Finite Group Databasebeta

← #15760492

Subgroups — #15760492

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123832C211yesmaximal, characteristic
2#13113451C211yesmaximal, characteristic, complemented
3#13113400C211yesmaximal, characteristic, complemented
4#13113374C211yesmaximal, characteristic
5#13112735C211yesmaximal, characteristic, complemented
6#13112718C211yesmaximal, characteristic, complemented
7C13×#3181C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#529C2211yescharacteristic
10C13×#501C411yescharacteristic, complemented
11C13×#497C411yescharacteristic, complemented
12C13×#491C411yescharacteristic, complemented
13C13×#489C411yescharacteristic, complemented
14C13×#467—21no—
15C13×#465—21no—
16C13×#441—21no—
17C13×#440—21no—
18C2×C13×#97C2211yescharacteristic
19#11718685—21no—
20#11718672—21no—
21#11718672—21no—
22D4×#1055—21no—
23#11718661—21no—
24#11718658—21no—
25#11718597C2211yescharacteristic
26#11718587C2211yescharacteristic
27#11718586C2211yescharacteristic
28C2×#88043C2211yescharacteristic
29#11718135—21no—
30#11718135—21no—
31#11718130—21no—
32#11718130—21no—
33#11718130—21no—
34#11718129—21no—
35C2×C13×Q16—21no—
36C2×C13×SD16—21no—
37C22×C8×C13—21no—
38C13×C4⋊Q8C2×C411yescharacteristic
39C13×C4⋊Q8C2×C411yescharacteristic
40C13×#126—21no—
41C13×#125—21no—
42C13×#125C2×C411yescharacteristic
43C13×#124C2×C411yescharacteristic
44C13×#123—21no—
45C13×C22⋊Q8—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8D411yescharacteristic
48C13×#121D411yescharacteristic
49C4×Q8×C13—21no—
50C4×Q8×C13—21no—
51C4×Q8×C13D411yescharacteristic
52C4×D4×C13—21no—
53C4×D4×C13D411yescharacteristic
54C13×#117—21no—
55C13×#117—21no—
56C2×C42×C13C2311yescharacteristic
57C2×C4⋊Dic13—21no—
58C2×#6099—21no—
59C22×#1055—21no—
60C22×#1055—21no—
61C13×#107—21no—
62C13×#106—21no—
63C13×#103—21no—
64C13×#103—21no—
65C13×#103—21no—
66C13×#102—21no—
67C13×#97—21no—
68C13×#97C2×C411yescharacteristic
69C13×#97C2×C411yescharacteristic
70#88071—21no—
71#88071—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055D411yescharacteristic
76C22⋊#1055D411yescharacteristic
77C4⋊#1055—21no—
78C4⋊#1055—21no—
79C4⋊#1055—21no—
80C4⋊#1055—21no—
81#88043—21no—
82#88043—21no—
83#88043—21no—
84#88043D411yescharacteristic
85#88043D411yescharacteristic
86C4×#1055—21no—
87C4×#1055—21no—
88#9431—131nomaximal, Sylow
89C2×Q8×C13—21no—
90C2×Q8×C13—21no—
91C2×Q8×C13C22⋊C411yescharacteristic
92C2×D4×C13—21no—
93C2×D4×C13C22⋊C411yescharacteristic
94C22×C4×C13—21no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C22×Dic13—41no—
99C13×Q16—42no—
100C13×SD16—42no—
101C2×C8×C13—21no—
102C2×C8×C13—21no—
103C2×C8×C13—42no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—41no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4C22⋊C411yescharacteristic
115C13×C4⋊C4C22⋊C411yescharacteristic
116C13×C22⋊C4—21no—
117C13×C22⋊C4—21no—
118C13×C22⋊C4—21no—
119C13×C22⋊C4—21no—
120C13×C22⋊C4—21no—
121C13×C22⋊C4—41no—
122C42×C13—21no—
123C42×C13—41no—
124C42×C13C22×C411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13C2×D411yescharacteristic
127C42×C13#4111yescharacteristic
128C4⋊Dic13—81no—
129#6099—42no—
130C2×#1055—21no—
131C2×#1055—21no—
132C2×#1055—21no—
133C2×#1055—21no—
134C2×#1055—42no—
135C2×#1055—42no—
136C2×#1055—41no—
137#3181D1311yescharacteristic
138#2968—131no—
139#1531—131no—
140#1518—131no—
141#1512—131no—
142#1302—131no—
143#1295—131no—
144C23×C13—21no—
145C23×C13#12111yescharacteristic
146Q8×C13—41no—
147Q8×C13—41no—
148Q8×C13—41no—
149Q8×C13—81no—
150D4×C13—41no—
151D4×C13—41no—
152D4×C13—41no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13C2×C22⋊C411yescharacteristic
165C2×C4×C13C4×D411yescharacteristic
166C2×C4×C13C4×D411yescharacteristic
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12111yescharacteristic
169C2×C4×C13#12311yescharacteristic
170C2×Dic13—81no—
171C2×Dic13—81no—
172C2×Dic13—81no—
173C8×C13—22no—
174C8×C13—41no—
175#1055—22no—
176#1055—41no—
177#1055—41no—
178#1055—41no—
179#1055—81no—
180#533C2×D1311yescharacteristic
181#529C2×D1311yescharacteristic
182#501Dic1311yescharacteristic, complemented
183#497Dic1311yescharacteristic, complemented
184#491Dic1311yescharacteristic, complemented
185#489Dic1311yescharacteristic, complemented
186#467—21no—
187#465—21no—
188#446—261no—
189#441—21no—
190#440—21no—
191#435—261no—
192#435—261no—
193C8×D4—261no—
194#433—261no—
195#432—131no—
196#431—131no—
197#405—261no—
198C2×#97—131no—
199C2×#97C2×D1311yescharacteristic
200#382—131no—
201#330—261no—
202#330—261no—
203#328—261no—
204#328—261no—
205#328—261no—
206#327—261no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13#38611yescharacteristic
213C22×C13#47111yescharacteristic
214C22×C13#47311yescharacteristic
215C4×C13—21no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—81no—
225C4×C13—81no—
226Dic13—161no—
227C2×Q16—21no—
228C2×SD16—21no—
229C2×M16—261no—
230C22×C8—21no—
231C22×C8—261no—
232C22×C8—261no—
233C4⋊Q8C2×Dic1311yescharacteristic
234C4⋊Q8C2×Dic1311yescharacteristic
235#126—21no—
236#125—21no—
237#125C2×Dic1311yescharacteristic
238#124C2×Dic1311yescharacteristic
239#123—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8C22⋊D1311yescharacteristic
243#121C22⋊D1311yescharacteristic
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8C22⋊D1311yescharacteristic
247C4×D4—21no—
248C4×D4C22⋊D1311yescharacteristic
249#117—21no—
250#117—21no—
251C2×C4⋊C4—261no—
252C2×C42C22×D1311yescharacteristic
253#107—21no—
254#106—21no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258C4⋊C8—261no—
259#103—21no—
260#103—21no—
261#103—21no—
262#102—21no—
263C22⋊C8—131no—
264C22⋊C8—131no—
265C22⋊C8—261no—
266C22⋊C8—261no—
267C22⋊C8—261no—
268#97—21no—
269#97—131no—
270#97—131no—
271#97—261no—
272#97—261no—
273#97—261no—
274#97C2×Dic1311yescharacteristic
275#97C2×Dic1311yescharacteristic
276C4×C8—261no—
277C4×C8—261no—
278#95—261no—
279#95—261no—
280C2×C13—21no—
281C2×C13—21no—
282C2×C13—81no—
283C2×C13#188411yescharacteristic
284C2×C13#190611yescharacteristic
285C2×C13#190811yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8C22⋊Dic1311yescharacteristic
289C2×D4—21no—
290C2×D4C22⋊Dic1311yescharacteristic
291C22×C4—21no—
292C22×C4—521no—
293C22×C4D4×D1311yescharacteristic
294C22×C4#612911yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296Q16—42no—
297SD16—42no—
298M16—522no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—42no—
302C2×C8—261no—
303C2×C8—261no—
304C2×C8—261no—
305C2×C8—261no—
306C2×C8—522no—
307C2×C8—522no—
308C2×C8—521no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—1041no—
320C4⋊C4C22⋊Dic1311yescharacteristic
321C4⋊C4C22⋊Dic1311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—41no—
330C42D4×D1311yescharacteristic
331C42#612911yescharacteristic
332C42C22×Dic1311yescharacteristic
333C42C2×C22⋊D1311yescharacteristic
334C13#943111yescharacteristic, complemented, Sylow
335C23—21no—
336C23#8819311yescharacteristic
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—81no—
341D4—41no—
342D4—41no—
343D4—41no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—1041no—
356C2×C4—1041no—
357C2×C4—1041no—
358C2×C4D4×Dic1311yescharacteristic
359C2×C4D4×Dic1311yescharacteristic
360C2×C4#8818911yescharacteristic
361C2×C4#8819111yescharacteristic
362C2×C4#8819311yescharacteristic
363C2×C4C2×C22⋊Dic1311yescharacteristic
364C8—22no—
365C8—41no—
366C8—262no—
367C8—521no—
368C8—521no—
369C8—521no—
370C8—1041no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22#1171886411yescharacteristic
377C22#1171886511yescharacteristic
378C22#1171888111yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—2081no—
391C2—21no—
392C2—21no—
393C2—81no—
394C2#1311522011yescharacteristic
395C2#1311533911yescharacteristic
396C2#1311535311yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3181C2
socleC22×C13#386
prime radicalC13×#121D4
cosocleC2×C42×C13C23
hypercenter#3181D13
hypocenterC13#9431
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3181

Complements

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

NH ≅ G/Ntype
2. #13113451C2semidirect
3. #13113400C2semidirect
5. #13112735C2semidirect
6. #13112718C2semidirect
10. C13×#501C4semidirect
11. C13×#497C4semidirect
12. C13×#491C4semidirect
13. C13×#489C4semidirect
182. #501Dic13semidirect
183. #497Dic13semidirect
184. #491Dic13semidirect
185. #489Dic13semidirect
334. C13#9431semidirect

Maximal subgroups

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

subgroupindex
#131238322
#131134512
#131134002
#131133742
#131127352
#131127182
C13×#31812
#943113