dic26—22no—
88C2×Dic26—42no—
89C2×C8×C13—44no—
90C2×C8×C13—42no—
91C22⋊Dic13—44no—
92C22⋊Dic13—48no—
93C22⋊Dic13—44no—
94C22⋊Dic13—41no—
95C22⋊Dic13—41no—
96C22⋊Dic13—42no—
97C4⋊Dic13—22no—
98C4⋊Dic13—42no—
99#6101—44no—
100#6101—42no—
101#2848—131no—
102C2×#381—131no—
103#1779D1311yescharacteristic
104C2×#328—132no—
105#1294—132no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—24no—
109C23×C13—24no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—48no—
117C23×C13—48no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—42no—
121C23×C13—42no—
122C23×C13#9914yes—
123C23×C13C2×C22⋊C411yescharacteristic
124C23×C13#12011yescharacteristic
125C23×C13#12311yescharacteristic
126C23×C13#13512yes—
127C23×C13#13712yes—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—22no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—48no—
136C2×C4×C13—48no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13C4×D412yes—
140C2×C4×C13#12112yes—
141C2×Dic13—44no—
142C2×Dic13—44no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—44no—
151C2×Dic13—84no—
152C2×Dic13—84no—
153Dic26—82no—
154C8×C13—82no—
155C24×C4C2×D1311yescharacteristic
156C2×C22⋊Q8—131no—
157C2×C22⋊Q8—132no—
158C22×C22⋊C4—261no—
159C2×C22⋊C8—22no—
160C2×C22⋊C8C2×D1312yes—
161#385—261no—
162#385—262no—
163#381—264no—
164#380—132no—
165#380—131no—
166#379—261no—
167C2×#95—132no—
168C2×#95—261no—
169#328—264no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—24no—
175C22×C13—24no—
176C22×C13—24no—
177C22×C13—24no—
178C22×C13—24no—
179C22×C13—48no—
180C22×C13—48no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13#38611yescharacteristic
186C22×C13C2×#9912yes—
187C22×C13#41611yescharacteristic
188C22×C13#41911yescharacteristic
189C22×C13#42112yes—
190C22×C13#45212yes—
191C22×C13#48512yes—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—42no—
195Dic13—84no—
196Dic13—81no—
197Dic13—81no—
198Dic13—82no—
199C25D5211yescharacteristic
200C22×Q8—131no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—44no—
204C23×C4—262no—
205C23×C4C4×D1312yes—
206C23×C4D5211yescharacteristic
207C23×C4C22⋊D1312yes—
208C23×C4C22×D1311yescharacteristic
209C22×C8—22no—
210C22⋊Q8—262no—
211C22⋊Q8—262no—
212C22⋊Q8—524no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—132no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—261no—
217C2×C22⋊C4—264no—
218C2×C22⋊C4—262no—
219C2×C22⋊C4—262no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4—524no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225C22⋊C8—44no—
226#95—134no—
227#95—264no—
228#95—262no—
229#95—262no—
230#95—261no—
231C2×C13—22no—
232C2×C13—22no—
233C2×C13—44no—
234C2×C13#151112yes—
235C2×C13#151612yes—
236C2×C13#187311yescharacteristic
237C2×C13#189711yescharacteristic
238C2×C13#189811yescharacteristic
239C24—21no—
240C24—21no—
241C24—24no—
242C24—22no—
243C24—22no—
244C24—42no—
245C24#610312yes—
246C24C2×D5211yescharacteristic
247C2×Q8—262no—
248C2×Q8—522no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—48no—
260C22×C4—48no—
261C22×C4—264no—
262C22×C4—262no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—524no—
266C22×C4—524no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4#610312yes—
270C22×C4C2×C4×D1311yescharacteristic
271C22×C4D4×D1312yes—
272C22×C4#612912yes—
273C22×C4C2×C22⋊D1311yescharacteristic
274C2×C8—44no—
275C2×C8—42no—
276C4⋊C4—262no—
277C4⋊C4—522no—
278C4⋊C4—524no—
279C4⋊C4—522no—
280C22⋊C4—528no—
281C22⋊C4—524no—
282C22⋊C4—521no—
283C22⋊C4—521no—
284C22⋊C4—522no—
285C22⋊C4—524no—
286C13#915411yescharacteristic, complemented, Sylow
287C23—22no—
288C23—22no—
289C23—24no—
290C23—24no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—48no—
298C23—48no—
299C23—42no—
300C23—42no—
301C23—42no—
302C23—42no—
303C23#8804614yes—
304C23#8813611yescharacteristic
305C23#8814011yescharacteristic
306C23#8815812yes—
307C23#8816312yes—
308C23C2×#610311yescharacteristic
309Q8—1042no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—524no—
322C2×C4—524no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—524no—
331C2×C4—1044no—
332C2×C4—1044no—
333C2×C4#8813512yes—
334C2×C4#8819312yes—
335C8—82no—
336C22—24no—
337C22—24no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—24no—
343C22—24no—
344C22—24no—
345C22—48no—
346C22—48no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1171838412yes—
352C22#1171839412yes—
353C22C2×#8804612yes—
354C22#1171861911yescharacteristic
355C22#1171877411yescharacteristic
356C22#1171878111yescharacteristic
357C22#1171880012yes—
358C4—22no—
359C4—22no—
360C4—42no—
361C4—1044no—
362C4—1042no—
363C4—1041no—
364C4—1041no—
365C2—22no—
366C2—22no—
367C2—44no—
368C2#1311337012yes—
369C2#1311339312yes—
370C2#1311514611yescharacteristic
371C2#1311528211yescharacteristic
372C2#1311528711yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1779C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#1779D13
hypocenterC13#9154
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. C2×#11718059C2semidirect
4. #13112716C2semidirect
8. C2×#88178C4semidirect
13. #11718873C4semidirect
286. C13#9154semidirect

Maximal subgroups

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

subgroupindex
#131231232
C2×#117188722
C2×#117180592
#131127162
C13×#17792
#915413