Finite Group Databasebeta

← #15766517

Subgroups — #15766517

Order 3328.

440 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 101 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#13114828C211yesmaximal, characteristic
2#13113606C211yesmaximal, characteristic, complemented
3#13113508C211yesmaximal, characteristic, complemented
4#13113508C211yesmaximal, characteristic, complemented
5#13113227C211yesmaximal, characteristic
6#13112733C211yesmaximal, characteristic, complemented
7C2×C13×#461C211yesmaximal, characteristic
8C22×C13×SD16—21no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C13×#461—22no—
12C13×#461—22no—
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×#103—21no—
15C2×#88073—21no—
16#11718586C2211yescharacteristic
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718139—22no—
21#11718139—22no—
22D4⋊#1055—22no—
23#11718122—21no—
24#11718072—22no—
25C22×Q8×C13—21no—
26C22×D4×C13D411yescharacteristic
27C23×C4×C13—21no—
28C2×C13×SD16—24no—
29C2×C13×SD16—42no—
30C2×C13×SD16—42no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D412yes—
36C4×D4×C13—21no—
37C4×D4×C13—21no—
38C4×D4×C13—21no—
39C4×D4×C13—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C42×C13C2311yescharacteristic
45C2×#6099—21no—
46C2×#6099—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D412yes—
49C13×#103—24no—
50#88073—42no—
51C22⋊#1055—21no—
52C22⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055D412yes—
59C4×#1055—21no—
60C4×#1055—21no—
61#10445—131nomaximal, Sylow
62C24×C13—21no—
63C2×Q8×C13—22no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13SD1612yes—
75C22×C4×C13—21no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—82no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C13×SD16—48no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13#4111yescharacteristic
99#6099—41no—
100#6099—41no—
101#6099—41no—
102#6099—41no—
103C2×#1055—22no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#461D1311yescharacteristic
108#1800—131no—
109#1570—131no—
110#1546—131no—
111#1546—131no—
112#1478—131no—
113#1301—131no—
114C23×C13—22no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—81no—
118C23×C13—81no—
119C23×C13#12311yescharacteristic
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13—81no—
123Q8×C13—81no—
124D4×C13—22no—
125D4×C13—22no—
126D4×C13—41no—
127D4×C13—41no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—82no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—82no—
136C2×C4×C13—81no—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13#12411yescharacteristic
143C2×C4×C13C2×SD1611yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C8×C13—42no—
148#1055—42no—
149#1055—81no—
150#1055—81no—
151#1055—81no—
152C22×SD16—21no—
153C2×C4⋊Q8C2×D1311yescharacteristic
154C2×C4×D4C2×D1311yescharacteristic
155#461—22no—
156#461—22no—
157#431—131no—
158#431—131no—
159#423—131no—
160#423—131no—
161C2×C4⋊C8C2×D1311yescharacteristic
162C2×#103—21no—
163C2×#100—261no—
164#343—261no—
165#334—262no—
166#332—262no—
167#332—262no—
168D4⋊C8—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—42no—
172C22×C13—82no—
173C22×C13—82no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13#39411yescharacteristic
177C22×C13#48111yescharacteristic
178C22×C13#48211yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—82no—
183C4×C13—81no—
184C4×C13#44911yescharacteristic
185C4×C13#45011yescharacteristic
186C4×C13#46511yescharacteristic
187C4×C13#46911yescharacteristic
188C4×C13#47112yes—
189C22×Q8—21no—
190C22×D4C22⋊D1311yescharacteristic
191C23×C4—21no—
192C2×SD16—24no—
193C2×SD16—42no—
194C2×SD16—42no—
195C2×M16—261no—
196C2×M16—261no—
197C22×C8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8C22⋊D1312yes—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C22⋊D1311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C42C22×D1311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—132no—
213C4⋊C8—261no—
214C4⋊C8—261no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8—261no—
218C4⋊C8C22⋊D1312yes—
219#103—24no—
220#100—522no—
221C22⋊C8—261no—
222C22⋊C8—261no—
223C4×C8—261no—
224C4×C8—261no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—82no—
228C2×C13#203411yescharacteristic
229C2×C13#204611yescharacteristic
230C2×C13#204911yescharacteristic
231C24—21no—
232C2×Q8—22no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4#610512yes—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—82no—
249C22×C4#612911yescharacteristic
250C22×C4#612911yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252SD16—48no—
253M16—521no—
254M16—521no—
255M16—521no—
256M16—521no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—262no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C42D4×D1311yescharacteristic
273C42#612911yescharacteristic
274C42C2×C22⋊D1311yescharacteristic
275C42C2×C22⋊D1311yescharacteristic
276C13#1044511yescharacteristic, complemented, Sylow
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23#8818911yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—81no—
286Q8—81no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4#8818611yescharacteristic
301C2×C4C2×#610511yescharacteristic
302C2×C4#8818911yescharacteristic
303C2×C4#8819011yescharacteristic
304C2×C4#8819211yescharacteristic
305C2×C4#8819311yescharacteristic
306C2×C4#8819311yescharacteristic
307C2×C4#8820311yescharacteristic
308C2×C4#8820411yescharacteristic
309C2×C4#8820711yescharacteristic
310C8—42no—
311C8—522no—
312C8—1041no—
313C8—1041no—
314C8—1041no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22#1171869511yescharacteristic
323C22#1171869611yescharacteristic
324C22#1171888311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—81no—
330C4#1171870011yescharacteristic
331C4#1171870211yescharacteristic
332C4#1171883812yes—
333C4#1171887911yescharacteristic
334C4#1171889911yescharacteristic
335C2—21no—
336C2—21no—
337C2—82no—
338C2#1311602211yescharacteristic
339C2#1311609411yescharacteristic
340C2#1311611311yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#461C2
socleC22×C13#394
prime radicalC22×D4×C13D4
hypercenterC2×#461D13
hypocenterC13#10445
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. #13113606C2semidirect
3. #13113508C2semidirect
4. #13113508C2semidirect
6. #13112733C2semidirect
276. C13#10445semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131136062
#131135082
#131132272
#131127332
C2×C13×#4612
#1044513