Finite Group Databasebeta

← #16778382

Subgroups — #16778382

Order 3328.

504 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 110 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#13130726C211yesmaximal, characteristic
2#13130690C211yesmaximal, characteristic
3#13129657C212yesmaximal, complemented
4#13129655C212yesmaximal, complemented
5#13117364C211yesmaximal, characteristic
6C2×#88178C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×#88141C411yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11C2×C4⋊#1057—21no—
12C13×#380C411yescharacteristic
13C4⋊C4×Dic13C411yescharacteristic
14#11718635C2211yescharacteristic
15#11718634C2211yescharacteristic
16#11718607—21no—
17C22⋊C4×Dic13—21no—
18#11718313—21no—
19#11718310—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×#1057—22no—
28C22×#1057—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—21no—
32C2×C22⋊Dic13—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34#88178—22no—
35#88178C814yescomplemented
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—42no—
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13C2311yescharacteristic
46#88141—42no—
47C22⋊#1057—42no—
48C22⋊#1057—42no—
49C4⋊#1057—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7600—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C2×C812yes—
63C22×C4×C13M1612yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—22no—
68C22×Dic13—21no—
69C22×Dic13—22no—
70C22×Dic13—21no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C2×D411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26C2×C812yes—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C22⋊C4—42no—
91C22⋊Dic13—24no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2×C812yes—
94#6101—24no—
95#6101—42no—
96#6101—41no—
97#6101—41no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—41no—
101C4×Dic13—41no—
102C4×Dic13—42no—
103C4×Dic13—42no—
104C4×C22⋊Q8—131no—
105#1817—131no—
106#1797—131no—
107#1272—132no—
108#1271—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C22⋊C812yes—
116C23×C13C2×C22⋊C411yescharacteristic
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13C22⋊C812yes—
130C2×C4×C13C22×C811yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—22no—
139C2×Dic13—22no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—44no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13#9912yes—
151C2×Dic13AGL(1,ℤ/8)11yescharacteristic
152C2×Dic13#13711yescharacteristic
153C2×Dic13#13712yes—
154Dic26—42no—
155Dic26—42no—
156#1057—82no—
157#1057—82no—
158C2×C22⋊Q8—131no—
159C2×C4×Q8—131no—
160C22×C42—131no—
161C2×C4⋊C8—261no—
162C2×C22⋊C8—261no—
163C2×C22⋊C8—261no—
164#391—131no—
165#389—131no—
166#387—261no—
167#385—261no—
168#380#26111yescharacteristic
169C4×C4⋊C4—131no—
170C4×C4⋊C4—261no—
171C4×C22⋊C4—261no—
172#336—132no—
173#336—132no—
174#336—261no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13C2×C22⋊C811yescharacteristic
183C22×C13C2×#9911yescharacteristic
184C22×C13#41311yescharacteristic
185C22×C13#41711yescharacteristic
186C22×C13#41911yescharacteristic
187C22×C13#42111yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—22no—
192C4×C13—81no—
193C4×C13—81no—
194Dic13—22no—
195Dic13—22no—
196Dic13—21no—
197Dic13—21no—
198Dic13—42no—
199Dic13—42no—
200Dic13—41no—
201C22×Q8—131no—
202C23×C4—131no—
203C23×C4—131no—
204C23×C4C2×#26111yescharacteristic
205C22×C8—262no—
206C22×C8—262no—
207C22⋊Q8—134no—
208C22⋊Q8—262no—
209C4×Q8—522no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4C2×#26111yescharacteristic
215C2×C4⋊C4C2×#26111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—261no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—261no—
223C2×C42—261no—
224C2×C42—522no—
225C4⋊C8—522no—
226C22⋊C8—522no—
227C22⋊C8—522no—
228#95—21no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—261no—
233C2×C13—42no—
234C2×C13#145911yescharacteristic
235C2×C13#147711yescharacteristic
236C2×C13#147911yescharacteristic
237C2×C13#151111yescharacteristic
238C2×C13#151311yescharacteristic
239C2×C13#153511yescharacteristic
240C2×C13#155911yescharacteristic
241C24C22⋊#26111yescharacteristic
242C2×Q8—132no—
243C2×Q8—261no—
244C2×Q8—521no—
245C2×Q8—521no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—261no—
255C22×C4—262no—
256C22×C4—262no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4D13⋊C812yes—
264C22×C4#611812yes—
265C22×C4C22⋊#26111yescharacteristic
266C22×C4C22×#26111yescharacteristic
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C2×C8—522no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—132no—
276C4⋊C4—264no—
277C4⋊C4—261no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4—522no—
281C22⋊C4—42no—
282C22⋊C4—264no—
283C42—262no—
284C42—262no—
285C42—521no—
286C42—521no—
287C42—522no—
288C42—522no—
289C13#760011yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23#8811112yes—
297C23C2×C22⋊#26111yescharacteristic
298Q8—522no—
299Q8—522no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—262no—
323C2×C4—262no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—524no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4#8811112yes—
335C2×C4C2×D13⋊C811yescharacteristic
336C2×C4C2×#611811yescharacteristic
337C8—1042no—
338C8—1042no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22C2×#8811111yescharacteristic
347C22#1171914011yescharacteristic
348C22D13⋊#9911yescharacteristic
349C22#1171914811yescharacteristic
350C22#1171915311yescharacteristic
351C22#1171916411yescharacteristic
352C22#1171916611yescharacteristic
353C4—22no—
354C4—21no—
355C4—21no—
356C4—81no—
357C4—81no—
358C4—262no—
359C4—262no—
360C4—261no—
361C4—261no—
362C4—521no—
363C4—522no—
364C4—522no—
365C2—42no—
366C2#1313007411yescharacteristic
367C2#1313013311yescharacteristic
368C2#1313014011yescharacteristic
369C2#1313024511yescharacteristic
370C2#1313025211yescharacteristic
371C2#1313032111yescharacteristic
372C2#1313037211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#7600
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129657C2semidirect
4. #13129655C2semidirect
35. #88178C8semidirect
289. C13#7600semidirect

Maximal subgroups

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

subgroupindex
#131307262
#131306902
#131296572
#131296552
#131173642
#760013