Finite Group Databasebeta

← #29584218

Subgroups — #29584218

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840138C211yesmaximal, characteristic
2#21446746C211yesmaximal, characteristic, complemented
3#21446538C211yesmaximal, characteristic, complemented
4C2×#16839506C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1982C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C22×#11758199—21no—
10C2×#14519774C2211yescharacteristic
11#16840138—22no—
12#16840138—22no—
13C2×C4⋊#92418—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×C4⋊#92418C2211yescharacteristic
16C2×#14519697—21no—
17C2×#14519697—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839517—21no—
20#16839506—22no—
21#16839505—22no—
22C2×#127×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×#102×C61—21no—
25C2×#102×C61—21no—
26C4×C4⋊C4×C61C2211yescharacteristic
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C2×#11758199—24no—
31C2×#11758199—24no—
32C2×#11758199—42no—
33C2×#11758199—42no—
34C2×#11758199—42no—
35C2×#11758199—42no—
36C22×#92418—21no—
37C22×#92418—21no—
38C22×#92418D411yescharacteristic
39C22×#92418D411yescharacteristic
40#14519774—21no—
41#14519774—21no—
42#14519774—21no—
43#14519774D412yes—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—42no—
49#14519697—42no—
50#14519697—42no—
51C4×#92418—21no—
52C4×#92418—21no—
53C22×D4×C61—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×C8×C61—21no—
57#127×C61—21no—
58#127×C61—21no—
59#127×C61—21no—
60#127×C61D412yes—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61C2311yescharacteristic
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67#102×C61—42no—
68#102×C61—42no—
69#95×C61—21no—
70C24×C61—41no—
71C23×D61—41no—
72C2×D4×C61—22no—
73C2×D4×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—81no—
87C2×D4×C61—81no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C2×D244—22no—
94C2×D244—22no—
95C2×D244—22no—
96C2×D244—41no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—81no—
108C2×D244—81no—
109C2×C8×C61—41no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—21no—
113C4⋊C4×C61—21no—
114C4⋊C4×C61—21no—
115C4⋊C4×C61D812yescomplemented
116C42×C61—41no—
117C42×C61—41no—
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C42×C61#4111yescharacteristic
121C42×C61#4111yescharacteristic
122#11758199—48no—
123#11758199—48no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—21no—
127C2×#92418—21no—
128C2×#92418—41no—
129C2×#92418—41no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418—41no—
133C2×#92418—41no—
134C2×#92418D812yes—
135C2×#92418SD1612yes—
136C23×C61—42no—
137C23×C61—81no—
138C23×C61—81no—
139C23×C61—81no—
140C23×C61—81no—
141C23×C61—81no—
142C23×C61—81no—
143C23×C61#12111yescharacteristic
144C22×D61—42no—
145C22×D61—81no—
146C22×D61—81no—
147C22×D61—81no—
148C22×D61—81no—
149C22×D61—81no—
150C22×D61—81no—
151D4×C61—42no—
152D4×C61—42no—
153D4×C61—42no—
154D4×C61—42no—
155D4×C61—82no—
156D4×C61—82no—
157D4×C61—81no—
158D4×C61—81no—
159D4×C61—81no—
160D4×C61—81no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—22no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61#12011yescharacteristic
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12311yescharacteristic
173C2×C4×C61#12311yescharacteristic
174C2×C4×C61#12411yescharacteristic
175C2×C4×C61C2×D811yescharacteristic
176C2×C4×C61C2×D811yescharacteristic
177C2×C4×C61C2×SD1611yescharacteristic
178C2×C4×C61#13511yescharacteristic
179C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
183D244—42no—
184D244—42no—
185D244—42no—
186D244—42no—
187D244—82no—
188D244—82no—
189D244—81no—
190D244—81no—
191D244—81no—
192D244—81no—
193C8×C61—81no—
194#92418—22no—
195#92418—22no—
196#92418—81no—
197#92418—81no—
198#10536—611nomaximal, Sylow
199C22×C61—82no—
200C22×C61—82no—
201C22×C61—82no—
202C22×C61—161no—
203C22×C61—161no—
204C22×C61—161no—
205C22×C61—161no—
206C22×C61#39411yescharacteristic
207C22×C61#45911yescharacteristic
208C22×C61#46011yescharacteristic
209C22×C61#46611yescharacteristic
210C22×C61#46911yescharacteristic
211C22×C61#47211yescharacteristic
212C22×C61#47211yescharacteristic
213C2×D61—82no—
214C2×D61—82no—
215C2×D61—82no—
216C2×D61—161no—
217C2×D61—161no—
218C2×D61—161no—
219C2×D61—161no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—42no—
223C4×C61—81no—
224C4×C61#44711yescharacteristic
225C4×C61#45011yescharacteristic
226C4×C61#45911yescharacteristic
227C4×C61#45911yescharacteristic
228C4×C61#46311yescharacteristic
229C4×C61#46311yescharacteristic
230C4×C61#48611yescharacteristic
231C4×C61#49011yescharacteristic
232C2×#493—611no—
233#1982—611no—
234#1982D6111yescharacteristic, complemented
235#1939—611no—
236C2×#331—611no—
237C2×#331—611no—
238#1277—611no—
239C2×C61—162no—
240C2×C61#166711yescharacteristic
241C2×C61#166811yescharacteristic
242C2×C61#168711yescharacteristic
243C2×C61#168811yescharacteristic
244C2×C61#204111yescharacteristic
245C2×C61#204511yescharacteristic
246C2×C61#205411yescharacteristic
247D61—162no—
248C22×D8—1221no—
249C22×D8—1221no—
250C2×#127—611no—
251C2×#127C2×D6111yescharacteristic
252#493—1222no—
253#493—1222no—
254C2×C4⋊C8—611no—
255C2×C4⋊C8—611no—
256C2×C4⋊C8—1221no—
257C2×C4⋊C8C2×D6111yescharacteristic
258C2×#102—21no—
259C2×#102—21no—
260C2×#102—1221no—
261C2×#102—1221no—
262C2×C4×C8—611no—
263C4×C4⋊C4C2×D6111yescharacteristic
264#336—1221no—
265#331—1222no—
266#331—1222no—
267C61#1053611yescharacteristic, complemented, Sylow
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—1221no—
272C22×D4—1221no—
273C22×D4—1221no—
274C2×D8—1224no—
275C2×D8—1224no—
276C2×D8—2442no—
277C2×D8—2442no—
278C2×D8—2442no—
279C2×D8—2442no—
280C22×C8—21no—
281C22×C8—611no—
282C22×C8—611no—
283C22×C8—1221no—
284C22×C8—1221no—
285#127—21no—
286#127—21no—
287#127—21no—
288#127—612no—
289#127—1221no—
290#127—1221no—
291#127—1221no—
292#127D24412yes—
293C2×C4⋊C4C22⋊D6111yescharacteristic
294C2×C4⋊C4C22⋊D6111yescharacteristic
295C2×C42—21no—
296C2×C42C22×D6111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—1221no—
300C4⋊C8—1221no—
301C4⋊C8—1221no—
302C4⋊C8—1221no—
303C4⋊C8—2442no—
304#102—42no—
305#102—42no—
306#102—2442no—
307#102—2442no—
308C4×C8—1221no—
309C4×C8—1221no—
310#95—21no—
311C24—41no—
312C24—2441no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—81no—
328C2×D4—81no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—4881no—
333C2×D4—4881no—
334C2×D4—2441no—
335C2×D4—2441no—
336C2×D4—2441no—
337C2×D4—2441no—
338C2×D4—2441no—
339C2×D4—2441no—
340C2×D4—2441no—
341C2×D4—2441no—
342C2×D4—2441no—
343C2×D4—2441no—
344C2×D4—2441no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4D4×D6111yescharacteristic
348C22×C4#1175822411yescharacteristic
349C22×C4C2×C22⋊D6111yescharacteristic
350D8—2448no—
351D8—2448no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—612no—
356C2×C8—612no—
357C2×C8—1221no—
358C2×C8—1221no—
359C2×C8—1221no—
360C2×C8—1221no—
361C2×C8—2441no—
362C2×C8—2441no—
363C2×C8—2441no—
364C2×C8—2441no—
365C2×C8—2441no—
366C2×C8—2441no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4#1175819912yescomplemented
371C42—41no—
372C42—41no—
373C42C2×D24411yescharacteristic
374C42#1175822211yescharacteristic
375C42D4×D6111yescharacteristic
376C42#1175822411yescharacteristic
377C23—42no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—4881no—
385C23—4881no—
386C23—4881no—
387C23—4881no—
388C23—4881no—
389C23—4881no—
390C23—2442no—
391C23#1451974911yescharacteristic
392D4—42no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—82no—
397D4—82no—
398D4—81no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—4882no—
403D4—4882no—
404D4—4881no—
405D4—4881no—
406D4—4881no—
407D4—4881no—
408D4—2442no—
409D4—2442no—
410D4—2442no—
411D4—2442no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4#1451974711yescharacteristic
421C2×C4#1451974811yescharacteristic
422C2×C4#1451975111yescharacteristic
423C2×C4#1451975911yescharacteristic
424C2×C4#1451976111yescharacteristic
425C2×C4#1451976311yescharacteristic
426C2×C4D8×D6111yescharacteristic
427C2×C4C2×#1175819911yescharacteristic
428C2×C4SD16×D6111yescharacteristic
429C2×C4#1451979711yescharacteristic
430C2×C4#1451980111yescharacteristic
431C2×C4#1451980211yescharacteristic
432C2×C4#1451980311yescharacteristic
433C2×C4#1451980411yescharacteristic
434C8—81no—
435C8—1222no—
436C8—1222no—
437C8—4881no—
438C8—4881no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—161no—
443C22—161no—
444C22—161no—
445C22—161no—
446C22—9761no—
447C22—9761no—
448C22—9761no—
449C22—9761no—
450C22—4882no—
451C22—4882no—
452C22—4882no—
453C22#1683967811yescharacteristic
454C22#1683995511yescharacteristic
455C22#1683996011yescharacteristic
456C22#1683999611yescharacteristic
457C22#1684001311yescharacteristic
458C22#1684003011yescharacteristic
459C22#1684003011yescharacteristic
460C4—21no—
461C4—21no—
462C4—42no—
463C4—81no—
464C4#1683989711yescharacteristic
465C4#1683991411yescharacteristic
466C4#1683995411yescharacteristic
467C4#1683995711yescharacteristic
468C4#1683997411yescharacteristic
469C4#1683997711yescharacteristic
470C4#1684010711yescharacteristic
471C4#1684012511yescharacteristic
472C2—162no—
473C2—9762no—
474C2#2144517211yescharacteristic
475C2#2144517711yescharacteristic
476C2#2144529611yescharacteristic
477C2#2144530111yescharacteristic
478C2#2144705211yescharacteristic
479C2#2144707411yescharacteristic
480C2#2144712911yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1982C2
socleC23×C61#121
prime radicalC2×#16840138C2
hypercenter#1982D61
hypocenterC61#10536
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #21446746C2semidirect
3. #21446538C2semidirect
4. C2×#16839506C2semidirect
5. C2×#16839505C2semidirect
6. #21443653C2semidirect
7. C61×#1982C2semidirect
115. C4⋊C4×C61D8semidirect
234. #1982D61semidirect
267. C61#10536semidirect
370. C4⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168401382
#214467462
#214465382
C2×#168395062
C2×#168395052
#214436532
C61×#19822
#1053661