Finite Group Databasebeta

← #15766645

Subgroups — #15766645

Order 3328.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13124637C211yesmaximal, characteristic
2#13114829C211yesmaximal, characteristic
3#13113595C211yesmaximal, characteristic
4#13113526C211yesmaximal, characteristic
5C2×#11718048C211yesmaximal, characteristic
6#13112710C211yesmaximal, characteristic
7C13×#1493C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88064—21no—
13#11718755—21no—
14#11718752—21no—
15#11718724—22no—
16#11718665—21no—
17#11718656—21no—
18#11718585C2211yescharacteristic
19#11718585C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C13×Q8⋊C8—21no—
22C13×Q8⋊C8—21no—
23#11718146—21no—
24#11718139—21no—
25#11718138—21no—
26#11718050—22no—
27#11718048—21no—
28#11718048—21no—
29C22×Dic26D411yescharacteristic
30C2×C13×M16—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8D411yescharacteristic
33C13×C4⋊Q8D411yescharacteristic
34C13×#125—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C13×#117—21no—
40C2×C42×C13C2311yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×#6099—21no—
45C2×#6099—21no—
46C22×#1055—21no—
47C4×Dic26—21no—
48C4×Dic26—21no—
49C4×Dic26—21no—
50C4×Dic26—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C4×C8×C13—21no—
54C4×C8×C13D411yescharacteristic
55C4×C8×C13D411yescharacteristic
56#88064—42no—
57#88050—22no—
58#88050—22no—
59#88048—22no—
60#88047—22no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67#10463—131nomaximal, Sylow
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×Dic26Q1612yes—
81C13×M16—41no—
82C13×M16—41no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—42no—
86C2×C8×C13—41no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C22⋊C4—41no—
94C42×C13—41no—
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13#4111yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101#6101—41no—
102#6101—41no—
103C4×Dic13—41no—
104C4×Dic13—41no—
105#6099—41no—
106#6099—41no—
107#6099—41no—
108#6099—41no—
109C2×#1055—22no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—81no—
113#3078—131no—
114#1801—131no—
115#1567—131no—
116#1550—131no—
117#1493D1311yescharacteristic
118C2×Q8⋊C8—131no—
119#1292—131no—
120C23×C13#12311yescharacteristic
121Q8×C13—41no—
122Q8×C13—41no—
123Q8×C13—81no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×C4×C13#12411yescharacteristic
135C2×C4×C13C2×Q1611yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×Dic13—22no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—81no—
144Dic26—22no—
145Dic26—22no—
146Dic26—41no—
147Dic26—41no—
148C8×C13—22no—
149C8×C13—41no—
150C8×C13—81no—
151#1055—42no—
152#1055—81no—
153#1055—81no—
154#533C2×D1311yescharacteristic
155C2×C4×Q8—131no—
156#479—262no—
157#477—261no—
158#475—261no—
159#428—261no—
160#423—131no—
161#423—131no—
162#423C2×D1311yescharacteristic
163C2×C4⋊C8—131no—
164#419—261no—
165C2×#101—261no—
166C2×C4×C8C2×D1311yescharacteristic
167#343—261no—
168#335—262no—
169#333—261no—
170#332—261no—
171Q8⋊C8—21no—
172Q8⋊C8—21no—
173Q8⋊C8—261no—
174Q8⋊C8—261no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13#39411yescharacteristic
178C22×C13#48411yescharacteristic
179C22×C13#48511yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13#44911yescharacteristic
186C4×C13#45111yescharacteristic
187C4×C13#46711yescharacteristic
188C4×C13#46811yescharacteristic
189C4×C13#47111yescharacteristic
190C4×C13#47311yescharacteristic
191Dic13—42no—
192Dic13—81no—
193C22×Q8—131no—
194C2×M16—21no—
195C2×M16—261no—
196C2×M16—261no—
197C22×C8—21no—
198C22×C8—261no—
199C4⋊Q8D5211yescharacteristic
200C4⋊Q8D5211yescharacteristic
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—261no—
207C4×Q8—261no—
208C4×Q8—261no—
209C4×Q8—261no—
210#117—21no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C42—261no—
214C2×C42C22×D1311yescharacteristic
215#107—262no—
216#106—262no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—132no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8—261no—
225#103—262no—
226#103—262no—
227#101—522no—
228C4×C8—21no—
229C4×C8C22⋊D1311yescharacteristic
230C4×C8C22⋊D1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#203611yescharacteristic
234C2×C13#205011yescharacteristic
235C2×C13#205211yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—132no—
239C2×Q8—261no—
240C2×Q8—261no—
241C2×Q8—261no—
242C2×Q8—261no—
243C2×Q8—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4#612711yescharacteristic
247C22×C4D4×D1311yescharacteristic
248C22×C4#612911yescharacteristic
249M16—41no—
250M16—41no—
251M16—521no—
252M16—521no—
253M16—521no—
254M16—521no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—262no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—1041no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C22⋊C4—41no—
274C42—41no—
275C42—521no—
276C42—521no—
277C42C2×D5211yescharacteristic
278C42D4×D1311yescharacteristic
279C42#612911yescharacteristic
280C42C2×C22⋊D1311yescharacteristic
281C13#1046311yescharacteristic, complemented, Sylow
282C23#8813711yescharacteristic
283Q8—41no—
284Q8—41no—
285Q8—81no—
286Q8—262no—
287Q8—262no—
288Q8—521no—
289Q8—521no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—262no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—1041no—
300C2×C4#8813611yescharacteristic
301C2×C4#8813911yescharacteristic
302C2×C4#8814011yescharacteristic
303C2×C4#8816811yescharacteristic
304C2×C4#8816911yescharacteristic
305C2×C4Q16×D1311yescharacteristic
306C2×C4#8817311yescharacteristic
307C2×C4#8818411yescharacteristic
308C2×C4#8819211yescharacteristic
309C2×C4#8819311yescharacteristic
310C8—22no—
311C8—41no—
312C8—81no—
313C8—522no—
314C8—1041no—
315C8—1041no—
316C22—21no—
317C22—21no—
318C22#1171847011yescharacteristic
319C22#1171847511yescharacteristic
320C22#1171862211yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—81no—
325C4—81no—
326C4—522no—
327C4—1041no—
328C4#1171846911yescharacteristic
329C4#1171847211yescharacteristic
330C4#1171880211yescharacteristic
331C4#1171880411yescharacteristic
332C4#1171883511yescharacteristic
333C4#1171884911yescharacteristic
334C2—21no—
335C2—21no—
336C2#1311603811yescharacteristic
337C2#1311612211yescharacteristic
338C2#1311613411yescharacteristic
subgroupG/H
centerC22#11718622
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1493C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1493D13
hypocenterC13#10463
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
281. C13#10463semidirect

Maximal subgroups

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

subgroupindex
#131246372
#131148292
#131135952
#131135262
C2×#117180482
#131127102
C13×#14932
#1046313