Finite Group Databasebeta

← #15830749

Subgroups — #15830749

Order 3328.

974 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128639C211yesmaximal, characteristic
2#13117809C211yesmaximal, characteristic
3#13113401C212yesmaximal, complemented
4#13113370C214yesmaximal, complemented
5#13113357C214yesmaximal, complemented
6#13113336C212yesmaximal, complemented
7C13×#2975C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9#11719503—21no—
10C2×#88178C2214yes—
11#11719248C414yescomplemented
12#11719244—24no—
13D4×Dic26C414yescomplemented
14#11719205—21no—
15#11719188—22no—
16#11719175C2212yes—
17C13×#436—24no—
18C13×#431C2212yes—
19C13×#407C2214yes—
20#11718882—21no—
21#11718872C2212yes—
22C4×C22⋊Dic13C2212yes—
23C4⋊C4×Dic13—21no—
24#11718612—22no—
25#11718597C2211yescharacteristic
26C4×C4⋊Dic13C2211yescharacteristic
27#11718059C2214yes—
28#11718059C2218yes—
29#11718059C2214yes—
30C22×D4×C13D411yescharacteristic
31C23×C4×C13C2312yes—
32C22×Dic26C2×C414yes—
33C2×C13×M16—24no—
34C4×D4×C13C2×C414yes—
35C4×D4×C13D414yes—
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4D412yes—
38C2×C42×C13C2311yescharacteristic
39C2×C22⋊Dic13—24no—
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13—22no—
42D4×Dic13—24no—
43D4×Dic13—24no—
44#88180—22no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13C2×C414yes—
48#88178—22no—
49#88178—24no—
50#88178—24no—
51#88178C2×C418yes—
52#88178C2314yes—
53C2×#6101—24no—
54C2×C4×Dic13—21no—
55C2×C4×Dic13—22no—
56#88144—24no—
57#88142—24no—
58#88132—28no—
59#88132—28no—
60#88124—22no—
61#88123C2×C412yes—
62#88123C2×C412yes—
63C4×Dic26—22no—
64C4×Dic26C2×C414yes—
65C13×C4⋊C8—22no—
66C13×C22⋊C8—24no—
67C13×C22⋊C8C2314yes—
68C4×C8×C13—22no—
69#88071—21no—
70#88071—22no—
71#88071C2311yescharacteristic
72#88071C2311yescharacteristic
73#88071C2312yes—
74#17627—131nomaximal, Sylow
75C24×C13C2×D412yes—
76C2×D4×C13—22no—
77C2×D4×C13—22no—
78C2×D4×C13C22⋊C414yes—
79C22×C4×C13—82no—
80C22×C4×C13C22×C414yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D414yes—
85C22×C4×C13C2411yescharacteristic
86C22×Dic13—21no—
87C22×Dic13—24no—
88C22×Dic13—24no—
89C22×Dic13—22no—
90C22×Dic13—21no—
91C2×Dic26—22no—
92C2×Dic26—24no—
93C2×Dic26—84no—
94C2×Dic26C22×C414yes—
95C13×M16—84no—
96C2×C8×C13—24no—
97C13×C4⋊C4C22⋊C414yes—
98C13×C22⋊C4C22⋊C418yes—
99C42×C13C22×C412yes—
100C42×C13C2×D412yes—
101C22⋊Dic13—28no—
102C22⋊Dic13—24no—
103C22⋊Dic13—44no—
104C22⋊Dic13—82no—
105C4⋊Dic13—22no—
106C4⋊Dic13—22no—
107C4⋊Dic13—22no—
108C4⋊Dic13—24no—
109C4⋊Dic13—42no—
110C4⋊Dic13—42no—
111C4⋊Dic13C22×C414yes—
112#6101—24no—
113#6101—28no—
114#6101—24no—
115C4×Dic13—24no—
116C4×Dic13—42no—
117C4×Dic13—82no—
118#3501—131no—
119#2975D1311yescharacteristic
120#2357—131no—
121#1518—132no—
122#1511—134no—
123#1508—134no—
124#1503—132no—
125C23×C13—22no—
126C23×C13—22no—
127C23×C13—42no—
128C23×C13—42no—
129C23×C13C2×C22⋊C414yes—
130C23×C13C22×D411yescharacteristic
131D4×C13—28no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—41no—
137C2×C4×C13C2×C22⋊C412yes—
138C2×C4×C13C2×C22⋊C414yes—
139C2×C4×C13C2×C22⋊C412yes—
140C2×C4×C13#13712yes—
141C2×C4×C13#13712yes—
142C2×C4×C13C23×C411yescharacteristic
143C2×C4×C13C22×D411yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—24no—
146C2×Dic13—24no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—42no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—42no—
155C2×Dic13—84no—
156C2×Dic13—84no—
157Dic26—44no—
158Dic26—82no—
159Dic26—84no—
160C8×C13—44no—
161#554—134no—
162#554—264no—
163D4×Q8—134no—
164#544—261no—
165#543—262no—
166#533—132no—
167C2×C22⋊Q8—134no—
168#518—261no—
169C2×C4×D4C2×D1311yescharacteristic
170#436—24no—
171#431C2×D1312yes—
172#407C2×D1314yes—
173#390—261no—
174#388—262no—
175#382—131no—
176#381—132no—
177C4×C4⋊C4—131no—
178C4×C4⋊C4—261no—
179C4×C22⋊C4—132no—
180#328—134no—
181#328—134no—
182#328—138no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—24no—
186C22×C13—24no—
187C22×C13—24no—
188C22×C13—82no—
189C22×C13—82no—
190C22×C13C22×C22⋊C411yescharacteristic
191C22×C13C2×#13711yescharacteristic
192C22×C13C2×#13711yescharacteristic
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—24no—
196C4×C13—22no—
197C4×C13#41914yes—
198Dic13—42no—
199Dic13—44no—
200Dic13—44no—
201Dic13—81no—
202Dic13—82no—
203C22×Q8—134no—
204C22×D4D5211yescharacteristic
205C23×C4C22×D1312yes—
206C2×M16—24no—
207C4⋊Q8—132no—
208C4⋊Q8—132no—
209C4⋊Q8—264no—
210#125—264no—
211#125—262no—
212C22⋊Q8—138no—
213C22⋊Q8—134no—
214C22⋊Q8—264no—
215C22⋊Q8—262no—
216C22⋊Q8—264no—
217C22⋊Q8—268no—
218C22⋊Q8—268no—
219C4×Q8—134no—
220C4×Q8—262no—
221C4×D4—264no—
222C4×D4—264no—
223C4×D4C4×D1314yes—
224C4×D4C22⋊D1314yes—
225#117—262no—
226C2×C4⋊C4—134no—
227C2×C4⋊C4—264no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4D5211yescharacteristic
231C2×C22⋊C4—264no—
232C2×C22⋊C4—262no—
233C2×C22⋊C4—262no—
234C2×C22⋊C4D5212yes—
235C2×C42—261no—
236C2×C42—262no—
237C2×C42C22×D1311yescharacteristic
238C4⋊C8—22no—
239C22⋊C8—24no—
240C22⋊C8C22×D1314yes—
241C4×C8—22no—
242#95—131no—
243#95—132no—
244#95—131no—
245#95—262no—
246#95—261no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—44no—
250C2×C13#288311yescharacteristic
251C2×C13C2×#41911yescharacteristic
252C2×C13#290111yescharacteristic
253C24C2×D5212yes—
254C2×Q8—134no—
255C2×Q8—262no—
256C2×Q8—264no—
257C2×Q8—1044no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4#610314yes—
261C22×C4—82no—
262C22×C4—261no—
263C22×C4—264no—
264C22×C4—264no—
265C22×C4—262no—
266C22×C4—261no—
267C22×C4C2×C4×D1314yes—
268C22×C4C2×D5212yes—
269C22×C4C2×D5211yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4C2×C22⋊D1314yes—
272C22×C4C23×D1311yescharacteristic
273M16—84no—
274C2×C8—24no—
275C4⋊C4—134no—
276C4⋊C4—264no—
277C4⋊C4—268no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4—264no—
281C4⋊C4—262no—
282C4⋊C4—264no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C4⋊C4#610314yes—
286C22⋊C4—268no—
287C22⋊C4—264no—
288C22⋊C4—524no—
289C22⋊C4—1042no—
290C22⋊C4#610318yes—
291C42—264no—
292C42—522no—
293C42—1042no—
294C42C2×C4×D1312yes—
295C42C2×C22⋊D1312yes—
296C13#1762711yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—42no—
300C23—42no—
301C23C2×#610314yes—
302C23C22×D5211yescharacteristic
303Q8—524no—
304Q8—1042no—
305Q8—1044no—
306D4—28no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—44no—
312C2×C4—262no—
313C2×C4—264no—
314C2×C4—264no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—522no—
323C2×C4—1044no—
324C2×C4—1044no—
325C2×C4#8816312yes—
326C2×C4#8816312yes—
327C2×C4C2×#610312yes—
328C2×C4C2×#610314yes—
329C2×C4C2×#610312yes—
330C2×C4C22×C4×D1311yescharacteristic
331C2×C4C22×C22⋊D1311yescharacteristic
332C8—44no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—24no—
337C22—24no—
338C22—82no—
339C22—82no—
340C22C2×#8816311yescharacteristic
341C22C2×#8816311yescharacteristic
342C22C22×#610311yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—24no—
347C4—522no—
348C4—524no—
349C4—524no—
350C4—1041no—
351C4—1042no—
352C4#1171878114yes—
353C2—21no—
354C2—21no—
355C2—44no—
356C2#1312329611yescharacteristic
357C2C2×#1171878111yescharacteristic
358C2#1312338111yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2975C2
socleC22×C13C22×C22⋊C4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenter#2975D13
hypocenterC13#17627
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2975

Complements

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

NH ≅ G/Ntype
3. #13113401C2semidirect
4. #13113370C2semidirect
5. #13113357C2semidirect
6. #13113336C2semidirect
11. #11719248C4semidirect
13. D4×Dic26C4semidirect
296. C13#17627semidirect

Maximal subgroups

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

subgroupindex
#131286392
#131178092
#131134012
#131133702
#131133572
#131133362
C13×#29752
#1762713