Finite Group Databasebeta

← #15896209

Subgroups — #15896209

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×#11718704C212yesmaximal
2C2×#11718589C211yesmaximal, characteristic
3#13116166C212yesmaximal, complemented
4#13116079C212yesmaximal, complemented
5#13115144C212yesmaximal
6#13115104C214yesmaximal, complemented
7#13114904C211yesmaximal, characteristic
8C2×C13×#533C211yesmaximal, characteristic
9C13×#533—28no—
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×C13×#125—21no—
13C2×C13×C22⋊Q8—21no—
14C2×C13×C22⋊Q8C2212yes—
15C2×C4×Q8×C13—21no—
16C2×C4×Q8×C13C2212yes—
17C2×C13×#117—21no—
18C22×C42×C13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101—21no—
22C2×#88075C2214yes—
23C2×#88075C2214yes—
24C2×#88071—21no—
25C2×C22⋊#1055C2212yes—
26#11718704—28no—
27C2×#88048C2214yes—
28#11718589—21no—
29#11718589—21no—
30#11718589C2212yes—
31#11718589C2212yes—
32#11718121C2214yes—
33#11718116C2212yes—
34#11718116C2212yes—
35C22×Q8×C13—21no—
36C22×Q8×C13C2312yes—
37C23×C4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C23×Dic13—21no—
42C13×C4⋊Q8—24no—
43C13×C4⋊Q8—24no—
44C13×#125—28no—
45C13×C22⋊Q8—28no—
46C13×C22⋊Q8—24no—
47C13×C22⋊Q8D418yes—
48C4×Q8×C13—28no—
49C4×Q8×C13—24no—
50C4×Q8×C13—24no—
51C13×#117—28no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—21no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C22⋊C4—22no—
59C2×C42×C13—24no—
60C2×C42×C13—22no—
61C2×C42×C13D411yescharacteristic
62C2×C42×C13D411yescharacteristic
63C2×C42×C13C2311yescharacteristic
64C2×C42×C13C2311yescharacteristic
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13—24no—
67C2×C4⋊Dic13—24no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2312yes—
71C2×#6101—22no—
72C2×#6101—22no—
73C2×#6101—44no—
74C22×#1055C2314yes—
75#88075—28no—
76#88075—28no—
77#88071—22no—
78#88071—22no—
79C22⋊#1055—24no—
80#88048—28no—
81#24063—131nomaximal, Sylow
82C24×C13C2×D411yescharacteristic
83C2×Q8×C13—24no—
84C2×Q8×C13—22no—
85C2×Q8×C13—24no—
86C2×Q8×C13—24no—
87C2×Q8×C13—42no—
88C2×Q8×C13—42no—
89C2×Q8×C13C2×D414yes—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—41no—
99C22×C4×C13SD1614yes—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D414yes—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2411yescharacteristic
107C22×Dic13—24no—
108C22×Dic13—22no—
109C22×Dic13—22no—
110C22×Dic13—42no—
111C22×Dic13—42no—
112C22×Dic13—42no—
113C22×Dic13—42no—
114C22×Dic13—42no—
115C13×C4⋊C4—24no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—28no—
118C13×C4⋊C4—24no—
119C13×C4⋊C4—28no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4C2×D414yes—
122C13×C22⋊C4—28no—
123C42×C13—28no—
124C42×C13—22no—
125C42×C13—22no—
126C42×C13—22no—
127C42×C13—22no—
128C4⋊Dic13—24no—
129C4⋊Dic13—22no—
130C4⋊Dic13—24no—
131C4⋊Dic13—42no—
132C4⋊Dic13#4114yes—
133#6101—44no—
134#6101—44no—
135C2×#1055—24no—
136C2×#1055—24no—
137C2×#1055—24no—
138C2×#533D1311yescharacteristic
139C2×#483—132no—
140C2×#389—131no—
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
154Q8×C13—28no—
155Q8×C13—48no—
156Q8×C13—44no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—28no—
166C2×C4×C13—28no—
167C2×C4×C13—21no—
168C2×C4×C13—24no—
169C2×C4×C13—24no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—44no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13#12012yes—
178C2×C4×C13C2×SD1612yes—
179C2×C4×C13C2×SD1612yes—
180C2×C4×C13#13712yes—
181C2×C4×C13C22×D412yes—
182C2×C4×C13C2×#4112yes—
183C2×C4×C132−1+412yes—
184C2×Dic13—24no—
185C2×Dic13—48no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13—42no—
191C2×Dic13—84no—
192#1055—44no—
193#533—28no—
194C2×C4⋊Q8C2×D1311yescharacteristic
195C2×C4⋊Q8C2×D1311yescharacteristic
196C2×#125—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8C2×D1312yes—
199C2×C4×Q8—21no—
200C2×C4×Q8C2×D1312yes—
201C2×#117—21no—
202C22×C4⋊C4—131no—
203C22×C4⋊C4—131no—
204C22×C4⋊C4—261no—
205C22×C42C2×D1311yescharacteristic
206#483—268no—
207C2×#106—134no—
208C2×#103—134no—
209C2×#103—134no—
210C2×C22⋊C8—132no—
211#389—132no—
212#389—132no—
213#389—261no—
214#389—261no—
215C2×#95—261no—
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—44no—
240C4×C13#54714yes—
241Dic13—44no—
242Dic13—82no—
243C22×Q8—21no—
244C22×Q8C22×D1312yes—
245C23×C4—261no—
246C23×C4—261no—
247C23×C4C22⋊D1311yescharacteristic
248C23×C4C22⋊D1311yescharacteristic
249C23×C4C22×D1311yescharacteristic
250C22×C8—134no—
251C4⋊Q8—24no—
252C4⋊Q8—24no—
253#125—28no—
254C22⋊Q8—28no—
255C22⋊Q8—24no—
256C22⋊Q8C22⋊D1318yes—
257C4×Q8—28no—
258C4×Q8—24no—
259C4×Q8—24no—
260#117—28no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—132no—
267C2×C4⋊C4—132no—
268C2×C4⋊C4—264no—
269C2×C4⋊C4—261no—
270C2×C4⋊C4—264no—
271C2×C4⋊C4—261no—
272C2×C4⋊C4—262no—
273C2×C4⋊C4—262no—
274C2×C4⋊C4—524no—
275C2×C4⋊C4C22×D1312yes—
276C2×C22⋊C4—22no—
277C2×C42—22no—
278C2×C42—24no—
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—262no—
288#95—262no—
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—24no—
299C2×Q8—22no—
300C2×Q8—24no—
301C2×Q8—24no—
302C2×Q8—42no—
303C2×Q8—42no—
304C2×Q8C2×C22⋊D1314yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—41no—
314C22×C4—264no—
315C22×C4—262no—
316C22×C4—262no—
317C22×C4—522no—
318C22×C4—522no—
319C22×C4—522no—
320C22×C4—522no—
321C22×C4—522no—
322C22×C4#610614yes—
323C22×C4C2×C22⋊D1311yescharacteristic
324C22×C4C2×C22⋊D1311yescharacteristic
325C22×C4C2×C22⋊D1311yescharacteristic
326C22×C4C2×C22⋊D1311yescharacteristic
327C22×C4C2×C22⋊D1311yescharacteristic
328C22×C4C2×C22⋊D1314yes—
329C22×C4C23×D1311yescharacteristic
330C2×C8—264no—
331C2×C8—264no—
332C2×C8—264no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—28no—
336C4⋊C4—24no—
337C4⋊C4—28no—
338C4⋊C4—22no—
339C4⋊C4—134no—
340C4⋊C4—264no—
341C4⋊C4—262no—
342C4⋊C4—264no—
343C4⋊C4—524no—
344C4⋊C4—524no—
345C4⋊C4—522no—
346C4⋊C4C2×C22⋊D1314yes—
347C22⋊C4—28no—
348C42—28no—
349C42—22no—
350C42—22no—
351C42—22no—
352C42—22no—
353C13#2406311yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23C2×#610612yes—
359C23#8819612yes—
360C23#8820712yes—
361C23C22×C22⋊D1311yescharacteristic
362Q8—28no—
363Q8—48no—
364Q8—44no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—28no—
374C2×C4—28no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—264no—
386C2×C4—528no—
387C2×C4—522no—
388C2×C4—522no—
389C2×C4—522no—
390C2×C4—522no—
391C2×C4—522no—
392C2×C4—1044no—
393C2×C4C2×#610612yes—
394C2×C4C2×#610612yes—
395C2×C4#8820512yes—
396C2×C4#8820712yes—
397C2×C4#41×D1312yes—
398C2×C4#8825712yes—
399C2×C4C22×C22⋊D1312yes—
400C8—524no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22#1171888814yes—
408C22C22×#610611yescharacteristic
409C22C2×#8819611yescharacteristic
410C22#1171952711yescharacteristic
411C22C2×#8820511yescharacteristic
412C22#1171953011yescharacteristic
413C22#1171953311yescharacteristic
414C22C2×#8820711yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—41no—
420C4—44no—
421C4—44no—
422C4—524no—
423C4—1042no—
424C4#1171952914yes—
425C2—24no—
426C2#1311816711yescharacteristic
427C2C2×#1171888811yescharacteristic
428C2#1312409611yescharacteristic
429C2#1312484011yescharacteristic
430C2#1312496211yescharacteristic
431C2#1312597711yescharacteristic
432C2#1312603811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#533C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#533D13
hypocenterC13#24063
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
3. #13116166C2semidirect
4. #13116079C2semidirect
6. #13115104C2semidirect
353. C13#24063semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117185892
#131161662
#131160792
#131151442
#131151042
#131149042
C2×C13×#5332
#2406313