Finite Group Databasebeta

← #16068994

Subgroups — #16068994

Order 3328.

2782 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×#11719175C211yesmaximal, characteristic, complemented
2C2×#11719182C211yesmaximal, characteristic
3#13123214C212yesmaximal, complemented
4#13123208C214yesmaximal, complemented
5#13123193C212yesmaximal, complemented
6#13123137C218yesmaximal, complemented
7C4×#88129C218yesmaximal, complemented
8#13117326C214yesmaximal, complemented
9C2×C43×C13C211yesmaximal, characteristic, complemented
10C22×#6127C2212yes—
11C22×C42×C13C2214yes—
12C22×C42×C13C2212yes—
13C22×C42×C13C2211yescharacteristic
14C2×#88184C2214yes—
15C2×#88180C2212yes—
16C2×#88178C2214yes—
17#11719182—28no—
18C2×#88129C2218yes—
19C2×#88129C2212yes—
20C2×#88128C2211yescharacteristic
21C2×C4×D52C2214yes—
22#11719175—28no—
23C2×#88124C2212yes—
24C2×#88123C2212yes—
25C2×#88123C2211yescharacteristic
26C2×C4×Dic26C2214yes—
27C43×C13C2212yes—
28C43×C13C2212yes—
29C43×C13C2214yes—
30#11718874C22116yes—
31#11718601C22132yes—
32#11718600C2218yes—
33#11718600C2218yes—
34C4×#6103C22116yes—
35#11718597C2218yes—
36#11718590C2218yes—
37#11718590C2218yes—
38C23×C4×C13C2314yes—
39C23×C4×C13C2312yes—
40C23×C4×C13C2311yescharacteristic
41C22×C22⋊D13C2314yes—
42C2×#6127—28no—
43C2×#6127—216no—
44C22×D52C2314yes—
45C22×D52C2312yes—
46C22×C4×D13C2314yes—
47C22×Dic26C2314yes—
48C22×Dic26C2312yes—
49C2×C42×C13—28no—
50C2×C42×C13—216no—
51C2×C42×C13D418yes—
52C2×C42×C13C2314yes—
53C2×C42×C13C2314yes—
54C2×C42×C13C2314yes—
55C2×C42×C13C2318yes—
56C2×C42×C13C2312yes—
57C2×C42×C13C2311yescharacteristic
58C2×C42×C13C2311yescharacteristic
59C2×C42×C13C2314yes—
60C2×C22⋊Dic13C2314yes—
61#88184—216no—
62C2×#6103C2318yes—
63C2×#6103C23132yes—
64#88180—28no—
65C2×C4⋊Dic13C2314yes—
66C2×C4⋊Dic13C2314yes—
67C2×C4⋊Dic13C2314yes—
68#88178—216no—
69C2×#6101C2318yes—
70C2×C4×Dic13C2314yes—
71#88129—28no—
72#88129—232no—
73#88128—24no—
74C4×D52—216no—
75#88124—28no—
76#88123—28no—
77#88123—24no—
78C4×Dic26—216no—
79#88071C23132yes—
80#36639—131nomaximal, Sylow
81C24×C13C2411yescharacteristic
82C23×D13C2414yes—
83C22×C4×C13—28no—
84C22×C4×C13—216no—
85C22×C4×C13—28no—
86C22×C4×C13C2×D418yes—
87C22×C4×C13C2×D414yes—
88C22×C4×C13#4118yes—
89C22×C4×C13C2412yes—
90C22×C4×C13C2418yes—
91C22×C4×C13C2411yescharacteristic
92C22×C4×C13C2412yes—
93C22×C4×C13C2411yescharacteristic
94C2×C22⋊D13—28no—
95C2×C22⋊D13—216no—
96C22×Dic13C2414yes—
97C22×Dic13C2418yes—
98#6127—432no—
99C2×D52—28no—
100C2×D52—24no—
101C2×D52—216no—
102C2×D52—28no—
103C2×C4×D13—28no—
104C2×C4×D13—216no—
105C2×Dic26—28no—
106C2×Dic26—24no—
107C2×Dic26—216no—
108C2×Dic26—28no—
109C42×C13—216no—
110C42×C13—28no—
111C42×C13—28no—
112C42×C13—28no—
113C42×C13C2×D418yes—
114C42×C13C2×D414yes—
115C42×C13C2×D414yes—
116C42×C13#41116yescomplemented
117C22⋊Dic13—28no—
118#6103—216no—
119#6103—264no—
120C4⋊Dic13—28no—
121C4⋊Dic13—28no—
122C4⋊Dic13—28no—
123#6101—216no—
124C4×Dic13—28no—
125C2×#533—131no—
126C2×#532—131no—
127#2862—132no—
128#2861—134no—
129#2858—132no—
130#2850—138no—
131C4×#124—138no—
132#2297—134no—
133C2×C43D1311yescharacteristic, complemented
134C23×C13—24no—
135C23×C13C22×D412yes—
136C23×C13C2×#4114yes—
137C23×C13C2511yescharacteristic
138C22×D13—24no—
139C22×D13—216no—
140C22×D13—28no—
141C2×C4×C13—232no—
142C2×C4×C13—24no—
143C2×C4×C13—28no—
144C2×C4×C13—28no—
145C2×C4×C13—216no—
146C2×C4×C13#124116yescomplemented
147C2×C4×C13C22×D414yes—
148C2×C4×C13C22×D412yes—
149C2×C4×C13C22×D412yes—
150C2×C4×C13C22×D414yes—
151C2×C4×C13C2×#41116yes—
152C2×C4×C13C2×#4114yes—
153C2×C4×C13C2×#4114yes—
154C2×C4×C13C2×#4118yes—
155C22⋊D13—416no—
156C2×Dic13—28no—
157C2×Dic13—24no—
158C2×Dic13—216no—
159C2×Dic13—28no—
160D52—48no—
161D52—416no—
162C4×D13—416no—
163Dic26—48no—
164Dic26—416no—
165C22×#41—132no—
166#533—268no—
167#532—268no—
168C2×C4⋊Q8—132no—
169C2×C4⋊Q8—131no—
170C2×#127—131no—
171C2×#125—132no—
172C2×#124—138no—
173C2×#124—132no—
174C2×C22⋊Q8—134no—
175C2×#121—134no—
176C2×C4×Q8—134no—
177C2×C4×D4—134no—
178C2×#117—132no—
179C22×C42C2×D1314yes—
180C22×C42C2×D1312yes—
181C22×C42C2×D1311yescharacteristic
182#391—138no—
183#391—138no—
184#390—138no—
185#390—138no—
186#388—1332no—
187#386—1316no—
188#382—138no—
189C4×C22⋊C4—1316no—
190C43C2×D1312yes—
191C43C2×D1312yes—
192C43C2×D1314yes—
193C22×C13—24no—
194C22×C13—28no—
195C22×C13C2×#12414yes—
196C22×C13C23×D411yescharacteristic
197C22×C13C22×#4112yes—
198C22×C13C22×#4114yes—
199C2×D13—44no—
200C2×D13—48no—
201C2×D13—416no—
202C4×C13—24no—
203C4×C13—216no—
204C4×C13C2×#12414yes—
205C4×C13C2×#12414yes—
206C4×C13#53218yes—
207Dic13—44no—
208Dic13—48no—
209C2×#41—268no—
210C2×#41—2616no—
211C22×Q8—134no—
212C22×Q8—132no—
213C22×D4—134no—
214C22×D4—134no—
215C22×D4—132no—
216C23×C4—134no—
217C23×C4C22×D1314yes—
218C23×C4C22×D1312yes—
219C23×C4C22×D1311yescharacteristic
220C4⋊Q8—264no—
221C4⋊Q8—268no—
222#127—264no—
223#125—268no—
224#124—268no—
225#124—2632no—
226C22⋊Q8—2616no—
227#121—2616no—
228C4×Q8—2616no—
229C4×D4—2616no—
230#117—268no—
231C2×C4⋊C4—134no—
232C2×C4⋊C4—134no—
233C2×C4⋊C4—138no—
234C2×C4⋊C4—134no—
235C2×C22⋊C4—134no—
236C2×C22⋊C4—138no—
237C2×C22⋊C4—1332no—
238C2×C42—28no—
239C2×C42—216no—
240C2×C42—134no—
241C2×C42D5218yes—
242C2×C42C22×D1318yes—
243C2×C42C22×D1314yes—
244C2×C42C22×D1314yes—
245C2×C42C22×D1314yes—
246C2×C42C22×D1311yescharacteristic
247C2×C42C22×D1311yescharacteristic
248C2×C42C22×D1312yes—
249C2×C42C22×D1314yes—
250#95—1332no—
251C2×C13—24no—
252C2×C13C22×#12411yescharacteristic
253C2×C13C2×#53212yes—
254C2×C13#344414yes—
255D13—84no—
256C24—134no—
257C24C23×D1311yescharacteristic
258#41—5232no—
259C2×Q8—268no—
260C2×Q8—264no—
261C2×Q8—2616no—
262C2×Q8—268no—
263C2×D4—268no—
264C2×D4—2616no—
265C2×D4—268no—
266C2×D4—264no—
267C2×D4—2616no—
268C2×D4—268no—
269C22×C4—28no—
270C22×C4—216no—
271C22×C4—28no—
272C22×C4—134no—
273C22×C4—138no—
274C22×C4—268no—
275C22×C4—2616no—
276C22×C4C2×D5218yes—
277C22×C4C2×D5214yes—
278C22×C4#612718yes—
279C22×C4C23×D1312yes—
280C22×C4C23×D1318yes—
281C22×C4C23×D1311yescharacteristic
282C22×C4C23×D1312yes—
283C22×C4C23×D1311yescharacteristic
284C4⋊C4—268no—
285C4⋊C4—268no—
286C4⋊C4—2616no—
287C4⋊C4—268no—
288C22⋊C4—268no—
289C22⋊C4—2616no—
290C22⋊C4—2664no—
291C42—216no—
292C42—28no—
293C42—28no—
294C42—28no—
295C42—268no—
296C42C2×D5218yes—
297C42C2×D5214yes—
298C42C2×D5214yes—
299C42#6127116yescomplemented
300C13#3663911yescharacteristic, complemented, Sylow
301C23—24no—
302C23—264no—
303C23—2616no—
304C23—268no—
305C23C22×D5212yes—
306C23C2×#612714yes—
307C23C24×D1311yescharacteristic
308Q8—528no—
309Q8—5216no—
310D4—5216no—
311D4—528no—
312D4—5216no—
313C2×C4—232no—
314C2×C4—24no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—216no—
318C2×C4—268no—
319C2×C4—264no—
320C2×C4—2616no—
321C2×C4—268no—
322C2×C4—5216no—
323C2×C4#88129116yescomplemented
324C2×C4C22×D5214yes—
325C2×C4C22×D5212yes—
326C2×C4C22×D5212yes—
327C2×C4C22×D5214yes—
328C2×C4C2×#6127116yes—
329C2×C4C2×#612714yes—
330C2×C4C2×#612714yes—
331C2×C4C2×#612718yes—
332C22—24no—
333C22—28no—
334C22—524no—
335C22—528no—
336C22—5216no—
337C22C2×#8812914yes—
338C22C23×D5211yescharacteristic
339C22C22×#612712yes—
340C22C22×#612714yes—
341C4—24no—
342C4—216no—
343C4—524no—
344C4—528no—
345C4C2×#8812914yes—
346C4C2×#8812914yes—
347C4#1171918218yes—
348C2—24no—
349C2—1044no—
350C2C22×#8812911yescharacteristic
351C2C2×#1171918212yes—
352C2#1312813214yes—
subgroupG/H
centerC22×C4C23×D13
commutator, socle, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C43×C13C2
prime radicalC2×#11719182C2
hypercenterC2×C43D13
hypocenterC13#36639
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
3. #13123214C2semidirect
4. #13123208C2semidirect
5. #13123193C2semidirect
6. #13123137C2semidirect
7. C4×#88129C2semidirect
8. #13117326C2semidirect
9. C2×C43×C13C2semidirect
116. C42×C13#41semidirect
133. C2×C43D13semidirect
146. C2×C4×C13#124semidirect
299. C42#6127semidirect
300. C13#36639semidirect
323. C2×C4#88129semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
C2×#117191822
#131232142
#131232082
#131231932
#131231372
C4×#881292
#131173262
C2×C43×C132
#3663913