Finite Group Databasebeta

← #16778286

Subgroups — #16778286

Order 3328.

520 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 118 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#13130752C211yesmaximal, characteristic, complemented
2C4×#88112C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129652C212yesmaximal
5#13117298C211yesmaximal, characteristic
6C2×D4×Dic13C411yescharacteristic
7C2×#88131—21no—
8C2×#88112—21no—
9C2×#88112—21no—
10C2×C4×#1057—21no—
11C13×#390C411yescharacteristic
12#11718882C2211yescharacteristic
13C4⋊C4×Dic13C411yescharacteristic
14#11718634C2211yescharacteristic
15#11718606—21no—
16#11718605—21no—
17C22⋊C4×Dic13—21no—
18C42×Dic13C2211yescharacteristic
19#11718589C411yescharacteristic
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×Dic13—21no—
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—21no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34D4×Dic13—22no—
35D4×Dic13C814yescomplemented
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13C2311yescharacteristic
47#88131—42no—
48#88131—42no—
49#88112—24no—
50#88112—42no—
51C4×#1057—42no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#7574—131nomaximal, Sylow
56C24×C13—21no—
57C2×D4×C13—21no—
58C2×D4×C13—41no—
59C2×D4×C13—41no—
60C2×D4×C13C2×C812yes—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—24no—
67C22×Dic13—21no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C2×#1057—24no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C13×C4⋊C4—41no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—42no—
83C42×C13—41no—
84C22⋊Dic13—24no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C22⋊Dic13—41no—
88C22⋊Dic13—41no—
89C4⋊Dic13—21no—
90C4⋊Dic13—41no—
91C4⋊Dic13C2×C812yes—
92#6101—42no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—22no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100C4×Dic13—42no—
101C4×Dic13C2×C812yes—
102C4×Dic13M1612yes—
103C4×Dic13D812yes—
104C4×Dic13SD1612yes—
105#2293—131no—
106#1831—131no—
107C4×C4⋊C8—131no—
108#1271—132no—
109#1270—132no—
110C23×C13—22no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13C2×C22⋊C411yescharacteristic
118D4×C13—42no—
119D4×C13—42no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13#10212yes—
131C2×C4×C13C22×C811yescharacteristic
132C2×C4×C13C2×M1611yescharacteristic
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—22no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—48no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13C22⋊C812yes—
147C2×Dic13C22⋊C812yes—
148C2×Dic13#10212yes—
149C2×Dic13#10412yes—
150C2×Dic13C2×D811yescharacteristic
151C2×Dic13C2×SD1611yescharacteristic
152C2×Dic13AGL(1,ℤ/8)11yescharacteristic
153C2×Dic13#13711yescharacteristic
154#1057—44no—
155#1057—82no—
156C2×C4×D4—131no—
157C2×#117—261no—
158C2×C4⋊C8—261no—
159C2×C4⋊C8—261no—
160C2×C4×C8—261no—
161#390—131no—
162#390#26111yescharacteristic
163#389—131no—
164#389—131no—
165#388—261no—
166#388—261no—
167C4×C4⋊C4—131no—
168C4×C22⋊C4—261no—
169C43—131no—
170#336—132no—
171#336—132no—
172#336—261no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13C2×C22⋊C811yescharacteristic
181C22×C13#41011yescharacteristic
182C22×C13#41311yescharacteristic
183C22×C13C2×#10211yescharacteristic
184C22×C13#41711yescharacteristic
185C22×C13C2×#10411yescharacteristic
186C22×C13#42111yescharacteristic
187C4×C13—22no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—41no—
191C4×C13—81no—
192Dic13—22no—
193Dic13—21no—
194Dic13—21no—
195Dic13—21no—
196Dic13—21no—
197Dic13—42no—
198Dic13—81no—
199Dic13D4⋊C814yes—
200C22×D4C2×#26111yescharacteristic
201C23×C4—261no—
202C22×C8—262no—
203C22×C8—262no—
204C4×D4—134no—
205C4×D4—262no—
206#117—522no—
207#117—522no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4C2×#26111yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—261no—
225C2×C42C2×#26111yescharacteristic
226C4⋊C8—264no—
227C4⋊C8—522no—
228C4×C8—522no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—82no—
233C2×C13#145811yescharacteristic
234C2×C13C2×D4⋊C811yescharacteristic
235C2×C13#147711yescharacteristic
236C2×C13#150911yescharacteristic
237C2×C13#151711yescharacteristic
238C2×C13#152911yescharacteristic
239C2×C13#154711yescharacteristic
240C24—21no—
241C2×D4—21no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4D13⋊C812yes—
245C22×C4—21no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—264no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—522no—
254C22×C4—522no—
255C22×C4C22⋊#26111yescharacteristic
256C22×C4C22⋊#26111yescharacteristic
257C22×C4C22×#26111yescharacteristic
258C2×C8—264no—
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C2×C8—522no—
263C2×C8—522no—
264C4⋊C4—41no—
265C4⋊C4—132no—
266C4⋊C4—261no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—522no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—264no—
274C22⋊C4—521no—
275C22⋊C4—521no—
276C22⋊C4—521no—
277C22⋊C4—521no—
278C42—41no—
279C42—132no—
280C42—132no—
281C42—132no—
282C42—132no—
283C42—261no—
284C42—262no—
285C42—261no—
286C42—521no—
287C42—521no—
288C42—522no—
289C13#757411yescharacteristic, complemented, Sylow
290C23—22no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊#26111yescharacteristic
298D4—42no—
299D4—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—132no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—262no—
325C2×C4—528no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4#8811512yes—
332C2×C4C2×D13⋊C811yescharacteristic
333C2×C4D13⋊M1611yescharacteristic
334C8—524no—
335C8—1042no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22D13⋊(C22⋊C8)11yescharacteristic
344C22C2×#8811511yescharacteristic
345C22#1171914011yescharacteristic
346C22#1171914211yescharacteristic
347C22#1171914811yescharacteristic
348C22D13⋊#10411yescharacteristic
349C22#1171916411yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—81no—
355C4—134no—
356C4—261no—
357C4—261no—
358C4—262no—
359C4—261no—
360C4—261no—
361C4—522no—
362C4—1041no—
363C2—82no—
364C2#1313006811yescharacteristic
365C2D13⋊(D4⋊C8)11yescharacteristic
366C2#1313013211yescharacteristic
367C2#1313023711yescharacteristic
368C2#1313026511yescharacteristic
369C2#1313030211yescharacteristic
370C2#1313034811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#390C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenter#390#261
hypocenterC13#7574
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #13130752C2semidirect
2. C4×#88112C2semidirect
3. #13129655C2semidirect
35. D4×Dic13C8semidirect
289. C13#7574semidirect

Maximal subgroups

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

subgroupindex
#131307522
C4×#881122
#131296552
#131296522
#131172982
#757413