Finite Group Databasebeta

← #29599615

Subgroups — #29599615

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×#16839567C211yesmaximal, characteristic, complemented
3C2×#16839564C211yesmaximal, characteristic
4#21446685C211yesmaximal, characteristic
5#21446680C211yesmaximal, characteristic, complemented
6#21443911C211yesmaximal, characteristic, complemented
7C2×C61×C4⋊C16C211yesmaximal, characteristic, complemented
8C22×Dic244C2211yescharacteristic
9C22×D488C2211yescharacteristic
10C2×#14519722—22no—
11C2×#14519722—22no—
12C2×#14519722—22no—
13C2×#14519711C2211yescharacteristic
14C2×#14519711C2211yescharacteristic
15C2×#14519702—21no—
16C2×#14519699—21no—
17#16839668—21no—
18#16839664—21no—
19#16839567—22no—
20#16839564—22no—
21C22×C16×C61C2211yescharacteristic
22C22×C16×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C61×C4⋊C16—22no—
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—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×#11758198—41no—
42C2×#11758198—41no—
43#14519722—28no—
44#14519711—21no—
45#14519711—21no—
46#14519711—21no—
47#14519711—21no—
48#14519702—42no—
49#14519699—42no—
50#14519684—41no—
51#14519684—41no—
52C22×C8×C61D411yescharacteristic
53C22×C8×C61C2311yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C16×C61—21no—
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C2×C16×C61—21no—
59C2×C16×C61—21no—
60C2×C16×C61D412yes—
61C4×C8×C61—21no—
62C4×C8×C61—21no—
63C23×D61—41no—
64C22×C4×C61D811yescharacteristic
65C22×C4×C61D811yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—41no—
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×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61C2×D411yescharacteristic
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61#4111yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C42×C61—21no—
92C42×C61—21no—
93#11758198—82no—
94#11758198—82no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99Dic244—22no—
100Dic244—22no—
101Dic244—41no—
102Dic244—41no—
103D488—22no—
104D488—22no—
105D488—41no—
106D488—41no—
107C16×C61—22no—
108C16×C61—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—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61SD3212yescomplemented
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—42no—
130C2×Dic61—81no—
131C2×Dic61—81no—
132C2×Dic61—81no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138D244—42no—
139D244—42no—
140D244—81no—
141D244—81no—
142Dic122—42no—
143Dic122—42no—
144Dic122—81no—
145Dic122—81no—
146C8×C61—41no—
147C8×C61#12011yescharacteristic
148C8×C61#12311yescharacteristic
149C8×C61#12311yescharacteristic
150C8×C61#12411yescharacteristic
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—22no—
167C4×C61—41no—
168C4×C61#39411yescharacteristic
169C4×C61#46311yescharacteristic
170C4×C61#46311yescharacteristic
171C4×C61#46911yescharacteristic
172Dic61—82no—
173Dic61—161no—
174Dic61—161no—
175C22×SD32—611no—
176C2×C4⋊C16D6111yescharacteristic, complemented
177C2×#358—611no—
178C2×#357—611no—
179#1970—611no—
180#1969—611no—
181#1380—611no—
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×C16C2×D6111yescharacteristic
196C22×C16C2×D6111yescharacteristic
197C2×#107—611no—
198C2×#107—611no—
199C2×#103—1221no—
200C2×#102—1221no—
201C2×C4×C8C2×D6111yescharacteristic
202#391—1221no—
203#390—1221no—
204C4⋊C16—22no—
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×C8D24411yescharacteristic
223C22×C8C22×D6111yescharacteristic
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C22⋊C4—2441no—
227C2×C22⋊C4—2441no—
228C2×C42D24411yescharacteristic
229SD32—1228no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16C22⋊D6112yes—
236#107—1221no—
237#107—1221no—
238#107—1221no—
239#107—1221no—
240#103—2442no—
241#102—2442no—
242C4×C8—21no—
243C4×C8—21no—
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—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4D48811yescharacteristic
263C22×C4D48811yescharacteristic
264C22×C4C2×D24411yescharacteristic
265Q16—1222no—
266Q16—1222no—
267Q16—2441no—
268Q16—2441no—
269D8—1222no—
270D8—1222no—
271D8—2441no—
272D8—2441no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8#1175822211yescharacteristic
277C2×C8D4×D6111yescharacteristic
278C2×C8D4×D6111yescharacteristic
279C2×C8#1175822611yescharacteristic
280C2×C8#1175822611yescharacteristic
281C2×C8C2×C22⋊D6111yescharacteristic
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—4882no—
287C22⋊C4—4882no—
288C42—21no—
289C42—21no—
290C16—22no—
291C16—41no—
292C23—4881no—
293C23—4881no—
294C23—4881no—
295C23—4881no—
296C23—4881no—
297C23—4881no—
298C23—2442no—
299C23C2×D48811yescharacteristic
300Q8—4881no—
301Q8—4881no—
302Q8—2442no—
303Q8—2442no—
304D4—4881no—
305D4—4881no—
306D4—2442no—
307D4—2442no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—4881no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2442no—
322C2×C4#1451972212yescomplemented
323C2×C4#1451975111yescharacteristic
324C2×C4#1451975211yescharacteristic
325C2×C4#1451975211yescharacteristic
326C2×C4#1451979911yescharacteristic
327C2×C4#1451980511yescharacteristic
328C2×C4#1451980511yescharacteristic
329C8—41no—
330C8#1451974511yescharacteristic
331C8#1451976211yescharacteristic
332C8#1451976211yescharacteristic
333C8#1451976611yescharacteristic
334C22—9761no—
335C22—9761no—
336C22—9761no—
337C22—9761no—
338C22—4882no—
339C22—4882no—
340C22—4882no—
341C22#1683995811yescharacteristic
342C22#1683995811yescharacteristic
343C22#1683999811yescharacteristic
344C22C2×#1451972211yescharacteristic
345C22#1684019411yescharacteristic
346C22#1684020011yescharacteristic
347C22#1684020511yescharacteristic
348C4—22no—
349C4—41no—
350C4—9761no—
351C4—9761no—
352C4—4882no—
353C4#1683967911yescharacteristic
354C4#1683997811yescharacteristic
355C4#1683997811yescharacteristic
356C4#1684001511yescharacteristic
357C2—9762no—
358C2#2144713011yescharacteristic
359C2#2144786011yescharacteristic
360C2#2144786511yescharacteristic
361C2#2144787511yescharacteristic
362C2#2144788211yescharacteristic
363C2#2144791511yescharacteristic
364C2#2144793211yescharacteristic
subgroupG/H
centerC23C2×D488
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC2×C61×C4⋊C16C2
socleC23×C61C2×D8
prime radicalC22×D488C22
hypercenterC2×C4⋊C16D61
hypocenterC61#13449
LCSG ▷ C22×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#16839567C2semidirect
5. #21446680C2semidirect
6. #21443911C2semidirect
7. C2×C61×C4⋊C16C2semidirect
122. C2×C4×C61SD32semidirect
176. C2×C4⋊C16D61semidirect
207. C61#13449semidirect
322. C2×C4#14519722semidirect

Maximal subgroups

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

subgroupindex
C22×#145197222
C2×#168395672
C2×#168395642
#214466852
#214466802
#214439112
C2×C61×C4⋊C162
#1344961