Finite Group Databasebeta

← #15837114

Subgroups — #15837114

Order 3328.

950 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 183 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#13125657C212yesmaximal
2#13120216C211yesmaximal, characteristic
3#13113844C214yesmaximal, complemented
4#13113810C214yesmaximal, complemented
5#13113356C212yesmaximal
6#13113166C211yesmaximal, characteristic
7C2×C13×#544C211yesmaximal, characteristic
8C13×#544—24no—
9C13×#544—22no—
10C13×#544C2214yes—
11C2×C13×C4⋊Q8—22no—
12C2×C13×#125—22no—
13C2×C13×C22⋊Q8—21no—
14C2×C13×C22⋊Q8C2212yes—
15C2×C13×#117—21no—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18#11718889—22no—
19#11718871—21no—
20#11718871—21no—
21C4×C22⋊Dic13C2211yescharacteristic
22#11718868C2212yes—
23#11718713—24no—
24#11718711C2214yes—
25#11718704C2214yes—
26#11718644C2212yes—
27#11718640C2212yes—
28#11718633—22no—
29#11718632—22no—
30#11718130C2218yes—
31#11718120C2214yes—
32C22×Q8×C13—21no—
33C22×Q8×C13D412yes—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×Dic26C2311yescharacteristic
38C13×C4⋊Q8—28no—
39C13×C4⋊Q8—28no—
40C13×#125—28no—
41C13×#125—28no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8—24no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8D414yes—
47C13×C22⋊Q8C2314yes—
48C13×#117—24no—
49C13×#117—24no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4D412yes—
58C2×C13×C4⋊C4D412yes—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C22⋊C4—22no—
61C2×C42×C13—22no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—21no—
64C2×#6107—24no—
65C2×C4⋊Dic13C2311yescharacteristic
66#88178—22no—
67#88178—22no—
68C2×#6101—21no—
69C2×#6101—22no—
70C2×#6101—22no—
71C2×C4×Dic13—21no—
72C2×#6099—22no—
73#88075—24no—
74#88071—22no—
75#88071—22no—
76#88071C2312yes—
77C22⋊#1055—22no—
78C22⋊#1055C2314yes—
79#88050—24no—
80#88048—24no—
81#18327—131nomaximal, Sylow
82C24×C13C2×D411yescharacteristic
83C2×Q8×C13—24no—
84C2×Q8×C13—22no—
85C2×Q8×C13—82no—
86C2×Q8×C13—82no—
87C2×Q8×C13C2×D414yes—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—24no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—81no—
96C22×C4×C13—81no—
97C22×C4×C13C2×D412yes—
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D412yes—
101C22×C4×C13C2×D412yes—
102C22×C4×C13C2411yescharacteristic
103C22×Dic13—22no—
104C22×Dic13—21no—
105C22×Dic13—21no—
106C2×Dic26—22no—
107C2×Dic26—81no—
108C13×C4⋊C4—24no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—28no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—24no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—24no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4C2×D414yes—
118C13×C22⋊C4—24no—
119C13×C22⋊C4—24no—
120C42×C13—28no—
121C22⋊Dic13—24no—
122C22⋊Dic13—41no—
123C22⋊Dic13—41no—
124#6107—84no—
125C4⋊Dic13—22no—
126#6101—42no—
127#6101—44no—
128#6101—82no—
129C4×Dic13—81no—
130#6099—82no—
131C2×#1055—24no—
132C2×#544D1311yescharacteristic
133#3195—132no—
134#2583—131no—
135#1611—134no—
136#1605—134no—
137#1508—132no—
138#1463—131no—
139C23×C13—22no—
140C23×C13—22no—
141C23×C13—41no—
142C23×C13#12011yescharacteristic
143C23×C13#12011yescharacteristic
144C23×C13C22×D411yescharacteristic
145Q8×C13—44no—
146Q8×C13—82no—
147Q8×C13—84no—
148C2×C4×C13—24no—
149C2×C4×C13—24no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—22no—
155C2×C4×C13—42no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—44no—
162C2×C4×C13—42no—
163C2×C4×C13—81no—
164C2×C4×C13#12012yes—
165C2×C4×C13#13714yes—
166C2×C4×C13C22×D412yes—
167C2×Dic13—24no—
168C2×Dic13—42no—
169C2×Dic13—42no—
170C2×Dic13—42no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—42no—
174Dic26—44no—
175#1055—44no—
176#544—24no—
177#544—22no—
178#544C2×D1314yes—
179C2×C4⋊Q8—22no—
180C2×#125—22no—
181C2×C22⋊Q8—21no—
182C2×C22⋊Q8—131no—
183C2×C22⋊Q8C2×D1312yes—
184C2×#117—21no—
185C22×C4⋊C4C2×D1311yescharacteristic
186#483—134no—
187#483—262no—
188#470—264no—
189#451—134no—
190#451—262no—
191#407—132no—
192#398—132no—
193#395—132no—
194#389—262no—
195#385—261no—
196#385—261no—
197C4×C22⋊C4—131no—
198#328—138no—
199#324—134no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—44no—
208C22×C13#45612yes—
209C22×C13C2×#12011yescharacteristic
210C22×C13C2×#13712yes—
211C4×C13—24no—
212C4×C13—22no—
213C4×C13—22no—
214C4×C13—44no—
215C4×C13—42no—
216C4×C13—44no—
217Dic13—44no—
218Dic13—81no—
219Dic13—81no—
220C22×Q8—21no—
221C22×Q8—131no—
222C22×Q8C22⋊D1312yes—
223C23×C4C22⋊D1311yescharacteristic
224C23×C4C22⋊D1311yescharacteristic
225C23×C4C22×D1311yescharacteristic
226C2×Q16—264no—
227C2×M16—262no—
228C4⋊Q8—28no—
229C4⋊Q8—28no—
230#125—28no—
231#125—28no—
232C22⋊Q8—24no—
233C22⋊Q8—24no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8—262no—
237C22⋊Q8—262no—
238C22⋊Q8C22⋊D1314yes—
239C22⋊Q8C22×D1314yes—
240#117—24no—
241#117—24no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—131no—
250C2×C4⋊C4—261no—
251C2×C4⋊C4—262no—
252C2×C4⋊C4—262no—
253C2×C4⋊C4C22⋊D1312yes—
254C2×C4⋊C4C22⋊D1312yes—
255C2×C4⋊C4C22×D1312yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—261no—
258C2×C22⋊C4—261no—
259C2×C42—22no—
260C2×C42—261no—
261#106—264no—
262#103—264no—
263#103—264no—
264C22⋊C8—134no—
265C22⋊C8—262no—
266#95—132no—
267#95—262no—
268#95—262no—
269C2×C13—22no—
270C2×C13—22no—
271C2×C13—41no—
272C2×C13#300411yescharacteristic
273C2×C13C2×#45611yescharacteristic
274C2×C13#302611yescharacteristic
275C24C2×C22⋊D1311yescharacteristic
276C2×Q8—24no—
277C2×Q8—22no—
278C2×Q8—82no—
279C2×Q8—82no—
280C2×Q8—262no—
281C2×Q8—1041no—
282C2×Q8C2×C22⋊D1314yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—262no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4C2×C22⋊D1312yes—
296C22×C4C2×C22⋊D1312yes—
297C22×C4C2×C22⋊D1311yescharacteristic
298C22×C4C2×C22⋊D1312yes—
299C22×C4C2×C22⋊D1312yes—
300C22×C4C23×D1311yescharacteristic
301Q16—1044no—
302M16—1042no—
303C2×C8—264no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—28no—
308C4⋊C4—24no—
309C4⋊C4—24no—
310C4⋊C4—22no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—262no—
314C4⋊C4—524no—
315C4⋊C4—522no—
316C4⋊C4—1042no—
317C4⋊C4C2×C22⋊D1314yes—
318C22⋊C4—24no—
319C22⋊C4—24no—
320C22⋊C4—264no—
321C22⋊C4—521no—
322C22⋊C4—521no—
323C42—28no—
324C42—1041no—
325C13#1832711yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23—41no—
329C23#8820711yescharacteristic
330C23#8820711yescharacteristic
331C23C22×C22⋊D1311yescharacteristic
332Q8—44no—
333Q8—82no—
334Q8—84no—
335Q8—524no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—264no—
353C2×C4—522no—
354C2×C4—522no—
355C2×C4—522no—
356C2×C4—522no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4#8819614yes—
360C2×C4#8820712yes—
361C2×C4C22×C22⋊D1312yes—
362C8—524no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22#1171890712yes—
372C22C2×#8819612yes—
373C22C2×#8820711yescharacteristic
374C4—22no—
375C4—22no—
376C4—24no—
377C4—44no—
378C4—42no—
379C4—44no—
380C4—524no—
381C4—1041no—
382C4—1041no—
383C2—22no—
384C2—22no—
385C2—41no—
386C2#1312407011yescharacteristic
387C2C2×#1171890711yescharacteristic
388C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13#18327
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13113844C2semidirect
4. #13113810C2semidirect
325. C13#18327semidirect

Maximal subgroups

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

subgroupindex
#131256572
#131202162
#131138442
#131138102
#131133562
#131131662
C2×C13×#5442
#1832713