Finite Group Databasebeta

← #13121313

Subgroups — #13121313

Order 1664.

554 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#121C211yesmaximal, characteristic
2C2×#88133C211yesmaximal, characteristic, complemented
3#11718883C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718883C211yesmaximal, characteristic, complemented
6#11718882C211yesmaximal, characteristic, complemented
7#11718881C211yesmaximal, characteristic, complemented
8#11718881C211yesmaximal, characteristic, complemented
9#11718873C211yesmaximal, characteristic, complemented
10#11718871C211yesmaximal, characteristic, complemented
11#11718645C211yesmaximal, characteristic, complemented
12#11718639C211yesmaximal, characteristic, complemented
13#11718614C211yesmaximal, characteristic, complemented
14#11718611C211yesmaximal, characteristic, complemented
15#11718609C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C23×C4×C13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C13×#121—24no—
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
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×C22⋊Dic13C2211yescharacteristic
35C2×C22⋊Dic13C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic
38C2×C4⋊Dic13C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×#6101C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×C4×Dic13C2211yescharacteristic
44#88133—24no—
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C24×C13C2311yescharacteristic
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—41no—
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C13×C4⋊C4—22no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4D414yes—
86C22⋊Dic13—22no—
87C22⋊Dic13—22no—
88C22⋊Dic13—22no—
89C22⋊Dic13—41no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95C22⋊Dic13—41no—
96C22⋊Dic13—41no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6101—22no—
101#6101—22no—
102#6101—22no—
103#6101—41no—
104C4×Dic13—22no—
105#2691—131nomaximal, Sylow
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—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13C2×D412yes—
126C23×C13#4112yes—
127C23×C13C2411yescharacteristic
128D4×C13—44no—
129D4×C13—44no—
130D4×C13—44no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—44no—
141C2×C4×C13C2×D412yes—
142C2×C4×C13C2×D412yes—
143C2×C4×C13#4112yes—
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—21no—
161C2×Dic13—21no—
162C2×Dic13—21no—
163C2×Dic13—21no—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—44no—
169C2×#126—131no—
170C2×#121D1311yescharacteristic
171#398—131no—
172#397—131no—
173#396—131no—
174#394—131no—
175#394—131no—
176#394—131no—
177#390—131no—
178#387—131no—
179#386—131no—
180#386—131no—
181#385—131no—
182#385—131no—
183#380—131no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
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×C13—41no—
199C22×C13—41no—
200C22×C13—41no—
201C22×C13—41no—
202C22×C13—41no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13C22×D411yescharacteristic
206C22×C13C2×#4111yescharacteristic
207C22×C13C2×#4111yescharacteristic
208C22×C13H(5,𝔽2)11yescharacteristic
209C22×C13H(5,𝔽2)11yescharacteristic
210C22×C13H(5,𝔽2)11yescharacteristic
211C22×C132−1+411yescharacteristic
212C4×C13—22no—
213C4×C13—22no—
214C4×C13—22no—
215C4×C13—41no—
216Dic13—41no—
217Dic13—41no—
218Dic13—41no—
219Dic13—41no—
220Dic13—41no—
221Dic13—41no—
222Dic13—41no—
223Dic13—41no—
224C22×D4C2×D1311yescharacteristic
225C22×D4C2×D1311yescharacteristic
226C22×D4C2×D1311yescharacteristic
227C23×C4—131no—
228C23×C4C2×D1311yescharacteristic
229#126—264no—
230#121—24no—
231C2×C4⋊C4—131no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—131no—
234C2×C4⋊C4—131no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—131no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4C2×D1311yescharacteristic
239C2×C22⋊C4—131no—
240C2×C22⋊C4—131no—
241C2×C22⋊C4—131no—
242C2×C22⋊C4—131no—
243C2×C22⋊C4—131no—
244C2×C22⋊C4—131no—
245C2×C22⋊C4—131no—
246C2×C22⋊C4—131no—
247C2×C22⋊C4—131no—
248C2×C22⋊C4—131no—
249C2×C22⋊C4—131no—
250C2×C22⋊C4C2×D1311yescharacteristic
251C2×C22⋊C4C2×D1311yescharacteristic
252C2×C42—131no—
253#95—131no—
254#95—131no—
255#95—131no—
256#95—131no—
257#95—131no—
258#95—131no—
259#95—131no—
260#95—131no—
261C2×C13—42no—
262C2×C13—42no—
263C2×C13—81no—
264C2×C13#53711yescharacteristic
265C2×C13#53911yescharacteristic
266C2×C13#54211yescharacteristic
267C2×C13#54611yescharacteristic
268C2×C13#54611yescharacteristic
269C2×C13#55311yescharacteristic
270C2×C13#56011yescharacteristic
271C24C22×D1311yescharacteristic
272C24C22×D1311yescharacteristic
273C24C22×D1311yescharacteristic
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4—131no—
287C22×C4—131no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4C22×D1311yescharacteristic
298C22×C4C22×D1311yescharacteristic
299C22×C4C22×D1311yescharacteristic
300C22×C4C22×D1311yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—262no—
303C4⋊C4—262no—
304C4⋊C4—262no—
305C4⋊C4—262no—
306C4⋊C4—521no—
307C4⋊C4—521no—
308C4⋊C4—521no—
309C22⋊C4—22no—
310C22⋊C4—262no—
311C22⋊C4—262no—
312C22⋊C4—262no—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C22⋊C4—521no—
318C22⋊C4—521no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C22⋊C4C22⋊D1314yes—
322C42—262no—
323C13#269111yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23#612912yes—
344C23C2×C22⋊D1312yes—
345C23C23×D1311yescharacteristic
346D4—44no—
347D4—44no—
348D4—44no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—44no—
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—261no—
372C2×C4—261no—
373C2×C4—261no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—261no—
383C2×C4—524no—
384C2×C4#612912yes—
385C2×C4C2×C22⋊D1312yes—
386C2×C4C2×C22⋊D1312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C2×#612911yescharacteristic
409C22C2×#612911yescharacteristic
410C22#8825111yescharacteristic
411C22#8825111yescharacteristic
412C22#8825611yescharacteristic
413C22#8825711yescharacteristic
414C22C22×C22⋊D1311yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—41no—
419C4—521no—
420C4—521no—
421C4—521no—
422C4—521no—
423C4—521no—
424C4—521no—
425C4—521no—
426C4—521no—
427C2—42no—
428C2—42no—
429C2—81no—
430C2#1171930711yescharacteristic
431C2#1171930811yescharacteristic
432C2#1171932311yescharacteristic
433C2#1171932511yescharacteristic
434C2#1171951111yescharacteristic
435C2#1171951111yescharacteristic
436C2#1171953811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC2×C13×#121C2
hypercenterC2×#121D13
hypocenterC13#2691
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#88133C2semidirect
3. #11718883C2semidirect
4. #11718883C2semidirect
5. #11718883C2semidirect
6. #11718882C2semidirect
7. #11718881C2semidirect
8. #11718881C2semidirect
9. #11718873C2semidirect
10. #11718871C2semidirect
11. #11718645C2semidirect
12. #11718639C2semidirect
13. #11718614C2semidirect
14. #11718611C2semidirect
15. #11718609C2semidirect
323. C13#2691semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C2×#881332
#117188832
#117188822
#117188812
#117188732
#117188712
#117186452
#117186392
#117186142
#117186112
#117186092
#269113