Finite Group Databasebeta

← #13118583

Subgroups — #13118583

Order 1664.

610 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88192C211yesmaximal, characteristic
2C2×C4×C22⋊D13C211yesmaximal, characteristic, complemented
3C13×#386C211yesmaximal, characteristic, complemented
4#11718883C211yesmaximal, characteristic, complemented
5#11718872C211yesmaximal, characteristic, complemented
6#11718617C211yesmaximal, characteristic, complemented
7#11718617C211yesmaximal, characteristic, complemented
8#11718617C211yesmaximal, characteristic, complemented
9#11718614C211yesmaximal, characteristic, complemented
10#11718613C211yesmaximal, characteristic, complemented
11#11718612C211yesmaximal, characteristic, complemented
12#11718329C211yesmaximal, characteristic, complemented
13D13×#95C211yesmaximal, characteristic, complemented
14#11718321C211yesmaximal, characteristic, complemented
15#11718316C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C23×C4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C2×C13×C22⋊C4C2211yescharacteristic
24C2×C13×C22⋊C4C2211yescharacteristic
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C22⋊Dic13C2211yescharacteristic
27C2×C22⋊Dic13C2211yescharacteristic
28C2×C22⋊Dic13C2211yescharacteristic
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32#88192—24no—
33C4×C22⋊D13—24no—
34C2×#6103C2211yescharacteristic
35C2×#6103C2211yescharacteristic
36C2×C4⋊Dic13C2211yescharacteristic
37C2×C4⋊Dic13C2211yescharacteristic
38C2×#6101C2211yescharacteristic
39C2×#6101C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41C13×#95C2211yescharacteristic
42C13×#95C2211yescharacteristic
43#88071C2211yescharacteristic
44#88071C2211yescharacteristic
45#88071C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53C24×C13C2311yescharacteristic
54C24×C13C2311yescharacteristic
55C23×D13C2311yescharacteristic
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13—41no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C22×C4×C13C2311yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—22no—
68C2×C22⋊D13—22no—
69C2×C22⋊D13—22no—
70C2×C22⋊D13—22no—
71C2×C22⋊D13—22no—
72C2×C22⋊D13D414yes—
73C22×Dic13C2311yescharacteristic
74C22×Dic13C2311yescharacteristic
75C22×Dic13C2311yescharacteristic
76C22×Dic13C2311yescharacteristic
77C22×Dic13C2311yescharacteristic
78C22×Dic13C2311yescharacteristic
79C22×Dic13C2311yescharacteristic
80C2×C4×D13—22no—
81C2×C4×D13—22no—
82C2×C4×D13—22no—
83C2×C4×D13—22no—
84C2×C4×D13—22no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C22⋊Dic13—22no—
93C22⋊Dic13—22no—
94C22⋊Dic13—22no—
95C22⋊Dic13—41no—
96C22⋊Dic13—41no—
97C22⋊Dic13—41no—
98#6103—22no—
99#6103—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—41no—
102#6101—22no—
103#6101—22no—
104C4×Dic13—22no—
105#2444—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×C13C2×D412yes—
120C23×C13C2411yescharacteristic
121C22×D13—21no—
122C22×D13—21no—
123C22×D13—21no—
124C22×D13—21no—
125C22×D13C2×D412yes—
126C22×D13#4112yes—
127C22×D13#4112yes—
128D4×C13—44no—
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—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—44no—
143C2×C4×C13#4112yes—
144C2×C4×C13#4112yes—
145C22⋊D13—28no—
146C22⋊D13—44no—
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×Dic13C2×D412yes—
168C4×D13—44no—
169C4×D13—44no—
170C4×D13—44no—
171C2×#121—131no—
172C2×C4×D4—131no—
173#400—131no—
174#397—131no—
175#397—131no—
176#394—131no—
177#388—131no—
178#387—131no—
179#386—131no—
180#386—131no—
181#386—131no—
182#386D1311yescharacteristic, complemented
183#385—131no—
184#381—131no—
185C2×#95—131no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
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×C13—41no—
199C22×C13—41no—
200C22×C13C22×D411yescharacteristic
201C22×C13C2×#4111yescharacteristic
202C22×C13C2×#4111yescharacteristic
203C22×C13C2×#4111yescharacteristic
204C22×C13C2×#4111yescharacteristic
205C22×C13H(5,𝔽2)11yescharacteristic
206C22×C13H(5,𝔽2)11yescharacteristic
207C2×D13—22no—
208C2×D13—22no—
209C2×D13—22no—
210C2×D13—22no—
211C2×D13—22no—
212C2×D13—22no—
213C2×D13#12314yes—
214C4×C13—22no—
215C4×C13—22no—
216C4×C13—41no—
217C4×C13—41no—
218C4×C13—41no—
219Dic13—22no—
220Dic13—41no—
221Dic13—41no—
222Dic13—41no—
223Dic13—41no—
224Dic13—41no—
225Dic13—41no—
226C22×D4—131no—
227C22×D4—131no—
228C22×D4C2×D1311yescharacteristic
229C23×C4—131no—
230C23×C4—131no—
231C23×C4—131no—
232C23×C4C2×D1311yescharacteristic
233#121—264no—
234C4×D4—264no—
235C2×C4⋊C4—131no—
236C2×C4⋊C4—131no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
248C2×C22⋊C4C2×D1311yescharacteristic
249C2×C22⋊C4C2×D1311yescharacteristic
250C2×C42—131no—
251#95—131no—
252#95—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—
261#95C2×D1311yescharacteristic
262#95C2×D1311yescharacteristic
263C2×C13—42no—
264C2×C13—81no—
265C2×C13C2×#12311yescharacteristic
266C2×C13#52911yescharacteristic
267C2×C13#53811yescharacteristic
268C2×C13#54611yescharacteristic
269C2×C13#54611yescharacteristic
270C2×C13#55311yescharacteristic
271C2×C13#55311yescharacteristic
272D13—24no—
273C24—131no—
274C24C22×D1311yescharacteristic
275C24C22×D1311yescharacteristic
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—41no—
279C2×D4—134no—
280C2×D4—262no—
281C2×D4—262no—
282C2×D4—262no—
283C2×D4—262no—
284C2×D4—262no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—41no—
288C22×C4—131no—
289C22×C4—131no—
290C22×C4—131no—
291C22×C4—131no—
292C22×C4—131no—
293C22×C4—131no—
294C22×C4—131no—
295C22×C4—262no—
296C22×C4—262no—
297C22×C4—262no—
298C22×C4—262no—
299C22×C4—262no—
300C22×C4—521no—
301C22×C4—521no—
302C22×C4—521no—
303C22×C4—521no—
304C22×C4C22×D1311yescharacteristic
305C22×C4C22×D1311yescharacteristic
306C22×C4C22×D1311yescharacteristic
307C22×C4C22×D1311yescharacteristic
308C22×C4C22×D1311yescharacteristic
309C4⋊C4—262no—
310C4⋊C4—262no—
311C4⋊C4—262no—
312C4⋊C4—521no—
313C22⋊C4—22no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—262no—
317C22⋊C4—262no—
318C22⋊C4—262no—
319C22⋊C4—262no—
320C22⋊C4—262no—
321C22⋊C4—521no—
322C22⋊C4—521no—
323C22⋊C4—521no—
324C42—262no—
325C13#244411yescharacteristic, complemented, Sylow
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—132no—
340C23—132no—
341C23—132no—
342C23—261no—
343C23—261no—
344C23—261no—
345C23—261no—
346C23D4×D1312yes—
347C23C23×D1311yescharacteristic
348D4—44no—
349D4—268no—
350D4—524no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—44no—
365C2×C4—132no—
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—261no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—524no—
387C2×C4—524no—
388C2×C4—524no—
389C2×C4#612712yes—
390C2×C4#612912yes—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—134no—
406C22—262no—
407C22—262no—
408C22—262no—
409C22—262no—
410C22—262no—
411C22—262no—
412C22C2×#612711yescharacteristic
413C22C2×D4×D1311yescharacteristic
414C22C2×#612911yescharacteristic
415C22#8825111yescharacteristic
416C22#8825111yescharacteristic
417C22#41×D1311yescharacteristic
418C22#41×D1311yescharacteristic
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—262no—
425C4—521no—
426C4—521no—
427C4—521no—
428C4—521no—
429C4—521no—
430C4—521no—
431C2—42no—
432C2—81no—
433C2—264no—
434C2#1171919511yescharacteristic
435C2#1171926211yescharacteristic
436C2#1171926311yescharacteristic
437C2#1171929611yescharacteristic
438C2#1171931811yescharacteristic
439C2#1171931911yescharacteristic
440C2D13×#12311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88192C2
hypercenter#386D13
hypocenterC13#2444
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D13C2semidirect
3. C13×#386C2semidirect
4. #11718883C2semidirect
5. #11718872C2semidirect
6. #11718617C2semidirect
7. #11718617C2semidirect
8. #11718617C2semidirect
9. #11718614C2semidirect
10. #11718613C2semidirect
11. #11718612C2semidirect
12. #11718329C2semidirect
13. D13×#95C2semidirect
14. #11718321C2semidirect
15. #11718316C2semidirect
182. #386D13semidirect
325. C13#2444semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
C2×C4×C22⋊D132
C13×#3862
#117188832
#117188722
#117186172
#117186142
#117186132
#117186122
#117183292
D13×#952
#117183212
#117183162
#244413