Finite Group Databasebeta

← #15757986

Subgroups — #15757986

Order 3328.

534 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 103 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#13123865C211yesmaximal, characteristic
2#13118120C211yesmaximal, characteristic
3#13113284C212yesmaximal, complemented
4#13112730C212yesmaximal, complemented
5C4×C13×#100C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×C13×#100—21no—
9C4×C13×M16C2212yes—
10#11718883—21no—
11C4×C22⋊Dic13—21no—
12C4×C22⋊Dic13—21no—
13#11718868—21no—
14C2×C22⋊#1055—21no—
15#11718672—24no—
16#11718643—21no—
17#11718614C411yescharacteristic
18#11718614C411yescharacteristic
19#11718608C411yescharacteristic
20#11718608C411yescharacteristic
21#11718593C2211yescharacteristic
22#11718587C2212yes—
23C13×#343—21no—
24#11718048—24no—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C22×Dic26C2×C411yescharacteristic
29C2×C13×M16—22no—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×#6099—22no—
45C22×#1055—22no—
46C4×Dic26—22no—
47C4×Dic26—22no—
48C13×#100—24no—
49C13×#97—22no—
50C4×C8×C13—22no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic
57#88071C2×C411yescharacteristic
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055—22no—
61C4⋊#1055D414yes—
62#88043—22no—
63#9029—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C22⋊C411yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C2×Dic26—22no—
85C2×Dic26—42no—
86C13×M16—24no—
87C13×M16—42no—
88C2×C8×C13—42no—
89C13×C4⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—22no—
92C42×C13C2×D412yes—
93C42×C13#4112yes—
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C22⋊Dic13—42no—
98C4⋊Dic13—22no—
99#6101—42no—
100C4×Dic13—42no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103#6099—82no—
104C2×#1055—24no—
105C2×#1055—82no—
106#2973—131no—
107#2398—131no—
108C4×#100D1311yescharacteristic
109#1491—132no—
110#1300—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#10412yes—
121C23×C13C2×C22⋊C411yescharacteristic
122D4×C13—44no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13C4×D412yes—
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12112yes—
138C2×C4×C13#12311yescharacteristic
139C2×Dic13—22no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151Dic26—24no—
152Dic26—42no—
153C8×C13—44no—
154#1055—44no—
155C2×C4×Q8—131no—
156C2×C4×D4C2×D1311yescharacteristic
157#435—264no—
158#432—132no—
159C2×#100—21no—
160#407—261no—
161C2×C22⋊C8—261no—
162C4×M16C2×D1312yes—
163#400—261no—
164#397—131no—
165#397—131no—
166#394—261no—
167#393—131no—
168#393—131no—
169C4×C22⋊C4—261no—
170C4×C22⋊C4—261no—
171#376—131no—
172#343—21no—
173Q8⋊C8—264no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—22no—
177C22×C13—42no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13#38611yescharacteristic
187C22×C13C2×#10411yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—22no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13#45512yes—
195Dic13—42no—
196Dic13—81no—
197Dic13—81no—
198Dic13—81no—
199C22×Q8—131no—
200C22×D4C22⋊D1311yescharacteristic
201C23×C4D5211yescharacteristic
202C23×C4D5211yescharacteristic
203C2×M16—22no—
204C2×M16—262no—
205C22×C8—262no—
206C4×Q8—262no—
207C4×Q8—262no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4C22⋊D1311yescharacteristic
213C2×C22⋊C4—261no—
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4C4×D1311yescharacteristic
218C2×C22⋊C4C4×D1311yescharacteristic
219C2×C42—261no—
220C2×C42—261no—
221C2×C42C22×D1311yescharacteristic
222C4⋊C8—134no—
223#100—24no—
224C22⋊C8—262no—
225C22⋊C8—262no—
226C22⋊C8—262no—
227#97—22no—
228#97—262no—
229C4×C8—22no—
230#95—131no—
231#95—131no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—42no—
240C2×C13—81no—
241C2×C13#187111yescharacteristic
242C2×C13#188511yescharacteristic
243C2×C13#189111yescharacteristic
244C24#610311yescharacteristic
245C24#610311yescharacteristic
246C2×Q8—262no—
247C2×Q8—522no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4#610311yescharacteristic
262C22×C4#610311yescharacteristic
263C22×C4C2×C4×D1311yescharacteristic
264C22×C4C2×D5211yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266M16—24no—
267M16—42no—
268M16—1042no—
269C2×C8—42no—
270C2×C8—264no—
271C2×C8—1042no—
272C4⋊C4—22no—
273C4⋊C4—262no—
274C4⋊C4—522no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—522no—
278C22⋊C4—522no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C42—522no—
282C42—521no—
283C42—521no—
284C42D4×D1312yes—
285C42#612912yes—
286C13#902911yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#8804512yes—
297C23C2×#610311yescharacteristic
298Q8—264no—
299Q8—522no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—262no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4#8813512yes—
326C2×C4#8813611yescharacteristic
327C2×C4#8814011yescharacteristic
328C2×C4#8819312yes—
329C8—44no—
330C8—524no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22C2×#8804511yescharacteristic
344C22#1171861911yescharacteristic
345C22#1171866611yescharacteristic
346C4—22no—
347C4—21no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—522no—
352C4—1041no—
353C4—1041no—
354C4—1041no—
355C4#1171840712yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#1311513611yescharacteristic
361C2#1311522211yescharacteristic
362C2#1311525211yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#100C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenterC4×#100D13
hypocenterC13#9029
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
3. #13113284C2semidirect
4. #13112730C2semidirect
286. C13#9029semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131181202
#131132842
#131127302
C4×C13×#1002
#902913