Finite Group Databasebeta

← #13118798

Subgroups — #13118798

Order 1664.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88190C211yesmaximal, characteristic, complemented
2C2×#88189C211yesmaximal, characteristic, complemented
3C2×D4×Dic13C211yesmaximal, characteristic, complemented
4C2×#88132C211yesmaximal, characteristic, complemented
5C13×#392C211yesmaximal, characteristic
6#11718883C211yesmaximal, characteristic, complemented
7#11718882C211yesmaximal, characteristic, complemented
8#11718881C211yesmaximal, characteristic, complemented
9#11718612C211yesmaximal, characteristic, complemented
10#11718611C211yesmaximal, characteristic, complemented
11#11718609C211yesmaximal, characteristic, complemented
12#11718606C211yesmaximal, characteristic, complemented
13#11718605C211yesmaximal, characteristic, complemented
14#11718317C211yesmaximal, characteristic, complemented
15#11718310C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×D4×C13C2211yescharacteristic
19C23×Dic13C2211yescharacteristic
20C23×Dic13C2211yescharacteristic
21C22×Dic26C2211yescharacteristic
22C2×C13×C22⋊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
35#88190—24no—
36#88189—24no—
37D4×Dic13—24no—
38C2×C4⋊Dic13C2211yescharacteristic
39C2×C4⋊Dic13C2211yescharacteristic
40C2×C4⋊Dic13C2211yescharacteristic
41C2×#6101C2211yescharacteristic
42C2×#6101C2211yescharacteristic
43C2×#6101C2211yescharacteristic
44C2×#6101C2211yescharacteristic
45C2×C4×Dic13C2211yescharacteristic
46C2×C4×Dic13C2211yescharacteristic
47C2×C4×Dic13C2211yescharacteristic
48#88132—24no—
49C13×#95C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54#88071C2211yescharacteristic
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C24×C13C2311yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—22no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13C2311yescharacteristic
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—22no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C2×Dic26—22no—
86C2×Dic26—22no—
87C2×Dic26—41no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C22⋊Dic13—22no—
92C22⋊Dic13—22no—
93C22⋊Dic13—22no—
94C22⋊Dic13—22no—
95C22⋊Dic13—22no—
96C22⋊Dic13—22no—
97C22⋊Dic13—22no—
98C22⋊Dic13—22no—
99C22⋊Dic13—22no—
100C22⋊Dic13D414yescomplemented
101C4⋊Dic13—22no—
102C4⋊Dic13—22no—
103C4⋊Dic13—41no—
104#6101—22no—
105#6101—22no—
106#6101—22no—
107#6101D414yescomplemented
108C4×Dic13—22no—
109C4×Dic13—22no—
110C4×Dic13—22no—
111#2461—131nomaximal, Sylow
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×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13C2×D412yes—
132C23×C13#4112yes—
133C23×C13C2411yescharacteristic
134D4×C13—28no—
135D4×C13—44no—
136D4×C13—44no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13C2×D412yes—
147C2×C4×C13#4112yes—
148C2×C4×C13#4112yes—
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—21no—
169C2×Dic13—44no—
170C2×Dic13—44no—
171C2×Dic13C2×D412yes—
172C2×Dic13C2×D412yes—
173C2×Dic13C2×D412yes—
174C2×Dic13C2×D412yes—
175Dic26—44no—
176C2×#124—131no—
177C2×#123—131no—
178C2×C22⋊Q8—131no—
179C2×C4×D4—131no—
180#396—131no—
181#395—131no—
182#394—131no—
183#392D1311yescharacteristic
184#390—131no—
185#388—131no—
186#388—131no—
187#388—131no—
188#386—131no—
189#385—131no—
190C4×C4⋊C4—131no—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—22no—
196C22×C13—22no—
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×C13—41no—
206C22×C13—41no—
207C22×C13—41no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13C22×D411yescharacteristic
213C22×C13C22×D411yescharacteristic
214C22×C13C2×#4111yescharacteristic
215C22×C13C2×#4111yescharacteristic
216C22×C13C2×#4111yescharacteristic
217C22×C13H(5,𝔽2)11yescharacteristic
218C22×C132−1+411yescharacteristic
219C4×C13—22no—
220C4×C13—22no—
221C4×C13—22no—
222C4×C13—41no—
223Dic13—22no—
224Dic13—22no—
225Dic13—22no—
226Dic13—22no—
227Dic13—41no—
228Dic13—41no—
229Dic13—41no—
230Dic13—41no—
231C22×Q8—131no—
232C22×D4C2×D1311yescharacteristic
233C22×D4C2×D1311yescharacteristic
234C22×D4C2×D1311yescharacteristic
235C23×C4—131no—
236C23×C4—131no—
237#124—264no—
238#123—264no—
239C22⋊Q8—264no—
240C4×D4—264no—
241C2×C4⋊C4—131no—
242C2×C4⋊C4—131no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—131no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4—131no—
247C2×C4⋊C4—131no—
248C2×C22⋊C4—131no—
249C2×C22⋊C4—131no—
250C2×C22⋊C4—131no—
251C2×C22⋊C4—131no—
252C2×C22⋊C4—131no—
253C2×C22⋊C4—131no—
254C2×C22⋊C4—131no—
255C2×C22⋊C4—131no—
256C2×C22⋊C4—131no—
257C2×C22⋊C4—131no—
258C2×C22⋊C4C2×D1311yescharacteristic
259C2×C22⋊C4C2×D1311yescharacteristic
260C2×C22⋊C4C2×D1311yescharacteristic
261C2×C42—131no—
262C2×C42—131no—
263C2×C42—131no—
264#95—131no—
265#95—131no—
266#95—131no—
267#95—131no—
268#95—131no—
269#95C2×D1311yescharacteristic
270C2×C13—42no—
271C2×C13—42no—
272C2×C13—81no—
273C2×C13#52511yescharacteristic
274C2×C13#53211yescharacteristic
275C2×C13#54211yescharacteristic
276C2×C13D4211yescharacteristic
277C2×C13#54711yescharacteristic
278C2×C13#54811yescharacteristic
279C2×C13#55111yescharacteristic
280C24C22×D1311yescharacteristic
281C24C22×D1311yescharacteristic
282C24C22×D1311yescharacteristic
283C2×Q8—262no—
284C2×Q8—262no—
285C2×Q8—521no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—131no—
299C22×C4—131no—
300C22×C4—131no—
301C22×C4—131no—
302C22×C4—131no—
303C22×C4—262no—
304C22×C4—262no—
305C22×C4—262no—
306C22×C4—262no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4C22×D1311yescharacteristic
310C22×C4C22×D1311yescharacteristic
311C22×C4C22×D1311yescharacteristic
312C22×C4C22×D1311yescharacteristic
313C4⋊C4—134no—
314C4⋊C4—262no—
315C4⋊C4—262no—
316C4⋊C4—262no—
317C4⋊C4—262no—
318C4⋊C4—262no—
319C4⋊C4—521no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—134no—
324C22⋊C4—262no—
325C22⋊C4—262no—
326C22⋊C4—262no—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C22⋊C4—262no—
330C22⋊C4—262no—
331C22⋊C4—262no—
332C22⋊C4—262no—
333C42—262no—
334C42—262no—
335C42—262no—
336C13#246111yescharacteristic, complemented, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23D4×D1312yes—
357C23#612912yes—
358C23C23×D1311yescharacteristic
359Q8—524no—
360D4—28no—
361D4—44no—
362D4—44no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—132no—
373C2×C4—132no—
374C2×C4—132no—
375C2×C4—132no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—261no—
379C2×C4—261no—
380C2×C4—261no—
381C2×C4—261no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—261no—
390C2×C4—261no—
391C2×C4—261no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—524no—
397C2×C4—524no—
398C2×C4D4×D1312yes—
399C2×C4#612912yes—
400C2×C4#612912yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22C2×D4×D1311yescharacteristic
423C22C2×D4×D1311yescharacteristic
424C22C2×#612911yescharacteristic
425C22C2×#612911yescharacteristic
426C22C2×#612911yescharacteristic
427C22#8825111yescharacteristic
428C22#8825711yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—262no—
434C4—262no—
435C4—262no—
436C4—262no—
437C4—521no—
438C4—521no—
439C4—521no—
440C4—521no—
441C2—42no—
442C2—42no—
443C2—81no—
444C2#1171929111yescharacteristic
445C2#1171929211yescharacteristic
446C2#1171929511yescharacteristic
447C2#1171930311yescharacteristic
448C2#1171930811yescharacteristic
449C2#1171931611yescharacteristic
450C2#1171942111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2461
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#88190C2semidirect
2. C2×#88189C2semidirect
3. C2×D4×Dic13C2semidirect
4. C2×#88132C2semidirect
6. #11718883C2semidirect
7. #11718882C2semidirect
8. #11718881C2semidirect
9. #11718612C2semidirect
10. #11718611C2semidirect
11. #11718609C2semidirect
12. #11718606C2semidirect
13. #11718605C2semidirect
14. #11718317C2semidirect
15. #11718310C2semidirect
100. C22⋊Dic13D4semidirect
107. #6101D4semidirect
336. C13#2461semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
C2×#881892
C2×D4×Dic132
C2×#881322
C13×#3922
#117188832
#117188822
#117188812
#117186122
#117186112
#117186092
#117186062
#117186052
#117183172
#117183102
#246113