Finite Group Databasebeta

← #15866885

Subgroups — #15866885

Order 3328.

1474 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719453C211yesmaximal, characteristic
2C2×#11718800C212yesmaximal, complemented
3C2×#11718790C212yesmaximal, complemented
4C2×#11718783C211yesmaximal, characteristic, complemented
5#13115727C214yesmaximal, complemented
6#13115722C214yesmaximal, complemented
7C2×C13×#430C211yesmaximal, characteristic, complemented
8C22×#6127C2212yes—
9C22×C13×M16C2212yes—
10C22×C13×M16C2211yescharacteristic
11C2×#88180C2211yescharacteristic
12C23×#1055C2211yescharacteristic
13#11719453—24no—
14#11719453—24no—
15C2×#88163C414yescomplemented
16C2×#88162C414yescomplemented
17C2×#88158C2214yes—
18C13×#430—24no—
19C2×C13×#108C2214yescomplemented
20#11718800—28no—
21C2×#88065C2218yescomplemented
22#11718790—24no—
23#11718790C2214yescomplemented
24#11718790C2214yescomplemented
25#11718783—24no—
26C2×#88060—24no—
27C2×#88055C2212yescomplemented
28C2×C8×Dic13C2212yescomplemented
29C23×C4×C13C2311yescharacteristic
30C22×C22⋊D13—22no—
31C2×#6127—22no—
32C2×#6127—22no—
33C2×#6127—24no—
34C2×#6127—24no—
35C2×#6127—24no—
36C2×#6127—24no—
37C2×#6127C2×C414yes—
38C2×#6127C2314yes—
39C22×D52C2×C412yes—
40C22×C4×D13—22no—
41C22×Dic26C2×C412yes—
42C2×C13×M16—22no—
43C2×C13×M16—24no—
44C2×C13×M16—24no—
45C2×C13×M16C2×C414yes—
46C2×C13×M16D414yes—
47C2×C13×M16D414yes—
48C2×C13×M16C2314yes—
49C22×C8×C13—22no—
50C22×C8×C13C2312yes—
51C2×C22⋊Dic13—21no—
52#88180—22no—
53#88180D414yes—
54C2×C4⋊Dic13—21no—
55C2×C4×Dic13C2312yes—
56C22×#1055—22no—
57C22×#1055—22no—
58C22×#1055D414yes—
59C22×#1055C2311yescharacteristic
60C22×#1055C2311yescharacteristic
61#88163—216no—
62#88162—216no—
63C2×Dic52C2×C414yes—
64#88158—28no—
65#88158—28no—
66C2×D104C2×C414yes—
67C2×#6095C2×C418yes—
68C13×#108—28no—
69#88065—216no—
70#88060—28no—
71#88060—28no—
72#88055—24no—
73C8×Dic13—24no—
74#21242—131nomaximal, Sylow
75C24×C13#4111yescharacteristic
76C23×D13—22no—
77C22×C4×C13C22×C412yes—
78C22×C4×C13C2×D412yes—
79C22×C4×C13C2×D412yes—
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13#4111yescharacteristic
83C22×C4×C13#4112yes—
84C22×C4×C13C2411yescharacteristic
85C2×C22⋊D13—24no—
86C2×C22⋊D13—24no—
87C2×C22⋊D13—44no—
88C2×C22⋊D13—44no—
89C22×Dic13—22no—
90C22×Dic13—22no—
91#6127—28no—
92#6127—28no—
93#6127—24no—
94#6127—24no—
95#6127—24no—
96#6127—24no—
97#6127—44no—
98#6127—44no—
99#6127—44no—
100#6127—44no—
101C2×D52—24no—
102C2×D52—24no—
103C2×D52—22no—
104C2×D52C22×C414yes—
105C2×C4×D13—24no—
106C2×C4×D13—24no—
107C2×C4×D13—44no—
108C2×C4×D13—44no—
109C2×Dic26—24no—
110C2×Dic26—24no—
111C2×Dic26—22no—
112C2×Dic26C22×C414yes—
113C13×M16—24no—
114C13×M16—24no—
115C13×M16—44no—
116C13×M16C22⋊C4116yes—
117C2×C8×C13—24no—
118C2×C8×C13—44no—
119C2×C8×C13C22×C414yes—
120C2×C8×C13C2×D414yes—
121C2×C8×C13C2×D414yes—
122C22⋊Dic13—24no—
123C4⋊Dic13—24no—
124C4×Dic13—22no—
125C4×Dic13C2×D414yes—
126C2×#1055—28no—
127C2×#1055—21no—
128C2×#1055—21no—
129C2×#1055—21no—
130C2×#1055—21no—
131C2×#1055C2×D412yes—
132C2×#1055C2×D412yes—
133Dic52—28no—
134D104—28no—
135#6095—216no—
136C2×#575—131no—
137C2×#430D1311yescharacteristic, complemented
138C2×#421—132no—
139C2×#408—132no—
140C2×#405—131no—
141#1975—134no—
142#1974—134no—
143C23×C13—42no—
144C23×C13C4×D412yes—
145C23×C13#12112yes—
146C23×C13#12412yes—
147C23×C13C2×#4111yescharacteristic
148C22×D13—24no—
149C22×D13—48no—
150C22×D13—44no—
151C2×C4×C13C2×C22⋊C414yes—
152C2×C4×C13C4×D414yes—
153C2×C4×C13C4×D412yes—
154C2×C4×C13#12114yes—
155C2×C4×C13#12112yes—
156C2×C4×C13#12412yes—
157C2×C4×C13#12714yes—
158C2×C4×C13C23×C411yescharacteristic
159C2×C4×C13C22×D411yescharacteristic
160C2×C4×C13C22×D411yescharacteristic
161C2×C4×C13C22×D411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C22⋊D13—44no—
165C22⋊D13—44no—
166C22⋊D13—48no—
167C2×Dic13—24no—
168C2×Dic13—24no—
169C2×Dic13—44no—
170C2×Dic13—44no—
171D52—24no—
172D52—24no—
173D52—44no—
174C4×D13—44no—
175C4×D13—44no—
176C4×D13—48no—
177Dic26—24no—
178Dic26—24no—
179Dic26—44no—
180C8×C13—44no—
181C8×C13C2×C22⋊C418yes—
182#1055—22no—
183#1055—22no—
184C22×#41—132no—
185#575—264no—
186#575—264no—
187C2×#137—134no—
188C2×AGL(1,ℤ/8)—134no—
189C2×#135—134no—
190C22×M16C2×D1312yes—
191C22×M16C2×D1311yescharacteristic
192C23×C8—131no—
193C2×#117—131no—
194#430—24no—
195C2×#108C2×D1314yescomplemented
196#421—268no—
197C2×#104—138no—
198#408—134no—
199#408—134no—
200#408—264no—
201C2×C22⋊C8—264no—
202#405—264no—
203C2×#97—132no—
204C2×C4×C8—132no—
205C22×C13—22no—
206C22×C13—24no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13#39014yes—
210C22×C13C2×C4×D411yescharacteristic
211C22×C13C2×#12111yescharacteristic
212C22×C13C2×#12411yescharacteristic
213C2×D13—48no—
214C2×D13—44no—
215C2×D13—88no—
216C4×C13#39014yes—
217C4×C13C22×C22⋊C411yescharacteristic
218C4×C13C2×C4×D411yescharacteristic
219C4×C13C2×#12111yescharacteristic
220C4×C13C2×#12711yescharacteristic
221Dic13—44no—
222Dic13—44no—
223C2×#41—134no—
224C2×#41—134no—
225C2×#41—262no—
226C2×#41—262no—
227C2×#41—264no—
228C2×#41—264no—
229C2×#41—264no—
230C2×#41—264no—
231C22×Q8—132no—
232C22×D4—132no—
233C22×D4—262no—
234C23×C4—262no—
235C23×C4C22×D1311yescharacteristic
236#137—2616no—
237AGL(1,ℤ/8)—2616no—
238#135—268no—
239#135—268no—
240C2×Q16—134no—
241C2×SD16—138no—
242C2×D8—134no—
243C2×M16—22no—
244C2×M16—24no—
245C2×M16—24no—
246C2×M16C4×D1314yes—
247C2×M16D5214yes—
248C2×M16C22⋊D1314yes—
249C2×M16C22×D1314yes—
250C22×C8—22no—
251C22×C8—134no—
252C22×C8—131no—
253C22×C8—131no—
254C22×C8—262no—
255C22×C8—262no—
256C22×C8C22×D1312yes—
257#117—134no—
258#117—262no—
259C2×C4⋊C4—261no—
260C2×C22⋊C4—261no—
261C2×C42—132no—
262#108—28no—
263#104—2616no—
264C22⋊C8—268no—
265C22⋊C8—268no—
266#97—264no—
267C4×C8—264no—
268C2×C13—21no—
269C2×C13—24no—
270C2×C13—21no—
271C2×C13C2×#39011yescharacteristic
272C2×C13#295512yes—
273D13—84no—
274C24—262no—
275C24#613111yescharacteristic
276#41—268no—
277#41—268no—
278#41—264no—
279#41—264no—
280#41—264no—
281#41—264no—
282#41—524no—
283#41—524no—
284#41—524no—
285#41—524no—
286C2×Q8—134no—
287C2×Q8—262no—
288C2×Q8—264no—
289C2×Q8—264no—
290C2×D4—134no—
291C2×D4—264no—
292C2×D4—264no—
293C2×D4—264no—
294C2×D4—262no—
295C2×D4—264no—
296C2×D4—524no—
297C2×D4—524no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—264no—
301C22×C4—264no—
302C22×C4—524no—
303C22×C4—524no—
304C22×C4C2×C4×D1312yes—
305C22×C4C2×D5212yes—
306C22×C4D4×D1312yes—
307C22×C4D4×D1312yes—
308C22×C4#613111yescharacteristic
309C22×C4#613112yes—
310C22×C4C2×C22⋊D1312yes—
311C22×C4C23×D1311yescharacteristic
312Q16—268no—
313SD16—2616no—
314D8—268no—
315M16—24no—
316M16—24no—
317M16—44no—
318M16#6103116yes—
319C2×C8—24no—
320C2×C8—44no—
321C2×C8—132no—
322C2×C8—132no—
323C2×C8—268no—
324C2×C8—261no—
325C2×C8—261no—
326C2×C8—261no—
327C2×C8—261no—
328C2×C8C2×C4×D1314yes—
329C2×C8C2×D5214yes—
330C2×C8C2×C22⋊D1314yes—
331C4⋊C4—264no—
332C22⋊C4—264no—
333C42—134no—
334C42—262no—
335C13#2124211yescharacteristic, complemented, Sylow
336C23—42no—
337C23—264no—
338C23—528no—
339C23—524no—
340C23#8814712yes—
341C23#8814912yes—
342C23#8820112yes—
343C23C2×#613111yescharacteristic
344Q8—264no—
345Q8—264no—
346Q8—524no—
347D4—264no—
348D4—264no—
349D4—524no—
350D4—524no—
351D4—528no—
352D4—524no—
353C2×C4—264no—
354C2×C4—264no—
355C2×C4—524no—
356C2×C4—524no—
357C2×C4—524no—
358C2×C4—524no—
359C2×C4—528no—
360C2×C4#8814714yes—
361C2×C4#8814712yes—
362C2×C4#8814914yes—
363C2×C4#8814912yes—
364C2×C4C2×#610314yes—
365C2×C4#8819414yes—
366C2×C4#8820112yes—
367C2×C4C22×C4×D1311yescharacteristic
368C2×C4C22×D5211yescharacteristic
369C2×C4C2×D4×D1311yescharacteristic
370C2×C4C2×D4×D1311yescharacteristic
371C2×C4C2×#613111yescharacteristic
372C2×C4C22×C22⋊D1311yescharacteristic
373C8—44no—
374C8—262no—
375C8—262no—
376C8C2×#610318yes—
377C22—22no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—524no—
382C22—528no—
383C22—1048no—
384C22#1171864914yes—
385C22C2×#8814711yescharacteristic
386C22C2×#8814911yescharacteristic
387C22C2×#8820111yescharacteristic
388C4—524no—
389C4—524no—
390C4#1171864914yes—
391C4C2×#8814711yescharacteristic
392C4C2×#8814911yescharacteristic
393C4C22×#610311yescharacteristic
394C4C2×#8819411yescharacteristic
395C2—21no—
396C2—24no—
397C2—21no—
398C2—1044no—
399C2C2×#1171864911yescharacteristic
400C2#1312373812yes—
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#430C2
socleC22×C13C2×C4×D4
prime radicalC2×#11719453C2
cosocleC22×C4×C13C24
hypercenterC2×#430D13
hypocenterC13#21242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
2. C2×#11718800C2semidirect
3. C2×#11718790C2semidirect
4. C2×#11718783C2semidirect
5. #13115727C2semidirect
6. #13115722C2semidirect
7. C2×C13×#430C2semidirect
15. C2×#88163C4semidirect
16. C2×#88162C4semidirect
19. C2×C13×#108C22semidirect
21. C2×#88065C22semidirect
23. #11718790C22semidirect
24. #11718790C22semidirect
27. C2×#88055C22semidirect
28. C2×C8×Dic13C22semidirect
137. C2×#430D13semidirect
195. C2×#108C2×D13semidirect
335. C13#21242semidirect

Maximal subgroups

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

subgroupindex
C2×#117194532
C2×#117188002
C2×#117187902
C2×#117187832
#131157272
#131157222
C2×C13×#4302
#2124213