Finite Group Databasebeta

← #15756041

Subgroups — #15756041

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#1055C211yesmaximal, characteristic
2#13115007C211yesmaximal, characteristic, complemented
3#13113582C211yesmaximal, characteristic, complemented
4#13113261C211yesmaximal, characteristic
5#13112732C211yesmaximal, characteristic, complemented
6#13112731C211yesmaximal, characteristic, complemented
7C13×#1486C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9C23×#1055—21no—
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C22⋊#1055—21no—
13C2×#88062—21no—
14C2×#88062—21no—
15D4×#1055—21no—
16D4×#1055—21no—
17D4×#1055C412yes—
18D4×#1055C412yes—
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21C2×C4⋊#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23C13×D4⋊C8—22no—
24D4⋊#1055—22no—
25#11718072—21no—
26#11718071—21no—
27C22×D4×C13Q811yescharacteristic
28C23×C4×C13—21no—
29C2×C13×M16—21no—
30C4×D4×C13—21no—
31C4×D4×C13—21no—
32C4×D4×C13C2×C412yes—
33C4×D4×C13D412yes—
34C2×C13×C4⋊C4Q811yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6099—21no—
38C22×#1055—21no—
39C22×#1055—22no—
40C22×#1055—22no—
41C22×#1055—42no—
42C22×#1055—42no—
43C22×#1055D411yescharacteristic
44C22×#1055D411yescharacteristic
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C22⋊C8—21no—
49C4×C8×C13—21no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C22⋊#1055—21no—
53#88062—42no—
54#88062—42no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055C2×C412yes—
60C4×#1055—21no—
61C4×#1055C2×C411yescharacteristic
62C4×#1055C2×C411yescharacteristic
63C4×#1055D411yescharacteristic
64C4×#1055D411yescharacteristic
65#8658—131nomaximal, Sylow
66C24×C13—21no—
67C2×D4×C13—24no—
68C2×D4×C13—21no—
69C2×D4×C13C4⋊C412yes—
70C22×C4×C13—21no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×Q811yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C13×M16—41no—
81C13×M16—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4C4⋊C412yes—
86C13×C22⋊C4—22no—
87C13×C22⋊C4—22no—
88C42×C13C22×C411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13C2×D411yescharacteristic
91C42×C13#4111yescharacteristic
92#6099—41no—
93#6099—41no—
94C2×#1055—21no—
95C2×#1055—21no—
96C2×#1055—22no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—44no—
100C2×#1055—44no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055C22⋊C411yescharacteristic
104C2×#1055C22⋊C411yescharacteristic
105C2×#1055C22⋊C411yescharacteristic
106C2×#1055C22⋊C411yescharacteristic
107C2×#1055D812yes—
108C2×#1055SD1612yes—
109C2×C8×D4—131no—
110#1848—131no—
111#1564—131no—
112#1486—131no—
113#1486D1311yescharacteristic
114#1301—131no—
115#1301—131no—
116C23×C13—24no—
117C23×C13—22no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C22⋊Q811yescharacteristic
122D4×C13—24no—
123D4×C13—22no—
124D4×C13#10814yescomplemented
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13C2×C22⋊C411yescharacteristic
135C2×C4×C13C2×C4⋊C411yescharacteristic
136C2×C4×C13#11711yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13C22⋊Q811yescharacteristic
140C2×C4×C13C2×D811yescharacteristic
141C2×C4×C13C2×SD1611yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C8×C13—81no—
145C8×C13—81no—
146#1055—21no—
147#1055—21no—
148#1055—42no—
149#1055—81no—
150#1055—81no—
151#1055#10212yes—
152#1055#10212yes—
153C23×C8—261no—
154C2×C4×D4C2×D1311yescharacteristic
155C8×D4—132no—
156C8×D4—132no—
157C8×D4—261no—
158C8×D4—261no—
159#431—131no—
160#431C2×D1311yescharacteristic
161C2×#108—261no—
162C2×#108—261no—
163#423—131no—
164#423C2×D1311yescharacteristic
165C2×C4⋊C8—131no—
166C2×C22⋊C8—261no—
167C2×C4×C8—131no—
168#335—261no—
169#334—261no—
170D4⋊C8—22no—
171D4⋊C8—262no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—24no—
175C22×C13—44no—
176C22×C13—44no—
177C22×C13—42no—
178C22×C13—42no—
179C22×C13#38011yescharacteristic
180C22×C13#47411yescharacteristic
181C22×C13#47611yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—42no—
186C4×C13C2×#10211yescharacteristic
187C4×C13#41711yescharacteristic
188C4×C13C2×#10812yes—
189C4×C13#45911yescharacteristic
190C4×C13#46111yescharacteristic
191C22×D4Dic2611yescharacteristic
192C23×C4—21no—
193C2×M16—21no—
194C2×M16—261no—
195C22×C8—131no—
196C22×C8—131no—
197C22×C8—262no—
198C22×C8—262no—
199C22×C8—261no—
200C22×C8—522no—
201C22×C8—522no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C4×D1312yes—
205C4×D4C22⋊D1312yes—
206C2×C4⋊C4Dic2611yescharacteristic
207C2×C22⋊C4—21no—
208C2×C42C22×D1311yescharacteristic
209#108—522no—
210#108—522no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219C22⋊C8—21no—
220C22⋊C8—262no—
221C22⋊C8—262no—
222C22⋊C8—261no—
223C4×C8—21no—
224C4×C8—131no—
225C4×C8—131no—
226C4×C8—131no—
227C4×C8—131no—
228C4×C8—261no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—44no—
232C2×C13#180211yescharacteristic
233C2×C13#181011yescharacteristic
234C2×C13#181411yescharacteristic
235C24—21no—
236C2×D4—24no—
237C2×D4—21no—
238C2×D4#610112yes—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4C2×Dic2611yescharacteristic
247C22×C4D4×D1311yescharacteristic
248C22×C4#612911yescharacteristic
249M16—41no—
250M16—41no—
251M16—521no—
252M16—521no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—131no—
256C2×C8—131no—
257C2×C8—132no—
258C2×C8—132no—
259C2×C8—131no—
260C2×C8—131no—
261C2×C8—261no—
262C2×C8—261no—
263C2×C8—262no—
264C2×C8—524no—
265C2×C8—524no—
266C2×C8—521no—
267C2×C8—521no—
268C2×C8—521no—
269C2×C8—521no—
270C4⋊C4—21no—
271C4⋊C4#610112yes—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C42C2×C4×D1311yescharacteristic
275C42D4×D1311yescharacteristic
276C42#612911yescharacteristic
277C42C2×C22⋊D1311yescharacteristic
278C13#865811yescharacteristic, complemented, Sylow
279C23—24no—
280C23—22no—
281C23—42no—
282C23—41no—
283C23—41no—
284C23#8813211yescharacteristic
285D4—24no—
286D4—22no—
287D4#8806214yescomplemented
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4#8813111yescharacteristic
298C2×C4#8813211yescharacteristic
299C2×C4C22⋊C4×D1311yescharacteristic
300C2×C4D8×D1311yescharacteristic
301C2×C4#8816511yescharacteristic
302C2×C4SD16×D1311yescharacteristic
303C2×C4#8816911yescharacteristic
304C2×C4C2×#610111yescharacteristic
305C2×C4#8819311yescharacteristic
306C2×C4#8819311yescharacteristic
307C8—81no—
308C8—81no—
309C8—132no—
310C8—132no—
311C8—261no—
312C8—261no—
313C8—522no—
314C8—1041no—
315C8—1041no—
316C22—21no—
317C22—21no—
318C22—24no—
319C22—44no—
320C22—44no—
321C22—42no—
322C22—42no—
323C22#1171842011yescharacteristic
324C22#1171842211yescharacteristic
325C22#1171860311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4D13×#10211yescharacteristic
331C4#1171843211yescharacteristic
332C4C2×#8806212yes—
333C4#1171881111yescharacteristic
334C4#1171882311yescharacteristic
335C2—21no—
336C2—21no—
337C2—44no—
338C2#1311483411yescharacteristic
339C2#1311487211yescharacteristic
340C2#1311488811yescharacteristic
subgroupG/H
centerC2×C4#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1486C2
socleC22×C13#380
prime radicalC22×D4×C13Q8
cosocleC2×C42×C13C23
hypercenter#1486D13
hypocenterC13#8658
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13115007C2semidirect
3. #13113582C2semidirect
5. #13112732C2semidirect
6. #13112731C2semidirect
124. D4×C13#108semidirect
278. C13#8658semidirect
287. D4#88062semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#10552
#131150072
#131135822
#131132612
#131127322
#131127312
C13×#14862
#865813