Finite Group Databasebeta

← #15760610

Subgroups — #15760610

Order 3328.

448 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123920C211yesmaximal, characteristic
2#13120045C211yesmaximal, characteristic
3#13113553C211yesmaximal, characteristic
4#13113179C211yesmaximal, characteristic
5#13112693C211yesmaximal, characteristic
6#13112691C211yesmaximal, characteristic
7C13×#1556C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#432C2211yescharacteristic
12#11718890—21no—
13#11718890—21no—
14#11718637C412yes—
15#11718635C412yes—
16#11718634—21no—
17#11718634—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718587C2211yescharacteristic
20#11718587C2211yescharacteristic
21#11718489—22no—
22#11718380—21no—
23#11718379—21no—
24#11718362—22no—
25C13×#332—22no—
26#11718139—22no—
27#11718061—21no—
28#11718061—21no—
29C22×Q8×C13—21no—
30C22×Dic26C2×C411yescharacteristic
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C412yes—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—22no—
41C2×#6101—22no—
42C2×#6101D411yescharacteristic
43C2×#6101D411yescharacteristic
44C2×C4×Dic13C2×C412yes—
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C4×Dic26—21no—
48C4×Dic26—21no—
49C4×Dic26—21no—
50C4×Dic26—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8D412yes—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×#97—21no—
56C13×#97—21no—
57#88071—21no—
58#88071—22no—
59#88071—22no—
60C22⋊#1055—21no—
61C22⋊#1055—21no—
62#88055—22no—
63#88054—22no—
64#88054—22no—
65C8×Dic13—22no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68#88043—21no—
69#88043—21no—
70#9454—131nomaximal, Sylow
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—82no—
74C22×C4×C13—22no—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—22no—
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C22⋊C411yescharacteristic
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C2×Dic26—21no—
84C2×Dic26—21no—
85C2×Dic26—22no—
86C2×Dic26—41no—
87C2×C8×C13—22no—
88C2×C8×C13—41no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13#4111yescharacteristic
96C42×C13#4111yescharacteristic
97C4⋊Dic13—24no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—82no—
105#6101—82no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C4×Dic13—42no—
111C2×#1055—22no—
112C2×#1055—41no—
113#2983—131no—
114#2567—131no—
115#1556—131no—
116#1556D1311yescharacteristic
117#1467—131no—
118#1285—131no—
119#1285—131no—
120C23×C13C2×C22⋊C411yescharacteristic
121Q8×C13—82no—
122Q8×C13—82no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—24no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13#10112yes—
149Dic26—42no—
150Dic26—42no—
151C8×C13—42no—
152C8×C13—81no—
153#1055—42no—
154#1055—81no—
155C2×C4⋊Q8C2×D1311yescharacteristic
156C2×C4×Q8—131no—
157#446—262no—
158#446—262no—
159#432—131no—
160#432—131no—
161#432—261no—
162#432C2×D1311yescharacteristic
163#432C2×D1311yescharacteristic
164#431—261no—
165#395—261no—
166#395—261no—
167#391—132no—
168#389—261no—
169#389—261no—
170#384—132no—
171C4×C4⋊C4—131no—
172#332—22no—
173#332—262no—
174#324—261no—
175#324—261no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13#38611yescharacteristic
179C22×C13C2×#10111yescharacteristic
180C22×C13#41311yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—82no—
187C4×C13#45612yes—
188Dic13—22no—
189Dic13—44no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193C22×Q8—21no—
194C22×Q8—131no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4×Q8—261no—
200C4×Q8—261no—
201C4×Q8—261no—
202C4×Q8—261no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—262no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4C4×D1312yes—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—132no—
214C2×C42C22×D1311yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—132no—
217C4⋊C8—262no—
218C4⋊C8—262no—
219C4⋊C8—261no—
220C4⋊C8C22⋊D1312yes—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—261no—
224C22⋊C8—261no—
225#97—21no—
226#97—21no—
227#97—262no—
228#97—261no—
229#97—261no—
230C4×C8—262no—
231#95—262no—
232#95—262no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13#188611yescharacteristic
237C2×C13#190111yescharacteristic
238C2×C13#191011yescharacteristic
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—82no—
242C2×Q8—262no—
243C2×Q8—261no—
244C2×Q8—261no—
245C2×Q8—521no—
246C22×C4—22no—
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—262no—
252C22×C4C2×C4×D1311yescharacteristic
253C22×C4D4×D1311yescharacteristic
254C22×C4D4×D1311yescharacteristic
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—262no—
258C2×C8—521no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—264no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—1042no—
271C4⋊C4—1042no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42—522no—
277C42#612711yescharacteristic
278C42D4×D1311yescharacteristic
279C42#612911yescharacteristic
280C42C2×C22⋊D1311yescharacteristic
281C13#945411yescharacteristic, complemented, Sylow
282C23C22⋊C4×D1311yescharacteristic
283Q8—82no—
284Q8—82no—
285Q8—522no—
286Q8—522no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—132no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—264no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4#8813511yescharacteristic
308C2×C4#8813711yescharacteristic
309C2×C4#8813811yescharacteristic
310C2×C4C4×C22⋊D1311yescharacteristic
311C2×C4#8819111yescharacteristic
312C2×C4#8819211yescharacteristic
313C8—42no—
314C8—81no—
315C8—522no—
316C8—1041no—
317C22—21no—
318C22—21no—
319C22D13×#10111yescharacteristic
320C22#1171841211yescharacteristic
321C22#1171861711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—262no—
329C4—524no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#1171886612yes—
334C2—21no—
335C2—21no—
336C2#1311522611yescharacteristic
337C2#1311530111yescharacteristic
338C2#1311536011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1556C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1556D13
hypocenterC13#9454
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
281. C13#9454semidirect

Maximal subgroups

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

subgroupindex
#131239202
#131200452
#131135532
#131131792
#131126932
#131126912
C13×#15562
#945413