Finite Group Databasebeta

← #13122160

Subgroups — #13122160

Order 1664.

484 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#392C211yesmaximal, characteristic
2#11718883C211yesmaximal, characteristic, complemented
3#11718883C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718882C211yesmaximal, characteristic, complemented
6#11718881C211yesmaximal, characteristic, complemented
7#11718881C211yesmaximal, characteristic, complemented
8#11718613C211yesmaximal, characteristic, complemented
9#11718612C211yesmaximal, characteristic, complemented
10#11718606C211yesmaximal, characteristic, complemented
11#11718605C211yesmaximal, characteristic, complemented
12#11718605C211yesmaximal, characteristic, complemented
13#11718603C211yesmaximal, characteristic, complemented
14#11718318C211yesmaximal, characteristic, complemented
15#11718312C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊Dic13C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic
33C2×C22⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×#6101C2211yescharacteristic
37C2×#6101C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C13×#95C2211yescharacteristic
42#88071C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51C24×C13C2311yescharacteristic
52C24×C13C2311yescharacteristic
53C24×C13C2311yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×Dic13—22no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13C2311yescharacteristic
71C22×Dic13C2311yescharacteristic
72C22×Dic13C2311yescharacteristic
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C13×C22⋊C4—22no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C22⋊Dic13—22no—
82C22⋊Dic13—22no—
83C22⋊Dic13—22no—
84C22⋊Dic13—41no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C22⋊Dic13—41no—
88C22⋊Dic13—41no—
89C22⋊Dic13—41no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—41no—
94#6101—41no—
95#6101—41no—
96#6101—41no—
97C4×Dic13—22no—
98C4×Dic13—41no—
99#2756—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×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13#4112yes—
121C23×C13C2411yescharacteristic
122D4×C13—44no—
123D4×C13—44no—
124D4×C13—44no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13#4112yes—
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—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—21no—
158C2×Dic13—21no—
159C2×Dic13—21no—
160C2×Dic13—44no—
161C2×Dic13#4112yes—
162#398—131no—
163#397—131no—
164#394—131no—
165#394—131no—
166#394—131no—
167#392D1311yescharacteristic
168#390—131no—
169#388—131no—
170#388—131no—
171#388—131no—
172#388—131no—
173#386—131no—
174#386—131no—
175#383—131no—
176#380—131no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—41no—
197C22×C13—41no—
198C22×C13C2×#4111yescharacteristic
199C22×C13C2×#4111yescharacteristic
200C22×C13C2×#4111yescharacteristic
201C22×C13H(5,𝔽2)11yescharacteristic
202C22×C13H(5,𝔽2)11yescharacteristic
203C22×C13H(5,𝔽2)11yescharacteristic
204C22×C13H(5,𝔽2)11yescharacteristic
205C4×C13—22no—
206C4×C13—41no—
207C4×C13—41no—
208C4×C13—41no—
209Dic13—22no—
210Dic13—41no—
211Dic13—41no—
212Dic13—41no—
213Dic13—41no—
214Dic13—41no—
215Dic13—41no—
216Dic13—41no—
217C22×D4C2×D1311yescharacteristic
218C22×D4C2×D1311yescharacteristic
219C22×D4C2×D1311yescharacteristic
220C23×C4—131no—
221C2×C4⋊C4—131no—
222C2×C4⋊C4—131no—
223C2×C4⋊C4—131no—
224C2×C4⋊C4—131no—
225C2×C4⋊C4—131no—
226C2×C22⋊C4—131no—
227C2×C22⋊C4—131no—
228C2×C22⋊C4—131no—
229C2×C22⋊C4—131no—
230C2×C22⋊C4—131no—
231C2×C22⋊C4—131no—
232C2×C22⋊C4—131no—
233C2×C22⋊C4—131no—
234C2×C22⋊C4—131no—
235C2×C22⋊C4—131no—
236C2×C22⋊C4—131no—
237C2×C22⋊C4C2×D1311yescharacteristic
238C2×C22⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4C2×D1311yescharacteristic
240C2×C42—131no—
241C2×C42—131no—
242#95—131no—
243#95—131no—
244#95—131no—
245#95—131no—
246#95—131no—
247#95—131no—
248#95—131no—
249#95—131no—
250#95—131no—
251#95C2×D1311yescharacteristic
252C2×C13—42no—
253C2×C13—81no—
254C2×C13—81no—
255C2×C13#53811yescharacteristic
256C2×C13#53811yescharacteristic
257C2×C13#54011yescharacteristic
258C2×C13#55111yescharacteristic
259C2×C13#55311yescharacteristic
260C2×C13#55511yescharacteristic
261C2×C13#56011yescharacteristic
262C24C22×D1311yescharacteristic
263C24C22×D1311yescharacteristic
264C24C22×D1311yescharacteristic
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—131no—
282C22×C4—262no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4C22×D1311yescharacteristic
286C22×C4C22×D1311yescharacteristic
287C22×C4C22×D1311yescharacteristic
288C22×C4C22×D1311yescharacteristic
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—262no—
298C22⋊C4—262no—
299C22⋊C4—262no—
300C22⋊C4—521no—
301C22⋊C4—521no—
302C22⋊C4—521no—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C22⋊C4—521no—
306C22⋊C4—521no—
307C22⋊C4—521no—
308C42—262no—
309C42—521no—
310C13#275611yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23#612912yes—
332C23C23×D1311yescharacteristic
333D4—44no—
334D4—44no—
335D4—44no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—132no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—261no—
362C2×C4—261no—
363C2×C4—261no—
364C2×C4—261no—
365C2×C4—261no—
366C2×C4—261no—
367C2×C4—261no—
368C2×C4—261no—
369C2×C4—261no—
370C2×C4—261no—
371C2×C4—524no—
372C2×C4#612912yes—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22C2×#612911yescharacteristic
395C22C2×#612911yescharacteristic
396C22#8825111yescharacteristic
397C22#8825111yescharacteristic
398C22#8825111yescharacteristic
399C22#8825111yescharacteristic
400C22#41×D1311yescharacteristic
401C4—22no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—262no—
406C4—521no—
407C4—521no—
408C4—521no—
409C4—521no—
410C4—521no—
411C4—521no—
412C4—521no—
413C2—42no—
414C2—81no—
415C2—81no—
416C2#1171929211yescharacteristic
417C2#1171929811yescharacteristic
418C2#1171930011yescharacteristic
419C2#1171930611yescharacteristic
420C2#1171931811yescharacteristic
421C2#1171932111yescharacteristic
422C2#1171942411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2756
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
2. #11718883C2semidirect
3. #11718883C2semidirect
4. #11718883C2semidirect
5. #11718882C2semidirect
6. #11718881C2semidirect
7. #11718881C2semidirect
8. #11718613C2semidirect
9. #11718612C2semidirect
10. #11718606C2semidirect
11. #11718605C2semidirect
12. #11718605C2semidirect
13. #11718603C2semidirect
14. #11718318C2semidirect
15. #11718312C2semidirect
310. C13#2756semidirect

Maximal subgroups

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

subgroupindex
C13×#3922
#117188832
#117188822
#117188812
#117186132
#117186122
#117186062
#117186052
#117186032
#117183182
#117183122
#275613