Finite Group Databasebeta

← #16780728

Subgroups — #16780728

Order 3328.

528 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130621C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3C2×#11718245C212yesmaximal
4#13129714C212yesmaximal
5#13117407C211yesmaximal, characteristic
6C2×#88142C2211yescharacteristic
7C2×#88141—21no—
8C2×#88112C2212yes—
9C2×#88112C2212yes—
10C2×#88110—21no—
11C2×C4×#1057—21no—
12C13×#389C411yescharacteristic
13#11718637C2211yescharacteristic
14C4⋊C4×Dic13C411yescharacteristic
15C4⋊C4×Dic13C411yescharacteristic
16#11718633—21no—
17C42×Dic13C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718310—21no—
20#11718307—21no—
21#11718290—21no—
22#11718290—21no—
23#11718245C418yescomplemented
24C22×Dic26—21no—
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88142—22no—
46#88142C2×C414yes—
47#88141—42no—
48#88141—42no—
49#88112—22no—
50#88112—22no—
51#88112C2×C414yes—
52#88112C2×C414yes—
53#88110—42no—
54C4×#1057—42no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#8236—131nomaximal, Sylow
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C2×Dic26—24no—
72C2×Dic26—41no—
73C2×Dic26—41no—
74C2×Dic26—42no—
75C2×#1057—24no—
76C2×#1057—24no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4C4212yes—
85C42×C13—41no—
86C4⋊Dic13—21no—
87C4⋊Dic13—41no—
88C4⋊Dic13C4212yes—
89#6101—24no—
90#6101—42no—
91#6101—41no—
92#6101—41no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—22no—
100C4×Dic13—42no—
101C4×Dic13—42no—
102C4×Dic13D812yes—
103C4×Dic13SD1612yes—
104C4×Dic13C22×C412yes—
105C4×Dic13#4112yes—
106C4×C4⋊Q8—131no—
107#1767—131no—
108C4×C4⋊C8—131no—
109C2×#332—132no—
110#1296—132no—
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13#10212yes—
126C2×C4×C13C2×C4211yescharacteristic
127C2×C4×C13#11711yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13#10112yes—
139C2×Dic13#10212yes—
140C2×Dic13C4×D412yes—
141C2×Dic13C4×D412yes—
142C2×Dic13C2×D811yescharacteristic
143C2×Dic13C2×SD1611yescharacteristic
144C2×Dic13#13512yes—
145C2×Dic13AGL(1,ℤ/8)11yescharacteristic
146C2×Dic13#13712yes—
147C2×Dic13#13711yescharacteristic
148Dic26—44no—
149Dic26—44no—
150#1057—44no—
151#1057—44no—
152C2×C4⋊Q8—131no—
153C2×C4×Q8—261no—
154C2×C4⋊C8—132no—
155C2×C4⋊C8—132no—
156C2×#97—261no—
157C2×C4×C8—261no—
158#391—261no—
159#389—131no—
160#389—261no—
161#389#26111yescharacteristic
162#384—131no—
163C4×C4⋊C4—131no—
164C4×C4⋊C4—131no—
165C4×C4⋊C4—261no—
166C43—131no—
167#336—261no—
168#336—261no—
169#332—138no—
170C22×C13C4×C22⋊C411yescharacteristic
171C22×C13C2×#10111yescharacteristic
172C22×C13#41311yescharacteristic
173C22×C13C2×#10211yescharacteristic
174C22×C13#41611yescharacteristic
175C22×C13#41711yescharacteristic
176C22×C13#41911yescharacteristic
177C4×C13—22no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—42no—
182C4×C13—81no—
183Dic13—22no—
184Dic13—22no—
185Dic13—42no—
186Dic13—81no—
187Dic13C4×D812yes—
188Dic13C4×SD1612yes—
189Dic13#44012yes—
190Dic13#44112yes—
191C22×Q8—261no—
192C22×C8—262no—
193C22×C8—262no—
194C4⋊Q8—134no—
195C4⋊Q8—262no—
196C4×Q8—522no—
197C4×Q8—522no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C2×#26111yescharacteristic
206C2×C4⋊C4C2×#26111yescharacteristic
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—261no—
214C2×C42—261no—
215C2×C42C2×#26111yescharacteristic
216C4⋊C8—134no—
217C4⋊C8—134no—
218C4⋊C8—262no—
219C4⋊C8—262no—
220#97—522no—
221C4×C8—522no—
222#95—21no—
223#95—261no—
224#95—261no—
225#95—261no—
226C2×C13#154611yescharacteristic
227C2×C13#154711yescharacteristic
228C2×C13#155211yescharacteristic
229C2×C13#155411yescharacteristic
230C2×C13C4×#10111yescharacteristic
231C2×C13C4×#10211yescharacteristic
232C2×C13#176311yescharacteristic
233C2×Q8—264no—
234C2×Q8—521no—
235C2×Q8—521no—
236C2×Q8—522no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—131no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4C22⋊#26111yescharacteristic
246C22×C4C22⋊#26111yescharacteristic
247C22×C4C22×#26111yescharacteristic
248C2×C8—264no—
249C2×C8—264no—
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C2×C8—522no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—132no—
258C4⋊C4—264no—
259C4⋊C4—261no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4C4×#26112yes—
267C42—41no—
268C42—132no—
269C42—132no—
270C42—132no—
271C42—132no—
272C42—261no—
273C42—262no—
274C42—261no—
275C42—262no—
276C42—262no—
277C42—522no—
278C42—522no—
279C13#823611yescharacteristic, complemented, Sylow
280C23C2×C22⋊#26111yescharacteristic
281Q8—524no—
282Q8—524no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—132no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—132no—
304C2×C4—132no—
305C2×C4—132no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—262no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4#8811512yes—
317C2×C4C2×C4×#26111yescharacteristic
318C2×C4#8823711yescharacteristic
319C8—524no—
320C8—524no—
321C22C4×C22⋊#26111yescharacteristic
322C22C2×#8811511yescharacteristic
323C22#1171914811yescharacteristic
324C22#1171915311yescharacteristic
325C22D13⋊#10111yescharacteristic
326C22#1171916411yescharacteristic
327C22#1171916511yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—42no—
332C4—41no—
333C4—81no—
334C4—132no—
335C4—132no—
336C4—132no—
337C4—132no—
338C4—262no—
339C4—262no—
340C4—522no—
341C4—1041no—
342C2#1313034611yescharacteristic
343C2#1313034811yescharacteristic
344C2#1313035811yescharacteristic
345C2#1313036211yescharacteristic
346C2#1313058911yescharacteristic
347C2C4×#8811511yescharacteristic
348C2#1313060811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#8236
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
23. #11718245C4semidirect
279. C13#8236semidirect

Maximal subgroups

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

subgroupindex
#131306212
C4×#881122
C2×#117182452
#131297142
#131174072
#823613