Finite Group Databasebeta

← #16778799

Subgroups — #16778799

Order 3328.

506 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 88 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
2#13130726C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129652C212yesmaximal, complemented
5#13123162C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic
7C2×#88189—21no—
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11#11718882C411yescharacteristic
12#11718882C2211yescharacteristic
13#11718881—21no—
14#11718873C411yescharacteristic
15#11718634C411yescharacteristic
16#11718634C2211yescharacteristic
17#11718605—21no—
18#11718605—21no—
19#11718290—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×#1057—22no—
29C22×#1057—22no—
30C13×#121—42no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38#88189—44no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—42no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13C2311yescharacteristic
48C22⋊#1057—42no—
49C22⋊#1057—42no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7718—131nomaximal, Sylow
54C24×C13—21no—
55C24×C13C22⋊C411yescharacteristic
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C2×D411yescharacteristic
79C22×Dic13C2×D411yescharacteristic
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C2×#1057—42no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—42no—
88C22⋊Dic13—42no—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C4⋊Dic13—22no—
94C4⋊Dic13—41no—
95#6101—42no—
96#6101—42no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101#2854—131no—
102#1817—131no—
103#1817—131no—
104#1271—132no—
105#1270—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13#9912yes—
120C23×C13C2×C22⋊C411yescharacteristic
121D4×C13—82no—
122D4×C13—84no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—44no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#13112yes—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—44no—
144C2×Dic13—44no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13#13512yes—
152C2×Dic13AGL(1,ℤ/8)12yes—
153#1057—82no—
154#1057—82no—
155C2×#123—261no—
156C2×#121#26111yescharacteristic
157C22×C42—131no—
158C2×C22⋊C8—261no—
159C2×C22⋊C8—261no—
160#390—131no—
161#390—131no—
162#389—131no—
163#389—131no—
164#388—261no—
165#388—261no—
166#386—261no—
167#380—131no—
168#336—132no—
169#336—132no—
170#336—261no—
171#336—261no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#40811yescharacteristic
187C22×C13C2×#9911yescharacteristic
188C22×C13#41311yescharacteristic
189C22×C13#41611yescharacteristic
190C22×C13#41811yescharacteristic
191C22×C13#42111yescharacteristic
192C22×C13#42111yescharacteristic
193C4×C13—22no—
194C4×C13—41no—
195C4×C13—81no—
196Dic13—22no—
197Dic13—22no—
198Dic13—41no—
199Dic13—41no—
200Dic13—81no—
201Dic13—81no—
202C22×D4—21no—
203C22×D4C2×#26111yescharacteristic
204C23×C4—131no—
205C23×C4—131no—
206C23×C4C2×#26111yescharacteristic
207C22×C8—262no—
208C22×C8—262no—
209#123—524no—
210#121—42no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4C2×#26111yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—522no—
227C22⋊C8—522no—
228C22⋊C8—522no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—42no—
233C2×C13—161no—
234C2×C13#146811yescharacteristic
235C2×C13#148211yescharacteristic
236C2×C13#149611yescharacteristic
237C2×C13#151011yescharacteristic
238C2×C13#151611yescharacteristic
239C2×C13#153511yescharacteristic
240C2×C13#155311yescharacteristic
241C24—21no—
242C24C22⋊#26111yescharacteristic
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—262no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—521no—
264C22×C4—521no—
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—262no—
275C4⋊C4—521no—
276C4⋊C4—522no—
277C4⋊C4—522no—
278C22⋊C4—42no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C22⋊C4—522no—
284C42—521no—
285C42—521no—
286C42—521no—
287C42—521no—
288C13#771811yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23#8811912yes—
303C23C2×C22⋊#26111yescharacteristic
304D4—82no—
305D4—84no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—132no—
316C2×C4—132no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—524no—
328C2×C4—524no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4#8823812yes—
336C8—1042no—
337C8—1042no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#1171913811yescharacteristic
353C22#1171914011yescharacteristic
354C22#1171914611yescharacteristic
355C22#1171914811yescharacteristic
356C22#1171916511yescharacteristic
357C22#1171916611yescharacteristic
358C22C2×#8811911yescharacteristic
359C4—22no—
360C4—41no—
361C4—81no—
362C4—262no—
363C4—262no—
364C4—521no—
365C4—521no—
366C4—1041no—
367C4—1041no—
368C2—42no—
369C2—161no—
370C2#1313010111yescharacteristic
371C2#1313014711yescharacteristic
372C2#1313019511yescharacteristic
373C2#1313024111yescharacteristic
374C2#1313026211yescharacteristic
375C2#1313032111yescharacteristic
376C2#1313036011yescharacteristic
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#7718
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. #13130726C2semidirect
3. #13129655C2semidirect
4. #13129652C2semidirect
288. C13#7718semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131307262
#131296552
#131296522
#131231622
#771813