Finite Group Databasebeta

← #13125790

Subgroups — #13125790

Order 1664.

394 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719537C211yesmaximal, characteristic
2#11719327C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718846C211yesmaximal, characteristic, complemented
6#11718842C211yesmaximal, characteristic, complemented
7#11718836C211yesmaximal, characteristic, complemented
8#11718827C211yesmaximal, characteristic, complemented
9#11718708C211yesmaximal, characteristic, complemented
10#11718459C211yesmaximal, characteristic, complemented
11#11718453C211yesmaximal, characteristic, complemented
12#11718428C211yesmaximal, characteristic, complemented
13#11718421C211yesmaximal, characteristic, complemented
14#11718394C211yesmaximal, characteristic, complemented
15#11718379C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21#88201C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88198C2211yescharacteristic
24#88198C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26C2×#6107C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28#88194C2211yescharacteristic
29#88193—21no—
30#88193—21no—
31#88190C2211yescharacteristic
32C2×#6105C2211yescharacteristic
33C4×C22⋊D13—21no—
34C4×C22⋊D13—21no—
35#88178C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×Dic52C2211yescharacteristic
38C2×#6095C2211yescharacteristic
39#88143—21no—
40#88142C2211yescharacteristic
41#88141—21no—
42#88141C2211yescharacteristic
43#88132—21no—
44#88131—21no—
45C13×#103C2211yescharacteristic
46C13×#102C2211yescharacteristic
47C13×C22⋊C8C2211yescharacteristic
48#88075C2211yescharacteristic
49#88072C2211yescharacteristic
50C22⋊#1055C2211yescharacteristic
51#88061C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88050C2211yescharacteristic
58#88049C2211yescharacteristic
59C13×#41—41no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C22×Dic13D411yescharacteristic
71C22×Dic13D411yescharacteristic
72#6127—41no—
73#6127—41no—
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C2×Dic26C2311yescharacteristic
79C13×Q16—41no—
80C13×SD16—41no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4—21no—
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89#6107—41no—
90#6107—41no—
91#6106—41no—
92#6105—41no—
93#6103—21no—
94#6103—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13D411yescharacteristic
107C4×Dic13D411yescharacteristic
108C4×Dic13C2311yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112Dic52—41no—
113#6095—41no—
114#3210—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13C2×D411yescharacteristic
117C22×D13—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—42no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—42no—
134C22⋊D13—42no—
135C22⋊D13—42no—
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C2×Dic13C2×D411yescharacteristic
145D52—21no—
146D52—21no—
147C4×D13—42no—
148Dic26—21no—
149Dic26—21no—
150Dic26—21no—
151Dic26—21no—
152Dic26—42no—
153C8×C13—21no—
154C8×C13—21no—
155#1055—21no—
156#1055—21no—
157#533—131no—
158#532—131no—
159#494—131no—
160#492—131no—
161#487—131no—
162#486—131no—
163#464—131no—
164#464—131no—
165#464—131no—
166#464—131no—
167#452—131no—
168#452—131no—
169#452—131no—
170#452D1311yescharacteristic, complemented
171#431—131no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13C22×D411yescharacteristic
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—41no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13H(5,𝔽2)11yescharacteristic
187C4×C13H(5,𝔽2)11yescharacteristic
188Dic13—21no—
189Dic13—21no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13#13512yes—
194Dic13#13712yes—
195C2×#41—131no—
196C2×#41C2×D1311yescharacteristic
197C2×Q16—131no—
198C2×Q16—131no—
199C2×Q16—131no—
200C2×Q16C2×D1311yescharacteristic
201C2×SD16—131no—
202C2×SD16—131no—
203C2×SD16—131no—
204C2×SD16C2×D1311yescharacteristic
205C4⋊Q8—131no—
206C4⋊Q8—131no—
207C4⋊Q8—131no—
208#127—131no—
209#125—261no—
210#124—131no—
211#124—131no—
212C22⋊Q8—131no—
213C22⋊Q8—261no—
214C22⋊Q8C2×D1311yescharacteristic
215#121—261no—
216#121—261no—
217C4×Q8—131no—
218C4×Q8—131no—
219C4×Q8—261no—
220C4×D4—261no—
221C4×D4—261no—
222#117—261no—
223C2×C42—131no—
224C4⋊C8—131no—
225C4⋊C8—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103C2×D1311yescharacteristic
230#102—131no—
231#102—131no—
232#102—131no—
233#102C2×D1311yescharacteristic
234C22⋊C8—131no—
235C22⋊C8C2×D1311yescharacteristic
236C4×C8—131no—
237C4×C8—131no—
238C2×C13—41no—
239C2×C13—81no—
240C2×C13#53511yescharacteristic
241C2×C13C2×#13511yescharacteristic
242C2×C13C2×#13711yescharacteristic
243D13—81no—
244#41—41no—
245#41—41no—
246#41—521no—
247#41—521no—
248C2×Q8—131no—
249C2×Q8—131no—
250C2×Q8—261no—
251C2×Q8C22×D1311yescharacteristic
252C2×Q8C22×D1311yescharacteristic
253C2×D4—21no—
254C2×D4—131no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4C22×D1311yescharacteristic
259C22×C4—21no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—261no—
263C22×C4C22×D1311yescharacteristic
264Q16—41no—
265Q16—521no—
266Q16—521no—
267Q16—521no—
268SD16—41no—
269SD16—521no—
270SD16—521no—
271SD16—521no—
272C2×C8—131no—
273C2×C8—131no—
274C2×C8C22×D1311yescharacteristic
275C2×C8C22×D1311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—131no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—131no—
294C42—131no—
295C42—131no—
296C42—131no—
297C42—261no—
298C42—261no—
299C13#321011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—261no—
302C23D4×D1311yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—261no—
308Q8—261no—
309Q8—261no—
310Q8—261no—
311Q8—522no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—261no—
316D4—261no—
317D4—522no—
318D4—522no—
319D4—522no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—131no—
330C2×C4—262no—
331C2×C4—262no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—522no—
336C2×C4D4×D1311yescharacteristic
337C2×C4C23×D1311yescharacteristic
338C8—21no—
339C8—21no—
340C8—261no—
341C8—261no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—521no—
349C22—521no—
350C22—521no—
351C22C2×D4×D1311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—132no—
357C4—132no—
358C4—261no—
359C4—261no—
360C4—521no—
361C4—521no—
362C4—521no—
363C4#8825111yescharacteristic
364C4#8825111yescharacteristic
365C2—41no—
366C2—81no—
367C2—1041no—
368C2#1171929711yescharacteristic
369C2D13×#13511yescharacteristic
370C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
prime radical#11719537C2
hypercenter#452D13
hypocenterC13#3210
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #11719327C2semidirect
3. C13×#452C2semidirect
4. #11718900C2semidirect
5. #11718846C2semidirect
6. #11718842C2semidirect
7. #11718836C2semidirect
8. #11718827C2semidirect
9. #11718708C2semidirect
10. #11718459C2semidirect
11. #11718453C2semidirect
12. #11718428C2semidirect
13. #11718421C2semidirect
14. #11718394C2semidirect
15. #11718379C2semidirect
170. #452D13semidirect
299. C13#3210semidirect

Maximal subgroups

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

subgroupindex
#117195372
#117193272
C13×#4522
#117189002
#117188462
#117188422
#117188362
#117188272
#117187082
#117184592
#117184532
#117184282
#117184212
#117183942
#117183792
#321013