Finite Group Databasebeta

← #15896213

Subgroups — #15896213

Order 3328.

1144 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic
2C2×#11718632C212yesmaximal
3#13116169C212yesmaximal, complemented
4#13116082C212yesmaximal, complemented
5#13115143C212yesmaximal
6#13115103C214yesmaximal, complemented
7#13114904C211yesmaximal, characteristic
8C2×C13×#389C211yesmaximal, characteristic
9C22×C13×C4⋊C4—21no—
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C42×C13C2211yescharacteristic
13C2×#88180—21no—
14C2×#88178—21no—
15C2×#88178C2212yes—
16#11719175—28no—
17C2×#88124—21no—
18C2×#88123C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C2×C4×Dic26—21no—
21C2×C4×Dic26C2212yes—
22C13×#389—21no—
23C13×#389—21no—
24C13×#389C2212yes—
25C13×#389C2212yes—
26C2×C13×#95—21no—
27C2×C22⋊#1055C2212yes—
28#11718632—28no—
29C2×#88050C2214yes—
30C2×#88050C2214yes—
31C2×#88048C2214yes—
32#11718121C2214yes—
33#11718116C2212yes—
34#11718116C2212yes—
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C22×Dic26—21no—
41C22×Dic26C2312yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—24no—
44C2×C13×C4⋊C4—24no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—22no—
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4—44no—
49C2×C13×C4⋊C4C2312yes—
50C2×C13×C4⋊C4C2312yes—
51C2×C42×C13—24no—
52C2×C42×C13D411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C2×C42×C13C2311yescharacteristic
55C2×C42×C13C2311yescharacteristic
56C2×C22⋊Dic13—22no—
57#88180—28no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13C2312yes—
62#88178—28no—
63#88178—24no—
64#88178D418yes—
65C2×#6101—22no—
66C2×#6101—22no—
67C2×C4×Dic13—22no—
68C22×#1055C2314yes—
69#88124—28no—
70#88123—24no—
71#88123—24no—
72C4×Dic26—28no—
73C4×Dic26—24no—
74C4×Dic26—24no—
75C13×#95—22no—
76C13×#95—22no—
77C22⋊#1055—24no—
78#88050—28no—
79#88050—28no—
80#88048—28no—
81#24063—131nomaximal, Sylow
82C24×C13C2×D411yescharacteristic
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—22no—
86C22×C4×C13—22no—
87C22×C4×C13—24no—
88C22×C4×C13—22no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—41no—
93C22×C4×C13—42no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—42no—
97C22×C4×C13—42no—
98C22×C4×C13SD1614yes—
99C22×C4×C13C2×D414yes—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2411yescharacteristic
106C22×Dic13—22no—
107C22×Dic13—22no—
108C2×Dic26—24no—
109C2×Dic26—24no—
110C2×Dic26—24no—
111C2×Dic26—22no—
112C2×Dic26—42no—
113C2×Dic26—42no—
114C2×Dic26C2×D414yes—
115C13×C4⋊C4—24no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4—24no—
118C13×C4⋊C4—42no—
119C13×C4⋊C4—44no—
120C13×C4⋊C4—44no—
121C13×C4⋊C4#4114yes—
122C42×C13—22no—
123C42×C13—22no—
124C42×C13—22no—
125C42×C13—22no—
126C22⋊Dic13—28no—
127C4⋊Dic13—24no—
128C4⋊Dic13—24no—
129C4⋊Dic13—24no—
130C4⋊Dic13—22no—
131C4⋊Dic13C2×D414yes—
132#6101—28no—
133#6101—28no—
134C4×Dic13—28no—
135C2×#1055—24no—
136C2×#1055—24no—
137C2×#1055—24no—
138C2×#533—131no—
139C2×#483—132no—
140C2×#389D1311yescharacteristic
141#2058—132no—
142#2043—132no—
143#1872—132no—
144#1865—134no—
145#1817—131no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—21no—
149C23×C13—21no—
150C23×C13#12012yes—
151C23×C13C2×SD1612yes—
152C23×C13#13712yes—
153C23×C13C22×D411yescharacteristic
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—28no—
163C2×C4×C13—28no—
164C2×C4×C13—21no—
165C2×C4×C13—24no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—44no—
169C2×C4×C13—48no—
170C2×C4×C13—42no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—84no—
176C2×C4×C13#12012yes—
177C2×C4×C13C2×SD1612yes—
178C2×C4×C13C2×SD1612yes—
179C2×C4×C13#13712yes—
180C2×C4×C13C22×D412yes—
181C2×C4×C13C2×#4112yes—
182C2×C4×C132−1+412yes—
183C2×Dic13—24no—
184C2×Dic13—24no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189Dic26—28no—
190Dic26—48no—
191Dic26—44no—
192#1055—44no—
193#533—268no—
194C2×C4⋊Q8—131no—
195C2×C4⋊Q8—131no—
196C2×#125—261no—
197C2×C22⋊Q8—132no—
198C2×C22⋊Q8—261no—
199C2×C4×Q8—132no—
200C2×C4×Q8—261no—
201C2×#117—261no—
202C22×C4⋊C4—21no—
203C22×C4⋊C4C2×D1311yescharacteristic
204C22×C4⋊C4C2×D1311yescharacteristic
205C22×C42C2×D1311yescharacteristic
206#483—268no—
207C2×#106—134no—
208C2×#103—134no—
209C2×#103—134no—
210C2×C22⋊C8—132no—
211#389—21no—
212#389—21no—
213#389C2×D1312yes—
214#389C2×D1312yes—
215C2×#95—21no—
216#340—134no—
217#336—132no—
218#336—132no—
219C22×C13—22no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—22no—
224C22×C13—22no—
225C22×C13#44814yes—
226C22×C13C2×#12011yescharacteristic
227C22×C13#52511yescharacteristic
228C22×C13#53611yescharacteristic
229C22×C13C22×SD1611yescharacteristic
230C22×C13C2×#13711yescharacteristic
231C22×C13C2×#13711yescharacteristic
232C22×C13#57511yescharacteristic
233C4×C13—22no—
234C4×C13—22no—
235C4×C13—22no—
236C4×C13—22no—
237C4×C13—44no—
238C4×C13—41no—
239C4×C13—82no—
240C4×C13#54714yes—
241Dic13—44no—
242Dic13—44no—
243C22×Q8—132no—
244C22×Q8—261no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4C22⋊D1311yescharacteristic
248C23×C4C22⋊D1311yescharacteristic
249C23×C4C22×D1311yescharacteristic
250C22×C8—134no—
251C4⋊Q8—264no—
252C4⋊Q8—264no—
253#125—268no—
254C22⋊Q8—138no—
255C22⋊Q8—268no—
256C22⋊Q8—264no—
257C4×Q8—264no—
258C4×Q8—264no—
259C4×Q8—268no—
260#117—268no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4—132no—
269C2×C4⋊C4—261no—
270C2×C4⋊C4—261no—
271C2×C4⋊C4—262no—
272C2×C4⋊C4—262no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4C22×D1312yes—
275C2×C4⋊C4C22×D1312yes—
276C2×C22⋊C4—262no—
277C2×C42—24no—
278C2×C42—262no—
279C2×C42C22⋊D1311yescharacteristic
280C2×C42C22⋊D1311yescharacteristic
281C2×C42C22×D1311yescharacteristic
282C2×C42C22×D1311yescharacteristic
283#106—268no—
284#103—268no—
285#103—268no—
286C22⋊C8—264no—
287#95—22no—
288#95—22no—
289C2×C13—24no—
290C2×C13#240611yescharacteristic
291C2×C13C2×#44811yescharacteristic
292C2×C13#300711yescharacteristic
293C2×C13#310111yescharacteristic
294C2×C13#311311yescharacteristic
295C2×C13#322911yescharacteristic
296C2×C13#323611yescharacteristic
297C24C2×C22⋊D1311yescharacteristic
298C2×Q8—134no—
299C2×Q8—264no—
300C2×Q8—262no—
301C2×Q8—264no—
302C2×Q8—264no—
303C2×Q8—522no—
304C2×Q8—522no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—262no—
321C22×C4—262no—
322C22×C4#610514yes—
323C22×C4D4×D1314yes—
324C22×C4C2×C22⋊D1311yescharacteristic
325C22×C4C2×C22⋊D1311yescharacteristic
326C22×C4C2×C22⋊D1311yescharacteristic
327C22×C4C2×C22⋊D1311yescharacteristic
328C22×C4C2×C22⋊D1311yescharacteristic
329C22×C4C23×D1311yescharacteristic
330C2×C8—264no—
331C2×C8—264no—
332C2×C8—264no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—24no—
336C4⋊C4—44no—
337C4⋊C4—44no—
338C4⋊C4—42no—
339C4⋊C4—134no—
340C4⋊C4—264no—
341C4⋊C4—264no—
342C4⋊C4—268no—
343C4⋊C4—264no—
344C4⋊C4—268no—
345C4⋊C4—262no—
346C4⋊C4#612714yes—
347C22⋊C4—268no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—268no—
353C13#2406311yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23C2×#610512yes—
359C23#8819112yes—
360C23#8820512yes—
361C23C22×C22⋊D1311yescharacteristic
362Q8—268no—
363Q8—528no—
364Q8—524no—
365C2×C4—28no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—28no—
375C2×C4—24no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—44no—
380C2×C4—48no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—84no—
387C2×C4—264no—
388C2×C4—264no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4C2×#610512yes—
394C2×C4C2×#610512yes—
395C2×C4#8819112yes—
396C2×C4#8819612yes—
397C2×C4C2×#612712yes—
398C2×C4C2×D4×D1312yes—
399C2×C4#8825412yes—
400C8—524no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22#1171870114yes—
408C22#1171949611yescharacteristic
409C22C22×#610511yescharacteristic
410C22C2×#8819111yescharacteristic
411C22C2×#8819611yescharacteristic
412C22#1171952111yescharacteristic
413C22#1171952711yescharacteristic
414C22C2×#8820511yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—44no—
420C4—41no—
421C4—82no—
422C4—524no—
423C4—524no—
424C4#1171921214yes—
425C2—24no—
426C2#1311817111yescharacteristic
427C2C2×#1171870111yescharacteristic
428C2#1312409411yescharacteristic
429C2#1312484411yescharacteristic
430C2#1312496611yescharacteristic
431C2#1312598011yescharacteristic
432C2#1312604211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#389C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#389D13
hypocenterC13#24063
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. #13116169C2semidirect
4. #13116082C2semidirect
6. #13115103C2semidirect
353. C13#24063semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
C2×#117186322
#131161692
#131160822
#131151432
#131151032
#131149042
C2×C13×#3892
#2406313