Finite Group Databasebeta

← #15762639

Subgroups — #15762639

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114874C211yesmaximal, characteristic, complemented
2#13114612C211yesmaximal, characteristic, complemented
3#13113356C211yesmaximal, characteristic, complemented
4#13113352C211yesmaximal, characteristic
5#13113200C211yesmaximal, characteristic, complemented
6#13113196C211yesmaximal, characteristic
7C2×C13×#465C211yesmaximal, characteristic
8C22×C13×SD16C411yescharacteristic, complemented
9C23×C8×C13C2211yescharacteristic
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×C13×#121C2211yescharacteristic
12C13×#465—21no—
13C13×#465—21no—
14C13×#465—21no—
15C13×#465—21no—
16C2×C13×#106C411yescharacteristic, complemented
17C2×C13×#103C411yescharacteristic, complemented
18C2×C13×#102C411yescharacteristic, complemented
19C4×C22⋊Dic13C2211yescharacteristic
20#11718868C2211yescharacteristic
21#11718868C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23C2×#88059—21no—
24C2×#88055—21no—
25#11718144—21no—
26#11718142—21no—
27#11718130—22no—
28#11718129—22no—
29#11718120—22no—
30#11718117—22no—
31C22×Q8×C13C2×C411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13C2×C411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C2×C13×SD16—21no—
36C2×C13×SD16—21no—
37C2×C13×SD16—42no—
38C22×C8×C13—42no—
39C22×C8×C13C2×C411yescharacteristic
40C22×C8×C13C2×C411yescharacteristic
41C22×C8×C13D411yescharacteristic
42C22×C8×C13D411yescharacteristic
43C22×C8×C13D411yescharacteristic
44C22×C8×C13D411yescharacteristic
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C13×C22⋊Q8—21no—
49C13×#121—21no—
50C13×#121—21no—
51C13×#121—21no—
52C13×#121—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4C2×C411yescharacteristic
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C22⋊Dic13—21no—
59C2×C4×Dic13—21no—
60C2×#6099—21no—
61C2×#6099—21no—
62C22×#1055—21no—
63C13×#106—21no—
64C13×#106—21no—
65C13×#103—21no—
66C13×#103—21no—
67C13×#102—21no—
68C13×#102—21no—
69#88071D412yes—
70C22⋊#1055—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055D412yes—
76#88059—42no—
77#88055—42no—
78#9816—131nomaximal, Sylow
79C24×C13—21no—
80C24×C13#4111yescharacteristic
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—41no—
84C2×Q8×C13—41no—
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—82no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C22×Dic13—22no—
104C13×SD16—42no—
105C13×SD16—42no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13—41no—
110C2×C8×C13—41no—
111C2×C8×C13—41no—
112C2×C8×C13C22⋊C411yescharacteristic
113C2×C8×C13C22⋊C411yescharacteristic
114C2×C8×C13C22⋊C411yescharacteristic
115C2×C8×C13C22⋊C411yescharacteristic
116C13×C4⋊C4—21no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—21no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C22⋊Dic13—42no—
127C4×Dic13—41no—
128C4×Dic13—41no—
129#6099—41no—
130#6099—41no—
131#6099—41no—
132#6099—41no—
133C2×#1055—22no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—41no—
137C2×#1055—41no—
138C2×#465D1311yescharacteristic
139#1810—131no—
140#1752—131no—
141#1508—131no—
142#1507—131no—
143#1472—131no—
144#1471—131no—
145C23×C13—22no—
146C23×C13—22no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—42no—
150C23×C13—81no—
151C23×C13—81no—
152C23×C13C4×D411yescharacteristic
153C23×C13#12111yescharacteristic
154C23×C13#12411yescharacteristic
155Q8×C13—41no—
156Q8×C13—41no—
157Q8×C13—81no—
158D4×C13—41no—
159D4×C13—41no—
160D4×C13—81no—
161D4×C13—82no—
162D4×C13—82no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13C2×C22⋊C411yescharacteristic
179C2×C4×C13C4×D411yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12711yescharacteristic
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C8×C13—21no—
186C8×C13—21no—
187C8×C13—21no—
188C8×C13#9912yes—
189#1055—42no—
190#1055—81no—
191#1055—81no—
192C22×SD16Dic1311yescharacteristic, complemented
193C23×C8C2×D1311yescharacteristic
194C2×C22⋊Q8C2×D1311yescharacteristic
195C2×#121C2×D1311yescharacteristic
196#465—21no—
197#465—21no—
198#465—21no—
199#465—21no—
200C2×#108—261no—
201C2×#106Dic1311yescharacteristic, complemented
202C2×#103Dic1311yescharacteristic, complemented
203C2×#102Dic1311yescharacteristic, complemented
204#407—131no—
205#407—131no—
206C2×C22⋊C8—131no—
207C2×#97—261no—
208C4×C22⋊C4—131no—
209#341—261no—
210#336—261no—
211#328—262no—
212#327—262no—
213#324—262no—
214#323—262no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—21no—
220C22×C13—21no—
221C22×C13—21no—
222C22×C13—44no—
223C22×C13—81no—
224C22×C13—81no—
225C22×C13—81no—
226C22×C13—162no—
227C22×C13#39011yescharacteristic
228C22×C13#44412yes—
229C22×C13#47112yes—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—21no—
233C4×C13—81no—
234C4×C13—81no—
235C4×C13—81no—
236C4×C13C2×#9911yescharacteristic
237C4×C13#41011yescharacteristic
238Dic13—82no—
239C22×Q8C2×Dic1311yescharacteristic
240C22×D4—21no—
241C22×D4C2×Dic1311yescharacteristic
242C23×C4C22×D1311yescharacteristic
243C2×SD16—21no—
244C2×SD16—21no—
245C2×SD16—42no—
246C2×M16—261no—
247C2×M16—261no—
248C22×C8—42no—
249C22×C8—261no—
250C22×C8C2×Dic1311yescharacteristic
251C22×C8C2×Dic1311yescharacteristic
252C22×C8C22⋊D1311yescharacteristic
253C22×C8C22⋊D1311yescharacteristic
254C22×C8C22⋊D1311yescharacteristic
255C22×C8C22⋊D1311yescharacteristic
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#121—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×Dic1311yescharacteristic
266C2×C4⋊C4C2×Dic1311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—261no—
270C2×C42—261no—
271#108—522no—
272#106—21no—
273#106—21no—
274#103—21no—
275#103—21no—
276#102—21no—
277#102—21no—
278C22⋊C8—132no—
279C22⋊C8—261no—
280C22⋊C8—261no—
281C22⋊C8—261no—
282C22⋊C8—261no—
283C22⋊C8—261no—
284#97—522no—
285#95—132no—
286C2×C13—22no—
287C2×C13—22no—
288C2×C13—41no—
289C2×C13—161no—
290C2×C13#196411yescharacteristic
291C2×C13#197511yescharacteristic
292C2×C13#197711yescharacteristic
293C24—21no—
294C24#612911yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—82no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—262no—
312C22×C4D4×D1311yescharacteristic
313C22×C4D4×D1311yescharacteristic
314C22×C4#612911yescharacteristic
315C22×C4C22×Dic1311yescharacteristic
316C22×C4C2×C22⋊D1311yescharacteristic
317C22×C4C2×C22⋊D1311yescharacteristic
318SD16—42no—
319SD16—42no—
320M16—521no—
321M16—521no—
322M16—521no—
323M16—521no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—262no—
331C2×C8—521no—
332C2×C8—521no—
333C2×C8—521no—
334C2×C8—521no—
335C2×C8C22⋊Dic1311yescharacteristic
336C2×C8C22⋊Dic1311yescharacteristic
337C2×C8C22⋊Dic1311yescharacteristic
338C2×C8C22⋊Dic1311yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—522no—
350C42—521no—
351C42—521no—
352C13#981611yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—81no—
359C23—81no—
360C23D4×Dic1311yescharacteristic
361C23#8819011yescharacteristic
362C23#8819211yescharacteristic
363Q8—41no—
364Q8—41no—
365Q8—81no—
366D4—41no—
367D4—41no—
368D4—81no—
369D4—82no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—522no—
387C2×C4—522no—
388C2×C4—522no—
389C2×C4D4×Dic1311yescharacteristic
390C2×C4#8819211yescharacteristic
391C2×C4#8819411yescharacteristic
392C2×C4C2×C22⋊Dic1311yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—522no—
397C8—1041no—
398C8—1041no—
399C8#8807412yes—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—44no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—162no—
412C22#1171883812yes—
413C22#1171885812yes—
414C22#1171888211yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4—1042no—
422C4C2×#8807411yescharacteristic
423C4#1171890111yescharacteristic
424C2—22no—
425C2—22no—
426C2—41no—
427C2—161no—
428C2#1311567311yescharacteristic
429C2#1311573011yescharacteristic
430C2#1311574111yescharacteristic
subgroupG/H
centerC22#11718882
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#465C2
socleC22×C13#390
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenterC2×#465D13
hypocenterC13#9816
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. #13114874C2semidirect
2. #13114612C2semidirect
3. #13113356C2semidirect
5. #13113200C2semidirect
8. C22×C13×SD16C4semidirect
16. C2×C13×#106C4semidirect
17. C2×C13×#103C4semidirect
18. C2×C13×#102C4semidirect
192. C22×SD16Dic13semidirect
201. C2×#106Dic13semidirect
202. C2×#103Dic13semidirect
203. C2×#102Dic13semidirect
352. C13#9816semidirect

Maximal subgroups

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

subgroupindex
#131148742
#131146122
#131133562
#131133522
#131132002
#131131962
C2×C13×#4652
#981613