Finite Group Databasebeta

← #13119540

Subgroups — #13119540

Order 1664.

518 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88190C211yesmaximal, characteristic
2C2×#88133C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic
4#11718881C211yesmaximal, characteristic
5#11718640C211yesmaximal, characteristic, complemented
6C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
7#11718614C211yesmaximal, characteristic, complemented
8#11718612C211yesmaximal, characteristic, complemented
9#11718610C211yesmaximal, characteristic, complemented
10#11718606C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718603C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
14#11718316C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31#88190—24no—
32C2×C4⋊Dic13C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C2×C4×Dic13C2211yescharacteristic
42#88133—24no—
43C13×#95C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—41no—
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C22×Dic13C2311yescharacteristic
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C2×Dic26—22no—
75C2×Dic26—22no—
76C2×Dic26—41no—
77C13×C4⋊C4—22no—
78C13×C22⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—41no—
82C22⋊Dic13—22no—
83C22⋊Dic13—22no—
84C22⋊Dic13—22no—
85C22⋊Dic13—22no—
86C22⋊Dic13—22no—
87C22⋊Dic13—22no—
88C22⋊Dic13D414yes—
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91#6101—22no—
92#6101—22no—
93#6101—22no—
94#6101—41no—
95C4×Dic13—22no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98C4×Dic13—41no—
99#2521—131nomaximal, Sylow
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13C2×D412yes—
114C23×C13C2411yescharacteristic
115D4×C13—44no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13#4112yes—
130C2×C4×C13#4112yes—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—44no—
152C2×Dic13C2×D412yes—
153C2×Dic13C2×D412yes—
154C2×Dic13#4112yes—
155C2×Dic13#4112yes—
156Dic26—44no—
157C2×#126—131no—
158C2×#124—131no—
159#399—131no—
160#397—131no—
161#395—131no—
162#394D1311yescharacteristic
163#391—131no—
164#388—131no—
165#388—131no—
166#388—131no—
167#387—131no—
168#386—131no—
169#380—131no—
170C4×C4⋊C4—131no—
171C4×C22⋊C4—131no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×D411yescharacteristic
187C22×C13C2×#4111yescharacteristic
188C22×C13C2×#4111yescharacteristic
189C22×C13C2×#4111yescharacteristic
190C22×C13C2×#4111yescharacteristic
191C22×C13H(5,𝔽2)11yescharacteristic
192C22×C132−1+411yescharacteristic
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198Dic13—22no—
199Dic13—22no—
200Dic13—22no—
201Dic13—22no—
202Dic13—41no—
203Dic13—41no—
204Dic13—41no—
205Dic13—41no—
206C22×Q8—131no—
207C22×D4C2×D1311yescharacteristic
208C23×C4—131no—
209#126—264no—
210#124—264no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4C2×D1311yescharacteristic
218C2×C22⋊C4—131no—
219C2×C22⋊C4—131no—
220C2×C22⋊C4—131no—
221C2×C22⋊C4—131no—
222C2×C22⋊C4—131no—
223C2×C22⋊C4—131no—
224C2×C22⋊C4—131no—
225C2×C22⋊C4C2×D1311yescharacteristic
226C2×C22⋊C4C2×D1311yescharacteristic
227C2×C22⋊C4C2×D1311yescharacteristic
228C2×C22⋊C4C2×D1311yescharacteristic
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—131no—
232C2×C42—131no—
233#95—131no—
234#95—131no—
235#95—131no—
236#95—131no—
237#95—131no—
238#95—131no—
239#95—131no—
240#95—131no—
241#95—131no—
242#95C2×D1311yescharacteristic
243C2×C13—42no—
244C2×C13—81no—
245C2×C13#52911yescharacteristic
246C2×C13#53211yescharacteristic
247C2×C13#54211yescharacteristic
248C2×C13#54611yescharacteristic
249C2×C13#54711yescharacteristic
250C2×C13#55111yescharacteristic
251C2×C13#55611yescharacteristic
252C24C22×D1311yescharacteristic
253C24C22×D1311yescharacteristic
254C2×Q8—262no—
255C2×Q8—262no—
256C2×Q8—521no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—41no—
260C22×C4—131no—
261C22×C4—131no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—262no—
269C22×C4—262no—
270C22×C4—521no—
271C22×C4C22×D1311yescharacteristic
272C22×C4C22×D1311yescharacteristic
273C22×C4C22×D1311yescharacteristic
274C22×C4C22×D1311yescharacteristic
275C22×C4C22×D1311yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—521no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—134no—
288C22⋊C4—262no—
289C22⋊C4—262no—
290C22⋊C4—262no—
291C22⋊C4—262no—
292C22⋊C4—262no—
293C22⋊C4—262no—
294C42—262no—
295C42—262no—
296C42—262no—
297C42—521no—
298C13#252111yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23D4×D1312yes—
313C23C23×D1311yescharacteristic
314Q8—524no—
315D4—44no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—132no—
330C2×C4—132no—
331C2×C4—132no—
332C2×C4—132no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—524no—
354C2×C4#612912yes—
355C2×C4#612912yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×D4×D1311yescharacteristic
371C22C2×#612911yescharacteristic
372C22C2×#612911yescharacteristic
373C22#8825111yescharacteristic
374C22#41×D1311yescharacteristic
375C22#41×D1311yescharacteristic
376C22#8825711yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—262no—
383C4—262no—
384C4—262no—
385C4—262no—
386C4—521no—
387C4—521no—
388C4—521no—
389C4—521no—
390C2—42no—
391C2—81no—
392C2#1171929611yescharacteristic
393C2#1171930111yescharacteristic
394C2#1171930511yescharacteristic
395C2#1171930811yescharacteristic
396C2#1171936011yescharacteristic
397C2#1171936411yescharacteristic
398C2#1171937611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2521
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88133C2semidirect
5. #11718640C2semidirect
6. C4⋊C4×Dic13C2semidirect
7. #11718614C2semidirect
8. #11718612C2semidirect
9. #11718610C2semidirect
10. #11718606C2semidirect
11. #11718605C2semidirect
12. #11718603C2semidirect
13. C22⋊C4×Dic13C2semidirect
14. #11718316C2semidirect
15. #11718307C2semidirect
298. C13#2521semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
C2×#881332
C13×#3942
#117188812
#117186402
C4⋊C4×Dic132
#117186142
#117186122
#117186102
#117186062
#117186052
#117186032
C22⋊C4×Dic132
#117183162
#117183072
#252113