Finite Group Databasebeta

← #15781579

Subgroups — #15781579

Order 3328.

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

normal subgroups only

This group has 616 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#13118201C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13112955C214yesmaximal
4C13×#1800C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic, complemented
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178—21no—
8C13×#423—21no—
9C2×C13×#100C2212yes—
10#11718881C2212yes—
11C2×#88074C2212yes—
12#11718873C411yescharacteristic, complemented
13C4×C22⋊Dic13—21no—
14#11718640—21no—
15#11718608—21no—
16#11718607C412yescomplemented
17#11718590—21no—
18C13×#343—21no—
19#11718118—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13C2×C412yes—
24C22×Dic26—21no—
25C22×Dic26—21no—
26C22×Dic26—44no—
27C22×Dic26—41no—
28C22×Dic26—41no—
29C2×C13×M16—22no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13C2×C412yes—
39C2×C4⋊Dic13—21no—
40#88178—44no—
41C2×#6101—22no—
42C2×C4×Dic13—41no—
43C13×C4⋊C8—41no—
44C13×C4⋊C8—41no—
45C13×#100—24no—
46#88074—22no—
47#88074Q814yescomplemented
48#88071—22no—
49#88071—21no—
50#88071—22no—
51#88071—41no—
52#13296—131nomaximal, Sylow
53C24×C13C22×C411yescharacteristic
54C24×C13C2×D411yescharacteristic
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13C2×Q812yes—
58C2×D4×C13#4112yes—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—44no—
73C22×Dic13—42no—
74C22×Dic13—42no—
75C2×Dic26—24no—
76C2×Dic26—44no—
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×Dic26—48no—
80C2×Dic26—44no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—44no—
84C13×M16—42no—
85C13×M16—42no—
86C2×C8×C13—42no—
87C13×C4⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—21no—
91C42×C13—21no—
92C22⋊Dic13—24no—
93C22⋊Dic13—44no—
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C4⋊Dic13—42no—
97#6101—44no—
98C4×Dic13—82no—
99#2409—131no—
100#1800D1311yescharacteristic
101C4×#99—131no—
102#1390—134no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13C4×Q812yes—
113C23×C13C22⋊Q812yes—
114D4×C13—42no—
115D4×C13—42no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—81no—
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#12411yescharacteristic
132C2×C4×C13C4⋊Q811yescharacteristic
133C2×Dic13—24no—
134C2×Dic13—42no—
135C2×Dic13—44no—
136C2×Dic13—42no—
137C2×Dic13—44no—
138C2×Dic13—42no—
139C2×Dic13—44no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144Dic26—44no—
145Dic26—48no—
146Dic26—44no—
147C8×C13—82no—
148C23×Q8—131no—
149C2×C22⋊Q8—261no—
150C2×C4×D4C2×D1311yescharacteristic
151#423—21no—
152C2×#100C2×D1312yes—
153C2×#99—132no—
154#395—261no—
155#393—261no—
156#391—261no—
157#386—132no—
158#385—132no—
159#380—131no—
160C4×C22⋊C4—261no—
161#343—21no—
162#342—261no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13#39111yescharacteristic
176C22×C13C2×#9911yescharacteristic
177C22×C13#41011yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13AΣL(1,𝔽16)12yes—
185Dic13—44no—
186Dic13—82no—
187Dic13—84no—
188C22×Q8—261no—
189C22×Q8—261no—
190C22×Q8—521no—
191C22×Q8—521no—
192C22×Q8—524no—
193C22×D4C22×D1311yescharacteristic
194C23×C4—132no—
195C23×C4C4×D1311yescharacteristic
196C23×C4D5211yescharacteristic
197C2×M16—22no—
198C22⋊Q8—524no—
199C4×D4—41no—
200C4×D4—41no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C22⋊C4—132no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4—262no—
207C2×C22⋊C4C4×D1311yescharacteristic
208C2×C22⋊C4D5211yescharacteristic
209C2×C42—521no—
210C2×C42C22⋊D1311yescharacteristic
211C4⋊C8—41no—
212C4⋊C8—41no—
213#100—24no—
214#99—134no—
215#99—262no—
216#95—261no—
217#95—262no—
218#95—262no—
219#95—521no—
220C2×C13—21no—
221C2×C13—21no—
222C2×C13—42no—
223C2×C13—42no—
224C2×C13#199611yescharacteristic
225C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
226C2×C13#212311yescharacteristic
227C24C2×C4×D1311yescharacteristic
228C24C2×D5211yescharacteristic
229C2×Q8—264no—
230C2×Q8—522no—
231C2×Q8—522no—
232C2×Q8—524no—
233C2×Q8—524no—
234C2×Q8—528no—
235C2×Q8—524no—
236C2×Q8—521no—
237C2×Q8—521no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4#612912yes—
241C2×D4Q8×D1312yes—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—262no—
249C22×C4—262no—
250C22×C4—524no—
251C22×C4—522no—
252C22×C4—522no—
253C22×C4#610311yescharacteristic
254C22×C4#610311yescharacteristic
255C22×C4#610311yescharacteristic
256C22×C4#610311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—42no—
259M16—42no—
260C2×C8—42no—
261C4⋊C4—41no—
262C4⋊C4—522no—
263C4⋊C4—524no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—264no—
267C22⋊C4—524no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C42—21no—
271C42—21no—
272C42—1042no—
273C13#1329611yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#8814112yes—
283C23#8815112yes—
284C23C2×#610311yescharacteristic
285Q8—524no—
286Q8—528no—
287Q8—524no—
288D4—42no—
289D4—42no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—264no—
304C2×C4—522no—
305C2×C4—524no—
306C2×C4—522no—
307C2×C4—524no—
308C2×C4—524no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4#8804611yescharacteristic
315C2×C4#8804611yescharacteristic
316C2×C4#8819011yescharacteristic
317C2×C4#8819811yescharacteristic
318C8—82no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#8804611yescharacteristic
332C22#1171863511yescharacteristic
333C22#1171866711yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—524no—
341C4—1042no—
342C4—1044no—
343C4#1171806712yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1311582011yescharacteristic
349C2C2×#1171806711yescharacteristic
350C2#1311649111yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#1800C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#1800D13
hypocenterC13#13296
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
5. C23×Dic26C4semidirect
12. #11718873C4semidirect
16. #11718607C4semidirect
47. #88074Q8semidirect
273. C13#13296semidirect

Maximal subgroups

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

subgroupindex
#131182012
C4×#880742
#131129552
C13×#18002
#1329613