Finite Group Databasebeta

← #16778624

Subgroups — #16778624

Order 3328.

538 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130727C211yesmaximal, characteristic, complemented
2C4×C22⋊#1057C211yesmaximal, characteristic, complemented
3#13129657C212yesmaximal, complemented
4#13129652C212yesmaximal, complemented
5#13123135C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic
7C2×#88190C411yescharacteristic
8C2×#88178C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057—21no—
11C2×C22⋊#1057—21no—
12C2×C4×#1057—21no—
13#11718882C2211yescharacteristic
14#11718881—21no—
15#11718881—21no—
16#11718638C411yescharacteristic
17#11718635C2211yescharacteristic
18#11718606—21no—
19#11718606—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13D411yescharacteristic
27C23×Dic13D411yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C22×#1057—22no—
30C22×#1057—22no—
31C13×#121—42no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4—21no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39#88190—42no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41#88178—42no—
42C2×#6101—21no—
43C2×C4×Dic13—42no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13C2311yescharacteristic
48C22⋊#1057—24no—
49C22⋊#1057—42no—
50C4×#1057—42no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7670—131nomaximal, Sylow
56C24×C13—21no—
57C24×C13C22⋊C411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—41no—
77C22×Dic13—41no—
78C22×Dic13C22⋊C411yescharacteristic
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C2×D411yescharacteristic
81C22×Dic13C2×D411yescharacteristic
82C2×Dic26—22no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×#1057—24no—
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—42no—
89C2×#1057—42no—
90C2×#1057—42no—
91C13×C4⋊C4—41no—
92C13×C22⋊C4—42no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C22⋊Dic13—42no—
98C4⋊Dic13—41no—
99#6101—42no—
100C4×Dic13—22no—
101C4×Dic13—22no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104#2850—131no—
105#1817—131no—
106C4×C22⋊C8—131no—
107#1272—132no—
108#1270—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13#10412yes—
123C23×C13C2×C22⋊C411yescharacteristic
124D4×C13—82no—
125D4×C13—84no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—44no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13#10012yes—
135C2×C4×C13#13112yes—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—44no—
146C2×Dic13—44no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13#9912yes—
154C2×Dic13#13512yes—
155C2×Dic13#13512yes—
156Dic26—82no—
157#1057—44no—
158#1057—82no—
159C2×#124—131no—
160C2×C22⋊Q8—131no—
161C2×#121#26111yescharacteristic
162C22×C42—131no—
163C2×C22⋊C8—261no—
164C2×C22⋊C8—261no—
165C2×C4×C8—261no—
166#391—131no—
167#390—131no—
168#388—261no—
169#388—261no—
170#386—261no—
171#386—261no—
172#382—131no—
173#336—132no—
174#336—132no—
175#336—261no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13#40811yescharacteristic
191C22×C13C2×#9911yescharacteristic
192C22×C13C2×#10011yescharacteristic
193C22×C13#41611yescharacteristic
194C22×C13#41611yescharacteristic
195C22×C13C2×#10411yescharacteristic
196C22×C13#42111yescharacteristic
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—81no—
200Dic13—22no—
201Dic13—22no—
202Dic13—22no—
203Dic13—41no—
204Dic13—81no—
205Dic13—81no—
206C22×Q8—131no—
207C22×D4—21no—
208C22×D4C2×#26111yescharacteristic
209C23×C4—131no—
210C23×C4—131no—
211C23×C4C2×#26111yescharacteristic
212C22×C8—262no—
213C22×C8—262no—
214#124—522no—
215C22⋊Q8—522no—
216#121—42no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4C2×#26111yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C22⋊C4—261no—
225C2×C22⋊C4—261no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—522no—
231C22⋊C8—264no—
232C22⋊C8—522no—
233C4×C8—522no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238C2×C13—42no—
239C2×C13—161no—
240C2×C13#147111yescharacteristic
241C2×C13#148211yescharacteristic
242C2×C13#149411yescharacteristic
243C2×C13#150111yescharacteristic
244C2×C13#151611yescharacteristic
245C2×C13#152711yescharacteristic
246C2×C13#154311yescharacteristic
247C24—21no—
248C24C22⋊#26111yescharacteristic
249C2×Q8—262no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×D4—22no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—42no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—262no—
267C22×C4—262no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—521no—
273C22×C4—521no—
274C22×C4C22⋊#26111yescharacteristic
275C22×C4C22×#26111yescharacteristic
276C2×C8—264no—
277C2×C8—522no—
278C2×C8—522no—
279C2×C8—522no—
280C2×C8—522no—
281C2×C8—522no—
282C4⋊C4—41no—
283C4⋊C4—521no—
284C4⋊C4—522no—
285C22⋊C4—42no—
286C22⋊C4—522no—
287C22⋊C4—522no—
288C22⋊C4—522no—
289C22⋊C4—522no—
290C22⋊C4—522no—
291C42—262no—
292C42—262no—
293C42—521no—
294C42—521no—
295C13#767011yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#8811612yes—
310C23C2×C22⋊#26111yescharacteristic
311Q8—1042no—
312D4—82no—
313D4—84no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—44no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—132no—
323C2×C4—132no—
324C2×C4—132no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—524no—
335C2×C4—524no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4#8812112yes—
343C2×C4#8823812yes—
344C8—524no—
345C8—1042no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22C2×#8811611yescharacteristic
361C22#1171914011yescharacteristic
362C22D13⋊#9911yescharacteristic
363C22#1171914611yescharacteristic
364C22#1171916511yescharacteristic
365C22#1171916511yescharacteristic
366C22C2×#8812111yescharacteristic
367C4—22no—
368C4—22no—
369C4—81no—
370C4—262no—
371C4—262no—
372C4—262no—
373C4—521no—
374C4—1041no—
375C4—1041no—
376C2—42no—
377C2—161no—
378C2#1313011211yescharacteristic
379C2#1313014711yescharacteristic
380C2#1313018711yescharacteristic
381C2#1313021211yescharacteristic
382C2#1313026111yescharacteristic
383C2#1313029511yescharacteristic
384C2#1313033911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
Fitting, prime radicalC2×C13×#121C4
socleC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#121#261
hypocenterC13#7670
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #13130727C2semidirect
2. C4×C22⋊#1057C2semidirect
3. #13129657C2semidirect
4. #13129652C2semidirect
295. C13#7670semidirect

Maximal subgroups

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

subgroupindex
#131307272
C4×C22⋊#10572
#131296572
#131296522
#131231352
#767013