Finite Group Databasebeta

← #15758647

Subgroups — #15758647

Order 3328.

1010 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 143 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×C4×C22⋊Dic13C211yesmaximal, characteristic
3C2×#11718059C212yesmaximal, complemented
4#13112716C212yesmaximal, complemented
5C13×#1779C211yesmaximal, characteristic
6C24×C4×C13C2211yescharacteristic
7C22×C22⋊Dic13—21no—
8C2×#88178C412yescomplemented
9C2×#88178C2211yescharacteristic
10C22×C4×Dic13—21no—
11C2×C13×C22⋊C8—22no—
12C2×C13×C22⋊C8C2212yes—
13#11718908—21no—
14#11718873C412yescomplemented
15#11718873C2211yescharacteristic
16#11718871—21no—
17#11718871—22no—
18C4×C22⋊Dic13—24no—
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—28no—
33C2×C22⋊Dic13—24no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C412yes—
40#88178—22no—
41#88178—22no—
42#88178—44no—
43C2×#6101—22no—
44C2×#6101—21no—
45C2×C4×Dic13—24no—
46C2×C4×Dic13—44no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—44no—
50#88071—22no—
51#88071—22no—
52#88071—21no—
53#88071D414yes—
54#9146—131nomaximal, Sylow
55C24×C13—24no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—22no—
59C24×C13—22no—
60C24×C13—42no—
61C24×C13C22⋊C412yes—
62C24×C13C2×D411yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—24no—
66C22×C4×C13—24no—
67C22×C4×C13—24no—
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—48no—
74C22×C4×C13—48no—
75C22×C4×C13C22⋊C412yes—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D412yes—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4112yes—
80C22×Dic13—28no—
81C22×Dic13—24no—
82C22×Dic13—21no—
83C22×Dic13—22no—
84C22×Dic13—21no—
85C22×Dic13—44no—
86C22×Dic13—42no—
87C22×Dic13—42no—
88C2×Dic26—22no—
89C2×Dic26—42no—
90C2×C8×C13—44no—
91C2×C8×C13—42no—
92C22⋊Dic13—216no—
93C22⋊Dic13—44no—
94C22⋊Dic13—44no—
95C22⋊Dic13—41no—
96C22⋊Dic13—41no—
97C22⋊Dic13—42no—
98C4⋊Dic13—22no—
99C4⋊Dic13—42no—
100#6101—44no—
101#6101—42no—
102C4×Dic13—48no—
103#2848—131no—
104C2×C4×C22⋊C4—131no—
105#1779D1311yescharacteristic
106C2×#328—132no—
107#1294—132no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—24no—
111C23×C13—24no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—48no—
119C23×C13—48no—
120C23×C13—42no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13#10414yes—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13#12011yescharacteristic
127C23×C13#12311yescharacteristic
128C23×C13#13512yes—
129C23×C13#13712yes—
130C2×C4×C13—24no—
131C2×C4×C13—24no—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—48no—
139C2×C4×C13—48no—
140C2×C4×C13#9914yes—
141C2×C4×C13C4×D412yes—
142C2×C4×C13#12112yes—
143C2×Dic13—28no—
144C2×Dic13—44no—
145C2×Dic13—48no—
146C2×Dic13—48no—
147C2×Dic13—44no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155Dic26—82no—
156C8×C13—82no—
157C24×C4C2×D1311yescharacteristic
158C2×C22⋊Q8—131no—
159C2×C22⋊Q8—132no—
160C22×C22⋊C4—261no—
161C22×C42—261no—
162C2×C22⋊C8—22no—
163C2×C22⋊C8C2×D1312yes—
164#385—261no—
165#385—262no—
166#380—132no—
167#380—131no—
168#379—261no—
169C4×C22⋊C4—264no—
170C2×#95—132no—
171#328—264no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—24no—
178C22×C13—24no—
179C22×C13—24no—
180C22×C13—24no—
181C22×C13—48no—
182C22×C13—48no—
183C22×C13—42no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13#38611yescharacteristic
188C22×C13C2×#9912yes—
189C22×C13#41611yescharacteristic
190C22×C13#41911yescharacteristic
191C22×C13C2×#10412yes—
192C22×C13#45212yes—
193C22×C13#48512yes—
194C4×C13—22no—
195C4×C13—22no—
196C4×C13—24no—
197Dic13—48no—
198Dic13—81no—
199Dic13—81no—
200Dic13—82no—
201C25D5211yescharacteristic
202C22×Q8—131no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—44no—
206C23×C4—262no—
207C23×C4C4×D1312yes—
208C23×C4D5211yescharacteristic
209C23×C4C22⋊D1312yes—
210C23×C4C22×D1311yescharacteristic
211C22×C8—22no—
212C22⋊Q8—262no—
213C22⋊Q8—262no—
214C22⋊Q8—524no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4—262no—
218C2×C4⋊C4—261no—
219C2×C22⋊C4—264no—
220C2×C22⋊C4—268no—
221C2×C22⋊C4—262no—
222C2×C22⋊C4—262no—
223C2×C22⋊C4—261no—
224C2×C22⋊C4—261no—
225C2×C42—264no—
226C2×C42—524no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—44no—
230#95—134no—
231#95—262no—
232#95—262no—
233#95—261no—
234C2×C13—22no—
235C2×C13—22no—
236C2×C13—44no—
237C2×C13#150112yes—
238C2×C13#150812yes—
239C2×C13#187311yescharacteristic
240C2×C13#189611yescharacteristic
241C2×C13#189811yescharacteristic
242C24—24no—
243C24—21no—
244C24—21no—
245C24—22no—
246C24—22no—
247C24—42no—
248C24#610312yes—
249C24C2×D5211yescharacteristic
250C2×Q8—262no—
251C2×Q8—522no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—48no—
263C22×C4—48no—
264C22×C4—268no—
265C22×C4—264no—
266C22×C4—262no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—524no—
270C22×C4—522no—
271C22×C4—522no—
272C22×C4#610312yes—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4D4×D1312yes—
275C22×C4#612912yes—
276C22×C4C2×C22⋊D1311yescharacteristic
277C2×C8—44no—
278C2×C8—42no—
279C4⋊C4—262no—
280C4⋊C4—522no—
281C4⋊C4—522no—
282C4⋊C4—524no—
283C22⋊C4—2616no—
284C22⋊C4—524no—
285C22⋊C4—524no—
286C22⋊C4—521no—
287C22⋊C4—521no—
288C22⋊C4—522no—
289C42—528no—
290C13#914611yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—24no—
294C23—24no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—48no—
302C23—48no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23#8806514yes—
308C23#8813611yescharacteristic
309C23#8814011yescharacteristic
310C23#8815812yes—
311C23#8816312yes—
312C23C2×#610311yescharacteristic
313Q8—1042no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—48no—
323C2×C4—48no—
324C2×C4—268no—
325C2×C4—524no—
326C2×C4—528no—
327C2×C4—528no—
328C2×C4—524no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4#8804614yes—
337C2×C4#8813512yes—
338C2×C4#8819312yes—
339C8—82no—
340C22—24no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—24no—
346C22—24no—
347C22—24no—
348C22—24no—
349C22—48no—
350C22—48no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22#1171838412yes—
356C22#1171839412yes—
357C22C2×#8804612yes—
358C22#1171861911yescharacteristic
359C22#1171877411yescharacteristic
360C22#1171878111yescharacteristic
361C22C2×#8806512yes—
362C4—22no—
363C4—24no—
364C4—22no—
365C4—528no—
366C4—1041no—
367C4—1041no—
368C4—1042no—
369C2—22no—
370C2—22no—
371C2—44no—
372C2#1311332812yes—
373C2#1311335712yes—
374C2#1311514611yescharacteristic
375C2#1311527711yescharacteristic
376C2#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#9146
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
14. #11718873C4semidirect
290. C13#9146semidirect

Maximal subgroups

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

subgroupindex
#131231232
C2×C4×C22⋊Dic132
C2×#117180592
#131127162
C13×#17792
#914613