Finite Group Databasebeta

← #29583610

Subgroups — #29583610

Order 15616.

440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839968C211yesmaximal, characteristic
2#21445808C211yesmaximal, characteristic
3#21444593C211yesmaximal, characteristic, complemented
4#21444492C211yesmaximal, characteristic, complemented
5#21444490C211yesmaximal, characteristic, complemented
6#21444211C211yesmaximal, characteristic
7C61×#1301C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839968—22no—
12#16839968—22no—
13#16839815C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519702—21no—
16C2×#14519693—21no—
17#16839530—21no—
18#16839514—22no—
19#16839509—22no—
20#16839507—22no—
21#16839491—22no—
22C61×#431C2211yescharacteristic
23C61×#423C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C22×Dic122—21no—
26C22×D244D411yescharacteristic
27C22×C4×D61—21no—
28C2×#11758190—24no—
29C2×#11758190—42no—
30C2×#11758190—42no—
31C2×#11758194—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777D412yes—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758198—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418D412yes—
47#14519702—24no—
48#14519693—42no—
49C22⋊#92418—21no—
50C4×#92418—21no—
51C2×M16×C61—21no—
52C22×C8×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58C4⋊C8×C61D412yes—
59C22⋊C8×C61—21no—
60C4×C8×C61—21no—
61C23×D61—21no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61#4111yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—41no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244D812yes—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—82no—
76C2×Dic122—22no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C42×C61C2×D411yescharacteristic
90C42×C61C2×D411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61—22no—
97C4⋊Dic61—21no—
98C4⋊Dic61—22no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101#11758194—41no—
102#11758194—41no—
103C2×#92418—22no—
104C2×#92418—41no—
105#11758190—48no—
106C23×C61#12311yescharacteristic
107C22×D61—22no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—81no—
111C22×D61—81no—
112C2×C4×C61—22no—
113C2×C4×C61—41no—
114C2×C4×C61#12011yescharacteristic
115C2×C4×C61#12111yescharacteristic
116C2×C4×C61#12111yescharacteristic
117C2×C4×C61#12111yescharacteristic
118C2×C4×C61#12311yescharacteristic
119C2×C4×C61#12411yescharacteristic
120C2×C4×C61C2×D811yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C61#13711yescharacteristic
124C2×Dic61—42no—
125C2×Dic61—41no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129D244—22no—
130D244—22no—
131D244—41no—
132D244—41no—
133C4×D61—82no—
134C4×D61—82no—
135Dic122—42no—
136Dic122—42no—
137Dic122—81no—
138Dic122—81no—
139C8×C61—42no—
140C8×C61—81no—
141C8×C61—81no—
142#92418—42no—
143#92418—81no—
144#10444—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61#39411yescharacteristic
148C22×C61#48011yescharacteristic
149C22×C61#48211yescharacteristic
150C2×D61—42no—
151C2×D61—82no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—82no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61#44711yescharacteristic
159C4×C61#45211yescharacteristic
160C4×C61#46611yescharacteristic
161C4×C61#46811yescharacteristic
162C4×C61#47112yes—
163Dic61—82no—
164Dic61—81no—
165C2×#461—611no—
166#1800—611no—
167#1571—611no—
168#1546—611no—
169#1546—611no—
170#1478—611no—
171#1301D6111yescharacteristic, complemented
172C2×C61—21no—
173C2×C61—21no—
174C2×C61#203311yescharacteristic
175C2×C61#204611yescharacteristic
176C2×C61#204911yescharacteristic
177D61—82no—
178C22×SD16—1221no—
179C2×C4⋊Q8—611no—
180C2×C4×D4—611no—
181#461—1222no—
182#461—1222no—
183#431—611no—
184#431C2×D6111yescharacteristic
185#423—611no—
186#423C2×D6111yescharacteristic
187C2×C4⋊C8C2×D6111yescharacteristic
188C2×#103—1221no—
189C2×#100—1221no—
190#343—1221no—
191#335—1222no—
192#332—1222no—
193#332—1222no—
194D4⋊C8—1222no—
195C61#1044411yescharacteristic, complemented, Sylow
196C22×Q8—1221no—
197C22×D4—611no—
198C23×C4—1221no—
199C2×SD16—1224no—
200C2×SD16—2442no—
201C2×SD16—2442no—
202C2×M16—21no—
203C2×M16—1221no—
204C22×C8—21no—
205C4⋊Q8—612no—
206C4⋊Q8—1221no—
207C4⋊Q8—1221no—
208C4⋊Q8—1221no—
209C4×D4—1221no—
210C4×D4—1221no—
211C4×D4—1221no—
212C4×D4—1221no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C42C22×D6111yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—612no—
223C4⋊C8—1221no—
224C4⋊C8—1221no—
225C4⋊C8D24412yes—
226#103—1224no—
227#100—2442no—
228C22⋊C8—21no—
229C22⋊C8—1221no—
230C4×C8—21no—
231C4×C8—1221no—
232C24—1221no—
233C2×Q8—1222no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×Q8—2441no—
237C2×Q8—2441no—
238C2×Q8—2441no—
239C2×D4—612no—
240C2×D4—1221no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—1221no—
245C22×C4—1221no—
246C22×C4—4882no—
247C22×C4—2441no—
248C22×C4—2441no—
249C22×C4—2441no—
250C22×C4#1175822211yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C22×C4#1175822611yescharacteristic
253SD16—2448no—
254M16—41no—
255M16—41no—
256M16—2441no—
257M16—2441no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—1222no—
264C2×C8—2441no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C22⋊C4—2441no—
272C22⋊C4—2441no—
273C42C2×D24411yescharacteristic
274C42#1175822211yescharacteristic
275C42D4×D6111yescharacteristic
276C42D4×D6111yescharacteristic
277C23—1222no—
278C23—4881no—
279C23—4881no—
280C23—2441no—
281C23—2441no—
282C23#1451976211yescharacteristic
283Q8—4881no—
284Q8—4881no—
285Q8—2442no—
286Q8—2442no—
287D4—1222no—
288D4—1222no—
289D4—2441no—
290D4—2441no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—4882no—
294C2×C4—4881no—
295C2×C4—4881no—
296C2×C4—4882no—
297C2×C4—4881no—
298C2×C4—2441no—
299C2×C4—2442no—
300C2×C4#1451974711yescharacteristic
301C2×C4#1451975011yescharacteristic
302C2×C4#1451975011yescharacteristic
303C2×C4#1451975211yescharacteristic
304C2×C4#1451976211yescharacteristic
305C2×C4#1451976511yescharacteristic
306C2×C4D8×D6111yescharacteristic
307C2×C4#1451979811yescharacteristic
308C2×C4#1451980411yescharacteristic
309C2×C4#1451980911yescharacteristic
310C8—42no—
311C8—81no—
312C8—81no—
313C8—4881no—
314C8—2442no—
315C22—21no—
316C22—21no—
317C22—4882no—
318C22—4882no—
319C22—4881no—
320C22—4881no—
321C22—2442no—
322C22#1683968011yescharacteristic
323C22#1684007711yescharacteristic
324C22#1684008811yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—4882no—
329C4—4881no—
330C4#1683989711yescharacteristic
331C4#1683992711yescharacteristic
332C4#1683999711yescharacteristic
333C4#1684001111yescharacteristic
334C4#1684002612yes—
335C2—21no—
336C2—21no—
337C2—4882no—
338C2#2144700411yescharacteristic
339C2#2144708311yescharacteristic
340C2#2144710211yescharacteristic
subgroupG/H
centerC22#16839680
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1301C2
socleC22×C61#394
prime radicalC22×D244D4
hypercenter#1301D61
hypocenterC61#10444
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #21444593C2semidirect
4. #21444492C2semidirect
5. #21444490C2semidirect
7. C61×#1301C2semidirect
171. #1301D61semidirect
195. C61#10444semidirect

Maximal subgroups

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

subgroupindex
C2×#168399682
#214458082
#214445932
#214444922
#214444902
#214442112
C61×#13012
#1044461