Finite Group Databasebeta

← #15765222

Subgroups — #15765222

Order 3328.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718688C211yesmaximal, characteristic, complemented
2C2×#11718676C211yesmaximal, characteristic
3#13115641C211yesmaximal, characteristic, complemented
4C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
5C2×D4⋊#1055C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#2538C211yesmaximal, characteristic, complemented
8C2×C13×C22⋊Q8—21no—
9C2×C4×Q8×C13C2211yescharacteristic
10C2×C4×D4×C13C2211yescharacteristic
11C22×#6106—21no—
12C22×#6104—21no—
13C2×#88128C2211yescharacteristic
14C13×#396—22no—
15C13×#390—21no—
16C13×#389—21no—
17C13×#384C2211yescharacteristic
18C13×#380—21no—
19#11718688—22no—
20#11718688—22no—
21#11718676—22no—
22#11718676—22no—
23C2×#88049—21no—
24C2×#88049—21no—
25C2×#88049—22no—
26C2×C4⋊#1055C2211yescharacteristic
27C2×C4⋊#1055C2211yescharacteristic
28C2×C4×#1055C2211yescharacteristic
29Q8⋊#1055—22no—
30D4⋊#1055—22no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C22×D52—21no—
35C22×D52—21no—
36C22×D52—21no—
37C13×C22⋊Q8—42no—
38C13×C22⋊Q8—42no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C2×C13×C4⋊C4—22no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C4⋊C4D412yes—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—22no—
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59C2×#6106—24no—
60C2×#6106—42no—
61C2×#6106—42no—
62C2×#6104—24no—
63C2×#6104—42no—
64C2×#6104—42no—
65C22×#1055—21no—
66C22×#1055—21no—
67C22×#1055—21no—
68#88128—21no—
69#88128—21no—
70#88128—21no—
71#88128D412yes—
72C13×#95—22no—
73#88049—24no—
74#88049—24no—
75#88049—44no—
76C4⋊#1055—21no—
77C4⋊#1055—21no—
78C4⋊#1055D412yes—
79C4⋊#1055D412yes—
80C4×#1055—21no—
81C4×#1055—21no—
82#10229—131nomaximal, Sylow
83C24×C13—21no—
84C23×D13—41no—
85C2×Q8×C13—21no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13D812yescomplemented
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13SD1612yescomplemented
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C2×D52—22no—
111C2×D52—22no—
112C2×D52—22no—
113C2×D52—42no—
114C2×D52—42no—
115C2×D52—41no—
116C2×D52—41no—
117C2×D52—41no—
118C2×D52—41no—
119C2×D52—41no—
120C2×D52—41no—
121C2×D52—41no—
122C2×D52—41no—
123C2×D52—41no—
124C2×D52—41no—
125C2×D52—41no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4—44no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4—41no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C22⋊C4—44no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—82no—
142C42×C13—41no—
143C42×C13—41no—
144C42×C13C2×D411yescharacteristic
145C42×C13C2×D411yescharacteristic
146C42×C13C2×D411yescharacteristic
147C42×C13#4111yescharacteristic
148#6106—48no—
149#6104—48no—
150C2×#1055—22no—
151C2×#1055—22no—
152C2×#1055—22no—
153C2×#1055—41no—
154C2×#1055—41no—
155C2×#1055—41no—
156C2×#1055—41no—
157C2×#1055—41no—
158C2×#1055—41no—
159C2×#460—131no—
160C2×#459—131no—
161#2538D1311yescharacteristic, complemented
162#1957—131no—
163C2×Q8⋊C8—131no—
164C2×D4⋊C8—131no—
165#1296—131no—
166C23×C13—22no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13#12011yescharacteristic
174C22×D13—42no—
175C22×D13—81no—
176C22×D13—81no—
177C22×D13—81no—
178C22×D13—81no—
179C22×D13—81no—
180C22×D13—81no—
181Q8×C13—22no—
182Q8×C13—22no—
183Q8×C13—41no—
184Q8×C13—41no—
185D4×C13—22no—
186D4×C13—22no—
187D4×C13—41no—
188D4×C13—41no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—22no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—42no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—41no—
200C2×C4×C13—41no—
201C2×C4×C13—42no—
202C2×C4×C13—41no—
203C2×C4×C13—81no—
204C2×C4×C13—81no—
205C2×C4×C13—81no—
206C2×C4×C13—81no—
207C2×C4×C13#12011yescharacteristic
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12111yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12111yescharacteristic
212C2×C4×C13#12711yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C2×SD1611yescharacteristic
215C2×C4×C13#13511yescharacteristic
216C2×C4×C13#13511yescharacteristic
217C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
218C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
219C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C13#13711yescharacteristic
221D52—44no—
222D52—42no—
223D52—42no—
224D52—42no—
225D52—42no—
226D52—82no—
227D52—81no—
228D52—81no—
229D52—81no—
230D52—81no—
231#1055—42no—
232#1055—42no—
233#1055—42no—
234C22×SD16—261no—
235C22×D8—261no—
236C2×#127—131no—
237C2×C22⋊Q8—21no—
238C2×C4×Q8C2×D1311yescharacteristic
239C2×C4×D4C2×D1311yescharacteristic
240#460—262no—
241#460—262no—
242#459—262no—
243#459—262no—
244C2×C4⋊C8—131no—
245C2×C4⋊C8—131no—
246C2×#102—261no—
247C2×#102—261no—
248C2×#102—262no—
249C2×C4×C8—131no—
250#396—22no—
251#390—21no—
252#389—21no—
253#384C2×D1311yescharacteristic
254#380—21no—
255Q8⋊C8—262no—
256D4⋊C8—262no—
257C22×C13—42no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13#39211yescharacteristic
265C22×C13#44711yescharacteristic
266C22×C13#44811yescharacteristic
267C22×C13#44911yescharacteristic
268C22×C13#44911yescharacteristic
269C22×C13#45311yescharacteristic
270C22×C13#45411yescharacteristic
271C2×D13—82no—
272C2×D13—82no—
273C2×D13—82no—
274C2×D13—161no—
275C2×D13—161no—
276C2×D13—161no—
277C2×D13—161no—
278C4×C13—21no—
279C4×C13—21no—
280C4×C13—42no—
281C4×C13—82no—
282C4×C13—81no—
283C4×C13—81no—
284C4×C13#44711yescharacteristic
285C4×C13#44911yescharacteristic
286C4×C13#45011yescharacteristic
287C4×C13#45211yescharacteristic
288C4×C13#46511yescharacteristic
289C4×C13#46611yescharacteristic
290C4×C13#46811yescharacteristic
291C4×C13#46911yescharacteristic
292C22×Q8C22⋊D1311yescharacteristic
293C22×D4—261no—
294C22×D4—261no—
295C22×D4—261no—
296C22×D4C22⋊D1311yescharacteristic
297C23×C4—21no—
298C2×SD16—264no—
299C2×SD16—522no—
300C2×SD16—522no—
301C2×D8—264no—
302C2×D8—522no—
303C2×D8—522no—
304C22×C8—261no—
305C22×C8—261no—
306C22×C8—261no—
307#127—132no—
308#127—261no—
309#127—261no—
310#127—261no—
311C22⋊Q8—42no—
312C22⋊Q8—42no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4C22⋊D1311yescharacteristic
326C2×C4⋊C4C22⋊D1311yescharacteristic
327C2×C4⋊C4C22⋊D1312yes—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C42—21no—
332C2×C42C22×D1311yescharacteristic
333C4⋊C8—132no—
334C4⋊C8—132no—
335C4⋊C8—261no—
336C4⋊C8—261no—
337#102—264no—
338#102—264no—
339#102—524no—
340C4×C8—261no—
341C4×C8—261no—
342#95—22no—
343C2×C13—82no—
344C2×C13#162111yescharacteristic
345C2×C13#162211yescharacteristic
346C2×C13#162711yescharacteristic
347C2×C13#162811yescharacteristic
348C2×C13#199911yescharacteristic
349C2×C13#200011yescharacteristic
350C2×C13#200611yescharacteristic
351D13—162no—
352C24—21no—
353C24—521no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8#610412yescomplemented
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—262no—
366C2×D4—262no—
367C2×D4—262no—
368C2×D4—522no—
369C2×D4—522no—
370C2×D4—521no—
371C2×D4—521no—
372C2×D4—521no—
373C2×D4—521no—
374C2×D4—521no—
375C2×D4—521no—
376C2×D4—521no—
377C2×D4—521no—
378C2×D4—521no—
379C2×D4—521no—
380C2×D4—521no—
381C2×D4#610612yescomplemented
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4C2×C22⋊D1311yescharacteristic
393C22×C4C2×C22⋊D1311yescharacteristic
394C22×C4C2×C22⋊D1311yescharacteristic
395SD16—528no—
396D8—528no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—521no—
401C2×C8—521no—
402C2×C8—521no—
403C2×C8—521no—
404C2×C8—521no—
405C2×C8—521no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—42no—
411C4⋊C4—44no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C22⋊C4—44no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—82no—
422C42—41no—
423C42—41no—
424C42D4×D1311yescharacteristic
425C42D4×D1311yescharacteristic
426C42D4×D1311yescharacteristic
427C42#612911yescharacteristic
428C13#1022911yescharacteristic, complemented, Sylow
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—522no—
437C23—1041no—
438C23—1041no—
439C23—1041no—
440C23—1041no—
441C23—1041no—
442C23—1041no—
443C23#8820711yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—22no—
449D4—22no—
450D4—41no—
451D4—41no—
452D4—524no—
453D4—522no—
454D4—522no—
455D4—522no—
456D4—522no—
457D4—1042no—
458D4—1041no—
459D4—1041no—
460D4—1041no—
461D4—1041no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4C2×#610411yescharacteristic
481C2×C4#8818611yescharacteristic
482C2×C4#8819111yescharacteristic
483C2×C4#8819111yescharacteristic
484C2×C4#8819211yescharacteristic
485C2×C4#8819311yescharacteristic
486C2×C4#8819311yescharacteristic
487C2×C4#8819411yescharacteristic
488C2×C4C2×#610611yescharacteristic
489C2×C4#8819611yescharacteristic
490C2×C4#8820311yescharacteristic
491C2×C4#8820311yescharacteristic
492C2×C4#8820411yescharacteristic
493C2×C4#8820411yescharacteristic
494C8—522no—
495C8—522no—
496C8—522no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—1042no—
505C22—1042no—
506C22—1042no—
507C22—2081no—
508C22—2081no—
509C22—2081no—
510C22—2081no—
511C22#1171887811yescharacteristic
512C22#1171888411yescharacteristic
513C22#1171888811yescharacteristic
514C22#1171889911yescharacteristic
515C22#1171889911yescharacteristic
516C22#1171890211yescharacteristic
517C22#1171890611yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—82no—
522C4—81no—
523C4—81no—
524C4#1171869711yescharacteristic
525C4#1171869811yescharacteristic
526C4#1171869911yescharacteristic
527C4#1171870011yescharacteristic
528C4#1171870711yescharacteristic
529C4#1171870811yescharacteristic
530C4#1171870911yescharacteristic
531C4#1171871011yescharacteristic
532C2—82no—
533C2—2082no—
534C2#1311390111yescharacteristic
535C2#1311390811yescharacteristic
536C2#1311393911yescharacteristic
537C2#1311394611yescharacteristic
538C2#1311583211yescharacteristic
539C2#1311583711yescharacteristic
540C2#1311587811yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2538C2
socleC23×C13#120
prime radicalC2×#11718676C2
hypercenter#2538D13
hypocenterC13#10229
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#11718688C2semidirect
3. #13115641C2semidirect
4. C2×Q8⋊#1055C2semidirect
5. C2×D4⋊#1055C2semidirect
6. #13112719C2semidirect
7. C13×#2538C2semidirect
90. C2×Q8×C13D8semidirect
96. C2×D4×C13SD16semidirect
161. #2538D13semidirect
359. C2×Q8#6104semidirect
381. C2×D4#6106semidirect
428. C13#10229semidirect

Maximal subgroups

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

subgroupindex
C2×#117186882
C2×#117186762
#131156412
C2×Q8⋊#10552
C2×D4⋊#10552
#131127192
C13×#25382
#1022913