Finite Group Databasebeta

← #16778293

Subgroups — #16778293

Order 3328.

604 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 126 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#13130693C211yesmaximal, characteristic
2C4×#88111C211yesmaximal, characteristic
3#13129655C212yesmaximal, complemented
4#13129654C212yesmaximal, complemented
5D13×#389C211yesmaximal, characteristic
6C2×C4⋊C4×D13—21no—
7C2×C4⋊C4×D13C411yescharacteristic
8C2×C4⋊C4×D13C411yescharacteristic
9C2×C42×D13C2211yescharacteristic
10C2×#88112—21no—
11C2×#88111—21no—
12C2×#88111—21no—
13C2×C4×#1057—21no—
14C13×#389C411yescharacteristic
15#11718646C2211yescharacteristic
16#11718634C2211yescharacteristic
17#11718633—21no—
18#11718589C411yescharacteristic
19D13×#95—21no—
20#11718308—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×C4×D13—21no—
24C22×C4×D13—21no—
25C22×C4×D13C2×C411yescharacteristic
26C22×C4×D13D411yescharacteristic
27C22×C4×D13D411yescharacteristic
28C22×#1057—22no—
29C22×#1057—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44C4⋊C4×D13—22no—
45C4⋊C4×D13—44no—
46C4⋊C4×D13—42no—
47C4⋊C4×D13C814yescomplemented
48C42×D13—42no—
49#88112—42no—
50#88111—24no—
51#88111—42no—
52C4×#1057—42no—
53C13×#95—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#7576—131nomaximal, Sylow
58C23×D13C22⋊C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—24no—
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—42no—
78C2×C4×D13—42no—
79C2×C4×D13—42no—
80C2×C4×D13—42no—
81C2×C4×D13—42no—
82C2×C4×D13C2×C812yes—
83C2×C4×D13M1612yes—
84C2×C4×D13SD1612yes—
85C2×C4×D13Q1612yes—
86C2×#1057—24no—
87C2×#1057—42no—
88C2×#1057—42no—
89C2×#1057—42no—
90C2×#1057—42no—
91C2×#1057—42no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4C2×C812yes—
96C42×C13—41no—
97C4⋊Dic13—21no—
98C4⋊Dic13—42no—
99C4⋊Dic13—41no—
100C4⋊Dic13C2×C812yes—
101#6101—24no—
102#6101—42no—
103#6101—42no—
104#6101—42no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C4×Dic13—41no—
108C2×#389—131no—
109#1797—131no—
110C4×C22⋊C8—131no—
111#1271—132no—
112#1271—132no—
113C23×C13C2×C22⋊C411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13—21no—
118C22×D13C22⋊C812yes—
119C22×D13#10312yes—
120C22×D13#10412yes—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13#10312yes—
135C2×C4×C13C22×C811yescharacteristic
136C2×C4×C13C2×M1611yescharacteristic
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—22no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13C22⋊C812yes—
148C2×Dic13#9912yes—
149C2×Dic13#10112yes—
150C2×Dic13C2×SD1611yescharacteristic
151C2×Dic13C2×Q1611yescharacteristic
152C2×Dic13AGL(1,ℤ/8)12yes—
153C4×D13—24no—
154C4×D13—24no—
155C4×D13—42no—
156C4×D13—42no—
157C4×D13—44no—
158C4×D13—48no—
159C4×D13—84no—
160#1057—44no—
161#1057—82no—
162C22×C4⋊C4—131no—
163C22×C4⋊C4—131no—
164C22×C4⋊C4—261no—
165C22×C42—131no—
166C2×C4⋊C8—261no—
167C2×C22⋊C8—261no—
168C2×C22⋊C8—261no—
169C2×C4×C8—261no—
170#389—131no—
171#389—131no—
172#389—131no—
173#389—261no—
174#389—261no—
175#389#26111yescharacteristic
176C2×#95—261no—
177#336—132no—
178#336—132no—
179C22×C13C2×C22⋊C811yescharacteristic
180C22×C13C2×#9911yescharacteristic
181C22×C13C2×#10111yescharacteristic
182C22×C13C2×#10311yescharacteristic
183C22×C13#41811yescharacteristic
184C22×C13C2×#10411yescharacteristic
185C22×C13#42111yescharacteristic
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—22no—
189C2×D13—22no—
190C2×D13—22no—
191C2×D13—22no—
192C2×D13Q8⋊C814yes—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—22no—
196C4×C13—42no—
197C4×C13—41no—
198C4×C13—81no—
199Dic13—22no—
200Dic13—21no—
201Dic13—21no—
202Dic13—42no—
203Dic13—81no—
204Dic13#32414yes—
205C23×C4—131no—
206C23×C4—131no—
207C23×C4—131no—
208C23×C4—261no—
209C23×C4—261no—
210C22×C8—262no—
211C22×C8—262no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—134no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—262no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—524no—
223C2×C4⋊C4—522no—
224C2×C4⋊C4C2×#26111yescharacteristic
225C2×C4⋊C4C2×#26111yescharacteristic
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—522no—
230C2×C42C2×#26111yescharacteristic
231C4⋊C8—522no—
232C22⋊C8—264no—
233C22⋊C8—522no—
234C4×C8—522no—
235#95—21no—
236#95—261no—
237#95—261no—
238#95—261no—
239C2×C13C2×#32411yescharacteristic
240C2×C13C2×Q8⋊C811yescharacteristic
241C2×C13#147811yescharacteristic
242C2×C13#150711yescharacteristic
243C2×C13#152011yescharacteristic
244C2×C13#152811yescharacteristic
245C2×C13#154911yescharacteristic
246D13—24no—
247C24—131no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—132no—
254C22×C4—132no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—262no—
261C22×C4—264no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4—522no—
270C22×C4—522no—
271C22×C4—522no—
272C22×C4C22⋊#26111yescharacteristic
273C22×C4C22⋊#26111yescharacteristic
274C22×C4C22×#26111yescharacteristic
275C2×C8—264no—
276C2×C8—522no—
277C2×C8—522no—
278C2×C8—522no—
279C2×C8—522no—
280C2×C8—522no—
281C4⋊C4—21no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—132no—
285C4⋊C4—264no—
286C4⋊C4—261no—
287C4⋊C4—521no—
288C4⋊C4—522no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C4⋊C4—522no—
292C4⋊C4D13⋊C812yes—
293C42—41no—
294C42—262no—
295C42—262no—
296C42—521no—
297C13#757611yescharacteristic, complemented, Sylow
298C23—132no—
299C23—132no—
300C23—132no—
301C23—261no—
302C23—261no—
303C23—261no—
304C23—261no—
305C23C2×C22⋊#26111yescharacteristic
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—132no—
320C2×C4—132no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—264no—
326C2×C4—264no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—262no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—524no—
335C2×C4—528no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—1044no—
342C2×C4#8811712yes—
343C2×C4C2×D13⋊C811yescharacteristic
344C2×C4D13⋊M1611yescharacteristic
345C8—524no—
346C8—1042no—
347C22—134no—
348C22—262no—
349C22—262no—
350C22—262no—
351C22—262no—
352C22—262no—
353C22—262no—
354C22D13⋊(C22⋊C8)11yescharacteristic
355C22#1171913811yescharacteristic
356C22D13⋊#9911yescharacteristic
357C22C2×#8811711yescharacteristic
358C22D13⋊#10111yescharacteristic
359C22D13⋊#10411yescharacteristic
360C22#1171916611yescharacteristic
361C4—22no—
362C4—21no—
363C4—21no—
364C4—42no—
365C4—41no—
366C4—81no—
367C4—134no—
368C4—261no—
369C4—261no—
370C4—262no—
371C4—522no—
372C4—1041no—
373C2—264no—
374C2D13⋊#32411yescharacteristic
375C2D13⋊(Q8⋊C8)11yescharacteristic
376C2#1313013611yescharacteristic
377C2#1313023111yescharacteristic
378C2#1313027411yescharacteristic
379C2#1313029911yescharacteristic
380C2#1313035211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#7576
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #13129655C2semidirect
4. #13129654C2semidirect
47. C4⋊C4×D13C8semidirect
297. C13#7576semidirect

Maximal subgroups

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

subgroupindex
#131306932
C4×#881112
#131296552
#131296542
D13×#3892
#757613