Finite Group Databasebeta

← #15799632

Subgroups — #15799632

Order 3328.

1934 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88123C211yesmaximal, characteristic
2C2×#11718317C214yesmaximal
3C2×#11718589C211yesmaximal, characteristic
4C2×#11718596C212yesmaximal
5#13113101C214yesmaximal
6#13113066C212yesmaximal
7C4×C13×#95C211yesmaximal, characteristic
8C23×Dic26C2212yes—
9C22×C42×C13C2211yescharacteristic
10C22×C42×C13C2212yes—
11C22×C4⋊Dic13C2212yes—
12C22×C4⋊Dic13C2211yescharacteristic
13C22×C4⋊Dic13C2218yes—
14C22×C4⋊Dic13C2212yes—
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101C2212yes—
17C2×#88123—24no—
18C2×#88123—28no—
19C2×C13×#95C2212yes—
20C2×C13×#95C2212yes—
21C2×#88071C2212yes—
22C2×#88071C2218yes—
23#11718596—28no—
24#11718589—24no—
25#11718317—216no—
26C23×C4×C13C2311yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C23×C4×C13C2314yes—
29C23×C4×C13C2311yescharacteristic
30C23×Dic13C2312yes—
31C23×Dic13C2314yes—
32C23×Dic13C2312yes—
33C22×Dic26—24no—
34C22×Dic26—28no—
35C22×Dic26—28no—
36C22×Dic26—44no—
37C2×C42×C13—24no—
38C2×C42×C13—24no—
39C2×C42×C13—24no—
40C2×C42×C13D414yes—
41C2×C42×C13Q818yescomplemented
42C2×C4⋊Dic13—24no—
43C2×C4⋊Dic13—24no—
44C2×C4⋊Dic13—24no—
45C2×C4⋊Dic13—22no—
46C2×C4⋊Dic13—22no—
47C2×C4⋊Dic13—28no—
48C2×C4⋊Dic13—216no—
49C2×C4⋊Dic13—22no—
50C2×C4⋊Dic13—24no—
51C2×C4⋊Dic13—216no—
52C2×C4⋊Dic13—48no—
53C2×C4⋊Dic13D418yes—
54C2×C4⋊Dic13Q814yescomplemented
55C2×#6101—28no—
56C2×#6101—24no—
57#88123—232no—
58C13×#95D418yes—
59C13×#95Q818yescomplemented
60#88071—216no—
61#88071—24no—
62#15143—131nomaximal, Sylow
63C24×C13C2411yescharacteristic
64C22×C4×C13—22no—
65C22×C4×C13—24no—
66C22×C4×C13—22no—
67C22×C4×C13—24no—
68C22×C4×C13—24no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—24no—
72C22×C4×C13C2×D414yes—
73C22×C4×C13C2×D412yes—
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D418yes—
76C22×C4×C13C2×D412yes—
77C22×C4×C13C2×D414yes—
78C22×C4×C13C2×Q814yes—
79C22×C4×C13C2×Q818yes—
80C22×C4×C13C2×Q818yes—
81C22×C4×C13C2×Q814yes—
82C22×C4×C13C2×Q812yes—
83C22×C4×C13#4112yes—
84C22×Dic13—24no—
85C22×Dic13—22no—
86C22×Dic13—28no—
87C22×Dic13—24no—
88C22×Dic13—24no—
89C22×Dic13—22no—
90C22×Dic13—28no—
91C22×Dic13—24no—
92C22×Dic13—22no—
93C22×Dic13—24no—
94C22×Dic13—24no—
95C22×Dic13—24no—
96C22×Dic13C2×D418yes—
97C22×Dic13C2×Q814yes—
98C2×Dic26—216no—
99C2×Dic26—432no—
100C2×Dic26—48no—
101C2×Dic26—48no—
102C42×C13—28no—
103C42×C13—216no—
104C4⋊Dic13—216no—
105C4⋊Dic13—216no—
106C4⋊Dic13—28no—
107C4⋊Dic13—432no—
108C4⋊Dic13—44no—
109#6101—48no—
110C22×C4⋊Q8—131no—
111C2×#395—134no—
112C2×#389—131no—
113C2×#384—132no—
114#1444—134no—
115C4⋊#95—132no—
116C4×#95D1311yescharacteristic
117C23×C13C22×D411yescharacteristic
118C23×C13C22×D412yes—
119C23×C13C22×D412yes—
120C23×C13C22×Q812yes—
121C23×C13C22×Q811yescharacteristic
122C23×C13C22×Q812yes—
123C23×C13C2×#4111yescharacteristic
124C23×C13H(5,𝔽2)12yes—
125C23×C132−1+412yes—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—28no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—28no—
132C2×C4×C13—28no—
133C2×C4×C13—28no—
134C2×C4×C13—28no—
135C2×C4×C13—28no—
136C2×C4×C13—28no—
137C2×C4×C13—28no—
138C2×C4×C13#12014yes—
139C2×C4×C13C22⋊Q818yes—
140C2×C4×C13C22⋊Q814yes—
141C2×C4×C13#12714yes—
142C2×C4×C13C4⋊Q814yes—
143C2×C4×C13C4⋊Q814yes—
144C2×C4×C13C4⋊Q818yes—
145C2×C4×C13C4⋊Q8116yescomplemented
146C2×Dic13—28no—
147C2×Dic13—24no—
148C2×Dic13—216no—
149C2×Dic13—28no—
150C2×Dic13—42no—
151C2×Dic13—44no—
152C2×Dic13—44no—
153C2×Dic13—42no—
154C2×Dic13—48no—
155C2×Dic13—44no—
156C2×Dic13—42no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—48no—
160Dic26—432no—
161C23×Q8—132no—
162C2×C4⋊Q8—268no—
163C2×C4⋊Q8—264no—
164C22×C4⋊C4—132no—
165C22×C4⋊C4—131no—
166C22×C4⋊C4—132no—
167C22×C4⋊C4—132no—
168C22×C4⋊C4—131no—
169C22×C4⋊C4—138no—
170C22×C42C2×D1312yes—
171C22×C42C2×D1311yescharacteristic
172#395—2616no—
173#389—264no—
174#384—268no—
175C2×#95—138no—
176C2×#95—132no—
177C2×#95C2×D1312yes—
178C2×#95C2×D1312yes—
179C22×C13C2×#12011yescharacteristic
180C22×C13C2×C22⋊Q812yes—
181C22×C13C2×C22⋊Q811yescharacteristic
182C22×C13C2×#12711yescharacteristic
183C22×C13C2×C4⋊Q811yescharacteristic
184C22×C13C2×C4⋊Q811yescharacteristic
185C22×C13C2×C4⋊Q814yes—
186C22×C13C2×C4⋊Q812yes—
187C22×C13#53511yescharacteristic
188C22×C13#53611yescharacteristic
189C22×C13#54414yes—
190C22×C13D4214yes—
191C22×C13#54712yes—
192C22×C13D4×Q814yes—
193C22×C13D4×Q812yes—
194C22×C13#55412yes—
195C22×C13Q8212yes—
196C4×C13—24no—
197C4×C13—24no—
198C4×C13—216no—
199C4×C13#39518yescomplemented
200Dic13—48no—
201Dic13—44no—
202Dic13—82no—
203C22×Q8—268no—
204C22×Q8—264no—
205C22×Q8—268no—
206C22×Q8—524no—
207C23×C4—134no—
208C23×C4—132no—
209C23×C4—132no—
210C23×C4C22×D1311yescharacteristic
211C23×C4C22×D1314yes—
212C23×C4C22×D1311yescharacteristic
213C23×C4C22×D1311yescharacteristic
214C4⋊Q8—2632no—
215C2×C4⋊C4—138no—
216C2×C4⋊C4—134no—
217C2×C4⋊C4—268no—
218C2×C4⋊C4—264no—
219C2×C4⋊C4—264no—
220C2×C4⋊C4—262no—
221C2×C4⋊C4—264no—
222C2×C4⋊C4—262no—
223C2×C4⋊C4—2616no—
224C2×C4⋊C4—264no—
225C2×C4⋊C4—268no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4—2616no—
228C2×C4⋊C4—264no—
229C2×C4⋊C4—528no—
230C2×C42—24no—
231C2×C42—24no—
232C2×C42—24no—
233C2×C42Dic2618yescomplemented
234C2×C42D5214yes—
235#95—264no—
236#95—2616no—
237#95Dic2618yescomplemented
238#95D5218yes—
239C2×C13C2×#39511yescharacteristic
240C2×C13#243311yescharacteristic
241C2×C13#243411yescharacteristic
242C2×C13#244014yes—
243C2×C13#254211yescharacteristic
244C2×C13#255114yes—
245C2×C13#256711yescharacteristic
246C2×C13#266011yescharacteristic
247C2×C13#286811yescharacteristic
248C24C23×D1311yescharacteristic
249C2×Q8—2616no—
250C2×Q8—5232no—
251C2×Q8—528no—
252C2×Q8—528no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—138no—
262C22×C4—134no—
263C22×C4—264no—
264C22×C4—262no—
265C22×C4—268no—
266C22×C4—264no—
267C22×C4—264no—
268C22×C4—262no—
269C22×C4—268no—
270C22×C4—264no—
271C22×C4—262no—
272C22×C4—264no—
273C22×C4—264no—
274C22×C4—264no—
275C22×C4C2×Dic2614yes—
276C22×C4C2×Dic2618yes—
277C22×C4C2×Dic2618yes—
278C22×C4C2×Dic2614yes—
279C22×C4C2×D5212yes—
280C22×C4C2×D5218yes—
281C22×C4C2×D5214yes—
282C22×C4C2×D5212yes—
283C22×C4C2×D5212yes—
284C22×C4D4×D1314yes—
285C22×C4#612912yes—
286C22×C4Q8×D1312yes—
287C4⋊C4—2616no—
288C4⋊C4—2616no—
289C4⋊C4—268no—
290C4⋊C4—5232no—
291C4⋊C4—528no—
292C4⋊C4—524no—
293C42—216no—
294C42—28no—
295C13#1514311yescharacteristic, complemented, Sylow
296C23C22×Dic2612yes—
297C23C22×Dic2612yes—
298C23C22×D5211yescharacteristic
299C23C22×D5212yes—
300C23C2×D4×D1312yes—
301C23C2×#612911yescharacteristic
302C23C2×Q8×D1311yescharacteristic
303C23#8825612yes—
304C23#8825712yes—
305Q8—5232no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—28no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—28no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—268no—
319C2×C4—264no—
320C2×C4—2616no—
321C2×C4—268no—
322C2×C4—522no—
323C2×C4—524no—
324C2×C4—524no—
325C2×C4—522no—
326C2×C4—528no—
327C2×C4—524no—
328C2×C4—522no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—528no—
332C2×C4#8812314yes—
333C2×C4#8812314yes—
334C2×C4#88123116yescomplemented
335C2×C4#8812814yes—
336C2×C4#8813218yes—
337C2×C4#8813614yes—
338C2×C4#8814218yes—
339C2×C4#8815114yes—
340C22C2×#8812311yescharacteristic
341C22C2×#8812314yes—
342C22C2×#8812311yescharacteristic
343C22C2×#8812811yescharacteristic
344C22C2×#8813212yes—
345C22C2×#8813611yescharacteristic
346C22C2×#8814212yes—
347C22C2×#8815111yescharacteristic
348C22#1171922414yes—
349C22#1171923011yescharacteristic
350C22#1171923111yescharacteristic
351C22D4×Dic2614yes—
352C22#1171924812yes—
353C22D4×D5214yes—
354C22#1171926012yes—
355C22Q8×Dic2612yes—
356C22Q8×D5212yes—
357C4—24no—
358C4—24no—
359C4—216no—
360C4—528no—
361C4—524no—
362C4—1042no—
363C4#1171831718yescomplemented
364C2C2×#1171831711yescharacteristic
365C2#1311847311yescharacteristic
366C2#1311848011yescharacteristic
367C2#1311853814yes—
368C2#1311978511yescharacteristic
369C2#1311986214yes—
370C2#1312004411yescharacteristic
371C2#1312095511yescharacteristic
372C2#1312323411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, prime radical, cosocleC24×C13C24
FittingC4×C13×#95C2
hypercenterC4×#95D13
hypocenterC13#15143
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
41. C2×C42×C13Q8semidirect
54. C2×C4⋊Dic13Q8semidirect
59. C13×#95Q8semidirect
145. C2×C4×C13C4⋊Q8semidirect
199. C4×C13#395semidirect
233. C2×C42Dic26semidirect
237. #95Dic26semidirect
295. C13#15143semidirect
334. C2×C4#88123semidirect
363. C4#11718317semidirect

Maximal subgroups

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

subgroupindex
C22×#881232
C2×#117183172
C2×#117185892
C2×#117185962
#131131012
#131130662
C4×C13×#952
#1514313