Finite Group Databasebeta

← #15835984

Subgroups — #15835984

Order 3328.

974 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 203 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#13124871C212yesmaximal, complemented
2#13120190C211yesmaximal, characteristic
3#13113861C214yesmaximal, complemented
4#13113793C214yesmaximal, complemented
5#13113400C212yesmaximal, complemented
6#13113157C211yesmaximal, characteristic
7C13×#3501C211yesmaximal, characteristic
8C13×#554—22no—
9C13×#554—24no—
10D4×Q8×C13—22no—
11C13×#544—21no—
12C13×#543C2214yes—
13C13×#533C2212yes—
14C2×C13×C22⋊Q8—22no—
15C13×#518—21no—
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18#11718882—21no—
19#11718871—22no—
20#11718752—22no—
21#11718751—22no—
22#11718711C2214yes—
23#11718705C2214yes—
24C4×#6107—24no—
25#11718634—21no—
26#11718610C2212yes—
27#11718608C2212yes—
28#11718597C2211yescharacteristic
29#11718586C2212yes—
30#11718130C2218yes—
31#11718117C2214yes—
32C22×Q8×C13—22no—
33C22×D4×C13D411yescharacteristic
34C23×C4×C13D412yes—
35C22×Dic26C2311yescharacteristic
36C13×C4⋊Q8—24no—
37C13×C4⋊Q8D412yes—
38C13×C4⋊Q8D412yes—
39C13×#125—24no—
40C13×#125—22no—
41C13×C22⋊Q8—24no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8—28no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—24no—
46C13×C22⋊Q8—28no—
47C13×C22⋊Q8C2314yes—
48C4×Q8×C13—22no—
49C4×Q8×C13D414yes—
50C4×D4×C13—24no—
51C4×D4×C13—24no—
52C4×D4×C13—22no—
53C4×D4×C13—22no—
54C13×#117—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—24no—
57C2×C13×C4⋊C4D411yescharacteristic
58C2×C13×C22⋊C4—24no—
59C2×C13×C22⋊C4C2312yes—
60C2×C42×C13C2311yescharacteristic
61C2×C22⋊Dic13—22no—
62C2×C22⋊Dic13—22no—
63C2×#6107—24no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13C2311yescharacteristic
66C2×#6101—21no—
67C2×#6101—22no—
68C2×C4×Dic13—21no—
69C4×Dic26—22no—
70C4×Dic26—22no—
71#88075—24no—
72#88071—21no—
73#88071—22no—
74#88071C2312yes—
75C22⋊#1055C2314yes—
76#88050—24no—
77#88047—24no—
78C4⋊#1055—22no—
79C4×#1055—22no—
80#18213—131nomaximal, Sylow
81C24×C13C2×D412yes—
82C2×Q8×C13—24no—
83C2×Q8×C13—22no—
84C2×Q8×C13—84no—
85C2×Q8×C13C2×D414yes—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13Q1614yescomplemented
89C22×C4×C13—24no—
90C22×C4×C13—24no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—82no—
94C22×C4×C13C2×D412yes—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2411yescharacteristic
98C22×Dic13—21no—
99C22×Dic13—22no—
100C22×Dic13—21no—
101C2×Dic26—22no—
102C2×Dic26—42no—
103C13×C4⋊C4—24no—
104C13×C4⋊C4—28no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—24no—
107C13×C4⋊C4—22no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4C2×D414yes—
112C13×C22⋊C4—28no—
113C13×C22⋊C4—24no—
114C13×C22⋊C4—24no—
115C42×C13—24no—
116C42×C13C2×D412yes—
117C42×C13C2×D412yes—
118C22⋊Dic13—44no—
119C22⋊Dic13—82no—
120#6107—48no—
121C4⋊Dic13—22no—
122C4⋊Dic13—42no—
123#6101—41no—
124#6101—41no—
125#6101—82no—
126C4×Dic13—42no—
127C2×#1055—24no—
128#3501D1311yescharacteristic
129#3104—132no—
130#2580—131no—
131#1614—134no—
132#1602—134no—
133#1518—132no—
134#1460—131no—
135C23×C13—22no—
136C23×C13—22no—
137C23×C13—42no—
138C23×C13—42no—
139C23×C13C2×Q1614yes—
140C23×C13C22×D411yescharacteristic
141Q8×C13—44no—
142Q8×C13—44no—
143Q8×C13—84no—
144D4×C13—28no—
145C2×C4×C13—24no—
146C2×C4×C13—24no—
147C2×C4×C13—22no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—44no—
151C2×C4×C13—42no—
152C2×C4×C13—82no—
153C2×C4×C13—84no—
154C2×C4×C13—84no—
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12012yes—
158C2×C4×C13C2×Q1612yes—
159C2×C4×C13#13712yes—
160C2×C4×C13C22×D412yes—
161C2×Dic13—22no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—42no—
166C2×Dic13—42no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—42no—
170Dic26—24no—
171Dic26—42no—
172#1055—44no—
173#554—22no—
174#554—24no—
175D4×Q8—22no—
176#544—21no—
177#543C2×D1314yes—
178#533C2×D1312yes—
179C2×C22⋊Q8—22no—
180#518—21no—
181C2×C4×Q8—131no—
182C2×C4×D4C2×D1311yescharacteristic
183#484—134no—
184#477—262no—
185#462—262no—
186#451—134no—
187C4×Q16—264no—
188#431—132no—
189#399—132no—
190#393—132no—
191#390—261no—
192#389—261no—
193#385—262no—
194#382—131no—
195#328—138no—
196#323—134no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—24no—
200C22×C13—44no—
201C22×C13—42no—
202C22×C13—42no—
203C22×C13—82no—
204C22×C13C2×#12011yescharacteristic
205C22×C13C22×Q1611yescharacteristic
206C22×C13C2×#13711yescharacteristic
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—22no—
210C4×C13—42no—
211C4×C13—44no—
212C4×C13—44no—
213C4×C13#45114yes—
214Dic13—42no—
215Dic13—82no—
216Dic13—81no—
217C22×Q8—22no—
218C22×Q8—131no—
219C22×D4C22⋊D1311yescharacteristic
220C23×C4C22⋊D1312yes—
221C2×Q16—264no—
222C4⋊Q8—24no—
223C4⋊Q8C22⋊D1312yes—
224C4⋊Q8C22⋊D1312yes—
225#125—24no—
226#125—22no—
227C22⋊Q8—24no—
228C22⋊Q8—24no—
229C22⋊Q8—28no—
230C22⋊Q8—22no—
231C22⋊Q8—24no—
232C22⋊Q8—28no—
233C22⋊Q8C22×D1314yes—
234C4×Q8—22no—
235C4×Q8—262no—
236C4×Q8—262no—
237C4×Q8C22⋊D1314yes—
238C4×D4—24no—
239C4×D4—24no—
240C4×D4—22no—
241C4×D4—22no—
242#117—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—262no—
249C2×C4⋊C4C22⋊D1311yescharacteristic
250C2×C22⋊C4—24no—
251C2×C22⋊C4—262no—
252C2×C22⋊C4—262no—
253C2×C22⋊C4C22×D1312yes—
254C2×C42—261no—
255C2×C42C22×D1311yescharacteristic
256#107—264no—
257C4⋊C8—262no—
258#103—264no—
259#103—264no—
260C22⋊C8—134no—
261C4×C8—262no—
262#95—132no—
263#95—261no—
264#95—262no—
265C2×C13—21no—
266C2×C13—21no—
267C2×C13—44no—
268C2×C13C2×#45111yescharacteristic
269C2×C13#301911yescharacteristic
270C2×C13#302511yescharacteristic
271C24C2×C22⋊D1312yes—
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—84no—
275C2×Q8—262no—
276C2×Q8—522no—
277C2×Q8C2×C22⋊D1314yes—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4#610714yescomplemented
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—82no—
286C22×C4—261no—
287C22×C4—262no—
288C22×C4—261no—
289C22×C4C2×C22⋊D1312yes—
290C22×C4C2×C22⋊D1311yescharacteristic
291C22×C4C2×C22⋊D1311yescharacteristic
292C22×C4C23×D1311yescharacteristic
293Q16—528no—
294C2×C8—264no—
295C4⋊C4—24no—
296C4⋊C4—28no—
297C4⋊C4—22no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—24no—
303C4⋊C4—262no—
304C4⋊C4—522no—
305C4⋊C4—521no—
306C4⋊C4—521no—
307C4⋊C4—1042no—
308C4⋊C4C2×C22⋊D1314yes—
309C22⋊C4—28no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—524no—
313C22⋊C4—1042no—
314C42—24no—
315C42—522no—
316C42C2×C22⋊D1312yes—
317C42C2×C22⋊D1312yes—
318C13#1821311yescharacteristic, complemented, Sylow
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C2×#610714yes—
324C23C22×C22⋊D1311yescharacteristic
325Q8—44no—
326Q8—44no—
327Q8—84no—
328Q8—264no—
329Q8—522no—
330D4—28no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—82no—
339C2×C4—84no—
340C2×C4—84no—
341C2×C4—262no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—522no—
345C2×C4—521no—
346C2×C4—522no—
347C2×C4—521no—
348C2×C4—522no—
349C2×C4—521no—
350C2×C4#8819612yes—
351C2×C4C2×#610712yes—
352C2×C4#8820711yescharacteristic
353C2×C4#8820711yescharacteristic
354C2×C4#8820712yes—
355C2×C4C22×C22⋊D1312yes—
356C8—524no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22C2×#8819611yescharacteristic
365C22C22×#610711yescharacteristic
366C22C2×#8820711yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—44no—
372C4—44no—
373C4—522no—
374C4—1042no—
375C4—1041no—
376C4#1171888914yes—
377C2—21no—
378C2—21no—
379C2—44no—
380C2C2×#1171888911yescharacteristic
381C2#1312419311yescharacteristic
382C2#1312422811yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3501C2
socleC22×C13C2×#120
prime radicalC22×D4×C13D4
hypercenter#3501D13
hypocenterC13#18213
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13124871C2semidirect
3. #13113861C2semidirect
4. #13113793C2semidirect
5. #13113400C2semidirect
88. C2×D4×C13Q16semidirect
280. C2×D4#6107semidirect
318. C13#18213semidirect

Maximal subgroups

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

subgroupindex
#131248712
#131201902
#131138612
#131137932
#131134002
#131131572
C13×#35012
#1821313