Finite Group Databasebeta

← #29574352

Subgroups — #29574352

Order 15616.

454 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454554C211yesmaximal, characteristic
2#21446592C211yesmaximal, characteristic, complemented
3#21444243C211yesmaximal, characteristic
4C2×#16839491C211yesmaximal, characteristic
5#21443714C211yesmaximal, characteristic, complemented
6#21443656C211yesmaximal, characteristic, complemented
7C61×#1566C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16839839—21no—
11#16839832—22no—
12#16839827—21no—
13#16839815C2211yescharacteristic
14C2×#14519712—21no—
15C2×C4⋊#92418C2211yescharacteristic
16#16839725—21no—
17C4×#11758194C2211yescharacteristic
18#16839526—21no—
19#16839491C411yescharacteristic
20#16839491C411yescharacteristic
21#16839491C411yescharacteristic
22#16839491C411yescharacteristic
23#16839489—21no—
24#16839489—21no—
25C61×#423C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×C4×C8×C61C2211yescharacteristic
28C61×#334—22no—
29C22×D244Q811yescharacteristic
30C22×C4×D61—21no—
31C2×#11758194D411yescharacteristic
32C2×#11758194D411yescharacteristic
33C2×#11758189—22no—
34M16×D61—42no—
35M16×D61—42no—
36C22×#92418—21no—
37C2×C8×D61—22no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244C2×C411yescharacteristic
41C4×D244C2×C411yescharacteristic
42C4×D244D411yescharacteristic
43C4×D244D411yescharacteristic
44C2×C4⋊Dic61Q811yescharacteristic
45C2×#11758198—21no—
46#14519712—42no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418C2×C411yescharacteristic
50C4⋊#92418C2×C411yescharacteristic
51C22⋊#92418—21no—
52#14519689—22no—
53#14519689—22no—
54#14519688—21no—
55C4×#92418—21no—
56C4×#92418—21no—
57C2×M16×C61—21no—
58C2×M16×C61—21no—
59C22×C8×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61D412yes—
65C4×C8×C61—21no—
66C4×C8×C61C2×C411yescharacteristic
67C4×C8×C61C2×C411yescharacteristic
68C23×D61—21no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×Q811yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C22×Dic61—21no—
73C2×D244—22no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244C4⋊C411yescharacteristic
77C2×D244C4⋊C411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86M16×C61—41no—
87M16×C61—41no—
88M16×C61—41no—
89M16×C61—41no—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—22no—
93C2×C8×C61—42no—
94C2×C8×C61—41no—
95C42×C61C22×C411yescharacteristic
96C42×C61C2×D411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C4⋊C411yescharacteristic
105C4⋊Dic61C4⋊C411yescharacteristic
106#11758194—21no—
107#11758194—21no—
108#11758194—21no—
109#11758194SD1612yes—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117#11758189—44no—
118C8×D61—44no—
119C23×C61C22⋊Q811yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—42no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—81no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—41no—
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61#12311yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—42no—
147D244#10812yescomplemented
148C4×D61—41no—
149C4×D61—41no—
150C4×D61—41no—
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C8×C61—22no—
157C8×C61—41no—
158C8×C61—42no—
159C8×C61—81no—
160#92418—22no—
161#92418—41no—
162#92418—41no—
163#92418—41no—
164#92418—81no—
165#8908—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61#38511yescharacteristic
169C22×C61#47611yescharacteristic
170C22×C61#47811yescharacteristic
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—82no—
178C2×D61—82no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61C2×#10811yescharacteristic
183C4×C61#43011yescharacteristic
184C4×C61C4×SD1611yescharacteristic
185C4×C61#44211yescharacteristic
186C4×C61#44911yescharacteristic
187C4×C61#45011yescharacteristic
188Dic61—41no—
189Dic61—41no—
190D4×M16—611no—
191#1950—611no—
192#1566D6111yescharacteristic, complemented
193#1486—611no—
194C2×D4⋊C8—611no—
195#1301—611no—
196#1278—611no—
197C2×C61—21no—
198C2×C61—21no—
199C2×C61#185511yescharacteristic
200C2×C61#186111yescharacteristic
201C2×C61#186411yescharacteristic
202D61—42no—
203D61—81no—
204C22×M16—1221no—
205C2×C4×D4—611no—
206#436—1221no—
207#435—1222no—
208C8×D4—1221no—
209#431—611no—
210C2×#108—1221no—
211#423C2×D6111yescharacteristic
212#423C2×D6111yescharacteristic
213C2×C4⋊C8—611no—
214#407—1221no—
215C4×M16—611no—
216C2×C4×C8C2×D6111yescharacteristic
217#341—1221no—
218#334—22no—
219D4⋊C8—611no—
220D4⋊C8—611no—
221D4⋊C8—611no—
222D4⋊C8—611no—
223D4⋊C8—1221no—
224D4⋊C8—1221no—
225C61#890811yescharacteristic, complemented, Sylow
226C22×D4—611no—
227C23×C4—1221no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—611no—
231C2×M16—611no—
232C2×M16—1222no—
233C2×M16—2442no—
234C2×M16—2442no—
235C22×C8—21no—
236C22×C8—1222no—
237C22×C8—1221no—
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—611no—
241C4×D4—611no—
242C4×D4—1221no—
243C4×D4—1221no—
244C2×C4⋊C4—611no—
245C2×C22⋊C4—1221no—
246C2×C42C22×D6111yescharacteristic
247#108—2442no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—611no—
252C4⋊C8—611no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255C4⋊C8C22⋊D6112yes—
256C22⋊C8—1222no—
257C22⋊C8—1222no—
258C22⋊C8—1221no—
259#97—1221no—
260C4×C8—21no—
261C4×C8—1221no—
262C4×C8—1221no—
263C4×C8C4×D6111yescharacteristic
264C4×C8C4×D6111yescharacteristic
265C24—1221no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—2441no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4#1175822211yescharacteristic
281C22×C4D4×D6111yescharacteristic
282C22×C4Q8×D6111yescharacteristic
283M16—41no—
284M16—41no—
285M16—41no—
286M16—41no—
287M16—612no—
288M16—1221no—
289M16—1221no—
290M16—1221no—
291M16—2444no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—22no—
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—1221no—
298C2×C8—1221no—
299C2×C8—1221no—
300C2×C8—1221no—
301C2×C8—2444no—
302C2×C8—2441no—
303C2×C8—2441no—
304C2×C8—2441no—
305C4⋊C4—611no—
306C4⋊C4—611no—
307C4⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C42C2×C4×D6111yescharacteristic
313C42D4×D6111yescharacteristic
314C42#1175822611yescharacteristic
315C42C2×C22⋊D6111yescharacteristic
316C23—1221no—
317C23—1221no—
318C23—4881no—
319C23—2442no—
320C23—2441no—
321C23—2441no—
322C23#1451975511yescharacteristic
323D4—612no—
324D4—1221no—
325D4—1221no—
326D4—1221no—
327D4—2442no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4C4⋊C4×D6111yescharacteristic
344C2×C4C4×C22⋊D6111yescharacteristic
345C2×C4#1451973911yescharacteristic
346C2×C4#1451974511yescharacteristic
347C2×C4#1451975311yescharacteristic
348C2×C4#1451976211yescharacteristic
349C2×C4SD16×D6111yescharacteristic
350C2×C4#1451979811yescharacteristic
351C2×C4#1451980411yescharacteristic
352C2×C4#1451980411yescharacteristic
353C8—22no—
354C8—41no—
355C8—42no—
356C8—81no—
357C8—1222no—
358C8—4881no—
359C8—2441no—
360C8—2441no—
361C8—2441no—
362C22—21no—
363C22—21no—
364C22—1222no—
365C22—4882no—
366C22—4882no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22#1683963311yescharacteristic
373C22#1684005111yescharacteristic
374C22#1684006111yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—2441no—
379C4—2441no—
380C4#108×D6111yescharacteristic
381C4#1683980911yescharacteristic
382C4#1683984911yescharacteristic
383C4#1683987311yescharacteristic
384C4#1683990611yescharacteristic
385C4#1683991111yescharacteristic
386C2—21no—
387C2—21no—
388C2—4881no—
389C2—2442no—
390C2#2144602211yescharacteristic
391C2#2144605811yescharacteristic
392C2#2144607711yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1566C2
socleC22×C61#385
prime radicalC22×D244Q8
cosocleC2×C42×C61C23
hypercenter#1566D61
hypocenterC61#8908
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
2. #21446592C2semidirect
5. #21443714C2semidirect
6. #21443656C2semidirect
7. C61×#1566C2semidirect
147. D244#108semidirect
192. #1566D61semidirect
225. C61#8908semidirect

Maximal subgroups

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

subgroupindex
#214545542
#214465922
#214442432
C2×#168394912
#214437142
#214436562
C61×#15662
#890861