Finite Group Databasebeta

← #29583372

Subgroups — #29583372

Order 15616.

708 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450765C211yesmaximal, characteristic
2#21446625C211yesmaximal, characteristic, complemented
3#21446578C211yesmaximal, characteristic, complemented
4#21445819C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6#21443659C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×#14519773—21no—
10C2×#14519751—21no—
11C2×#14519751—21no—
12C2×#14519711—21no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—22no—
15C2×#14519698—21no—
16#16839671—22no—
17#16839663—21no—
18#16839632C2211yescharacteristic
19C4×C4⋊Dic61C2211yescharacteristic
20#16839525—21no—
21#16839524—21no—
22#16839505—22no—
23C2×C4×D4×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4×C8×C61C2211yescharacteristic
26C61×D4⋊C8—22no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244D412yes—
30C22×C22⋊D61—22no—
31C22×C22⋊D61—22no—
32C22×#92418—21no—
33#14519774—21no—
34#14519774—21no—
35#14519774—21no—
36#14519774—21no—
37#14519773—42no—
38#14519773—42no—
39#14519751—42no—
40#14519751—42no—
41#14519751—42no—
42#14519751—42no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×C4⋊Dic61D411yescharacteristic
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×C4×Dic61—21no—
51#14519711—42no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54#14519699—44no—
55#14519698—42no—
56#14519684—21no—
57C22×D4×C61D411yescharacteristic
58C23×C4×C61—21no—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61C4×D4×C61—21no—
62C4×D4×C61—21no—
63C4×D4×C61—21no—
64C4×D4×C61—21no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61D412yescomplemented
70C4×C8×C61—21no—
71C4×C8×C61—21no—
72C24×C61—21no—
73C23×D61—22no—
74C2×D4×C61—21no—
75C2×D4×C61—21no—
76C2×D4×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—21no—
79C2×D4×C61D812yes—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C2×C22⋊D61—44no—
91C2×C22⋊D61—44no—
92C2×C22⋊D61—44no—
93C2×C22⋊D61—44no—
94C2×C22⋊D61—82no—
95C2×C22⋊D61—82no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—41no—
99C2×D244—22no—
100C2×D244—22no—
101C2×D244—42no—
102C2×D244—42no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244—41no—
113C2×D244—41no—
114C2×D244—41no—
115C2×C8×C61—22no—
116C2×C8×C61—22no—
117C2×C8×C61—41no—
118C2×C8×C61—41no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C42×C61C2×D411yescharacteristic
126C42×C61#4111yescharacteristic
127C42×C61#4111yescharacteristic
128C42×C61#4111yescharacteristic
129#11758198—44no—
130#11758198—44no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61—42no—
134C4⋊Dic61—41no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4⋊Dic61—41no—
138C4⋊Dic61D812yes—
139C4⋊Dic61SD1612yes—
140C4×Dic61—41no—
141C4×Dic61—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C23×C61—22no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61#12011yescharacteristic
153C22×D61—42no—
154C22×D61—42no—
155C22×D61—42no—
156C22×D61—42no—
157C22×D61—42no—
158C22×D61—42no—
159C22×D61—42no—
160D4×C61—22no—
161D4×C61—22no—
162D4×C61—41no—
163D4×C61—41no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12311yescharacteristic
177C2×C4×C61#12311yescharacteristic
178C2×C4×C61#12411yescharacteristic
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C2×SD1611yescharacteristic
182C2×C4×C61#13511yescharacteristic
183C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C61#13711yescharacteristic
187C22⋊D61—88no—
188C22⋊D61—88no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61—81no—
198D244—44no—
199D244—82no—
200D244—81no—
201D244—81no—
202D244—81no—
203D244—81no—
204D244—81no—
205D244—81no—
206D244—81no—
207D244—81no—
208C8×C61—42no—
209C8×C61—42no—
210#92418—81no—
211#10408—611nomaximal, Sylow
212C22×C61—42no—
213C22×C61—42no—
214C22×C61—42no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61—81no—
219C22×C61#39411yescharacteristic
220C22×C61#44711yescharacteristic
221C22×C61#44711yescharacteristic
222C22×C61#45011yescharacteristic
223C22×C61#45211yescharacteristic
224C22×C61#45311yescharacteristic
225C22×C61#45511yescharacteristic
226C2×D61—82no—
227C2×D61—82no—
228C2×D61—82no—
229C2×D61—82no—
230C2×D61—82no—
231C2×D61—82no—
232C2×D61—82no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61#45911yescharacteristic
237C4×C61#46011yescharacteristic
238C4×C61#46611yescharacteristic
239C4×C61#46811yescharacteristic
240C4×C61#48011yescharacteristic
241C4×C61#48211yescharacteristic
242C4×C61#48611yescharacteristic
243C4×C61#49011yescharacteristic
244Dic61—42no—
245Dic61—42no—
246Dic61—161no—
247#2541—611no—
248#1957—611no—
249#1947—611no—
250#1802—611no—
251C2×#331—611no—
252C2×D4⋊C8D6111yescharacteristic, complemented
253#1279—611no—
254C2×C61—82no—
255C2×C61#161911yescharacteristic
256C2×C61#163111yescharacteristic
257C2×C61#163911yescharacteristic
258C2×C61#164111yescharacteristic
259C2×C61#203311yescharacteristic
260C2×C61#203711yescharacteristic
261C2×C61#204111yescharacteristic
262D61—162no—
263C2×#127—611no—
264C2×#127—1221no—
265C2×#121—1221no—
266C2×#121—1221no—
267C2×C4×D4C2×D6111yescharacteristic
268C2×#107—1221no—
269C2×C4⋊C8—611no—
270C2×C4⋊C8C2×D6111yescharacteristic
271C2×#102—1222no—
272C2×#102—1221no—
273C2×C4×C8C2×D6111yescharacteristic
274#392—1222no—
275#390—1221no—
276#384—611no—
277C4×C4⋊C4—611no—
278#340—1221no—
279#340—1221no—
280#331—1222no—
281D4⋊C8—22no—
282C61#1040811yescharacteristic, complemented, Sylow
283C22×D4—612no—
284C22×D4—1222no—
285C22×D4—1222no—
286C22×D4—1221no—
287C22×D4—1221no—
288C22×D4D24411yescharacteristic
289C23×C4—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—1221no—
293#127—1221no—
294#127—1221no—
295#127—1221no—
296#127—1221no—
297#127—2442no—
298#127—2442no—
299#121—2442no—
300#121—2442no—
301#121—2442no—
302#121—2442no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C2×C4⋊C4—611no—
308C2×C4⋊C4—611no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4D24411yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—1222no—
315C2×C22⋊C4—1222no—
316C2×C42—1221no—
317C2×C42C22×D6111yescharacteristic
318#107—2442no—
319C4⋊C8—21no—
320C4⋊C8—1221no—
321C4⋊C8—1221no—
322C4⋊C8C22⋊D6112yescomplemented
323#102—2444no—
324#102—2442no—
325C4×C8—21no—
326C4×C8—21no—
327#95—1221no—
328C24—21no—
329C24—1222no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—1222no—
336C2×D4—1222no—
337C2×D4—4882no—
338C2×D4—4882no—
339C2×D4—2442no—
340C2×D4—2442no—
341C2×D4—2444no—
342C2×D4—2444no—
343C2×D4—2444no—
344C2×D4—2444no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4D48812yes—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—2441no—
368C22×C4C2×D24411yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—2441no—
378C2×C8—2441no—
379C2×C8—2441no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—612no—
383C4⋊C4—612no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C4⋊C4—2442no—
387C4⋊C4—2441no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—2444no—
394C22⋊C4—2444no—
395C42—2441no—
396C42—2441no—
397C42#1175822211yescharacteristic
398C42#1175822411yescharacteristic
399C42#1175822411yescharacteristic
400C42C2×C22⋊D6111yescharacteristic
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—2442no—
409C23—2442no—
410C23—2442no—
411C23—2442no—
412C23—2442no—
413C23—2442no—
414C23—2442no—
415C23#1451974711yescharacteristic
416D4—22no—
417D4—22no—
418D4—41no—
419D4—41no—
420D4—4882no—
421D4—4888no—
422D4—4888no—
423D4—4881no—
424D4—4881no—
425D4—4881no—
426D4—4881no—
427D4—4881no—
428D4—4881no—
429D4—4881no—
430D4—4881no—
431D4—2444no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—1222no—
442C2×C4—1222no—
443C2×C4—4881no—
444C2×C4—4881no—
445C2×C4—4881no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4#1451974811yescharacteristic
451C2×C4#1451974911yescharacteristic
452C2×C4#1451975111yescharacteristic
453C2×C4#1451975911yescharacteristic
454C2×C4#1451976111yescharacteristic
455C2×C4#1451976311yescharacteristic
456C2×C4D8×D6111yescharacteristic
457C2×C4C2×D48811yescharacteristic
458C2×C4SD16×D6111yescharacteristic
459C2×C4#1451979911yescharacteristic
460C2×C4#1451980111yescharacteristic
461C2×C4#1451980411yescharacteristic
462C2×C4#1451980511yescharacteristic
463C2×C4#1451981011yescharacteristic
464C8—42no—
465C8—42no—
466C8—4881no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—4882no—
475C22—4882no—
476C22—4882no—
477C22—4882no—
478C22—4882no—
479C22—4882no—
480C22—4882no—
481C22#1683967811yescharacteristic
482C22#1683989711yescharacteristic
483C22#1683989811yescharacteristic
484C22#1683991411yescharacteristic
485C22#1683992611yescharacteristic
486C22#1683993111yescharacteristic
487C22#1683994111yescharacteristic
488C4—21no—
489C4—21no—
490C4—81no—
491C4—9761no—
492C4—2442no—
493C4—2442no—
494C4#1683995511yescharacteristic
495C4#1683996011yescharacteristic
496C4#1683999811yescharacteristic
497C4#1684000811yescharacteristic
498C4#1684007611yescharacteristic
499C4#1684008711yescharacteristic
500C4#1684010711yescharacteristic
501C4#1684012511yescharacteristic
502C2—82no—
503C2—9762no—
504C2#2144487511yescharacteristic
505C2#2144494911yescharacteristic
506C2#2144500011yescharacteristic
507C2#2144501511yescharacteristic
508C2#2144700211yescharacteristic
509C2#2144702811yescharacteristic
510C2#2144705211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radical#21450765C2
hypercenterC2×D4⋊C8D61
hypocenterC61#10408
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #21446625C2semidirect
3. #21446578C2semidirect
4. #21445819C2semidirect
5. C2×#16839505C2semidirect
6. #21443659C2semidirect
7. C2×C61×D4⋊C8C2semidirect
69. C4⋊C8×C61D4semidirect
252. C2×D4⋊C8D61semidirect
282. C61#10408semidirect
322. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214507652
#214466252
#214465782
#214458192
C2×#168395052
#214436592
C2×C61×D4⋊C82
#1040861