Finite Group Databasebeta

← #15872370

Subgroups — #15872370

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719188C211yesmaximal, characteristic
2#13117434C211yesmaximal, characteristic
3#13115821C214yesmaximal, complemented
4#13115820C214yesmaximal, complemented
5#13114908C214yesmaximal
6C13×#2312C211yesmaximal, characteristic
7C22×C13×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic13C2212yes—
9C2×#88178C2212yes—
10C2×#88178C2212yes—
11#11719188—24no—
12#11719188—24no—
13C2×#88132C414yescomplemented
14C2×#88132C414yescomplemented
15C13×#388—24no—
16C13×#380C2212yes—
17C13×#379C2212yes—
18C4×C13×C22⋊C4C2212yes—
19#11718908C2212yes—
20#11718873C2212yes—
21C4×C22⋊Dic13C2212yes—
22#11718612—24no—
23#11718119C22116yes—
24C25×C13C2311yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C23×Dic13C2×C412yes—
28C23×Dic13C2×C412yes—
29C22×Dic26C2×C412yes—
30C22×Dic26C2×C412yes—
31C2×C13×C4⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4C2×C414yes—
35C2×C13×C22⋊C4D414yes—
36C2×C13×C22⋊C4D414yes—
37C2×C13×C22⋊C4C2314yes—
38C2×C42×C13—22no—
39C2×C22⋊Dic13—24no—
40C2×C22⋊Dic13—24no—
41C2×C22⋊Dic13—22no—
42C2×C22⋊Dic13—22no—
43C2×C22⋊Dic13C2×C414yes—
44C2×C22⋊Dic13C2314yes—
45C2×C22⋊Dic13C2314yes—
46C2×C4⋊Dic13—22no—
47C2×C4⋊Dic13C2×C412yes—
48C2×C4⋊Dic13C2×C412yes—
49#88178—24no—
50#88178—24no—
51#88178—24no—
52#88178—24no—
53C2×#6101C2×C414yes—
54C2×#6101C2×C414yes—
55C2×C4×Dic13—22no—
56#88132—216no—
57#88132—216no—
58C13×#95—22no—
59C13×#95—22no—
60#88071—22no—
61#88071—22no—
62#21827—131nomaximal, Sylow
63C24×C13—24no—
64C24×C13—81no—
65C24×C13—81no—
66C24×C13C22×C412yes—
67C24×C13C2×D412yes—
68C24×C13C2×D412yes—
69C24×C13C2411yescharacteristic
70C22×C4×C13—24no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13C22×C412yes—
74C22×C4×C13C22×C412yes—
75C22×C4×C13C2×D412yes—
76C22×C4×C13C2×D412yes—
77C22×C4×C13C2×D412yes—
78C22×C4×C13C2×D412yes—
79C22×Dic13—24no—
80C22×Dic13—24no—
81C22×Dic13—24no—
82C22×Dic13—82no—
83C22×Dic13—82no—
84C22×Dic13C22×C414yes—
85C22×Dic13C22×C414yes—
86C2×Dic26—24no—
87C2×Dic26—24no—
88C2×Dic26—82no—
89C2×Dic26—82no—
90C13×C4⋊C4—82no—
91C13×C22⋊C4—28no—
92C13×C22⋊C4—82no—
93C13×C22⋊C4—82no—
94C13×C22⋊C4C22⋊C4116yes—
95C42×C13—82no—
96C22⋊Dic13—28no—
97C22⋊Dic13—24no—
98C22⋊Dic13—24no—
99C22⋊Dic13—28no—
100C22⋊Dic13—82no—
101C22⋊Dic13—82no—
102C4⋊Dic13—24no—
103C4⋊Dic13—24no—
104C4⋊Dic13—82no—
105#6101—28no—
106#6101—28no—
107C4×Dic13—82no—
108C2×#543—131no—
109#2312—131no—
110#2312D1311yescharacteristic
111#1996—134no—
112#1996—134no—
113#1819—134no—
114C23×C13—24no—
115C23×C13—24no—
116C23×C13—24no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—42no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—88no—
126C23×C13C2×C22⋊C414yes—
127C23×C13C23×C411yescharacteristic
128C23×C13C22×D411yescharacteristic
129C23×C13C22×D411yescharacteristic
130C23×C132−1+414yes—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—44no—
138C2×C4×C13—44no—
139C2×C4×C13—44no—
140C2×C4×C13C2×C22⋊C414yes—
141C2×C4×C13C2×C22⋊C414yes—
142C2×Dic13—24no—
143C2×Dic13—24no—
144C2×Dic13—44no—
145C2×Dic13—44no—
146C2×Dic13—44no—
147C2×Dic13—44no—
148C2×Dic13—44no—
149C2×Dic13—84no—
150C2×Dic13—84no—
151Dic26—84no—
152Dic26—84no—
153#543—264no—
154#543—264no—
155C2×C22⋊Q8—132no—
156C2×C22⋊Q8—132no—
157C2×C22⋊Q8—134no—
158C2×C22⋊Q8—134no—
159C22×C22⋊C4—132no—
160C22×C22⋊C4C2×D1311yescharacteristic
161#388—24no—
162#388—264no—
163#380—132no—
164#380C2×D1312yes—
165#379—132no—
166#379C2×D1312yes—
167C4×C22⋊C4—132no—
168C4×C22⋊C4C2×D1312yes—
169#342—1316no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—24no—
178C22×C13—24no—
179C22×C13—44no—
180C22×C13—48no—
181C22×C13—84no—
182C22×C13—84no—
183C22×C13C22×C22⋊C411yescharacteristic
184C22×C13#51912yes—
185C22×C13#53612yes—
186C22×C13#53612yes—
187C4×C13—24no—
188C4×C13—24no—
189C4×C13—84no—
190Dic13—44no—
191Dic13—44no—
192Dic13—84no—
193C25C22×D1311yescharacteristic
194C22×Q8—132no—
195C22×Q8—132no—
196C23×C4—132no—
197C23×C4—132no—
198C23×C4C22×D1311yescharacteristic
199C23×C4C22×D1311yescharacteristic
200C22⋊Q8—264no—
201C22⋊Q8—264no—
202C22⋊Q8—264no—
203C22⋊Q8—264no—
204C22⋊Q8—2616no—
205C22⋊Q8—2616no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—134no—
208C2×C4⋊C4—134no—
209C2×C4⋊C4—132no—
210C2×C4⋊C4—132no—
211C2×C4⋊C4—262no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—134no—
215C2×C22⋊C4—134no—
216C2×C22⋊C4—134no—
217C2×C22⋊C4—264no—
218C2×C22⋊C4—264no—
219C2×C22⋊C4—262no—
220C2×C22⋊C4—262no—
221C2×C22⋊C4C4×D1314yes—
222C2×C22⋊C4D5214yes—
223C2×C22⋊C4C22⋊D1314yes—
224C2×C22⋊C4C22×D1314yes—
225C2×C42—22no—
226C2×C42—262no—
227#95—22no—
228#95—22no—
229#95—262no—
230#95—262no—
231C2×C13—22no—
232C2×C13—22no—
233C2×C13—22no—
234C2×C13—44no—
235C2×C13#231011yescharacteristic
236C2×C13#288311yescharacteristic
237C2×C13#288311yescharacteristic
238C24—24no—
239C24—81no—
240C24—81no—
241C24C2×C4×D1312yes—
242C24C2×D5212yes—
243C24C2×C22⋊D1312yes—
244C24C23×D1311yescharacteristic
245C2×Q8—264no—
246C2×Q8—264no—
247C2×Q8—1042no—
248C2×Q8—1042no—
249C22×C4—24no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—134no—
253C22×C4—134no—
254C22×C4—264no—
255C22×C4—264no—
256C22×C4—264no—
257C22×C4—1042no—
258C22×C4—1042no—
259C22×C4C2×C4×D1312yes—
260C22×C4C2×C4×D1312yes—
261C22×C4C2×D5212yes—
262C22×C4C2×D5212yes—
263C22×C4C2×C22⋊D1312yes—
264C22×C4C2×C22⋊D1312yes—
265C4⋊C4—82no—
266C4⋊C4—268no—
267C4⋊C4—268no—
268C4⋊C4—264no—
269C4⋊C4—264no—
270C4⋊C4—1042no—
271C22⋊C4—28no—
272C22⋊C4—82no—
273C22⋊C4—82no—
274C22⋊C4—268no—
275C22⋊C4—264no—
276C22⋊C4—264no—
277C22⋊C4—268no—
278C22⋊C4—1042no—
279C22⋊C4—1042no—
280C22⋊C4#6103116yes—
281C42—82no—
282C42—1042no—
283C13#2182711yescharacteristic, complemented, Sylow
284C23—24no—
285C23—24no—
286C23—24no—
287C23—41no—
288C23—41no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—88no—
296C23C2×#610314yes—
297C23C22×C4×D1311yescharacteristic
298C23C22×D5211yescharacteristic
299C23#8825714yes—
300C23C22×C22⋊D1311yescharacteristic
301Q8—1044no—
302Q8—1044no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—264no—
313C2×C4—264no—
314C2×C4—524no—
315C2×C4—524no—
316C2×C4—524no—
317C2×C4—524no—
318C2×C4—524no—
319C2×C4—1044no—
320C2×C4—1044no—
321C2×C4C2×#610314yes—
322C2×C4C2×#610314yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—24no—
330C22—24no—
331C22—24no—
332C22—44no—
333C22—48no—
334C22—84no—
335C22—84no—
336C22#1171922112yes—
337C22#1171923112yes—
338C22C22×#610311yescharacteristic
339C22#1171953012yes—
340C4—24no—
341C4—24no—
342C4—84no—
343C4—524no—
344C4—524no—
345C4—1044no—
346C2—22no—
347C2—22no—
348C2—22no—
349C2—44no—
350C2#1311742011yescharacteristic
351C2#1312329611yescharacteristic
352C2#1312329611yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#2312C2
socleC22×C13C22×C22⋊C4
prime radicalC25×C13C23
cosocleC24×C13C24
hypercenter#2312D13
hypocenterC13#21827
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
3. #13115821C2semidirect
4. #13115820C2semidirect
13. C2×#88132C4semidirect
14. C2×#88132C4semidirect
283. C13#21827semidirect

Maximal subgroups

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

subgroupindex
C2×#117191882
#131174342
#131158212
#131158202
#131149082
C13×#23122
#2182713