Finite Group Databasebeta

← #29599616

Subgroups — #29599616

Order 15616.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519722C211yesmaximal, characteristic
2C2×#16839580C211yesmaximal, characteristic, complemented
3C2×#16839565C211yesmaximal, characteristic, complemented
4C2×#16839562C211yesmaximal, characteristic
5#21446683C211yesmaximal, characteristic
6#21446678C211yesmaximal, characteristic, complemented
7C61×#1380C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C2×#14519722—22no—
11C2×#14519722—22no—
12C2×#14519722—22no—
13C22×#11758185C2211yescharacteristic
14C2×#14519700—21no—
15C2×#14519697—21no—
16C2×C8×Dic61C2211yescharacteristic
17#16839667—21no—
18#16839663—21no—
19#16839580—22no—
20#16839565—22no—
21#16839562—22no—
22C22×C16×C61C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C2×#107×C61C2211yescharacteristic
25C22×Dic122—21no—
26C22×D244—21no—
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×Dic244—21no—
30C2×Dic244—21no—
31C2×Dic244—21no—
32C2×Dic244D412yes—
33C2×D488—21no—
34C2×D488—21no—
35C2×D488—21no—
36C2×D488—21no—
37C2×D488—21no—
38C2×D488D412yes—
39C22×#92418D411yescharacteristic
40C2×#11758198—41no—
41C2×#11758198—41no—
42C2×C4×Dic61D411yescharacteristic
43#14519722—28no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47#14519700—42no—
48#14519697—42no—
49C8×Dic61—21no—
50C8×Dic61—21no—
51#14519684—41no—
52#14519684—41no—
53C22×C8×C61C2311yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C2×C16×C61D412yes—
59#107×C61—21no—
60#107×C61—21no—
61#107×C61—21no—
62#107×C61—21no—
63C23×D61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—41no—
68C22×Dic61D811yescharacteristic
69C22×Dic61D811yescharacteristic
70C2×D244—22no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—41no—
76C2×Dic122—22no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82C2×C8×C61C2×D411yescharacteristic
83C2×C8×C61C2×D411yescharacteristic
84C2×C8×C61C2×D411yescharacteristic
85C2×C8×C61#4111yescharacteristic
86C2×C8×C61#4111yescharacteristic
87C2×C8×C61#4111yescharacteristic
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92#11758198—82no—
93#11758198—82no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C2×#92418—21no—
97C2×#92418—21no—
98C2×#92418—21no—
99Dic244—22no—
100Dic244—22no—
101Dic244—41no—
102Dic244—41no—
103D488—22no—
104D488—22no—
105D488—41no—
106D488—41no—
107C16×C61—22no—
108#11758185—41no—
109C23×C61C2×D811yescharacteristic
110C22×D61—42no—
111C22×D61—81no—
112C22×D61—81no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61—81no—
116C22×D61—81no—
117C2×C4×C61—81no—
118C2×C4×C61—81no—
119C2×C4×C61—81no—
120C2×C4×C61—81no—
121C2×C4×C61—81no—
122C2×C4×C61—81no—
123C2×C4×C61#12111yescharacteristic
124C2×C4×C61#12111yescharacteristic
125C2×C4×C61#12111yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—42no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61SD3212yescomplemented
138D244—42no—
139D244—42no—
140D244—81no—
141D244—81no—
142Dic122—42no—
143Dic122—42no—
144Dic122—81no—
145Dic122—81no—
146C8×C61#12011yescharacteristic
147C8×C61#12311yescharacteristic
148C8×C61#12311yescharacteristic
149C8×C61#12411yescharacteristic
150#92418—41no—
151#13449—611nomaximal, Sylow
152C22×C61#45911yescharacteristic
153C22×C61#45911yescharacteristic
154C22×C61#46611yescharacteristic
155C22×C61C2×SD3211yescharacteristic
156C22×C61#50811yescharacteristic
157C22×C61#50911yescharacteristic
158C22×C61#51011yescharacteristic
159C2×D61—82no—
160C2×D61—82no—
161C2×D61—82no—
162C2×D61—161no—
163C2×D61—161no—
164C2×D61—161no—
165C2×D61—161no—
166C4×C61—161no—
167C4×C61—161no—
168C4×C61#39411yescharacteristic
169C4×C61#46311yescharacteristic
170C4×C61#46311yescharacteristic
171C4×C61#46911yescharacteristic
172Dic61—22no—
173Dic61—41no—
174Dic61—82no—
175C22×SD32—611no—
176C2×C4⋊C16—611no—
177C2×#358—611no—
178C2×#357—611no—
179#1970—611no—
180#1969—611no—
181#1380D6111yescharacteristic, complemented
182C2×C61#205411yescharacteristic
183C2×C61#220711yescharacteristic
184C2×C61#220811yescharacteristic
185C2×C61#221011yescharacteristic
186C2×C61#221111yescharacteristic
187C2×C61#221711yescharacteristic
188C2×C61#222011yescharacteristic
189D61—162no—
190C22×Q16—611no—
191C22×D8—611no—
192C2×SD32—1222no—
193C2×SD32—1222no—
194C2×SD32—1222no—
195C22×C16—611no—
196C22×C16C2×D6111yescharacteristic
197C2×#107C2×D6111yescharacteristic
198C2×#107C2×D6111yescharacteristic
199C2×#103—1221no—
200C2×#102—1221no—
201C2×C4×C8—611no—
202#391—1221no—
203#390—1221no—
204C4⋊C16—1222no—
205#358—1222no—
206#357—1222no—
207C61#1344911yescharacteristic, complemented, Sylow
208C22×Q8—1221no—
209C22×D4—1221no—
210C2×Q16—612no—
211C2×Q16—1221no—
212C2×Q16—1221no—
213C2×Q16—1221no—
214C2×Q16—1221no—
215C2×Q16—1221no—
216C2×D8—612no—
217C2×D8—1221no—
218C2×D8—1221no—
219C2×D8—1221no—
220C2×D8—1221no—
221C2×D8—1221no—
222C22×C8—611no—
223C22×C8C22×D6111yescharacteristic
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C22⋊C4—2441no—
227C2×C22⋊C4—2441no—
228C2×C42—611no—
229SD32—1228no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—1221no—
233C2×C16—1221no—
234C2×C16—1221no—
235C2×C16D24412yes—
236#107—21no—
237#107—21no—
238#107—21no—
239#107—21no—
240#103—2442no—
241#102—2442no—
242C4×C8—1221no—
243C4×C8—1221no—
244#95—2441no—
245#95—2441no—
246C24—2441no—
247C2×Q8—1222no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×D4—1222no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2441no—
257C2×D4—2441no—
258C2×D4—2441no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—2441no—
264C22×C4D4×D6111yescharacteristic
265Q16—1222no—
266Q16—1222no—
267Q16—2441no—
268Q16—2441no—
269D8—1222no—
270D8—1222no—
271D8—2441no—
272D8—2441no—
273C2×C8—1221no—
274C2×C8—1221no—
275C2×C8—1221no—
276C2×C8C2×D24411yescharacteristic
277C2×C8#1175822211yescharacteristic
278C2×C8#1175822211yescharacteristic
279C2×C8D4×D6111yescharacteristic
280C2×C8D4×D6111yescharacteristic
281C2×C8#1175822611yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—4882no—
287C22⋊C4—4882no—
288C42—1221no—
289C42—1221no—
290C16—22no—
291C16—2441no—
292C23—4881no—
293C23—4881no—
294C23—4881no—
295C23—4881no—
296C23—4881no—
297C23—4881no—
298C23—2442no—
299C23D8×D6111yescharacteristic
300Q8—4881no—
301Q8—4881no—
302Q8—2442no—
303Q8—2442no—
304D4—4881no—
305D4—4881no—
306D4—2442no—
307D4—2442no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—612no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—2442no—
323C2×C4#1451975011yescharacteristic
324C2×C4#1451975011yescharacteristic
325C2×C4#1451975211yescharacteristic
326C2×C4#1451980011yescharacteristic
327C2×C4#1451980411yescharacteristic
328C2×C4#1451980411yescharacteristic
329C8—2441no—
330C8#1451974711yescharacteristic
331C8#1451976211yescharacteristic
332C8#1451976211yescharacteristic
333C8#1451976511yescharacteristic
334C22—9761no—
335C22—9761no—
336C22—9761no—
337C22—9761no—
338C22—4882no—
339C22—4882no—
340C22—4882no—
341C22#1683995611yescharacteristic
342C22#1683995611yescharacteristic
343C22#1683999911yescharacteristic
344C22SD32×D6111yescharacteristic
345C22#1684019311yescharacteristic
346C22#1684019611yescharacteristic
347C22#1684020411yescharacteristic
348C4—161no—
349C4—161no—
350C4—1222no—
351C4—4882no—
352C4—2441no—
353C4#1683968011yescharacteristic
354C4#1683998011yescharacteristic
355C4#1683998011yescharacteristic
356C4#1684001611yescharacteristic
357C2—9762no—
358C2#2144713111yescharacteristic
359C2#2144785811yescharacteristic
360C2#2144786311yescharacteristic
361C2#2144787311yescharacteristic
362C2#2144788411yescharacteristic
363C2#2144791611yescharacteristic
364C2#2144793311yescharacteristic
subgroupG/H
centerC23D8×D61
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1380C2
socleC23×C61C2×D8
prime radicalC22×D488C22
hypercenter#1380D61
hypocenterC61#13449
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#16839580C2semidirect
3. C2×#16839565C2semidirect
6. #21446678C2semidirect
7. C61×#1380C2semidirect
137. C2×Dic61SD32semidirect
181. #1380D61semidirect
207. C61#13449semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×#168395802
C2×#168395652
C2×#168395622
#214466832
#214466782
C61×#13802
#1344961