Finite Group Databasebeta

← #13118227

Subgroups — #13118227

Order 1664.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88191C211yesmaximal, characteristic
2C2×#88137C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D13C211yesmaximal, characteristic, complemented
5C13×#394C211yesmaximal, characteristic, complemented
6#11718883C211yesmaximal, characteristic, complemented
7#11718650C211yesmaximal, characteristic, complemented
8#11718648C211yesmaximal, characteristic, complemented
9#11718617C211yesmaximal, characteristic, complemented
10#11718617C211yesmaximal, characteristic, complemented
11#11718617C211yesmaximal, characteristic, complemented
12#11718614C211yesmaximal, characteristic, complemented
13#11718613C211yesmaximal, characteristic, complemented
14#11718328C211yesmaximal, characteristic, complemented
15#11718325C211yesmaximal, characteristic, complemented
16C24×D13C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C22×C22⋊D13C2211yescharacteristic
19C22×C22⋊D13C2211yescharacteristic
20C22×C4×D13C2211yescharacteristic
21C22×C4×D13C2211yescharacteristic
22C22×C4×D13C2211yescharacteristic
23C22×C4×D13C2211yescharacteristic
24C2×C13×C4⋊C4C2211yescharacteristic, complemented
25C2×C13×C22⋊C4C2211yescharacteristic
26C2×C13×C22⋊C4C2211yescharacteristic
27C2×C13×C22⋊C4C2211yescharacteristic, complemented
28C2×C13×C22⋊C4C2211yescharacteristic, complemented
29C2×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊Dic13C2211yescharacteristic
32C2×C22⋊Dic13C2211yescharacteristic, complemented
33C2×C22⋊Dic13C2211yescharacteristic, complemented
34#88191—24no—
35C2×#6103C2211yescharacteristic
36C2×#6103C2211yescharacteristic
37C2×#6103C2211yescharacteristic
38C2×#6103C2211yescharacteristic
39C2×#6103C2211yescharacteristic
40C2×#6103C2211yescharacteristic
41C2×C4⋊Dic13C2211yescharacteristic, complemented
42C2×#6101C2211yescharacteristic, complemented
43C2×#6101C2211yescharacteristic, complemented
44#88137—24no—
45C22⋊C4×D13—24no—
46C22⋊C4×D13—24no—
47C13×#95C2211yescharacteristic, complemented
48#88071C2211yescharacteristic, complemented
49#88071C2211yescharacteristic, complemented
50#88071C2211yescharacteristic, complemented
51#88071C2211yescharacteristic, complemented
52#88071C2211yescharacteristic, complemented
53#88071C2211yescharacteristic, complemented
54#88071C2211yescharacteristic, complemented
55C24×C13C2311yescharacteristic
56C24×C13C2311yescharacteristic
57C23×D13—22no—
58C23×D13—22no—
59C23×D13—22no—
60C23×D13—22no—
61C23×D13—41no—
62C23×D13—41no—
63C23×D13D414yes—
64C23×D13C2311yescharacteristic
65C23×D13C2311yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C22×C4×C13C2311yescharacteristic
70C22×C4×C13C2311yescharacteristic
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C2×C22⋊D13—22no—
75C2×C22⋊D13—22no—
76C2×C22⋊D13—22no—
77C2×C22⋊D13—22no—
78C2×C22⋊D13—22no—
79C2×C22⋊D13—22no—
80C22×Dic13C2311yescharacteristic
81C22×Dic13C2311yescharacteristic
82C22×Dic13C2311yescharacteristic
83C22×Dic13C2311yescharacteristic
84C22×Dic13C2311yescharacteristic
85C22×Dic13C2311yescharacteristic
86C2×C4×D13—22no—
87C2×C4×D13—22no—
88C2×C4×D13—22no—
89C2×C4×D13—22no—
90C2×C4×D13—22no—
91C2×C4×D13—22no—
92C2×C4×D13—22no—
93C2×C4×D13—22no—
94C2×C4×D13—41no—
95C2×C4×D13—41no—
96C2×C4×D13—41no—
97C2×C4×D13—41no—
98C13×C4⋊C4—41no—
99C13×C22⋊C4—22no—
100C13×C22⋊C4—22no—
101C13×C22⋊C4—22no—
102C13×C22⋊C4—41no—
103C22⋊Dic13—22no—
104C22⋊Dic13—22no—
105C22⋊Dic13—22no—
106C22⋊Dic13—22no—
107C22⋊Dic13—41no—
108#6103—22no—
109#6103—22no—
110#6103—22no—
111#6103—22no—
112#6103—22no—
113#6103D414yescomplemented
114C4⋊Dic13—22no—
115#6101—22no—
116#6101—41no—
117#2412—131nomaximal, Sylow
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×C13C2411yescharacteristic
133C22×D13—21no—
134C22×D13—21no—
135C22×D13—21no—
136C22×D13—21no—
137C22×D13—21no—
138C22×D13—21no—
139C22×D13—21no—
140C22×D13—21no—
141C22×D13—28no—
142C22×D13—28no—
143C22×D13—44no—
144C22×D13—44no—
145C22×D13—44no—
146C22×D13—44no—
147C22×D13—44no—
148C22×D13C2×D412yes—
149C22×D13C2×D412yes—
150C22×D13C2×D412yes—
151C22×D13#4112yes—
152C22×D13#4112yes—
153C22×D13#4112yes—
154D4×C13—44no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—21no—
169C2×C4×C13C2×D412yes—
170C22⋊D13—44no—
171C22⋊D13—44no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—21no—
187C2×Dic13—21no—
188C2×Dic13—21no—
189C2×Dic13C2×D412yes—
190C4×D13—44no—
191C4×D13—44no—
192C4×D13—44no—
193C4×D13—44no—
194C2×#123—131no—
195C2×#120—131no—
196C22×C22⋊C4—131no—
197C22×C22⋊C4—131no—
198#397—131no—
199#397—131no—
200#394—131no—
201#394D1311yescharacteristic, complemented
202#386—131no—
203#386—131no—
204#386—131no—
205#385—131no—
206#381—131no—
207#380—131no—
208#380—131no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—41no—
213C22×C13—41no—
214C22×C13—41no—
215C22×C13—41no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13C22×D411yescharacteristic
224C22×C13C22×D411yescharacteristic
225C22×C13C2×#4111yescharacteristic
226C22×C13C2×#4111yescharacteristic
227C22×C13C2×#4111yescharacteristic
228C22×C13H(5,𝔽2)11yescharacteristic
229C22×C13H(5,𝔽2)11yescharacteristic
230C2×D13—22no—
231C2×D13—22no—
232C2×D13—22no—
233C2×D13—22no—
234C2×D13—22no—
235C2×D13—22no—
236C2×D13—22no—
237C2×D13—22no—
238C2×D13—22no—
239C2×D13—22no—
240C2×D13—22no—
241C2×D13—22no—
242C2×D13—416no—
243C2×D13#12114yes—
244C2×D13#12314yescomplemented
245C4×C13—22no—
246C4×C13—41no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13—41no—
250Dic13—22no—
251Dic13—41no—
252Dic13—41no—
253Dic13—41no—
254Dic13—41no—
255Dic13—41no—
256C25—131no—
257C22×D4—131no—
258C22×D4—131no—
259C22×D4C2×D1311yescharacteristic
260C23×C4—131no—
261C23×C4—131no—
262C23×C4—131no—
263C23×C4—131no—
264#123—264no—
265#120—264no—
266C2×C4⋊C4—131no—
267C2×C4⋊C4—131no—
268C2×C4⋊C4—131no—
269C2×C4⋊C4C2×D1311yescharacteristic, complemented
270C2×C22⋊C4—131no—
271C2×C22⋊C4—131no—
272C2×C22⋊C4—131no—
273C2×C22⋊C4—131no—
274C2×C22⋊C4—131no—
275C2×C22⋊C4—131no—
276C2×C22⋊C4—131no—
277C2×C22⋊C4—131no—
278C2×C22⋊C4—131no—
279C2×C22⋊C4—131no—
280C2×C22⋊C4—131no—
281C2×C22⋊C4—264no—
282C2×C22⋊C4—264no—
283C2×C22⋊C4C2×D1311yescharacteristic
284C2×C22⋊C4C2×D1311yescharacteristic
285C2×C22⋊C4C2×D1311yescharacteristic, complemented
286C2×C22⋊C4C2×D1311yescharacteristic, complemented
287#95—131no—
288#95—131no—
289#95—131no—
290#95—131no—
291#95—131no—
292#95—131no—
293#95—131no—
294#95C2×D1311yescharacteristic, complemented
295C2×C13—42no—
296C2×C13—81no—
297C2×C13C2×#12111yescharacteristic
298C2×C13C2×#12311yescharacteristic
299C2×C13#53411yescharacteristic
300C2×C13#54611yescharacteristic
301C2×C13#54611yescharacteristic
302C2×C13#55111yescharacteristic
303C2×C13#55111yescharacteristic
304D13—24no—
305D13—24no—
306C24—131no—
307C24—131no—
308C24—134no—
309C24—262no—
310C24—262no—
311C24—262no—
312C24—262no—
313C24—521no—
314C24—521no—
315C24C22×D1311yescharacteristic
316C24C22×D1311yescharacteristic
317C2×D4—22no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—262no—
321C2×D4—262no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—262no—
325C2×D4—262no—
326C22×C4—131no—
327C22×C4—131no—
328C22×C4—131no—
329C22×C4—131no—
330C22×C4—131no—
331C22×C4—131no—
332C22×C4—262no—
333C22×C4—262no—
334C22×C4—262no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—262no—
340C22×C4—521no—
341C22×C4—521no—
342C22×C4—521no—
343C22×C4—521no—
344C22×C4C22×D1311yescharacteristic
345C22×C4C22×D1311yescharacteristic
346C22×C4C22×D1311yescharacteristic
347C22×C4C22×D1311yescharacteristic
348C22×C4C22×D1311yescharacteristic
349C4⋊C4—41no—
350C4⋊C4—262no—
351C4⋊C4—262no—
352C4⋊C4—521no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—41no—
357C22⋊C4—134no—
358C22⋊C4—262no—
359C22⋊C4—262no—
360C22⋊C4—262no—
361C22⋊C4—262no—
362C22⋊C4—262no—
363C22⋊C4—262no—
364C22⋊C4—262no—
365C22⋊C4—262no—
366C22⋊C4—262no—
367C22⋊C4—521no—
368C13#241211yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—132no—
383C23—132no—
384C23—132no—
385C23—132no—
386C23—132no—
387C23—132no—
388C23—268no—
389C23—268no—
390C23—261no—
391C23—261no—
392C23—261no—
393C23—261no—
394C23—261no—
395C23—261no—
396C23—261no—
397C23—261no—
398C23—524no—
399C23—524no—
400C23—524no—
401C23—524no—
402C23—524no—
403C23D4×D1312yes—
404C23C23×D1311yescharacteristic
405D4—44no—
406D4—524no—
407D4—524no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—132no—
423C2×C4—261no—
424C2×C4—261no—
425C2×C4—261no—
426C2×C4—261no—
427C2×C4—261no—
428C2×C4—261no—
429C2×C4—261no—
430C2×C4—261no—
431C2×C4—261no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—524no—
441C2×C4—524no—
442C2×C4—524no—
443C2×C4—524no—
444C2×C4D4×D1312yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—134no—
460C22—134no—
461C22—262no—
462C22—262no—
463C22—262no—
464C22—262no—
465C22—262no—
466C22—262no—
467C22—262no—
468C22—262no—
469C22—262no—
470C22—262no—
471C22—262no—
472C22—262no—
473C22—5216no—
474C22C2×D4×D1311yescharacteristic
475C22C2×D4×D1311yescharacteristic
476C22#8825111yescharacteristic
477C22#8825111yescharacteristic
478C22#41×D1311yescharacteristic
479C22#41×D1311yescharacteristic
480C22#41×D1311yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—262no—
487C4—521no—
488C4—521no—
489C4—521no—
490C4—521no—
491C4—521no—
492C2—42no—
493C2—81no—
494C2—264no—
495C2—264no—
496C2#1171929411yescharacteristic
497C2D13×#12111yescharacteristic
498C2#1171931511yescharacteristic
499C2#1171931711yescharacteristic
500C2D13×#12311yescharacteristic
501C2#1171936411yescharacteristic
502C2#1171938411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88191C2
hypercenter#394D13
hypocenterC13#2412
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88137C2semidirect
3. C2×C22⋊C4×D13C2semidirect
4. C2×C22⋊C4×D13C2semidirect
5. C13×#394C2semidirect
6. #11718883C2semidirect
7. #11718650C2semidirect
8. #11718648C2semidirect
9. #11718617C2semidirect
10. #11718617C2semidirect
11. #11718617C2semidirect
12. #11718614C2semidirect
13. #11718613C2semidirect
14. #11718328C2semidirect
15. #11718325C2semidirect
24. C2×C13×C4⋊C4C22semidirect
27. C2×C13×C22⋊C4C22semidirect
28. C2×C13×C22⋊C4C22semidirect
32. C2×C22⋊Dic13C22semidirect
33. C2×C22⋊Dic13C22semidirect
41. C2×C4⋊Dic13C22semidirect
42. C2×#6101C22semidirect
43. C2×#6101C22semidirect
47. C13×#95C22semidirect
48. #88071C22semidirect
49. #88071C22semidirect
50. #88071C22semidirect
51. #88071C22semidirect
52. #88071C22semidirect
53. #88071C22semidirect
54. #88071C22semidirect
113. #6103D4semidirect
201. #394D13semidirect
244. C2×D13#123semidirect
269. C2×C4⋊C4C2×D13semidirect
285. C2×C22⋊C4C2×D13semidirect
286. C2×C22⋊C4C2×D13semidirect
294. #95C2×D13semidirect
368. C13#2412semidirect

Maximal subgroups

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

subgroupindex
C2×#881912
C2×#881372
C2×C22⋊C4×D132
C13×#3942
#117188832
#117186502
#117186482
#117186172
#117186142
#117186132
#117183282
#117183252
#241213